Subgroups — #37575510

Order 24448.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259306	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊D₁₉₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#20259278	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132559	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132553	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132552	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132546	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132546	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132540	C₂	1	1	yes	maximal, characteristic
10	#27132534	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#27132510	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉₁⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
15	#385×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
17	C₂³×Dic₁₉₁	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₉₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
20	#20259306	C₄	1	8	yes	complemented
21	C₄×C₂²⋊D₁₉₁	—	2	4	no	—
22	#20259278	—	2	4	no	—
23	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₉₁	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×(C₂×D₁₉₁)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉₁	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	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
47	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₁₉₁	C₂²	1	1	yes	characteristic
52	#95×C₁₉₁	C₂²	1	1	yes	characteristic
53	#95×C₁₉₁	C₂²	1	1	yes	characteristic
54	C₂³×D₁₉₁	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊D₁₉₁	—	2	2	no	—
56	C₂×C₂²⋊D₁₉₁	—	2	2	no	—
57	C₂×C₂²⋊D₁₉₁	C₂×C₄	1	4	yes	—
58	C₂²×Dic₁₉₁	—	2	2	no	—
59	C₂²×Dic₁₉₁	—	2	2	no	—
60	C₂²×Dic₁₉₁	—	2	2	no	—
61	C₂²×Dic₁₉₁	—	2	2	no	—
62	C₂²×Dic₁₉₁	—	4	1	no	—
63	C₂²×Dic₁₉₁	C₂×C₄	1	4	yes	complemented
64	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
66	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₁₉₁	—	2	2	no	—
72	C₂×C₄×D₁₉₁	—	2	2	no	—
73	C₂×C₄×D₁₉₁	—	4	1	no	—
74	C₄⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
75	C₄⋊Dic₁₉₁	C₂×C₄	1	4	yes	complemented
76	Dic₁₉₁⋊C₄	—	2	2	no	—
77	Dic₁₉₁⋊C₄	—	2	2	no	—
78	Dic₁₉₁⋊C₄	—	2	2	no	—
79	C₂²⋊Dic₁₉₁	D₄	1	4	yes	—
80	(C₂×D₁₉₁)⋊C₄	—	2	2	no	—
81	(C₂×D₁₉₁)⋊C₄	—	2	2	no	—
82	(C₂×D₁₉₁)⋊C₄	—	4	1	no	—
83	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	complemented
84	(C₂×D₁₉₁)⋊C₄	C₂×C₄	1	4	yes	complemented
85	C₄×Dic₁₉₁	—	2	2	no	—
86	C₄×Dic₁₉₁	—	2	2	no	—
87	C₄×Dic₁₉₁	—	2	2	no	—
88	C₄×Dic₁₉₁	—	2	2	no	—
89	C₄×Dic₁₉₁	—	4	1	no	—
90	C₂⁴×C₁₉₁	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₉₁	—	2	2	no	—
92	C₂²×C₄×C₁₉₁	—	2	2	no	—
93	C₂²×C₄×C₁₉₁	—	4	1	no	—
94	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
100	C₄⋊C₄×C₁₉₁	—	2	2	no	—
