Subgroups — #31963080

Order 18176.

874 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22596973	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#22586633	C₂	1	2	yes	maximal, complemented
4	#22586630	C₂	1	2	yes	maximal, complemented
5	#22586627	C₂	1	2	yes	maximal, complemented
6	#22586624	C₂	1	2	yes	maximal, complemented
7	#22586621	C₂	1	2	yes	maximal, complemented
8	M₁₆×C₇₁⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₇₁×#2920	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₇₁⋊C₈	C₄	1	2	yes	—
11	#17986056	C₄	1	2	yes	—
12	#17986056	C₄	1	2	yes	—
13	#17986052	C₂²	1	2	yes	—
14	#17986052	C₂²	1	2	yes	—
15	#17986023	C₄	1	2	yes	—
16	#17985963	C₄	1	2	yes	—
17	C₄×#11765849	C₂²	1	2	yes	—
18	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
19	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
20	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
21	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
27	#17985721	C₂²	1	4	yes	complemented
28	#17985721	C₂²	1	4	yes	complemented
29	#17985720	C₂²	1	4	yes	complemented
30	C₈×C₇₁⋊C₈	C₂²	1	4	yes	complemented
31	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
32	#432×C₇₁	C₄	1	2	yes	—
33	#432×C₇₁	C₄	1	2	yes	—
34	#431×C₇₁	C₂²	1	2	yes	—
35	#431×C₇₁	C₂²	1	2	yes	—
36	#423×C₇₁	C₄	1	2	yes	—
37	#407×C₇₁	C₄	1	2	yes	—
38	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
39	C₂×#11765849	C₂×C₄	1	4	yes	—
40	C₂²×C₇₁⋊C₈	—	2	8	no	—
41	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
47	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
48	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
49	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
50	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
51	#14556039	C₂×C₄	1	4	yes	—
52	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
53	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
54	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
55	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
56	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
57	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
58	C₄×C₇₁⋊C₈	C₂³	1	4	yes	—
59	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
60	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
61	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₇₁	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
80	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
81	C₂²⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
82	C₂²⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
83	#97×C₇₁	C₂×C₄	1	4	yes	—
84	C₄×C₈×C₇₁	C₂³	1	4	yes	—
85	#11765849	—	2	8	no	—
86	C₂×C₇₁⋊C₈	—	2	4	no	—
87	C₂×C₇₁⋊C₈	—	2	4	no	—
88	C₂×C₇₁⋊C₈	—	2	4	no	—
89	C₂×C₇₁⋊C₈	—	2	4	no	—
90	C₂×C₇₁⋊C₈	—	2	4	no	—
91	C₂×C₇₁⋊C₈	M₁₆	1	8	yes	complemented
92	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
93	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
94	C₂×C₇₁⋊C₈	C₂²×C₄	1	8	yes	—
95	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
96	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₇₁	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	—	2	4	no	—
99	C₂²×C₄×C₇₁	—	2	4	no	—
100	C₂²×C₄×C₇₁	—	2	4	no	—
101	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
119	M₁₆×C₇₁	—	2	8	no	—
120	C₂×C₈×C₇₁	C₂²×C₄	1	8	yes	—
121	C₄²×C₇₁	C₄²	1	1	yes	characteristic
122	C₄²×C₇₁	C₄²	1	1	yes	characteristic
123	C₄²×C₇₁	C₄²	1	1	yes	characteristic
124	C₄²×C₇₁	C₄²	1	1	yes	characteristic
125	C₄²×C₇₁	C₄²	1	1	yes	characteristic
126	C₄²×C₇₁	C₄²	1	1	yes	characteristic
127	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
137	C₂³×C₇₁	—	2	2	no	—
138	C₂³×C₇₁	—	2	2	no	—
139	C₂³×C₇₁	—	2	2	no	—
140	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
141	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₇₁	—	2	2	no	—
144	C₂×C₄×C₇₁	—	2	2	no	—
