Subgroups — #37584114

Order 24448.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259346	C₂	1	1	yes	maximal, characteristic, complemented
2	#27133312	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#27133034	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132909	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132906	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132866	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132856	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132814	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132812	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132808	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132805	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×Dic₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#27132739	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15690286	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉₁	—	2	1	no	—
18	C₂×D₄×D₁₉₁	C₂²	1	1	yes	characteristic
19	#20259346	—	2	4	no	—
20	C₂×#15690276	C₂²	1	1	yes	characteristic, complemented
21	C₂×#15690275	C₂²	1	1	yes	characteristic
22	C₂×#15690275	C₂²	1	1	yes	characteristic, complemented
23	C₂×#15690274	C₂²	1	1	yes	characteristic, complemented
24	C₂×#15690272	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15690270	C₂²	1	1	yes	characteristic, complemented
26	#20259320	C₂²	1	1	yes	characteristic, complemented
27	#20259318	C₂²	1	1	yes	characteristic
28	#20259305	—	2	1	no	—
29	#20259303	—	2	1	no	—
30	#20259301	C₂²	1	1	yes	characteristic, complemented
31	#20259298	C₂²	1	1	yes	characteristic, complemented
32	#20259296	C₂²	1	1	yes	characteristic
33	#20259294	—	2	1	no	—
34	#20259294	—	2	1	no	—
35	#20259293	C₂²	1	1	yes	characteristic
36	#20259291	—	2	1	no	—
37	#20259290	—	2	1	no	—
38	D₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
39	D₄×Dic₁₉₁	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₉₁⋊C₄	—	2	1	no	—
42	#20259256	C₂²	1	1	yes	characteristic, complemented
43	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#20259247	C₂²	1	1	yes	characteristic, complemented
45	#20259246	C₂²	1	1	yes	characteristic, complemented
46	#20259244	C₂²	1	1	yes	characteristic, complemented
47	#20259243	C₂²	1	1	yes	characteristic
48	#20259243	C₂²	1	1	yes	characteristic, complemented
49	#20259243	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₉₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₁₉₁	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₁₉₁	—	2	4	no	—
56	C₂×SD₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₁₉₁	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉₁	—	2	1	no	—
62	#15690286	—	2	2	no	—
63	#15690286	—	4	1	no	—
64	C₂×Dic₃₈₂	C₂³	1	1	yes	characteristic
