Subgroups — #32150656

Order 18176.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986416	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14556068	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590172	C₂	1	2	yes	maximal, complemented
4	#22590166	C₂	1	2	yes	maximal, complemented
5	#22590166	C₂	1	2	yes	maximal, complemented
6	D₄×C₇₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
7	#22590099	C₂	1	1	yes	maximal, characteristic, complemented
8	#22589954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊(C₇₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#22589937	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#2929	C₂	1	1	yes	maximal, characteristic
12	#17986416	—	2	4	no	—
13	C₂×#14556068	—	2	4	no	—
14	C₂×#14556068	C₂²	1	1	yes	characteristic
15	C₂×#14556068	C₂²	1	2	yes	—
16	C₂×#14556068	C₂²	1	1	yes	characteristic
17	C₂×#14556068	C₂²	1	2	yes	complemented
18	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇₁⋊C₁₆	C₂²	1	2	yes	—
21	C₂²×C₇₁⋊C₁₆	C₂²	1	2	yes	complemented
22	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
23	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
24	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
25	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
26	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
27	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
28	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
29	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	complemented
30	#17985775	C₂²	1	2	yes	complemented
31	C₄×C₇₁⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
34	#525×C₇₁	C₄	1	1	yes	characteristic
35	#435×C₇₁	C₄	1	2	yes	—
36	#435×C₇₁	C₄	1	2	yes	—
37	C₈×D₄×C₇₁	C₂²	1	2	yes	—
38	C₈×D₄×C₇₁	C₂²	1	2	yes	—
39	#424×C₇₁	C₄	1	1	yes	characteristic
40	#408×C₇₁	C₄	1	1	yes	characteristic
41	#407×C₇₁	C₄	1	1	yes	characteristic
42	#405×C₇₁	C₂²	1	1	yes	characteristic
43	#14556068	—	2	4	no	—
44	#14556068	—	2	4	no	—
45	#14556068	—	2	2	no	—
46	#14556068	D₄	1	4	yes	complemented
47	C₂×C₇₁⋊C₁₆	—	2	4	no	—
48	C₂×C₇₁⋊C₁₆	—	2	4	no	—
49	C₂×C₇₁⋊C₁₆	—	2	2	no	—
50	C₂×C₇₁⋊C₁₆	—	2	2	no	—
51	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₇₁⋊C₁₆	C₂³	1	2	yes	—
53	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₇₁⋊C₁₆	C₂³	1	2	yes	—
57	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
59	#131×C₇₁	—	2	2	no	—
60	#131×C₇₁	—	2	2	no	—
61	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₇₁	—	2	2	no	—
65	C₂²×C₈×C₇₁	—	2	2	no	—
66	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
73	#123×C₇₁	C₈	1	2	yes	—
74	C₂²⋊Q₈×C₇₁	C₈	1	1	yes	characteristic
75	C₂²⋊Q₈×C₇₁	C₈	1	1	yes	characteristic
76	#121×C₇₁	C₈	1	1	yes	characteristic
77	#121×C₇₁	C₈	1	1	yes	characteristic
78	#120×C₇₁	C₈	1	2	yes	—
79	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
81	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
83	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
84	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
85	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
87	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
88	#97×C₇₁	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₇₁	C₂³	1	2	yes	—
90	C₇₁⋊C₁₆	—	2	1	no	—
91	C₇₁⋊C₁₆	—	2	2	no	—
92	C₇₁⋊C₁₆	—	2	1	no	—
93	C₇₁⋊C₁₆	—	2	1	no	—
