Subgroups — #32150618

Order 18176.

710 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986415	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#22597029	C₂	1	1	yes	maximal, characteristic
4	#22590168	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590166	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590164	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×D₂₈₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×C₂²⋊D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₆×C₂²⋊D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#22590097	C₂	1	1	yes	maximal, characteristic, complemented
12	#22589952	C₂	1	1	yes	maximal, characteristic, complemented
13	#22589949	C₂	1	1	yes	maximal, characteristic, complemented
14	#22589935	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556134	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
18	#17986508	C₄	1	1	yes	characteristic
19	#17986415	—	2	4	no	—
20	C₂×#14556068	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14556067	C₂²	1	1	yes	characteristic
22	C₂×#14556067	C₂²	1	1	yes	characteristic
23	C₂×#14556067	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₇₁	—	2	4	no	—
26	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
29	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
30	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic, complemented
31	#17986073	C₄	1	1	yes	characteristic
32	#17986071	C₄	1	1	yes	characteristic
33	#17986069	C₄	1	1	yes	characteristic
34	#17986067	C₄	1	1	yes	characteristic
35	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
37	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
38	#17986024	C₄	1	1	yes	characteristic
39	#17985964	C₄	1	1	yes	characteristic
40	#17985961	C₄	1	1	yes	characteristic
41	#17985953	C₂²	1	1	yes	characteristic
42	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
43	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
44	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
48	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
49	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	#17985775	C₂²	1	1	yes	characteristic, complemented
52	#17985774	C₂²	1	1	yes	characteristic, complemented
53	C₁₆×Dic₇₁	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
55	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
56	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
57	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
59	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	C₂×#11765865	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
63	#14556134	—	2	2	no	—
64	#14556134	—	2	2	no	—
65	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
66	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
67	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
68	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₇₁	—	2	2	no	—
71	C₂×C₈×D₇₁	—	2	2	no	—
72	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
77	#14556113	C₈	1	1	yes	characteristic
78	#14556110	C₈	1	1	yes	characteristic
79	#14556106	C₈	1	1	yes	characteristic
80	#14556105	C₈	1	1	yes	characteristic
81	#14556101	C₈	1	1	yes	characteristic
82	#14556100	C₈	1	1	yes	characteristic
83	#14556098	C₈	1	1	yes	characteristic
84	#14556096	C₈	1	1	yes	characteristic
85	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
88	#14556085	C₂×C₄	1	1	yes	characteristic
89	#14556068	—	2	2	no	—
90	#14556067	—	2	2	no	—
91	#14556067	—	2	2	no	—
92	#14556067	—	2	2	no	—
93	C₂×C₇₁⋊C₁₆	—	2	2	no	—
94	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
98	C₁₆×D₇₁	—	2	2	no	—
99	C₁₆×D₇₁	—	2	2	no	—
