Subgroups — #32151055

Order 18176.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597032	C₂	1	1	yes	maximal, characteristic
2	#22590170	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590169	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590168	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590165	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590163	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₇₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590144	C₂	1	1	yes	maximal, characteristic, complemented
11	#22590144	C₂	1	1	yes	maximal, characteristic, complemented
12	#22589954	C₂	1	1	yes	maximal, characteristic, complemented
13	#22589949	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
17	#17986506	C₄	1	1	yes	characteristic
18	C₂×#14556068	C₂²	1	1	yes	characteristic, complemented
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, complemented
22	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
24	#17986068	C₄	1	1	yes	characteristic
25	#17986068	C₄	1	1	yes	characteristic
26	#17986068	C₄	1	1	yes	characteristic
27	#17986068	C₄	1	1	yes	characteristic
28	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
32	#17986027	C₄	1	1	yes	characteristic
33	#17985966	C₄	1	1	yes	characteristic
34	#17985962	C₄	1	1	yes	characteristic
35	#17985954	C₂²	1	1	yes	characteristic
36	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
44	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
46	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
48	#17985774	C₂²	1	1	yes	characteristic, complemented
49	#17985774	C₂²	1	1	yes	characteristic, complemented
50	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
51	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
53	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²⋊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, complemented
58	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
60	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₁	—	4	1	no	—
63	C₂×C₈×D₇₁	—	4	1	no	—
64	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
68	#14556109	C₈	1	1	yes	characteristic
69	#14556109	C₈	1	1	yes	characteristic
70	#14556104	C₈	1	1	yes	characteristic
71	#14556104	C₈	1	1	yes	characteristic
72	#14556099	C₈	1	1	yes	characteristic
73	#14556099	C₈	1	1	yes	characteristic
74	#14556096	C₈	1	1	yes	characteristic
75	#14556096	C₈	1	1	yes	characteristic
76	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
80	#14556087	C₂×C₄	1	1	yes	characteristic
81	#14556068	—	4	1	no	—
82	#14556067	—	4	1	no	—
83	#14556067	—	4	1	no	—
84	C₂×C₇₁⋊C₁₆	—	4	1	no	—
85	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
89	C₁₆×D₇₁	—	4	1	no	—
90	C₁₆×D₇₁	—	4	1	no	—
91	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
94	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
103	#14556038	C₂×C₄	1	1	yes	characteristic
104	#14556038	C₂×C₄	1	1	yes	characteristic
105	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
106	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
107	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
108	#131×C₇₁	—	4	1	no	—
109	#131×C₇₁	—	4	1	no	—
110	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
111	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
112	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
113	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	M₃₂×C₇₁	—	4	1	no	—
