Subgroups — #37575152

Order 24448.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259284	C₂	1	1	yes	maximal, characteristic
2	#27132554	C₂	1	1	yes	maximal, characteristic, complemented
3	#27132552	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132549	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132541	C₂	1	1	yes	maximal, characteristic
6	#27132541	C₂	1	1	yes	maximal, characteristic
7	#27132537	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132534	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132530	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132527	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132525	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×(C₂×D₁₉₁)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#95×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#387×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₇₆₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
21	#20259284	C₄	1	8	yes	complemented
22	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
23	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
35	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
36	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
37	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
38	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
39	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
40	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
41	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
42	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₁₉₁	C₂²	1	1	yes	characteristic
48	#95×C₁₉₁	C₂²	1	1	yes	characteristic
49	#95×C₁₉₁	C₂²	1	1	yes	characteristic
50	#95×C₁₉₁	C₂²	1	1	yes	characteristic
51	#95×C₁₉₁	C₂²	1	1	yes	characteristic
52	C₂³×D₁₉₁	C₂³	1	1	yes	characteristic
53	C₂³×D₁₉₁	C₂³	1	1	yes	characteristic
54	C₂×D₇₆₄	—	2	2	no	—
55	C₂×D₇₆₄	—	2	2	no	—
56	C₂×D₇₆₄	C₂×C₄	1	4	yes	—
57	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₁₉₁	—	2	2	no	—
64	C₂×C₄×D₁₉₁	—	2	2	no	—
65	C₂×C₄×D₁₉₁	—	4	1	no	—
66	C₂×C₄×D₁₉₁	—	4	1	no	—
67	C₂×C₄×D₁₉₁	—	4	1	no	—
68	C₂×C₄×D₁₉₁	—	4	1	no	—
69	C₂×C₄×D₁₉₁	—	4	1	no	—
70	C₂×C₄×D₁₉₁	—	4	1	no	—
71	C₂×C₄×D₁₉₁	—	4	1	no	—
72	C₂×C₄×D₁₉₁	—	4	1	no	—
73	C₂×C₄×D₁₉₁	C₂×C₄	1	4	yes	—
74	C₂×C₄×D₁₉₁	C₂×C₄	1	4	yes	complemented
75	C₄⋊Dic₁₉₁	—	4	1	no	—
76	Dic₁₉₁⋊C₄	—	4	1	no	—
77	Dic₁₉₁⋊C₄	—	4	1	no	—
78	(C₂×D₁₉₁)⋊C₄	—	2	2	no	—
79	(C₂×D₁₉₁)⋊C₄	—	2	2	no	—
80	(C₂×D₁₉₁)⋊C₄	—	4	1	no	—
81	(C₂×D₁₉₁)⋊C₄	—	4	1	no	—
82	(C₂×D₁₉₁)⋊C₄	—	4	1	no	—
83	(C₂×D₁₉₁)⋊C₄	—	4	1	no	—
84	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	—
85	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	complemented
86	C₄×Dic₁₉₁	—	4	1	no	—
87	C₄×Dic₁₉₁	C₂×C₄	1	4	yes	complemented
88	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₁₉₁	—	4	1	no	—
96	C₄⋊C₄×C₁₉₁	C₂×C₄	1	4	yes	complemented
97	C₄²×C₁₉₁	—	4	1	no	—
