Crystal Lab › The 230 space groups

The 230 space groups

3D crystal patterns. Open a group to see its symmetry elements drawn in the cell, its operations, and its Wyckoff positions with a model atom you can move.

The 230 space groups · The 17 plane groups · The 7 frieze groups · The 75 rod groups · The 80 layer groups

Triclinic (2)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
1	P 1	1	1	1
2	P -1	2	9	1

Monoclinic (13)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
3	P 1 2 1	2	5	3
4	P 1 21 1	2	1	3
5	C 1 2 1	4	3	9
6	P 1 m 1	2	3	3
7	P 1 c 1	2	1	9
8	C 1 m 1	4	2	9
9	C 1 c 1	4	1	18
10	P 1 2/m 1	4	15	3
11	P 1 21/m 1	4	6	3
12	C 1 2/m 1	8	10	9
13	P 1 2/c 1	4	7	9
14	P 1 21/c 1	4	5	9	SiO₂ (MFI)
15	C 1 2/c 1	8	6	18

Orthorhombic (59)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
16	P 2 2 2	4	21	1
17	P 2 2 21	4	5	3
18	P 21 21 2	4	3	3
19	P 21 21 21	4	1	1
20	C 2 2 21	8	3	3
21	C 2 2 2	8	12	3
22	F 2 2 2	16	11	1
23	I 2 2 2	8	11	1
24	I 21 21 21	8	4	1
25	P m m 2	4	9	3
26	P m c 21	4	3	6
27	P c c 2	4	5	3
28	P m a 2	4	4	6
29	P c a 21	4	1	6
30	P n c 2	4	3	6
31	P m n 21	4	2	6
32	P b a 2	4	3	3
33	P n a 21	4	1	6
34	P n n 2	4	3	3
35	C m m 2	8	6	3
36	C m c 21	8	2	6
37	C c c 2	8	4	3
38	A m m 2	8	6	6
39	A e m 2	8	4	6
40	A m a 2	8	3	6
41	A e a 2	8	2	6
42	F m m 2	16	5	3
43	F d d 2	16	2	3
44	I m m 2	8	5	3
45	I b a 2	8	3	3
46	I m a 2	8	3	6
47	P m m m	8	27	1
48	P n n n :2	8	13	2
49	P c c m	8	18	3
50	P b a n :2	8	13	6
51	P m m a	8	12	6
52	P n n a	8	5	6
53	P m n a	8	9	6
54	P c c a	8	6	6
55	P b a m	8	9	3
56	P c c n	8	5	3
57	P b c m	8	5	6
58	P n n m	8	8	3
59	P m m n :2	8	7	6
60	P b c n	8	4	6
61	P b c a	8	3	2
62	P n m a	8	4	6	LiFePO₄
63	C m c m	16	8	6
64	C m c e	16	7	6
65	C m m m	16	18	3
66	C c c m	16	13	3
67	C m m e	16	15	6
68	C c c e :2	16	9	12
69	F m m m	32	16	1
70	F d d d :2	32	8	2
71	I m m m	16	15	1
72	I b a m	16	11	3
73	I b c a	16	6	2
74	I m m a	16	10	6

Tetragonal (68)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
75	P 4	4	4	2
76	P 41	4	1	2
77	P 42	4	4	2
78	P 43	4	1	2
79	I 4	8	3	2
80	I 41	8	2	2
81	P -4	4	8	2
82	I -4	8	7	2
83	P 4/m	8	12	2
84	P 42/m	8	11	2
85	P 4/n :2	8	7	4
86	P 42/n :2	8	7	4
87	I 4/m	16	9	2
88	I 41/a :2	16	6	4	CaWO₄, NaAlH₄
89	P 4 2 2	8	16	2
90	P 4 21 2	8	7	2
91	P 41 2 2	8	4	2
92	P 41 21 2	8	2	2
93	P 42 2 2	8	16	2
94	P 42 21 2	8	7	2
95	P 43 2 2	8	4	2
96	P 43 21 2	8	2	2
97	I 4 2 2	16	11	2
98	I 41 2 2	16	7	2
99	P 4 m m	8	7	2
100	P 4 b m	8	4	2
101	P 42 c m	8	5	2
102	P 42 n m	8	4	2
103	P 4 c c	8	4	2
104	P 4 n c	8	3	2
105	P 42 m c	8	6	2
106	P 42 b c	8	3	2
107	I 4 m m	16	5	2
108	I 4 c m	16	4	2
109	I 41 m d	16	3	2
110	I 41 c d	16	2	2
111	P -4 2 m	8	15	2
112	P -4 2 c	8	14	2
113	P -4 21 m	8	6	2
114	P -4 21 c	8	5	2
115	P -4 m 2	8	12	2
116	P -4 c 2	8	10	2
117	P -4 b 2	8	9	2
118	P -4 n 2	8	9	2
119	I -4 m 2	16	10	2
120	I -4 c 2	16	9	2
121	I -4 2 m	16	10	2
122	I -4 2 d	16	5	2
123	P 4/m m m	16	21	2
124	P 4/m c c	16	14	2
125	P 4/n b m :2	16	14	4
126	P 4/n n c :2	16	11	4
127	P 4/m b m	16	12	2
128	P 4/m n c	16	9	2
129	P 4/n m m :2	16	11	4
130	P 4/n c c :2	16	7	4	CaCuSi₄O₁₀
131	P 42/m m c	16	18	2
132	P 42/m c m	16	16	2
133	P 42/n b c :2	16	11	4
134	P 42/n n m :2	16	14	4
135	P 42/m b c	16	9	2
136	P 42/m n m	16	11	2	TiO₂, MgH₂
137	P 42/n m c :2	16	8	4
138	P 42/n c m :2	16	10	4
139	I 4/m m m	32	15	2
140	I 4/m c m	32	13	2
141	I 41/a m d :2	32	9	4	TiO₂
142	I 41/a c d :2	32	7	4

