Subgroups — C₇₁×#23698 #31844570

Order 18176.

894 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#431×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₇₁	C₂	1	2	yes	maximal
4	C₇₁×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2076	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#2068	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#2036	C₂	1	2	yes	maximal
9	C₇₁×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₇₁	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₇₁	—	2	4	no	—
17	#431×C₇₁	—	2	4	no	—
18	C₂×#107×C₇₁	C₂²	1	2	yes	—
19	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₇₁	C₂²	1	2	yes	—
23	C₂×#103×C₇₁	C₂²	1	2	yes	—
24	C₂×#103×C₇₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
29	#391×C₇₁	C₂²	1	2	yes	—
30	#389×C₇₁	C₂²	1	2	yes	—
31	#387×C₇₁	—	2	2	no	—
32	#385×C₇₁	—	2	2	no	—
33	#380×C₇₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₇₁	—	2	2	no	—
35	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₇₁	—	2	2	no	—
37	#340×C₇₁	C₂²	1	2	yes	—
38	#340×C₇₁	C₂²	1	2	yes	—
39	#340×C₇₁	C₂²	1	1	yes	characteristic
40	#340×C₇₁	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₇₁	—	2	4	no	—
46	C₂×Q₁₆×C₇₁	—	2	2	no	—
47	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
51	C₂²⋊Q₈×C₇₁	—	2	4	no	—
52	C₂²⋊Q₈×C₇₁	—	2	4	no	—
53	C₄×Q₈×C₇₁	—	2	4	no	—
54	C₄×Q₈×C₇₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
63	C₂×C₄²×C₇₁	—	2	2	no	—
64	C₂×C₄²×C₇₁	—	2	2	no	—
65	C₂×C₄²×C₇₁	—	2	2	no	—
66	C₂×C₄²×C₇₁	—	2	2	no	—
67	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
71	#107×C₇₁	—	2	2	no	—
72	#107×C₇₁	—	2	4	no	—
73	C₄⋊C₈×C₇₁	—	2	2	no	—
74	C₄⋊C₈×C₇₁	—	2	2	no	—
75	#103×C₇₁	—	2	4	no	—
76	#103×C₇₁	—	2	4	no	—
77	#103×C₇₁	—	2	4	no	—
78	C₂²⋊C₈×C₇₁	—	2	2	no	—
79	C₂²⋊C₈×C₇₁	—	2	2	no	—
80	C₄×C₈×C₇₁	—	2	2	no	—
81	C₄×C₈×C₇₁	D₄	1	4	yes	—
82	#95×C₇₁	—	2	2	no	—
83	#95×C₇₁	—	2	2	no	—
84	#95×C₇₁	—	2	2	no	—
85	#95×C₇₁	—	2	2	no	—
86	#95×C₇₁	—	2	2	no	—
87	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₇₁	—	2	2	no	—
89	C₂×Q₈×C₇₁	—	2	2	no	—
90	C₂×Q₈×C₇₁	—	2	2	no	—
91	C₂×Q₈×C₇₁	—	2	2	no	—
92	C₂×Q₈×C₇₁	—	2	2	no	—
93	C₂×Q₈×C₇₁	#41	1	4	yes	—
94	C₂²×C₄×C₇₁	—	2	2	no	—
95	C₂²×C₄×C₇₁	—	2	2	no	—
96	C₂²×C₄×C₇₁	—	2	2	no	—
97	C₂²×C₄×C₇₁	—	2	2	no	—
98	C₂²×C₄×C₇₁	—	2	2	no	—
99	C₂²×C₄×C₇₁	—	2	1	no	—
100	C₂²×C₄×C₇₁	—	2	1	no	—
101	C₂²×C₄×C₇₁	—	2	2	no	—
102	C₂²×C₄×C₇₁	—	2	2	no	—