65	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
67	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
68	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
69	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
70	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
71	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
72	C₂×C₂²⋊D₁₉₁	—	4	4	no	—
73	C₂×C₂²⋊D₁₉₁	D₄	1	1	yes	characteristic
74	D₄×D₁₉₁	—	2	2	no	—
75	D₄×D₁₉₁	—	4	1	no	—
76	C₂²×Dic₁₉₁	—	2	1	no	—
77	C₂²×Dic₁₉₁	—	2	1	no	—
78	C₂²×Dic₁₉₁	—	2	1	no	—
79	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
80	#15690276	—	2	2	no	—
81	#15690275	—	2	2	no	—
82	#15690275	—	4	1	no	—
83	#15690274	—	4	1	no	—
84	#15690272	—	2	2	no	—
85	#15690270	—	2	2	no	—
86	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
90	Dic₁₉₁⋊C₄	—	2	1	no	—
91	Dic₁₉₁⋊C₄	—	2	1	no	—
92	Dic₁₉₁⋊C₄	—	2	1	no	—
93	Dic₁₉₁⋊C₄	—	2	1	no	—
94	Dic₁₉₁⋊C₄	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₁₉₁	—	2	1	no	—
96	C₂²⋊Dic₁₉₁	—	2	1	no	—
97	C₂²⋊Dic₁₉₁	—	2	1	no	—
98	C₂²⋊Dic₁₉₁	—	2	1	no	—
99	C₂²⋊Dic₁₉₁	D₄	1	1	yes	characteristic
100	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
101	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
102	(C₂×D₁₉₁)⋊C₄	D₄	1	1	yes	characteristic
103	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
104	C₂⁴×C₁₉₁	—	2	1	no	—
105	#41×C₁₉₁	—	2	2	no	—
106	#41×C₁₉₁	—	4	1	no	—
107	C₂×Q₈×C₁₉₁	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₉₁	—	2	2	no	—
109	C₂×D₄×C₁₉₁	—	2	1	no	—
110	C₂×D₄×C₁₉₁	—	2	1	no	—
111	C₂×D₄×C₁₉₁	—	4	1	no	—
112	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₉₁	—	2	1	no	—
116	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
117	SD₁₆×C₁₉₁	—	2	2	no	—
118	SD₁₆×C₁₉₁	—	2	2	no	—
119	D₈×C₁₉₁	—	2	2	no	—
120	D₈×C₁₉₁	D₄	1	4	yes	complemented
121	M₁₆×C₁₉₁	—	2	2	no	—
122	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
124	C₂²×D₁₉₁	—	2	1	no	—
125	C₂²×D₁₉₁	—	4	2	no	—
126	C₂²×D₁₉₁	—	4	2	no	—
127	C₂²×D₁₉₁	—	8	1	no	—
128	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
129	Dic₃₈₂	—	2	1	no	—
130	Dic₃₈₂	—	2	1	no	—
131	D₇₆₄	—	2	1	no	—
132	D₇₆₄	—	2	1	no	—
133	C₂²⋊D₁₉₁	—	2	2	no	—
134	C₂²⋊D₁₉₁	—	4	2	no	—
135	C₂²⋊D₁₉₁	—	4	2	no	—
136	C₂²⋊D₁₉₁	—	4	2	no	—
137	C₂²⋊D₁₉₁	—	4	2	no	—
138	C₂²⋊D₁₉₁	—	4	2	no	—
139	C₂²⋊D₁₉₁	—	8	1	no	—
140	C₂×Dic₁₉₁	—	2	1	no	—
141	C₂×Dic₁₉₁	—	2	1	no	—
142	C₂×Dic₁₉₁	—	2	1	no	—
143	C₂×Dic₁₉₁	—	4	2	no	—
144	C₂×Dic₁₉₁	—	4	2	no	—
145	C₂×Dic₁₉₁	—	4	2	no	—
146	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
147	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
149	C₄×D₁₉₁	—	2	1	no	—
150	C₄×D₁₉₁	—	2	1	no	—
151	C₁₉₁⋊C₈	—	2	1	no	—
152	C₁₉₁⋊C₈	—	2	1	no	—
153	C₂³×C₁₉₁	—	2	1	no	—
154	C₂³×C₁₉₁	—	2	1	no	—
155	C₂³×C₁₉₁	—	2	1	no	—
156	C₂³×C₁₉₁	—	4	2	no	—
157	C₂³×C₁₉₁	—	4	2	no	—