98	C₂²×D₁₉₁	—	2	1	no	—
99	C₂²×D₁₉₁	—	2	1	no	—
100	C₂²×D₁₉₁	—	2	1	no	—
101	C₂²×D₁₉₁	—	2	1	no	—
102	C₂²×D₁₉₁	—	2	1	no	—
103	C₂²×D₁₉₁	—	2	1	no	—
104	C₂²×D₁₉₁	—	2	1	no	—
105	C₂²×D₁₉₁	—	2	1	no	—
106	C₂²×D₁₉₁	—	2	1	no	—
107	C₂²×D₁₉₁	—	2	1	no	—
108	C₂²×D₁₉₁	C₂²×C₄	1	2	yes	—
109	C₂²×D₁₉₁	C₂²×C₄	1	2	yes	—
110	C₂²×D₁₉₁	#41	1	2	yes	—
111	C₂²×D₁₉₁	#41	1	2	yes	—
112	D₇₆₄	—	2	8	no	—
113	C₂×Dic₁₉₁	—	2	1	no	—
114	C₂×Dic₁₉₁	—	2	1	no	—
115	C₂×Dic₁₉₁	—	2	1	no	—
116	C₂×Dic₁₉₁	—	2	1	no	—
117	C₂×Dic₁₉₁	—	2	1	no	—
118	C₂×Dic₁₉₁	—	2	1	no	—
119	C₂×Dic₁₉₁	—	2	1	no	—
120	C₂×Dic₁₉₁	—	2	1	no	—
121	C₂×Dic₁₉₁	—	2	1	no	—
122	C₂×Dic₁₉₁	—	2	1	no	—
123	C₂×Dic₁₉₁	—	2	1	no	—
124	C₂×Dic₁₉₁	—	2	1	no	—
125	C₂×Dic₁₉₁	—	2	1	no	—
126	C₂×Dic₁₉₁	—	2	1	no	—
127	C₂×Dic₁₉₁	—	2	1	no	—
128	C₂×Dic₁₉₁	—	2	1	no	—
129	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
130	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
131	C₄×D₁₉₁	—	4	4	no	—
132	C₄×D₁₉₁	—	4	4	no	—
133	C₄×D₁₉₁	—	4	4	no	—
134	C₄×D₁₉₁	—	4	4	no	—
135	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
136	C₂×C₄×C₁₉₁	—	2	1	no	—
137	C₂×C₄×C₁₉₁	—	2	1	no	—
138	C₂×C₄×C₁₉₁	—	2	1	no	—
139	C₂×C₄×C₁₉₁	—	2	1	no	—
140	C₂×C₄×C₁₉₁	—	2	1	no	—
141	C₂×C₄×C₁₉₁	—	2	1	no	—
142	C₂×C₄×C₁₉₁	—	2	1	no	—
143	C₂×C₄×C₁₉₁	—	2	1	no	—
144	C₂×C₄×C₁₉₁	—	2	1	no	—
145	C₂×C₄×C₁₉₁	—	2	1	no	—
146	C₂×C₄×C₁₉₁	—	2	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	—	2	1	no	—
154	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
155	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
156	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
157	C₂²×C₁₉₁	C₂³×C₄	1	1	yes	characteristic
158	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
159	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
160	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂²×C₁₉₁	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×D₁₉₁	—	2	2	no	—
165	C₂×D₁₉₁	—	2	2	no	—
166	C₂×D₁₉₁	—	2	2	no	—
167	C₂×D₁₉₁	—	2	2	no	—
168	C₂×D₁₉₁	—	2	2	no	—
169	C₂×D₁₉₁	—	2	2	no	—
170	C₂×D₁₉₁	—	2	2	no	—
171	C₂×D₁₉₁	—	2	2	no	—
172	C₂×D₁₉₁	—	2	2	no	—
173	C₂×D₁₉₁	—	4	1	no	—
174	C₂×D₁₉₁	—	4	1	no	—
175	C₂×D₁₉₁	—	4	1	no	—
176	C₂×D₁₉₁	—	4	1	no	—
177	C₂×D₁₉₁	#117	1	4	yes	—
178	C₄×C₁₉₁	—	2	2	no	—
179	C₄×C₁₉₁	—	2	2	no	—
180	C₄×C₁₉₁	—	2	2	no	—
181	C₄×C₁₉₁	—	4	1	no	—
182	C₄×C₁₉₁	—	4	1	no	—
183	C₄×C₁₉₁	—	4	1	no	—
184	C₄×C₁₉₁	—	4	1	no	—
185	Dic₁₉₁	—	2	2	no	—
186	Dic₁₉₁	—	2	2	no	—
187	Dic₁₉₁	—	4	1	no	—
188	Dic₁₉₁	—	4	1	no	—
189	Dic₁₉₁	—	4	1	no	—
190	Dic₁₉₁	—	4	1	no	—
191	C₂×C₁₉₁	C₂×#117	1	1	yes	characteristic
192	C₂×C₁₉₁	#518	1	1	yes	characteristic
193	C₂×C₁₉₁	#520	1	1	yes	characteristic
194	C₂×C₁₉₁	#538	1	1	yes	characteristic
195	C₂×C₁₉₁	#538	1	1	yes	characteristic
196	C₂×C₁₉₁	#539	1	1	yes	characteristic
197	C₂×C₁₉₁	#539	1	1	yes	characteristic
198	D₁₉₁	—	2	4	no	—
199	D₁₉₁	—	4	2	no	—
200	C₁₉₁	#2318	1	1	yes	characteristic, complemented, Sylow
