List of room groups

There are 230 three-dimensional room groups . Each space group has a number and a complete Hermann Mauguin symbol as well as a short symbol (international short symbol). The full symbols have spaces between the symmetry operations for ease of reading.

Symbols

In the Hermann Mauguin symbolism , groups of spaces are represented by a symbol that combines the point group with a capital letter indicating the Bravais grid . Translational symmetry in the form of screw axes and glide mirror planes are also given, resulting in a complete crystallographic space group.

These are the centerings of the Bravais grids in three dimensions:

• P primitive
• I body- centered or body-centered
• F face-centered
• A only the A surfaces are centered
• B only the B surfaces are centered
• C only the C surfaces are centered
• R rhombohedral

A mirror plane m in the point group can be replaced by a glide mirror plane , which is designated with a , b or c depending on the direction of the translation vector . There is also an n sliding mirror plane in which the translation is half the vector of the diagonals of a surface. There is also a d- sliding mirror plane in which the translation is a quarter of the diagonal of a surface.

• ${\displaystyle a}$, , Or translation along the respective vector by the amount of half of this vector. ${\displaystyle b}$ ${\displaystyle c}$
• ${\displaystyle n}$ Translation with half the diagonal of a surface.
• ${\displaystyle d}$ Translation with a quarter of the diagonal of a surface.
• ${\displaystyle e}$ Two sliding mirror planes with the same sliding plane and a translation with the amount of half of both axes of this surface.

An axis of rotation can be replaced by a screw axis , n , in which the angle of rotation is. The amount of translation is then given as an index x, so that the amount of translation is given as a fraction of the lattice vector. For example, 2 ₁ denotes a rotation of 180 ° (twice) followed by a translation of ½ of the grid vector. 3 ₁ denotes a rotation of 120 ° (three-fold rotation) followed by a translation of ⅓ of the grid vector. ${\displaystyle \color {Black}{\tfrac {360^{\circ }}{n}}}$ ${\displaystyle \color {Black}{\tfrac {x}{n}}}$

The possible screw axes are: 2 ₁ , 3 ₁ , 3 ₂ , 4 ₁ , 4 ₂ , 4 ₃ , 6 ₁ , 6 ₂ , 6 ₃ , 6 ₄ , and 6 ₅ .

Depending on the choice of axes, different symbols can designate the same space group. For example, space group no. 14 can be specified as P 2 ₁ / c (no. 14) , P 2 ₁ / n (no. 14, position 2) or P 2 ₁ / a (no. 14, position 3) ; however, no numbering of the axis positions is used in the specialist literature. The numbering of the axis positions in the German language Wikipedia follows the order in which they are listed in Chapter 4 of the International Tables for Crystallography . In the lists only the so-called standard statements are given, which should preferably be used.

List of triclinic space groups

Triclinic (a ≠ b ≠ c and α ≠ β ≠ γ)

Triclinic crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	Examples
1	1	P 1	P 1	${\displaystyle C_{1}^{1}}$	p- Bromonitrobenzene , Abelsonite , Hartite , Kylindrite
2	1	P 1	P 1	${\displaystyle C_{i}^{1}}$	Molybdenum acetate , abramovite , aenigmatite , diadochite , ulexite

List of monoclinic room groups

Monoclinic Bravais lattice

Primitive (P)	Base-centered (C)

Monoclinic crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	Example (s)
3	2	P 2	P 1 2 1	${\displaystyle C_{2}^{1}}$	Leguernit
4th	2	P 2 1	P 1 2 1 1	${\displaystyle C_{2}^{2}}$	Lithium sulfate
5	2	C 2	C 1 2 1	${\displaystyle C_{2}^{3}}$	Thallium (I) hydroxide , fettelite
6th	m	Pm	P 1 m 1	${\displaystyle C_{s}^{1}}$	InVSe 2 O 8
7th	m	Pc	P 1 c 1	${\displaystyle C_{s}^{2}}$	Masuyit
8th	m	Cm	C 1 m 1	${\displaystyle C_{s}^{3}}$	Antigorite , chapmanite
9	m	Cc	C 1 c 1	${\displaystyle C_{s}^{4}}$	Aluminum selenide , afwillite , halloysite-7Å , kampfite
10	2 / m	P 2 / m	P 1 2 / m 1	${\displaystyle C_{2h}^{1}}$	Barnesite
11	2 / m	P 2 1 / m	P 1 2 1 / m 1	${\displaystyle C_{2h}^{2}}$	Tantalum (IV) chloride , charoite , jordanite
12	2 / m	C 2 / m	C 1 2 / m 1	${\displaystyle C_{2h}^{3}}$	Copper (II) chloride , actinolite , erythrin
13	2 / m	P 2 / c	P 1 2 / c 1	${\displaystyle C_{2h}^{4}}$	Rhenium (IV) chloride
14th	2 / m	P 2 1 / c	P 1 2 1 / c 1	${\displaystyle C_{2h}^{5}}$	Rubidium ozonide , nickel diphosphate
15th	2 / m	C 2 / c	C 1 2 / c 1	${\displaystyle C_{2h}^{6}}$	Uranium (IV) fluoride