103	C₂²×C₄×C₇₁	—	2	2	no	—
104	C₂²×C₄×C₇₁	—	2	2	no	—
105	C₂²×C₄×C₇₁	—	4	2	no	—
106	C₂²×C₄×C₇₁	Q₁₆	1	4	yes	complemented
107	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₇₁	—	2	8	no	—
114	C₂×C₈×C₇₁	—	2	2	no	—
115	C₂×C₈×C₇₁	—	2	2	no	—
116	C₂×C₈×C₇₁	—	2	1	no	—
117	C₂×C₈×C₇₁	—	2	1	no	—
118	C₂×C₈×C₇₁	—	2	2	no	—
119	C₂×C₈×C₇₁	—	2	2	no	—
120	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₇₁	—	2	8	no	—
123	C₄⋊C₄×C₇₁	—	2	2	no	—
124	C₄⋊C₄×C₇₁	—	2	2	no	—
125	C₄⋊C₄×C₇₁	—	2	2	no	—
126	C₄⋊C₄×C₇₁	—	2	2	no	—
127	C₄⋊C₄×C₇₁	—	2	2	no	—
128	C₄⋊C₄×C₇₁	—	4	4	no	—
129	C₄⋊C₄×C₇₁	—	4	4	no	—
130	C₄⋊C₄×C₇₁	#41	1	4	yes	—
131	C₂²⋊C₄×C₇₁	—	2	8	no	—
132	C₂²⋊C₄×C₇₁	—	4	4	no	—
133	C₄²×C₇₁	—	2	2	no	—
134	C₄²×C₇₁	—	2	2	no	—
135	C₄²×C₇₁	—	2	1	no	—
136	C₄²×C₇₁	—	2	1	no	—
137	C₄²×C₇₁	—	4	4	no	—
138	C₄²×C₇₁	—	4	4	no	—
139	C₄²×C₇₁	C₂×D₄	1	2	yes	—
140	C₄²×C₇₁	#41	1	2	yes	—
141	C₂³×C₇₁	—	2	1	no	—
142	C₂³×C₇₁	—	2	2	no	—
143	C₂³×C₇₁	—	2	1	no	—
144	C₂³×C₇₁	—	2	2	no	—
145	C₂³×C₇₁	C₂×Q₁₆	1	2	yes	—
146	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₇₁	—	2	4	no	—
148	Q₈×C₇₁	—	2	4	no	—
149	Q₈×C₇₁	—	4	2	no	—
150	Q₈×C₇₁	—	4	2	no	—
151	C₂×C₄×C₇₁	—	2	1	no	—
152	C₂×C₄×C₇₁	—	2	1	no	—
153	C₂×C₄×C₇₁	—	2	2	no	—
154	C₂×C₄×C₇₁	—	2	8	no	—
155	C₂×C₄×C₇₁	—	2	1	no	—
156	C₂×C₄×C₇₁	—	2	1	no	—
157	C₂×C₄×C₇₁	—	2	4	no	—
158	C₂×C₄×C₇₁	—	2	4	no	—
159	C₂×C₄×C₇₁	—	2	2	no	—
160	C₂×C₄×C₇₁	—	2	2	no	—
161	C₂×C₄×C₇₁	—	4	4	no	—
162	C₂×C₄×C₇₁	—	4	2	no	—
163	C₂×C₄×C₇₁	—	4	2	no	—
164	C₂×C₄×C₇₁	—	4	2	no	—
165	C₂×C₄×C₇₁	—	4	2	no	—
166	C₂×C₄×C₇₁	—	4	1	no	—
167	C₂×C₄×C₇₁	—	4	2	no	—
168	C₂×C₄×C₇₁	—	4	1	no	—
169	C₂×C₄×C₇₁	—	4	2	no	—
170	C₂×C₄×C₇₁	—	4	2	no	—
171	C₂×C₄×C₇₁	—	4	2	no	—
172	C₂×C₄×C₇₁	—	4	2	no	—
173	C₂×C₄×C₇₁	—	4	2	no	—
174	C₂×C₄×C₇₁	—	4	2	no	—
175	C₂×C₄×C₇₁	#121	1	2	yes	—
176	C₂×C₄×C₇₁	#121	1	2	yes	—
177	C₂×C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
178	C₂×C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
179	C₂×C₄×C₇₁	#135	1	2	yes	—
180	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
182	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
184	C₈×C₇₁	—	2	2	no	—
185	C₈×C₇₁	—	2	2	no	—
186	C₈×C₇₁	—	4	1	no	—
187	C₈×C₇₁	—	4	1	no	—
188	C₂²×C₇₁	—	2	4	no	—
189	C₂²×C₇₁	—	2	2	no	—
190	C₂²×C₇₁	—	4	2	no	—
191	C₂²×C₇₁	—	4	1	no	—
192	C₂²×C₇₁	—	4	1	no	—
193	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
194	C₂²×C₇₁	#525	1	2	yes	—
