Subgroups — #32150994

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	#22597312	C₂	1	1	yes	maximal, characteristic
2	#22590247	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590246	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590170	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590169	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590166	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590165	C₂	1	1	yes	maximal, characteristic, complemented
8	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590144	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590144	C₂	1	1	yes	maximal, characteristic, complemented
11	#22590142	C₂	1	1	yes	maximal, characteristic, complemented
12	#22589939	C₂	1	1	yes	maximal, characteristic, complemented
13	#22589936	C₂	1	1	yes	maximal, characteristic, complemented
14	#22589933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986531	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	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
21	#17986126	C₄	1	1	yes	characteristic
22	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
23	#17986077	C₄	1	1	yes	characteristic
24	#17986073	C₄	1	1	yes	characteristic
25	#17986073	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
28	#17986057	C₄	1	1	yes	characteristic
29	#17986057	C₄	1	1	yes	characteristic
30	#17986055	C₄	1	1	yes	characteristic
31	#17985954	C₂²	1	1	yes	characteristic
32	#17985954	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
34	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
35	Dic₇₁⋊C₁₆	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	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
40	C₂²⋊(C₇₁⋊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	#17985775	C₂²	1	1	yes	characteristic
44	#17985774	C₂²	1	1	yes	characteristic
45	#17985774	C₂²	1	1	yes	characteristic
46	#17985774	C₂²	1	1	yes	characteristic
47	#17985774	C₂²	1	1	yes	characteristic
48	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
49	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
52	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
57	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
58	#346×C₇₁	C₂²	1	1	yes	characteristic
59	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
60	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
63	#14556121	C₈	1	1	yes	characteristic
64	#14556121	C₈	1	1	yes	characteristic
65	#14556119	C₈	1	1	yes	characteristic
66	#14556115	C₈	1	1	yes	characteristic
67	#14556110	C₈	1	1	yes	characteristic
68	#14556110	C₈	1	1	yes	characteristic
69	#14556108	C₈	1	1	yes	characteristic
70	#14556099	C₈	1	1	yes	characteristic
71	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
74	#14556087	C₂×C₄	1	1	yes	characteristic
75	#14556087	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	C₂×C₇₁⋊C₁₆	—	2	2	no	—
81	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
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	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
86	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
87	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
88	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
89	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
93	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
94	#14556038	C₂×C₄	1	1	yes	characteristic
95	#14556038	C₂×C₄	1	1	yes	characteristic
96	#14556038	C₂×C₄	1	1	yes	characteristic
97	#14556038	C₂×C₄	1	1	yes	characteristic
98	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
101	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
102	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
106	M₃₂×C₇₁	—	2	2	no	—
107	C₂×C₁₆×C₇₁	—	2	2	no	—
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	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	C₂×Dic₁₄₂	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
122	#11765849	—	2	2	no	—
123	#11765849	—	2	2	no	—
124	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₇₁	—	2	1	no	—
129	C₈×D₇₁	—	2	1	no	—
130	C₈×D₇₁	—	2	2	no	—
131	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
132	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
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	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
141	C₂²⋊Dic₇₁	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	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
145	C₂²⋊Dic₇₁	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	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₇₁⋊C₁₆	—	2	1	no	—
154	C₇₁⋊C₁₆	—	2	1	no	—
155	C₇₁⋊C₁₆	—	2	1	no	—
156	C₇₁⋊C₁₆	#41	1	2	yes	—
157	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
158	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₇₁	—	2	1	no	—
161	C₂×C₈×C₇₁	—	2	1	no	—
162	C₂×C₈×C₇₁	—	2	1	no	—
163	C₂×C₈×C₇₁	—	2	1	no	—
164	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
168	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₇₁	C₂×C₈	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	#41	1	2	yes	—
176	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
178	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
179	D₄×C₇₁	—	4	1	no	—
180	C₂×C₄×C₇₁	—	2	1	no	—
