Subgroups — #46845407

Order 34688.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31774404	C₂	1	1	yes	maximal, characteristic
2	#31773973	C₂	1	1	yes	maximal, characteristic, complemented
3	#31773972	C₂	1	1	yes	maximal, characteristic, complemented
4	#31773971	C₂	1	1	yes	maximal, characteristic, complemented
5	#31773968	C₂	1	1	yes	maximal, characteristic, complemented
6	#31773966	C₂	1	1	yes	maximal, characteristic, complemented
7	#31773965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₂²⋊D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₂₇₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#31773955	C₂	1	1	yes	maximal, characteristic, complemented
11	#31773955	C₂	1	1	yes	maximal, characteristic, complemented
12	#31773864	C₂	1	1	yes	maximal, characteristic, complemented
13	#31773859	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#408×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₄×D₂₇₁	C₂²	1	1	yes	characteristic
17	C₂×#16864638	C₂²	1	1	yes	characteristic, complemented
18	C₂×#16864637	C₂²	1	1	yes	characteristic
19	C₂×#16864637	C₂²	1	1	yes	characteristic
20	C₂²×C₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₈×D₂₇₁	C₂²	1	1	yes	characteristic
22	C₂×C₈×D₂₇₁	C₂²	1	1	yes	characteristic
23	#22576141	C₄	1	1	yes	characteristic
24	#22576141	C₄	1	1	yes	characteristic
25	#22576136	C₄	1	1	yes	characteristic
26	#22576136	C₄	1	1	yes	characteristic
27	#22576131	C₄	1	1	yes	characteristic
28	#22576131	C₄	1	1	yes	characteristic
29	#22576128	C₄	1	1	yes	characteristic
30	#22576128	C₄	1	1	yes	characteristic
31	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊D₂₇₁	C₂²	1	1	yes	characteristic
35	#22576119	C₂²	1	1	yes	characteristic
36	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	Dic₂₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₂₇₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
44	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic
46	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic
47	(C₂×D₂₇₁)⋊C₈	C₂²	1	1	yes	characteristic
48	#22576070	C₂²	1	1	yes	characteristic, complemented
49	#22576070	C₂²	1	1	yes	characteristic, complemented
50	C₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₂₇₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×#41×C₂₇₁	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₇₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₂₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×D₂₇₁	—	4	1	no	—
66	C₂×C₄×D₂₇₁	—	4	1	no	—
67	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₂₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
70	C₂×C₄×D₂₇₁	C₂³	1	1	yes	characteristic
71	#16864638	—	4	1	no	—
72	#16864637	—	4	1	no	—
73	#16864637	—	4	1	no	—
74	C₂×C₂₇₁⋊C₈	—	4	1	no	—
75	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×C₂₇₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×D₂₇₁	—	4	1	no	—
80	C₈×D₂₇₁	—	4	1	no	—
81	C₄⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
83	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
84	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