List of orthorhombic space groups

Orthorhombic Bravais grids

Primitive (P)	Inside centered (I)
Base-centered (A, B or C)	Face-centered (F)

Orthorhombic crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	example
16	222	P 222	P 2 2 2	${\displaystyle D_{2}^{1}}$	Haycockite
17th	222	P 222 1	P 2 2 2 1	${\displaystyle D_{2}^{2}}$	Olsacherite
18th	222	P 2 1 2 1 2	P 2 1 2 1 2	${\displaystyle D_{2}^{3}}$	Capgaronnite , MgTeMoO 6
19th	222	P 2 1 2 1 2 1	P 2 1 2 1 2 1	${\displaystyle D_{2}^{4}}$	Sodium dithiophosphate , epsomite
20th	222	C 222 1	C 2 2 2 1	${\displaystyle D_{2}^{5}}$	Frondelit
21st	222	C 222	C 2 2 2	${\displaystyle D_{2}^{6}}$	Avidin
22nd	222	F 222	F 2 2 2	${\displaystyle D_{2}^{7}}$
23	222	I 222	I 2 2 2	${\displaystyle D_{2}^{8}}$	Stannoidite
24	222	I 2 1 2 1 2 1	I 2 1 2 1 2 1	${\displaystyle D_{2}^{9}}$	Crotamine
25th	mm 2	Pmm 2	P mm 2	${\displaystyle C_{2v}^{1}}$	Dyscrasite
26th	mm 2	Pmc 2 1	P mc 2 1	${\displaystyle C_{2v}^{2}}$	Europium (II) hydroxide
27	mm 2	Pcc 2	P cc 2	${\displaystyle C_{2v}^{3}}$
28	mm 2	Pma 2	P ma 2	${\displaystyle C_{2v}^{4}}$	Thallium (I) fluoride
29	mm 2	Pca 2 1	P ca 2 1	${\displaystyle C_{2v}^{5}}$	Boracite , silver (I) iodate
30th	mm 2	Pnc 2	P nc 2	${\displaystyle C_{2v}^{6}}$	Armenite
31	mm 2	Pmn 2 1	P mn 2 1	${\displaystyle C_{2v}^{7}}$	Söhngeit , struvite
32	mm 2	Pba 2	P ba 2	${\displaystyle C_{2v}^{8}}$	Walkerit
33	mm 2	Pna 2 1	P na 2 1	${\displaystyle C_{2v}^{9}}$	o- bromonitrobenzene
34	mm 2	Pnn 2	P nn 2	${\displaystyle C_{2v}^{10}}$	Lepersonnit- (Gd)
35	mm 2	Cmm 2	C mm 2	${\displaystyle C_{2v}^{11}}$	Lithium acetate
36	mm 2	Cmc 2 1	C mc 2 1	${\displaystyle C_{2v}^{12}}$	Bromine chloride
37	mm 2	Ccc 2	C cc 2	${\displaystyle C_{2v}^{13}}$	Li 2 Si 2 O 5
38	mm 2	Amm 2	A mm 2	${\displaystyle C_{2v}^{14}}$	Uranium (V, VI) oxide
39	mm 2	Aem 2 (formerly Abm 2)	A em 2	${\displaystyle C_{2v}^{15}}$	Smirnit
40	mm 2	Ama 2	A ma 2	${\displaystyle C_{2v}^{16}}$	Bavenite
41	mm 2	Aea 2 (formerly Aba 2)	A ea 2	${\displaystyle C_{2v}^{17}}$	Junitoite
42	mm 2	Fmm 2	F mm 2	${\displaystyle C_{2v}^{18}}$
43	mm 2	Fdd 2	F dd 2	${\displaystyle C_{2v}^{19}}$	Germanium (IV) sulfide
44	mm 2	Imm 2	I mm 2	${\displaystyle C_{2v}^{20}}$	Sodium nitrite
45	mm 2	Iba 2	I ba 2	${\displaystyle C_{2v}^{21}}$	Stronalsite
46	mm 2	Ima 2	I ma 2	${\displaystyle C_{2v}^{22}}$	Batisite
47	2 / m 2 / m 2 / m	Pmmm	P 2 / m 2 / m 2 / m	${\displaystyle D_{2h}^{1}}$	Zellerit
48	2 / m 2 / m 2 / m	Pnnn	P 2 / n 2 / n 2 / n	${\displaystyle D_{2h}^{2}}$
49	2 / m 2 / m 2 / m	Pccm	P 2 / c 2 / c 2 / m	${\displaystyle D_{2h}^{3}}$
