Subgroups — #32150995

Order 18176.

508 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597311	C₂	1	1	yes	maximal, characteristic
2	#22590247	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590245	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590171	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590169	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590168	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590164	C₂	1	1	yes	maximal, characteristic, complemented
8	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590145	C₂	1	1	yes	maximal, characteristic, complemented
11	#22590141	C₂	1	1	yes	maximal, characteristic, complemented
12	#22589938	C₂	1	1	yes	maximal, characteristic, complemented
13	#22589937	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14556067	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986527	C₄	1	1	yes	characteristic
17	C₂×#14556068	C₂²	1	1	yes	characteristic
18	C₂×#14556067	C₂²	1	1	yes	characteristic
19	C₂×#14556067	C₂²	1	1	yes	characteristic
20	C₂×#14556067	C₂²	1	1	yes	characteristic
21	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
23	#17986127	C₄	1	1	yes	characteristic
24	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
25	#17986075	C₄	1	1	yes	characteristic
26	#17986072	C₄	1	1	yes	characteristic
27	#17986068	C₄	1	1	yes	characteristic
28	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
31	#17986061	C₄	1	1	yes	characteristic
32	#17986060	C₄	1	1	yes	characteristic
33	#17986054	C₄	1	1	yes	characteristic
34	#17985953	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
36	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
37	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
38	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
39	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
40	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
41	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
42	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
43	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
44	#17985775	C₂²	1	1	yes	characteristic
45	#17985775	C₂²	1	1	yes	characteristic
46	#17985774	C₂²	1	1	yes	characteristic
47	#17985774	C₂²	1	1	yes	characteristic
48	#17985774	C₂²	1	1	yes	characteristic
49	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
52	#405×C₇₁	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
55	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
57	#346×C₇₁	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
59	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
63	#14556123	C₈	1	1	yes	characteristic
64	#14556121	C₈	1	1	yes	characteristic
65	#14556118	C₈	1	1	yes	characteristic
66	#14556114	C₈	1	1	yes	characteristic
67	#14556113	C₈	1	1	yes	characteristic
68	#14556110	C₈	1	1	yes	characteristic
69	#14556106	C₈	1	1	yes	characteristic
70	#14556101	C₈	1	1	yes	characteristic
71	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
72	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
75	#14556085	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
77	#14556068	—	2	2	no	—
78	#14556067	—	2	2	no	—
79	#14556067	—	2	2	no	—
80	#14556067	—	2	2	no	—
81	C₂×C₇₁⋊C₁₆	—	2	2	no	—
82	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
86	C₁₆×D₇₁	—	2	2	no	—
87	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
90	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
99	#14556039	C₂×C₄	1	1	yes	characteristic
100	#14556038	C₂×C₄	1	1	yes	characteristic
101	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
104	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
