Subgroups — #37575329

Order 24448.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259309	C₂	1	1	yes	maximal, characteristic
2	#27132567	C₂	1	1	yes	maximal, characteristic, complemented
3	#27132567	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132557	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132557	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132551	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132551	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132543	C₂	1	1	yes	maximal, characteristic
9	#27132536	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132535	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132530	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132514	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#386×C₁₉₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
17	C₂³×Dic₁₉₁	C₂²	1	1	yes	characteristic
18	#20259309	C₄	1	8	yes	complemented
19	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₁₉₁	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	C₂²×D₄×C₁₉₁	C₂²	1	1	yes	characteristic
46	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
50	#95×C₁₉₁	C₂²	1	1	yes	characteristic
51	#95×C₁₉₁	C₂²	1	1	yes	characteristic
52	C₂×Dic₃₈₂	—	4	1	no	—
53	C₂×Dic₃₈₂	—	4	1	no	—
54	C₂×Dic₃₈₂	C₂×C₄	1	4	yes	complemented
55	C₂²×Dic₁₉₁	—	2	2	no	—
56	C₂²×Dic₁₉₁	—	4	1	no	—
57	C₂²×Dic₁₉₁	—	4	1	no	—
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	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
66	Dic₁₉₁⋊C₄	—	2	2	no	—
67	Dic₁₉₁⋊C₄	—	2	2	no	—
68	Dic₁₉₁⋊C₄	—	4	1	no	—
69	Dic₁₉₁⋊C₄	—	4	1	no	—
70	C₂²⋊Dic₁₉₁	—	2	2	no	—
71	C₂²⋊Dic₁₉₁	—	4	1	no	—
72	C₂²⋊Dic₁₉₁	—	4	1	no	—
73	C₂²⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
74	C₂²⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
75	C₂²⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
76	C₂²⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
77	C₄×Dic₁₉₁	—	4	1	no	—
78	C₄×Dic₁₉₁	—	4	1	no	—
79	C₄×Dic₁₉₁	—	4	1	no	—
80	C₄×Dic₁₉₁	—	4	1	no	—
81	C₄×Dic₁₉₁	C₂×C₄	1	4	yes	complemented
82	C₂⁴×C₁₉₁	C₂³	1	1	yes	characteristic
83	C₂⁴×C₁₉₁	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₉₁	—	4	1	no	—
85	C₂×D₄×C₁₉₁	—	4	1	no	—
86	C₂×D₄×C₁₉₁	C₂×C₄	1	4	yes	—
87	C₂²×C₄×C₁₉₁	—	2	2	no	—
88	C₂²×C₄×C₁₉₁	—	4	1	no	—
89	C₂²×C₄×C₁₉₁	—	4	1	no	—
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	C₂²⋊C₄×C₁₉₁	—	2	2	no	—
96	C₂²⋊C₄×C₁₉₁	—	4	1	no	—
97	C₂²⋊C₄×C₁₉₁	—	4	1	no	—
98	Dic₃₈₂	—	4	4	no	—
99	C₂×Dic₁₉₁	—	2	1	no	—
100	C₂×Dic₁₉₁	—	2	1	no	—
101	C₂×Dic₁₉₁	—	2	1	no	—
102	C₂×Dic₁₉₁	—	2	1	no	—
103	C₂×Dic₁₉₁	—	2	1	no	—
104	C₂×Dic₁₉₁	—	2	1	no	—
105	C₂×Dic₁₉₁	—	2	1	no	—
106	C₂×Dic₁₉₁	—	2	1	no	—
107	C₂×Dic₁₉₁	—	2	1	no	—
108	C₂×Dic₁₉₁	—	2	1	no	—
109	C₂×Dic₁₉₁	—	2	1	no	—
110	C₂×Dic₁₉₁	—	2	1	no	—
111	C₂×Dic₁₉₁	—	2	1	no	—
112	C₂×Dic₁₉₁	—	2	1	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	—	4	4	no	—
119	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
120	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
121	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
122	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
123	C₂×Dic₁₉₁	#41	1	2	yes	—
124	C₂³×C₁₉₁	—	2	1	no	—
125	C₂³×C₁₉₁	—	2	1	no	—
126	C₂³×C₁₉₁	—	2	1	no	—
127	C₂³×C₁₉₁	—	2	1	no	—
