Subgroups — C₇₁×#8849 #31829721

Order 18176.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#102×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#334×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×M₁₆×C₇₁	—	2	1	no	—
9	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
10	#436×C₇₁	—	2	2	no	—
11	#436×C₇₁	—	2	2	no	—
12	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
13	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×#102×C₇₁	C₄	1	1	yes	characteristic
16	C₂×#102×C₇₁	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
18	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
22	#340×C₇₁	C₄	1	1	yes	characteristic
23	#340×C₇₁	C₄	1	1	yes	characteristic
24	#336×C₇₁	—	2	1	no	—
25	#334×C₇₁	—	2	2	no	—
26	D₄⋊C₈×C₇₁	—	2	2	no	—
27	C₂²×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₇₁	—	2	1	no	—
29	C₂×M₁₆×C₇₁	—	2	4	no	—
30	C₂×M₁₆×C₇₁	—	4	2	no	—
31	C₂×M₁₆×C₇₁	—	4	2	no	—
32	C₂²×C₈×C₇₁	—	2	1	no	—
33	C₂²×C₈×C₇₁	—	2	1	no	—
34	C₂²×C₈×C₇₁	—	2	1	no	—
35	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
39	C₄×D₄×C₇₁	—	2	1	no	—
40	C₄×D₄×C₇₁	—	2	1	no	—
41	C₄×D₄×C₇₁	D₄	1	2	yes	—
42	C₄×D₄×C₇₁	Q₈	1	2	yes	—
43	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
47	C₂×C₄²×C₇₁	—	2	1	no	—
48	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
49	C₄⋊C₈×C₇₁	—	2	1	no	—
50	C₄⋊C₈×C₇₁	—	2	1	no	—
51	C₄⋊C₈×C₇₁	—	2	1	no	—
52	C₄⋊C₈×C₇₁	—	4	2	no	—
53	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
54	#102×C₇₁	—	2	2	no	—
55	#102×C₇₁	—	2	2	no	—
56	C₂²⋊C₈×C₇₁	—	2	4	no	—
57	C₄×C₈×C₇₁	—	2	1	no	—
58	C₄×C₈×C₇₁	—	2	1	no	—
59	C₄×C₈×C₇₁	—	2	1	no	—
60	C₄×C₈×C₇₁	—	2	1	no	—
61	C₄×C₈×C₇₁	—	2	1	no	—
62	C₄×C₈×C₇₁	—	2	1	no	—
63	#95×C₇₁	—	2	1	no	—
64	C₂⁴×C₇₁	—	2	1	no	—
65	C₂×D₄×C₇₁	—	2	1	no	—
66	C₂×D₄×C₇₁	—	2	1	no	—
67	C₂×D₄×C₇₁	—	2	1	no	—
68	C₂×D₄×C₇₁	—	2	1	no	—
69	C₂×D₄×C₇₁	—	2	1	no	—
70	C₂×D₄×C₇₁	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₇₁	—	2	1	no	—
72	C₂²×C₄×C₇₁	—	2	1	no	—
73	C₂²×C₄×C₇₁	—	2	2	no	—
74	C₂²×C₄×C₇₁	—	2	2	no	—
75	C₂²×C₄×C₇₁	—	2	1	no	—
76	C₂²×C₄×C₇₁	—	4	1	no	—
77	C₂²×C₄×C₇₁	—	4	1	no	—
78	C₂²×C₄×C₇₁	—	4	1	no	—
79	C₂²×C₄×C₇₁	—	4	1	no	—
80	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
83	M₁₆×C₇₁	—	4	8	no	—
84	C₂×C₈×C₇₁	—	2	1	no	—
85	C₂×C₈×C₇₁	—	2	1	no	—
86	C₂×C₈×C₇₁	—	2	1	no	—
87	C₂×C₈×C₇₁	—	2	1	no	—
88	C₂×C₈×C₇₁	—	2	2	no	—
89	C₂×C₈×C₇₁	—	2	1	no	—
90	C₂×C₈×C₇₁	—	2	1	no	—
91	C₂×C₈×C₇₁	—	2	2	no	—
92	C₂×C₈×C₇₁	—	2	1	no	—
93	C₂×C₈×C₇₁	—	2	1	no	—
94	C₂×C₈×C₇₁	—	2	1	no	—
95	C₂×C₈×C₇₁	—	2	1	no	—
96	C₂×C₈×C₇₁	—	4	1	no	—
97	C₂×C₈×C₇₁	—	4	1	no	—
98	C₂×C₈×C₇₁	—	4	1	no	—
99	C₂×C₈×C₇₁	—	4	1	no	—
