Subgroups — #37581593

Order 24448.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133209	C₂	1	1	yes	maximal, characteristic
2	#27132739	C₂	1	1	yes	maximal, characteristic, complemented
3	#27132738	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132737	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132734	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132732	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132731	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₂²⋊D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₁₉₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132717	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132713	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132630	C₂	1	1	yes	maximal, characteristic, complemented
13	#27132628	C₂	1	1	yes	maximal, characteristic, complemented
14	#27132628	C₂	1	1	yes	maximal, characteristic, complemented
15	#408×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15690287	C₂²	1	1	yes	characteristic
17	C₂×#15690271	C₂²	1	1	yes	characteristic
18	C₂×#15690270	C₂²	1	1	yes	characteristic
19	C₂×#15690270	C₂²	1	1	yes	characteristic
20	C₂²×C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₁₉₁	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₁₉₁	C₂²	1	1	yes	characteristic
23	#20259320	C₄	1	1	yes	characteristic
24	#20259318	C₄	1	1	yes	characteristic
25	#20259311	C₄	1	1	yes	characteristic
26	#20259309	C₄	1	1	yes	characteristic
27	#20259294	C₄	1	1	yes	characteristic
28	#20259294	C₄	1	1	yes	characteristic
29	#20259294	C₄	1	1	yes	characteristic
30	#20259294	C₄	1	1	yes	characteristic
31	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
36	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
37	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
38	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
39	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
40	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic
44	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic
48	#20259232	C₂²	1	1	yes	characteristic
49	#20259232	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₉₁	C₂²	1	1	yes	characteristic
51	C₈×Dic₁₉₁	C₂²	1	1	yes	characteristic
52	C₂×#41×C₁₉₁	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
54	C₂²×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
55	C₂²⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic
59	#15690287	—	4	1	no	—
60	#15690287	—	4	1	no	—
61	C₂×Dic₃₈₂	C₂×C₄	1	1	yes	characteristic
62	C₂×D₇₆₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
70	C₂²×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
72	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
73	#15690271	—	4	1	no	—
74	#15690270	—	4	1	no	—
75	#15690270	—	4	1	no	—
76	C₂×C₁₉₁⋊C₈	—	4	1	no	—
77	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
81	C₈×D₁₉₁	—	4	1	no	—
82	C₈×D₁₉₁	—	4	1	no	—