128	C₂³×C₁₉₁	—	2	1	no	—
129	C₂³×C₁₉₁	—	2	1	no	—
130	C₂³×C₁₉₁	—	2	1	no	—
131	C₂³×C₁₉₁	—	2	1	no	—
132	C₂³×C₁₉₁	—	2	1	no	—
133	C₂³×C₁₉₁	—	2	1	no	—
134	C₂³×C₁₉₁	—	2	1	no	—
135	C₂³×C₁₉₁	—	2	1	no	—
136	C₂³×C₁₉₁	C₂²×C₄	1	2	yes	—
137	C₂³×C₁₉₁	C₂²×C₄	1	2	yes	—
138	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
139	D₄×C₁₉₁	—	4	4	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	—	4	4	no	—
154	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
155	C₂×C₄×C₁₉₁	#41	1	2	yes	—
156	C₂²×C₁₉₁	—	2	2	no	—
157	C₂²×C₁₉₁	—	2	2	no	—
158	C₂²×C₁₉₁	—	2	2	no	—
159	C₂²×C₁₉₁	—	2	2	no	—
160	C₂²×C₁₉₁	—	2	2	no	—
161	C₂²×C₁₉₁	—	2	2	no	—
162	C₂²×C₁₉₁	—	4	1	no	—
163	C₂²×C₁₉₁	—	4	1	no	—
164	C₂²×C₁₉₁	—	4	1	no	—
165	C₂²×C₁₉₁	—	4	1	no	—
166	C₂²×C₁₉₁	—	4	1	no	—
167	C₂²×C₁₉₁	—	4	1	no	—
168	C₂²×C₁₉₁	—	4	1	no	—
169	C₂²×C₁₉₁	—	4	1	no	—
170	C₂²×C₁₉₁	C₂³×C₄	1	1	yes	characteristic
171	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
172	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
173	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂²×C₁₉₁	2₋¹⁺⁴	1	1	yes	characteristic
177	C₄×C₁₉₁	—	2	2	no	—
178	C₄×C₁₉₁	—	2	2	no	—
179	C₄×C₁₉₁	—	4	1	no	—
180	C₄×C₁₉₁	—	4	1	no	—
181	C₄×C₁₉₁	—	4	1	no	—
182	Dic₁₉₁	—	2	2	no	—
183	Dic₁₉₁	—	2	2	no	—
184	Dic₁₉₁	—	2	2	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	C₂×C₁₉₁	—	4	2	no	—
191	C₂×C₁₉₁	—	4	2	no	—
192	C₂×C₁₉₁	C₄×#41	1	1	yes	characteristic
193	C₂×C₁₉₁	#518	1	1	yes	characteristic
194	C₂×C₁₉₁	#520	1	1	yes	characteristic
195	C₂×C₁₉₁	#538	1	1	yes	characteristic
196	C₂×C₁₉₁	#538	1	1	yes	characteristic
197	C₂×C₁₉₁	#542	1	1	yes	characteristic
198	C₂×C₁₉₁	#542	1	1	yes	characteristic
199	C₁₉₁	#2337	1	1	yes	characteristic, complemented, Sylow
200	#2337	—	191	1	no	maximal, Sylow
201	C₂×#124	—	191	1	no	—
202	#391	—	191	1	no	—
203	#391	—	191	1	no	—
204	#388	—	191	1	no	—
205	#388	—	191	1	no	—
206	#388	—	191	1	no	—
207	#388	—	191	1	no	—
208	#386	—	191	1	no	—
209	#386	D₁₉₁	1	1	yes	characteristic
210	#385	—	191	1	no	—
211	#385	—	191	1	no	—
212	#383	—	191	1	no	—
213	C₄×C₄⋊C₄	—	191	1	no	—
214	C₄×C₂²⋊C₄	—	191	1	no	—
215	C₄×C₂²⋊C₄	—	191	1	no	—
216	C₂²×Q₈	—	191	1	no	—
217	C₂²×D₄	C₂×D₁₉₁	1	1	yes	characteristic
218	C₂³×C₄	—	191	1	no	—
219	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
220	#124	—	191	8	no	—
221	C₂×C₄⋊C₄	—	191	1	no	—
222	C₂×C₄⋊C₄	—	191	1	no	—
223	C₂×C₄⋊C₄	—	191	1	no	—
224	C₂×C₄⋊C₄	—	191	1	no	—
225	C₂×C₂²⋊C₄	—	191	1	no	—
226	C₂×C₂²⋊C₄	—	191	1	no	—
227	C₂×C₂²⋊C₄	—	191	1	no	—
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	C₂×D₁₉₁	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
235	C₂×C₄²	—	191	1	no	—
236	C₂×C₄²	—	191	1	no	—
237	C₂×C₄²	—	191	1	no	—
238	C₂×C₄²	—	191	1	no	—
239	C₂×C₄²	—	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	—	191	1	no	—
250	#95	C₂×D₁₉₁	1	1	yes	characteristic
251	#95	C₂×D₁₉₁	1	1	yes	characteristic
252	C₂⁴	C₂²×D₁₉₁	1	1	yes	characteristic
253	C₂⁴	C₂²×D₁₉₁	1	1	yes	characteristic
254	C₂×Q₈	—	191	4	no	—
255	C₂×Q₈	—	764	1	no	—
256	C₂×Q₈	—	764	1	no	—
257	C₂×D₄	—	4	1	no	—
258	C₂×D₄	—	4	1	no	—
259	C₂×D₄	C₄×D₁₉₁	1	4	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	382	2	no	—
264	C₂²×C₄	—	191	1	no	—
265	C₂²×C₄	—	191	1	no	—
266	C₂²×C₄	—	191	1	no	—
267	C₂²×C₄	—	191	1	no	—