145	C₂×C₄×C₇₁	—	2	2	no	—
146	C₂×C₄×C₇₁	—	2	2	no	—
147	C₂×C₄×C₇₁	—	2	2	no	—
148	C₂×C₄×C₇₁	—	2	2	no	—
149	C₂×C₄×C₇₁	—	2	2	no	—
150	C₂×C₄×C₇₁	—	2	2	no	—
151	C₂×C₄×C₇₁	—	2	2	no	—
152	C₂×C₄×C₇₁	—	2	2	no	—
153	C₂×C₄×C₇₁	—	2	2	no	—
154	C₂×C₄×C₇₁	—	2	2	no	—
155	C₂×C₄×C₇₁	—	2	2	no	—
156	C₂×C₄×C₇₁	—	2	2	no	—
157	C₂×C₄×C₇₁	—	2	2	no	—
158	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₇₁	C₂×M₁₆	1	4	yes	—
168	C₂×C₄×C₇₁	#131	1	4	yes	—
169	C₂×C₄×C₇₁	#131	1	4	yes	—
170	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₇₁	—	2	8	no	—
174	C₇₁⋊C₈	—	2	2	no	—
175	C₇₁⋊C₈	—	2	2	no	—
176	C₇₁⋊C₈	—	2	8	no	—
177	C₇₁⋊C₈	C₂×M₁₆	1	4	yes	—
178	C₇₁⋊C₈	C₂×M₁₆	1	4	yes	—
179	C₂²×C₇₁	—	2	8	no	—
180	C₂²×C₇₁	—	2	1	no	—
181	C₂²×C₇₁	—	2	1	no	—
182	C₂²×C₇₁	—	2	1	no	—
183	C₂²×C₇₁	—	2	1	no	—
184	C₂²×C₇₁	—	2	1	no	—
185	C₂²×C₇₁	—	2	1	no	—
186	C₂²×C₇₁	C₄×M₁₆	1	2	yes	—
187	C₂²×C₇₁	#405	1	2	yes	—
188	C₂²×C₇₁	#405	1	2	yes	—
189	C₂²×C₇₁	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₇₁	—	2	1	no	—
191	C₄×C₇₁	—	2	1	no	—
192	C₄×C₇₁	—	2	1	no	—
193	C₄×C₇₁	—	2	1	no	—
194	C₄×C₇₁	—	2	1	no	—
195	C₄×C₇₁	—	2	1	no	—
196	C₄×C₇₁	C₄×M₁₆	1	2	yes	—
197	C₄×C₇₁	#405	1	2	yes	—
198	C₄×C₇₁	#405	1	2	yes	—
199	C₄×C₇₁	C₂²×M₁₆	1	2	yes	—
200	C₄×C₇₁	C₂×#131	1	2	yes	—
201	C₄×C₇₁	C₂×#131	1	2	yes	—
202	#17323	—	71	1	no	maximal, Sylow
203	C₂×C₇₁	—	2	2	no	—
204	C₂×C₇₁	—	2	2	no	—
205	C₂×C₇₁	—	2	2	no	—
206	C₂×C₇₁	C₂×C₄×M₁₆	1	1	yes	characteristic
207	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
208	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
209	#2920	—	71	1	no	—
210	#2920	D₇₁	1	1	yes	characteristic
211	C₂²×C₄×C₈	—	71	1	no	—
212	#1452	—	71	2	no	—
213	#1451	—	71	2	no	—
214	#1451	—	71	2	no	—
215	#1450	—	71	2	no	—
216	C₈×M₁₆	—	71	2	no	—
217	C₈×M₁₆	—	71	2	no	—
218	C₇₁	#17323	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₈	—	71	2	no	—
220	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
221	#432	—	71	2	no	—
222	#432	—	71	2	no	—
223	#432	Dic₇₁	1	2	yes	—
224	#432	Dic₇₁	1	2	yes	—
225	#431	—	71	2	no	—
226	#431	—	71	2	no	—
227	#431	C₂×D₇₁	1	2	yes	—
228	#431	C₂×D₇₁	1	2	yes	—
229	#423	—	71	2	no	—
230	#423	Dic₇₁	1	2	yes	—
231	#407	—	71	2	no	—
232	#407	Dic₇₁	1	2	yes	—
233	C₄×M₁₆	—	71	2	no	—
234	C₄×M₁₆	C₂×D₇₁	1	2	yes	—
235	C₂×C₄×C₈	—	71	2	no	—
236	C₂×C₄×C₈	—	71	2	no	—
237	C₂×C₄×C₈	—	71	2	no	—
238	C₂×C₄×C₈	—	71	1	no	—
239	C₂×C₄×C₈	—	71	1	no	—
240	C₂×C₄×C₈	—	71	1	no	—
241	C₂×C₄×C₈	—	71	1	no	—
242	C₂×C₄×C₈	—	71	1	no	—
243	C₂×C₄×C₈	—	71	1	no	—
244	#322	—	71	4	no	—
245	#322	—	71	4	no	—
246	#322	—	71	4	no	—
247	C₈²	—	71	4	no	—
248	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
249	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
250	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
251	C₂×M₁₆	—	71	4	no	—
252	C₂×M₁₆	C₂×Dic₇₁	1	4	yes	—
253	C₂²×C₈	—	71	2	no	—
254	C₂²×C₈	—	71	2	no	—
255	C₂²×C₈	—	71	2	no	—
256	C₂²×C₈	—	71	2	no	—
257	C₂²×C₈	—	71	2	no	—
258	C₂²×C₈	—	71	2	no	—
259	C₂²×C₈	—	142	8	no	—
260	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
261	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
262	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
263	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
264	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
265	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
266	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
267	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
268	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
271	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
272	C₄⋊C₈	—	71	4	no	—
273	C₄⋊C₈	—	71	4	no	—
274	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	—
275	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	—
276	C₂²⋊C₈	—	71	4	no	—
277	C₂²⋊C₈	—	71	4	no	—
278	C₂²⋊C₈	C₂×Dic₇₁	1	4	yes	—