50	2 / m 2 / m 2 / m	Pban	P 2 / b 2 / a 2 / n	${\displaystyle D_{2h}^{4}}$	Retzian
51	2 / m 2 / m 2 / m	Pmma	P 2 1 / m 2 / m 2 / a	${\displaystyle D_{2h}^{5}}$	Potassium Heptafluorotantalate
52	2 / m 2 / m 2 / m	Pnna	P 2 / n 2 1 / n 2 / a	${\displaystyle D_{2h}^{6}}$	Indium (I, III) bromide
53	2 / m 2 / m 2 / m	Pmna	P 2 / m 2 / n 2 1 / a	${\displaystyle D_{2h}^{7}}$	Tetraphosphorus trisulfide
54	2 / m 2 / m 2 / m	Pcca	P 2 1 / c 2 / c 2 / a	${\displaystyle D_{2h}^{8}}$	Nordite- (La)
55	2 / m 2 / m 2 / m	Pbam	P 2 1 / b 2 1 / a 2 / m	${\displaystyle D_{2h}^{9}}$	Iodine azide
56	2 / m 2 / m 2 / m	Pccn	P 2 1 / c 2 1 / c 2 / n	${\displaystyle D_{2h}^{10}}$	Valentinite
57	2 / m 2 / m 2 / m	Pbcm	P 2 / b 2 1 / c 2 1 / m	${\displaystyle D_{2h}^{11}}$	Evenkit
58	2 / m 2 / m 2 / m	Pnnm	P 2 1 / n 2 1 / n 2 / m	${\displaystyle D_{2h}^{12}}$	Adamin , dicobalt carbide
59	2 / m 2 / m 2 / m	Pmmn	P 2 1 / m 2 1 / m 2 / n	${\displaystyle D_{2h}^{13}}$	Molybdenum (III) bromide
60	2 / m 2 / m 2 / m	Pbcn	P 2 1 / b 2 / c 2 1 / n	${\displaystyle D_{2h}^{14}}$	Iron (II) acetate
61	2 / m 2 / m 2 / m	Pbca	P 2 1 / b 2 1 / c 2 1 / a	${\displaystyle D_{2h}^{15}}$	Bornite , platinum (IV) bromide
62	2 / m 2 / m 2 / m	Pnma	P 2 1 / n 2 1 / m 2 1 / a	${\displaystyle D_{2h}^{16}}$	Anglesite , topaz , uranium (VI) fluoride
63	2 / m 2 / m 2 / m	Cmcm	C 2 / m 2 / c 2 1 / m	${\displaystyle D_{2h}^{17}}$	Anhydrite , boehmite , plutonium (III) bromide
64	2 / m 2 / m 2 / m	Cmce (formerly Cmca )	C 2 / m 2 / c 2 1 / e	${\displaystyle D_{2h}^{18}}$	Molybdenum (II) chloride
65	2 / m 2 / m 2 / m	Cmmm	C 2 / m 2 / m 2 / m	${\displaystyle D_{2h}^{19}}$	Gold (I) chloride
66	2 / m 2 / m 2 / m	Cccm	C 2 / c 2 / c 2 / m	${\displaystyle D_{2h}^{20}}$	Thorium (III) iodide
67	2 / m 2 / m 2 / m	Cmme (formerly Cmma )	C 2 / m 2 / m 2 / e	${\displaystyle D_{2h}^{21}}$	Johachidolite
68	2 / m 2 / m 2 / m	Ccce (formerly Ccca )	C 2 / c 2 / c 2 / e	${\displaystyle D_{2h}^{22}}$	Calcium chlorite
69	2 / m 2 / m 2 / m	Fmmm	F 2 / m 2 / m 2 / m	${\displaystyle D_{2h}^{23}}$	Stellerite
70	2 / m 2 / m 2 / m	Fddd	F 2 / d 2 / d 2 / d	${\displaystyle D_{2h}^{24}}$	sulfur
71	2 / m 2 / m 2 / m	Immm	I 2 / m 2 / m 2 / m	${\displaystyle D_{2h}^{25}}$	Lithium carbide
72	2 / m 2 / m 2 / m	Ibam	I 2 / b 2 / a 2 / m	${\displaystyle D_{2h}^{26}}$	Silicon disulfide
73	2 / m 2 / m 2 / m	Ibca	I 2 / b 2 / c 2 / a	${\displaystyle D_{2h}^{27}}$	Chesnokovite
74	2 / m 2 / m 2 / m	Imma	I 2 / m 2 / m 2 / a	${\displaystyle D_{2h}^{28}}$	Iron (II, III) fluoride

