Subgroups — C₇₁×#23685 #31844557

Order 18176.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#441×C₇₁	C₂	1	2	yes	maximal
2	C₄×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#2295	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2084	C₂	1	1	yes	maximal, characteristic
5	C₇₁×#2072	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#2066	C₂	1	2	yes	maximal
7	C₇₁×#2056	C₂	1	2	yes	maximal
8	C₇₁×#2043	C₂	1	1	yes	maximal, characteristic
9	C₇₁×#2016	C₂	1	1	yes	maximal, characteristic
10	C₇₁×#1767	C₂	1	1	yes	maximal, characteristic
11	C₇₁×#1763	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₇₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
16	#441×C₇₁	—	2	8	no	—
17	C₂×#106×C₇₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
19	C₂×#103×C₇₁	C₂²	1	2	yes	—
20	C₂×#103×C₇₁	C₂²	1	2	yes	—
21	C₂×#103×C₇₁	C₂²	1	2	yes	—
22	C₂×#103×C₇₁	C₂²	1	2	yes	—
23	C₂×#97×C₇₁	C₂²	1	2	yes	—
24	#391×C₇₁	C₂²	1	1	yes	characteristic
25	#391×C₇₁	C₂²	1	1	yes	characteristic
26	#391×C₇₁	C₂²	1	2	yes	—
27	#389×C₇₁	—	2	1	no	—
28	#389×C₇₁	—	2	1	no	—
29	#389×C₇₁	C₂²	1	1	yes	characteristic
30	#389×C₇₁	C₂²	1	1	yes	characteristic
31	#387×C₇₁	—	2	1	no	—
32	#387×C₇₁	—	2	1	no	—
33	#384×C₇₁	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
38	#376×C₇₁	—	2	1	no	—
39	C₄³×C₇₁	C₂²	1	1	yes	characteristic
40	#340×C₇₁	C₂²	1	2	yes	—
41	#340×C₇₁	C₂²	1	2	yes	—
42	#336×C₇₁	C₂²	1	1	yes	characteristic
43	#336×C₇₁	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
46	C₂×Q₁₆×C₇₁	—	2	4	no	—
47	C₂×Q₁₆×C₇₁	—	2	4	no	—
48	C₂×Q₁₆×C₇₁	—	2	4	no	—
49	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₇₁	—	2	4	no	—
52	C₄×Q₈×C₇₁	—	2	2	no	—
53	C₄×Q₈×C₇₁	—	2	4	no	—
54	C₄×Q₈×C₇₁	—	2	4	no	—
55	C₄×Q₈×C₇₁	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₇₁	—	2	1	no	—
69	C₂×C₄²×C₇₁	—	2	2	no	—
70	C₂×C₄²×C₇₁	—	2	1	no	—
71	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
78	#106×C₇₁	—	2	4	no	—
79	C₄⋊C₈×C₇₁	—	2	4	no	—
80	#103×C₇₁	—	2	4	no	—
81	#103×C₇₁	—	2	4	no	—
82	#103×C₇₁	—	2	4	no	—
83	#103×C₇₁	—	2	4	no	—
84	#97×C₇₁	—	2	4	no	—
85	#95×C₇₁	—	2	1	no	—
86	#95×C₇₁	—	2	1	no	—
87	#95×C₇₁	—	2	1	no	—
88	#95×C₇₁	—	2	1	no	—
89	#95×C₇₁	—	2	1	no	—
90	#95×C₇₁	—	2	1	no	—
91	#95×C₇₁	—	2	2	no	—
92	#95×C₇₁	—	2	2	no	—
93	#95×C₇₁	—	2	1	no	—
94	C₂×Q₈×C₇₁	—	2	1	no	—
95	C₂×Q₈×C₇₁	—	2	2	no	—
96	C₂×Q₈×C₇₁	—	2	2	no	—
97	C₂×Q₈×C₇₁	—	2	2	no	—
98	C₂×Q₈×C₇₁	—	2	2	no	—
99	C₂×Q₈×C₇₁	—	2	2	no	—
100	C₂×Q₈×C₇₁	—	2	2	no	—
