Subgroups — C₇₁×#34324 #31855196

Order 18176.

2244 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇₁×#2373	C₂	1	4	yes	maximal, complemented
3	C₇₁×#2367	C₂	1	2	yes	maximal
4	C₇₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2362	C₂	1	2	yes	maximal, complemented
6	C₇₁×#2355	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2354	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₄⋊C₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2346	C₂	1	2	yes	maximal, complemented
10	C₇₁×#2334	C₂	1	4	yes	maximal, complemented
11	C₇₁×#2326	C₂	1	2	yes	maximal
12	C₄×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂²⋊Q₈×C₇₁	C₂	1	2	yes	maximal, complemented
14	C₇₁×#2296	C₂	1	2	yes	maximal, complemented
15	C₇₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₁×#2276	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₇₁	C₂	1	1	yes	maximal, characteristic
18	#556×C₇₁	C₄	1	16	yes	complemented
19	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#126×C₇₁	C₂²	1	4	yes	—
21	C₂×#124×C₇₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₇₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₁	C₂²	1	2	yes	—
32	C₂×#117×C₇₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₇₁	C₂²	1	2	yes	—
34	#391×C₇₁	C₂²	1	1	yes	characteristic
35	#391×C₇₁	C₂²	1	1	yes	characteristic
36	#391×C₇₁	C₂²	1	2	yes	—
37	#391×C₇₁	C₂²	1	2	yes	—
38	#390×C₇₁	C₂²	1	2	yes	—
39	#389×C₇₁	C₂²	1	1	yes	characteristic
40	#389×C₇₁	C₂²	1	1	yes	characteristic
41	#389×C₇₁	C₂²	1	2	yes	—
42	#389×C₇₁	C₂²	1	2	yes	—
43	#389×C₇₁	C₂²	1	2	yes	—
44	#389×C₇₁	C₂²	1	2	yes	—
45	#389×C₇₁	C₂²	1	4	yes	—
46	#388×C₇₁	C₂²	1	4	yes	—
47	#388×C₇₁	C₂²	1	4	yes	—
48	#388×C₇₁	C₂²	1	4	yes	—
49	#388×C₇₁	C₂²	1	4	yes	—
50	#388×C₇₁	C₂²	1	4	yes	—
51	#387×C₇₁	C₂²	1	2	yes	—
52	#387×C₇₁	C₂²	1	2	yes	—
53	#387×C₇₁	C₂²	1	4	yes	—
54	#387×C₇₁	C₂²	1	4	yes	—
55	#387×C₇₁	C₂²	1	4	yes	—
56	#385×C₇₁	C₂²	1	4	yes	—
57	#385×C₇₁	C₂²	1	4	yes	—
58	#385×C₇₁	C₂²	1	4	yes	—
59	#384×C₇₁	C₂²	1	1	yes	characteristic
60	#384×C₇₁	C₂²	1	2	yes	—
61	#382×C₇₁	C₂²	1	4	yes	—
62	#380×C₇₁	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₇₁	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₇₁	C₂²	1	4	yes	—
68	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₇₁	C₂²	1	4	yes	—
71	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₇₁	C₂²	1	4	yes	—
74	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₇₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₇₁	C₂²	1	4	yes	—
81	#376×C₇₁	C₂²	1	2	yes	—
82	#376×C₇₁	C₂²	1	4	yes	—
83	C₄³×C₇₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₇₁	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₇₁	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
91	#126×C₇₁	C₂×C₄	1	32	yes	complemented
92	#124×C₇₁	C₂×C₄	1	16	yes	—
93	C₂²⋊Q₈×C₇₁	C₂×C₄	1	16	yes	complemented
94	C₄×Q₈×C₇₁	—	2	8	no	—
95	C₄×Q₈×C₇₁	—	2	8	no	—
96	C₄×Q₈×C₇₁	—	4	4	no	—
97	C₄×Q₈×C₇₁	C₂×C₄	1	16	yes	complemented