List of tetragonal space groups

Tetragonal Bravais grids

Primitive (P)	Inside centered (I)

Tetragonal crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	example
75	4th	P 4	P 4	${\displaystyle C_{4}^{1}}$	Copper diarsenite
76	4th	P 4 1	P 4 1	${\displaystyle C_{4}^{2}}$
77	4th	P 4 2	P 4 2	${\displaystyle C_{4}^{3}}$
78	4th	P 4 3	P 4 3	${\displaystyle C_{4}^{4}}$
79	4th	I 4	I 4	${\displaystyle C_{4}^{5}}$	Tungsten (VI) oxide tetrachloride
80	4th	I 4 1	I 4 1	${\displaystyle C_{4}^{6}}$
81	4th	P 4	P 4	${\displaystyle S_{4}^{1}}$
82	4th	I 4	I 4	${\displaystyle S_{4}^{2}}$	Lithium amide
83	4 / m	P 4 / m	P 4 / m	${\displaystyle C_{4h}^{1}}$	Sword mannite
84	4 / m	P 4 2 / m	P 4 2 / m	${\displaystyle C_{4h}^{2}}$	Palladium (II) sulfide
85	4 / m	P 4 / n	P 4 / n	${\displaystyle C_{4h}^{3}}$	Dysprosium (II) chloride
86	4 / m	P 4 2 / n	P 4 2 / n	${\displaystyle C_{4h}^{4}}$	Trimethylthallium
87	4 / m	I 4 / m	I 4 / m	${\displaystyle C_{4h}^{5}}$	Plutonium (V) fluoride
88	4 / m	I 4 1 / a	I 4 1 / a	${\displaystyle C_{4h}^{6}}$	Rubidium periodate
89	422	P 422	P 4 2 2	${\displaystyle D_{4}^{1}}$
90	422	P 42 1 2	P 4 2 1 2	${\displaystyle D_{4}^{2}}$
91	422	P 4 1 22	P 4 1 2 2	${\displaystyle D_{4}^{3}}$
92	422	P 4 1 2 1 2	P 4 1 2 1 2	${\displaystyle D_{4}^{4}}$	2-pyrimidinone
93	422	P 4 2 22	P 4 2 2 2	${\displaystyle D_{4}^{5}}$
94	422	P 4 2 2 1 2	P 4 2 2 1 2	${\displaystyle D_{4}^{6}}$	Sphaerobismoit
95	422	P 4 3 22	P 4 3 2 2	${\displaystyle D_{4}^{7}}$
96	422	P 4 3 2 1 2	P 4 3 2 1 2	${\displaystyle D_{4}^{8}}$	Paratellurite , aluminum dodecaboride
97	422	I 422	I 4 2 2	${\displaystyle D_{4}^{9}}$
98	422	I 4 1 22	I 4 1 2 2	${\displaystyle D_{4}^{10}}$	Cadmium diarsenide , pottsite
99	4 mm	P 4 mm	P 4 mm	${\displaystyle C_{4v}^{1}}$	Diaboleit , Nielsenit
100	4 mm	P 4 bm	P 4 bm	${\displaystyle C_{4v}^{2}}$
101	4 mm	P 4 2 cm	P 4 2 c m	${\displaystyle C_{4v}^{3}}$
102	4 mm	P 4 2 nm	P 4 2 n m	${\displaystyle C_{4v}^{4}}$
103	4 mm	P 4 cc	P 4 cc	${\displaystyle C_{4v}^{5}}$
104	4 mm	P 4 nc	P 4 nc	${\displaystyle C_{4v}^{6}}$
105	4 mm	P 4 2 mc	P 4 2 m c	${\displaystyle C_{4v}^{7}}$	Lenait
106	4 mm	P 4 2 bc	P 4 2 b c	${\displaystyle C_{4v}^{8}}$
107	4 mm	I 4 mm	I 4 mm	${\displaystyle C_{4v}^{9}}$
108	4 mm	I 4 cm	I 4 cm	${\displaystyle C_{4v}^{10}}$
109	4 mm	I 4 1 md	I 4 1 m d	${\displaystyle C_{4v}^{11}}$	Diethyl zinc
110	4 mm	I 4 1 cd	I 4 1 c d	${\displaystyle C_{4v}^{12}}$	Zinc arsenide
111	4 2 m	P 4 2 m	P 4 2 m	${\displaystyle D_{2d}^{1}}$	Potassium hexafluoroantimonate (V) , bariophamacosiderite
112	4 2 m	P 4 2 c	P 4 2 c	${\displaystyle D_{2d}^{2}}$	Renierite
113	4 2 m	P 4 2 1 m	P 4 2 1 m	${\displaystyle D_{2d}^{3}}$	Niobium oxide trichloride
