Subgroups — #32151037

Order 18176.

618 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	C₈×D₄×D₇₁	C₂	1	1	yes	maximal, characteristic
2	#22590168	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590167	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590166	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590165	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590164	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590163	C₂	1	1	yes	maximal, characteristic, complemented
8	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590142	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590141	C₂	1	1	yes	maximal, characteristic, complemented
11	#22589950	C₂	1	1	yes	maximal, characteristic, complemented
12	#22589949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂×D₇₁)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₇₁	C₄	1	1	yes	characteristic
19	C₂×#14556068	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14556067	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14556067	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic, complemented
25	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
26	D₄×C₇₁⋊C₈	C₄	1	1	yes	characteristic
27	#17986064	C₄	1	1	yes	characteristic
28	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₇₁)⋊C₈	C₄	1	1	yes	characteristic
31	(C₂²⋊D₇₁)⋊C₈	C₄	1	1	yes	characteristic
32	C₄⋊C₈×D₇₁	C₄	1	1	yes	characteristic
33	C₂²⋊C₈×D₇₁	C₄	1	1	yes	characteristic
34	C₂²⋊C₈×D₇₁	C₄	1	1	yes	characteristic
35	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
36	C₄⋊(C₇₁⋊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	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
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	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
49	#17985775	C₂²	1	1	yes	characteristic, complemented
50	#17985774	C₂²	1	1	yes	characteristic, complemented
51	#17985774	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
54	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	#346×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×D₄×D₇₁	C₈	1	1	yes	characteristic
60	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₇₁	—	4	1	no	—
65	C₂×C₈×D₇₁	—	4	1	no	—
66	C₂×C₈×D₇₁	—	4	1	no	—
67	C₂×C₈×D₇₁	—	4	1	no	—
68	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
76	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
77	D₄×Dic₇₁	C₈	1	1	yes	characteristic
78	#14556090	C₈	1	1	yes	characteristic
79	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
81	(C₂²⋊D₇₁)⋊C₄	C₈	1	1	yes	characteristic
82	(C₂²⋊D₇₁)⋊C₄	C₈	1	1	yes	characteristic
83	C₄⋊C₄×D₇₁	C₈	1	1	yes	characteristic
84	C₂²⋊C₄×D₇₁	C₈	1	1	yes	characteristic
85	C₂²⋊C₄×D₇₁	C₈	1	1	yes	characteristic
86	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
87	#14556068	—	4	1	no	—
88	#14556067	—	4	1	no	—
89	#14556067	—	4	1	no	—
90	C₂×C₇₁⋊C₁₆	—	4	1	no	—
91	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
92	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
93	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
95	C₁₆×D₇₁	—	4	1	no	—
96	C₁₆×D₇₁	—	4	1	no	—
97	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
99	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
103	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
104	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
105	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