101	C₄⋊C₄×C₁₉₁	—	4	1	no	—
102	C₂²⋊C₄×C₁₉₁	—	2	2	no	—
103	C₂²⋊C₄×C₁₉₁	C₂×C₄	1	4	yes	complemented
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	—	2	1	no	—
109	C₂²×D₁₉₁	—	2	1	no	—
110	C₂²×D₁₉₁	C₂²×C₄	1	2	yes	—
111	C₂²⋊D₁₉₁	—	2	8	no	—
112	C₂×Dic₁₉₁	—	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	—	4	4	no	—
129	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
130	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
131	C₂×Dic₁₉₁	C₂²×C₄	1	2	yes	—
132	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
133	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
134	C₂×Dic₁₉₁	#41	1	2	yes	—
135	C₄×D₁₉₁	—	4	4	no	—
136	C₂³×C₁₉₁	—	2	1	no	—
137	C₂³×C₁₉₁	—	2	1	no	—
138	C₂³×C₁₉₁	—	2	1	no	—
139	C₂³×C₁₉₁	—	2	1	no	—
140	C₂³×C₁₉₁	C₂²×C₄	1	2	yes	—
141	C₂³×C₁₉₁	C₂×D₄	1	2	yes	—
142	C₂³×C₁₉₁	#41	1	2	yes	—
143	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
155	C₂×C₄×C₁₉₁	—	2	1	no	—
156	C₂×C₄×C₁₉₁	—	2	1	no	—
157	C₂×C₄×C₁₉₁	—	2	1	no	—
158	C₂×C₄×C₁₉₁	—	2	1	no	—
159	C₂×C₄×C₁₉₁	—	4	4	no	—
160	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
161	C₂×C₄×C₁₉₁	C₂²×C₄	1	2	yes	—
162	C₂×C₄×C₁₉₁	#41	1	2	yes	—
163	C₂²×C₁₉₁	—	2	2	no	—
164	C₂²×C₁₉₁	—	2	2	no	—
165	C₂²×C₁₉₁	—	2	2	no	—
166	C₂²×C₁₉₁	—	2	2	no	—
167	C₂²×C₁₉₁	—	2	2	no	—
168	C₂²×C₁₉₁	—	2	2	no	—
169	C₂²×C₁₉₁	C₄×D₄	1	4	yes	—
170	C₂²×C₁₉₁	C₂³×C₄	1	1	yes	characteristic
171	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
172	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
173	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
174	C₂²×C₁₉₁	C₂×#41	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	C₂×D₁₉₁	—	2	2	no	—
178	C₂×D₁₉₁	—	2	2	no	—
179	C₂×D₁₉₁	—	2	2	no	—
180	C₂×D₁₉₁	—	4	1	no	—
181	C₂×D₁₉₁	—	4	1	no	—
182	C₂×D₁₉₁	—	4	1	no	—
183	C₂×D₁₉₁	—	4	1	no	—
184	C₄×C₁₉₁	—	2	2	no	—
185	C₄×C₁₉₁	—	2	2	no	—
186	C₄×C₁₉₁	—	2	2	no	—
187	C₄×C₁₉₁	—	4	1	no	—
188	C₄×C₁₉₁	—	4	1	no	—
189	C₄×C₁₉₁	—	4	1	no	—
190	Dic₁₉₁	—	2	2	no	—
191	Dic₁₉₁	—	2	2	no	—
192	Dic₁₉₁	—	2	2	no	—
193	Dic₁₉₁	—	2	2	no	—
194	Dic₁₉₁	—	2	2	no	—
195	Dic₁₉₁	—	2	2	no	—
196	Dic₁₉₁	—	4	1	no	—
197	C₂×C₁₉₁	—	2	4	no	—
198	C₂×C₁₉₁	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₁₉₁	C₄×#41	1	1	yes	characteristic
200	C₂×C₁₉₁	#520	1	1	yes	characteristic
201	C₂×C₁₉₁	#546	1	1	yes	characteristic
202	C₂×C₁₉₁	#547	1	1	yes	characteristic
203	C₂×C₁₉₁	#551	1	1	yes	characteristic
204	C₂×C₁₉₁	#552	1	1	yes	characteristic
205	D₁₉₁	—	4	2	no	—
206	C₁₉₁	#2359	1	1	yes	characteristic, complemented, Sylow
207	#2359	—	191	1	no	maximal, Sylow
208	C₂×#123	—	191	1	no	—
209	C₂×C₄×D₄	—	191	1	no	—
210	C₂×#117	—	191	1	no	—
211	#389	—	191	1	no	—
212	#388	—	191	1	no	—
213	#388	—	191	1	no	—
214	#387	—	191	1	no	—
215	#387	—	191	1	no	—
216	#386	—	191	1	no	—
217	#385	—	191	1	no	—