98	C₄×Q₈×C₇₁	C₂×C₄	1	8	yes	complemented
99	C₄×D₄×C₇₁	—	2	4	no	—
100	C₄×D₄×C₇₁	—	2	4	no	—
101	C₄×D₄×C₇₁	C₂×C₄	1	8	yes	—
102	#117×C₇₁	—	4	4	no	—
103	#117×C₇₁	C₂×C₄	1	16	yes	complemented
104	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₁	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₇₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₇₁	C₂³	1	4	yes	—
130	C₂×C₄²×C₇₁	—	4	4	no	—
131	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
133	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₇₁	C₂³	1	4	yes	—
145	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
148	#95×C₇₁	C₂³	1	2	yes	—
149	#95×C₇₁	C₂³	1	2	yes	—
150	#95×C₇₁	C₂³	1	4	yes	—
151	#95×C₇₁	C₂³	1	2	yes	—
152	#95×C₇₁	C₂³	1	2	yes	—
153	#95×C₇₁	C₂³	1	4	yes	—
154	#95×C₇₁	C₂³	1	2	yes	—
155	#95×C₇₁	C₂³	1	2	yes	—
156	#95×C₇₁	C₂³	1	2	yes	—
157	#95×C₇₁	C₂³	1	2	yes	—
158	#95×C₇₁	C₂³	1	4	yes	—
159	#95×C₇₁	C₂³	1	4	yes	—
160	#95×C₇₁	C₂³	1	4	yes	—
161	#95×C₇₁	C₂³	1	4	yes	—
162	#95×C₇₁	C₂³	1	2	yes	—
163	#95×C₇₁	C₂³	1	2	yes	—
164	C₂⁴×C₇₁	C₂⁴	1	2	yes	—
165	C₂×Q₈×C₇₁	—	2	4	no	—
166	C₂×Q₈×C₇₁	—	2	4	no	—
167	C₂×Q₈×C₇₁	—	2	2	no	—
168	C₂×Q₈×C₇₁	—	2	2	no	—
169	C₂×Q₈×C₇₁	C₂²×C₄	1	4	yes	—
170	C₂×Q₈×C₇₁	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₇₁	—	2	2	no	—
172	C₂×D₄×C₇₁	—	2	2	no	—
173	C₂×D₄×C₇₁	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₇₁	—	2	4	no	—
175	C₂²×C₄×C₇₁	—	2	4	no	—
176	C₂²×C₄×C₇₁	—	2	4	no	—
177	C₂²×C₄×C₇₁	—	2	4	no	—
178	C₂²×C₄×C₇₁	—	2	4	no	—
179	C₂²×C₄×C₇₁	—	4	2	no	—
180	C₂²×C₄×C₇₁	—	4	2	no	—
181	C₂²×C₄×C₇₁	—	4	2	no	—
182	C₂²×C₄×C₇₁	C₂²×C₄	1	8	yes	—
183	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₇₁	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₇₁	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₇₁	—	2	2	no	—
200	C₄⋊C₄×C₇₁	—	2	8	no	—
201	C₄⋊C₄×C₇₁	—	2	8	no	—
202	C₄⋊C₄×C₇₁	—	2	4	no	—
203	C₄⋊C₄×C₇₁	—	2	2	no	—
204	C₄⋊C₄×C₇₁	—	2	4	no	—
205	C₄⋊C₄×C₇₁	—	2	4	no	—
206	C₄⋊C₄×C₇₁	—	2	2	no	—
207	C₄⋊C₄×C₇₁	—	4	2	no	—
208	C₄⋊C₄×C₇₁	—	4	2	no	—
209	C₄⋊C₄×C₇₁	—	4	4	no	—
210	C₄⋊C₄×C₇₁	—	4	4	no	—
211	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₇₁	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₇₁	C₂²×C₄	1	16	yes	—
215	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
216	C₄⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
217	C₄⋊C₄×C₇₁	#41	1	4	yes	—
218	C₂²⋊C₄×C₇₁	—	2	4	no	—
219	C₂²⋊C₄×C₇₁	—	2	4	no	—
220	C₂²⋊C₄×C₇₁	—	4	4	no	—
221	C₂²⋊C₄×C₇₁	—	4	4	no	—
222	C₂²⋊C₄×C₇₁	C₂²×C₄	1	16	yes	—
223	C₂²⋊C₄×C₇₁	C₂²×C₄	1	8	yes	—
224	C₂²⋊C₄×C₇₁	C₂²×C₄	1	16	yes	—
225	C₄²×C₇₁	—	2	2	no	—
226	C₄²×C₇₁	—	2	8	no	—
227	C₄²×C₇₁	—	2	8	no	—
228	C₄²×C₇₁	—	2	4	no	—
229	C₄²×C₇₁	—	2	2	no	—
230	C₄²×C₇₁	—	2	4	no	—
231	C₄²×C₇₁	—	2	2	no	—
232	C₄²×C₇₁	—	2	2	no	—
233	C₄²×C₇₁	—	4	2	no	—
234	C₄²×C₇₁	—	4	2	no	—
235	C₄²×C₇₁	—	4	1	no	—
236	C₄²×C₇₁	—	4	4	no	—
237	C₄²×C₇₁	—	4	4	no	—
238	C₄²×C₇₁	C₂²×C₄	1	16	yes	—
239	C₄²×C₇₁	C₂²×C₄	1	4	yes	—
240	C₄²×C₇₁	C₂²×C₄	1	8	yes	—
