Subgroups — #37584117

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×#20259350	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20259349	C₂	1	1	yes	maximal, characteristic, complemented
3	#27133315	C₂	1	1	yes	maximal, characteristic, complemented
4	#27133297	C₂	1	1	yes	maximal, characteristic, complemented
5	#27133034	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132910	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132867	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132857	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132815	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132813	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132811	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132806	C₂	1	1	yes	maximal, characteristic, complemented
13	#27132745	C₂	1	1	yes	maximal, characteristic, complemented
14	#27132739	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15690288	C₂²	1	1	yes	characteristic, complemented
17	C₂×#15690287	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₇₆₄	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₉₁	—	2	1	no	—
20	C₂×D₄×D₁₉₁	C₂²	1	1	yes	characteristic
21	#20259350	—	2	4	no	—
22	#20259349	—	2	4	no	—
23	C₂×#15690276	C₂²	1	1	yes	characteristic
24	C₂×#15690276	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15690275	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15690274	C₂²	1	1	yes	characteristic
27	C₂×#15690274	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₁₅₂₈	C₂²	1	1	yes	characteristic
29	C₂×D₁₅₂₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×#15690272	C₂²	1	1	yes	characteristic, complemented
31	C₂×#15690270	C₂²	1	1	yes	characteristic, complemented
32	#20259320	C₂²	1	1	yes	characteristic, complemented
33	#20259318	C₂²	1	1	yes	characteristic
34	#20259307	—	2	1	no	—
35	#20259304	—	2	1	no	—
36	#20259302	C₂²	1	1	yes	characteristic, complemented
37	#20259297	C₂²	1	1	yes	characteristic
38	#20259295	—	2	1	no	—
39	#20259295	—	2	1	no	—
40	#20259292	—	2	1	no	—
41	#20259290	—	2	1	no	—
42	#20259284	C₂²	1	1	yes	characteristic
43	#20259284	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
45	C₄⋊C₄×D₁₉₁	—	2	1	no	—
46	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	#20259245	C₂²	1	1	yes	characteristic, complemented
48	#20259242	C₂²	1	1	yes	characteristic
49	#20259242	C₂²	1	1	yes	characteristic, complemented
50	#20259242	C₂²	1	1	yes	characteristic, complemented
51	C₂²⋊(C₁₉₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₁₉₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₁₉₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
57	#121×C₁₉₁	C₂²	1	1	yes	characteristic
58	#107×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₉₁	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉₁	—	2	1	no	—
62	C₂³×D₁₉₁	—	2	1	no	—
63	#15690288	—	2	2	no	—
64	#15690288	—	4	1	no	—
65	#15690287	—	2	2	no	—
66	#15690287	—	4	1	no	—
67	C₂×Dic₃₈₂	C₂³	1	1	yes	characteristic
68	C₂×D₇₆₄	—	2	2	no	—
69	C₂×D₇₆₄	—	2	1	no	—
70	C₂×D₇₆₄	—	2	1	no	—
71	C₂×D₇₆₄	—	2	1	no	—
72	C₂×D₇₆₄	—	4	1	no	—
73	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
74	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
75	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