101	C₂×Q₈×C₇₁	—	2	2	no	—
102	C₂×Q₈×C₇₁	C₂×D₄	1	2	yes	—
103	C₂×Q₈×C₇₁	#41	1	4	yes	—
104	C₂²×C₄×C₇₁	—	2	1	no	—
105	C₂²×C₄×C₇₁	—	2	1	no	—
106	C₂²×C₄×C₇₁	—	2	2	no	—
107	C₂²×C₄×C₇₁	—	2	1	no	—
108	C₂²×C₄×C₇₁	—	2	1	no	—
109	C₂²×C₄×C₇₁	—	2	2	no	—
110	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₇₁	—	2	16	no	—
118	C₂×C₈×C₇₁	—	2	2	no	—
119	C₂×C₈×C₇₁	—	2	2	no	—
120	C₂×C₈×C₇₁	—	2	2	no	—
121	C₂×C₈×C₇₁	—	2	2	no	—
122	C₂×C₈×C₇₁	—	2	2	no	—
123	C₂×C₈×C₇₁	#41	1	4	yes	—
124	C₄⋊C₄×C₇₁	—	2	4	no	—
125	C₄⋊C₄×C₇₁	—	2	4	no	—
126	C₄⋊C₄×C₇₁	—	2	4	no	—
127	C₄⋊C₄×C₇₁	—	2	1	no	—
128	C₄⋊C₄×C₇₁	—	2	2	no	—
129	C₄⋊C₄×C₇₁	—	2	2	no	—
130	C₄⋊C₄×C₇₁	—	2	2	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	—	4	2	no	—
133	C₄⋊C₄×C₇₁	—	4	4	no	—
134	C₄⋊C₄×C₇₁	—	4	2	no	—
135	C₄⋊C₄×C₇₁	—	4	2	no	—
136	C₄⋊C₄×C₇₁	—	4	2	no	—
137	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
138	C₄²×C₇₁	—	2	4	no	—
139	C₄²×C₇₁	—	2	2	no	—
140	C₄²×C₇₁	—	2	2	no	—
141	C₄²×C₇₁	—	2	2	no	—
142	C₄²×C₇₁	—	2	2	no	—
143	C₄²×C₇₁	—	2	2	no	—
144	C₄²×C₇₁	—	4	1	no	—
145	C₄²×C₇₁	—	4	2	no	—
146	C₄²×C₇₁	—	4	4	no	—
147	C₄²×C₇₁	C₂×D₄	1	2	yes	—
148	C₄²×C₇₁	#41	1	2	yes	—
149	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₇₁	—	2	4	no	—
151	Q₈×C₇₁	—	2	4	no	—
152	Q₈×C₇₁	—	2	4	no	—
153	Q₈×C₇₁	—	4	2	no	—
154	Q₈×C₇₁	—	4	2	no	—
155	Q₈×C₇₁	—	4	2	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	2	1	no	—
158	C₂×C₄×C₇₁	—	2	1	no	—
159	C₂×C₄×C₇₁	—	2	1	no	—
160	C₂×C₄×C₇₁	—	2	1	no	—
161	C₂×C₄×C₇₁	—	2	1	no	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	2	1	no	—
164	C₂×C₄×C₇₁	—	2	1	no	—
165	C₂×C₄×C₇₁	—	2	1	no	—
166	C₂×C₄×C₇₁	—	2	2	no	—
167	C₂×C₄×C₇₁	—	2	2	no	—
168	C₂×C₄×C₇₁	—	2	4	no	—
169	C₂×C₄×C₇₁	—	2	1	no	—
170	C₂×C₄×C₇₁	—	2	1	no	—
171	C₂×C₄×C₇₁	—	2	1	no	—
172	C₂×C₄×C₇₁	—	4	2	no	—
173	C₂×C₄×C₇₁	—	4	1	no	—
174	C₂×C₄×C₇₁	—	4	1	no	—
175	C₂×C₄×C₇₁	—	4	2	no	—
176	C₂×C₄×C₇₁	—	4	1	no	—
177	C₂×C₄×C₇₁	—	4	1	no	—
178	C₂×C₄×C₇₁	—	4	2	no	—
179	C₂×C₄×C₇₁	—	4	1	no	—
180	C₂×C₄×C₇₁	—	4	1	no	—
181	C₂×C₄×C₇₁	—	4	1	no	—
182	C₂×C₄×C₇₁	—	4	1	no	—
183	C₂×C₄×C₇₁	—	4	2	no	—
184	C₂×C₄×C₇₁	—	4	1	no	—
185	C₂×C₄×C₇₁	—	4	1	no	—
186	C₂×C₄×C₇₁	—	4	2	no	—
187	C₂×C₄×C₇₁	#121	1	2	yes	—
188	C₂×C₄×C₇₁	#121	1	2	yes	—
189	C₂×C₄×C₇₁	#137	1	2	yes	—
190	C₂×C₄×C₇₁	#137	1	2	yes	—
191	C₂×C₄×C₇₁	#137	1	2	yes	—
192	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
194	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
196	C₈×C₇₁	—	2	4	no	—