85	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
86	Dic₂₇₁⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊Dic₂₇₁	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₂₇₁)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
98	C₄×Dic₂₇₁	C₂³	1	1	yes	characteristic
99	#41×C₂₇₁	—	4	1	no	—
100	#41×C₂₇₁	—	4	1	no	—
101	C₂×Q₈×C₂₇₁	C₂×C₄	1	1	yes	characteristic
102	C₂×D₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
103	C₂×D₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
104	C₂×D₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
108	M₁₆×C₂₇₁	—	4	1	no	—
109	C₂×C₈×C₂₇₁	—	4	1	no	—
110	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
114	C₂²×D₂₇₁	—	2	2	no	—
115	C₂²×D₂₇₁	—	4	1	no	—
116	C₂²×D₂₇₁	—	4	1	no	—
117	C₂²×D₂₇₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×D₂₇₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊D₂₇₁	—	2	2	no	—
120	C₂²⋊D₂₇₁	—	2	2	no	—
121	C₂²⋊D₂₇₁	—	4	1	no	—
122	C₂²⋊D₂₇₁	—	4	1	no	—
123	C₂×Dic₂₇₁	—	4	1	no	—
124	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₂₇₁	C₂²×C₄	1	1	yes	characteristic
130	C₄×D₂₇₁	—	2	1	no	—
131	C₄×D₂₇₁	—	2	1	no	—
132	C₄×D₂₇₁	—	2	1	no	—
133	C₄×D₂₇₁	—	2	1	no	—
134	C₄×D₂₇₁	—	4	1	no	—
135	C₄×D₂₇₁	—	4	1	no	—
136	C₂₇₁⋊C₈	—	2	1	no	—
137	C₂₇₁⋊C₈	—	2	1	no	—
138	C₂₇₁⋊C₈	—	2	1	no	—
139	C₂₇₁⋊C₈	—	2	1	no	—
140	C₂³×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
141	C₂³×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
142	C₂³×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
143	Q₈×C₂₇₁	—	4	1	no	—
144	D₄×C₂₇₁	—	4	1	no	—
145	D₄×C₂₇₁	—	4	1	no	—
146	D₄×C₂₇₁	—	4	1	no	—
147	C₂×C₄×C₂₇₁	—	2	1	no	—
148	C₂×C₄×C₂₇₁	—	2	1	no	—
149	C₂×C₄×C₂₇₁	—	2	1	no	—
150	C₂×C₄×C₂₇₁	—	2	1	no	—
151	C₂×C₄×C₂₇₁	—	2	1	no	—
152	C₂×C₄×C₂₇₁	—	2	1	no	—
153	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
157	C₈×C₂₇₁	—	2	1	no	—
158	C₈×C₂₇₁	—	2	1	no	—
159	C₈×C₂₇₁	—	2	1	no	—
160	C₈×C₂₇₁	—	2	1	no	—
161	C₂²×C₂₇₁	—	2	1	no	—
162	C₂²×C₂₇₁	—	2	1	no	—
163	C₂²×C₂₇₁	—	2	1	no	—
164	C₂²×C₂₇₁	—	2	1	no	—
165	C₂²×C₂₇₁	—	2	1	no	—
166	C₂²×C₂₇₁	—	2	1	no	—
167	C₂²×C₂₇₁	—	2	1	no	—
168	C₂²×C₂₇₁	—	2	1	no	—
169	C₂²×C₂₇₁	—	2	1	no	—
170	C₂²×C₂₇₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×D₂₇₁	—	2	1	no	—
172	C₂×D₂₇₁	—	2	1	no	—
173	C₂×D₂₇₁	—	2	1	no	—
174	C₂×D₂₇₁	—	2	1	no	—
175	C₂×D₂₇₁	—	2	1	no	—
176	C₂×D₂₇₁	—	4	4	no	—
177	C₂×D₂₇₁	#131	1	2	yes	—
178	C₄×C₂₇₁	—	2	1	no	—
179	C₄×C₂₇₁	—	2	1	no	—
180	C₄×C₂₇₁	—	2	1	no	—
181	C₄×C₂₇₁	H(5,𝔽₂)	1	1	yes	characteristic
182	C₄×C₂₇₁	H(5,𝔽₂)	1	1	yes	characteristic
183	Dic₂₇₁	—	2	1	no	—
184	Dic₂₇₁	—	2	1	no	—
185	Dic₂₇₁	—	2	1	no	—
186	Dic₂₇₁	—	2	1	no	—
187	Dic₂₇₁	—	2	1	no	—
188	Dic₂₇₁	—	2	1	no	—
189	C₂×C₂₇₁	—	4	1	no	—
190	C₂×C₂₇₁	—	4	1	no	—
191	C₂×C₂₇₁	—	4	1	no	—
192	C₂×C₂₇₁	#518	1	1	yes	characteristic
193	C₂×C₂₇₁	C₂×#131	1	1	yes	characteristic
194	C₂×C₂₇₁	#568	1	1	yes	characteristic
195	D₂₇₁	—	2	2	no	—
196	D₂₇₁	—	4	1	no	—
197	C₂₇₁	#2976	1	1	yes	characteristic, complemented, Sylow
198	#2976	—	271	1	no	maximal, Sylow
199	#525	—	271	1	no	—
200	#436	—	271	1	no	—
201	#436	—	271	1	no	—
202	#435	—	271	1	no	—
203	#435	—	271	1	no	—
