Subgroups — #452×D₁₉₁ #37581725

Order 24448.

760 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₉₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×SD₁₆×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊Q₈×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132828	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132827	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132826	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132825	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132824	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132823	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132822	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#452×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15690288	C₂²	1	1	yes	characteristic
17	C₂×#15690287	—	2	1	no	—
18	C₂×#15690287	C₂²	1	1	yes	characteristic
19	C₂×#15690286	—	2	1	no	—
20	C₂×#15690286	C₂²	1	1	yes	characteristic
21	#41×D₁₉₁	—	2	4	no	—
22	#41×D₁₉₁	—	2	4	no	—
23	C₂×Q₈×D₁₉₁	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₁₉₁	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₉₁	—	2	1	no	—
26	C₂×D₄×D₁₉₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉₁	—	2	1	no	—
28	C₂²×C₄×D₁₉₁	C₂²	1	1	yes	characteristic
29	C₂×Dic₇₆₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×#15690277	C₂²	1	1	yes	characteristic, complemented
31	C₂×#15690277	C₂²	1	1	yes	characteristic, complemented
32	Q₁₆×D₁₉₁	—	2	4	no	—
33	C₂×#15690276	C₂²	1	1	yes	characteristic, complemented
34	C₂×#15690275	C₂²	1	1	yes	characteristic, complemented
35	C₂×#15690274	C₂²	1	1	yes	characteristic, complemented
36	SD₁₆×D₁₉₁	—	2	4	no	—
37	C₂×C₈×D₁₉₁	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₁₉₁	C₂²	1	1	yes	characteristic
39	#20259302	C₂²	1	1	yes	characteristic, complemented
40	#20259301	C₂²	1	1	yes	characteristic, complemented
41	#20259300	—	2	1	no	—
42	#20259299	—	2	1	no	—
43	#20259298	C₂²	1	1	yes	characteristic, complemented
44	C₄⋊C₄×D₁₉₁	—	2	1	no	—
45	C₄⋊C₄×D₁₉₁	C₂²	1	1	yes	characteristic
46	C₂²⋊C₄×D₁₉₁	—	2	1	no	—
47	#20259247	C₂²	1	1	yes	characteristic, complemented
48	#20259246	C₂²	1	1	yes	characteristic, complemented
49	#20259245	C₂²	1	1	yes	characteristic, complemented
50	#20259244	C₂²	1	1	yes	characteristic, complemented
51	#20259243	C₂²	1	1	yes	characteristic, complemented
52	#20259242	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₁₉₁	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
60	#103×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