114	4 2 m	P 4 2 1 c	P 4 2 1 c	${\displaystyle D_{2d}^{4}}$	Tetraphenyl germanium
115	4 2 m	P 4 m 2	P 4 m 2	${\displaystyle D_{2d}^{5}}$	Uranium (IV) fluoride
116	4 2 m	P 4 c 2	P 4 c 2	${\displaystyle D_{2d}^{6}}$
117	4 2 m	P 4 b 2	P 4 b 2	${\displaystyle D_{2d}^{7}}$
118	4 2 m	P 4 n 2	P 4 n 2	${\displaystyle D_{2d}^{8}}$
119	4 2 m	I 4 m 2	I 4 m 2	${\displaystyle D_{2d}^{9}}$
120	4 2 m	I 4 c 2	I 4 c 2	${\displaystyle D_{2d}^{10}}$
121	4 2 m	I 4 2 m	I 4 2 m	${\displaystyle D_{2d}^{11}}$	Potassium tetraperoxochromate
122	4 2 m	I 4 2 d	I 4 2 d	${\displaystyle D_{2d}^{12}}$	Uranium (V) fluoride
123	4 / m 2 / m 2 / m	P 4 / mmm	P 4 / m 2 / m 2 / m	${\displaystyle D_{4h}^{1}}$	Potassium tetrachloridoplatinate
124	4 / m 2 / m 2 / m	P 4 / mcc	P 4 / m 2 / c 2 / c	${\displaystyle D_{4h}^{2}}$
125	4 / m 2 / m 2 / m	P 4 / nbm	P 4 / n 2 / b 2 / m	${\displaystyle D_{4h}^{3}}$	Nickel (II) sulfite
126	4 / m 2 / m 2 / m	P 4 / nnc	P 4 / n 2 / n 2 / c	${\displaystyle D_{4h}^{4}}$	Zeunerite , Vesuvianite
127	4 / m 2 / m 2 / m	P 4 / mbm	P 4 / m 2 1 / b 2 / m	${\displaystyle D_{4h}^{5}}$	Phosgenite , carletonite
128	4 / m 2 / m 2 / m	P 4 / mnc	P 4 / m 2 1 / n 2 / c	${\displaystyle D_{4h}^{6}}$	Fluorapophyllite (K)
129	4 / m 2 / m 2 / m	P 4 / nmm	P 4 / n 2 1 / m 2 / m	${\displaystyle D_{4h}^{7}}$	Tin (II) oxide , lead (II) oxide
130	4 / m 2 / m 2 / m	P 4 / ncc	P 4 / n 2 1 / c 2 / c	${\displaystyle D_{4h}^{8}}$	Strontium hydroxide octahydrate , abernathyite
131	4 / m 2 / m 2 / m	P 4 2 / mmc	P 4 2 / m 2 / m 2 / c	${\displaystyle D_{4h}^{9}}$	Platinum (II) sulfide
132	4 / m 2 / m 2 / m	P 4 2 / mcm	P 4 2 / m 2 / c 2 / m	${\displaystyle D_{4h}^{10}}$	Ammonium cyanide
133	4 / m 2 / m 2 / m	P 4 2 / nbc	P 4 2 / n 2 / b 2 / c	${\displaystyle D_{4h}^{11}}$
134	4 / m 2 / m 2 / m	P 4 2 / nnm	P 4 2 / n 2 / n 2 / m	${\displaystyle D_{4h}^{12}}$
135	4 / m 2 / m 2 / m	P 4 2 / mbc	P 4 2 / m 2 1 / b 2 / c	${\displaystyle D_{4h}^{13}}$	Minium , selenium dioxide
136	4 / m 2 / m 2 / m	P 4 2 / mnm	P 4 2 / m 2 1 / n 2 / m	${\displaystyle D_{4h}^{14}}$	Palladium (IV) oxide , rutile
137	4 / m 2 / m 2 / m	P 4 2 / nmc	P 4 2 / n 2 1 / m 2 / c	${\displaystyle D_{4h}^{15}}$	Zinc phosphide
138	4 / m 2 / m 2 / m	P 4 2 / ncm	P 4 2 / n 2 1 / c 2 / m	${\displaystyle D_{4h}^{16}}$	Gold (I) iodide
139	4 / m 2 / m 2 / m	I 4 / mmm	I 4 / m 2 / m 2 / m	${\displaystyle D_{4h}^{17}}$	Lanthanum carbide , tin (IV) fluoride
140	4 / m 2 / m 2 / m	I 4 / mcm	I 4 / m 2 / c 2 / m	${\displaystyle D_{4h}^{18}}$	Rubidium azide , indium (I, III) telluride
141	4 / m 2 / m 2 / m	I 4 1 / amd	I 4 1 / a 2 / m 2 / d	${\displaystyle D_{4h}^{19}}$	Manganese (III) oxide
142	4 / m 2 / m 2 / m	I 4 1 / acd	I 4 1 / a 2 / c 2 / d	${\displaystyle D_{4h}^{20}}$	Zinc amide