195	C₂²×C₇₁	C₂²×Q₁₆	1	1	yes	characteristic
196	C₂²×C₇₁	C₂×#135	1	1	yes	characteristic
197	C₂²×C₇₁	#575	1	2	yes	—
198	C₄×C₇₁	—	2	2	no	—
199	C₄×C₇₁	—	2	2	no	—
200	C₄×C₇₁	—	4	4	no	—
201	C₄×C₇₁	—	4	1	no	—
202	C₄×C₇₁	—	4	4	no	—
203	C₄×C₇₁	—	4	1	no	—
204	C₄×C₇₁	—	8	2	no	—
205	C₄×C₇₁	—	8	2	no	—
206	C₄×C₇₁	#467	1	4	yes	—
207	C₄×C₇₁	#525	1	1	yes	characteristic
208	C₄×C₇₁	#529	1	2	yes	—
209	C₄×C₇₁	#532	1	1	yes	characteristic
210	#23698	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₇₁	—	4	2	no	—
212	C₂×C₇₁	#2392	1	1	yes	characteristic
213	C₂×C₇₁	C₂×#467	1	1	yes	characteristic
214	C₂×C₇₁	#3054	1	1	yes	characteristic
215	C₂×C₇₁	#3102	1	2	yes	—
216	C₂×C₇₁	#3104	1	2	yes	—
217	C₂×C₄×Q₁₆	C₂×C₇₁	1	1	yes	characteristic, complemented
218	C₂×#431	C₂×C₇₁	1	1	yes	characteristic
219	C₄×C₂²⋊Q₈	C₂×C₇₁	1	2	yes	—
220	#2087	C₂×C₇₁	1	1	yes	characteristic, complemented
221	#2076	C₂×C₇₁	1	1	yes	characteristic
222	#2068	C₂×C₇₁	1	2	yes	complemented
223	#2056	C₂×C₇₁	1	1	yes	characteristic, complemented
224	#2036	C₂×C₇₁	1	2	yes	—
225	#2001	C₂×C₇₁	1	1	yes	characteristic
226	C₄×#107	C₂×C₇₁	1	1	yes	characteristic, complemented
227	C₄×#103	C₂×C₇₁	1	2	yes	complemented
228	C₇₁	#23698	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
232	C₂²×C₄²	C₂²×C₇₁	1	1	yes	characteristic
233	C₄×Q₁₆	—	2	4	no	—
234	#431	—	2	4	no	—
235	C₂×#107	C₂²×C₇₁	1	2	yes	—
236	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
239	C₂×#103	C₂²×C₇₁	1	2	yes	—
240	C₂×#103	C₂²×C₇₁	1	2	yes	—
241	C₂×#103	C₂²×C₇₁	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
246	#391	C₂²×C₇₁	1	2	yes	—
247	#389	C₂²×C₇₁	1	2	yes	—
248	#387	—	2	2	no	—
249	#385	—	2	2	no	—
250	#380	C₂²×C₇₁	1	2	yes	—
251	C₄×C₄⋊C₄	—	2	2	no	—
252	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
253	C₄×C₂²⋊C₄	—	2	2	no	—
254	#340	C₂²×C₇₁	1	1	yes	characteristic
255	#340	C₂²×C₇₁	1	2	yes	—
256	#340	C₂²×C₇₁	1	1	yes	characteristic
257	#340	C₂²×C₇₁	1	2	yes	—
258	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
259	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
260	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
262	C₂×Q₁₆	—	2	4	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
268	C₂²⋊Q₈	—	2	4	no	—
269	C₂²⋊Q₈	—	2	4	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#107	—	2	4	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#103	—	2	4	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	D₄×C₇₁	1	4	yes	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	#41×C₇₁	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	Q₁₆×C₇₁	1	4	yes	complemented