268	C₂²×C₄	—	191	1	no	—
269	C₂²×C₄	—	191	1	no	—
270	C₂²×C₄	—	191	1	no	—
271	C₂²×C₄	—	191	1	no	—
272	C₂²×C₄	—	764	1	no	—
273	C₂²×C₄	—	764	1	no	—
274	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
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	C₄⋊C₄	—	382	2	no	—
280	C₄⋊C₄	—	382	2	no	—
281	C₄⋊C₄	—	764	1	no	—
282	C₄⋊C₄	—	764	1	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	382	2	no	—
287	C₂²⋊C₄	—	191	4	no	—
288	C₂²⋊C₄	—	191	4	no	—
289	C₂²⋊C₄	—	191	4	no	—
290	C₂²⋊C₄	—	191	4	no	—
291	C₂²⋊C₄	—	764	1	no	—
292	C₂²⋊C₄	—	764	1	no	—
293	C₄²	—	191	4	no	—
294	C₄²	—	764	1	no	—
295	C₄²	—	764	1	no	—
296	C₄²	—	764	1	no	—
297	C₄²	—	764	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	C₂×C₄×D₁₉₁	1	2	yes	—
311	C₂³	C₂×C₄×D₁₉₁	1	2	yes	—
312	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
313	Q₈	—	764	4	no	—
314	D₄	—	4	4	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	—	4	4	no	—
329	C₂×C₄	—	382	1	no	—
330	C₂×C₄	—	382	1	no	—
331	C₂×C₄	—	382	1	no	—
332	C₂×C₄	—	382	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	—	191	2	no	—
349	C₂×C₄	—	191	2	no	—
350	C₂×C₄	—	191	2	no	—
351	C₂×C₄	—	191	2	no	—
352	C₂×C₄	—	191	2	no	—
353	C₂×C₄	—	764	4	no	—
354	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
355	C₂×C₄	#15690286	1	2	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	C₂²×C₄×D₁₉₁	1	1	yes	characteristic
371	C₂²	#41×D₁₉₁	1	1	yes	characteristic
372	C₂²	C₂×#15690286	1	1	yes	characteristic
373	C₂²	#20259367	1	1	yes	characteristic
374	C₂²	#20259367	1	1	yes	characteristic
375	C₂²	#20259367	1	1	yes	characteristic
376	C₂²	#20259369	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	382	2	no	—
383	C₄	—	382	2	no	—
384	C₄	—	382	2	no	—
385	C₄	—	382	2	no	—
386	C₄	—	382	2	no	—
387	C₄	—	764	1	no	—
388	C₄	—	764	1	no	—
389	C₄	—	764	1	no	—
390	C₂	—	4	2	no	—
391	C₂	—	4	2	no	—
392	C₂	C₄×#15690286	1	1	yes	characteristic
393	C₂	#27133136	1	1	yes	characteristic
394	C₂	#27133142	1	1	yes	characteristic
395	C₂	#27133245	1	1	yes	characteristic
396	C₂	#27133248	1	1	yes	characteristic
397	C₂	#27133280	1	1	yes	characteristic
398	C₂	#27133281	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator	C₂²×C₁₉₁	C₂³×C₄
Fitting	#386×C₁₉₁	C₂
socle, cosocle	C₂³×C₁₉₁	C₂⁴
prime radical	C₂²×D₄×C₁₉₁	C₂²
hypercenter	#386	D₁₉₁
hypocenter	C₁₉₁	#2337
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ #386

Complements

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

N	H ≅ G/N	type
2. #27132567	C₂	semidirect
3. #27132567	C₂	semidirect
4. #27132557	C₂	semidirect
5. #27132557	C₂	semidirect
6. #27132551	C₂	semidirect
7. #27132551	C₂	semidirect
9. #27132536	C₂	semidirect
10. #27132535	C₂	semidirect
11. #27132530	C₂	semidirect
12. #27132514	C₂	semidirect
13. C₂²⋊C₄×Dic₁₉₁	C₂	semidirect
14. C₄×C₂²⋊Dic₁₉₁	C₂	semidirect
18. #20259309	C₄	semidirect
54. C₂×Dic₃₈₂	C₂×C₄	semidirect
73. C₂²⋊Dic₁₉₁	C₂×C₄	semidirect
74. C₂²⋊Dic₁₉₁	C₂×C₄	semidirect
75. C₂²⋊Dic₁₉₁	C₂×C₄	semidirect
76. C₂²⋊Dic₁₉₁	C₂×C₄	semidirect
81. C₄×Dic₁₉₁	C₂×C₄	semidirect
199. C₁₉₁	#2337	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259309	2
#27132567	2
#27132557	2
#27132551	2
#27132543	2
#27132536	2
#27132535	2
#27132530	2
#27132514	2
C₂²⋊C₄×Dic₁₉₁	2
C₄×C₂²⋊Dic₁₉₁	2
#386×C₁₉₁	2
#2337	191