204	#435	—	271	1	no	—
205	#435	—	271	1	no	—
206	C₈×D₄	—	271	1	no	—
207	C₈×D₄	—	271	1	no	—
208	#433	—	271	1	no	—
209	#433	—	271	1	no	—
210	#408	—	271	1	no	—
211	#408	D₂₇₁	1	1	yes	characteristic, complemented
212	#407	—	271	1	no	—
213	C₂×C₂²⋊C₈	—	271	1	no	—
214	C₂×#41	C₂×D₂₇₁	1	1	yes	characteristic
215	C₂³×C₄	—	271	1	no	—
216	C₂×M₁₆	—	271	1	no	—
217	C₂×M₁₆	—	271	1	no	—
218	C₂×M₁₆	—	271	1	no	—
219	C₂×M₁₆	C₂×D₂₇₁	1	1	yes	characteristic, complemented
220	C₂²×C₈	—	271	1	no	—
221	C₂²×C₈	—	271	1	no	—
222	C₂²×C₈	—	271	1	no	—
223	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
224	#123	—	271	1	no	—
225	#123	—	271	1	no	—
226	C₂²⋊Q₈	—	271	1	no	—
227	C₂²⋊Q₈	—	271	1	no	—
228	#121	—	271	1	no	—
229	#121	—	271	1	no	—
230	#120	—	271	1	no	—
231	#120	—	271	1	no	—
232	C₄×D₄	—	271	1	no	—
233	C₄×D₄	—	271	1	no	—
234	C₄×D₄	—	271	1	no	—
235	C₄×D₄	—	271	1	no	—
236	#117	—	271	1	no	—
237	C₄⋊C₈	—	271	1	no	—
238	C₄⋊C₈	—	271	1	no	—
239	C₄⋊C₈	—	271	1	no	—
240	C₄⋊C₈	—	271	1	no	—
241	C₂²⋊C₈	—	271	1	no	—
242	C₂²⋊C₈	—	271	1	no	—
243	C₂²⋊C₈	—	271	1	no	—
244	C₂²⋊C₈	—	271	1	no	—
245	C₂²⋊C₈	—	271	1	no	—
246	C₂²⋊C₈	—	271	1	no	—
247	C₂²⋊C₈	—	271	1	no	—
248	C₂²⋊C₈	—	271	1	no	—
249	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic
250	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic
251	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	C₂×D₂₇₁	1	1	yes	characteristic, complemented
253	#97	—	271	1	no	—
254	#97	—	271	1	no	—
255	C₄×C₈	—	271	1	no	—
256	C₄×C₈	—	271	1	no	—
257	C₂⁴	—	271	1	no	—
258	#41	—	4	1	no	—
259	#41	—	4	1	no	—
260	C₂×Q₈	C₄×D₂₇₁	1	1	yes	characteristic
261	C₂×D₄	—	271	1	no	—
262	C₂×D₄	—	271	1	no	—
263	C₂×D₄	—	271	1	no	—
264	C₂×D₄	—	271	1	no	—
265	C₂×D₄	C₄×D₂₇₁	1	1	yes	characteristic
266	C₂×D₄	C₄×D₂₇₁	1	1	yes	characteristic
267	C₂×D₄	C₄×D₂₇₁	1	1	yes	characteristic
268	C₂²×C₄	—	271	1	no	—
269	C₂²×C₄	—	271	1	no	—
270	C₂²×C₄	—	271	1	no	—
271	C₂²×C₄	—	271	1	no	—
272	C₂²×C₄	—	271	1	no	—
273	C₂²×C₄	—	1084	1	no	—
274	C₂²×C₄	—	1084	1	no	—
275	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
278	M₁₆	—	4	1	no	—
279	M₁₆	—	1084	1	no	—
280	M₁₆	—	1084	1	no	—
281	M₁₆	—	1084	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	271	1	no	—
284	C₂×C₈	—	271	1	no	—
285	C₂×C₈	—	271	1	no	—
286	C₂×C₈	—	271	1	no	—
287	C₂×C₈	—	1084	1	no	—
288	C₂×C₈	—	1084	1	no	—
289	C₂×C₈	—	1084	1	no	—
290	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
291	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
292	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
294	C₄⋊C₄	—	271	1	no	—
295	C₄⋊C₄	—	271	1	no	—
296	C₄⋊C₄	—	271	1	no	—
297	C₄⋊C₄	—	271	1	no	—
298	C₄⋊C₄	—	271	1	no	—
299	C₄⋊C₄	—	271	1	no	—
300	C₂²⋊C₄	—	271	1	no	—
301	C₂²⋊C₄	—	271	1	no	—
302	C₂²⋊C₄	—	271	1	no	—
303	C₂²⋊C₄	—	271	1	no	—
304	C₂²⋊C₄	—	271	1	no	—
305	C₂²⋊C₄	—	271	1	no	—
306	C₂²⋊C₄	—	271	1	no	—
307	C₂²⋊C₄	—	271	1	no	—
308	C₂²⋊C₄	—	271	1	no	—
309	C₂²⋊C₄	—	271	1	no	—
310	C₄²	—	271	1	no	—
311	C₄²	—	271	1	no	—
312	C₂³	—	271	1	no	—
313	C₂³	—	271	1	no	—
314	C₂³	—	542	2	no	—
315	C₂³	—	1084	1	no	—
316	C₂³	—	1084	1	no	—
317	C₂³	C₂×C₄×D₂₇₁	1	1	yes	characteristic