100	C₂×C₈×C₇₁	—	4	1	no	—
101	C₂×C₈×C₇₁	—	4	1	no	—
102	C₂×C₈×C₇₁	—	4	1	no	—
103	C₂×C₈×C₇₁	M₁₆	1	2	yes	complemented
104	C₂×C₈×C₇₁	SD₁₆	1	2	yes	—
105	C₄⋊C₄×C₇₁	—	2	1	no	—
106	C₄⋊C₄×C₇₁	—	2	1	no	—
107	C₄⋊C₄×C₇₁	—	2	1	no	—
108	C₄⋊C₄×C₇₁	—	2	1	no	—
109	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
110	C₄⋊C₄×C₇₁	M₁₆	1	2	yes	complemented
111	C₂²⋊C₄×C₇₁	—	2	2	no	—
112	C₂²⋊C₄×C₇₁	—	2	2	no	—
113	C₄²×C₇₁	—	4	1	no	—
114	C₄²×C₇₁	—	4	1	no	—
115	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₇₁	#41	1	1	yes	characteristic
119	C₂³×C₇₁	—	2	2	no	—
120	C₂³×C₇₁	—	4	1	no	—
121	C₂³×C₇₁	—	4	1	no	—
122	C₂³×C₇₁	—	4	1	no	—
123	C₂³×C₇₁	—	4	1	no	—
124	C₂³×C₇₁	—	4	1	no	—
125	C₂³×C₇₁	—	4	1	no	—
126	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
127	D₄×C₇₁	—	2	2	no	—
128	D₄×C₇₁	—	2	2	no	—
129	D₄×C₇₁	—	4	1	no	—
130	D₄×C₇₁	—	4	1	no	—
131	C₂×C₄×C₇₁	—	2	1	no	—
132	C₂×C₄×C₇₁	—	2	1	no	—
133	C₂×C₄×C₇₁	—	2	2	no	—
134	C₂×C₄×C₇₁	—	2	2	no	—
135	C₂×C₄×C₇₁	—	4	1	no	—
136	C₂×C₄×C₇₁	—	4	1	no	—
137	C₂×C₄×C₇₁	—	4	1	no	—
138	C₂×C₄×C₇₁	—	4	1	no	—
139	C₂×C₄×C₇₁	—	4	2	no	—
140	C₂×C₄×C₇₁	—	4	2	no	—
141	C₂×C₄×C₇₁	—	4	2	no	—
142	C₂×C₄×C₇₁	—	4	2	no	—
143	C₂×C₄×C₇₁	—	4	1	no	—
144	C₂×C₄×C₇₁	—	4	1	no	—
145	C₂×C₄×C₇₁	—	4	1	no	—
146	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
156	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
158	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₈×C₇₁	—	2	2	no	—
161	C₈×C₇₁	—	2	2	no	—
162	C₈×C₇₁	—	4	2	no	—
163	C₈×C₇₁	—	4	1	no	—
164	C₈×C₇₁	—	4	1	no	—
165	C₈×C₇₁	—	4	2	no	—
166	C₈×C₇₁	—	8	1	no	—
167	C₂²×C₇₁	—	4	2	no	—
168	C₂²×C₇₁	—	4	2	no	—
169	C₂²×C₇₁	—	4	2	no	—
170	C₂²×C₇₁	—	8	1	no	—
171	C₂²×C₇₁	—	8	1	no	—
172	C₂²×C₇₁	—	8	1	no	—
173	C₂²×C₇₁	—	8	1	no	—
174	C₂²×C₇₁	#385	1	1	yes	characteristic
175	C₂²×C₇₁	#435	1	1	yes	characteristic
176	C₂²×C₇₁	#436	1	1	yes	characteristic
177	C₂²×C₇₁	C₄×SD₁₆	1	1	yes	characteristic
178	C₂²×C₇₁	#442	1	1	yes	characteristic
179	C₂²×C₇₁	#443	1	1	yes	characteristic
180	C₂²×C₇₁	#444	1	1	yes	characteristic
181	C₄×C₇₁	—	2	1	no	—
182	C₄×C₇₁	—	2	1	no	—
183	C₄×C₇₁	—	4	2	no	—
184	C₄×C₇₁	—	4	2	no	—
185	C₄×C₇₁	—	8	1	no	—
186	C₄×C₇₁	#423	1	1	yes	characteristic
187	C₄×C₇₁	#424	1	1	yes	characteristic
188	C₄×C₇₁	#435	1	1	yes	characteristic
189	C₄×C₇₁	#436	1	1	yes	characteristic
190	C₄×C₇₁	#449	1	1	yes	characteristic
191	C₄×C₇₁	#450	1	1	yes	characteristic
192	C₄×C₇₁	#476	1	1	yes	characteristic
193	C₄×C₇₁	#478	1	1	yes	characteristic
194	#8849	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₇₁	—	8	2	no	—
196	C₂×C₇₁	#1583	1	1	yes	characteristic
197	C₂×C₇₁	#1586	1	1	yes	characteristic
