Subgroups — C₇₁×#23149 #31844021

Order 18176.

836 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₇₁	C₂	1	2	yes	maximal
2	C₄×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁×#1984	C₂	1	2	yes	maximal
4	C₇₁×#1939	C₂	1	2	yes	maximal
5	C₇₁×#1916	C₂	1	4	yes	maximal
6	C₈×C₄⋊C₄×C₇₁	C₂	1	2	yes	maximal
7	C₄×C₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
8	C₄×C₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄⋊Q₈×C₇₁	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
11	C₈×Q₈×C₇₁	—	2	8	no	—
12	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₇₁	C₂²	1	4	yes	—
15	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₁	C₂²	1	4	yes	—
20	#391×C₇₁	C₄	1	2	yes	—
21	#389×C₇₁	C₄	1	2	yes	—
22	#389×C₇₁	C₄	1	2	yes	—
23	#384×C₇₁	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
26	C₄³×C₇₁	C₂²	1	1	yes	characteristic
27	#336×C₇₁	C₂²	1	2	yes	—
28	#336×C₇₁	C₂²	1	2	yes	—
29	#336×C₇₁	C₂²	1	4	yes	—
30	#336×C₇₁	C₂²	1	4	yes	—
31	C₂²×Q₈×C₇₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
33	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
36	C₄⋊Q₈×C₇₁	C₈	1	8	yes	complemented
37	C₄×Q₈×C₇₁	—	2	4	no	—
38	C₄×Q₈×C₇₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
50	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
53	C₄⋊C₈×C₇₁	—	2	8	no	—
54	C₄⋊C₈×C₇₁	—	2	2	no	—
55	C₄⋊C₈×C₇₁	—	2	2	no	—
56	C₄⋊C₈×C₇₁	D₄	1	4	yes	—
57	C₄⋊C₈×C₇₁	Q₈	1	4	yes	complemented
58	C₄×C₈×C₇₁	—	2	8	no	—
59	C₄×C₈×C₇₁	—	2	4	no	—
60	C₄×C₈×C₇₁	—	2	4	no	—
61	#95×C₇₁	C₂×C₄	1	4	yes	—
62	#95×C₇₁	C₂×C₄	1	4	yes	—
63	C₂×Q₈×C₇₁	—	2	4	no	—
64	C₂×Q₈×C₇₁	—	2	4	no	—
65	C₂×Q₈×C₇₁	C₂×C₈	1	8	yes	—
66	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₇₁	C₂²×C₄	1	4	yes	—
68	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₁	C₂²×C₄	1	4	yes	—
71	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
75	C₂×C₈×C₇₁	—	2	2	no	—
76	C₂×C₈×C₇₁	—	2	2	no	—
77	C₂×C₈×C₇₁	—	2	2	no	—
78	C₂×C₈×C₇₁	—	2	2	no	—
79	C₂×C₈×C₇₁	—	2	2	no	—
80	C₂×C₈×C₇₁	—	2	2	no	—
81	C₂×C₈×C₇₁	—	2	2	no	—
82	C₂×C₈×C₇₁	—	2	2	no	—
83	C₂×C₈×C₇₁	—	2	2	no	—
84	C₂×C₈×C₇₁	—	2	2	no	—
85	C₂×C₈×C₇₁	C₂×D₄	1	4	yes	—
86	C₂×C₈×C₇₁	C₂×Q₈	1	4	yes	—
87	C₄⋊C₄×C₇₁	—	2	8	no	—
88	C₄⋊C₄×C₇₁	—	2	4	no	—
89	C₄⋊C₄×C₇₁	—	2	4	no	—
90	C₄⋊C₄×C₇₁	—	4	2	no	—
91	C₄⋊C₄×C₇₁	C₂×C₈	1	8	yes	—
92	C₄⋊C₄×C₇₁	C₂×C₈	1	8	yes	—
93	C₄²×C₇₁	—	2	2	no	—
94	C₄²×C₇₁	—	2	2	no	—
95	C₄²×C₇₁	—	2	4	no	—
96	C₄²×C₇₁	—	2	4	no	—
97	C₄²×C₇₁	—	2	1	no	—
98	C₄²×C₇₁	—	2	1	no	—
99	C₄²×C₇₁	—	4	1	no	—
100	C₄²×C₇₁	C₂×C₈	1	4	yes	—
101	C₄²×C₇₁	C₂×D₄	1	2	yes	—
102	C₄²×C₇₁	C₂×Q₈	1	2	yes	—
103	C₄²×C₇₁	#41	1	2	yes	—
104	C₄²×C₇₁	#41	1	2	yes	—
105	C₂³×C₇₁	C₂³×C₄	1	1	yes	characteristic
106	Q₈×C₇₁	—	2	16	no	—
107	C₂×C₄×C₇₁	—	2	4	no	—
108	C₂×C₄×C₇₁	—	2	1	no	—
109	C₂×C₄×C₇₁	—	2	1	no	—
110	C₂×C₄×C₇₁	—	2	1	no	—
111	C₂×C₄×C₇₁	—	2	4	no	—
112	C₂×C₄×C₇₁	—	2	1	no	—
113	C₂×C₄×C₇₁	—	2	1	no	—
114	C₂×C₄×C₇₁	—	2	1	no	—
115	C₂×C₄×C₇₁	—	2	4	no	—
116	C₂×C₄×C₇₁	—	2	1	no	—
117	C₂×C₄×C₇₁	—	2	1	no	—
118	C₂×C₄×C₇₁	—	2	1	no	—
119	C₂×C₄×C₇₁	—	2	4	no	—
120	C₂×C₄×C₇₁	—	2	4	no	—
121	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₇₁	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₇₁	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
126	C₂×C₄×C₇₁	C₂²×C₈	1	8	yes	—
127	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
128	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₇₁	#131	1	2	yes	—