318	C₂³	C₂×C₄×D₂₇₁	1	1	yes	characteristic
319	C₂³	C₂×C₄×D₂₇₁	1	1	yes	characteristic
320	Q₈	—	4	1	no	—
321	D₄	—	4	1	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	1	no	—
324	D₄	—	542	2	no	—
325	D₄	—	542	2	no	—
326	D₄	—	1084	1	no	—
327	D₄	—	1084	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	—	271	1	no	—
335	C₂×C₄	—	271	1	no	—
336	C₂×C₄	—	271	1	no	—
337	C₂×C₄	—	271	1	no	—
338	C₂×C₄	—	271	1	no	—
339	C₂×C₄	—	271	1	no	—
340	C₂×C₄	—	542	1	no	—
341	C₂×C₄	—	542	1	no	—
342	C₂×C₄	—	542	1	no	—
343	C₂×C₄	—	542	1	no	—
344	C₂×C₄	—	1084	1	no	—
345	C₂×C₄	—	1084	1	no	—
346	C₂×C₄	—	1084	1	no	—
347	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×D₂₇₁	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	542	1	no	—
356	C₈	—	542	1	no	—
357	C₈	—	542	1	no	—
358	C₈	—	542	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	271	2	no	—
369	C₂²	—	542	1	no	—
370	C₂²	—	542	1	no	—
371	C₂²	—	542	1	no	—
372	C₂²	—	542	1	no	—
373	C₂²	—	542	1	no	—
374	C₂²	—	1084	4	no	—
375	C₂²	C₂²×C₄×D₂₇₁	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	542	1	no	—
380	C₄	—	542	1	no	—
381	C₄	—	542	1	no	—
382	C₄	—	542	1	no	—
383	C₄	—	542	1	no	—
384	C₄	—	542	1	no	—
385	C₄	#22576205	1	1	yes	characteristic
386	C₄	#22576205	1	1	yes	characteristic
387	C₂	—	4	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	4	1	no	—
390	C₂	—	542	2	no	—
391	C₂	—	1084	1	no	—
392	C₂	#31774370	1	1	yes	characteristic
393	C₂	#131×D₂₇₁	1	1	yes	characteristic
394	C₂	#31774662	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₇₁
commutator, socle	C₂²×C₂₇₁	C₂³×C₄
Fitting	#408×C₂₇₁	C₂
prime radical	#31774404	C₂
cosocle	C₂×C₄×C₂₇₁	C₂⁴
hypercenter	#408	D₂₇₁
hypocenter	C₂₇₁	#2976
LCS	G ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
2. #31773973	C₂	semidirect
3. #31773972	C₂	semidirect
4. #31773971	C₂	semidirect
5. #31773968	C₂	semidirect
6. #31773966	C₂	semidirect
7. #31773965	C₂	semidirect
8. C₈×C₂²⋊D₂₇₁	C₂	semidirect
9. (C₂²⋊D₂₇₁)⋊C₈	C₂	semidirect
10. #31773955	C₂	semidirect
11. #31773955	C₂	semidirect
12. #31773864	C₂	semidirect
13. #31773859	C₂	semidirect
14. C₂²⋊C₈×D₂₇₁	C₂	semidirect
15. #408×C₂₇₁	C₂	semidirect
17. C₂×#16864638	C₂²	semidirect
20. C₂²×C₂₇₁⋊C₈	C₂²	semidirect
36. Dic₂₇₁⋊C₈	C₂²	semidirect
37. Dic₂₇₁⋊C₈	C₂²	semidirect
38. Dic₂₇₁⋊C₈	C₂²	semidirect
39. Dic₂₇₁⋊C₈	C₂²	semidirect
42. C₂²⋊(C₂₇₁⋊C₈)	C₂²	semidirect
43. C₂²⋊(C₂₇₁⋊C₈)	C₂²	semidirect
48. #22576070	C₂²	semidirect
49. #22576070	C₂²	semidirect
50. C₈×Dic₂₇₁	C₂²	semidirect
51. C₈×Dic₂₇₁	C₂²	semidirect
53. C₂×M₁₆×C₂₇₁	C₂²	semidirect
54. C₂²×C₈×C₂₇₁	C₂²	semidirect
57. C₂²⋊C₈×C₂₇₁	C₂²	semidirect
58. C₂²⋊C₈×C₂₇₁	C₂²	semidirect
197. C₂₇₁	#2976	semidirect
211. #408	D₂₇₁	semidirect
219. C₂×M₁₆	C₂×D₂₇₁	semidirect
223. C₂²×C₈	C₂×D₂₇₁	semidirect
251. C₂²⋊C₈	C₂×D₂₇₁	semidirect
252. C₂²⋊C₈	C₂×D₂₇₁	semidirect

Maximal subgroups

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

subgroup	index
#31774404	2
#31773973	2
#31773972	2
#31773971	2
#31773968	2
#31773966	2
#31773965	2
C₈×C₂²⋊D₂₇₁	2
(C₂²⋊D₂₇₁)⋊C₈	2
#31773955	2
#31773864	2
#31773859	2
C₂²⋊C₈×D₂₇₁	2
#408×C₂₇₁	2
#2976	271