61	#102×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₁₉₁	—	2	1	no	—
64	C₂³×D₁₉₁	D₄	1	1	yes	characteristic
65	#15690288	—	2	2	no	—
66	#15690288	—	2	2	no	—
67	#15690287	—	2	8	no	—
68	#15690287	—	2	2	no	—
69	#15690287	—	2	2	no	—
70	#15690286	—	2	8	no	—
71	#15690286	—	2	2	no	—
72	#15690286	—	2	2	no	—
73	C₂×Dic₃₈₂	—	2	1	no	—
74	C₂×Dic₃₈₂	—	2	1	no	—
75	C₂×Dic₃₈₂	C₂³	1	1	yes	characteristic
76	C₂×Dic₃₈₂	C₂³	1	1	yes	characteristic
77	Q₈×D₁₉₁	—	2	2	no	—
78	Q₈×D₁₉₁	—	2	2	no	—
79	Q₈×D₁₉₁	—	2	2	no	—
80	Q₈×D₁₉₁	D₄	1	4	yes	—
81	C₂×D₇₆₄	—	2	1	no	—
82	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
84	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
85	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
86	D₄×D₁₉₁	—	2	8	no	—
87	D₄×D₁₉₁	—	2	2	no	—
88	D₄×D₁₉₁	D₄	1	4	yes	—
89	C₂²×Dic₁₉₁	—	2	1	no	—
90	C₂²×Dic₁₉₁	D₄	1	1	yes	characteristic
91	C₂×C₄×D₁₉₁	—	2	8	no	—
92	C₂×C₄×D₁₉₁	—	2	1	no	—
93	C₂×C₄×D₁₉₁	—	2	1	no	—
94	C₂×C₄×D₁₉₁	—	2	2	no	—
95	C₂×C₄×D₁₉₁	—	2	2	no	—
96	C₂×C₄×D₁₉₁	—	2	1	no	—
97	C₂×C₄×D₁₉₁	—	2	1	no	—
98	C₂×C₄×D₁₉₁	—	2	1	no	—
99	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
100	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
103	Dic₇₆₄	—	2	2	no	—
104	#15690277	—	2	2	no	—
105	#15690277	—	2	2	no	—
106	#15690276	—	2	2	no	—
107	#15690275	—	2	2	no	—
108	#15690274	—	2	2	no	—
109	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
111	C₈×D₁₉₁	—	2	2	no	—
112	C₈×D₁₉₁	—	2	2	no	—
113	C₄⋊Dic₁₉₁	—	2	1	no	—
114	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
115	Dic₁₉₁⋊C₄	—	2	1	no	—
116	Dic₁₉₁⋊C₄	—	2	1	no	—
117	Dic₁₉₁⋊C₄	—	2	1	no	—
118	C₂²⋊Dic₁₉₁	—	2	1	no	—
119	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
120	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
121	#41×C₁₉₁	—	2	2	no	—
122	#41×C₁₉₁	—	2	2	no	—
123	C₂×Q₈×C₁₉₁	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₉₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₉₁	—	2	1	no	—
126	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉₁	—	2	1	no	—
128	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
129	Q₁₆×C₁₉₁	—	2	2	no	—
130	SD₁₆×C₁₉₁	—	2	2	no	—
131	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
132	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₁₉₁	—	2	1	no	—
134	C₄⋊C₄×C₁₉₁	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
136	C₂²×D₁₉₁	—	2	1	no	—
137	C₂²×D₁₉₁	—	2	2	no	—
138	C₂²×D₁₉₁	—	2	4	no	—
139	C₂²×D₁₉₁	—	2	2	no	—
140	C₂²×D₁₉₁	—	2	2	no	—
141	C₂²×D₁₉₁	—	4	2	no	—