100	C₁₆×D₇₁	—	2	2	no	—
101	C₁₆×D₇₁	—	2	2	no	—
102	C₁₆×D₇₁	D₄	1	4	yes	complemented
103	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
104	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
108	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
112	#14556039	C₂×C₄	1	1	yes	characteristic
113	#14556038	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
118	C₂×C₁₆×C₇₁	—	2	2	no	—
119	C₂×C₁₆×C₇₁	—	2	2	no	—
120	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
122	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
127	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
128	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
129	#11765865	—	2	2	no	—
130	#11765865	—	2	2	no	—
131	C₂×Dic₁₄₂	C₂×C₈	1	1	yes	characteristic
132	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
133	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
137	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
138	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₇₁	—	2	2	no	—
140	C₂×C₄×D₇₁	—	2	2	no	—
141	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
146	#11765849	—	2	2	no	—
147	#11765848	—	2	2	no	—
148	#11765848	—	2	2	no	—
149	#11765848	—	2	2	no	—
150	C₂×C₇₁⋊C₈	—	2	2	no	—
151	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₈×D₇₁	—	2	2	no	—
156	C₈×D₇₁	—	2	1	no	—
157	C₈×D₇₁	—	2	1	no	—
158	C₈×D₇₁	—	2	1	no	—
159	C₈×D₇₁	—	2	1	no	—
160	C₈×D₇₁	—	2	2	no	—
161	C₈×D₇₁	C₂×D₄	1	2	yes	—
162	C₈×D₇₁	#41	1	2	yes	—
163	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
164	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
165	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
166	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
167	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
168	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
170	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
171	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
172	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
173	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
174	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
175	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
177	C₇₁⋊C₁₆	—	2	1	no	—
178	C₇₁⋊C₁₆	—	2	1	no	—
179	C₇₁⋊C₁₆	—	2	1	no	—
180	C₇₁⋊C₁₆	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
182	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₇₁	—	2	1	no	—
185	C₂×C₈×C₇₁	—	2	1	no	—
186	C₂×C₈×C₇₁	—	2	1	no	—
187	C₂×C₈×C₇₁	—	2	1	no	—
188	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
193	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
194	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
195	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
196	C₁₆×C₇₁	—	2	1	no	—
197	C₁₆×C₇₁	—	2	1	no	—
198	C₁₆×C₇₁	—	2	1	no	—
199	C₁₆×C₇₁	C₂×D₄	1	2	yes	—
200	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
201	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
202	C₂²×D₇₁	—	2	2	no	—
203	C₂²×D₇₁	—	2	2	no	—
204	C₂²×D₇₁	—	2	2	no	—
205	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
206	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
207	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
208	D₄×C₇₁	—	2	2	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	—	2	1	no	—
213	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
215	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
216	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
217	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
218	C₂²⋊D₇₁	—	2	2	no	—
219	C₂²⋊D₇₁	—	2	2	no	—
220	C₂²⋊D₇₁	—	2	2	no	—
221	C₂²⋊D₇₁	—	2	2	no	—
222	C₂×Dic₇₁	—	2	2	no	—