201	#2318	—	191	1	no	maximal, Sylow
202	C₂×C₄×D₄	—	191	1	no	—
203	#388	—	191	1	no	—
204	#388	—	191	1	no	—
205	#387	—	191	1	no	—
206	#387	D₁₉₁	1	1	yes	characteristic, complemented
207	#386	—	191	1	no	—
208	#386	—	191	1	no	—
209	#385	—	191	1	no	—
210	#385	—	191	1	no	—
211	#383	—	191	1	no	—
212	#382	—	191	1	no	—
213	#381	—	191	1	no	—
214	#380	—	191	1	no	—
215	C₄×C₂²⋊C₄	—	191	1	no	—
216	C₂×#95	—	191	1	no	—
217	C₂²×D₄	—	191	1	no	—
218	C₂³×C₄	—	191	1	no	—
219	C₂³×C₄	—	191	1	no	—
220	C₂³×C₄	—	191	1	no	—
221	C₂³×C₄	—	191	1	no	—
222	C₄×D₄	—	191	8	no	—
223	C₂×C₄⋊C₄	—	191	1	no	—
224	C₂×C₄⋊C₄	—	191	1	no	—
225	C₂×C₄⋊C₄	—	191	1	no	—
226	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	—	191	1	no	—
229	C₂×C₂²⋊C₄	—	191	1	no	—
230	C₂×C₂²⋊C₄	—	191	1	no	—
231	C₂×C₂²⋊C₄	—	191	1	no	—
232	C₂×C₂²⋊C₄	—	191	1	no	—
233	C₂×C₂²⋊C₄	—	191	1	no	—
234	C₂×C₂²⋊C₄	—	191	1	no	—
235	C₂×C₂²⋊C₄	—	191	1	no	—
236	C₂×C₄²	—	191	1	no	—
237	C₂×C₄²	—	191	1	no	—
238	C₂×C₄²	C₂×D₁₉₁	1	1	yes	characteristic
239	#95	—	191	1	no	—
240	#95	—	191	1	no	—
241	#95	—	191	1	no	—
242	#95	—	191	1	no	—
243	#95	—	191	1	no	—
244	#95	—	191	1	no	—
245	#95	—	191	1	no	—
246	#95	—	191	1	no	—
247	#95	—	191	1	no	—
248	#95	—	191	1	no	—
249	#95	C₂×D₁₉₁	1	1	yes	characteristic
250	#95	C₂×D₁₉₁	1	1	yes	characteristic
251	#95	C₂×D₁₉₁	1	1	yes	characteristic
252	#95	C₂×D₁₉₁	1	1	yes	characteristic
253	C₂⁴	—	191	1	no	—
254	C₂⁴	—	191	1	no	—
255	C₂×D₄	—	382	2	no	—
256	C₂×D₄	—	382	2	no	—
257	C₂×D₄	—	191	4	no	—
258	C₂²×C₄	—	382	2	no	—
259	C₂²×C₄	—	382	2	no	—
260	C₂²×C₄	—	191	1	no	—
261	C₂²×C₄	—	191	1	no	—
262	C₂²×C₄	—	191	1	no	—
263	C₂²×C₄	—	191	1	no	—
264	C₂²×C₄	—	191	1	no	—
265	C₂²×C₄	—	191	1	no	—
266	C₂²×C₄	—	191	4	no	—
267	C₂²×C₄	—	191	4	no	—
268	C₂²×C₄	—	764	1	no	—
269	C₂²×C₄	—	764	1	no	—
270	C₂²×C₄	—	764	1	no	—
271	C₂²×C₄	—	764	1	no	—
272	C₂²×C₄	—	764	1	no	—
273	C₂²×C₄	—	764	1	no	—
274	C₂²×C₄	—	764	1	no	—
275	C₂²×C₄	—	764	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	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	764	1	no	—
285	C₄⋊C₄	—	764	1	no	—
286	C₄⋊C₄	—	764	1	no	—
287	C₄⋊C₄	C₄×D₁₉₁	1	4	yes	complemented
288	C₂²⋊C₄	—	382	2	no	—
289	C₂²⋊C₄	—	382	2	no	—
290	C₂²⋊C₄	—	191	4	no	—
291	C₂²⋊C₄	—	191	4	no	—
292	C₂²⋊C₄	—	764	1	no	—
293	C₂²⋊C₄	—	764	1	no	—
294	C₂²⋊C₄	—	764	1	no	—
295	C₂²⋊C₄	—	764	1	no	—
296	C₄²	—	4	1	no	—
297	C₄²	—	191	4	no	—
298	C₄²	—	764	1	no	—
299	C₂³	—	382	1	no	—
300	C₂³	—	382	1	no	—
301	C₂³	—	382	1	no	—
302	C₂³	—	382	1	no	—
303	C₂³	—	382	1	no	—
304	C₂³	—	382	1	no	—
305	C₂³	—	382	1	no	—
306	C₂³	—	382	1	no	—
307	C₂³	—	382	1	no	—
308	C₂³	—	382	1	no	—
309	C₂³	—	191	2	no	—
310	C₂³	—	191	2	no	—
311	C₂³	—	191	2	no	—
312	C₂³	—	191	2	no	—
313	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
314	D₄	—	382	8	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