108	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
112	M₃₂×C₇₁	—	4	1	no	—
113	C₂×C₁₆×C₇₁	—	4	1	no	—
114	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
115	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
116	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
117	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
121	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
122	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
123	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
124	C₂×D₂₈₄	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	D₄×D₇₁	—	2	4	no	—
128	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
129	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
130	C₂×C₄×D₇₁	—	4	1	no	—
131	C₂×C₄×D₇₁	—	4	1	no	—
132	C₂×C₄×D₇₁	—	4	1	no	—
133	C₂×C₄×D₇₁	—	4	1	no	—
134	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
135	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₇₁⋊C₈	—	4	1	no	—
144	C₂×C₇₁⋊C₈	—	4	1	no	—
145	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₈×D₇₁	—	2	1	no	—
150	C₈×D₇₁	—	2	1	no	—
151	C₈×D₇₁	—	2	1	no	—
152	C₈×D₇₁	—	2	1	no	—
153	C₈×D₇₁	—	2	1	no	—
154	C₈×D₇₁	—	2	1	no	—
155	C₈×D₇₁	—	4	1	no	—
156	C₈×D₇₁	—	4	1	no	—
157	C₈×D₇₁	—	4	1	no	—
158	C₈×D₇₁	—	4	1	no	—
159	C₈×D₇₁	—	4	1	no	—
160	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
161	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
162	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
163	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
164	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
165	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
166	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
167	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
168	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
169	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
170	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
171	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₇₁⋊C₁₆	—	2	1	no	—
173	C₇₁⋊C₁₆	—	2	1	no	—
174	C₇₁⋊C₁₆	—	2	1	no	—
175	C₇₁⋊C₁₆	—	2	1	no	—
176	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
177	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₇₁	—	2	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	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
187	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
188	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
189	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
190	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₁₆×C₇₁	—	2	1	no	—
192	C₁₆×C₇₁	—	2	1	no	—
193	C₁₆×C₇₁	—	2	1	no	—
194	C₁₆×C₇₁	—	2	1	no	—
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	—	4	1	no	—
201	C₂²×D₇₁	—	4	1	no	—
202	C₂²×D₇₁	M₃₂	1	4	yes	complemented
203	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
204	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
205	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
206	D₄×C₇₁	—	2	2	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	C₂²×C₈	1	1	yes	characteristic
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	C₂×Dic₇₁	—	4	1	no	—
219	C₂×Dic₇₁	—	4	1	no	—
220	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
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	D₂₈₄	—	2	2	no	—
226	C₄×D₇₁	—	2	2	no	—
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	—	2	1	no	—
