Subgroups — #121414

Order 512.

577 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21972	C₂	1	1	yes	maximal, characteristic
2	#17787	C₂	1	1	yes	maximal, characteristic
3	C₂×#1565	C₂	1	1	yes	maximal, characteristic
4	C₄×#344	C₂	1	1	yes	maximal, characteristic
5	#7924	C₂	1	1	yes	maximal, characteristic
6	#7882	C₂	1	1	yes	maximal, characteristic
7	#7873	C₂	1	1	yes	maximal, characteristic
8	C₂×#431	C₂²	1	1	yes	characteristic
9	C₂×#431	C₂²	1	1	yes	characteristic
10	C₂×#431	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
14	C₄×#117	C₂²	1	1	yes	characteristic
15	#1939	—	2	2	no	—
16	#1850	—	2	2	no	—
17	#1842	—	2	1	no	—
18	#1831	—	2	1	no	—
19	C₂×#344	C₄	1	1	yes	characteristic
20	C₂×#344	C₄	1	1	yes	characteristic
21	C₂×#344	C₄	1	1	yes	characteristic
22	C₂×#344	C₄	1	1	yes	characteristic
23	#1565	—	2	2	no	—
24	#1565	—	2	1	no	—
25	#1565	—	2	1	no	—
26	#1565	—	2	1	no	—
27	#1565	—	2	1	no	—
28	#1565	—	2	2	no	—
29	#1564	—	2	2	no	—
30	C₂×#335	—	2	1	no	—
31	C₂×#334	—	2	1	no	—
32	#1282	—	2	2	no	—
33	#1278	—	2	2	no	—
34	#1277	—	2	2	no	—
35	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
36	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
38	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₈	—	2	1	no	—
40	C₂×#117	C₂×C₄	1	1	yes	characteristic
41	C₂×#117	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄²	C₂³	1	1	yes	characteristic
43	#431	—	2	1	no	—
44	#431	—	2	1	no	—
45	#431	—	2	1	no	—
46	#431	—	2	1	no	—
47	#431	—	2	1	no	—
48	#431	—	2	1	no	—
49	#431	—	2	1	no	—
50	#431	—	2	1	no	—
51	#431	—	2	1	no	—
52	#431	—	2	1	no	—
53	#431	—	2	1	no	—
54	#431	Q₈	1	2	yes	—
55	C₂×C₄⋊C₈	—	2	1	no	—
56	C₂×C₄⋊C₈	—	2	1	no	—
57	C₂×C₄⋊C₈	—	2	1	no	—
58	C₂×C₄⋊C₈	—	2	1	no	—
59	C₂×C₄⋊C₈	—	2	1	no	—
60	C₂×C₄⋊C₈	—	2	1	no	—
61	C₂×C₄⋊C₈	—	2	4	no	—
62	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₈	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₈	D₄	1	2	yes	—
67	C₂×C₂²⋊C₈	—	2	1	no	—
68	C₂×C₂²⋊C₈	—	2	1	no	—
69	C₂×C₂²⋊C₈	—	2	1	no	—
70	C₄×M₁₆	—	2	1	no	—
71	C₄×M₁₆	—	2	1	no	—
72	C₄×M₁₆	—	2	1	no	—
73	C₄×M₁₆	—	2	1	no	—
74	C₄×M₁₆	—	2	1	no	—
75	C₄×M₁₆	—	2	1	no	—
76	C₄×M₁₆	D₄	1	2	yes	—
77	C₄×M₁₆	Q₈	1	2	yes	—
78	C₂×#97	—	2	1	no	—
79	C₂×#97	Q₈	1	2	yes	—
80	C₂×C₄×C₈	—	2	1	no	—
81	C₂×C₄×C₈	—	2	1	no	—
82	C₂×C₄×C₈	—	2	1	no	—
83	C₂×C₄×C₈	—	2	1	no	—
84	C₂×C₄×C₈	D₄	1	2	yes	—
85	C₄×C₄⋊C₄	—	2	1	no	—
86	C₄×C₄⋊C₄	—	2	1	no	—
87	C₄×C₂²⋊C₄	D₄	1	2	yes	—
88	C₄×C₂²⋊C₄	Q₈	1	2	yes	—
89	#376	—	2	1	no	—
90	C₄³	—	2	1	no	—
91	#344	—	2	2	no	—
92	#344	—	2	2	no	—
93	#344	—	2	2	no	—
94	#344	C₈	1	4	yes	complemented
95	#336	—	2	4	no	—
96	#335	—	2	4	no	—
97	#335	—	2	2	no	—
98	#335	—	2	2	no	—
99	#334	—	2	4	no	—
100	#334	—	2	2	no	—
101	#334	—	2	2	no	—
102	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂³×C₄	C₂×Q₈	1	1	yes	characteristic