198	C₂×C₇₁	#1590	1	1	yes	characteristic
199	C₂×C₇₁	#1594	1	1	yes	characteristic
200	C₂×C₇₁	#1851	1	1	yes	characteristic
201	C₂×C₇₁	#1864	1	1	yes	characteristic
202	C₂×C₇₁	#1866	1	1	yes	characteristic
203	C₂×#436	C₂×C₇₁	1	1	yes	characteristic
204	#1939	C₂×C₇₁	1	1	yes	characteristic, complemented
205	C₄×#102	C₂×C₇₁	1	1	yes	characteristic
206	C₂×#334	C₂×C₇₁	1	1	yes	characteristic, complemented
207	C₂×D₄⋊C₈	C₂×C₇₁	1	1	yes	characteristic
208	#1279	C₂×C₇₁	1	1	yes	characteristic, complemented
209	#1273	C₂×C₇₁	1	1	yes	characteristic, complemented
210	C₇₁	#8849	1	1	yes	characteristic, direct product factor, Sylow
211	C₂²×M₁₆	—	2	1	no	—
212	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
213	#436	—	2	2	no	—
214	#436	—	2	2	no	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
218	C₂×#102	C₄×C₇₁	1	1	yes	characteristic
219	C₂×#102	C₄×C₇₁	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
224	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
225	#340	C₄×C₇₁	1	1	yes	characteristic
226	#340	C₄×C₇₁	1	1	yes	characteristic
227	#336	—	2	1	no	—
228	#334	—	2	2	no	—
229	D₄⋊C₈	—	2	2	no	—
230	C₂²×D₄	C₂×C₄×C₇₁	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	4	2	no	—
234	C₂×M₁₆	—	4	2	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	C₂×C₄×C₇₁	1	1	yes	characteristic
239	C₂²×C₈	C₂×C₄×C₇₁	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₇₁	1	1	yes	characteristic
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	D₄×C₇₁	1	2	yes	—
245	C₄×D₄	Q₈×C₇₁	1	2	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	4	2	no	—
256	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
257	#102	—	2	2	no	—
258	#102	—	2	2	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	2	1	no	—
265	C₄×C₈	—	2	1	no	—
266	#95	—	2	1	no	—
267	C₂⁴	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	C₄⋊C₄×C₇₁	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
285	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
286	M₁₆	—	4	8	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	M₁₆×C₇₁	1	2	yes	complemented
307	C₂×C₈	SD₁₆×C₇₁	1	2	yes	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	C₄⋊C₄×C₇₁	1	2	yes	—
313	C₄⋊C₄	M₁₆×C₇₁	1	2	yes	complemented
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₄²	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
320	C₄²	C₂×Q₈×C₇₁	1	1	yes	characteristic
321	C₄²	#41×C₇₁	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₄×D₄×C₇₁	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	2	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	C₂×C₄⋊C₄×C₇₁	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₇₁	1	1	yes	characteristic