List of trigonal space groups

Unit cells of the trigonal crystal system

Rhombohedral (R)	Hexagonal (P)

Trigonal crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	example
143	3	P 3	P 3	${\displaystyle C_{3}^{1}}$	Tetrairidium dodecacarbonyl
144	3	P 3 1	P 3 1	${\displaystyle C_{3}^{2}}$	Calcium carbonate monohydrate, rubidium nitrate
145	3	P 3 2	P 3 2	${\displaystyle C_{3}^{3}}$	Calcium carbonate monohydrate
146	3	R 3	R 3	${\displaystyle C_{3}^{4}}$	Magnesium sulfite
147	3	P 3	P 3	${\displaystyle C_{3i}^{1}}$	Strontium iodide hexahydrate
148	3	R 3	R 3	${\displaystyle C_{3i}^{2}}$	Tungsten (VI) bromide
149	32	P 312	P 3 1 2	${\displaystyle D_{3}^{1}}$	Strontium bromide hexahydrate
150	32	P 321	P 3 2 1	${\displaystyle D_{3}^{2}}$	Rubidium dithionate
151	32	P 3 1 12	P 3 1 1 2	${\displaystyle D_{3}^{3}}$
152	32	P 3 1 21	P 3 1 2 1	${\displaystyle D_{3}^{4}}$	Tellurium
153	32	P 3 2 12	P 3 2 1 2	${\displaystyle D_{3}^{5}}$
154	32	P 3 2 21	P 3 2 2 1	${\displaystyle D_{3}^{6}}$	Tellurium
155	32	R 32	R 3 2	${\displaystyle D_{3}^{7}}$	Trinickel disulfide
156	3 m	P 3 m 1	P 3 m 1	${\displaystyle C_{3v}^{1}}$	Titanium (II) bromide
157	3 m	P 31 m	P 3 1 m	${\displaystyle C_{3v}^{2}}$
158	3 m	P 3 c 1	P 3 c 1	${\displaystyle C_{3v}^{3}}$
159	3 m	P 31 c	P 3 1 c	${\displaystyle C_{3v}^{4}}$
160	3 m	R 3 m	R 3 m	${\displaystyle C_{3v}^{5}}$	Rhenium (III) chloride
161	3 m	R 3 c	R 3 c	${\displaystyle C_{3v}^{6}}$	Vanadium (III) chloride
162	3 2 / m	P 3 1 m	P 3 1 2 / m	${\displaystyle D_{3d}^{1}}$
163	3 2 / m	P 3 1 c	P 3 1 2 / c	${\displaystyle D_{3d}^{2}}$	Chromium (III) sulfide
164	3 2 / m	P 3 m 1	P 3 2 / m 1	${\displaystyle D_{3d}^{3}}$	Uranium (VI) chloride
165	3 2 / m	P 3 c 1	P 3 2 / c 1	${\displaystyle D_{3d}^{4}}$	Lanthanum fluoride
166	3 2 / m	R 3 m	R 3 2 / m	${\displaystyle D_{3d}^{5}}$	Thallium (I) oxide
167	3 2 / m	R 3 c	R 3 2 / c	${\displaystyle D_{3d}^{6}}$	Sodium metaborate

