Subgroups — C₂×C₇₁×#3195 #31881610

Order 18176.

2322 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₇₁	C₂	1	2	yes	maximal
2	C₇₁×#3195	C₂	1	16	yes	maximal, direct product factor
3	C₂×#483×C₇₁	C₂	1	4	yes	maximal, complemented
4	C₂×#470×C₇₁	C₂	1	4	yes	maximal, complemented
5	C₂×#451×C₇₁	C₂	1	4	yes	maximal, complemented
6	C₂×#407×C₇₁	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₇₁	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₇₁	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₇₁	C₂²	1	4	yes	complemented
10	C₂²×M₁₆×C₇₁	C₂²	1	2	yes	—
11	C₂×C₂²⋊Q₈×C₇₁	—	2	2	no	—
12	C₂×C₂²⋊Q₈×C₇₁	—	2	8	no	—
13	C₂×C₂²⋊Q₈×C₇₁	—	2	2	no	—
14	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	4	yes	—
15	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	16	yes	—
17	C₂²×C₄⋊C₄×C₇₁	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₇₁	—	2	2	no	—
20	#483×C₇₁	C₂²	1	32	yes	complemented
21	#470×C₇₁	C₂²	1	32	yes	complemented
22	#451×C₇₁	C₂²	1	32	yes	complemented
23	C₂×#106×C₇₁	C₂²	1	4	yes	complemented
24	C₂×#103×C₇₁	C₂²	1	8	yes	complemented
25	#407×C₇₁	C₂²	1	8	yes	—
26	C₂×C₂²⋊C₈×C₇₁	C₂²	1	4	yes	—
27	C₂⁵×C₇₁	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₇₁	—	2	4	no	—
29	C₂²×Q₈×C₇₁	—	2	2	no	—
30	C₂²×Q₈×C₇₁	—	4	8	no	—
31	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
32	C₂²×Q₈×C₇₁	C₂³	1	8	yes	—
33	C₂³×C₄×C₇₁	—	2	2	no	—
34	C₂³×C₄×C₇₁	—	2	2	no	—
35	C₂³×C₄×C₇₁	—	4	4	no	—
36	C₂³×C₄×C₇₁	D₄	1	2	yes	—
37	C₂³×C₄×C₇₁	D₄	1	4	yes	—
38	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₇₁	C₂³	1	4	yes	—
42	C₂×Q₁₆×C₇₁	—	4	8	no	—
43	C₂×Q₁₆×C₇₁	C₂³	1	16	yes	complemented
44	C₂×M₁₆×C₇₁	—	4	4	no	—
45	C₂×M₁₆×C₇₁	C₂³	1	8	yes	—
46	C₂²×C₈×C₇₁	C₂³	1	4	yes	—
47	C₂²⋊Q₈×C₇₁	—	2	8	no	—
48	C₂²⋊Q₈×C₇₁	—	2	8	no	—
49	C₂²⋊Q₈×C₇₁	—	2	16	no	—
50	C₂²⋊Q₈×C₇₁	—	2	16	no	—
51	C₂²⋊Q₈×C₇₁	C₂³	1	16	yes	—
52	C₂²⋊Q₈×C₇₁	C₂³	1	16	yes	—
53	C₂×C₄⋊C₄×C₇₁	—	2	16	no	—
54	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₇₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₇₁	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₇₁	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
63	#106×C₇₁	C₂³	1	16	yes	complemented
64	#103×C₇₁	C₂³	1	32	yes	complemented
65	C₂²⋊C₈×C₇₁	C₂³	1	16	yes	—
66	C₂⁴×C₇₁	—	2	8	no	—
67	C₂⁴×C₇₁	—	4	2	no	—
68	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
69	C₂⁴×C₇₁	C₂×D₄	1	4	yes	—
70	C₂⁴×C₇₁	C₂×D₄	1	2	yes	—
71	C₂×Q₈×C₇₁	—	2	8	no	—
72	C₂×Q₈×C₇₁	—	2	4	no	—
73	C₂×Q₈×C₇₁	—	2	16	no	—
74	C₂×Q₈×C₇₁	—	4	16	no	—
75	C₂×Q₈×C₇₁	—	4	8	no	—
76	C₂×Q₈×C₇₁	—	4	16	no	—
77	C₂×Q₈×C₇₁	C₂⁴	1	8	yes	—
78	C₂²×C₄×C₇₁	—	2	4	no	—
79	C₂²×C₄×C₇₁	—	2	8	no	—
80	C₂²×C₄×C₇₁	—	2	8	no	—
81	C₂²×C₄×C₇₁	—	2	8	no	—
82	C₂²×C₄×C₇₁	—	2	4	no	—
83	C₂²×C₄×C₇₁	—	2	4	no	—
