Subgroups — #37584134

Order 24448.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259349	C₂	1	1	yes	maximal, characteristic, complemented
2	#27133332	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#27133038	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132916	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132913	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132861	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132856	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132808	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132807	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132797	C₂	1	1	yes	maximal, characteristic, complemented
12	#27132795	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×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×#15690288	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₉₁	—	2	1	no	—
18	C₂×D₄×D₁₉₁	C₂²	1	1	yes	characteristic
19	#20259349	—	2	4	no	—
20	C₂×#15690274	C₂²	1	1	yes	characteristic, complemented
21	C₂×D₁₅₂₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×#15690272	C₂²	1	1	yes	characteristic
23	C₂×#15690272	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	#20259318	—	2	1	no	—
27	#20259318	C₂²	1	1	yes	characteristic
28	#20259318	C₂²	1	1	yes	characteristic, complemented
29	#20259296	—	2	1	no	—
30	#20259296	C₂²	1	1	yes	characteristic
31	#20259296	C₂²	1	1	yes	characteristic, complemented
32	#20259294	—	2	1	no	—
33	#20259293	—	2	1	no	—
34	#20259293	C₂²	1	1	yes	characteristic
35	#20259293	C₂²	1	1	yes	characteristic, complemented
36	#20259291	—	2	1	no	—
37	#20259290	—	2	1	no	—
38	Q₈×Dic₁₉₁	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₉₁	—	2	1	no	—
41	C₄×C₂²⋊D₁₉₁	C₂²	1	1	yes	characteristic
42	#20259254	C₂²	1	1	yes	characteristic, complemented
43	Dic₁₉₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#20259246	C₂²	1	1	yes	characteristic, complemented
45	#20259244	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	#15690288	—	2	2	no	—
63	#15690288	—	4	1	no	—
64	C₂×D₇₆₄	—	2	1	no	—
65	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
66	C₂×D₇₆₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
73	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
74	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
75	C₂×C₂²⋊D₁₉₁	—	2	1	no	—
76	C₂×C₂²⋊D₁₉₁	—	4	4	no	—
77	C₂×C₂²⋊D₁₉₁	D₄	1	1	yes	characteristic
78	D₄×D₁₉₁	—	2	2	no	—
79	D₄×D₁₉₁	—	4	1	no	—
80	C₂²×Dic₁₉₁	—	2	1	no	—
81	C₂×C₄×D₁₉₁	—	2	1	no	—