279	C₂²⋊C₈	C₂×Dic₇₁	1	4	yes	—
280	#97	—	71	4	no	—
281	#97	C₂×Dic₇₁	1	4	yes	—
282	C₄×C₈	—	71	2	no	—
283	C₄×C₈	—	71	2	no	—
284	C₄×C₈	—	71	2	no	—
285	C₄×C₈	—	71	2	no	—
286	C₄×C₈	—	71	2	no	—
287	C₄×C₈	—	71	2	no	—
288	C₄×C₈	—	71	1	no	—
289	C₄×C₈	—	71	4	no	—
290	C₄×C₈	—	71	1	no	—
291	C₄×C₈	—	71	1	no	—
292	C₄×C₈	—	71	1	no	—
293	C₄×C₈	C₂²×D₇₁	1	4	yes	—
294	C₂⁴	C₄×Dic₇₁	1	1	yes	characteristic
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
299	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
300	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
301	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
302	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
303	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
304	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
305	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
306	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
316	M₁₆	—	2	8	no	—
317	M₁₆	—	142	8	no	—
318	C₂×C₈	—	71	2	no	—
319	C₂×C₈	—	71	2	no	—
320	C₂×C₈	—	71	8	no	—
321	C₂×C₈	—	71	2	no	—
322	C₂×C₈	—	71	2	no	—
323	C₂×C₈	—	71	8	no	—
324	C₂×C₈	—	142	4	no	—
325	C₂×C₈	—	142	4	no	—
326	C₂×C₈	—	142	4	no	—
327	C₂×C₈	—	142	4	no	—
328	C₂×C₈	—	142	4	no	—
329	C₂×C₈	C₂²×Dic₇₁	1	8	yes	—
330	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
331	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
332	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
333	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
334	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
335	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
336	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
337	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
339	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
342	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
343	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
344	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
345	C₄²	C₂³×D₇₁	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
350	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
351	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
376	C₂×C₄	M₁₆×D₇₁	1	4	yes	—
377	C₂×C₄	#14556135	1	4	yes	—
378	C₂×C₄	#14556136	1	4	yes	—
379	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
381	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
382	C₈	—	2	8	no	—
383	C₈	—	71	4	no	—
384	C₈	—	71	4	no	—
385	C₈	—	142	2	no	—
386	C₈	—	142	2	no	—
387	C₈	—	142	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	M₁₆×Dic₇₁	1	2	yes	—
396	C₂²	#17985955	1	2	yes	—
397	C₂²	#17985957	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₇₁	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	M₁₆×Dic₇₁	1	2	yes	—
406	C₄	#17985955	1	2	yes	—
407	C₄	#17985957	1	2	yes	—
408	C₄	C₂×M₁₆×D₇₁	1	2	yes	—
409	C₄	C₂×#14556135	1	2	yes	—
410	C₄	C₂×#14556136	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	C₂×M₁₆×Dic₇₁	1	1	yes	characteristic
415	C₂	C₂×#17985955	1	1	yes	characteristic
416	C₂	C₂×#17985957	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂²×C₄²
Fitting	C₇₁×#2920	C₂
prime radical	C₂⁴×C₇₁	C₄²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#2920	D₇₁
hypocenter	C₇₁	#17323
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #22586633	C₂	semidirect
4. #22586630	C₂	semidirect
5. #22586627	C₂	semidirect
6. #22586624	C₂	semidirect
7. #22586621	C₂	semidirect
8. M₁₆×C₇₁⋊C₈	C₂	semidirect
27. #17985721	C₂²	semidirect
28. #17985721	C₂²	semidirect
29. #17985720	C₂²	semidirect
30. C₈×C₇₁⋊C₈	C₂²	semidirect
91. C₂×C₇₁⋊C₈	M₁₆	semidirect
218. C₇₁	#17323	semidirect

Maximal subgroups

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

subgroup	index
#22596973	2
C₂²×C₄×C₇₁⋊C₈	2
#22586633	2
#22586630	2
#22586627	2
#22586624	2
#22586621	2
M₁₆×C₇₁⋊C₈	2
C₇₁×#2920	2
#17323	71