232	C₄×D₇₁	—	2	1	no	—
233	C₄×D₇₁	—	4	1	no	—
234	C₄×D₇₁	—	4	1	no	—
235	C₄×D₇₁	—	4	1	no	—
236	C₄×D₇₁	—	4	1	no	—
237	C₄×D₇₁	—	4	1	no	—
238	C₈×C₇₁	—	2	1	no	—
239	C₈×C₇₁	—	2	1	no	—
240	C₈×C₇₁	—	2	1	no	—
241	C₈×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
242	C₈×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
243	C₇₁⋊C₈	—	2	1	no	—
244	C₇₁⋊C₈	—	2	1	no	—
245	C₇₁⋊C₈	—	2	1	no	—
246	C₇₁⋊C₈	—	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	—	2	1	no	—
252	C₂²×C₇₁	C₂×M₃₂	1	2	yes	—
253	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
254	C₂×D₇₁	—	2	1	no	—
255	C₂×D₇₁	—	2	1	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	—	4	4	no	—
262	C₂×D₇₁	—	4	4	no	—
263	C₂×D₇₁	C₂×M₃₂	1	2	yes	—
264	C₂×D₇₁	C₂×M₃₂	1	2	yes	—
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	#518	1	1	yes	characteristic
270	C₄×C₇₁	#568	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	—	2	1	no	—
276	#33487	—	71	1	no	maximal, Sylow
277	C₂×C₇₁	—	2	2	no	—
278	C₂×C₇₁	—	4	1	no	—
279	C₂×C₇₁	#2972	1	1	yes	characteristic
280	C₂×C₇₁	C₂²×M₃₂	1	1	yes	characteristic
281	C₂×C₇₁	#3407	1	1	yes	characteristic
282	D₇₁	—	2	2	no	—
283	D₇₁	—	2	2	no	—
284	D₇₁	—	4	1	no	—
285	C₂×C₈×D₄	—	71	1	no	—
286	#2168	—	71	1	no	—
287	#2168	—	71	1	no	—
288	#2168	—	71	1	no	—
289	#2168	—	71	1	no	—
290	#2168	—	71	1	no	—
291	#2168	—	71	1	no	—
292	#2168	—	71	1	no	—
293	#2168	D₇₁	1	1	yes	characteristic, complemented
294	#2163	—	71	1	no	—
295	#2163	—	71	1	no	—
296	#2112	—	71	1	no	—
297	#2112	—	71	1	no	—
298	C₂×C₂²⋊C₁₆	—	71	1	no	—
299	C₂×C₂²⋊C₁₆	—	71	1	no	—
300	C₇₁	#33487	1	1	yes	characteristic, complemented, Sylow
301	C₂³×C₈	—	71	1	no	—
302	C₂³×C₈	—	71	1	no	—
303	C₂×C₄×D₄	—	71	1	no	—
304	C₂×M₃₂	—	71	1	no	—
305	C₂×M₃₂	—	71	1	no	—
306	C₂×M₃₂	—	71	1	no	—
307	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic, complemented
308	C₂²×C₁₆	—	71	1	no	—
309	C₂²×C₁₆	—	71	1	no	—
310	C₂²×C₁₆	—	71	1	no	—
311	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
312	C₈×D₄	—	71	1	no	—
313	C₈×D₄	—	71	1	no	—
314	C₈×D₄	—	71	1	no	—
315	C₈×D₄	—	71	1	no	—
316	C₈×D₄	—	71	1	no	—
317	C₈×D₄	—	71	1	no	—
318	C₈×D₄	—	71	1	no	—
319	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
320	C₂×C₄⋊C₈	—	71	1	no	—
321	C₂×C₂²⋊C₈	—	71	1	no	—
322	C₂×C₂²⋊C₈	—	71	1	no	—
323	C₂×C₄×C₈	—	71	1	no	—
324	C₄⋊C₁₆	—	71	1	no	—
325	C₄⋊C₁₆	—	71	1	no	—
326	C₄⋊C₁₆	—	71	1	no	—
327	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
328	C₂²⋊C₁₆	—	71	1	no	—
329	C₂²⋊C₁₆	—	71	1	no	—
330	C₂²⋊C₁₆	—	71	1	no	—
331	C₂²⋊C₁₆	—	71	1	no	—
332	C₂²⋊C₁₆	—	71	1	no	—
333	C₂²⋊C₁₆	—	71	1	no	—
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	C₂×D₇₁	1	1	yes	characteristic, complemented
339	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
340	#346	—	71	1	no	—
341	#346	—	71	1	no	—
342	#346	—	71	1	no	—
343	#346	C₂×D₇₁	1	1	yes	characteristic, complemented
344	C₂²×D₄	—	71	1	no	—
345	C₂³×C₄	—	71	1	no	—
346	C₂³×C₄	—	71	1	no	—
347	C₂²×C₈	—	284	1	no	—
348	C₂²×C₈	—	284	1	no	—
349	C₂²×C₈	—	284	1	no	—
350	C₂²×C₈	—	284	1	no	—
351	C₂²×C₈	—	71	1	no	—
352	C₂²×C₈	—	71	1	no	—
353	C₂²×C₈	—	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	—	71	1	no	—
361	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
362	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
363	C₄×D₄	—	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	C₄×D₄	—	71	1	no	—
369	C₄×D₄	—	71	1	no	—