351	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
352	C₂×C₄	C₂²⋊Q₈×C₇₁	1	1	yes	characteristic
353	C₂×C₄	C₂²⋊Q₈×C₇₁	1	1	yes	characteristic
354	C₂×C₄	#123×C₇₁	1	1	yes	characteristic
355	C₂×C₄	C₂×M₁₆×C₇₁	1	1	yes	characteristic
356	C₂×C₄	C₂×M₁₆×C₇₁	1	1	yes	characteristic
357	C₂×C₄	#131×C₇₁	1	1	yes	characteristic
358	C₂×C₄	#131×C₇₁	1	1	yes	characteristic
359	C₂×C₄	C₂×SD₁₆×C₇₁	1	1	yes	characteristic
360	C₂×C₄	#135×C₇₁	1	1	yes	characteristic
361	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
362	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	8	1	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	8	1	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	1	no	—
376	C₂²	—	8	1	no	—
377	C₂²	#385×C₇₁	1	1	yes	characteristic
378	C₂²	#435×C₇₁	1	1	yes	characteristic
379	C₂²	#436×C₇₁	1	1	yes	characteristic
380	C₂²	C₄×SD₁₆×C₇₁	1	1	yes	characteristic
381	C₂²	#442×C₇₁	1	1	yes	characteristic
382	C₂²	#443×C₇₁	1	1	yes	characteristic
383	C₂²	#444×C₇₁	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	1	no	—
389	C₄	#423×C₇₁	1	1	yes	characteristic
390	C₄	#424×C₇₁	1	1	yes	characteristic
391	C₄	#435×C₇₁	1	1	yes	characteristic
392	C₄	#436×C₇₁	1	1	yes	characteristic
393	C₄	#449×C₇₁	1	1	yes	characteristic
394	C₄	#450×C₇₁	1	1	yes	characteristic
395	C₄	#476×C₇₁	1	1	yes	characteristic
396	C₄	#478×C₇₁	1	1	yes	characteristic
397	C₂	—	8	2	no	—
398	C₂	C₇₁×#1583	1	1	yes	characteristic
399	C₂	C₇₁×#1586	1	1	yes	characteristic
400	C₂	C₇₁×#1590	1	1	yes	characteristic
401	C₂	C₇₁×#1594	1	1	yes	characteristic
402	C₂	C₇₁×#1851	1	1	yes	characteristic
403	C₂	C₇₁×#1864	1	1	yes	characteristic
404	C₂	C₇₁×#1866	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₇₁
Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
socle	C₂³×C₇₁	C₄×D₄
prime radical	C₂²×D₄×C₇₁	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ C₂×C₄×C₈×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₁×#1939	C₂	semidirect
4. C₂×#334×C₇₁	C₂	semidirect
6. C₇₁×#1279	C₂	semidirect
7. C₇₁×#1273	C₂	semidirect
103. C₂×C₈×C₇₁	M₁₆	semidirect
110. C₄⋊C₄×C₇₁	M₁₆	semidirect
194. #8849	C₇₁	direct (N × H)
204. #1939	C₂×C₇₁	semidirect
206. C₂×#334	C₂×C₇₁	semidirect
208. #1279	C₂×C₇₁	semidirect
209. #1273	C₂×C₇₁	semidirect
210. C₇₁	#8849	direct (N × H)
306. C₂×C₈	M₁₆×C₇₁	semidirect
313. C₄⋊C₄	M₁₆×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#436×C₇₁	2
C₇₁×#1939	2
C₄×#102×C₇₁	2
C₂×#334×C₇₁	2
C₂×D₄⋊C₈×C₇₁	2
C₇₁×#1279	2
C₇₁×#1273	2
#8849	71

Subgroups — C71×#8849 #31829721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#8849 #31829721