84	C₂²×C₄×C₇₁	—	4	8	no	—
85	C₂²×C₄×C₇₁	—	4	8	no	—
86	C₂²×C₄×C₇₁	—	4	4	no	—
87	C₂²×C₄×C₇₁	—	4	2	no	—
88	C₂²×C₄×C₇₁	—	4	8	no	—
89	C₂²×C₄×C₇₁	—	4	8	no	—
90	C₂²×C₄×C₇₁	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₇₁	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₇₁	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₇₁	—	4	16	no	—
100	M₁₆×C₇₁	—	4	8	no	—
101	C₂×C₈×C₇₁	—	2	8	no	—
102	C₂×C₈×C₇₁	C₂⁴	1	8	yes	—
103	C₄⋊C₄×C₇₁	—	2	16	no	—
104	C₄⋊C₄×C₇₁	—	2	16	no	—
105	C₄⋊C₄×C₇₁	—	2	8	no	—
106	C₄⋊C₄×C₇₁	—	2	4	no	—
107	C₄⋊C₄×C₇₁	C₂⁴	1	8	yes	—
108	C₂²⋊C₄×C₇₁	—	2	16	no	—
109	C₂²⋊C₄×C₇₁	—	2	16	no	—
110	C₂³×C₇₁	—	2	4	no	—
111	C₂³×C₇₁	—	2	4	no	—
112	C₂³×C₇₁	—	2	2	no	—
113	C₂³×C₇₁	—	2	16	no	—
114	C₂³×C₇₁	—	2	4	no	—
115	C₂³×C₇₁	—	4	4	no	—
116	C₂³×C₇₁	—	4	16	no	—
117	C₂³×C₇₁	#137	1	8	yes	—
118	C₂³×C₇₁	C₂²×D₄	1	2	yes	—
119	C₂³×C₇₁	C₂²×D₄	1	4	yes	—
120	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
121	Q₈×C₇₁	—	2	16	no	—
122	Q₈×C₇₁	—	4	16	no	—
123	Q₈×C₇₁	—	4	8	no	—
124	C₂×C₄×C₇₁	—	2	2	no	—
125	C₂×C₄×C₇₁	—	2	4	no	—
126	C₂×C₄×C₇₁	—	2	4	no	—
127	C₂×C₄×C₇₁	—	2	8	no	—
128	C₂×C₄×C₇₁	—	2	4	no	—
129	C₂×C₄×C₇₁	—	2	8	no	—
130	C₂×C₄×C₇₁	—	2	8	no	—
131	C₂×C₄×C₇₁	—	2	8	no	—
132	C₂×C₄×C₇₁	—	4	8	no	—
133	C₂×C₄×C₇₁	—	4	4	no	—
134	C₂×C₄×C₇₁	—	4	16	no	—
135	C₂×C₄×C₇₁	—	4	8	no	—
136	C₂×C₄×C₇₁	—	4	16	no	—
137	C₂×C₄×C₇₁	—	4	8	no	—
138	C₂×C₄×C₇₁	C₂²×D₄	1	2	yes	—
139	C₂×C₄×C₇₁	C₂²×D₄	1	4	yes	—
140	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₇₁	H(5,𝔽₂)	1	4	yes	—
142	C₂×C₄×C₇₁	C₂⁵	1	1	yes	characteristic
143	C₈×C₇₁	—	2	8	no	—
144	C₂²×C₇₁	—	2	4	no	—
145	C₂²×C₇₁	—	2	16	no	—
146	C₂²×C₇₁	—	2	4	no	—
147	C₂²×C₇₁	—	2	2	no	—
148	C₂²×C₇₁	—	2	4	no	—
149	C₂²×C₇₁	—	4	16	no	—
150	C₂²×C₇₁	—	4	4	no	—
151	C₂²×C₇₁	#534	1	2	yes	—
152	C₂²×C₇₁	C₂×#137	1	8	yes	—
153	C₂²×C₇₁	C₂×#137	1	4	yes	—
154	C₂²×C₇₁	C₂³×D₄	1	1	yes	characteristic
155	C₄×C₇₁	—	2	2	no	—
156	C₄×C₇₁	—	2	4	no	—
157	C₄×C₇₁	—	4	8	no	—
158	C₄×C₇₁	—	4	8	no	—
159	C₄×C₇₁	#534	1	2	yes	—
160	C₄×C₇₁	C₂×H(5,𝔽₂)	1	2	yes	—
161	C₂×#3195	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂×C₇₁	—	2	8	no	—
163	C₂×C₇₁	—	4	2	no	—
164	C₂×C₇₁	#3195	1	4	yes	direct product factor
165	C₂×C₇₁	C₂×#534	1	1	yes	characteristic
166	C₂×C₇₁	C₂²×#137	1	2	yes	—
167	C₂²×C₂²⋊Q₈	C₂×C₇₁	1	2	yes	—
168	#3195	C₂×C₇₁	1	16	yes	direct product factor
169	C₂×#483	C₂×C₇₁	1	4	yes	complemented
170	C₂×#470	C₂×C₇₁	1	4	yes	complemented
171	C₂×#451	C₂×C₇₁	1	4	yes	complemented
172	C₂×#407	C₂×C₇₁	1	1	yes	characteristic
173	C₇₁	C₂×#3195	1	1	yes	characteristic, direct product factor, Sylow
174	C₂³×Q₈	C₂²×C₇₁	1	2	yes	—
175	C₂⁴×C₄	C₂²×C₇₁	1	1	yes	characteristic
176	C₂²×Q₁₆	C₂²×C₇₁	1	4	yes	complemented
177	C₂²×M₁₆	C₂²×C₇₁	1	2	yes	—