158	C₂³×C₁₉₁	—	8	1	no	—
159	C₂³×C₁₉₁	C₂×D₄	1	1	yes	characteristic
160	Q₈×C₁₉₁	—	2	1	no	—
161	Q₈×C₁₉₁	—	2	1	no	—
162	D₄×C₁₉₁	—	2	1	no	—
163	D₄×C₁₉₁	—	2	1	no	—
164	D₄×C₁₉₁	—	2	1	no	—
165	D₄×C₁₉₁	—	2	1	no	—
166	D₄×C₁₉₁	—	4	2	no	—
167	D₄×C₁₉₁	—	4	2	no	—
168	D₄×C₁₉₁	C₂×D₄	1	2	yes	—
169	D₄×C₁₉₁	C₂×D₄	1	2	yes	complemented
170	C₂×C₄×C₁₉₁	—	2	1	no	—
171	C₂×C₄×C₁₉₁	—	2	1	no	—
172	C₂×C₄×C₁₉₁	—	2	1	no	—
173	C₂×C₄×C₁₉₁	—	4	2	no	—
174	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
176	C₈×C₁₉₁	—	2	1	no	—
177	C₈×C₁₉₁	C₂×D₄	1	2	yes	complemented
178	C₂²×C₁₉₁	—	2	1	no	—
179	C₂²×C₁₉₁	—	2	2	no	—
180	C₂²×C₁₉₁	—	2	2	no	—
181	C₂²×C₁₉₁	—	2	1	no	—
182	C₂²×C₁₉₁	—	2	1	no	—
183	C₂²×C₁₉₁	—	4	1	no	—
184	C₂²×C₁₉₁	—	4	1	no	—
185	C₂²×C₁₉₁	—	4	1	no	—
186	C₂²×C₁₉₁	—	4	1	no	—
187	C₂²×C₁₉₁	—	4	1	no	—
188	C₂²×C₁₉₁	—	4	1	no	—
189	C₂²×C₁₉₁	—	4	1	no	—
190	C₂²×C₁₉₁	—	8	4	no	—
191	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₁₉₁	—	2	1	no	—
193	C₂×D₁₉₁	—	2	1	no	—
194	C₂×D₁₉₁	—	2	1	no	—
195	C₂×D₁₉₁	—	4	1	no	—
196	C₂×D₁₉₁	—	4	1	no	—
197	C₂×D₁₉₁	—	4	1	no	—
198	C₂×D₁₉₁	—	8	4	no	—
199	C₄×C₁₉₁	—	2	1	no	—
200	C₄×C₁₉₁	—	4	1	no	—
201	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₁₉₁	—	2	1	no	—
204	Dic₁₉₁	—	2	1	no	—
205	Dic₁₉₁	—	4	1	no	—
206	Dic₁₉₁	—	4	1	no	—
207	Dic₁₉₁	—	4	1	no	—
208	Dic₁₉₁	AGL(1,ℤ/8)	1	2	yes	complemented
209	C₂×C₁₉₁	—	4	2	no	—
210	C₂×C₁₉₁	—	4	1	no	—
211	C₂×C₁₉₁	—	4	2	no	—
212	C₂×C₁₉₁	—	8	1	no	—
213	C₂×C₁₉₁	D₄²	1	1	yes	characteristic
214	C₂×C₁₉₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₁₉₁	#577	1	1	yes	characteristic
216	D₁₉₁	—	4	1	no	—
217	D₁₉₁	—	8	1	no	—
218	C₁₉₁	#3272	1	1	yes	characteristic, complemented, Sylow
219	#3272	—	191	1	no	maximal, Sylow
220	C₂×AGL(1,ℤ/8)	—	191	1	no	—
221	C₂×AGL(1,ℤ/8)	D₁₉₁	1	1	yes	characteristic, complemented
222	#547	—	191	1	no	—
223	D₄²	—	191	1	no	—
224	#492	—	191	1	no	—
225	#468	—	191	1	no	—
226	#468	—	191	1	no	—
227	#461	—	191	1	no	—
228	#459	—	191	1	no	—
229	#450	—	191	1	no	—
230	#450	—	191	1	no	—
231	#449	—	191	1	no	—
232	#449	—	191	1	no	—
233	C₄×D₈	—	191	1	no	—
234	#436	—	191	1	no	—
235	C₂×#41	—	191	1	no	—
236	C₂×#41	C₂×D₁₉₁	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	382	1	no	—
238	C₂²×D₄	—	191	1	no	—
239	C₂²×D₄	C₂×D₁₉₁	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	AGL(1,ℤ/8)	—	382	4	no	—
242	C₂×SD₁₆	—	191	1	no	—
243	C₂×SD₁₆	—	191	1	no	—
244	C₂×SD₁₆	—	191	1	no	—
245	C₂×SD₁₆	—	191	1	no	—
246	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
248	C₂×D₈	—	191	1	no	—
249	C₂×D₈	C₂×D₁₉₁	1	1	yes	characteristic
250	C₂×D₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
251	C₂×M₁₆	—	191	1	no	—
252	C₂×M₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	—	191	1	no	—
254	#127	—	191	1	no	—
255	#123	—	382	1	no	—
256	#123	—	382	1	no	—