130	C₂×C₄×C₇₁	#131	1	2	yes	—
131	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
135	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
136	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
137	C₈×C₇₁	—	2	4	no	—
138	C₈×C₇₁	—	2	4	no	—
139	C₈×C₇₁	—	4	2	no	—
140	C₈×C₇₁	—	4	2	no	—
141	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
142	C₂²×C₇₁	C₂×C₄×Q₈	1	1	yes	characteristic
143	C₂²×C₇₁	#519	1	1	yes	characteristic
144	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
145	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
146	C₂²×C₇₁	C₂×#131	1	1	yes	characteristic
147	C₂²×C₇₁	#568	1	1	yes	characteristic
148	C₄×C₇₁	—	2	8	no	—
149	C₄×C₇₁	—	2	2	no	—
150	C₄×C₇₁	—	2	2	no	—
151	C₄×C₇₁	—	2	2	no	—
152	C₄×C₇₁	—	4	4	no	—
153	C₄×C₇₁	—	4	1	no	—
154	C₄×C₇₁	C₈×D₄	1	4	yes	—
155	C₄×C₇₁	C₈×Q₈	1	4	yes	complemented
156	C₄×C₇₁	#547	1	1	yes	characteristic
157	C₄×C₇₁	D₄×Q₈	1	1	yes	characteristic
158	C₄×C₇₁	#556	1	1	yes	characteristic
159	C₄×C₇₁	#557	1	1	yes	characteristic
160	#23149	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂×C₇₁	#2365	1	1	yes	characteristic
162	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
163	C₂×C₇₁	#2935	1	1	yes	characteristic
164	C₂×C₇₁	C₂×C₈×Q₈	1	1	yes	characteristic
165	C₂×C₇₁	#2962	1	1	yes	characteristic
166	C₂×C₇₁	#2982	1	1	yes	characteristic
167	C₂×C₇₁	#2986	1	1	yes	characteristic
168	C₂×C₈×Q₈	C₂×C₇₁	1	2	yes	—
169	C₄×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic
170	#1984	C₂×C₇₁	1	2	yes	—
171	#1939	C₂×C₇₁	1	2	yes	—
172	#1916	C₂×C₇₁	1	4	yes	—
173	C₈×C₄⋊C₄	C₂×C₇₁	1	2	yes	—
174	C₄×C₄⋊C₈	C₂×C₇₁	1	1	yes	characteristic
175	C₄×C₄⋊C₈	C₂×C₇₁	1	1	yes	characteristic
176	C₇₁	#23149	1	1	yes	characteristic, direct product factor, Sylow
177	C₂×C₄⋊Q₈	C₄×C₇₁	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
179	C₈×Q₈	—	2	8	no	—
180	C₂×C₄⋊C₈	C₂²×C₇₁	1	4	yes	—
181	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
182	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
185	C₂×C₄×C₈	C₂²×C₇₁	1	4	yes	—
186	C₂×C₄×C₈	C₂²×C₇₁	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₇₁	1	2	yes	—
188	#391	C₄×C₇₁	1	2	yes	—
189	#389	C₄×C₇₁	1	2	yes	—
190	#389	C₄×C₇₁	1	2	yes	—
191	#384	C₄×C₇₁	1	1	yes	characteristic
192	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
194	C₄³	C₂²×C₇₁	1	1	yes	characteristic
195	#336	C₂²×C₇₁	1	2	yes	—
196	#336	C₂²×C₇₁	1	2	yes	—
197	#336	C₂²×C₇₁	1	4	yes	—
198	#336	C₂²×C₇₁	1	4	yes	—
199	C₂²×Q₈	C₂×C₄×C₇₁	1	2	yes	—
200	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
201	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
202	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
203	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
204	C₄⋊Q₈	C₈×C₇₁	1	8	yes	complemented
205	C₄×Q₈	—	2	4	no	—
206	C₄×Q₈	—	2	4	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
208	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	4	yes	—
209	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₇₁	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
214	C₂×C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
218	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
221	C₄⋊C₈	—	2	8	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	D₄×C₇₁	1	4	yes	—
225	C₄⋊C₈	Q₈×C₇₁	1	4	yes	complemented
226	C₄×C₈	—	2	8	no	—