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	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
228	D₂₈₄	—	2	2	no	—
229	D₂₈₄	—	2	2	no	—
230	C₄×D₇₁	—	2	2	no	—
231	C₄×D₇₁	—	2	1	no	—
232	C₄×D₇₁	—	2	1	no	—
233	C₄×D₇₁	—	2	1	no	—
234	C₄×D₇₁	—	2	1	no	—
235	C₄×D₇₁	—	2	2	no	—
236	C₄×D₇₁	C₄×D₄	1	2	yes	—
237	C₄×D₇₁	#131	1	2	yes	—
238	Dic₁₄₂	—	2	2	no	—
239	C₈×C₇₁	—	2	1	no	—
240	C₈×C₇₁	—	2	1	no	—
241	C₈×C₇₁	—	2	1	no	—
242	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
243	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
244	C₇₁⋊C₈	—	2	1	no	—
245	C₇₁⋊C₈	—	2	1	no	—
246	C₇₁⋊C₈	—	2	1	no	—
247	C₇₁⋊C₈	C₄×D₄	1	2	yes	—
248	C₂²×C₇₁	—	2	1	no	—
249	C₂²×C₇₁	—	2	1	no	—
250	C₂²×C₇₁	—	2	1	no	—
251	C₂²×C₇₁	—	2	1	no	—
252	C₂²×C₇₁	—	2	1	no	—
253	C₂²×C₇₁	#504	1	2	yes	complemented
254	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
255	C₂×D₇₁	—	2	8	no	—
256	C₂×D₇₁	—	2	1	no	—
257	C₂×D₇₁	—	2	1	no	—
258	C₂×D₇₁	—	2	1	no	—
259	C₂×D₇₁	—	2	1	no	—
260	C₂×D₇₁	—	2	1	no	—
261	C₂×D₇₁	—	2	1	no	—
262	C₂×D₇₁	—	2	1	no	—
263	C₂×D₇₁	C₈×D₄	1	2	yes	—
264	C₂×D₇₁	#504	1	2	yes	complemented
265	C₄×C₇₁	—	2	1	no	—
266	C₄×C₇₁	—	2	1	no	—
267	C₄×C₇₁	—	2	1	no	—
268	C₄×C₇₁	—	2	1	no	—
269	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
271	Dic₇₁	—	2	1	no	—
272	Dic₇₁	—	2	1	no	—
273	Dic₇₁	—	2	1	no	—
274	Dic₇₁	—	2	1	no	—
275	Dic₇₁	C₈×D₄	1	2	yes	—
276	#33432	—	71	1	no	maximal, Sylow
277	C₂×C₇₁	—	2	2	no	—
278	C₂×C₇₁	—	4	1	no	—
279	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
280	C₂×C₇₁	C₂×#504	1	1	yes	characteristic
281	C₂×C₇₁	C₂×#504	1	1	yes	characteristic
282	D₇₁	—	2	2	no	—
283	D₇₁	—	2	2	no	—
284	D₇₁	—	4	1	no	—
285	C₂×#504	—	71	1	no	—
286	C₂³×C₁₆	—	71	1	no	—
287	#2929	—	71	1	no	—
288	#2168	—	71	1	no	—
289	#2168	—	71	1	no	—
290	#2168	—	71	1	no	—
291	#2168	—	71	1	no	—
292	D₄×C₁₆	—	71	1	no	—
293	D₄×C₁₆	—	71	1	no	—
294	D₄×C₁₆	—	71	1	no	—
295	D₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
296	#2151	—	71	1	no	—
297	#2113	—	71	1	no	—
298	#2112	—	71	1	no	—
299	#2108	—	71	1	no	—
300	C₇₁	#33432	1	1	yes	characteristic, complemented, Sylow
301	C₂×#131	—	71	1	no	—
302	C₂³×C₈	—	71	1	no	—
303	#525	—	71	1	no	—
304	#504	—	142	4	no	—
305	C₂×M₃₂	—	71	1	no	—
306	C₂×M₃₂	—	71	1	no	—
307	C₂×M₃₂	—	71	1	no	—
308	C₂×M₃₂	—	71	1	no	—
309	C₂²×C₁₆	—	71	1	no	—
310	C₂²×C₁₆	—	71	1	no	—
311	C₂²×C₁₆	—	71	1	no	—
312	C₂²×C₁₆	—	71	1	no	—
313	C₂²×C₁₆	—	71	1	no	—
314	C₂²×C₁₆	—	71	1	no	—
315	C₂²×C₁₆	—	142	4	no	—
316	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
317	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
318	#435	—	71	1	no	—
319	#435	—	71	1	no	—
320	#435	—	71	1	no	—
321	#435	—	71	1	no	—
322	C₈×D₄	—	71	1	no	—
323	C₈×D₄	—	71	1	no	—
324	C₈×D₄	—	71	1	no	—
325	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
326	#424	—	71	1	no	—
327	#408	—	71	1	no	—
328	#407	—	71	1	no	—
329	#405	—	71	1	no	—
330	C₄⋊C₁₆	—	71	1	no	—
331	C₄⋊C₁₆	—	71	1	no	—
332	C₄⋊C₁₆	—	71	1	no	—
333	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
334	C₂²⋊C₁₆	—	71	1	no	—
335	C₂²⋊C₁₆	—	71	1	no	—
336	C₂²⋊C₁₆	—	71	1	no	—
337	C₂²⋊C₁₆	—	71	1	no	—
338	C₂²⋊C₁₆	—	71	1	no	—
339	C₂²⋊C₁₆	—	71	1	no	—
340	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
341	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
342	#346	—	71	1	no	—
343	#346	—	71	1	no	—
344	C₄×C₁₆	—	71	1	no	—
345	C₄×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
346	C₂×#41	—	71	1	no	—
347	C₂³×C₄	—	71	1	no	—
348	#131	—	142	2	no	—
349	#131	—	142	2	no	—
350	C₂×M₁₆	—	71	1	no	—
351	C₂×M₁₆	—	71	1	no	—
352	C₂×M₁₆	—	71	1	no	—
353	C₂×M₁₆	—	71	1	no	—
354	C₂²×C₈	—	71	1	no	—
355	C₂²×C₈	—	71	1	no	—