142	C₂²×D₁₉₁	—	4	2	no	—
143	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
145	Dic₃₈₂	—	2	1	no	—
146	Dic₃₈₂	—	2	4	no	—
147	Dic₃₈₂	—	2	1	no	—
148	Dic₃₈₂	—	2	1	no	—
149	Dic₃₈₂	—	4	2	no	—
150	Dic₃₈₂	C₂×D₄	1	2	yes	—
151	D₇₆₄	—	2	4	no	—
152	D₇₆₄	—	2	1	no	—
153	D₇₆₄	C₂×D₄	1	2	yes	—
154	C₂²⋊D₁₉₁	—	2	4	no	—
155	C₂²⋊D₁₉₁	—	2	4	no	—
156	C₂²⋊D₁₉₁	—	2	4	no	—
157	C₂×Dic₁₉₁	—	2	4	no	—
158	C₂×Dic₁₉₁	—	2	1	no	—
159	C₂×Dic₁₉₁	—	2	2	no	—
160	C₂×Dic₁₉₁	—	2	1	no	—
161	C₂×Dic₁₉₁	—	2	1	no	—
162	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
164	C₄×D₁₉₁	—	2	4	no	—
165	C₄×D₁₉₁	—	2	4	no	—
166	C₄×D₁₉₁	—	2	2	no	—
167	C₄×D₁₉₁	—	2	4	no	—
168	C₄×D₁₉₁	—	2	1	no	—
169	C₄×D₁₉₁	—	2	1	no	—
170	C₄×D₁₉₁	—	2	2	no	—
171	C₄×D₁₉₁	—	4	2	no	—
172	C₄×D₁₉₁	—	4	2	no	—
173	C₄×D₁₉₁	C₂×D₄	1	2	yes	—
174	C₄×D₁₉₁	C₂×D₄	1	2	yes	—
175	C₁₉₁⋊C₈	—	2	1	no	—
176	C₁₉₁⋊C₈	—	2	1	no	—
177	C₂³×C₁₉₁	—	2	1	no	—
178	C₂³×C₁₉₁	C₂×D₄	1	1	yes	characteristic
179	Q₈×C₁₉₁	—	2	1	no	—
180	Q₈×C₁₉₁	—	2	1	no	—
181	Q₈×C₁₉₁	—	2	1	no	—
182	Q₈×C₁₉₁	C₂×D₄	1	2	yes	—
183	D₄×C₁₉₁	—	2	4	no	—
184	D₄×C₁₉₁	—	2	1	no	—
185	D₄×C₁₉₁	C₂×D₄	1	2	yes	—
186	C₂×C₄×C₁₉₁	—	2	4	no	—
187	C₂×C₄×C₁₉₁	—	2	1	no	—
188	C₂×C₄×C₁₉₁	—	2	1	no	—
189	C₂×C₄×C₁₉₁	—	2	1	no	—
190	C₂×C₄×C₁₉₁	—	2	1	no	—
191	C₂×C₄×C₁₉₁	—	2	1	no	—
192	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
194	C₈×C₁₉₁	—	2	1	no	—
195	C₈×C₁₉₁	—	2	1	no	—
196	C₂²×C₁₉₁	—	2	1	no	—
197	C₂²×C₁₉₁	—	2	2	no	—
198	C₂²×C₁₉₁	—	2	1	no	—
199	C₂²×C₁₉₁	—	2	1	no	—
200	C₂²×C₁₉₁	—	4	1	no	—
201	C₂²×C₁₉₁	—	4	1	no	—
202	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×D₁₉₁	—	2	1	no	—
204	C₂×D₁₉₁	—	2	2	no	—
205	C₂×D₁₉₁	—	2	1	no	—
206	C₂×D₁₉₁	—	2	1	no	—
207	C₂×D₁₉₁	—	4	1	no	—
208	C₂×D₁₉₁	—	4	1	no	—
209	C₂×D₁₉₁	—	4	4	no	—
210	C₂×D₁₉₁	—	4	8	no	—
211	C₂×D₁₉₁	#120	1	2	yes	—
212	C₂×D₁₉₁	#135	1	2	yes	—
213	C₂×D₁₉₁	#137	1	2	yes	—
214	C₄×C₁₉₁	—	2	1	no	—
215	C₄×C₁₉₁	—	2	2	no	—
216	C₄×C₁₉₁	—	4	1	no	—
217	C₄×C₁₉₁	—	4	1	no	—
218	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
219	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
220	Dic₁₉₁	—	2	1	no	—
221	Dic₁₉₁	—	2	2	no	—
222	Dic₁₉₁	—	4	1	no	—
223	Dic₁₉₁	—	4	1	no	—
224	Dic₁₉₁	#120	1	2	yes	—
225	C₂×C₁₉₁	—	4	1	no	—
226	C₂×C₁₉₁	—	4	2	no	—
227	C₂×C₁₉₁	C₂×#120	1	1	yes	characteristic
228	C₂×C₁₉₁	C₂×#135	1	1	yes	characteristic
229	C₂×C₁₉₁	C₂×#137	1	1	yes	characteristic
230	D₁₉₁	—	4	1	no	—
231	D₁₉₁	—	4	2	no	—
232	D₁₉₁	#452	1	4	yes	direct product factor
233	C₁₉₁	C₂×#452	1	1	yes	characteristic, complemented, Sylow