105	C₂×M₁₆	—	2	1	no	—
106	C₂×M₁₆	—	2	1	no	—
107	C₂×M₁₆	—	2	1	no	—
108	C₂×M₁₆	—	2	1	no	—
109	C₂×M₁₆	—	2	1	no	—
110	C₂×M₁₆	—	2	1	no	—
111	C₂×M₁₆	—	2	1	no	—
112	C₂×M₁₆	—	2	1	no	—
113	C₂×M₁₆	—	2	1	no	—
114	C₂×M₁₆	—	2	1	no	—
115	C₂×M₁₆	—	2	1	no	—
116	C₂×M₁₆	—	2	1	no	—
117	C₂×M₁₆	—	2	1	no	—
118	C₂×M₁₆	—	2	1	no	—
119	C₂×M₁₆	—	2	1	no	—
120	C₂×M₁₆	—	2	1	no	—
121	C₂×M₁₆	—	2	1	no	—
122	C₂×M₁₆	—	2	1	no	—
123	C₂×M₁₆	C₄⋊C₄	1	2	yes	—
124	C₂×M₁₆	C₄⋊C₄	1	2	yes	—
125	C₂×M₁₆	C₂×C₈	1	2	yes	—
126	C₂×M₁₆	C₂×C₈	1	2	yes	—
127	C₂×M₁₆	M₁₆	1	2	yes	—
128	C₂×M₁₆	M₁₆	1	2	yes	—
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	—	2	1	no	—
131	C₂²×C₈	—	2	2	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	2	1	no	—
136	C₂²×C₈	—	4	1	no	—
137	C₂²×C₈	—	4	1	no	—
138	C₂²×C₈	—	4	1	no	—
139	C₂²×C₈	—	8	2	no	—
140	C₂²×C₈	C₄⋊C₄	1	2	yes	—
141	C₂²×C₈	C₄⋊C₄	1	2	yes	—
142	#117	—	2	1	no	—
143	#117	—	2	1	no	—
144	#117	—	2	1	no	—
145	#117	—	2	1	no	—
146	#117	—	2	1	no	—
147	#117	—	2	1	no	—
148	#117	C₂×C₈	1	2	yes	—
149	#117	M₁₆	1	2	yes	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	1	no	—
152	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
153	C₂×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	—	2	1	no	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	—	2	2	no	—
158	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
164	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
165	C₂×C₄²	C₂×Q₈	1	1	yes	characteristic
166	C₂×C₄²	#41	1	1	yes	characteristic
167	C₂×C₄²	#41	1	1	yes	characteristic
168	C₂×C₄²	#41	1	1	yes	characteristic
169	C₂×C₄²	#41	1	1	yes	characteristic
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	2	1	no	—
174	C₄⋊C₈	—	2	1	no	—
175	C₄⋊C₈	—	2	1	no	—
176	C₄⋊C₈	—	2	1	no	—
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	2	1	no	—
180	C₄⋊C₈	—	2	2	no	—
181	C₄⋊C₈	—	4	1	no	—
182	C₄⋊C₈	—	4	1	no	—
183	C₄⋊C₈	—	4	1	no	—
184	C₄⋊C₈	—	8	4	no	—
185	C₂²⋊C₈	—	2	2	no	—
186	C₂²⋊C₈	—	4	1	no	—
187	C₂²⋊C₈	—	4	1	no	—
188	C₂²⋊C₈	—	4	1	no	—
189	C₂²⋊C₈	—	4	1	no	—
190	C₂²⋊C₈	—	4	1	no	—
191	#97	—	2	2	no	—
192	#97	—	2	2	no	—
193	#97	—	2	2	no	—
194	#97	—	2	2	no	—
195	C₄×C₈	—	2	2	no	—
196	C₄×C₈	—	2	2	no	—
197	C₄×C₈	—	2	2	no	—
198	C₄×C₈	—	2	2	no	—
199	C₄×C₈	—	2	2	no	—
200	C₄×C₈	—	4	1	no	—
201	C₄×C₈	—	4	1	no	—
202	C₄×C₈	—	4	1	no	—
203	C₄×C₈	—	4	1	no	—
204	C₄×C₈	—	4	1	no	—
205	#95	—	2	2	no	—
206	#95	—	2	2	no	—
207	C₂⁴	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂²×C₄	—	2	2	no	—
209	C₂²×C₄	—	2	2	no	—
210	C₂²×C₄	—	4	1	no	—
211	C₂²×C₄	—	4	1	no	—
212	C₂²×C₄	—	8	1	no	—
213	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
216	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
217	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄	C₄×Q₈	1	1	yes	characteristic
219	C₂²×C₄	#120	1	1	yes	characteristic