356	C₂²×C₈	—	71	1	no	—
357	C₂²×C₈	—	71	1	no	—
358	C₂²×C₈	—	71	1	no	—
359	C₂²×C₈	—	71	1	no	—
360	C₂²×C₈	—	142	2	no	—
361	C₂²×C₈	—	142	2	no	—
362	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
364	#123	—	71	1	no	—
365	#123	—	71	1	no	—
366	C₂²⋊Q₈	—	71	1	no	—
367	C₂²⋊Q₈	—	71	1	no	—
368	#121	—	71	1	no	—
369	#121	—	71	1	no	—
370	#120	—	71	1	no	—
371	#120	—	71	1	no	—
372	C₄×D₄	—	71	1	no	—
373	C₄×D₄	—	71	1	no	—
374	C₄×D₄	—	71	1	no	—
375	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
376	#117	—	71	1	no	—
377	M₃₂	—	142	2	no	—
378	M₃₂	—	142	2	no	—
379	M₃₂	—	142	2	no	—
380	M₃₂	—	142	2	no	—
381	C₂×C₁₆	—	2	2	no	—
382	C₂×C₁₆	—	2	2	no	—
383	C₂×C₁₆	—	71	1	no	—
384	C₂×C₁₆	—	71	4	no	—
385	C₂×C₁₆	—	71	1	no	—
386	C₂×C₁₆	—	71	1	no	—
387	C₂×C₁₆	—	71	1	no	—
388	C₂×C₁₆	—	142	2	no	—
389	C₂×C₁₆	—	142	2	no	—
390	C₂×C₁₆	—	142	2	no	—
391	C₂×C₁₆	—	142	2	no	—
392	C₂×C₁₆	—	142	2	no	—
393	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
394	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
395	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
396	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
397	C₄⋊C₈	—	71	1	no	—
398	C₄⋊C₈	—	71	1	no	—
399	C₄⋊C₈	—	71	1	no	—
400	C₄⋊C₈	C₄×D₇₁	1	1	yes	characteristic
401	C₂²⋊C₈	—	71	1	no	—
402	C₂²⋊C₈	—	71	1	no	—
403	C₂²⋊C₈	—	71	1	no	—
404	C₂²⋊C₈	—	71	1	no	—
405	C₂²⋊C₈	—	71	1	no	—
406	C₂²⋊C₈	—	71	1	no	—
407	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
408	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
409	#97	—	71	1	no	—
410	#97	—	71	1	no	—
411	C₄×C₈	—	71	1	no	—
412	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
413	C₂⁴	—	71	1	no	—
414	#41	—	142	2	no	—
415	#41	—	142	2	no	—
416	C₂×Q₈	—	71	1	no	—
417	C₂×D₄	—	71	1	no	—
418	C₂×D₄	—	71	1	no	—
419	C₂×D₄	—	71	1	no	—
420	C₂×D₄	—	71	1	no	—
421	C₂×D₄	—	71	1	no	—
422	C₂×D₄	—	71	1	no	—
423	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
424	C₂²×C₄	—	71	1	no	—
425	C₂²×C₄	—	71	1	no	—
426	C₂²×C₄	—	71	1	no	—
427	C₂²×C₄	—	71	1	no	—
428	C₂²×C₄	—	71	1	no	—
429	C₂²×C₄	—	71	1	no	—
430	C₂²×C₄	—	142	2	no	—
431	C₂²×C₄	—	142	2	no	—
432	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
434	M₁₆	—	142	2	no	—
435	M₁₆	—	142	2	no	—
436	M₁₆	—	142	2	no	—
437	M₁₆	—	142	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	71	1	no	—
443	C₂×C₈	—	71	2	no	—
444	C₂×C₈	—	71	2	no	—
445	C₂×C₈	—	71	1	no	—
446	C₂×C₈	—	71	1	no	—
447	C₂×C₈	—	71	1	no	—
448	C₂×C₈	—	142	2	no	—
449	C₂×C₈	—	142	2	no	—
450	C₂×C₈	—	142	2	no	—
451	C₂×C₈	—	142	1	no	—
452	C₂×C₈	—	142	1	no	—
453	C₂×C₈	—	142	1	no	—
454	C₂×C₈	—	142	1	no	—
455	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
457	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
458	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
459	C₄⋊C₄	—	71	1	no	—
460	C₄⋊C₄	—	71	1	no	—
461	C₄⋊C₄	—	71	1	no	—
462	C₄⋊C₄	—	71	1	no	—
463	C₄⋊C₄	—	71	1	no	—
464	C₄⋊C₄	C₈×D₇₁	1	1	yes	characteristic
465	C₂²⋊C₄	—	71	1	no	—
466	C₂²⋊C₄	—	71	1	no	—
467	C₂²⋊C₄	—	71	1	no	—
468	C₂²⋊C₄	—	71	1	no	—
469	C₂²⋊C₄	—	71	1	no	—
470	C₂²⋊C₄	—	71	1	no	—
471	C₂²⋊C₄	—	71	1	no	—
472	C₂²⋊C₄	—	71	1	no	—
473	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
474	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
475	C₄²	—	71	1	no	—
476	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
477	C₁₆	—	2	1	no	—
478	C₁₆	—	2	1	no	—
479	C₁₆	—	2	1	no	—
480	C₁₆	—	71	2	no	—
481	C₁₆	—	142	1	no	—
482	C₁₆	—	142	1	no	—
483	C₁₆	—	142	1	no	—
484	C₁₆	D₄×D₇₁	1	2	yes	—
485	C₂³	—	71	1	no	—
486	C₂³	—	71	1	no	—
487	C₂³	—	71	1	no	—
488	C₂³	—	142	2	no	—
489	C₂³	—	142	2	no	—
490	C₂³	—	142	2	no	—
491	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