List of hexagonal space groups

Hexagonal Bravais Cell
(P)

Hexagonal crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	example
168	6th	P 6	P 6	${\displaystyle C_{6}^{1}}$
169	6th	P 6 1	P 6 1	${\displaystyle C_{6}^{2}}$
170	6th	P 6 5	P 6 5	${\displaystyle C_{6}^{3}}$
171	6th	P 6 2	P 6 2	${\displaystyle C_{6}^{4}}$
172	6th	P 6 4	P 6 4	${\displaystyle C_{6}^{5}}$
173	6th	P 6 3	P 6 3	${\displaystyle C_{6}^{6}}$
174	6th	P 6	P 6	${\displaystyle C_{3h}^{1}}$	Hydroxyl Bastnäsite
175	6 / m	P 6 / m	P 6 / m	${\displaystyle C_{6h}^{1}}$	Cesium acetate
176	6 / m	P 6 3 / m	P 6 3 / m	${\displaystyle C_{6h}^{2}}$	Cerium (III) bromide
177	622	P 622	P 6 2 2	${\displaystyle D_{6}^{1}}$
178	622	P 6 1 22	P 6 1 2 2	${\displaystyle D_{6}^{2}}$	Gold (III) fluoride
179	622	P 6 5 22	P 6 5 2 2	${\displaystyle D_{6}^{3}}$	Gold (III) fluoride
180	622	P 6 2 22	P 6 2 2 2	${\displaystyle D_{6}^{4}}$	High quartz
181	622	P 6 4 22	P 6 4 2 2	${\displaystyle D_{6}^{5}}$
182	622	P 6 3 22	P 6 3 2 2	${\displaystyle D_{6}^{6}}$
183	6 mm	P 6 mm	P 6 mm	${\displaystyle C_{6v}^{1}}$	Gold (I) cyanide
184	6 mm	P 6 cc	P 6 cc	${\displaystyle C_{6v}^{2}}$
185	6 mm	P 6 3 cm	P 6 3 c m	${\displaystyle C_{6v}^{3}}$	Sodium arsenide
186	6 mm	P 6 3 mc	P 6 3 m c	${\displaystyle C_{6v}^{4}}$	Wurtzit
187	6 m 2	P 6 m 2	P 6 m 2	${\displaystyle D_{3h}^{1}}$
188	6 m 2	P 6 c 2	P 6 c 2	${\displaystyle D_{3h}^{2}}$	Bazirit
189	6 m 2	P 6 2 m	P 6 2 m	${\displaystyle D_{3h}^{3}}$	Dipotassium nonahydridorhenate (VII)
190	6 m 2	P 6 2 c	P 6 2 c	${\displaystyle D_{3h}^{4}}$	Bastnesite
191	6 / m 2 / m 2 / m	P 6 / mmm	P 6 / m 2 / m 2 / m	${\displaystyle D_{6h}^{1}}$	Aluminum diboride
192	6 / m 2 / m 2 / m	P 6 / mcc	P 6 / m 2 / c 2 / c	${\displaystyle D_{6h}^{2}}$	beryl
193	6 / m 2 / m 2 / m	P 6 3 / mcm	P 6 3 / m 2 / c 2 / m	${\displaystyle D_{6h}^{3}}$	Cerium (III) fluoride
194	6 / m 2 / m 2 / m	P 6 3 / mmc	P 6 3 / m 2 / m 2 / c	${\displaystyle D_{6h}^{4}}$	magnesium

List of cubic space groups

Cubic Bravais Lattice

Primitive (P)	Inside centered (I)	Face-centered (F)