117	C₂×C₁₆×C₇₁	—	4	1	no	—
118	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
119	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
120	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
122	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
123	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
124	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
125	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
126	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
127	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₇₁	—	4	1	no	—
129	C₂×C₄×D₇₁	—	4	1	no	—
130	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
131	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
132	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
134	#11765849	—	4	1	no	—
135	C₂×C₇₁⋊C₈	—	4	1	no	—
136	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₈×D₇₁	—	2	1	no	—
141	C₈×D₇₁	—	2	1	no	—
142	C₈×D₇₁	—	2	1	no	—
143	C₈×D₇₁	—	2	1	no	—
144	C₈×D₇₁	—	4	1	no	—
145	C₈×D₇₁	—	4	1	no	—
146	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
148	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
149	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
150	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
151	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
153	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
154	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
155	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
158	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
159	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
160	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
161	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
162	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
164	C₇₁⋊C₁₆	—	2	1	no	—
165	C₇₁⋊C₁₆	—	2	1	no	—
166	C₇₁⋊C₁₆	—	2	1	no	—
167	C₇₁⋊C₁₆	—	2	1	no	—
168	#41×C₇₁	—	4	1	no	—
169	#41×C₇₁	—	4	1	no	—
170	C₂×Q₈×C₇₁	C₂×C₈	1	1	yes	characteristic
171	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
172	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
173	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
174	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
177	M₁₆×C₇₁	—	4	1	no	—
178	M₁₆×C₇₁	—	4	1	no	—
179	M₁₆×C₇₁	—	4	1	no	—
180	C₂×C₈×C₇₁	—	2	1	no	—
181	C₂×C₈×C₇₁	—	2	1	no	—
182	C₂×C₈×C₇₁	—	2	1	no	—
183	C₂×C₈×C₇₁	—	2	1	no	—
184	C₂×C₈×C₇₁	—	2	1	no	—
185	C₂×C₈×C₇₁	—	2	1	no	—
186	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
190	C₁₆×C₇₁	—	2	1	no	—
191	C₁₆×C₇₁	—	2	1	no	—
192	C₁₆×C₇₁	—	2	1	no	—
193	C₁₆×C₇₁	—	2	1	no	—
194	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
195	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
196	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
197	C₂²×D₇₁	—	2	2	no	—
198	C₂²×D₇₁	—	4	1	no	—
199	C₂²×D₇₁	—	4	1	no	—
200	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
201	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
202	Q₈×C₇₁	—	4	1	no	—
203	D₄×C₇₁	—	4	1	no	—
204	D₄×C₇₁	—	4	1	no	—
205	D₄×C₇₁	—	4	1	no	—
206	C₂×C₄×C₇₁	—	2	1	no	—
207	C₂×C₄×C₇₁	—	2	1	no	—
208	C₂×C₄×C₇₁	—	2	1	no	—
209	C₂×C₄×C₇₁	—	2	1	no	—
210	C₂×C₄×C₇₁	—	2	1	no	—
211	C₂×C₄×C₇₁	—	2	1	no	—
212	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
215	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
216	C₂²⋊D₇₁	—	2	2	no	—
217	C₂²⋊D₇₁	—	2	2	no	—
218	C₂²⋊D₇₁	—	4	1	no	—
219	C₂²⋊D₇₁	—	4	1	no	—