492	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
493	Q₈	—	142	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	142	2	no	—
496	D₄	—	142	2	no	—
497	D₄	—	142	2	no	—
498	D₄	—	142	2	no	—
499	D₄	—	142	2	no	—
500	D₄	—	142	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	71	1	no	—
506	C₂×C₄	—	71	2	no	—
507	C₂×C₄	—	71	2	no	—
508	C₂×C₄	—	71	1	no	—
509	C₂×C₄	—	71	1	no	—
510	C₂×C₄	—	71	1	no	—
511	C₂×C₄	—	71	1	no	—
512	C₂×C₄	—	142	2	no	—
513	C₂×C₄	—	142	2	no	—
514	C₂×C₄	—	142	2	no	—
515	C₂×C₄	—	142	1	no	—
516	C₂×C₄	—	142	1	no	—
517	C₂×C₄	—	142	1	no	—
518	C₂×C₄	—	142	1	no	—
519	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
520	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
521	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
522	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	71	2	no	—
528	C₈	—	142	1	no	—
529	C₈	—	142	1	no	—
530	C₈	—	142	1	no	—
531	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
532	C₈	#41×D₇₁	1	1	yes	characteristic
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	71	2	no	—
539	C₂²	—	71	2	no	—
540	C₂²	—	142	8	no	—
541	C₂²	—	142	1	no	—
542	C₂²	—	142	1	no	—
543	C₂²	—	142	1	no	—
544	C₂²	—	142	1	no	—
545	C₂²	—	142	1	no	—
546	C₂²	—	142	1	no	—
547	C₂²	—	142	1	no	—
548	C₂²	#17986415	1	2	yes	complemented
549	C₂²	C₂²×C₈×D₇₁	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	71	2	no	—
555	C₄	—	142	1	no	—
556	C₄	—	142	1	no	—
557	C₄	—	142	1	no	—
558	C₄	—	142	1	no	—
559	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
560	C₄	#131×D₇₁	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	284	1	no	—
564	C₂	—	142	2	no	—
565	C₂	—	142	2	no	—
566	C₂	C₈×D₄×D₇₁	1	1	yes	characteristic
567	C₂	#504×D₇₁	1	1	yes	characteristic
568	C₂	C₂×#17986415	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	D₄×C₁₆×C₇₁	C₂
prime radical	#17986508	C₄
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	D₄×C₁₆	D₇₁
hypocenter	C₇₁	#33432
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₁₆ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#17986415	C₂	semidirect
2. C₂²×C₁₆×D₇₁	C₂	semidirect
4. #22590168	C₂	semidirect
5. #22590166	C₂	semidirect
6. #22590164	C₂	semidirect
7. #22590162	C₂	semidirect
8. C₁₆×D₂₈₄	C₂	semidirect
9. C₁₆×C₂²⋊D₇₁	C₂	semidirect
10. C₁₆×C₂²⋊D₇₁	C₂	semidirect
11. #22590097	C₂	semidirect
12. #22589952	C₂	semidirect
13. #22589949	C₂	semidirect
14. #22589935	C₂	semidirect
15. D₄×C₁₆×C₇₁	C₂	semidirect
20. C₂×#14556068	C₂²	semidirect
23. C₂×#14556067	C₂²	semidirect
30. C₂×C₁₆×D₇₁	C₂²	semidirect
42. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
43. Dic₇₁⋊C₁₆	C₂²	semidirect
44. Dic₇₁⋊C₁₆	C₂²	semidirect
46. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
49. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
50. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
51. #17985775	C₂²	semidirect
52. #17985774	C₂²	semidirect
53. C₁₆×Dic₇₁	C₂²	semidirect
55. C₂²×C₁₆×C₇₁	C₂²	semidirect
57. C₄⋊C₁₆×C₇₁	C₂²	semidirect
59. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
60. C₄×C₁₆×C₇₁	C₂²	semidirect
102. C₁₆×D₇₁	D₄	semidirect
253. C₂²×C₇₁	#504	semidirect
264. C₂×D₇₁	#504	semidirect
295. D₄×C₁₆	D₇₁	semidirect
300. C₇₁	#33432	semidirect
317. C₂²×C₁₆	C₂×D₇₁	semidirect
333. C₄⋊C₁₆	C₂×D₇₁	semidirect
341. C₂²⋊C₁₆	C₂×D₇₁	semidirect
345. C₄×C₁₆	C₂×D₇₁	semidirect
548. C₂²	#17986415	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986415	2
C₂²×C₁₆×D₇₁	2
#22597029	2
#22590168	2
#22590166	2
#22590164	2
#22590162	2
C₁₆×D₂₈₄	2
C₁₆×C₂²⋊D₇₁	2
#22590097	2
#22589952	2
#22589949	2
#22589935	2
D₄×C₁₆×C₇₁	2
#33432	71