83	Dic₁₉₁⋊C₄	C₂×C₄	1	1	yes	characteristic
84	Dic₁₉₁⋊C₄	C₂×C₄	1	1	yes	characteristic
85	Dic₁₉₁⋊C₄	C₂×C₄	1	1	yes	characteristic
86	Dic₁₉₁⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
91	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₄×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
96	C₄×Dic₁₉₁	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
98	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
99	#41×C₁₉₁	—	4	1	no	—
100	#41×C₁₉₁	—	4	1	no	—
101	C₂×Q₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
102	C₂×D₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
103	C₂×D₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
104	C₂×D₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
108	M₁₆×C₁₉₁	—	4	1	no	—
109	C₂×C₈×C₁₉₁	—	4	1	no	—
110	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
114	C₂²×D₁₉₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×D₁₉₁	C₂²×C₄	1	1	yes	characteristic
116	Dic₃₈₂	—	4	1	no	—
117	D₇₆₄	—	4	1	no	—
118	C₂²⋊D₁₉₁	—	2	2	no	—
119	C₂²⋊D₁₉₁	—	2	2	no	—
120	C₂²⋊D₁₉₁	—	4	1	no	—
121	C₂²⋊D₁₉₁	—	4	1	no	—
122	C₂²⋊D₁₉₁	—	4	1	no	—
123	C₂²⋊D₁₉₁	—	4	1	no	—
124	C₂×Dic₁₉₁	—	2	2	no	—
125	C₂×Dic₁₉₁	—	4	1	no	—
126	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₁₉₁	C₂²×C₄	1	1	yes	characteristic
132	C₄×D₁₉₁	—	2	1	no	—
133	C₄×D₁₉₁	—	2	1	no	—
134	C₄×D₁₉₁	—	2	1	no	—
135	C₄×D₁₉₁	—	2	1	no	—
136	C₁₉₁⋊C₈	—	2	1	no	—
137	C₁₉₁⋊C₈	—	2	1	no	—
138	C₁₉₁⋊C₈	—	2	1	no	—
139	C₁₉₁⋊C₈	—	2	1	no	—
140	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
141	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
142	C₂³×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
143	Q₈×C₁₉₁	—	4	1	no	—
144	D₄×C₁₉₁	—	4	1	no	—
145	D₄×C₁₉₁	—	4	1	no	—
146	D₄×C₁₉₁	—	4	1	no	—
147	C₂×C₄×C₁₉₁	—	2	1	no	—
148	C₂×C₄×C₁₉₁	—	2	1	no	—
149	C₂×C₄×C₁₉₁	—	2	1	no	—
150	C₂×C₄×C₁₉₁	—	2	1	no	—
151	C₂×C₄×C₁₉₁	—	2	1	no	—
152	C₂×C₄×C₁₉₁	—	2	1	no	—
153	C₂×C₄×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
157	C₈×C₁₉₁	—	2	1	no	—
158	C₈×C₁₉₁	—	2	1	no	—
159	C₈×C₁₉₁	—	2	1	no	—
160	C₈×C₁₉₁	—	2	1	no	—
161	C₂²×C₁₉₁	—	2	1	no	—
162	C₂²×C₁₉₁	—	2	1	no	—
163	C₂²×C₁₉₁	—	2	1	no	—
164	C₂²×C₁₉₁	—	2	1	no	—
165	C₂²×C₁₉₁	—	2	1	no	—
166	C₂²×C₁₉₁	—	2	1	no	—
167	C₂²×C₁₉₁	—	2	1	no	—
168	C₂²×C₁₉₁	—	2	1	no	—
169	C₂²×C₁₉₁	—	2	1	no	—
170	C₂²×C₁₉₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×D₁₉₁	—	2	1	no	—
172	C₂×D₁₉₁	—	2	1	no	—
173	C₂×D₁₉₁	—	2	1	no	—
174	C₂×D₁₉₁	—	2	1	no	—
175	C₂×D₁₉₁	—	2	1	no	—
176	C₂×D₁₉₁	—	2	1	no	—
177	C₄×C₁₉₁	—	2	1	no	—
178	C₄×C₁₉₁	—	2	1	no	—
179	C₄×C₁₉₁	—	2	1	no	—
180	C₄×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
181	C₄×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
182	Dic₁₉₁	—	2	1	no	—
183	Dic₁₉₁	—	2	1	no	—
184	Dic₁₉₁	—	2	1	no	—
185	Dic₁₉₁	—	2	1	no	—
186	Dic₁₉₁	—	2	1	no	—
187	Dic₁₉₁	#131	1	2	yes	—
188	C₂×C₁₉₁	—	4	1	no	—
189	C₂×C₁₉₁	—	4	1	no	—
190	C₂×C₁₉₁	—	4	1	no	—
191	C₂×C₁₉₁	#518	1	1	yes	characteristic