370	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
371	C₂×C₄⋊C₄	—	71	1	no	—
372	C₂×C₂²⋊C₄	—	71	1	no	—
373	C₂×C₂²⋊C₄	—	71	1	no	—
374	C₂×C₄²	—	71	1	no	—
375	M₃₂	—	4	1	no	—
376	M₃₂	—	284	1	no	—
377	M₃₂	—	284	1	no	—
378	M₃₂	—	284	1	no	—
379	C₂×C₁₆	—	4	1	no	—
380	C₂×C₁₆	—	284	1	no	—
381	C₂×C₁₆	—	284	1	no	—
382	C₂×C₁₆	—	284	1	no	—
383	C₂×C₁₆	—	71	1	no	—
384	C₂×C₁₆	—	71	1	no	—
385	C₂×C₁₆	—	71	1	no	—
386	C₂×C₁₆	—	71	1	no	—
387	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
388	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
389	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
390	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
391	C₄⋊C₈	—	71	1	no	—
392	C₄⋊C₈	—	71	1	no	—
393	C₄⋊C₈	—	71	1	no	—
394	C₄⋊C₈	C₄×D₇₁	1	1	yes	characteristic
395	C₂²⋊C₈	—	71	1	no	—
396	C₂²⋊C₈	—	71	1	no	—
397	C₂²⋊C₈	—	71	1	no	—
398	C₂²⋊C₈	—	71	1	no	—
399	C₂²⋊C₈	—	71	1	no	—
400	C₂²⋊C₈	—	71	1	no	—
401	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
402	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
403	C₄×C₈	—	71	1	no	—
404	C₄×C₈	—	71	1	no	—
405	C₄×C₈	—	71	1	no	—
406	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
407	C₂⁴	—	71	1	no	—
408	C₂⁴	—	71	1	no	—
409	C₂×D₄	—	71	1	no	—
410	C₂×D₄	—	71	1	no	—
411	C₂×D₄	—	71	1	no	—
412	C₂×D₄	—	142	4	no	—
413	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
414	C₂²×C₄	—	284	1	no	—
415	C₂²×C₄	—	284	1	no	—
416	C₂²×C₄	—	284	1	no	—
417	C₂²×C₄	—	284	1	no	—
418	C₂²×C₄	—	71	1	no	—
419	C₂²×C₄	—	71	1	no	—
420	C₂²×C₄	—	71	1	no	—
421	C₂²×C₄	—	71	1	no	—
422	C₂²×C₄	—	71	1	no	—
423	C₂²×C₄	—	71	1	no	—
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	C₂×C₄×D₇₁	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	284	1	no	—
436	C₂×C₈	—	284	1	no	—
437	C₂×C₈	—	284	1	no	—
438	C₂×C₈	—	284	1	no	—
439	C₂×C₈	—	284	1	no	—
440	C₂×C₈	—	284	1	no	—
441	C₂×C₈	—	284	1	no	—
442	C₂×C₈	—	71	1	no	—
443	C₂×C₈	—	71	1	no	—
444	C₂×C₈	—	71	1	no	—
445	C₂×C₈	—	71	1	no	—
446	C₂×C₈	—	142	1	no	—
447	C₂×C₈	—	142	1	no	—
448	C₂×C₈	—	142	1	no	—
449	C₂×C₈	—	142	1	no	—
450	C₂×C₈	—	142	1	no	—
451	C₂×C₈	—	142	1	no	—
452	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
453	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
455	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
456	C₄⋊C₄	—	71	1	no	—
457	C₄⋊C₄	—	71	1	no	—
458	C₄⋊C₄	—	71	1	no	—
459	C₄⋊C₄	C₈×D₇₁	1	1	yes	characteristic
460	C₂²⋊C₄	—	71	1	no	—
461	C₂²⋊C₄	—	71	1	no	—
462	C₂²⋊C₄	—	71	1	no	—
463	C₂²⋊C₄	—	71	1	no	—
464	C₂²⋊C₄	—	71	1	no	—
465	C₂²⋊C₄	—	71	1	no	—
466	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
467	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
468	C₄²	—	71	1	no	—
469	C₄²	—	71	1	no	—
470	C₄²	—	71	1	no	—
471	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
472	C₁₆	—	2	1	no	—
473	C₁₆	—	2	1	no	—
474	C₁₆	—	2	1	no	—
475	C₁₆	—	2	1	no	—
476	C₁₆	—	142	1	no	—
477	C₁₆	—	142	1	no	—
478	C₁₆	—	142	1	no	—
479	C₁₆	—	142	1	no	—
480	C₂³	—	284	1	no	—
481	C₂³	—	284	1	no	—
482	C₂³	—	284	1	no	—
483	C₂³	—	284	1	no	—
484	C₂³	—	71	4	no	—
485	C₂³	—	71	1	no	—
486	C₂³	—	71	1	no	—
487	C₂³	—	71	1	no	—
488	C₂³	—	142	2	no	—
489	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
490	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
491	D₄	—	2	2	no	—
492	D₄	—	142	2	no	—
493	D₄	—	142	2	no	—
494	D₄	—	142	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	284	1	no	—