82	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
83	#15690274	—	2	2	no	—
84	D₁₅₂₈	—	2	2	no	—
85	#15690272	—	2	2	no	—
86	#15690272	—	4	1	no	—
87	#15690272	—	4	1	no	—
88	#15690270	—	2	2	no	—
89	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
90	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
91	C₄⋊Dic₁₉₁	—	2	1	no	—
92	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
93	C₄⋊Dic₁₉₁	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
99	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
100	(C₂×D₁₉₁)⋊C₄	—	2	1	no	—
101	(C₂×D₁₉₁)⋊C₄	D₄	1	1	yes	characteristic
102	C₄×Dic₁₉₁	—	2	1	no	—
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	D₄	1	4	yes	complemented
119	D₈×C₁₉₁	—	2	2	no	—
120	D₈×C₁₉₁	—	2	2	no	—
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	—	2	1	no	—
126	C₂²×D₁₉₁	—	4	2	no	—
127	C₂²×D₁₉₁	—	4	2	no	—
128	C₂²×D₁₉₁	—	8	1	no	—
129	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
130	D₇₆₄	—	2	1	no	—
131	D₇₆₄	—	2	1	no	—
132	D₇₆₄	—	2	1	no	—
133	D₇₆₄	—	2	1	no	—
134	D₇₆₄	—	4	2	no	—
135	C₂²⋊D₁₉₁	—	2	2	no	—
136	C₂²⋊D₁₉₁	—	4	2	no	—
137	C₂²⋊D₁₉₁	—	4	2	no	—
138	C₂²⋊D₁₉₁	—	4	2	no	—
139	C₂²⋊D₁₉₁	—	4	2	no	—
140	C₂²⋊D₁₉₁	—	4	2	no	—
141	C₂²⋊D₁₉₁	—	8	1	no	—
142	C₂²⋊D₁₉₁	—	8	1	no	—
143	C₂²⋊D₁₉₁	—	8	1	no	—
144	C₂²⋊D₁₉₁	—	8	1	no	—
145	C₂×Dic₁₉₁	—	2	1	no	—
146	C₂×Dic₁₉₁	—	2	1	no	—
147	C₂×Dic₁₉₁	—	4	2	no	—
148	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
150	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
151	C₄×D₁₉₁	—	2	1	no	—
152	C₄×D₁₉₁	—	2	1	no	—
153	C₄×D₁₉₁	—	4	2	no	—
154	C₁₉₁⋊C₈	—	2	1	no	—
155	C₁₉₁⋊C₈	—	2	1	no	—
156	C₂³×C₁₉₁	—	2	1	no	—
157	C₂³×C₁₉₁	—	2	1	no	—
158	C₂³×C₁₉₁	—	2	1	no	—
159	C₂³×C₁₉₁	—	4	2	no	—
160	C₂³×C₁₉₁	—	4	2	no	—
161	C₂³×C₁₉₁	—	8	1	no	—
162	C₂³×C₁₉₁	C₂×D₄	1	1	yes	characteristic
163	Q₈×C₁₉₁	—	2	1	no	—
164	Q₈×C₁₉₁	C₂×D₄	1	2	yes	complemented
165	D₄×C₁₉₁	—	2	1	no	—
166	D₄×C₁₉₁	—	2	1	no	—
167	D₄×C₁₉₁	—	2	1	no	—
168	D₄×C₁₉₁	—	2	1	no	—
169	D₄×C₁₉₁	—	2	1	no	—
170	D₄×C₁₉₁	—	4	2	no	—
171	D₄×C₁₉₁	—	4	2	no	—
172	D₄×C₁₉₁	C₂×D₄	1	2	yes	—
173	C₂×C₄×C₁₉₁	—	2	1	no	—
174	C₂×C₄×C₁₉₁	—	2	1	no	—
175	C₂×C₄×C₁₉₁	—	2	1	no	—
176	C₂×C₄×C₁₉₁	—	4	2	no	—
177	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
179	C₈×C₁₉₁	—	2	1	no	—
180	C₈×C₁₉₁	C₂×D₄	1	2	yes	complemented
181	C₂²×C₁₉₁	—	2	1	no	—
182	C₂²×C₁₉₁	—	2	2	no	—
183	C₂²×C₁₉₁	—	2	1	no	—
184	C₂²×C₁₉₁	—	2	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	—	4	1	no	—
191	C₂²×C₁₉₁	—	4	1	no	—
192	C₂²×C₁₉₁	—	4	1	no	—
193	C₂²×C₁₉₁	—	8	4	no	—