192	C₂×C₁₉₁	C₂×#131	1	1	yes	characteristic
193	C₂×C₁₉₁	#568	1	1	yes	characteristic
194	D₁₉₁	—	4	1	no	—
195	D₁₉₁	—	4	1	no	—
196	C₁₉₁	#2981	1	1	yes	characteristic, complemented, Sylow
197	#2981	—	191	1	no	maximal, Sylow
198	#532	—	191	1	no	—
199	#436	—	191	1	no	—
200	#436	—	191	1	no	—
201	#435	—	191	1	no	—
202	#435	—	191	1	no	—
203	#435	—	191	1	no	—
204	#435	—	191	1	no	—
205	C₈×D₄	—	191	1	no	—
206	C₈×D₄	—	191	1	no	—
207	#432	—	191	1	no	—
208	#431	—	191	1	no	—
209	#408	—	191	1	no	—
210	#408	—	191	1	no	—
211	#408	—	191	1	no	—
212	#408	D₁₉₁	1	1	yes	characteristic, complemented
213	C₂×#41	—	191	1	no	—
214	C₂×#41	C₂×D₁₉₁	1	1	yes	characteristic
215	C₂×M₁₆	—	191	1	no	—
216	C₂×M₁₆	—	191	1	no	—
217	C₂×M₁₆	—	191	1	no	—
218	C₂×M₁₆	C₂×D₁₉₁	1	1	yes	characteristic
219	C₂²×C₈	—	191	1	no	—
220	C₂²×C₈	—	191	1	no	—
221	C₂²×C₈	—	191	1	no	—
222	C₂²×C₈	C₂×D₁₉₁	1	1	yes	characteristic
223	C₄⋊Q₈	—	191	1	no	—
224	#127	—	191	1	no	—
225	#124	—	191	1	no	—
226	#124	—	191	1	no	—
227	#121	—	191	1	no	—
228	#121	—	191	1	no	—
229	#121	—	191	1	no	—
230	#121	—	191	1	no	—
231	C₄×D₄	—	191	1	no	—
232	C₄×D₄	—	191	1	no	—
233	C₄×D₄	—	191	1	no	—
234	C₄×D₄	—	191	1	no	—
235	C₂×C₄²	—	191	1	no	—
236	C₄⋊C₈	—	191	1	no	—
237	C₄⋊C₈	—	191	1	no	—
238	C₄⋊C₈	—	191	1	no	—
239	C₄⋊C₈	—	191	1	no	—
240	C₂²⋊C₈	—	191	1	no	—
241	C₂²⋊C₈	—	191	1	no	—
242	C₂²⋊C₈	—	191	1	no	—
243	C₂²⋊C₈	—	191	1	no	—
244	C₂²⋊C₈	—	191	1	no	—
245	C₂²⋊C₈	—	191	1	no	—
246	C₂²⋊C₈	—	191	1	no	—
247	C₂²⋊C₈	—	191	1	no	—
248	C₂²⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic
249	C₂²⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic
250	C₂²⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic
251	C₂²⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic
252	#97	—	191	1	no	—
253	#97	—	191	1	no	—
254	C₄×C₈	—	191	1	no	—
255	C₄×C₈	—	191	1	no	—
256	#41	—	4	1	no	—
257	#41	—	4	1	no	—
258	#41	—	764	1	no	—
259	#41	—	764	1	no	—
260	C₂×Q₈	—	191	1	no	—
261	C₂×Q₈	C₄×D₁₉₁	1	1	yes	characteristic
262	C₂×D₄	—	191	1	no	—
263	C₂×D₄	—	191	1	no	—
264	C₂×D₄	—	191	1	no	—
265	C₂×D₄	—	191	1	no	—
266	C₂×D₄	—	191	1	no	—
267	C₂×D₄	—	191	1	no	—
268	C₂×D₄	—	191	1	no	—
269	C₂×D₄	C₄×D₁₉₁	1	1	yes	characteristic
270	C₂×D₄	C₄×D₁₉₁	1	1	yes	characteristic
271	C₂×D₄	C₄×D₁₉₁	1	1	yes	characteristic
272	C₂²×C₄	—	191	1	no	—
273	C₂²×C₄	—	191	1	no	—
274	C₂²×C₄	—	191	1	no	—
275	C₂²×C₄	—	191	1	no	—
276	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
279	M₁₆	—	4	1	no	—
280	M₁₆	—	764	1	no	—
281	M₁₆	—	764	1	no	—
282	M₁₆	—	764	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	191	1	no	—
285	C₂×C₈	—	191	1	no	—
286	C₂×C₈	—	191	1	no	—
287	C₂×C₈	—	191	1	no	—
288	C₂×C₈	—	764	1	no	—
289	C₂×C₈	—	764	1	no	—
290	C₂×C₈	—	764	1	no	—
291	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
294	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
295	C₄⋊C₄	—	191	1	no	—
296	C₄⋊C₄	—	191	1	no	—
297	C₄⋊C₄	—	191	1	no	—