94	C₇₁⋊C₁₆	—	2	1	no	—
95	C₇₁⋊C₁₆	C₂×D₄	1	4	yes	—
96	C₂⁴×C₇₁	C₂×C₈	1	1	yes	characteristic
97	#41×C₇₁	—	2	2	no	—
98	#41×C₇₁	—	2	2	no	—
99	C₂×Q₈×C₇₁	C₂×C₈	1	1	yes	characteristic
100	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
101	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
102	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
103	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
104	C₂²×C₄×C₇₁	—	2	2	no	—
105	C₂²×C₄×C₇₁	—	2	2	no	—
106	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
113	M₁₆×C₇₁	—	2	2	no	—
114	M₁₆×C₇₁	—	2	2	no	—
115	M₁₆×C₇₁	—	2	4	no	—
116	C₂×C₈×C₇₁	—	2	2	no	—
117	C₂×C₈×C₇₁	—	2	2	no	—
118	C₂×C₈×C₇₁	—	2	2	no	—
119	C₂×C₈×C₇₁	—	2	1	no	—
120	C₂×C₈×C₇₁	—	2	1	no	—
121	C₂×C₈×C₇₁	—	2	2	no	—
122	C₂×C₈×C₇₁	—	2	1	no	—
123	C₂×C₈×C₇₁	—	2	1	no	—
124	C₂×C₈×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₇₁	#41	1	2	yes	—
132	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
133	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
134	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
135	C₄⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
136	C₄⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
137	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
138	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
139	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
140	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
141	C₂²⋊C₄×C₇₁	C₂×C₈	1	2	yes	—
142	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
143	C₂³×C₇₁	—	2	2	no	—
144	C₂³×C₇₁	—	2	2	no	—
145	C₂³×C₇₁	—	4	1	no	—
146	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₇₁	C₂²×C₈	1	2	yes	—
148	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
149	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
150	Q₈×C₇₁	—	2	2	no	—
151	D₄×C₇₁	—	2	4	no	—
152	D₄×C₇₁	—	2	4	no	—
153	D₄×C₇₁	—	2	2	no	—
154	D₄×C₇₁	—	4	2	no	—
155	C₂×C₄×C₇₁	—	2	2	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	2	1	no	—
158	C₂×C₄×C₇₁	—	2	2	no	—
159	C₂×C₄×C₇₁	—	2	1	no	—
160	C₂×C₄×C₇₁	—	2	1	no	—
161	C₂×C₄×C₇₁	—	2	2	no	—
162	C₂×C₄×C₇₁	—	2	2	no	—
163	C₂×C₄×C₇₁	—	2	2	no	—
164	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
166	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₇₁	#131	1	2	yes	—
172	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₇₁	—	2	1	no	—
174	C₈×C₇₁	—	2	1	no	—
175	C₈×C₇₁	—	2	2	no	—
176	C₈×C₇₁	—	2	2	no	—
177	C₈×C₇₁	C₄×D₄	1	2	yes	—
178	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
180	C₂²×C₇₁	—	2	1	no	—
181	C₂²×C₇₁	—	2	1	no	—
182	C₂²×C₇₁	—	2	1	no	—
183	C₂²×C₇₁	—	2	1	no	—
184	C₂²×C₇₁	—	2	2	no	—
185	C₂²×C₇₁	—	2	1	no	—
186	C₂²×C₇₁	—	2	1	no	—
187	C₂²×C₇₁	—	2	2	no	—
188	C₂²×C₇₁	—	2	1	no	—
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	—	4	4	no	—
191	C₂²×C₇₁	C₈×D₄	1	2	yes	—
192	C₂²×C₇₁	#504	1	2	yes	complemented
193	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
194	C₄×C₇₁	—	2	2	no	—
195	C₄×C₇₁	—	2	2	no	—
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	2	1	no	—
198	C₄×C₇₁	—	2	2	no	—
199	C₄×C₇₁	C₈×D₄	1	2	yes	—
200	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
201	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
202	#33436	—	71	1	no	maximal, Sylow
203	C₂×C₇₁	—	2	2	no	—
204	C₂×C₇₁	—	2	2	no	—