178	C₂×C₂²⋊Q₈	—	2	2	no	—
179	C₂×C₂²⋊Q₈	—	2	2	no	—
180	C₂×C₂²⋊Q₈	—	2	8	no	—
181	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	4	yes	—
182	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	16	yes	—
183	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	4	yes	—
184	C₂²×C₄⋊C₄	—	2	2	no	—
185	C₂²×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
186	C₂²×C₂²⋊C₄	—	2	2	no	—
187	#483	C₂²×C₇₁	1	32	yes	complemented
188	#470	C₂²×C₇₁	1	32	yes	complemented
189	#451	C₂²×C₇₁	1	32	yes	complemented
190	C₂×#106	C₂²×C₇₁	1	4	yes	complemented
191	C₂×#103	C₂²×C₇₁	1	8	yes	complemented
192	#407	C₂²×C₇₁	1	8	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₇₁	1	4	yes	—
194	C₂⁵	D₄×C₇₁	1	1	yes	characteristic
195	C₂²×Q₈	—	2	2	no	—
196	C₂²×Q₈	—	2	4	no	—
197	C₂²×Q₈	—	4	8	no	—
198	C₂²×Q₈	C₂³×C₇₁	1	4	yes	—
199	C₂²×Q₈	C₂³×C₇₁	1	8	yes	—
200	C₂³×C₄	—	2	2	no	—
201	C₂³×C₄	—	2	2	no	—
202	C₂³×C₄	—	4	4	no	—
203	C₂³×C₄	D₄×C₇₁	1	2	yes	—
204	C₂³×C₄	D₄×C₇₁	1	4	yes	—
205	C₂³×C₄	D₄×C₇₁	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
207	C₂³×C₄	C₂³×C₇₁	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₇₁	1	4	yes	—
209	C₂×Q₁₆	—	4	8	no	—
210	C₂×Q₁₆	C₂³×C₇₁	1	16	yes	complemented
211	C₂×M₁₆	—	4	4	no	—
212	C₂×M₁₆	C₂³×C₇₁	1	8	yes	—
213	C₂²×C₈	C₂³×C₇₁	1	4	yes	—
214	C₂²⋊Q₈	—	2	8	no	—
215	C₂²⋊Q₈	—	2	8	no	—
216	C₂²⋊Q₈	—	2	16	no	—
217	C₂²⋊Q₈	—	2	16	no	—
218	C₂²⋊Q₈	C₂³×C₇₁	1	16	yes	—
219	C₂²⋊Q₈	C₂³×C₇₁	1	16	yes	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	16	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
226	C₂×C₄⋊C₄	C₂³×C₇₁	1	8	yes	—
227	C₂×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₂²⋊C₄	—	2	16	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	#106	C₂³×C₇₁	1	16	yes	complemented
231	#103	C₂³×C₇₁	1	32	yes	complemented
232	C₂²⋊C₈	C₂³×C₇₁	1	16	yes	—
233	C₂⁴	—	2	8	no	—
234	C₂⁴	—	4	2	no	—
235	C₂⁴	C₂×D₄×C₇₁	1	1	yes	characteristic
236	C₂⁴	C₂×D₄×C₇₁	1	4	yes	—
237	C₂⁴	C₂×D₄×C₇₁	1	2	yes	—
238	C₂×Q₈	—	2	8	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	16	no	—
241	C₂×Q₈	—	4	16	no	—
242	C₂×Q₈	—	4	8	no	—
243	C₂×Q₈	—	4	16	no	—
244	C₂×Q₈	C₂⁴×C₇₁	1	8	yes	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	8	no	—
252	C₂²×C₄	—	4	8	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	8	no	—
256	C₂²×C₄	—	4	8	no	—
257	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₇₁	1	4	yes	—
260	C₂²×C₄	C₂×D₄×C₇₁	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₇₁	1	8	yes	—
262	C₂²×C₄	C₂×D₄×C₇₁	1	4	yes	—
263	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
265	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
266	Q₁₆	—	4	16	no	—
267	M₁₆	—	4	8	no	—
268	C₂×C₈	—	2	8	no	—
269	C₂×C₈	C₂⁴×C₇₁	1	8	yes	—