106	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
107	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
108	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
112	#97×C₇₁	C₂×C₄	1	1	yes	characteristic
113	#97×C₇₁	C₂×C₄	1	1	yes	characteristic
114	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	C₂×Dic₁₄₂	C₂×C₈	1	1	yes	characteristic
117	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
124	#11765848	—	2	2	no	—
125	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₇₁	—	2	2	no	—
130	C₈×D₇₁	—	2	1	no	—
131	C₈×D₇₁	—	2	1	no	—
132	C₈×D₇₁	—	2	1	no	—
133	C₈×D₇₁	—	2	1	no	—
134	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
135	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
136	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
137	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
138	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
144	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
145	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
146	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
147	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
148	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
149	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
154	C₇₁⋊C₁₆	—	2	1	no	—
155	C₇₁⋊C₁₆	—	2	1	no	—
156	C₇₁⋊C₁₆	#41	1	2	yes	—
157	C₇₁⋊C₁₆	#41	1	2	yes	—
158	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
159	M₁₆×C₇₁	—	2	2	no	—
160	C₂×C₈×C₇₁	—	2	1	no	—
161	C₂×C₈×C₇₁	—	2	1	no	—
162	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
166	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
167	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
168	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
170	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₁₆×C₇₁	—	2	1	no	—
173	C₁₆×C₇₁	—	2	1	no	—
174	C₁₆×C₇₁	—	2	1	no	—
175	C₁₆×C₇₁	—	2	1	no	—
176	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
177	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₇₁	—	2	1	no	—
180	C₂×C₄×C₇₁	—	2	1	no	—
181	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
187	C₂²⋊D₇₁	—	4	1	no	—
188	C₂²⋊D₇₁	—	4	1	no	—
189	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
191	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
192	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
193	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
195	D₂₈₄	—	4	1	no	—
196	C₄×D₇₁	—	2	1	no	—
197	C₄×D₇₁	—	2	1	no	—
198	C₄×D₇₁	—	2	1	no	—
199	C₄×D₇₁	—	2	1	no	—
200	C₄×D₇₁	—	4	1	no	—
201	C₄×D₇₁	—	4	1	no	—
202	Dic₁₄₂	—	4	1	no	—
203	C₈×C₇₁	—	2	1	no	—
204	C₈×C₇₁	—	2	1	no	—
205	C₈×C₇₁	#131	1	2	yes	—
206	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
207	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
208	C₇₁⋊C₈	—	2	1	no	—
209	C₇₁⋊C₈	—	2	1	no	—
210	C₇₁⋊C₈	—	2	1	no	—
211	C₇₁⋊C₈	—	2	1	no	—
212	C₂²×C₇₁	—	2	1	no	—
213	C₂²×C₇₁	—	2	1	no	—
214	C₂²×C₇₁	—	2	1	no	—
215	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
216	C₂×D₇₁	—	2	1	no	—
217	C₂×D₇₁	—	2	1	no	—
218	C₂×D₇₁	—	2	1	no	—
219	C₂×D₇₁	—	2	1	no	—
220	C₂×D₇₁	—	2	1	no	—
221	C₂×D₇₁	—	2	1	no	—
222	C₄×C₇₁	—	2	1	no	—
223	C₄×C₇₁	—	2	1	no	—
224	C₄×C₇₁	—	2	1	no	—
225	C₄×C₇₁	—	2	1	no	—
226	C₄×C₇₁	—	2	1	no	—
227	C₄×C₇₁	C₄×#41	1	1	yes	characteristic
228	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
229	Dic₇₁	—	2	1	no	—
230	Dic₇₁	—	2	1	no	—
231	Dic₇₁	—	2	1	no	—
232	Dic₇₁	—	2	1	no	—
233	Dic₇₁	—	2	1	no	—
234	Dic₇₁	—	2	1	no	—
235	#33481	—	71	1	no	maximal, Sylow
236	C₂×C₇₁	—	4	1	no	—
237	C₂×C₇₁	C₈×#41	1	1	yes	characteristic
238	C₂×C₇₁	#3407	1	1	yes	characteristic
239	C₂×C₇₁	#3407	1	1	yes	characteristic