234	C₂×#452	—	191	1	no	maximal, Sylow
235	C₂²×#41	—	191	1	no	—
236	C₂²×Q₁₆	—	191	1	no	—
237	C₂²×SD₁₆	—	191	1	no	—
238	C₂×C₂²⋊Q₈	—	191	1	no	—
239	#452	—	191	1	no	—
240	#452	—	191	1	no	—
241	#452	—	191	1	no	—
242	#452	—	191	1	no	—
243	#452	—	191	1	no	—
244	#452	—	191	1	no	—
245	#452	—	191	1	no	—
246	#452	D₁₉₁	1	1	yes	characteristic, direct product factor
247	C₂×#103	—	191	1	no	—
248	C₂×#102	—	191	1	no	—
249	C₂×C₂²⋊C₈	—	191	1	no	—
250	C₂×#41	—	382	1	no	—
251	C₂×#41	—	382	4	no	—
252	C₂×#41	—	382	4	no	—
253	C₂×#41	—	382	1	no	—
254	C₂×#41	—	191	1	no	—
255	C₂×#41	—	191	1	no	—
256	C₂×#41	—	191	1	no	—
257	C₂×#41	C₂×D₁₉₁	1	1	yes	characteristic
258	C₂²×Q₈	—	191	1	no	—
259	C₂²×Q₈	—	191	1	no	—
260	C₂²×D₄	—	382	1	no	—
261	C₂²×D₄	—	191	1	no	—
262	C₂³×C₄	—	382	1	no	—
263	C₂³×C₄	—	191	1	no	—
264	C₂×Q₁₆	—	382	4	no	—
265	C₂×Q₁₆	—	191	1	no	—
266	C₂×Q₁₆	—	191	1	no	—
267	C₂×Q₁₆	—	191	1	no	—
268	C₂×Q₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	—	382	4	no	—
270	C₂×SD₁₆	—	191	1	no	—
271	C₂×SD₁₆	—	191	1	no	—
272	C₂×SD₁₆	—	191	1	no	—
273	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
274	C₂²×C₈	—	191	1	no	—
275	C₂²×C₈	—	191	1	no	—
276	C₂²⋊Q₈	—	382	1	no	—
277	C₂²⋊Q₈	—	382	1	no	—
278	C₂²⋊Q₈	—	191	1	no	—
279	C₂²⋊Q₈	—	191	1	no	—
280	C₂²⋊Q₈	—	191	1	no	—
281	C₂²⋊Q₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
282	C₂×C₄⋊C₄	—	382	1	no	—
283	C₂×C₄⋊C₄	—	191	1	no	—
284	C₂×C₂²⋊C₄	—	382	1	no	—
285	#103	—	191	1	no	—
286	#103	—	191	1	no	—
287	#103	—	191	1	no	—
288	#103	C₂×D₁₉₁	1	1	yes	characteristic, complemented
289	#102	—	191	1	no	—
290	#102	—	191	1	no	—
291	#102	—	191	1	no	—
292	#102	C₂×D₁₉₁	1	1	yes	characteristic, complemented
293	C₂²⋊C₈	—	191	1	no	—
294	C₂²⋊C₈	—	191	1	no	—
295	C₂²⋊C₈	—	191	1	no	—
296	C₂²⋊C₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
297	C₂⁴	—	382	1	no	—
298	C₂⁴	—	191	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	382	8	no	—
302	#41	—	382	2	no	—
303	#41	—	382	2	no	—
304	#41	—	382	8	no	—
305	#41	—	382	2	no	—
306	#41	—	382	2	no	—
307	#41	—	382	2	no	—
308	#41	—	382	2	no	—
309	C₂×Q₈	—	382	1	no	—
310	C₂×Q₈	—	382	1	no	—
311	C₂×Q₈	—	382	2	no	—
312	C₂×Q₈	—	382	2	no	—
313	C₂×Q₈	—	382	2	no	—
314	C₂×Q₈	—	191	4	no	—
315	C₂×Q₈	—	191	1	no	—
316	C₂×Q₈	—	191	1	no	—
317	C₂×Q₈	C₂²×D₁₉₁	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₁₉₁	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	382	1	no	—
321	C₂×D₄	—	382	8	no	—
322	C₂×D₄	—	382	1	no	—
323	C₂×D₄	—	382	1	no	—
324	C₂×D₄	—	382	2	no	—
325	C₂×D₄	—	382	1	no	—