220	C₂×Dic₇₁	—	4	1	no	—
221	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
222	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
223	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
224	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
225	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
226	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
227	C₄×D₇₁	—	2	1	no	—
228	C₄×D₇₁	—	2	1	no	—
229	C₄×D₇₁	—	2	1	no	—
230	C₄×D₇₁	—	2	1	no	—
231	C₄×D₇₁	—	4	1	no	—
232	C₄×D₇₁	—	4	1	no	—
233	C₈×C₇₁	—	2	1	no	—
234	C₈×C₇₁	—	2	1	no	—
235	C₈×C₇₁	—	2	1	no	—
236	C₈×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
237	C₈×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
238	C₇₁⋊C₈	—	2	1	no	—
239	C₇₁⋊C₈	—	2	1	no	—
240	C₇₁⋊C₈	—	2	1	no	—
241	C₇₁⋊C₈	—	2	1	no	—
242	C₂²×C₇₁	—	2	1	no	—
243	C₂²×C₇₁	—	2	1	no	—
244	C₂²×C₇₁	—	2	1	no	—
245	C₂²×C₇₁	—	2	1	no	—
246	C₂²×C₇₁	—	2	1	no	—
247	C₂²×C₇₁	—	2	1	no	—
248	C₂²×C₇₁	—	2	1	no	—
249	C₂²×C₇₁	—	2	1	no	—
250	C₂²×C₇₁	—	2	1	no	—
251	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
252	C₂×D₇₁	—	2	1	no	—
253	C₂×D₇₁	—	2	1	no	—
254	C₂×D₇₁	—	2	1	no	—
255	C₂×D₇₁	—	2	1	no	—
256	C₂×D₇₁	—	2	1	no	—
257	C₂×D₇₁	—	4	4	no	—
258	C₂×D₇₁	#504	1	2	yes	—
259	C₄×C₇₁	—	2	1	no	—
260	C₄×C₇₁	—	2	1	no	—
261	C₄×C₇₁	—	2	1	no	—
262	C₄×C₇₁	#518	1	1	yes	characteristic
263	C₄×C₇₁	#568	1	1	yes	characteristic
264	Dic₇₁	—	2	1	no	—
265	Dic₇₁	—	2	1	no	—
266	Dic₇₁	—	2	1	no	—
267	Dic₇₁	—	2	1	no	—
268	Dic₇₁	—	2	1	no	—
269	Dic₇₁	—	2	1	no	—
270	#33490	—	71	1	no	maximal, Sylow
271	C₂×C₇₁	—	4	1	no	—
272	C₂×C₇₁	—	4	1	no	—
273	C₂×C₇₁	—	4	1	no	—
274	C₂×C₇₁	#2972	1	1	yes	characteristic
275	C₂×C₇₁	C₂×#504	1	1	yes	characteristic
276	C₂×C₇₁	#3407	1	1	yes	characteristic
277	D₇₁	—	2	2	no	—
278	D₇₁	—	4	1	no	—
279	#2929	—	71	1	no	—
280	#2169	—	71	1	no	—
281	#2169	—	71	1	no	—
282	#2168	—	71	1	no	—
283	#2168	—	71	1	no	—
284	#2168	—	71	1	no	—
285	#2168	—	71	1	no	—
286	D₄×C₁₆	—	71	1	no	—
287	D₄×C₁₆	—	71	1	no	—
288	#2164	—	71	1	no	—
289	#2164	—	71	1	no	—
290	#2113	—	71	1	no	—
291	#2113	D₇₁	1	1	yes	characteristic, complemented
292	#2112	—	71	1	no	—
293	C₂×C₂²⋊C₁₆	—	71	1	no	—
294	C₇₁	#33490	1	1	yes	characteristic, complemented, Sylow
295	C₂×#131	C₂×D₇₁	1	1	yes	characteristic
296	C₂³×C₈	—	71	1	no	—
297	#525	—	71	1	no	—
298	C₂×M₃₂	—	71	1	no	—
299	C₂×M₃₂	—	71	1	no	—
300	C₂×M₃₂	—	71	1	no	—
301	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic, complemented
302	C₂²×C₁₆	—	71	1	no	—
303	C₂²×C₁₆	—	71	1	no	—
304	C₂²×C₁₆	—	71	1	no	—
305	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
306	#435	—	71	1	no	—
307	#435	—	71	1	no	—
308	#435	—	71	1	no	—
309	#435	—	71	1	no	—
310	C₈×D₄	—	71	1	no	—
311	C₈×D₄	—	71	1	no	—
312	C₈×D₄	—	71	1	no	—
313	C₈×D₄	—	71	1	no	—
314	#424	—	71	1	no	—
315	#408	—	71	1	no	—
316	#407	—	71	1	no	—
317	#405	—	71	1	no	—
318	C₄⋊C₁₆	—	71	1	no	—
319	C₄⋊C₁₆	—	71	1	no	—
320	C₄⋊C₁₆	—	71	1	no	—
321	C₄⋊C₁₆	—	71	1	no	—
322	C₂²⋊C₁₆	—	71	1	no	—
323	C₂²⋊C₁₆	—	71	1	no	—
324	C₂²⋊C₁₆	—	71	1	no	—
325	C₂²⋊C₁₆	—	71	1	no	—
326	C₂²⋊C₁₆	—	71	1	no	—
327	C₂²⋊C₁₆	—	71	1	no	—
328	C₂²⋊C₁₆	—	71	1	no	—
329	C₂²⋊C₁₆	—	71	1	no	—
330	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
331	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
332	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
333	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
334	#346	—	71	1	no	—
335	#346	—	71	1	no	—
336	C₄×C₁₆	—	71	1	no	—