240	D₇₁	—	4	1	no	—
241	D₇₁	—	4	1	no	—
242	#2966	—	71	1	no	—
243	#2183	—	71	1	no	—
244	#2183	—	71	1	no	—
245	#2169	—	71	1	no	—
246	#2169	—	71	1	no	—
247	#2168	—	71	1	no	—
248	#2168	—	71	1	no	—
249	#2168	—	71	1	no	—
250	#2168	—	71	1	no	—
251	#2164	—	71	1	no	—
252	#2164	D₇₁	1	1	yes	characteristic, complemented
253	#2163	—	71	1	no	—
254	#2108	—	71	1	no	—
255	#2108	—	71	1	no	—
256	C₄×M₃₂	—	71	1	no	—
257	C₇₁	#33481	1	1	yes	characteristic, complemented, Sylow
258	#529	—	71	1	no	—
259	C₂×M₃₂	—	71	1	no	—
260	C₂×M₃₂	—	71	1	no	—
261	C₂×M₃₂	—	71	1	no	—
262	C₂×M₃₂	—	71	1	no	—
263	C₂²×C₁₆	—	71	1	no	—
264	C₂²×C₁₆	—	71	1	no	—
265	#446	—	71	1	no	—
266	C₈×Q₈	—	71	1	no	—
267	#436	—	71	1	no	—
268	#435	—	71	1	no	—
269	#435	—	71	1	no	—
270	C₈×D₄	—	71	1	no	—
271	C₈×D₄	—	71	1	no	—
272	C₈×D₄	—	71	1	no	—
273	#433	—	71	1	no	—
274	#433	—	71	1	no	—
275	#432	—	71	1	no	—
276	#405	—	71	1	no	—
277	#405	C₂×D₇₁	1	1	yes	characteristic
278	C₂×C₄×C₈	—	71	1	no	—
279	C₄⋊C₁₆	—	71	1	no	—
280	C₄⋊C₁₆	—	71	1	no	—
281	C₄⋊C₁₆	—	71	1	no	—
282	C₄⋊C₁₆	—	71	1	no	—
283	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
284	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
285	C₂²⋊C₁₆	—	71	1	no	—
286	C₂²⋊C₁₆	—	71	1	no	—
287	C₂²⋊C₁₆	—	71	1	no	—
288	C₂²⋊C₁₆	—	71	1	no	—
289	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
290	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
291	#346	—	71	1	no	—
292	#346	—	71	1	no	—
293	#346	—	71	1	no	—
294	#346	—	71	1	no	—
295	#346	—	71	1	no	—
296	#346	C₂×D₇₁	1	1	yes	characteristic
297	C₄×C₁₆	—	71	1	no	—
298	C₄×C₁₆	—	71	1	no	—
299	C₄×C₁₆	—	71	1	no	—
300	C₄×C₁₆	C₂×D₇₁	1	1	yes	characteristic
301	C₂×M₁₆	—	71	1	no	—
302	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
303	C₂²×C₈	—	71	1	no	—
304	C₂²×C₈	—	71	1	no	—
305	C₂²×C₈	—	71	1	no	—
306	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
307	#126	—	71	1	no	—
308	#126	—	71	1	no	—
309	#125	—	71	1	no	—
310	#124	—	71	1	no	—
311	#123	—	71	1	no	—
312	#123	—	71	1	no	—
313	C₂²⋊Q₈	—	71	1	no	—
314	#121	—	71	1	no	—
315	C₄×Q₈	—	71	1	no	—
316	C₄×D₄	—	71	1	no	—
317	C₄×D₄	—	71	1	no	—
318	C₄×D₄	—	71	1	no	—
319	#117	—	71	1	no	—
320	#117	C₄×D₇₁	1	1	yes	characteristic
321	C₂×C₄²	—	71	1	no	—
322	M₃₂	—	142	2	no	—
323	M₃₂	—	142	2	no	—
324	M₃₂	—	142	2	no	—
325	M₃₂	—	142	2	no	—
326	C₂×C₁₆	—	71	1	no	—
327	C₂×C₁₆	—	71	1	no	—
328	C₂×C₁₆	—	71	1	no	—
329	C₂×C₁₆	—	71	1	no	—
330	C₂×C₁₆	—	142	2	no	—
331	C₂×C₁₆	—	142	2	no	—
332	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
333	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
334	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
335	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
336	C₄⋊C₈	—	71	1	no	—
337	C₄⋊C₈	—	71	1	no	—
338	C₄⋊C₈	—	71	1	no	—
339	C₄⋊C₈	—	71	1	no	—
340	C₄⋊C₈	—	71	1	no	—
341	C₄⋊C₈	—	71	1	no	—
342	C₂²⋊C₈	—	71	1	no	—
343	C₂²⋊C₈	—	71	1	no	—
344	C₂²⋊C₈	—	71	1	no	—
345	C₂²⋊C₈	—	71	1	no	—
346	C₂²⋊C₈	—	71	1	no	—
347	C₂²⋊C₈	—	71	1	no	—
348	#97	—	71	1	no	—
349	#97	—	71	1	no	—
350	#97	C₄×D₇₁	1	1	yes	characteristic
351	#97	C₄×D₇₁	1	1	yes	characteristic
352	C₄×C₈	—	71	1	no	—
353	C₄×C₈	—	71	1	no	—
354	C₄×C₈	—	71	1	no	—
355	C₄×C₈	—	71	1	no	—
356	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
357	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
358	C₂×Q₈	—	71	1	no	—
359	C₂×D₄	—	71	1	no	—
360	C₂×D₄	—	71	1	no	—
361	C₂×D₄	—	71	1	no	—
362	C₂²×C₄	—	71	1	no	—
363	C₂²×C₄	—	71	1	no	—
364	C₂²×C₄	—	71	1	no	—
365	C₂²×C₄	—	71	1	no	—
366	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
367	M₁₆	—	2	2	no	—
368	M₁₆	—	142	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	71	1	no	—