500	C₂×C₄	—	284	1	no	—
501	C₂×C₄	—	284	1	no	—
502	C₂×C₄	—	284	1	no	—
503	C₂×C₄	—	284	1	no	—
504	C₂×C₄	—	284	1	no	—
505	C₂×C₄	—	284	1	no	—
506	C₂×C₄	—	71	1	no	—
507	C₂×C₄	—	71	1	no	—
508	C₂×C₄	—	71	1	no	—
509	C₂×C₄	—	71	1	no	—
510	C₂×C₄	—	71	1	no	—
511	C₂×C₄	—	142	2	no	—
512	C₂×C₄	—	142	1	no	—
513	C₂×C₄	—	142	1	no	—
514	C₂×C₄	—	142	1	no	—
515	C₂×C₄	—	142	1	no	—
516	C₂×C₄	—	142	1	no	—
517	C₂×C₄	—	142	1	no	—
518	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
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	C₂²×C₄×D₇₁	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	142	1	no	—
527	C₈	—	142	1	no	—
528	C₈	—	142	1	no	—
529	C₈	—	142	1	no	—
530	C₈	#14556173	1	1	yes	characteristic
531	C₈	#14556174	1	1	yes	characteristic
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	284	4	no	—
538	C₂²	—	284	4	no	—
539	C₂²	—	71	2	no	—
540	C₂²	—	71	2	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	M₃₂×D₇₁	1	2	yes	—
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	—	142	1	no	—
555	C₄	—	142	1	no	—
556	C₄	—	142	1	no	—
557	C₄	—	142	1	no	—
558	C₄	—	142	1	no	—
559	C₄	#17986471	1	1	yes	characteristic
560	C₄	#17986764	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	#22597361	1	1	yes	characteristic
567	C₂	C₂×M₃₂×D₇₁	1	1	yes	characteristic
568	C₂	#22601441	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	C₂×D₄×D₇₁	C₈
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2168	D₇₁
hypocenter	C₇₁	#33487
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. #22590168	C₂	semidirect
3. #22590167	C₂	semidirect
4. #22590166	C₂	semidirect
5. #22590165	C₂	semidirect
6. #22590164	C₂	semidirect
7. #22590163	C₂	semidirect
8. #22590162	C₂	semidirect
9. #22590142	C₂	semidirect
10. #22590141	C₂	semidirect
11. #22589950	C₂	semidirect
12. #22589949	C₂	semidirect
13. C₂×(C₂×D₇₁)⋊C₁₆	C₂	semidirect
14. C₂²⋊C₁₆×D₇₁	C₂	semidirect
15. C₇₁×#2168	C₂	semidirect
19. C₂×#14556068	C₂²	semidirect
20. C₂×#14556067	C₂²	semidirect
21. C₂×#14556067	C₂²	semidirect
22. C₂²×C₇₁⋊C₁₆	C₂²	semidirect
23. C₂×C₁₆×D₇₁	C₂²	semidirect
24. C₂×C₁₆×D₇₁	C₂²	semidirect
36. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
37. Dic₇₁⋊C₁₆	C₂²	semidirect
38. Dic₇₁⋊C₁₆	C₂²	semidirect
39. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
40. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
45. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
46. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
47. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
48. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
49. #17985775	C₂²	semidirect
50. #17985774	C₂²	semidirect
51. #17985774	C₂²	semidirect
52. C₂×M₃₂×C₇₁	C₂²	semidirect
53. C₂²×C₁₆×C₇₁	C₂²	semidirect
55. C₄⋊C₁₆×C₇₁	C₂²	semidirect
56. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
57. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
58. #346×C₇₁	C₂²	semidirect
202. C₂²×D₇₁	M₃₂	semidirect
293. #2168	D₇₁	semidirect
300. C₇₁	#33487	semidirect
307. C₂×M₃₂	C₂×D₇₁	semidirect
311. C₂²×C₁₆	C₂×D₇₁	semidirect
327. C₄⋊C₁₆	C₂×D₇₁	semidirect
338. C₂²⋊C₁₆	C₂×D₇₁	semidirect
339. C₂²⋊C₁₆	C₂×D₇₁	semidirect
343. #346	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₇₁	2
#22590168	2
#22590167	2
#22590166	2
#22590165	2
#22590164	2
#22590163	2
#22590162	2
#22590142	2
#22590141	2
#22589950	2
#22589949	2
C₂×(C₂×D₇₁)⋊C₁₆	2
C₂²⋊C₁₆×D₇₁	2
C₇₁×#2168	2
#33487	71