197	C₈×C₇₁	—	4	2	no	—
198	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
199	C₂²×C₇₁	#525	1	1	yes	characteristic
200	C₂²×C₇₁	#532	1	1	yes	characteristic
201	C₂²×C₇₁	C₂×#137	1	1	yes	characteristic
202	C₂²×C₇₁	C₂×#137	1	1	yes	characteristic
203	C₂²×C₇₁	C₂×#137	1	1	yes	characteristic
204	C₂²×C₇₁	#575	1	1	yes	characteristic
205	C₄×C₇₁	—	2	2	no	—
206	C₄×C₇₁	—	2	2	no	—
207	C₄×C₇₁	—	2	2	no	—
208	C₄×C₇₁	—	2	2	no	—
209	C₄×C₇₁	—	2	2	no	—
210	C₄×C₇₁	—	4	2	no	—
211	C₄×C₇₁	—	4	4	no	—
212	C₄×C₇₁	—	4	1	no	—
213	C₄×C₇₁	—	4	2	no	—
214	C₄×C₇₁	—	8	1	no	—
215	C₄×C₇₁	—	8	1	no	—
216	C₄×C₇₁	—	8	2	no	—
217	C₄×C₇₁	#525	1	2	yes	—
218	C₄×C₇₁	#529	1	2	yes	—
219	#23685	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₇₁	#2392	1	1	yes	characteristic
221	C₂×C₇₁	#3037	1	1	yes	characteristic
222	C₂×C₇₁	#3039	1	1	yes	characteristic
223	C₂×C₇₁	#3113	1	1	yes	characteristic
224	C₂×C₇₁	#3117	1	1	yes	characteristic
225	C₂×C₇₁	#3181	1	1	yes	characteristic
226	C₂×C₇₁	#3185	1	1	yes	characteristic
227	C₂×#441	C₂×C₇₁	1	2	yes	—
228	C₄×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic
229	#2295	C₂×C₇₁	1	1	yes	characteristic
230	#2084	C₂×C₇₁	1	1	yes	characteristic
231	#2072	C₂×C₇₁	1	1	yes	characteristic
232	#2066	C₂×C₇₁	1	2	yes	—
233	#2056	C₂×C₇₁	1	2	yes	—
234	#2043	C₂×C₇₁	1	1	yes	characteristic
235	#2016	C₂×C₇₁	1	1	yes	characteristic
236	#1767	C₂×C₇₁	1	1	yes	characteristic
237	#1763	C₂×C₇₁	1	2	yes	—
238	C₇₁	#23685	1	1	yes	characteristic, direct product factor, Sylow
239	C₂²×Q₁₆	C₂²×C₇₁	1	2	yes	—
240	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
243	#441	—	2	8	no	—
244	C₂×#106	C₂²×C₇₁	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
246	C₂×#103	C₂²×C₇₁	1	2	yes	—
247	C₂×#103	C₂²×C₇₁	1	2	yes	—
248	C₂×#103	C₂²×C₇₁	1	2	yes	—
249	C₂×#103	C₂²×C₇₁	1	2	yes	—
250	C₂×#97	C₂²×C₇₁	1	2	yes	—
251	#391	C₂²×C₇₁	1	2	yes	—
252	#391	C₂²×C₇₁	1	1	yes	characteristic
253	#391	C₂²×C₇₁	1	1	yes	characteristic
254	#389	—	2	1	no	—
255	#389	—	2	1	no	—
256	#389	C₂²×C₇₁	1	1	yes	characteristic
257	#389	C₂²×C₇₁	1	1	yes	characteristic
258	#387	—	2	1	no	—
259	#387	—	2	1	no	—
260	#384	C₂²×C₇₁	1	1	yes	characteristic
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	—	2	1	no	—
263	C₄×C₄⋊C₄	—	2	1	no	—
264	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
265	#376	—	2	1	no	—
266	C₄³	C₂²×C₇₁	1	1	yes	characteristic
267	#340	C₂²×C₇₁	1	2	yes	—
268	#340	C₂²×C₇₁	1	2	yes	—
269	#336	C₂²×C₇₁	1	1	yes	characteristic