372	C₂×C₈	—	71	1	no	—
373	C₂×C₈	—	71	1	no	—
374	C₂×C₈	—	71	1	no	—
375	C₂×C₈	—	142	1	no	—
376	C₂×C₈	—	142	1	no	—
377	C₂×C₈	—	142	1	no	—
378	C₂×C₈	—	142	1	no	—
379	C₂×C₈	—	142	2	no	—
380	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
381	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
383	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
384	C₄⋊C₄	—	71	1	no	—
385	C₄⋊C₄	—	71	1	no	—
386	C₄⋊C₄	—	71	1	no	—
387	C₄⋊C₄	—	71	1	no	—
388	C₄⋊C₄	—	71	1	no	—
389	C₄⋊C₄	—	71	1	no	—
390	C₄⋊C₄	—	71	1	no	—
391	C₄⋊C₄	—	71	1	no	—
392	C₄⋊C₄	C₈×D₇₁	1	1	yes	characteristic
393	C₄⋊C₄	C₈×D₇₁	1	1	yes	characteristic
394	C₂²⋊C₄	—	71	1	no	—
395	C₂²⋊C₄	—	71	1	no	—
396	C₂²⋊C₄	—	71	1	no	—
397	C₂²⋊C₄	—	71	1	no	—
398	C₂²⋊C₄	—	71	1	no	—
399	C₂²⋊C₄	—	71	1	no	—
400	C₂²⋊C₄	—	71	1	no	—
401	C₂²⋊C₄	—	71	1	no	—
402	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
403	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
404	C₄²	—	71	1	no	—
405	C₄²	—	71	1	no	—
406	C₄²	—	71	1	no	—
407	C₄²	—	71	1	no	—
408	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
409	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	2	1	no	—
413	C₁₆	—	2	1	no	—
414	C₁₆	—	71	2	no	—
415	C₁₆	—	71	2	no	—
416	C₁₆	—	142	1	no	—
417	C₁₆	—	142	1	no	—
418	C₂³	—	71	1	no	—
419	C₂³	—	71	1	no	—
420	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
421	Q₈	—	284	1	no	—
422	D₄	—	284	1	no	—
423	D₄	—	284	1	no	—
424	D₄	—	284	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	284	1	no	—
428	C₂×C₄	—	284	1	no	—
429	C₂×C₄	—	71	1	no	—
430	C₂×C₄	—	71	1	no	—
431	C₂×C₄	—	71	1	no	—
432	C₂×C₄	—	71	1	no	—
433	C₂×C₄	—	71	1	no	—
434	C₂×C₄	—	71	1	no	—
435	C₂×C₄	—	142	1	no	—
436	C₂×C₄	—	142	1	no	—
437	C₂×C₄	—	142	1	no	—
438	C₂×C₄	—	142	1	no	—
439	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
440	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
443	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	142	1	no	—
448	C₈	—	142	1	no	—
449	C₈	—	142	1	no	—
450	C₈	—	142	1	no	—
451	C₈	#14556136	1	2	yes	—
452	C₈	#41×D₇₁	1	1	yes	characteristic
453	C₈	#41×D₇₁	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	142	1	no	—
458	C₂²	—	142	1	no	—
459	C₂²	—	142	1	no	—
460	C₂²	—	142	1	no	—
461	C₂²	—	142	1	no	—
462	C₂²	—	142	1	no	—
463	C₂²	C₂²×C₈×D₇₁	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	142	1	no	—
470	C₄	—	142	1	no	—
471	C₄	—	142	1	no	—
472	C₄	—	142	1	no	—
473	C₄	—	142	1	no	—
474	C₄	—	142	1	no	—
475	C₄	#17986467	1	1	yes	characteristic
476	C₄	C₂×#14556136	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	284	1	no	—
479	C₂	—	284	1	no	—
480	C₂	#22597296	1	1	yes	characteristic
481	C₂	#22601441	1	1	yes	characteristic
482	C₂	#22601441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₇₁×#2164	C₂
prime radical	#14556101	C₈
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2164	D₇₁
hypocenter	C₇₁	#33481
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #22590247	C₂	semidirect
3. #22590245	C₂	semidirect
4. #22590171	C₂	semidirect
5. #22590169	C₂	semidirect
6. #22590168	C₂	semidirect
7. #22590164	C₂	semidirect
8. #22590162	C₂	semidirect
9. #22590162	C₂	semidirect
10. #22590145	C₂	semidirect
11. #22590141	C₂	semidirect
12. #22589938	C₂	semidirect
13. #22589937	C₂	semidirect
14. C₄×#14556067	C₂	semidirect
15. C₇₁×#2164	C₂	semidirect
252. #2164	D₇₁	semidirect
257. C₇₁	#33481	semidirect

Maximal subgroups

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

subgroup	index
#22597311	2
#22590247	2
#22590245	2
#22590171	2
#22590169	2
#22590168	2
#22590164	2
#22590162	2
#22590145	2
#22590141	2
#22589938	2
#22589937	2
C₄×#14556067	2
C₇₁×#2164	2
#33481	71