(221) Cesium chloride unit cell: Cs ⁺ Cl ^-
           

(216) Zincblende unit cell: Zn ²⁺ S ²⁻
           

(223) Weaire-Phelan Structure

Cubic crystal system

Num mer	Point group	Short symbol	Complete icon	Schoenflies symbol	example
195	23	P 23	P 2 3	${\displaystyle T^{1}}$
196	23	F 23	F 2 3	${\displaystyle T^{2}}$
197	23	I 23	I 2 3	${\displaystyle T^{3}}$	Moschellandsbergite , bismuth germanate
198	23	P 2 1 3	P 2 1 3	${\displaystyle T^{4}}$	Ullmannite , sodium chlorate
199	23	I 2 1 3	I 2 1 3	${\displaystyle T^{5}}$
200	2 / m 3	Pm 3	P 2 / m 3	${\displaystyle T_{h}^{1}}$
201	2 / m 3	Pn 3	P 2 / n 3	${\displaystyle T_{h}^{2}}$	Cafarsit
202	2 / m 3	Fm 3	F 2 / m 3	${\displaystyle T_{h}^{3}}$
203	2 / m 3	Fd 3	F 2 / d 3	${\displaystyle T_{h}^{4}}$
204	2 / m 3	In the 3rd	I 2 / m 3	${\displaystyle T_{h}^{5}}$	Dzhalindite , indium (III) hydroxide
205	2 / m 3	Pa 3	P 2 1 / a 3	${\displaystyle T_{h}^{6}}$	Nickel disulfide , germanium (IV) iodide
206	2 / m 3	Ia 3	I 2 1 / a 3	${\displaystyle T_{h}^{7}}$	Uranium sesquinitride , scandium oxide
207	432	P 432	P 4 3 2	${\displaystyle O^{1}}$
208	432	P 4 2 32	P 4 2 3 2	${\displaystyle O^{2}}$
209	432	F 432	F 4 3 2	${\displaystyle O^{2}}$	Calvertite
210	432	F 4 1 32	F 4 1 3 2	${\displaystyle O^{4}}$
211	432	I 432	I 4 3 2	${\displaystyle O^{5}}$
212	432	P 4 3 32	P 4 3 3 2	${\displaystyle O^{6}}$	Osmium (IV) chloride , maghemite
213	432	P 4 1 32	P 4 1 3 2	${\displaystyle O^{7}}$	Osmium (IV) chloride
214	432	I 4 1 32	I 4 1 3 2	${\displaystyle O^{8}}$	Ye'elimit
215	4 3 m	P 4 3 m	P 4 3 m	${\displaystyle T_{d}^{1}}$	Sulvanite , rhodicite
216	4 3 m	F 4 3 m	F 4 3 m	${\displaystyle T_{d}^{2}}$	Zinc blende , zinc telluride
217	4 3 m	I 4 3 m	I 4 3 m	${\displaystyle T_{d}^{3}}$	α-Manganese , Freibergite
218	4 3 m	P 4 3 n	P 4 3 n	${\displaystyle T_{d}^{4}}$	Silver phosphate , maikainite
219	4 3 m	F 4 3 c	F 4 3 c	${\displaystyle T_{d}^{5}}$	Boracite
220	4 3 m	I 4 3 d	I 4 3 d	${\displaystyle T_{d}^{6}}$	Diurantricarbide , bismuth germanate , wadalite
221	4 / m 3 2 / m	Pm 3 m	P 4 / m 3 2 / m	${\displaystyle O_{h}^{1}}$	Cesium chloride , lanthanum hexaboride , health
222	4 / m 3 2 / m	Pn 3 n	P 4 / n 3 2 / n	${\displaystyle O_{h}^{2}}$
223	4 / m 3 2 / m	Pm 3 n	P 4 2 / m 3 2 / n	${\displaystyle O_{h}^{3}}$	Niobium tin , niobium germanium
224	4 / m 3 2 / m	Pn 3 m	P 4 2 / n 3 2 / m	${\displaystyle O_{h}^{4}}$	Silver (I) oxide , cuprite
225	4 / m 3 2 / m	Fm 3 m	F 4 / m 3 2 / m	${\displaystyle O_{h}^{5}}$	Sodium chloride , β- bornite
226	4 / m 3 2 / m	Fm 3 c	F 4 / m 3 2 / c	${\displaystyle O_{h}^{6}}$
227	4 / m 3 2 / m	Fd 3 m	F 4 1 / d 3 2 / m	${\displaystyle O_{h}^{7}}$	Diamond , zinc-cobalt-spinel , cobalt (II, III) sulfide
228	4 / m 3 2 / m	Fd 3 c	F 4 1 / d 3 2 / c	${\displaystyle O_{h}^{8}}$	Voltaite
229	4 / m 3 2 / m	In the 3 m	I 4 / m 3 2 / m	${\displaystyle O_{h}^{9}}$	Sodium , argentite , rhenium (VII) fluoride
230	4 / m 3 2 / m	Ia 3 d	I 4 1 / a 3 2 / d	${\displaystyle O_{h}^{10}}$	garnet

Web links

Commons : Space groups  - collection of pictures, videos and audio files

• International Union of Crystallography
• Point groups and Bravais lattice
• Complete list of 230 room groups
• Interactive 3D visualization of all 230 room groups