270	C₄⋊C₄	—	2	16	no	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	8	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	C₂⁴×C₇₁	1	8	yes	—
275	C₂²⋊C₄	—	2	16	no	—
276	C₂²⋊C₄	—	2	16	no	—
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	16	no	—
281	C₂³	—	2	4	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	4	16	no	—
284	C₂³	#137×C₇₁	1	8	yes	—
285	C₂³	C₂²×D₄×C₇₁	1	2	yes	—
286	C₂³	C₂²×D₄×C₇₁	1	4	yes	—
287	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
288	Q₈	—	2	16	no	—
289	Q₈	—	4	16	no	—
290	Q₈	—	4	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	8	no	—
301	C₂×C₄	—	4	16	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	C₂²×D₄×C₇₁	1	2	yes	—
306	C₂×C₄	C₂²×D₄×C₇₁	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
308	C₂×C₄	H(5,𝔽₂)×C₇₁	1	4	yes	—
309	C₂×C₄	C₂⁵×C₇₁	1	1	yes	characteristic
310	C₈	—	2	8	no	—
311	C₂²	—	2	4	no	—
312	C₂²	—	2	4	no	—
313	C₂²	—	2	16	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	16	no	—
317	C₂²	—	4	4	no	—
318	C₂²	#534×C₇₁	1	2	yes	—
319	C₂²	C₂×#137×C₇₁	1	8	yes	—
320	C₂²	C₂×#137×C₇₁	1	4	yes	—
321	C₂²	C₂³×D₄×C₇₁	1	1	yes	characteristic
322	C₄	—	2	4	no	—
323	C₄	—	2	2	no	—
324	C₄	—	4	8	no	—
325	C₄	—	4	8	no	—
326	C₄	#534×C₇₁	1	2	yes	—
327	C₄	C₂×H(5,𝔽₂)×C₇₁	1	2	yes	—
328	C₂	—	2	8	no	—
329	C₂	—	4	2	no	—
330	C₂	C₇₁×#3195	1	4	yes	direct product factor
331	C₂	C₂×#534×C₇₁	1	1	yes	characteristic
332	C₂	C₂²×#137×C₇₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₁
prime radical	C₂⁵×C₇₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂⁴×C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₁×#3195	C₂	direct (N × H)
3. C₂×#483×C₇₁	C₂	semidirect
4. C₂×#470×C₇₁	C₂	semidirect
5. C₂×#451×C₇₁	C₂	semidirect
9. C₂²×Q₁₆×C₇₁	C₂²	semidirect
20. #483×C₇₁	C₂²	semidirect
21. #470×C₇₁	C₂²	semidirect
22. #451×C₇₁	C₂²	semidirect
23. C₂×#106×C₇₁	C₂²	semidirect
24. C₂×#103×C₇₁	C₂²	semidirect
43. C₂×Q₁₆×C₇₁	C₂³	semidirect
63. #106×C₇₁	C₂³	semidirect
64. #103×C₇₁	C₂³	semidirect
161. C₂×#3195	C₇₁	direct (N × H)
164. C₂×C₇₁	#3195	direct (N × H)
168. #3195	C₂×C₇₁	direct (N × H)
169. C₂×#483	C₂×C₇₁	semidirect
170. C₂×#470	C₂×C₇₁	semidirect
171. C₂×#451	C₂×C₇₁	semidirect
173. C₇₁	C₂×#3195	direct (N × H)
176. C₂²×Q₁₆	C₂²×C₇₁	semidirect
187. #483	C₂²×C₇₁	semidirect
188. #470	C₂²×C₇₁	semidirect
189. #451	C₂²×C₇₁	semidirect
190. C₂×#106	C₂²×C₇₁	semidirect
191. C₂×#103	C₂²×C₇₁	semidirect
210. C₂×Q₁₆	C₂³×C₇₁	semidirect
230. #106	C₂³×C₇₁	semidirect
231. #103	C₂³×C₇₁	semidirect
330. C₂	C₇₁×#3195	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₇₁	2
C₇₁×#3195	2
C₂×#483×C₇₁	2
C₂×#470×C₇₁	2
C₂×#451×C₇₁	2
C₂×#407×C₇₁	2
C₂×#3195	71

Subgroups — C2×C71×#3195 #31881610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₁×#3195 #31881610