77	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
78	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
79	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
80	C₂×C₂²⋊D₁₉₁	D₄	1	1	yes	characteristic
81	D₄×D₁₉₁	—	2	2	no	—
82	D₄×D₁₉₁	—	4	1	no	—
83	D₄×D₁₉₁	—	4	4	no	—
84	C₂×C₄×D₁₉₁	—	2	1	no	—
85	C₂×C₄×D₁₉₁	—	2	1	no	—
86	C₂×C₄×D₁₉₁	—	2	1	no	—
87	C₂×C₄×D₁₉₁	—	2	1	no	—
88	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
89	#15690276	—	2	2	no	—
90	#15690276	—	2	2	no	—
91	#15690275	—	4	1	no	—
92	#15690274	—	2	2	no	—
93	#15690274	—	4	1	no	—
94	D₁₅₂₈	—	2	2	no	—
95	D₁₅₂₈	D₄	1	4	yes	complemented
96	#15690272	—	2	2	no	—
97	#15690270	—	2	2	no	—
98	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₁₉₁	—	2	1	no	—
101	Dic₁₉₁⋊C₄	—	2	1	no	—
102	Dic₁₉₁⋊C₄	—	2	1	no	—
103	Dic₁₉₁⋊C₄	D₄	1	1	yes	characteristic
104	C₂²⋊Dic₁₉₁	D₄	1	1	yes	characteristic
105	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
106	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
107	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
108	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
109	(C₂×D₁₉₁)⋊C₄	D₄	1	1	yes	characteristic
110	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₁₉₁	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₁₉₁	—	2	1	no	—
113	C₂×D₄×C₁₉₁	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
115	SD₁₆×C₁₉₁	—	2	2	no	—
116	M₁₆×C₁₉₁	—	2	2	no	—
117	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₁₉₁	—	2	1	no	—
120	C₄⋊C₄×C₁₉₁	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₁₉₁	C₂³	1	1	yes	characteristic
122	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
123	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
124	C₂²×D₁₉₁	—	2	1	no	—
125	C₂²×D₁₉₁	—	2	1	no	—
126	C₂²×D₁₉₁	—	2	1	no	—
127	C₂²×D₁₉₁	—	4	2	no	—
128	C₂²×D₁₉₁	—	4	2	no	—
129	C₂²×D₁₉₁	—	4	2	no	—
130	C₂²×D₁₉₁	—	4	2	no	—
131	C₂²×D₁₉₁	—	8	1	no	—
132	C₂²×D₁₉₁	—	8	1	no	—
133	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
134	Dic₃₈₂	—	2	1	no	—
135	Dic₃₈₂	—	2	1	no	—
136	D₇₆₄	—	2	1	no	—
137	D₇₆₄	—	2	1	no	—
138	D₇₆₄	—	2	1	no	—
139	D₇₆₄	—	2	1	no	—
140	D₇₆₄	—	4	2	no	—
141	D₇₆₄	—	4	2	no	—
142	D₇₆₄	—	4	2	no	—
143	D₇₆₄	C₂×D₄	1	2	yes	—
144	D₇₆₄	C₂×D₄	1	2	yes	complemented
145	C₂²⋊D₁₉₁	—	2	2	no	—
146	C₂²⋊D₁₉₁	—	4	2	no	—
147	C₂²⋊D₁₉₁	—	4	2	no	—
148	C₂²⋊D₁₉₁	—	4	2	no	—
149	C₂²⋊D₁₉₁	—	8	1	no	—
150	C₂×Dic₁₉₁	—	2	1	no	—
151	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
153	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
154	C₄×D₁₉₁	—	2	1	no	—
155	C₄×D₁₉₁	—	2	1	no	—
156	C₄×D₁₉₁	—	4	2	no	—
157	C₄×D₁₉₁	—	4	2	no	—
158	C₄×D₁₉₁	—	4	2	no	—
159	C₄×D₁₉₁	—	4	2	no	—
160	C₁₉₁⋊C₈	—	2	1	no	—
161	C₁₉₁⋊C₈	—	2	1	no	—
162	C₂³×C₁₉₁	—	2	1	no	—
163	C₂³×C₁₉₁	C₂×D₄	1	1	yes	characteristic
164	Q₈×C₁₉₁	—	2	1	no	—
165	Q₈×C₁₉₁	—	2	1	no	—
166	D₄×C₁₉₁	—	2	1	no	—
167	D₄×C₁₉₁	—	2	1	no	—
168	D₄×C₁₉₁	—	4	2	no	—
169	C₂×C₄×C₁₉₁	—	2	1	no	—
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	—	2	1	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	1	no	—
180	C₂²×C₁₉₁	—	2	1	no	—
181	C₂²×C₁₉₁	—	4	1	no	—
182	C₂²×C₁₉₁	—	4	1	no	—
183	C₂²×C₁₉₁	—	4	1	no	—
184	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₁₉₁	—	2	1	no	—
186	C₂×D₁₉₁	—	2	2	no	—
187	C₂×D₁₉₁	—	2	2	no	—