194	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×D₁₉₁	—	2	1	no	—
196	C₂×D₁₉₁	—	2	1	no	—
197	C₂×D₁₉₁	—	2	1	no	—
198	C₂×D₁₉₁	—	4	1	no	—
199	C₂×D₁₉₁	—	4	1	no	—
200	C₂×D₁₉₁	—	4	1	no	—
201	C₂×D₁₉₁	—	4	1	no	—
202	C₂×D₁₉₁	—	4	1	no	—
203	C₂×D₁₉₁	—	4	1	no	—
204	C₂×D₁₉₁	—	8	4	no	—
205	C₄×C₁₉₁	—	2	1	no	—
206	C₄×C₁₉₁	—	2	2	no	—
207	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
209	Dic₁₉₁	—	2	1	no	—
210	Dic₁₉₁	—	2	1	no	—
211	Dic₁₉₁	—	4	1	no	—
212	Dic₁₉₁	—	4	1	no	—
213	Dic₁₉₁	AGL(1,ℤ/8)	1	2	yes	complemented
214	C₂×C₁₉₁	—	4	2	no	—
215	C₂×C₁₉₁	—	4	1	no	—
216	C₂×C₁₉₁	—	8	1	no	—
217	C₂×C₁₉₁	—	8	1	no	—
218	C₂×C₁₉₁	D₄²	1	1	yes	characteristic
219	C₂×C₁₉₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×C₁₉₁	#576	1	1	yes	characteristic
221	D₁₉₁	—	4	1	no	—
222	D₁₉₁	—	8	1	no	—
223	D₁₉₁	—	8	1	no	—
224	C₁₉₁	#3274	1	1	yes	characteristic, complemented, Sylow
225	#3274	—	191	1	no	maximal, Sylow
226	C₂×AGL(1,ℤ/8)	—	191	1	no	—
227	C₂×AGL(1,ℤ/8)	D₁₉₁	1	1	yes	characteristic, complemented
228	#550	—	191	1	no	—
229	D₄²	—	191	1	no	—
230	#493	—	191	1	no	—
231	#469	—	191	1	no	—
232	#469	—	191	1	no	—
233	#460	—	191	1	no	—
234	#459	—	191	1	no	—
235	#449	—	191	1	no	—
236	#449	—	191	1	no	—
237	#447	—	191	1	no	—
238	#447	—	191	1	no	—
239	C₄×SD₁₆	—	191	1	no	—
240	#436	—	191	1	no	—
241	C₂×#41	—	191	1	no	—
242	C₂×#41	C₂×D₁₉₁	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	382	1	no	—
244	C₂²×D₄	—	191	1	no	—
245	C₂²×D₄	C₂×D₁₉₁	1	1	yes	characteristic
246	AGL(1,ℤ/8)	—	2	4	no	—
247	AGL(1,ℤ/8)	—	382	4	no	—
248	C₂×SD₁₆	—	191	1	no	—
249	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
251	C₂×D₈	—	191	1	no	—
252	C₂×D₈	—	191	1	no	—
253	C₂×D₈	—	191	1	no	—
254	C₂×D₈	—	191	1	no	—
255	C₂×D₈	C₂×D₁₉₁	1	1	yes	characteristic
256	C₂×D₈	C₂×D₁₉₁	1	1	yes	characteristic, complemented
257	C₂×M₁₆	—	191	1	no	—
258	C₂×M₁₆	C₂×D₁₉₁	1	1	yes	characteristic, complemented
259	#127	—	382	1	no	—
260	#127	—	191	1	no	—
261	#127	—	191	1	no	—
262	#121	—	382	1	no	—
263	#121	—	382	1	no	—
264	#121	—	382	1	no	—
265	#121	—	191	1	no	—
266	#121	—	191	1	no	—
267	#121	—	191	1	no	—
268	#121	—	191	1	no	—
269	#120	—	382	1	no	—
270	#120	—	382	1	no	—
271	C₄×Q₈	—	191	1	no	—
272	C₄×D₄	—	382	1	no	—
273	C₄×D₄	—	191	1	no	—
274	C₄×D₄	—	191	1	no	—
275	#106	—	191	1	no	—
276	C₄⋊C₈	—	191	1	no	—
277	#103	—	191	1	no	—
278	#102	—	191	1	no	—
279	#102	—	191	1	no	—
280	#102	—	191	1	no	—
281	#102	—	191	1	no	—
282	#102	—	191	1	no	—
283	C₂²⋊C₈	—	191	1	no	—
284	C₂²⋊C₈	—	191	1	no	—