220	C₂²×C₄	#121	1	1	yes	characteristic
221	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂²×C₄	#123	1	1	yes	characteristic
225	C₂²×C₄	#125	1	1	yes	characteristic
226	C₂²×C₄	#127	1	1	yes	characteristic
227	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
228	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
229	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
230	C₂²×C₄	C₄⋊Q₈	1	1	yes	characteristic
231	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
232	C₂²×C₄	C₂×M₁₆	1	1	yes	characteristic
233	C₂²×C₄	C₂×M₁₆	1	1	yes	characteristic
234	C₂²×C₄	C₂×M₁₆	1	1	yes	characteristic
235	C₂²×C₄	#131	1	1	yes	characteristic
236	C₂²×C₄	#131	1	1	yes	characteristic
237	C₂²×C₄	#131	1	1	yes	characteristic
238	C₂²×C₄	#131	1	1	yes	characteristic
239	M₁₆	—	2	2	no	—
240	M₁₆	—	2	2	no	—
241	M₁₆	—	2	2	no	—
242	M₁₆	—	2	2	no	—
243	M₁₆	—	2	2	no	—
244	M₁₆	—	2	2	no	—
245	M₁₆	—	2	2	no	—
246	M₁₆	—	2	2	no	—
247	M₁₆	—	2	2	no	—
248	M₁₆	—	4	1	no	—
249	M₁₆	—	4	1	no	—
250	M₁₆	—	4	1	no	—
251	M₁₆	—	4	1	no	—
252	M₁₆	—	4	1	no	—
253	M₁₆	—	4	1	no	—
254	M₁₆	C₄⋊C₈	1	4	yes	complemented
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	4	1	no	—
265	C₂×C₈	—	4	1	no	—
266	C₂×C₈	—	4	2	no	—
267	C₂×C₈	—	4	4	no	—
268	C₂×C₈	—	4	2	no	—
269	C₂×C₈	—	4	1	no	—
270	C₂×C₈	—	4	1	no	—
271	C₂×C₈	—	4	1	no	—
272	C₂×C₈	—	4	1	no	—
273	C₂×C₈	—	4	2	no	—
274	C₂×C₈	—	4	2	no	—
275	C₂×C₈	—	8	1	no	—
276	C₂×C₈	—	8	1	no	—
277	C₂×C₈	—	8	2	no	—
278	C₂×C₈	—	8	2	no	—
279	C₂×C₈	—	8	1	no	—
280	C₂×C₈	—	8	1	no	—
281	C₂×C₈	C₄⋊C₈	1	4	yes	complemented
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	C₄⋊C₈	1	4	yes	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	4	2	no	—
293	C₄²	—	4	2	no	—
294	C₄²	—	4	1	no	—
295	C₄²	—	4	1	no	—
296	C₄²	—	8	2	no	—
297	C₄²	#120	1	1	yes	characteristic
298	C₄²	#120	1	1	yes	characteristic
299	C₄²	#121	1	1	yes	characteristic
300	C₄²	#121	1	1	yes	characteristic
301	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
302	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
303	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
304	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
305	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
306	C₄²	C₂²⋊Q₈	1	1	yes	characteristic
307	C₄²	#123	1	1	yes	characteristic
308	C₄²	#123	1	1	yes	characteristic
309	C₄²	#125	1	1	yes	characteristic
310	C₄²	#125	1	1	yes	characteristic
311	C₄²	C₄⋊Q₈	1	1	yes	characteristic
312	C₄²	C₄⋊Q₈	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	#384	1	1	yes	characteristic
316	C₂³	#385	1	1	yes	characteristic
317	C₂³	#389	1	1	yes	characteristic
318	C₂³	C₂×C₄⋊C₈	1	1	yes	characteristic
319	C₂³	#423	1	1	yes	characteristic
320	C₂³	#424	1	1	yes	characteristic
321	C₂³	#424	1	1	yes	characteristic
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	#385	1	1	yes	characteristic