298	C₄⋊C₄	—	191	1	no	—
299	C₂²⋊C₄	—	191	1	no	—
300	C₂²⋊C₄	—	191	1	no	—
301	C₂²⋊C₄	—	191	1	no	—
302	C₂²⋊C₄	—	191	1	no	—
303	C₂²⋊C₄	—	191	1	no	—
304	C₂²⋊C₄	—	191	1	no	—
305	C₂²⋊C₄	—	191	1	no	—
306	C₂²⋊C₄	—	191	1	no	—
307	C₄²	—	191	1	no	—
308	C₄²	—	191	1	no	—
309	C₄²	—	191	1	no	—
310	C₄²	—	191	1	no	—
311	C₂³	—	191	1	no	—
312	C₂³	—	191	1	no	—
313	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
314	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
315	C₂³	C₂×C₄×D₁₉₁	1	1	yes	characteristic
316	Q₈	—	4	1	no	—
317	Q₈	—	764	1	no	—
318	D₄	—	4	1	no	—
319	D₄	—	4	1	no	—
320	D₄	—	4	1	no	—
321	D₄	—	382	2	no	—
322	D₄	—	382	2	no	—
323	D₄	—	764	1	no	—
324	D₄	—	764	1	no	—
325	D₄	—	764	1	no	—
326	D₄	—	764	1	no	—
327	D₄	—	764	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	382	2	no	—
335	C₂×C₄	—	382	1	no	—
336	C₂×C₄	—	382	1	no	—
337	C₂×C₄	—	382	1	no	—
338	C₂×C₄	—	382	1	no	—
339	C₂×C₄	—	191	1	no	—
340	C₂×C₄	—	191	1	no	—
341	C₂×C₄	—	191	1	no	—
342	C₂×C₄	—	191	1	no	—
343	C₂×C₄	—	191	1	no	—
344	C₂×C₄	—	191	1	no	—
345	C₂×C₄	—	764	1	no	—
346	C₂×C₄	C₂×C₄×D₁₉₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×D₁₉₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₁₉₁	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	382	1	no	—
355	C₈	—	382	1	no	—
356	C₈	—	382	1	no	—
357	C₈	—	382	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	382	1	no	—
368	C₂²	—	382	1	no	—
369	C₂²	—	382	1	no	—
370	C₂²	—	382	1	no	—
371	C₂²	—	382	1	no	—
372	C₂²	—	382	1	no	—
373	C₂²	C₂²×C₄×D₁₉₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	382	1	no	—
378	C₄	—	382	1	no	—
379	C₄	—	382	1	no	—
380	C₄	—	382	1	no	—
381	C₄	—	382	1	no	—
382	C₄	—	191	2	no	—
383	C₄	#20259367	1	1	yes	characteristic
384	C₄	#20259367	1	1	yes	characteristic
385	C₂	—	4	1	no	—
386	C₂	—	4	1	no	—
387	C₂	—	4	1	no	—
388	C₂	—	764	1	no	—
389	C₂	—	764	1	no	—
390	C₂	#27133136	1	1	yes	characteristic
391	C₂	#131×D₁₉₁	1	1	yes	characteristic
392	C₂	#27133428	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉₁
commutator, socle	C₂²×C₁₉₁	C₂³×C₄
Fitting	#408×C₁₉₁	C₂
prime radical	#27133209	C₂
cosocle	C₂×C₄×C₁₉₁	C₂⁴
hypercenter	#408	D₁₉₁
hypocenter	C₁₉₁	#2981
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
2. #27132739	C₂	semidirect
3. #27132738	C₂	semidirect
4. #27132737	C₂	semidirect
5. #27132734	C₂	semidirect
6. #27132732	C₂	semidirect
7. #27132731	C₂	semidirect
8. C₈×C₂²⋊D₁₉₁	C₂	semidirect
9. (C₂²⋊D₁₉₁)⋊C₈	C₂	semidirect
10. #27132717	C₂	semidirect
11. #27132713	C₂	semidirect
12. #27132630	C₂	semidirect
13. #27132628	C₂	semidirect
14. #27132628	C₂	semidirect
15. #408×C₁₉₁	C₂	semidirect
196. C₁₉₁	#2981	semidirect
212. #408	D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
#27133209	2
#27132739	2
#27132738	2
#27132737	2
#27132734	2
#27132732	2
#27132731	2
C₈×C₂²⋊D₁₉₁	2
(C₂²⋊D₁₉₁)⋊C₈	2
#27132717	2
#27132713	2
#27132630	2
#27132628	2
#408×C₁₉₁	2
#2981	191