Trigonal (25)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
143	P 3	3	4	1
144	P 31	3	1	1
145	P 32	3	1	1
146	R 3 :h	9	2	2
147	P -3	6	7	1
148	R -3 :h	18	6	2
149	P 3 1 2	6	12	1
150	P 3 2 1	6	7	1
151	P 31 1 2	6	3	1
152	P 31 2 1	6	3	1
153	P 32 1 2	6	3	1
154	P 32 2 1	6	3	1
155	R 3 2 :h	18	6	2
156	P 3 m 1	6	5	1
157	P 3 1 m	6	4	1
158	P 3 c 1	6	4	1
159	P 3 1 c	6	3	1
160	R 3 m :h	18	3	2
161	R 3 c :h	18	2	2
162	P -3 1 m	12	12	1
163	P -3 1 c	12	9	1
164	P -3 m 1	12	10	1	CdI₂
165	P -3 c 1	12	7	1
166	R -3 m :h	36	9	2	CdCl₂, LiCoO₂
167	R -3 c :h	36	6	2	Al₂O₃, CaCO₃, Na₃Zr₂Si₂PO₁₂

Hexagonal (27)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
168	P 6	6	4	1
169	P 61	6	1	1
170	P 65	6	1	1
171	P 62	6	3	1
172	P 64	6	3	1
173	P 63	6	3	1
174	P -6	6	12	1
175	P 6/m	12	12	1
176	P 63/m	12	9	1
177	P 6 2 2	12	14	1
178	P 61 2 2	12	3	1
179	P 65 2 2	12	3	1
180	P 62 2 2	12	11	1
181	P 64 2 2	12	11	1
182	P 63 2 2	12	9	1
183	P 6 m m	12	6	1
184	P 6 c c	12	4	1
185	P 63 c m	12	4	1
186	P 63 m c	12	4	1	ZnS
187	P -6 m 2	12	15	1
188	P -6 c 2	12	12	1
189	P -6 2 m	12	12	1
190	P -6 2 c	12	9	1
191	P 6/m m m	24	18	1	Li₃N
192	P 6/m c c	24	13	1
193	P 63/m c m	24	12	1
194	P 63/m m c	24	12	1	Mg, C, NiAs, MoS₂, H₂O

Cubic (36)

No.	Symbol	Operations	Wyckoff positions	Settings	Structures here
195	P 2 3	12	10	1
196	F 2 3	48	8	1
197	I 2 3	24	6	1
198	P 21 3	12	2	1
199	I 21 3	24	3	1
200	P m -3	24	12	1
201	P n -3 :2	24	8	2
202	F m -3	96	9	1
203	F d -3 :2	96	7	2
204	I m -3	48	8	1
205	P a -3	24	4	1	FeS₂
206	I a -3	48	5	1
207	P 4 3 2	24	11	1
208	P 42 3 2	24	13	1
209	F 4 3 2	96	10	1
210	F 41 3 2	96	8	1
211	I 4 3 2	48	10	1
212	P 43 3 2	24	5	1
213	P 41 3 2	24	5	1
214	I 41 3 2	48	9	1
215	P -4 3 m	24	10	1
216	F -4 3 m	96	9	1	ZnS
217	I -4 3 m	48	8	1
218	P -4 3 n	24	9	1	Na₈(Al₆Si₆O₂₄)Cl₂
219	F -4 3 c	96	8	1
220	I -4 3 d	48	5	1
221	P m -3 m	48	14	1	Po, CsCl, SrTiO₃, ReO₃
222	P n -3 n :2	48	9	2
223	P m -3 n	48	12	1
224	P n -3 m :2	48	12	2	Cu₂O
225	F m -3 m	192	12	1	Cu, NaCl, CaF₂, Na₂O, AgCl, Zn₄O(BDC)₃, Cu₃(BTC)₂
226	F m -3 c	192	10	1
227	F d -3 m :2	192	9	2	C, MgAl₂O₄, Fe₃O₄, LiMn₂O₄, Na₅₆(Al,Si)₁₉₂O₃₈₄
228	F d -3 c :2	192	8	2
229	I m -3 m	96	12	1	W, AgI
230	I a -3 d	96	8	1

Operations are counted per conventional cell (lattice centring included). Symbols follow the International Tables; the first listed setting is the standard one.