218	#385	D₁₉₁	1	1	yes	characteristic, complemented
219	C₄×C₄⋊C₄	—	191	1	no	—
220	C₄×C₂²⋊C₄	—	191	1	no	—
221	C₄×C₂²⋊C₄	—	191	1	no	—
222	C₂×#95	—	191	1	no	—
223	C₂²×D₄	—	191	1	no	—
224	C₂³×C₄	—	191	1	no	—
225	C₂³×C₄	—	191	1	no	—
226	C₂³×C₄	—	191	1	no	—
227	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
228	#123	—	191	8	no	—
229	C₄×D₄	—	382	4	no	—
230	#117	—	382	4	no	—
231	C₂×C₄⋊C₄	—	191	1	no	—
232	C₂×C₄⋊C₄	—	191	1	no	—
233	C₂×C₄⋊C₄	—	191	1	no	—
234	C₂×C₄⋊C₄	—	191	1	no	—
235	C₂×C₄⋊C₄	—	191	1	no	—
236	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	—	191	1	no	—
239	C₂×C₂²⋊C₄	—	191	1	no	—
240	C₂×C₂²⋊C₄	—	191	1	no	—
241	C₂×C₂²⋊C₄	—	191	1	no	—
242	C₂×C₂²⋊C₄	—	191	1	no	—
243	C₂×C₂²⋊C₄	—	191	1	no	—
244	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×D₁₉₁	1	1	yes	characteristic
246	C₂×C₄²	—	191	1	no	—
247	C₂×C₄²	—	191	1	no	—
248	C₂×C₄²	—	191	1	no	—
249	C₂×C₄²	—	191	1	no	—
250	C₂×C₄²	—	191	1	no	—
251	#95	—	191	1	no	—
252	#95	—	191	1	no	—
253	#95	—	191	1	no	—
254	#95	—	191	1	no	—
255	#95	—	191	1	no	—
256	#95	—	191	1	no	—
257	#95	—	191	1	no	—
258	#95	—	191	1	no	—
259	#95	C₂×D₁₉₁	1	1	yes	characteristic
260	#95	C₂×D₁₉₁	1	1	yes	characteristic
261	C₂⁴	—	191	1	no	—
262	C₂⁴	C₂²×D₁₉₁	1	1	yes	characteristic
263	C₂×D₄	—	382	2	no	—
264	C₂×D₄	—	382	2	no	—
265	C₂×D₄	—	191	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	382	2	no	—
270	C₂²×C₄	—	382	2	no	—
271	C₂²×C₄	—	382	2	no	—
272	C₂²×C₄	—	382	2	no	—
273	C₂²×C₄	—	382	2	no	—
274	C₂²×C₄	—	382	2	no	—
275	C₂²×C₄	—	191	1	no	—
276	C₂²×C₄	—	191	4	no	—
277	C₂²×C₄	—	191	1	no	—
278	C₂²×C₄	—	191	1	no	—
279	C₂²×C₄	—	191	1	no	—
280	C₂²×C₄	—	191	1	no	—
281	C₂²×C₄	—	191	1	no	—
282	C₂²×C₄	—	191	1	no	—
283	C₂²×C₄	—	764	1	no	—
284	C₂²×C₄	—	764	1	no	—
285	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	382	2	no	—
294	C₄⋊C₄	—	382	2	no	—
295	C₄⋊C₄	—	382	2	no	—
296	C₄⋊C₄	—	191	4	no	—
297	C₄⋊C₄	—	191	4	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	382	2	no	—
300	C₂²⋊C₄	—	382	2	no	—
301	C₂²⋊C₄	—	191	4	no	—
302	C₂²⋊C₄	—	191	4	no	—
303	C₂²⋊C₄	—	191	4	no	—
304	C₂²⋊C₄	—	764	1	no	—
305	C₂²⋊C₄	C₄×D₁₉₁	1	4	yes	complemented
306	C₄²	—	382	2	no	—
307	C₄²	—	382	2	no	—
308	C₄²	—	382	2	no	—
309	C₄²	—	382	2	no	—
310	C₄²	—	764	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	382	1	no	—
316	C₂³	—	382	1	no	—
317	C₂³	—	382	1	no	—
318	C₂³	—	382	1	no	—
319	C₂³	—	382	1	no	—
320	C₂³	—	382	1	no	—
321	C₂³	—	191	2	no	—
322	C₂³	C₂×C₄×D₁₉₁	1	2	yes	—
323	C₂³	D₄×D₁₉₁	1	2	yes	—
324	C₂³	#15690288	1	2	yes	—
325	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
326	D₄	—	382	8	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	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	4	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	—	382	1	no	—
350	C₂×C₄	—	382	1	no	—