241	C₄²×C₇₁	#41	1	4	yes	—
242	C₂³×C₇₁	—	2	2	no	—
243	C₂³×C₇₁	—	2	2	no	—
244	C₂³×C₇₁	—	2	2	no	—
245	C₂³×C₇₁	—	2	2	no	—
246	C₂³×C₇₁	—	2	2	no	—
247	C₂³×C₇₁	—	2	2	no	—
248	C₂³×C₇₁	C₂³×C₄	1	4	yes	—
249	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
250	Q₈×C₇₁	—	2	16	no	—
251	Q₈×C₇₁	—	2	8	no	—
252	D₄×C₇₁	—	2	8	no	—
253	C₂×C₄×C₇₁	—	2	4	no	—
254	C₂×C₄×C₇₁	—	2	4	no	—
255	C₂×C₄×C₇₁	—	2	1	no	—
256	C₂×C₄×C₇₁	—	2	2	no	—
257	C₂×C₄×C₇₁	—	2	1	no	—
258	C₂×C₄×C₇₁	—	2	1	no	—
259	C₂×C₄×C₇₁	—	2	2	no	—
260	C₂×C₄×C₇₁	—	2	2	no	—
261	C₂×C₄×C₇₁	—	2	1	no	—
262	C₂×C₄×C₇₁	—	2	1	no	—
263	C₂×C₄×C₇₁	—	2	1	no	—
264	C₂×C₄×C₇₁	—	2	2	no	—
265	C₂×C₄×C₇₁	—	2	2	no	—
266	C₂×C₄×C₇₁	—	2	2	no	—
267	C₂×C₄×C₇₁	—	2	2	no	—
268	C₂×C₄×C₇₁	—	2	1	no	—
269	C₂×C₄×C₇₁	—	2	1	no	—
270	C₂×C₄×C₇₁	—	2	2	no	—
271	C₂×C₄×C₇₁	—	2	16	no	—
272	C₂×C₄×C₇₁	—	2	2	no	—
273	C₂×C₄×C₇₁	—	2	1	no	—
274	C₂×C₄×C₇₁	—	2	4	no	—
275	C₂×C₄×C₇₁	—	2	2	no	—
276	C₂×C₄×C₇₁	—	2	2	no	—
277	C₂×C₄×C₇₁	—	2	2	no	—
278	C₂×C₄×C₇₁	—	2	2	no	—
279	C₂×C₄×C₇₁	—	2	4	no	—
280	C₂×C₄×C₇₁	—	2	1	no	—
281	C₂×C₄×C₇₁	—	2	2	no	—
282	C₂×C₄×C₇₁	—	2	2	no	—
283	C₂×C₄×C₇₁	—	2	1	no	—
284	C₂×C₄×C₇₁	—	2	2	no	—
285	C₂×C₄×C₇₁	—	2	4	no	—
286	C₂×C₄×C₇₁	—	2	2	no	—
287	C₂×C₄×C₇₁	—	4	8	no	—
288	C₂×C₄×C₇₁	—	4	8	no	—
289	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
290	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
291	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₇₁	C₂³×C₄	1	8	yes	—
293	C₂×C₄×C₇₁	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
295	C₂×C₄×C₇₁	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
297	C₂×C₄×C₇₁	C₂×#41	1	4	yes	—
298	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
299	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
300	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
301	C₂×C₄×C₇₁	H(5,𝔽₂)	1	2	yes	—
302	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
303	C₂×C₄×C₇₁	2₋¹⁺⁴	1	2	yes	—
304	C₂²×C₇₁	—	2	4	no	—
305	C₂²×C₇₁	—	2	4	no	—
306	C₂²×C₇₁	—	2	4	no	—
307	C₂²×C₇₁	—	4	2	no	—
308	C₂²×C₇₁	—	4	2	no	—
309	C₂²×C₇₁	—	4	2	no	—
310	C₂²×C₇₁	—	4	2	no	—
311	C₂²×C₇₁	C₂⁴×C₄	1	1	yes	characteristic
312	C₂²×C₇₁	C₂²×#41	1	1	yes	characteristic
313	C₂²×C₇₁	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₇₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂²×C₇₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂²×C₇₁	#585	1	1	yes	characteristic
318	C₄×C₇₁	—	2	8	no	—
319	C₄×C₇₁	—	2	4	no	—
320	C₄×C₇₁	—	2	4	no	—
321	C₄×C₇₁	—	2	2	no	—
322	C₄×C₇₁	—	2	4	no	—
323	C₄×C₇₁	—	2	2	no	—
324	C₄×C₇₁	—	2	2	no	—
325	C₄×C₇₁	—	2	2	no	—
326	C₄×C₇₁	—	2	4	no	—
327	C₄×C₇₁	—	4	4	no	—
328	C₄×C₇₁	—	4	2	no	—
329	C₄×C₇₁	—	4	2	no	—
330	C₄×C₇₁	—	4	1	no	—
331	C₄×C₇₁	—	4	2	no	—
332	C₄×C₇₁	C₄×#41	1	4	yes	—
333	C₄×C₇₁	#520	1	4	yes	—
334	#34324	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂×C₇₁	—	4	4	no	—
336	C₂×C₇₁	C₂×C₄×#41	1	1	yes	characteristic
337	C₂×C₇₁	C₂×#520	1	1	yes	characteristic