181	C₂×C₄×C₇₁	—	2	1	no	—
182	C₂×C₄×C₇₁	—	2	1	no	—
183	C₂×C₄×C₇₁	—	2	1	no	—
184	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₇₁	—	4	1	no	—
190	C₂²⋊D₇₁	—	4	1	no	—
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	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
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	—	2	1	no	—
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	#131	1	2	yes	—
212	C₂²×C₇₁	—	2	1	no	—
213	C₂²×C₇₁	—	2	1	no	—
214	C₂²×C₇₁	—	2	1	no	—
215	C₂²×C₇₁	—	2	1	no	—
216	C₂²×C₇₁	—	2	1	no	—
217	C₂²×C₇₁	—	2	1	no	—
218	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
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	C₄×#41	1	1	yes	characteristic
227	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
228	Dic₇₁	—	2	1	no	—
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	—	4	1	no	—
238	C₂×C₇₁	C₈×#41	1	1	yes	characteristic
239	C₂×C₇₁	#3407	1	1	yes	characteristic
240	C₂×C₇₁	#3407	1	1	yes	characteristic
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	D₇₁	1	1	yes	characteristic, complemented
251	#2164	—	71	1	no	—
252	#2164	—	71	1	no	—
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	C₂×D₇₁	1	1	yes	characteristic
263	C₂²×C₁₆	—	71	1	no	—
264	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
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	C₂×D₇₁	1	1	yes	characteristic
273	#433	—	71	1	no	—
274	#433	—	71	1	no	—
275	#432	—	71	1	no	—
276	#405	—	71	1	no	—
277	#405	—	71	1	no	—
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	—	71	1	no	—
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	—	71	1	no	—
301	C₂×M₁₆	—	71	1	no	—
302	C₂×M₁₆	—	71	1	no	—
303	C₂²×C₈	—	71	1	no	—
304	C₂²×C₈	—	71	1	no	—
305	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
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	C₄×D₇₁	1	1	yes	characteristic
319	#117	—	71	1	no	—
320	#117	—	71	1	no	—
321	C₂×C₄²	—	71	1	no	—
322	M₃₂	—	2	2	no	—
323	M₃₂	—	142	2	no	—
324	M₃₂	—	142	2	no	—
325	M₃₂	—	142	2	no	—
326	C₂×C₁₆	—	2	2	no	—
327	C₂×C₁₆	—	71	1	no	—
328	C₂×C₁₆	—	71	1	no	—
329	C₂×C₁₆	—	71	1	no	—
330	C₂×C₁₆	—	71	1	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	C₄×D₇₁	1	1	yes	characteristic
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	C₄×D₇₁	1	1	yes	characteristic
347	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
348	#97	—	71	1	no	—
349	#97	—	71	1	no	—
350	#97	—	71	1	no	—
351	#97	—	71	1	no	—
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	—	71	1	no	—
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	C₈×D₇₁	1	1	yes	characteristic
362	C₂²×C₄	—	71	1	no	—
363	C₂²×C₄	—	71	1	no	—
364	C₂²×C₄	—	71	1	no	—
365	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
367	M₁₆	—	142	2	no	—
368	M₁₆	—	142	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	71	1	no	—
374	C₂×C₈	—	71	1	no	—
375	C₂×C₈	—	71	1	no	—
376	C₂×C₈	—	71	1	no	—
377	C₂×C₈	—	142	2	no	—
378	C₂×C₈	—	142	1	no	—
379	C₂×C₈	—	142	1	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	—	71	1	no	—
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	—	71	1	no	—
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	—	71	2	no	—
414	C₁₆	—	142	1	no	—
415	C₁₆	—	142	1	no	—
416	C₁₆	—	142	1	no	—
417	C₁₆	#11765864	1	2	yes	—
418	C₂³	—	71	1	no	—
419	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
420	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
421	Q₈	—	284	1	no	—
422	D₄	—	4	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	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	284	1	no	—
430	C₂×C₄	—	284	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	—	71	1	no	—
436	C₂×C₄	—	71	1	no	—
437	C₂×C₄	—	71	1	no	—
438	C₂×C₄	—	142	1	no	—
439	C₂×C₄	—	142	1	no	—
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	—	2	1	no	—
448	C₈	—	71	2	no	—
449	C₈	—	142	1	no	—
450	C₈	—	142	1	no	—
451	C₈	—	142	1	no	—
452	C₈	#41×D₇₁	1	1	yes	characteristic
453	C₈	C₂×#11765864	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	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	—	142	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	C₄×#11765864	1	1	yes	characteristic
476	C₄	#131×D₇₁	1	1	yes	characteristic
477	C₂	—	4	1	no	—
478	C₂	—	4	1	no	—
479	C₂	—	284	1	no	—
480	C₂	C₈×#11765864	1	1	yes	characteristic
481	C₂	#22601441	1	1	yes	characteristic
482	C₂	#22601442	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₇₁×#2168	C₂
prime radical	#14556099	C₈
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2168	D₇₁
hypocenter	C₇₁	#33481
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #22590247	C₂	semidirect
3. #22590246	C₂	semidirect
4. #22590170	C₂	semidirect
5. #22590169	C₂	semidirect
6. #22590166	C₂	semidirect
7. #22590165	C₂	semidirect
8. #22590162	C₂	semidirect
9. #22590144	C₂	semidirect
10. #22590144	C₂	semidirect
11. #22590142	C₂	semidirect
12. #22589939	C₂	semidirect
13. #22589936	C₂	semidirect
14. #22589933	C₂	semidirect
15. C₇₁×#2168	C₂	semidirect
250. #2168	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
#22597312	2
#22590247	2
#22590246	2
#22590170	2
#22590169	2
#22590166	2
#22590165	2
#22590162	2
#22590144	2
#22590142	2
#22589939	2
#22589936	2
#22589933	2
C₇₁×#2168	2
#33481	71