337	C₄×C₁₆	—	71	1	no	—
338	C₂×#41	C₄×D₇₁	1	1	yes	characteristic
339	C₂³×C₄	—	71	1	no	—
340	#131	—	4	1	no	—
341	#131	—	4	1	no	—
342	C₂×M₁₆	—	71	1	no	—
343	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
344	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
345	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
346	C₂²×C₈	—	284	1	no	—
347	C₂²×C₈	—	284	1	no	—
348	C₂²×C₈	—	71	1	no	—
349	C₂²×C₈	—	71	1	no	—
350	C₂²×C₈	—	71	1	no	—
351	C₂²×C₈	—	71	1	no	—
352	C₂²×C₈	—	71	1	no	—
353	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
356	#123	—	71	1	no	—
357	#123	—	71	1	no	—
358	C₂²⋊Q₈	—	71	1	no	—
359	C₂²⋊Q₈	—	71	1	no	—
360	#121	—	71	1	no	—
361	#121	—	71	1	no	—
362	#120	—	71	1	no	—
363	#120	—	71	1	no	—
364	C₄×D₄	—	71	1	no	—
365	C₄×D₄	—	71	1	no	—
366	C₄×D₄	—	71	1	no	—
367	C₄×D₄	—	71	1	no	—
368	#117	—	71	1	no	—
369	M₃₂	—	4	1	no	—
370	M₃₂	—	284	1	no	—
371	M₃₂	—	284	1	no	—
372	M₃₂	—	284	1	no	—
373	C₂×C₁₆	—	4	1	no	—
374	C₂×C₁₆	—	284	1	no	—
375	C₂×C₁₆	—	284	1	no	—
376	C₂×C₁₆	—	284	1	no	—
377	C₂×C₁₆	—	71	1	no	—
378	C₂×C₁₆	—	71	1	no	—
379	C₂×C₁₆	—	71	1	no	—
380	C₂×C₁₆	—	71	1	no	—
381	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
382	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
383	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
384	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
385	C₄⋊C₈	—	71	1	no	—
386	C₄⋊C₈	—	71	1	no	—
387	C₄⋊C₈	—	71	1	no	—
388	C₄⋊C₈	—	71	1	no	—
389	C₂²⋊C₈	—	71	1	no	—
390	C₂²⋊C₈	—	71	1	no	—
391	C₂²⋊C₈	—	71	1	no	—
392	C₂²⋊C₈	—	71	1	no	—
393	C₂²⋊C₈	—	71	1	no	—
394	C₂²⋊C₈	—	71	1	no	—
395	C₂²⋊C₈	—	71	1	no	—
396	C₂²⋊C₈	—	71	1	no	—
397	#97	—	71	1	no	—
398	#97	—	71	1	no	—
399	C₄×C₈	—	71	1	no	—
400	C₄×C₈	—	71	1	no	—
401	C₂⁴	—	71	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	C₂×Q₈	C₈×D₇₁	1	1	yes	characteristic
405	C₂×D₄	—	71	1	no	—
406	C₂×D₄	—	71	1	no	—
407	C₂×D₄	—	71	1	no	—
408	C₂×D₄	—	71	1	no	—
409	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
410	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
411	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
412	C₂²×C₄	—	284	1	no	—
413	C₂²×C₄	—	284	1	no	—
414	C₂²×C₄	—	71	1	no	—
415	C₂²×C₄	—	71	1	no	—
416	C₂²×C₄	—	71	1	no	—
417	C₂²×C₄	—	71	1	no	—
418	C₂²×C₄	—	71	1	no	—
419	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
422	M₁₆	—	4	1	no	—
423	M₁₆	—	4	1	no	—
424	M₁₆	—	4	1	no	—
425	M₁₆	—	284	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	284	1	no	—
433	C₂×C₈	—	284	1	no	—
434	C₂×C₈	—	284	1	no	—
435	C₂×C₈	—	71	1	no	—
436	C₂×C₈	—	71	1	no	—
437	C₂×C₈	—	71	1	no	—
438	C₂×C₈	—	71	1	no	—
439	C₂×C₈	—	142	1	no	—
440	C₂×C₈	—	142	1	no	—
441	C₂×C₈	—	142	1	no	—
442	C₂×C₈	—	142	1	no	—
443	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
445	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
446	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
447	C₄⋊C₄	—	71	1	no	—
448	C₄⋊C₄	—	71	1	no	—
449	C₄⋊C₄	—	71	1	no	—
450	C₄⋊C₄	—	71	1	no	—
451	C₄⋊C₄	—	71	1	no	—
452	C₄⋊C₄	—	71	1	no	—
453	C₂²⋊C₄	—	71	1	no	—
454	C₂²⋊C₄	—	71	1	no	—
455	C₂²⋊C₄	—	71	1	no	—
456	C₂²⋊C₄	—	71	1	no	—
457	C₂²⋊C₄	—	71	1	no	—
458	C₂²⋊C₄	—	71	1	no	—
459	C₂²⋊C₄	—	71	1	no	—
460	C₂²⋊C₄	—	71	1	no	—
461	C₂²⋊C₄	—	71	1	no	—
462	C₂²⋊C₄	—	71	1	no	—
463	C₄²	—	71	1	no	—
464	C₄²	—	71	1	no	—
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₁₆	—	2	1	no	—
468	C₁₆	—	2	1	no	—
469	C₁₆	—	142	1	no	—
470	C₁₆	—	142	1	no	—