338	C₂×C₇₁	C₄×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂×C₇₁	#3506	1	1	yes	characteristic
340	C₂×C₇₁	#3509	1	1	yes	characteristic
341	C₂×C₇₁	#3518	1	1	yes	characteristic
342	C₂×C₇₁	#3520	1	1	yes	characteristic
343	C₂×#556	C₂×C₇₁	1	1	yes	characteristic
344	#2373	C₂×C₇₁	1	4	yes	complemented
345	#2367	C₂×C₇₁	1	2	yes	—
346	#2365	C₂×C₇₁	1	1	yes	characteristic, complemented
347	#2362	C₂×C₇₁	1	2	yes	complemented
348	#2355	C₂×C₇₁	1	2	yes	complemented
349	#2354	C₂×C₇₁	1	1	yes	characteristic
350	Q₈×C₄⋊C₄	C₂×C₇₁	1	1	yes	characteristic, complemented
351	#2346	C₂×C₇₁	1	2	yes	complemented
352	#2334	C₂×C₇₁	1	4	yes	complemented
353	#2326	C₂×C₇₁	1	2	yes	—
354	C₄×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic, complemented
355	C₄×C₂²⋊Q₈	C₂×C₇₁	1	2	yes	complemented
356	#2296	C₂×C₇₁	1	2	yes	complemented
357	#2295	C₂×C₇₁	1	1	yes	characteristic, complemented
358	#2276	C₂×C₇₁	1	2	yes	complemented
359	C₄²×D₄	C₂×C₇₁	1	1	yes	characteristic
360	C₇₁	#34324	1	1	yes	characteristic, direct product factor, Sylow
361	#556	C₄×C₇₁	1	16	yes	complemented
362	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
363	C₂×#126	C₂²×C₇₁	1	4	yes	—
364	C₂×#124	C₂²×C₇₁	1	2	yes	—
365	C₂×C₂²⋊Q₈	C₂²×C₇₁	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
367	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
368	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
369	C₂×C₄×Q₈	C₂²×C₇₁	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
374	C₂×#117	C₂²×C₇₁	1	2	yes	—
375	C₂×#117	C₂²×C₇₁	1	2	yes	—
376	C₂²×C₄²	C₂²×C₇₁	1	2	yes	—
377	#391	C₂²×C₇₁	1	2	yes	—
378	#391	C₂²×C₇₁	1	2	yes	—
379	#391	C₂²×C₇₁	1	1	yes	characteristic
380	#391	C₂²×C₇₁	1	1	yes	characteristic
381	#390	C₂²×C₇₁	1	2	yes	—
382	#389	C₂²×C₇₁	1	2	yes	—
383	#389	C₂²×C₇₁	1	2	yes	—
384	#389	C₂²×C₇₁	1	4	yes	—
385	#389	C₂²×C₇₁	1	1	yes	characteristic
386	#389	C₂²×C₇₁	1	2	yes	—
387	#389	C₂²×C₇₁	1	2	yes	—
388	#389	C₂²×C₇₁	1	1	yes	characteristic
389	#388	C₂²×C₇₁	1	4	yes	—
390	#388	C₂²×C₇₁	1	4	yes	—
391	#388	C₂²×C₇₁	1	4	yes	—
392	#388	C₂²×C₇₁	1	4	yes	—
393	#388	C₂²×C₇₁	1	4	yes	—
394	#387	C₂²×C₇₁	1	2	yes	—
395	#387	C₂²×C₇₁	1	4	yes	—
396	#387	C₂²×C₇₁	1	4	yes	—
397	#387	C₂²×C₇₁	1	4	yes	—
398	#387	C₂²×C₇₁	1	2	yes	—
399	#385	C₂²×C₇₁	1	4	yes	—
400	#385	C₂²×C₇₁	1	4	yes	—
401	#385	C₂²×C₇₁	1	4	yes	—
402	#384	C₂²×C₇₁	1	1	yes	characteristic
403	#384	C₂²×C₇₁	1	2	yes	—
404	#382	C₂²×C₇₁	1	4	yes	—
405	#380	C₂²×C₇₁	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₇₁	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₇₁	1	4	yes	—
410	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
414	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
415	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
416	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
417	C₄×C₄⋊C₄	C₂²×C₇₁	1	4	yes	—
418	C₄×C₄⋊C₄	C₂²×C₇₁	1	4	yes	—
419	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