257	C₂²⋊Q₈	—	191	1	no	—
258	C₂²⋊Q₈	—	191	1	no	—
259	#121	—	382	1	no	—
260	#121	—	382	1	no	—
261	#121	—	191	1	no	—
262	#121	—	191	1	no	—
263	#120	—	382	1	no	—
264	#120	—	382	1	no	—
265	C₄×D₄	—	191	1	no	—
266	C₄×D₄	—	191	1	no	—
267	C₄×D₄	—	191	1	no	—
268	C₂×C₄⋊C₄	—	382	1	no	—
269	#107	—	191	1	no	—
270	C₄⋊C₈	—	191	1	no	—
271	#103	—	191	1	no	—
272	#103	—	191	1	no	—
273	#102	—	191	1	no	—
274	#102	—	191	1	no	—
275	#102	—	191	1	no	—
276	#102	—	191	1	no	—
277	C₂²⋊C₈	—	191	1	no	—
278	C₂²⋊C₈	—	191	1	no	—
279	C₄×C₈	—	191	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	382	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	#41	—	382	2	no	—
285	#41	—	764	1	no	—
286	C₂×Q₈	—	191	1	no	—
287	C₂×Q₈	C₂²×D₁₉₁	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	382	2	no	—
293	C₂×D₄	—	382	1	no	—
294	C₂×D₄	—	382	1	no	—
295	C₂×D₄	—	382	1	no	—
296	C₂×D₄	—	382	1	no	—
297	C₂×D₄	—	382	1	no	—
298	C₂×D₄	—	382	1	no	—
299	C₂×D₄	—	191	1	no	—
300	C₂×D₄	—	191	1	no	—
301	C₂×D₄	—	764	1	no	—
302	C₂×D₄	—	764	4	no	—
303	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
304	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	382	1	no	—
308	C₂²×C₄	—	382	1	no	—
309	C₂²×C₄	—	382	1	no	—
310	C₂²×C₄	—	191	1	no	—
311	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	382	2	no	—
315	SD₁₆	—	382	2	no	—
316	SD₁₆	—	764	1	no	—
317	SD₁₆	—	764	1	no	—
318	D₈	—	2	2	no	—
319	D₈	—	382	2	no	—
320	D₈	C₂²⋊D₁₉₁	1	4	yes	complemented
321	M₁₆	—	2	2	no	—
322	M₁₆	—	382	2	no	—
323	C₂×C₈	—	191	1	no	—
324	C₂×C₈	—	191	1	no	—
325	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
327	C₄⋊C₄	—	382	1	no	—
328	C₄⋊C₄	—	382	1	no	—
329	C₄⋊C₄	—	382	1	no	—
330	C₄⋊C₄	—	382	1	no	—
331	C₄⋊C₄	—	191	1	no	—
332	C₄⋊C₄	—	191	1	no	—
333	C₄⋊C₄	—	191	1	no	—
334	C₂²⋊C₄	—	382	1	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	—	382	1	no	—
340	C₂²⋊C₄	—	191	1	no	—
341	C₂²⋊C₄	—	191	1	no	—
342	C₄²	—	191	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	382	1	no	—
350	C₂³	—	191	1	no	—
351	C₂³	—	1528	1	no	—
352	C₂³	—	764	2	no	—
353	C₂³	—	764	2	no	—
354	C₂³	D₄×D₁₉₁	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	382	1	no	—
358	Q₈	—	382	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	382	2	no	—
366	D₄	—	382	1	no	—
367	D₄	—	382	1	no	—
368	D₄	—	1528	1	no	—
369	D₄	—	764	2	no	—
370	D₄	—	764	2	no	—
371	D₄	—	764	2	no	—
372	D₄	—	764	2	no	—
373	D₄	—	764	2	no	—
374	D₄	C₂×C₂²⋊D₁₉₁	1	2	yes	—
375	D₄	C₂×C₂²⋊D₁₉₁	1	2	yes	complemented
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	382	1	no	—
381	C₂×C₄	—	382	1	no	—
382	C₂×C₄	—	382	1	no	—
383	C₂×C₄	—	382	1	no	—
384	C₂×C₄	—	382	1	no	—
385	C₂×C₄	—	191	1	no	—
386	C₂×C₄	—	191	1	no	—
387	C₂×C₄	—	191	1	no	—
388	C₂×C₄	—	764	2	no	—
389	C₂×C₄	—	764	2	no	—
390	C₂×C₄	—	764	2	no	—