344	C₂×C₄	#385	1	1	yes	characteristic
345	C₂×C₄	#389	1	1	yes	characteristic
346	C₂×C₄	#389	1	1	yes	characteristic
347	C₂×C₄	#392	1	1	yes	characteristic
348	C₂×C₄	#395	1	1	yes	characteristic
349	C₂×C₄	#395	1	1	yes	characteristic
350	C₂×C₄	#395	1	1	yes	characteristic
351	C₂×C₄	#398	1	1	yes	characteristic
352	C₂×C₄	#398	1	1	yes	characteristic
353	C₂×C₄	#398	1	1	yes	characteristic
354	C₂×C₄	#399	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊C₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₈	1	1	yes	characteristic
357	C₂×C₄	#423	1	1	yes	characteristic
358	C₂×C₄	#423	1	1	yes	characteristic
359	C₂×C₄	#424	1	1	yes	characteristic
360	C₂×C₄	#424	1	1	yes	characteristic
361	C₂×C₄	#424	1	1	yes	characteristic
362	C₂×C₄	#424	1	1	yes	characteristic
363	C₂×C₄	C₈×D₄	1	1	yes	characteristic
364	C₂×C₄	C₈×D₄	1	1	yes	characteristic
365	C₂×C₄	C₈×D₄	1	1	yes	characteristic
366	C₂×C₄	#435	1	1	yes	characteristic
367	C₂×C₄	#435	1	1	yes	characteristic
368	C₂×C₄	#435	1	1	yes	characteristic
369	C₂×C₄	#435	1	1	yes	characteristic
370	C₂×C₄	#435	1	1	yes	characteristic
371	C₂×C₄	#435	1	1	yes	characteristic
372	C₂×C₄	#436	1	1	yes	characteristic
373	C₂×C₄	#436	1	1	yes	characteristic
374	C₂×C₄	#436	1	1	yes	characteristic
375	C₂×C₄	C₈×Q₈	1	1	yes	characteristic
376	C₂×C₄	#446	1	1	yes	characteristic
377	C₂×C₄	#446	1	1	yes	characteristic
378	C₂×C₄	#446	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₈	—	8	2	no	—
384	C₈	—	8	1	no	—
385	C₈	—	8	2	no	—
386	C₈	—	8	1	no	—
387	C₈	—	8	1	no	—
388	C₈	—	8	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	#1444	1	1	yes	characteristic
400	C₂²	#1842	1	1	yes	characteristic
401	C₂²	#1843	1	1	yes	characteristic
402	C₂²	#1850	1	1	yes	characteristic
403	C₂²	#1851	1	1	yes	characteristic
404	C₂²	#1939	1	1	yes	characteristic
405	C₂²	#1940	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	4	no	—
414	C₄	—	8	2	no	—
415	C₄	#1850	1	1	yes	characteristic
416	C₄	#1850	1	1	yes	characteristic
417	C₄	#1851	1	1	yes	characteristic
418	C₄	#1851	1	1	yes	characteristic
419	C₄	#1939	1	1	yes	characteristic
420	C₄	#1939	1	1	yes	characteristic
421	C₄	#1940	1	1	yes	characteristic
422	C₄	#1940	1	1	yes	characteristic
423	C₄	#2008	1	1	yes	characteristic
424	C₄	#2009	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	#11322	1	1	yes	characteristic
432	C₂	#11333	1	1	yes	characteristic
433	C₂	#11334	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#392
commutator	C₂²×C₄	C₂²×C₈
Frattini, cosocle	C₂²×C₄²	C₂³
socle	C₂²	#1444
prime radical	C₂⁴	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
94. #344	C₈	semidirect
254. M₁₆	C₄⋊C₈	semidirect
281. C₂×C₈	C₄⋊C₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#21972	2
#17787	2
C₂×#1565	2
C₄×#344	2
#7924	2
#7882	2
#7873	2