326	C₂×D₄	—	191	4	no	—
327	C₂×D₄	—	191	1	no	—
328	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	382	8	no	—
331	C₂²×C₄	—	382	1	no	—
332	C₂²×C₄	—	382	1	no	—
333	C₂²×C₄	—	382	2	no	—
334	C₂²×C₄	—	382	2	no	—
335	C₂²×C₄	—	382	1	no	—
336	C₂²×C₄	—	382	1	no	—
337	C₂²×C₄	—	382	1	no	—
338	C₂²×C₄	—	382	1	no	—
339	C₂²×C₄	—	191	1	no	—
340	C₂²×C₄	—	191	1	no	—
341	C₂²×C₄	—	191	1	no	—
342	C₂²×C₄	—	191	1	no	—
343	C₂²×C₄	—	191	1	no	—
344	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	382	2	no	—
347	Q₁₆	—	382	2	no	—
348	Q₁₆	—	382	2	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	382	2	no	—
351	SD₁₆	—	382	2	no	—
352	SD₁₆	—	382	2	no	—
353	C₂×C₈	—	382	2	no	—
354	C₂×C₈	—	382	2	no	—
355	C₂×C₈	—	191	1	no	—
356	C₂×C₈	—	191	1	no	—
357	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
358	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	382	1	no	—
361	C₄⋊C₄	—	382	1	no	—
362	C₄⋊C₄	—	382	1	no	—
363	C₄⋊C₄	—	382	1	no	—
364	C₄⋊C₄	—	191	1	no	—
365	C₄⋊C₄	C₂²×D₁₉₁	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	382	1	no	—
368	C₂²⋊C₄	—	382	1	no	—
369	C₂²⋊C₄	—	382	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	382	2	no	—
372	C₂³	—	382	4	no	—
373	C₂³	—	382	2	no	—
374	C₂³	—	382	2	no	—
375	C₂³	—	382	1	no	—
376	C₂³	—	191	1	no	—
377	C₂³	—	191	1	no	—
378	C₂³	—	764	2	no	—
379	C₂³	—	764	2	no	—
380	C₂³	D₄×D₁₉₁	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	382	4	no	—
385	Q₈	—	382	1	no	—
386	Q₈	—	382	1	no	—
387	Q₈	—	382	1	no	—
388	Q₈	—	191	2	no	—
389	Q₈	—	764	2	no	—
390	Q₈	D₄×D₁₉₁	1	2	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	382	4	no	—
394	D₄	—	382	4	no	—
395	D₄	—	382	4	no	—
396	D₄	—	382	4	no	—
397	D₄	—	382	1	no	—
398	D₄	—	191	2	no	—
399	D₄	D₄×D₁₉₁	1	2	yes	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	382	4	no	—
407	C₂×C₄	—	382	4	no	—
408	C₂×C₄	—	382	2	no	—
409	C₂×C₄	—	382	4	no	—
410	C₂×C₄	—	382	2	no	—
411	C₂×C₄	—	382	4	no	—
412	C₂×C₄	—	382	1	no	—
413	C₂×C₄	—	382	2	no	—
414	C₂×C₄	—	382	1	no	—
415	C₂×C₄	—	382	1	no	—
416	C₂×C₄	—	382	1	no	—
417	C₂×C₄	—	382	1	no	—
418	C₂×C₄	—	191	1	no	—
419	C₂×C₄	—	191	1	no	—
420	C₂×C₄	—	191	2	no	—
421	C₂×C₄	—	191	2	no	—
422	C₂×C₄	—	764	2	no	—
423	C₂×C₄	—	764	2	no	—
424	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	382	1	no	—
429	C₈	—	382	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	382	1	no	—
437	C₂²	—	382	1	no	—
438	C₂²	—	382	1	no	—
439	C₂²	—	382	2	no	—
440	C₂²	—	191	2	no	—
441	C₂²	—	191	2	no	—
442	C₂²	—	191	2	no	—
443	C₂²	—	764	4	no	—