391	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	382	1	no	—
395	C₈	—	382	1	no	—
396	C₈	C₂×C₂²⋊D₁₉₁	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	382	1	no	—
411	C₂²	—	382	1	no	—
412	C₂²	—	382	1	no	—
413	C₂²	—	1528	4	no	—
414	C₂²	—	764	1	no	—
415	C₂²	—	764	1	no	—
416	C₂²	—	764	1	no	—
417	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	382	1	no	—
421	C₄	—	382	1	no	—
422	C₄	—	191	2	no	—
423	C₄	—	764	1	no	—
424	C₄	—	764	1	no	—
425	C₄	—	764	1	no	—
426	C₄	C₂²×C₂²⋊D₁₉₁	1	1	yes	characteristic
427	C₄	#20259367	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	—	1528	1	no	—
433	C₂	—	764	1	no	—
434	C₂	D₄×C₂²⋊D₁₉₁	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₉₁	1	1	yes	characteristic
436	C₂	#27133473	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	C₂×AGL(1,ℤ/8)×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉₁
hypocenter	C₁₉₁	#3272
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#20259346	C₂	semidirect
2. #27133312	C₂	semidirect
3. D₄×C₂²⋊D₁₉₁	C₂	semidirect
4. #27133034	C₂	semidirect
5. #27132909	C₂	semidirect
6. #27132906	C₂	semidirect
7. #27132866	C₂	semidirect
8. #27132856	C₂	semidirect
9. #27132814	C₂	semidirect
10. #27132812	C₂	semidirect
11. #27132808	C₂	semidirect
12. #27132805	C₂	semidirect
13. D₈×Dic₁₉₁	C₂	semidirect
14. #27132739	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₁₉₁	C₂	semidirect
16. C₂×#15690286	C₂²	semidirect
20. C₂×#15690276	C₂²	semidirect
22. C₂×#15690275	C₂²	semidirect
23. C₂×#15690274	C₂²	semidirect
24. C₂×#15690272	C₂²	semidirect
25. C₂×#15690270	C₂²	semidirect
26. #20259320	C₂²	semidirect
30. #20259301	C₂²	semidirect
31. #20259298	C₂²	semidirect
39. D₄×Dic₁₉₁	C₂²	semidirect
42. #20259256	C₂²	semidirect
43. Dic₁₉₁⋊C₈	C₂²	semidirect
44. #20259247	C₂²	semidirect
45. #20259246	C₂²	semidirect
46. #20259244	C₂²	semidirect
48. #20259243	C₂²	semidirect
49. #20259243	C₂²	semidirect
50. C₂²⋊(C₁₉₁⋊C₈)	C₂²	semidirect
51. (C₂×D₁₉₁)⋊C₈	C₂²	semidirect
52. C₈×Dic₁₉₁	C₂²	semidirect
53. C₂×#41×C₁₉₁	C₂²	semidirect
57. C₂×SD₁₆×C₁₉₁	C₂²	semidirect
59. C₂×D₈×C₁₉₁	C₂²	semidirect
60. C₂×M₁₆×C₁₉₁	C₂²	semidirect
120. D₈×C₁₉₁	D₄	semidirect
169. D₄×C₁₉₁	C₂×D₄	semidirect
177. C₈×C₁₉₁	C₂×D₄	semidirect
208. Dic₁₉₁	AGL(1,ℤ/8)	semidirect
218. C₁₉₁	#3272	semidirect
221. C₂×AGL(1,ℤ/8)	D₁₉₁	semidirect
236. C₂×#41	C₂×D₁₉₁	semidirect
247. C₂×SD₁₆	C₂×D₁₉₁	semidirect
250. C₂×D₈	C₂×D₁₉₁	semidirect
252. C₂×M₁₆	C₂×D₁₉₁	semidirect
320. D₈	C₂²⋊D₁₉₁	semidirect
375. D₄	C₂×C₂²⋊D₁₉₁	semidirect
396. C₈	C₂×C₂²⋊D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259346	2
#27133312	2
D₄×C₂²⋊D₁₉₁	2
#27133034	2
#27132909	2
#27132906	2
#27132866	2
#27132856	2
#27132814	2
#27132812	2
#27132808	2
#27132805	2
D₈×Dic₁₉₁	2
#27132739	2
C₂×AGL(1,ℤ/8)×C₁₉₁	2
#3272	191