188	C₂×D₁₉₁	—	2	1	no	—
189	C₂×D₁₉₁	—	2	1	no	—
190	C₂×D₁₉₁	—	4	1	no	—
191	C₂×D₁₉₁	—	4	1	no	—
192	C₂×D₁₉₁	—	4	1	no	—
193	C₂×D₁₉₁	—	4	1	no	—
194	C₂×D₁₉₁	—	4	1	no	—
195	C₂×D₁₉₁	—	4	1	no	—
196	C₂×D₁₉₁	—	4	1	no	—
197	C₂×D₁₉₁	—	8	4	no	—
198	C₂×D₁₉₁	—	8	4	no	—
199	C₄×C₁₉₁	—	2	1	no	—
200	C₄×C₁₉₁	—	4	1	no	—
201	C₄×C₁₉₁	—	4	1	no	—
202	C₄×C₁₉₁	—	4	1	no	—
203	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
205	Dic₁₉₁	—	2	1	no	—
206	Dic₁₉₁	—	2	1	no	—
207	Dic₁₉₁	—	4	1	no	—
208	Dic₁₉₁	AGL(1,ℤ/8)	1	2	yes	complemented
209	C₂×C₁₉₁	—	4	1	no	—
210	C₂×C₁₉₁	—	8	1	no	—
211	C₂×C₁₉₁	D₄²	1	1	yes	characteristic
212	C₂×C₁₉₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₁₉₁	#577	1	1	yes	characteristic
214	D₁₉₁	—	4	1	no	—
215	D₁₉₁	—	4	2	no	—
216	D₁₉₁	—	4	2	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)	—	191	1	no	—
222	#547	—	191	1	no	—
223	D₄²	—	191	1	no	—
224	#492	—	191	1	no	—
225	#468	—	191	1	no	—
226	#468	D₁₉₁	1	1	yes	characteristic, complemented
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	—	191	1	no	—
237	C₂²×D₄	—	382	1	no	—
238	C₂²×D₄	—	191	1	no	—
239	C₂²×D₄	—	191	1	no	—
240	AGL(1,ℤ/8)	—	382	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	—	191	1	no	—
247	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
248	C₂×D₈	—	191	1	no	—
249	C₂×D₈	—	191	1	no	—
250	C₂×D₈	—	191	1	no	—
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	C₂×D₁₉₁	1	1	yes	characteristic, complemented
259	#121	—	382	1	no	—
260	#121	—	382	1	no	—
261	#121	—	191	1	no	—
262	#121	C₂×D₁₉₁	1	1	yes	characteristic
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	C₂×D₁₉₁	1	1	yes	characteristic, complemented
270	C₄⋊C₈	—	191	1	no	—
271	#103	—	191	1	no	—
272	#103	C₂×D₁₉₁	1	1	yes	characteristic, complemented
273	#102	—	191	1	no	—
274	#102	—	191	1	no	—
275	#102	—	191	1	no	—
276	#102	C₂×D₁₉₁	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	191	1	no	—
278	C₂²⋊C₈	—	191	1	no	—
279	C₄×C₈	—	191	1	no	—
280	C₂⁴	—	382	1	no	—
281	C₂⁴	—	382	1	no	—
282	#41	—	382	2	no	—
283	#41	—	382	2	no	—
284	#41	—	764	1	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	1	no	—
289	C₂×D₄	—	382	2	no	—
290	C₂×D₄	—	382	1	no	—
291	C₂×D₄	—	382	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	—	191	1	no	—
299	C₂×D₄	—	191	1	no	—
300	C₂×D₄	—	191	1	no	—
301	C₂×D₄	—	191	1	no	—
302	C₂×D₄	—	764	1	no	—
303	C₂×D₄	—	764	1	no	—
304	C₂×D₄	—	764	4	no	—
305	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
306	C₂²×C₄	—	382	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	—	382	2	no	—
314	SD₁₆	—	382	2	no	—
315	SD₁₆	—	382	2	no	—
316	SD₁₆	—	764	1	no	—
317	SD₁₆	—	764	1	no	—
318	D₈	—	382	2	no	—
319	D₈	—	382	2	no	—
320	D₈	—	191	4	no	—
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	—	2	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	C₂²×D₁₉₁	1	1	yes	characteristic
333	C₄⋊C₄	C₂²×D₁₉₁	1	1	yes	characteristic
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	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	—	382	1	no	—
345	C₂³	—	382	1	no	—
346	C₂³	—	382	1	no	—
347	C₂³	—	191	1	no	—
348	C₂³	—	1528	1	no	—
349	C₂³	—	1528	1	no	—
350	C₂³	—	764	2	no	—
351	C₂³	—	764	2	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	—	4	2	no	—
362	D₄	—	382	2	no	—
363	D₄	—	382	1	no	—
364	D₄	—	382	1	no	—