444	C₂²	—	764	8	no	—
445	C₂²	—	764	1	no	—
446	C₂²	—	764	1	no	—
447	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	382	1	no	—
453	C₄	—	382	2	no	—
454	C₄	—	191	2	no	—
455	C₄	—	764	1	no	—
456	C₄	—	764	1	no	—
457	C₄	C₂×D₄×D₁₉₁	1	1	yes	characteristic
458	C₄	C₂×D₄×D₁₉₁	1	1	yes	characteristic
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	191	4	no	—
462	C₂	—	764	1	no	—
463	C₂	—	764	2	no	—
464	C₂	#120×D₁₉₁	1	1	yes	characteristic
465	C₂	#135×D₁₉₁	1	1	yes	characteristic
466	C₂	#137×D₁₉₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	#452×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
prime radical	C₂×#41×D₁₉₁	C₂
hypercenter	#452	D₁₉₁
hypocenter	C₁₉₁	C₂×#452
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×D₁₉₁	C₂	semidirect
3. C₂×SD₁₆×D₁₉₁	C₂	semidirect
4. C₂²⋊Q₈×D₁₉₁	C₂	semidirect
5. #27132828	C₂	semidirect
6. #27132827	C₂	semidirect
7. #27132826	C₂	semidirect
8. #27132825	C₂	semidirect
9. #27132824	C₂	semidirect
10. #27132823	C₂	semidirect
11. #27132822	C₂	semidirect
12. #103×D₁₉₁	C₂	semidirect
13. #102×D₁₉₁	C₂	semidirect
14. C₂²⋊C₈×D₁₉₁	C₂	semidirect
15. #452×C₁₉₁	C₂	semidirect
29. C₂×Dic₇₆₄	C₂²	semidirect
30. C₂×#15690277	C₂²	semidirect
31. C₂×#15690277	C₂²	semidirect
33. C₂×#15690276	C₂²	semidirect
34. C₂×#15690275	C₂²	semidirect
35. C₂×#15690274	C₂²	semidirect
39. #20259302	C₂²	semidirect
40. #20259301	C₂²	semidirect
43. #20259298	C₂²	semidirect
47. #20259247	C₂²	semidirect
48. #20259246	C₂²	semidirect
49. #20259245	C₂²	semidirect
50. #20259244	C₂²	semidirect
51. #20259243	C₂²	semidirect
52. #20259242	C₂²	semidirect
53. C₂²⋊(C₁₉₁⋊C₈)	C₂²	semidirect
54. (C₂×D₁₉₁)⋊C₈	C₂²	semidirect
55. (C₂×D₁₉₁)⋊C₈	C₂²	semidirect
57. C₂×Q₁₆×C₁₉₁	C₂²	semidirect
58. C₂×SD₁₆×C₁₉₁	C₂²	semidirect
59. C₂²⋊Q₈×C₁₉₁	C₂²	semidirect
60. #103×C₁₉₁	C₂²	semidirect
61. #102×C₁₉₁	C₂²	semidirect
62. C₂²⋊C₈×C₁₉₁	C₂²	semidirect
232. D₁₉₁	#452	direct (N × H)
233. C₁₉₁	C₂×#452	semidirect
246. #452	D₁₉₁	direct (N × H)
268. C₂×Q₁₆	C₂×D₁₉₁	semidirect
273. C₂×SD₁₆	C₂×D₁₉₁	semidirect
281. C₂²⋊Q₈	C₂×D₁₉₁	semidirect
288. #103	C₂×D₁₉₁	semidirect
292. #102	C₂×D₁₉₁	semidirect
296. C₂²⋊C₈	C₂×D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₉₁	2
C₂×Q₁₆×D₁₉₁	2
C₂×SD₁₆×D₁₉₁	2
C₂²⋊Q₈×D₁₉₁	2
#27132828	2
#27132827	2
#27132826	2
#27132825	2
#27132824	2
#27132823	2
#27132822	2
#103×D₁₉₁	2
#102×D₁₉₁	2
C₂²⋊C₈×D₁₉₁	2
#452×C₁₉₁	2
C₂×#452	191

Subgroups — #452×D191 #37581725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #452×D₁₉₁ #37581725