205	C₂×C₇₁	—	4	2	no	—
206	C₂×C₇₁	—	4	1	no	—
207	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
208	C₂×C₇₁	C₂×#504	1	1	yes	characteristic
209	C₂×C₇₁	#3407	1	1	yes	characteristic
210	C₂×#504	—	71	1	no	—
211	C₂²×M₃₂	—	71	1	no	—
212	#2929	D₇₁	1	1	yes	characteristic
213	#2169	—	71	2	no	—
214	#2168	—	71	2	no	—
215	#2168	—	71	2	no	—
216	D₄×C₁₆	—	71	2	no	—
217	#2151	—	71	1	no	—
218	#2113	—	71	1	no	—
219	C₂×C₂²⋊C₁₆	—	71	1	no	—
220	#2108	—	71	1	no	—
221	C₇₁	#33436	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	C₂×D₇₁	1	1	yes	characteristic
223	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
224	#525	Dic₇₁	1	1	yes	characteristic
225	#504	—	142	4	no	—
226	C₂×M₃₂	—	71	1	no	—
227	C₂×M₃₂	—	71	1	no	—
228	C₂×M₃₂	—	71	2	no	—
229	C₂×M₃₂	—	71	2	no	—
230	C₂×M₃₂	—	142	4	no	—
231	C₂²×C₁₆	—	71	1	no	—
232	C₂²×C₁₆	—	71	1	no	—
233	C₂²×C₁₆	—	71	2	no	—
234	C₂²×C₁₆	—	71	2	no	—
235	#435	Dic₇₁	1	2	yes	—
236	#435	Dic₇₁	1	2	yes	—
237	C₈×D₄	C₂×D₇₁	1	2	yes	—
238	C₈×D₄	C₂×D₇₁	1	2	yes	—
239	#424	Dic₇₁	1	1	yes	characteristic
240	#408	Dic₇₁	1	1	yes	characteristic
241	#407	Dic₇₁	1	1	yes	characteristic
242	#405	C₂×D₇₁	1	1	yes	characteristic
243	C₄⋊C₁₆	—	71	2	no	—
244	C₄⋊C₁₆	—	71	2	no	—
245	C₂²⋊C₁₆	—	71	1	no	—
246	C₂²⋊C₁₆	—	71	1	no	—
247	C₂²⋊C₁₆	—	71	1	no	—
248	C₂²⋊C₁₆	—	71	1	no	—
249	C₂²⋊C₁₆	—	71	2	no	—
250	C₂²⋊C₁₆	—	71	2	no	—
251	#346	—	71	2	no	—
252	C₄×C₁₆	—	71	2	no	—
253	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
254	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	C₂×M₁₆	C₂×Dic₇₁	1	1	yes	characteristic
258	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
259	C₂×M₁₆	C₂×Dic₇₁	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
263	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
264	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₁	1	2	yes	—
268	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
269	#123	C₇₁⋊C₈	1	2	yes	—
270	C₂²⋊Q₈	C₇₁⋊C₈	1	1	yes	characteristic
271	C₂²⋊Q₈	C₇₁⋊C₈	1	1	yes	characteristic
272	#121	C₇₁⋊C₈	1	1	yes	characteristic
273	#121	C₇₁⋊C₈	1	1	yes	characteristic
274	#120	C₇₁⋊C₈	1	2	yes	—
275	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
276	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
277	#117	C₂×Dic₇₁	1	1	yes	characteristic
278	M₃₂	—	71	4	no	—
279	M₃₂	—	142	4	no	—
280	M₃₂	—	142	4	no	—
281	M₃₂	—	142	2	no	—
282	C₂×C₁₆	—	71	2	no	—
283	C₂×C₁₆	—	71	1	no	—
284	C₂×C₁₆	—	71	1	no	—
285	C₂×C₁₆	—	71	1	no	—
286	C₂×C₁₆	—	71	1	no	—
287	C₂×C₁₆	—	71	2	no	—
288	C₂×C₁₆	—	142	4	no	—
289	C₂×C₁₆	—	142	4	no	—
290	C₂×C₁₆	—	142	2	no	—
291	C₂×C₁₆	—	142	2	no	—
292	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
293	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
294	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
295	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
296	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
297	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
298	#97	C₂×Dic₇₁	1	2	yes	—
299	C₄×C₈	C₂²×D₇₁	1	2	yes	—
300	C₂⁴	C₂×C₇₁⋊C₈	1	1	yes	characteristic
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	C₂×C₇₁⋊C₈	1	1	yes	characteristic
304	C₂×D₄	C₂×C₇₁⋊C₈	1	2	yes	—
305	C₂×D₄	C₂×C₇₁⋊C₈	1	2	yes	—
306	C₂×D₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