420	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₇₁	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₇₁	1	2	yes	—
424	#376	C₂²×C₇₁	1	2	yes	—
425	#376	C₂²×C₇₁	1	4	yes	—
426	C₄³	C₂²×C₇₁	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₇₁	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
431	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
432	C₂³×C₄	C₂³×C₇₁	1	2	yes	—
433	C₄⋊Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
434	#126	C₂×C₄×C₇₁	1	32	yes	complemented
435	#124	C₂×C₄×C₇₁	1	16	yes	—
436	C₂²⋊Q₈	C₂×C₄×C₇₁	1	16	yes	complemented
437	C₄×Q₈	—	2	8	no	—
438	C₄×Q₈	—	2	8	no	—
439	C₄×Q₈	—	4	4	no	—
440	C₄×Q₈	C₂×C₄×C₇₁	1	16	yes	complemented
441	C₄×Q₈	C₂×C₄×C₇₁	1	8	yes	complemented
442	C₄×D₄	—	2	4	no	—
443	C₄×D₄	—	2	4	no	—
444	C₄×D₄	C₂×C₄×C₇₁	1	8	yes	—
445	#117	—	4	4	no	—
446	#117	C₂×C₄×C₇₁	1	16	yes	complemented
447	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂³×C₇₁	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₇₁	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₇₁	1	4	yes	—
473	C₂×C₄²	—	4	4	no	—
474	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
476	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
477	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
478	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
479	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
483	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
484	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
486	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
487	C₂×C₄²	C₂³×C₇₁	1	4	yes	—
488	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
491	#95	C₂³×C₇₁	1	2	yes	—
492	#95	C₂³×C₇₁	1	2	yes	—
493	#95	C₂³×C₇₁	1	4	yes	—
494	#95	C₂³×C₇₁	1	2	yes	—
495	#95	C₂³×C₇₁	1	2	yes	—
496	#95	C₂³×C₇₁	1	4	yes	—
497	#95	C₂³×C₇₁	1	2	yes	—
498	#95	C₂³×C₇₁	1	2	yes	—
499	#95	C₂³×C₇₁	1	2	yes	—
500	#95	C₂³×C₇₁	1	2	yes	—
501	#95	C₂³×C₇₁	1	4	yes	—
502	#95	C₂³×C₇₁	1	4	yes	—
503	#95	C₂³×C₇₁	1	4	yes	—
504	#95	C₂³×C₇₁	1	4	yes	—
505	#95	C₂³×C₇₁	1	2	yes	—
506	#95	C₂³×C₇₁	1	2	yes	—
507	C₂⁴	C₂⁴×C₇₁	1	2	yes	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	C₂²×C₄×C₇₁	1	4	yes	—
513	C₂×Q₈	C₂²×C₄×C₇₁	1	8	yes	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	C₂²×C₄×C₇₁	1	4	yes	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	C₂²×C₄×C₇₁	1	8	yes	—
526	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₇₁	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₇₁	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	8	no	—
544	C₄⋊C₄	—	2	8	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
555	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
556	C₄⋊C₄	C₂²×C₄×C₇₁	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₇₁	1	16	yes	—
558	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
559	C₄⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