351	C₂×C₄	—	382	1	no	—
352	C₂×C₄	—	382	1	no	—
353	C₂×C₄	—	382	1	no	—
354	C₂×C₄	—	382	1	no	—
355	C₂×C₄	—	382	8	no	—
356	C₂×C₄	—	382	1	no	—
357	C₂×C₄	—	382	1	no	—
358	C₂×C₄	—	382	1	no	—
359	C₂×C₄	—	191	2	no	—
360	C₂×C₄	—	191	2	no	—
361	C₂×C₄	—	191	2	no	—
362	C₂×C₄	—	191	2	no	—
363	C₂×C₄	—	191	2	no	—
364	C₂×C₄	—	191	2	no	—
365	C₂×C₄	—	764	4	no	—
366	C₂×C₄	—	764	4	no	—
367	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
368	C₂×C₄	C₂×C₄×D₁₉₁	1	2	yes	—
369	C₂×C₄	#15690286	1	2	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	382	2	no	—
377	C₂²	—	382	2	no	—
378	C₂²	—	382	2	no	—
379	C₂²	—	764	1	no	—
380	C₂²	—	764	1	no	—
381	C₂²	—	764	1	no	—
382	C₂²	—	764	1	no	—
383	C₂²	#20259284	1	4	yes	—
384	C₂²	C₂²×C₄×D₁₉₁	1	1	yes	characteristic
385	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
386	C₂²	#41×D₁₉₁	1	1	yes	characteristic
387	C₂²	C₂×#15690286	1	1	yes	characteristic
388	C₂²	C₂×#15690288	1	1	yes	characteristic
389	C₂²	#20259367	1	1	yes	characteristic
390	C₂²	#20259369	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	382	2	no	—
398	C₄	—	382	2	no	—
399	C₄	—	382	2	no	—
400	C₄	—	382	2	no	—
401	C₄	—	382	2	no	—
402	C₄	—	382	2	no	—
403	C₄	—	764	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	764	2	no	—
406	C₂	C₂×#20259284	1	1	yes	characteristic
407	C₂	C₄×#15690286	1	1	yes	characteristic
408	C₂	#27133142	1	1	yes	characteristic
409	C₂	#27133300	1	1	yes	characteristic
410	C₂	#27133311	1	1	yes	characteristic
411	C₂	#27133340	1	1	yes	characteristic
412	C₂	#27133355	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator	C₂²×C₁₉₁	C₂³×C₄
Fitting	#385×C₁₉₁	C₂
socle, cosocle	C₂³×C₁₉₁	C₂⁴
prime radical	C₂²×C₂²⋊D₁₉₁	C₂²
hypercenter	#385	D₁₉₁
hypocenter	C₁₉₁	#2359
LCS	G ▷ C₂²×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ #385

Complements

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

N	H ≅ G/N	type
3. C₂×#20259278	C₂	semidirect
4. #27132559	C₂	semidirect
5. #27132553	C₂	semidirect
6. #27132552	C₂	semidirect
7. #27132546	C₂	semidirect
8. #27132546	C₂	semidirect
10. #27132534	C₂	semidirect
11. C₄⋊C₄×Dic₁₉₁	C₂	semidirect
12. C₂²⋊C₄×Dic₁₉₁	C₂	semidirect
13. #27132510	C₂	semidirect
14. C₂×C₁₉₁⋊#95	C₂	semidirect
15. #385×C₁₉₁	C₂	semidirect
20. #20259306	C₄	semidirect
63. C₂²×Dic₁₉₁	C₂×C₄	semidirect
74. C₄⋊Dic₁₉₁	C₂×C₄	semidirect
75. C₄⋊Dic₁₉₁	C₂×C₄	semidirect
83. (C₂×D₁₉₁)⋊C₄	C₂×C₄	semidirect
84. (C₂×D₁₉₁)⋊C₄	C₂×C₄	semidirect
103. C₂²⋊C₄×C₁₉₁	C₂×C₄	semidirect
206. C₁₉₁	#2359	semidirect
218. #385	D₁₉₁	semidirect
305. C₂²⋊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×#20259306	2
C₂×C₄×C₂²⋊D₁₉₁	2
C₂×#20259278	2
#27132559	2
#27132553	2
#27132552	2
#27132546	2
#27132540	2
#27132534	2
C₄⋊C₄×Dic₁₉₁	2
C₂²⋊C₄×Dic₁₉₁	2
#27132510	2
C₂×C₁₉₁⋊#95	2
#385×C₁₉₁	2
#2359	191