307	C₂×D₄	C₂×C₇₁⋊C₈	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
330	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
331	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
332	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
333	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
334	C₂×C₈	D₄×D₇₁	1	2	yes	—
335	C₂×C₈	#11765864	1	2	yes	—
336	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
338	C₄⋊C₄	C₂×C₇₁⋊C₈	1	1	yes	characteristic
339	C₄⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
340	C₄⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
341	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
342	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
343	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
344	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
345	C₂²⋊C₄	C₂×C₇₁⋊C₈	1	2	yes	—
346	C₄²	C₂²×Dic₇₁	1	2	yes	—
347	C₁₆	—	71	4	no	—
348	C₁₆	—	142	1	no	—
349	C₁₆	—	142	2	no	—
350	C₁₆	—	142	1	no	—
351	C₁₆	—	142	1	no	—
352	C₁₆	—	142	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
357	C₂³	C₂²×C₇₁⋊C₈	1	2	yes	—
358	C₂³	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
359	C₂³	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	D₄×Dic₇₁	1	2	yes	—
375	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
376	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
377	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
380	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
381	C₂×C₄	#14556135	1	2	yes	—
382	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	D₄×Dic₇₁	1	2	yes	—
388	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
389	C₈	C₂×#11765864	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	D₄×C₇₁⋊C₈	1	2	yes	—
402	C₂²	#17986416	1	2	yes	complemented
403	C₂²	C₂³×C₇₁⋊C₈	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	D₄×C₇₁⋊C₈	1	2	yes	—
410	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
411	C₄	C₂×#14556135	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×D₄×C₇₁⋊C₈	1	1	yes	characteristic
417	C₂	C₂×#17986416	1	1	yes	characteristic
418	C₂	#22601443	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₇₁×#2929	C₂
prime radical	#525×C₇₁	C₄
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2929	D₇₁
hypocenter	C₇₁	#33436
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
1. C₂×#17986416	C₂	semidirect
2. C₂²×#14556068	C₂	semidirect
3. #22590172	C₂	semidirect
4. #22590166	C₂	semidirect
5. #22590166	C₂	semidirect
6. D₄×C₇₁⋊C₁₆	C₂	semidirect
7. #22590099	C₂	semidirect
8. #22589954	C₂	semidirect
9. C₂×C₂²⋊(C₇₁⋊C₁₆)	C₂	semidirect
10. #22589937	C₂	semidirect
17. C₂×#14556068	C₂²	semidirect
21. C₂²×C₇₁⋊C₁₆	C₂²	semidirect
22. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
23. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
28. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
29. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
30. #17985775	C₂²	semidirect
31. C₄×C₇₁⋊C₁₆	C₂²	semidirect
46. #14556068	D₄	semidirect
192. C₂²×C₇₁	#504	semidirect
221. C₇₁	#33436	semidirect
402. C₂²	#17986416	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986416	2
C₂²×#14556068	2
#22590172	2
#22590166	2
D₄×C₇₁⋊C₁₆	2
#22590099	2
#22589954	2
C₂×C₂²⋊(C₇₁⋊C₁₆)	2
#22589937	2
C₇₁×#2929	2
#33436	71