471	C₁₆	—	142	1	no	—
472	C₁₆	—	142	1	no	—
473	C₂³	—	284	1	no	—
474	C₂³	—	284	1	no	—
475	C₂³	—	71	1	no	—
476	C₂³	—	71	1	no	—
477	C₂³	—	142	2	no	—
478	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
479	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
480	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
481	Q₈	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	284	1	no	—
486	D₄	—	284	1	no	—
487	D₄	—	142	2	no	—
488	D₄	—	142	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	284	1	no	—
496	C₂×C₄	—	284	1	no	—
497	C₂×C₄	—	284	1	no	—
498	C₂×C₄	—	71	1	no	—
499	C₂×C₄	—	71	1	no	—
500	C₂×C₄	—	71	1	no	—
501	C₂×C₄	—	71	1	no	—
502	C₂×C₄	—	71	1	no	—
503	C₂×C₄	—	71	1	no	—
504	C₂×C₄	—	142	1	no	—
505	C₂×C₄	—	142	1	no	—
506	C₂×C₄	—	142	1	no	—
507	C₂×C₄	—	142	1	no	—
508	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
509	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
510	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	142	1	no	—
516	C₈	—	142	1	no	—
517	C₈	—	142	1	no	—
518	C₈	—	142	1	no	—
519	C₈	#14556173	1	1	yes	characteristic
520	C₈	#14556173	1	1	yes	characteristic
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	284	4	no	—
531	C₂²	—	71	2	no	—
532	C₂²	—	142	1	no	—
533	C₂²	—	142	1	no	—
534	C₂²	—	142	1	no	—
535	C₂²	—	142	1	no	—
536	C₂²	—	142	1	no	—
537	C₂²	C₂²×C₈×D₇₁	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	142	1	no	—
542	C₄	—	142	1	no	—
543	C₄	—	142	1	no	—
544	C₄	—	142	1	no	—
545	C₄	—	142	1	no	—
546	C₄	—	142	1	no	—
547	C₄	#17986472	1	1	yes	characteristic
548	C₄	#17986765	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	4	1	no	—
552	C₂	—	284	1	no	—
553	C₂	—	142	2	no	—
554	C₂	#22597362	1	1	yes	characteristic
555	C₂	#504×D₇₁	1	1	yes	characteristic
556	C₂	#22601441	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₇₁×#2113	C₂
prime radical	#17986506	C₄
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2113	D₇₁
hypocenter	C₇₁	#33490
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
2. #22590170	C₂	semidirect
3. #22590169	C₂	semidirect
4. #22590168	C₂	semidirect
5. #22590165	C₂	semidirect
6. #22590163	C₂	semidirect
7. #22590162	C₂	semidirect
8. C₁₆×C₂²⋊D₇₁	C₂	semidirect
9. (C₂²⋊D₇₁)⋊C₁₆	C₂	semidirect
10. #22590144	C₂	semidirect
11. #22590144	C₂	semidirect
12. #22589954	C₂	semidirect
13. #22589949	C₂	semidirect
14. C₂²⋊C₁₆×D₇₁	C₂	semidirect
15. C₇₁×#2113	C₂	semidirect
18. C₂×#14556068	C₂²	semidirect
21. C₂²×C₇₁⋊C₁₆	C₂²	semidirect
36. Dic₇₁⋊C₁₆	C₂²	semidirect
37. Dic₇₁⋊C₁₆	C₂²	semidirect
38. Dic₇₁⋊C₁₆	C₂²	semidirect
39. Dic₇₁⋊C₁₆	C₂²	semidirect
42. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
43. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
48. #17985774	C₂²	semidirect
49. #17985774	C₂²	semidirect
50. C₁₆×Dic₇₁	C₂²	semidirect
51. C₁₆×Dic₇₁	C₂²	semidirect
53. C₂×M₃₂×C₇₁	C₂²	semidirect
54. C₂²×C₁₆×C₇₁	C₂²	semidirect
57. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
58. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
291. #2113	D₇₁	semidirect
294. C₇₁	#33490	semidirect
301. C₂×M₃₂	C₂×D₇₁	semidirect
305. C₂²×C₁₆	C₂×D₇₁	semidirect
332. C₂²⋊C₁₆	C₂×D₇₁	semidirect
333. C₂²⋊C₁₆	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22597032	2
#22590170	2
#22590169	2
#22590168	2
#22590165	2
#22590163	2
#22590162	2
C₁₆×C₂²⋊D₇₁	2
(C₂²⋊D₇₁)⋊C₁₆	2
#22590144	2
#22589954	2
#22589949	2
C₂²⋊C₁₆×D₇₁	2
C₇₁×#2113	2
#33490	71