285	C₄×C₈	—	191	1	no	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	382	1	no	—
288	#41	—	2	2	no	—
289	#41	—	4	1	no	—
290	#41	—	382	2	no	—
291	#41	—	764	1	no	—
292	C₂×Q₈	C₂²×D₁₉₁	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	382	1	no	—
298	C₂×D₄	—	382	2	no	—
299	C₂×D₄	—	382	1	no	—
300	C₂×D₄	—	382	1	no	—
301	C₂×D₄	—	382	1	no	—
302	C₂×D₄	—	382	1	no	—
303	C₂×D₄	—	382	1	no	—
304	C₂×D₄	—	382	1	no	—
305	C₂×D₄	—	382	1	no	—
306	C₂×D₄	—	382	1	no	—
307	C₂×D₄	—	382	1	no	—
308	C₂×D₄	—	191	1	no	—
309	C₂×D₄	—	191	1	no	—
310	C₂×D₄	—	191	1	no	—
311	C₂×D₄	—	764	1	no	—
312	C₂×D₄	—	764	4	no	—
313	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
315	C₂×D₄	C₂²×D₁₉₁	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	382	1	no	—
318	C₂²×C₄	—	382	1	no	—
319	C₂²×C₄	—	191	1	no	—
320	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	382	2	no	—
323	SD₁₆	C₂²⋊D₁₉₁	1	4	yes	complemented
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	382	2	no	—
327	D₈	—	382	2	no	—
328	D₈	—	764	1	no	—
329	D₈	—	764	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	382	2	no	—
332	C₂×C₈	—	191	1	no	—
333	C₂×C₈	—	191	1	no	—
334	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
335	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
336	C₄⋊C₄	—	382	1	no	—
337	C₄⋊C₄	—	191	1	no	—
338	C₄⋊C₄	—	191	1	no	—
339	C₄⋊C₄	—	191	1	no	—
340	C₂²⋊C₄	—	382	1	no	—
341	C₂²⋊C₄	—	382	1	no	—
342	C₂²⋊C₄	—	382	1	no	—
343	C₂²⋊C₄	—	382	1	no	—
344	C₂²⋊C₄	—	382	1	no	—
345	C₂²⋊C₄	—	191	1	no	—
346	C₂²⋊C₄	—	191	1	no	—
347	C₄²	—	382	1	no	—
348	C₄²	—	191	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	382	1	no	—
356	C₂³	—	382	1	no	—
357	C₂³	—	191	1	no	—
358	C₂³	—	1528	1	no	—
359	C₂³	—	764	2	no	—
360	C₂³	—	764	2	no	—
361	C₂³	D₄×D₁₉₁	1	1	yes	characteristic
362	Q₈	—	2	1	no	—
363	Q₈	C₂×C₂²⋊D₁₉₁	1	2	yes	complemented
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	382	2	no	—
372	D₄	—	382	1	no	—
373	D₄	—	382	1	no	—
374	D₄	—	382	1	no	—
375	D₄	—	382	1	no	—
376	D₄	—	1528	1	no	—
377	D₄	—	1528	1	no	—
378	D₄	—	1528	1	no	—
379	D₄	—	1528	1	no	—
380	D₄	—	764	2	no	—
381	D₄	—	764	2	no	—
382	D₄	—	764	2	no	—
383	D₄	—	764	2	no	—
384	D₄	—	764	2	no	—
385	D₄	—	764	2	no	—
386	D₄	C₂×C₂²⋊D₁₉₁	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	382	1	no	—
392	C₂×C₄	—	382	1	no	—
393	C₂×C₄	—	382	1	no	—
394	C₂×C₄	—	382	1	no	—
395	C₂×C₄	—	191	1	no	—
396	C₂×C₄	—	191	1	no	—
397	C₂×C₄	—	191	1	no	—
398	C₂×C₄	—	764	2	no	—
399	C₂×C₄	—	764	2	no	—
400	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	382	1	no	—