270	#336	C₂²×C₇₁	1	1	yes	characteristic
271	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	—	2	4	no	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
277	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	4	no	—
282	C₄×Q₈	D₄×C₇₁	1	4	yes	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
301	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
305	#106	—	2	4	no	—
306	C₄⋊C₈	—	2	4	no	—
307	#103	—	2	4	no	—
308	#103	—	2	4	no	—
309	#103	—	2	4	no	—
310	#103	—	2	4	no	—
311	#97	—	2	4	no	—
312	#95	—	2	1	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂×D₄×C₇₁	1	2	yes	—
330	C₂×Q₈	#41×C₇₁	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
344	Q₁₆	—	2	16	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	#41×C₇₁	1	4	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	1	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	4	no	—
374	C₄²	C₂×D₄×C₇₁	1	2	yes	—
375	C₄²	#41×C₇₁	1	2	yes	—
376	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	4	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	#121×C₇₁	1	2	yes	—
415	C₂×C₄	#121×C₇₁	1	2	yes	—
416	C₂×C₄	#137×C₇₁	1	2	yes	—
417	C₂×C₄	#137×C₇₁	1	2	yes	—
418	C₂×C₄	#137×C₇₁	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
421	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
422	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
426	C₂²	#525×C₇₁	1	1	yes	characteristic
427	C₂²	#532×C₇₁	1	1	yes	characteristic
428	C₂²	C₂×#137×C₇₁	1	1	yes	characteristic
429	C₂²	C₂×#137×C₇₁	1	1	yes	characteristic
430	C₂²	C₂×#137×C₇₁	1	1	yes	characteristic
431	C₂²	#575×C₇₁	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	2	no	—
444	C₄	#525×C₇₁	1	2	yes	—
445	C₄	#529×C₇₁	1	2	yes	—
446	C₂	C₇₁×#2392	1	1	yes	characteristic
447	C₂	C₇₁×#3037	1	1	yes	characteristic
448	C₂	C₇₁×#3039	1	1	yes	characteristic
449	C₂	C₇₁×#3113	1	1	yes	characteristic
450	C₂	C₇₁×#3117	1	1	yes	characteristic
451	C₂	C₇₁×#3181	1	1	yes	characteristic
452	C₂	C₇₁×#3185	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₄³×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
219. #23685	C₇₁	direct (N × H)
238. C₇₁	#23685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#441×C₇₁	2
C₄×C₄⋊Q₈×C₇₁	2
C₇₁×#2295	2
C₇₁×#2084	2
C₇₁×#2072	2
C₇₁×#2066	2
C₇₁×#2056	2
C₇₁×#2043	2
C₇₁×#2016	2
C₇₁×#1767	2
C₇₁×#1763	2
#23685	71

Subgroups — C71×#23685 #31844557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23685 #31844557