324	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
330	Q₁₆	—	2	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	#41×C₇₁	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	4	4	no	—
355	C₄²	—	4	4	no	—
356	C₄²	C₂×D₄×C₇₁	1	2	yes	—
357	C₄²	#41×C₇₁	1	2	yes	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	C₂×Q₁₆×C₇₁	1	2	yes	—
363	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	#121×C₇₁	1	2	yes	—
393	C₂×C₄	#121×C₇₁	1	2	yes	—
394	C₂×C₄	C₂×Q₁₆×C₇₁	1	2	yes	—
395	C₂×C₄	C₂×Q₁₆×C₇₁	1	2	yes	—
396	C₂×C₄	#135×C₇₁	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
399	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
400	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
411	C₂²	#525×C₇₁	1	2	yes	—
412	C₂²	C₂²×Q₁₆×C₇₁	1	1	yes	characteristic
413	C₂²	C₂×#135×C₇₁	1	1	yes	characteristic
414	C₂²	#575×C₇₁	1	2	yes	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	#467×C₇₁	1	4	yes	—
424	C₄	#525×C₇₁	1	1	yes	characteristic
425	C₄	#529×C₇₁	1	2	yes	—
426	C₄	#532×C₇₁	1	1	yes	characteristic
427	C₂	—	4	2	no	—
428	C₂	C₇₁×#2392	1	1	yes	characteristic
429	C₂	C₂×#467×C₇₁	1	1	yes	characteristic
430	C₂	C₇₁×#3054	1	1	yes	characteristic
431	C₂	C₇₁×#3102	1	2	yes	—
432	C₂	C₇₁×#3104	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
socle	C₂³×C₇₁	C₂²×D₄
prime radical	C₂⁴×C₇₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ C₂²×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Q₁₆×C₇₁	C₂	semidirect
4. C₇₁×#2087	C₂	semidirect
6. C₇₁×#2068	C₂	semidirect
7. C₇₁×#2056	C₂	semidirect
10. C₄×#107×C₇₁	C₂	semidirect
11. C₄×#103×C₇₁	C₂	semidirect
106. C₂²×C₄×C₇₁	Q₁₆	semidirect
210. #23698	C₇₁	direct (N × H)
217. C₂×C₄×Q₁₆	C₂×C₇₁	semidirect
220. #2087	C₂×C₇₁	semidirect
222. #2068	C₂×C₇₁	semidirect
223. #2056	C₂×C₇₁	semidirect
226. C₄×#107	C₂×C₇₁	semidirect
227. C₄×#103	C₂×C₇₁	semidirect
228. C₇₁	#23698	direct (N × H)
323. C₂²×C₄	Q₁₆×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₇₁	2
C₂×#431×C₇₁	2
C₄×C₂²⋊Q₈×C₇₁	2
C₇₁×#2087	2
C₇₁×#2076	2
C₇₁×#2068	2
C₇₁×#2056	2
C₇₁×#2036	2
C₇₁×#2001	2
C₄×#107×C₇₁	2
C₄×#103×C₇₁	2
#23698	71

Subgroups — C71×#23698 #31844570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23698 #31844570