404	C₈	—	382	1	no	—
405	C₈	C₂×C₂²⋊D₁₉₁	1	2	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	382	1	no	—
420	C₂²	—	382	1	no	—
421	C₂²	—	382	1	no	—
422	C₂²	—	1528	4	no	—
423	C₂²	—	764	1	no	—
424	C₂²	—	764	1	no	—
425	C₂²	—	764	1	no	—
426	C₂²	—	764	1	no	—
427	C₂²	—	764	1	no	—
428	C₂²	—	764	1	no	—
429	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	382	1	no	—
433	C₄	—	382	1	no	—
434	C₄	—	191	2	no	—
435	C₄	—	764	1	no	—
436	C₄	—	764	1	no	—
437	C₄	C₂²×C₂²⋊D₁₉₁	1	1	yes	characteristic
438	C₄	#20259367	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	4	2	no	—
441	C₂	—	8	1	no	—
442	C₂	—	8	1	no	—
443	C₂	—	1528	1	no	—
444	C₂	—	1528	1	no	—
445	C₂	—	764	1	no	—
446	C₂	D₄×C₂²⋊D₁₉₁	1	1	yes	characteristic
447	C₂	AGL(1,ℤ/8)×D₁₉₁	1	1	yes	characteristic
448	C₂	#27133467	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	#3274
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×#20259349	C₂	semidirect
2. #27133332	C₂	semidirect
3. D₄×C₂²⋊D₁₉₁	C₂	semidirect
4. #27133038	C₂	semidirect
5. #27132916	C₂	semidirect
6. #27132913	C₂	semidirect
7. #27132861	C₂	semidirect
8. #27132856	C₂	semidirect
9. #27132808	C₂	semidirect
10. #27132807	C₂	semidirect
11. #27132797	C₂	semidirect
12. #27132795	C₂	semidirect
13. SD₁₆×Dic₁₉₁	C₂	semidirect
14. #27132739	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₁₉₁	C₂	semidirect
16. C₂×#15690288	C₂²	semidirect
20. C₂×#15690274	C₂²	semidirect
21. C₂×D₁₅₂₈	C₂²	semidirect
23. C₂×#15690272	C₂²	semidirect
24. C₂×#15690272	C₂²	semidirect
25. C₂×#15690270	C₂²	semidirect
28. #20259318	C₂²	semidirect
31. #20259296	C₂²	semidirect
35. #20259293	C₂²	semidirect
38. Q₈×Dic₁₉₁	C₂²	semidirect
42. #20259254	C₂²	semidirect
43. Dic₁₉₁⋊C₈	C₂²	semidirect
44. #20259246	C₂²	semidirect
45. #20259244	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
118. SD₁₆×C₁₉₁	D₄	semidirect
164. Q₈×C₁₉₁	C₂×D₄	semidirect
180. C₈×C₁₉₁	C₂×D₄	semidirect
213. Dic₁₉₁	AGL(1,ℤ/8)	semidirect
224. C₁₉₁	#3274	semidirect
227. C₂×AGL(1,ℤ/8)	D₁₉₁	semidirect
242. C₂×#41	C₂×D₁₉₁	semidirect
250. C₂×SD₁₆	C₂×D₁₉₁	semidirect
256. C₂×D₈	C₂×D₁₉₁	semidirect
258. C₂×M₁₆	C₂×D₁₉₁	semidirect
323. SD₁₆	C₂²⋊D₁₉₁	semidirect
363. Q₈	C₂×C₂²⋊D₁₉₁	semidirect
405. 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×#20259349	2
#27133332	2
D₄×C₂²⋊D₁₉₁	2
#27133038	2
#27132916	2
#27132913	2
#27132861	2
#27132856	2
#27132808	2
#27132807	2
#27132797	2
#27132795	2
SD₁₆×Dic₁₉₁	2
#27132739	2
C₂×AGL(1,ℤ/8)×C₁₉₁	2
#3274	191