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	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	—	382	1	no	—
334	C₂×C₄	—	382	1	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	—	382	1	no	—
340	C₂×C₄	—	382	1	no	—
341	C₂×C₄	—	382	1	no	—
342	C₂×C₄	—	382	1	no	—
343	C₂×C₄	—	382	1	no	—
344	C₂×C₄	—	382	1	no	—
345	C₂×C₄	—	382	1	no	—
346	C₂×C₄	—	382	1	no	—
347	C₂×C₄	—	382	1	no	—
348	C₂×C₄	—	382	1	no	—
349	C₂×C₄	—	191	2	no	—
350	C₂×C₄	—	191	2	no	—
351	C₂×C₄	—	764	4	no	—
352	C₂×C₄	—	764	4	no	—
353	C₂×C₄	—	764	4	no	—
354	C₂×C₄	—	764	4	no	—
355	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
356	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
357	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
358	C₂²	—	382	2	no	—
359	C₂²	—	382	2	no	—
360	C₂²	—	382	2	no	—
361	C₂²	—	382	2	no	—
362	C₂²	—	382	2	no	—
363	C₂²	—	382	2	no	—
364	C₂²	—	382	2	no	—
365	C₂²	—	382	2	no	—
366	C₂²	—	382	2	no	—
367	C₂²	—	191	4	no	—
368	C₂²	—	764	1	no	—
369	C₂²	—	764	1	no	—
370	C₂²	—	764	1	no	—
371	C₂²	—	764	1	no	—
372	C₂²	C₂²×C₄×D₁₉₁	1	1	yes	characteristic
373	C₂²	#41×D₁₉₁	1	1	yes	characteristic
374	C₂²	#41×D₁₉₁	1	1	yes	characteristic
375	C₂²	#20259367	1	1	yes	characteristic
376	C₂²	#20259368	1	1	yes	characteristic
377	C₂²	#20259368	1	1	yes	characteristic
378	C₂²	#20259370	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	382	2	no	—
387	C₄	—	382	2	no	—
388	C₄	—	764	1	no	—
389	C₄	—	764	1	no	—
390	C₄	—	764	1	no	—
391	C₄	—	764	1	no	—
392	C₂	—	382	4	no	—
393	C₂	—	764	2	no	—
394	C₂	#117×D₁₉₁	1	1	yes	characteristic
395	C₂	#27133135	1	1	yes	characteristic
396	C₂	#27133145	1	1	yes	characteristic
397	C₂	#27133249	1	1	yes	characteristic
398	C₂	#27133252	1	1	yes	characteristic
399	C₂	#27133259	1	1	yes	characteristic
400	C₂	#27133261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator	C₂²×C₁₉₁	C₂³×C₄
Fitting	#387×C₁₉₁	C₂
socle, cosocle	C₂³×C₁₉₁	C₂⁴
prime radical	C₂²×D₇₆₄	C₂²
hypercenter	#387	D₁₉₁
hypocenter	C₁₉₁	#2318
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ #387

Complements

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

N	H ≅ G/N	type
2. #27132554	C₂	semidirect
3. #27132552	C₂	semidirect
4. #27132549	C₂	semidirect
7. #27132537	C₂	semidirect
8. #27132534	C₂	semidirect
9. #27132530	C₂	semidirect
10. #27132527	C₂	semidirect
11. #27132525	C₂	semidirect
12. #27132520	C₂	semidirect
13. C₄×(C₂×D₁₉₁)⋊C₄	C₂	semidirect
14. #95×D₁₉₁	C₂	semidirect
15. #387×C₁₉₁	C₂	semidirect
21. #20259284	C₄	semidirect
74. C₂×C₄×D₁₉₁	C₂×C₄	semidirect
85. (C₂×D₁₉₁)⋊C₄	C₂×C₄	semidirect
87. C₄×Dic₁₉₁	C₂×C₄	semidirect
96. C₄⋊C₄×C₁₉₁	C₂×C₄	semidirect
200. C₁₉₁	#2318	semidirect
206. #387	D₁₉₁	semidirect
287. C₄⋊C₄	C₄×D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259284	2
#27132554	2
#27132552	2
#27132549	2
#27132541	2
#27132537	2
#27132534	2
#27132530	2
#27132527	2
#27132525	2
#27132520	2
C₄×(C₂×D₁₉₁)⋊C₄	2
#95×D₁₉₁	2
#387×C₁₉₁	2
#2318	191