227	C₄×C₈	—	2	4	no	—
228	C₄×C₈	—	2	4	no	—
229	#95	C₂×C₄×C₇₁	1	4	yes	—
230	#95	C₂×C₄×C₇₁	1	4	yes	—
231	C₂×Q₈	—	2	4	no	—
232	C₂×Q₈	—	2	4	no	—
233	C₂×Q₈	C₂×C₈×C₇₁	1	8	yes	—
234	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₄×C₇₁	1	4	yes	—
236	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₇₁	1	4	yes	—
239	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
242	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	C₂×D₄×C₇₁	1	4	yes	—
254	C₂×C₈	C₂×Q₈×C₇₁	1	4	yes	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	4	2	no	—
259	C₄⋊C₄	C₂×C₈×C₇₁	1	8	yes	—
260	C₄⋊C₄	C₂×C₈×C₇₁	1	8	yes	—
261	C₄²	—	2	2	no	—
262	C₄²	—	2	2	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₄²	—	4	1	no	—
268	C₄²	C₂×C₈×C₇₁	1	4	yes	—
269	C₄²	C₂×D₄×C₇₁	1	2	yes	—
270	C₄²	C₂×Q₈×C₇₁	1	2	yes	—
271	C₄²	#41×C₇₁	1	2	yes	—
272	C₄²	#41×C₇₁	1	2	yes	—
273	C₂³	C₂³×C₄×C₇₁	1	1	yes	characteristic
274	Q₈	—	2	16	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	C₄×D₄×C₇₁	1	2	yes	—
290	C₂×C₄	C₄×D₄×C₇₁	1	2	yes	—
291	C₂×C₄	C₄×Q₈×C₇₁	1	2	yes	—
292	C₂×C₄	C₄×Q₈×C₇₁	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₇₁	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₇₁	1	8	yes	—
295	C₂×C₄	C₂²×C₈×C₇₁	1	2	yes	—
296	C₂×C₄	C₂²×C₈×C₇₁	1	2	yes	—
297	C₂×C₄	#131×C₇₁	1	2	yes	—
298	C₂×C₄	#131×C₇₁	1	2	yes	—
299	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
300	C₂×C₄	C₂²×Q₈×C₇₁	1	1	yes	characteristic
301	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
302	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
303	C₂×C₄	2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
304	C₂×C₄	2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
305	C₈	—	2	4	no	—
306	C₈	—	2	4	no	—
307	C₈	—	4	2	no	—
308	C₈	—	4	2	no	—
309	C₂²	C₂×C₄×D₄×C₇₁	1	1	yes	characteristic
310	C₂²	C₂×C₄×Q₈×C₇₁	1	1	yes	characteristic
311	C₂²	#519×C₇₁	1	1	yes	characteristic
312	C₂²	C₂³×C₈×C₇₁	1	1	yes	characteristic
313	C₂²	C₂×#131×C₇₁	1	1	yes	characteristic
314	C₂²	C₂×#131×C₇₁	1	1	yes	characteristic
315	C₂²	#568×C₇₁	1	1	yes	characteristic
316	C₄	—	2	8	no	—
317	C₄	—	2	2	no	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	4	4	no	—
321	C₄	—	4	1	no	—
322	C₄	C₈×D₄×C₇₁	1	4	yes	—
323	C₄	C₈×Q₈×C₇₁	1	4	yes	complemented
324	C₄	#547×C₇₁	1	1	yes	characteristic
325	C₄	D₄×Q₈×C₇₁	1	1	yes	characteristic
326	C₄	#556×C₇₁	1	1	yes	characteristic
327	C₄	#557×C₇₁	1	1	yes	characteristic
328	C₂	C₇₁×#2365	1	1	yes	characteristic
329	C₂	C₂×C₈×D₄×C₇₁	1	1	yes	characteristic
330	C₂	C₇₁×#2935	1	1	yes	characteristic
331	C₂	C₂×C₈×Q₈×C₇₁	1	1	yes	characteristic
332	C₂	C₇₁×#2962	1	1	yes	characteristic
333	C₂	C₇₁×#2982	1	1	yes	characteristic
334	C₂	C₇₁×#2986	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₇₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
socle, prime radical	C₂³×C₇₁	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
36. C₄⋊Q₈×C₇₁	C₈	semidirect
57. C₄⋊C₈×C₇₁	Q₈	semidirect
155. C₄×C₇₁	C₈×Q₈	semidirect
160. #23149	C₇₁	direct (N × H)
176. C₇₁	#23149	direct (N × H)
204. C₄⋊Q₈	C₈×C₇₁	semidirect
225. C₄⋊C₈	Q₈×C₇₁	semidirect
323. C₄	C₈×Q₈×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₇₁	2
C₄×C₄⋊Q₈×C₇₁	2
C₇₁×#1984	2
C₇₁×#1939	2
C₇₁×#1916	2
C₈×C₄⋊C₄×C₇₁	2
C₄×C₄⋊C₈×C₇₁	2
#23149	71

Subgroups — C71×#23149 #31844021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23149 #31844021