365	D₄	—	382	1	no	—
366	D₄	—	382	1	no	—
367	D₄	—	191	2	no	—
368	D₄	—	191	2	no	—
369	D₄	—	1528	1	no	—
370	D₄	—	764	2	no	—
371	D₄	—	764	2	no	—
372	D₄	—	764	2	no	—
373	D₄	—	764	2	no	—
374	D₄	—	764	2	no	—
375	D₄	—	764	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	382	1	no	—
382	C₂×C₄	—	382	1	no	—
383	C₂×C₄	—	382	1	no	—
384	C₂×C₄	—	191	1	no	—
385	C₂×C₄	—	191	1	no	—
386	C₂×C₄	—	191	1	no	—
387	C₂×C₄	—	764	2	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	D₄×D₁₉₁	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	382	1	no	—
404	C₂²	—	382	1	no	—
405	C₂²	—	382	1	no	—
406	C₂²	—	382	2	no	—
407	C₂²	—	382	2	no	—
408	C₂²	—	1528	4	no	—
409	C₂²	—	1528	4	no	—
410	C₂²	—	764	1	no	—
411	C₂²	—	764	1	no	—
412	C₂²	—	764	1	no	—
413	C₂²	—	764	1	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	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	382	1	no	—
423	C₄	—	382	1	no	—
424	C₄	—	191	2	no	—
425	C₄	—	764	1	no	—
426	C₄	C₂×D₄×D₁₉₁	1	1	yes	characteristic
427	C₄	#20259368	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	8	1	no	—
430	C₂	—	1528	1	no	—
431	C₂	—	764	1	no	—
432	C₂	—	764	2	no	—
433	C₂	—	764	2	no	—
434	C₂	#27133297	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₉₁	1	1	yes	characteristic
436	C₂	#27133472	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	#468×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
hypercenter	#468	D₁₉₁
hypocenter	C₁₉₁	#3272
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×#20259350	C₂	semidirect
2. C₂×#20259349	C₂	semidirect
3. #27133315	C₂	semidirect
4. #27133297	C₂	semidirect
5. #27133034	C₂	semidirect
6. #27132910	C₂	semidirect
7. #27132867	C₂	semidirect
8. #27132857	C₂	semidirect
9. #27132815	C₂	semidirect
10. #27132813	C₂	semidirect
11. #27132811	C₂	semidirect
12. #27132806	C₂	semidirect
13. #27132745	C₂	semidirect
14. #27132739	C₂	semidirect
15. #468×C₁₉₁	C₂	semidirect
16. C₂×#15690288	C₂²	semidirect
17. C₂×#15690287	C₂²	semidirect
24. C₂×#15690276	C₂²	semidirect
25. C₂×#15690275	C₂²	semidirect
27. C₂×#15690274	C₂²	semidirect
29. C₂×D₁₅₂₈	C₂²	semidirect
30. C₂×#15690272	C₂²	semidirect
31. C₂×#15690270	C₂²	semidirect
32. #20259320	C₂²	semidirect
36. #20259302	C₂²	semidirect
43. #20259284	C₂²	semidirect
46. Dic₁₉₁⋊C₈	C₂²	semidirect
47. #20259245	C₂²	semidirect
49. #20259242	C₂²	semidirect
50. #20259242	C₂²	semidirect
51. C₂²⋊(C₁₉₁⋊C₈)	C₂²	semidirect
52. (C₂×D₁₉₁)⋊C₈	C₂²	semidirect
53. C₈×Dic₁₉₁	C₂²	semidirect
54. C₂×SD₁₆×C₁₉₁	C₂²	semidirect
55. C₂×M₁₆×C₁₉₁	C₂²	semidirect
56. C₂²⋊Q₈×C₁₉₁	C₂²	semidirect
58. #107×C₁₉₁	C₂²	semidirect
59. #103×C₁₉₁	C₂²	semidirect
60. #102×C₁₉₁	C₂²	semidirect
95. D₁₅₂₈	D₄	semidirect
144. D₇₆₄	C₂×D₄	semidirect
177. C₈×C₁₉₁	C₂×D₄	semidirect
208. Dic₁₉₁	AGL(1,ℤ/8)	semidirect
218. C₁₉₁	#3272	semidirect
226. #468	D₁₉₁	semidirect
247. C₂×SD₁₆	C₂×D₁₉₁	semidirect
252. C₂×M₁₆	C₂×D₁₉₁	semidirect
258. C₂²⋊Q₈	C₂×D₁₉₁	semidirect
269. #107	C₂×D₁₉₁	semidirect
272. #103	C₂×D₁₉₁	semidirect
276. #102	C₂×D₁₉₁	semidirect
396. C₈	D₄×D₁₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259350	2
C₂×#20259349	2
#27133315	2
#27133297	2
#27133034	2
#27132910	2
#27132867	2
#27132857	2
#27132815	2
#27132813	2
#27132811	2
#27132806	2
#27132745	2
#27132739	2
#468×C₁₉₁	2
#3272	191