560	C₄⋊C₄	#41×C₇₁	1	4	yes	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	C₂²×C₄×C₇₁	1	16	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₇₁	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₇₁	1	16	yes	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	8	no	—
570	C₄²	—	2	8	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	4	2	no	—
577	C₄²	—	4	2	no	—
578	C₄²	—	4	1	no	—
579	C₄²	—	4	4	no	—
580	C₄²	—	4	4	no	—
581	C₄²	C₂²×C₄×C₇₁	1	16	yes	—
582	C₄²	C₂²×C₄×C₇₁	1	4	yes	—
583	C₄²	C₂²×C₄×C₇₁	1	8	yes	—
584	C₄²	#41×C₇₁	1	4	yes	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	C₂³×C₄×C₇₁	1	4	yes	—
592	C₂³	C₂⁵×C₇₁	1	1	yes	characteristic
593	Q₈	—	2	16	no	—
594	Q₈	—	2	8	no	—
595	D₄	—	2	8	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	16	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	8	no	—
632	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
633	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
634	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₇₁	1	8	yes	—
636	C₂×C₄	C₂³×C₄×C₇₁	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₇₁	1	2	yes	—
639	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
640	C₂×C₄	C₂×#41×C₇₁	1	4	yes	—
641	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
642	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
643	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
644	C₂×C₄	H(5,𝔽₂)×C₇₁	1	2	yes	—
645	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
646	C₂×C₄	2₋¹⁺⁴×C₇₁	1	2	yes	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	2	no	—
654	C₂²	C₂⁴×C₄×C₇₁	1	1	yes	characteristic
655	C₂²	C₂²×#41×C₇₁	1	1	yes	characteristic
656	C₂²	C₂²×#41×C₇₁	1	1	yes	characteristic
657	C₂²	C₂×H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
658	C₂²	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
659	C₂²	C₂×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
660	C₂²	#585×C₇₁	1	1	yes	characteristic
661	C₄	—	2	8	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	4	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	4	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	2	no	—
675	C₄	C₄×#41×C₇₁	1	4	yes	—
676	C₄	#520×C₇₁	1	4	yes	—
677	C₂	—	4	4	no	—
678	C₂	C₂×C₄×#41×C₇₁	1	1	yes	characteristic
679	C₂	C₂×#520×C₇₁	1	1	yes	characteristic
680	C₂	C₄×2₋¹⁺⁴×C₇₁	1	1	yes	characteristic
681	C₂	C₇₁×#3506	1	1	yes	characteristic
682	C₂	C₇₁×#3509	1	1	yes	characteristic
683	C₂	C₇₁×#3518	1	1	yes	characteristic
684	C₂	C₇₁×#3520	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇₁×#2373	C₂	semidirect
4. C₇₁×#2365	C₂	semidirect
5. C₇₁×#2362	C₂	semidirect
6. C₇₁×#2355	C₂	semidirect
8. Q₈×C₄⋊C₄×C₇₁	C₂	semidirect
9. C₇₁×#2346	C₂	semidirect
10. C₇₁×#2334	C₂	semidirect
12. C₄×C₄⋊Q₈×C₇₁	C₂	semidirect
13. C₄×C₂²⋊Q₈×C₇₁	C₂	semidirect
14. C₇₁×#2296	C₂	semidirect
15. C₇₁×#2295	C₂	semidirect
16. C₇₁×#2276	C₂	semidirect
18. #556×C₇₁	C₄	semidirect
90. C₄⋊Q₈×C₇₁	C₂×C₄	semidirect
91. #126×C₇₁	C₂×C₄	semidirect
93. C₂²⋊Q₈×C₇₁	C₂×C₄	semidirect
97. C₄×Q₈×C₇₁	C₂×C₄	semidirect
98. C₄×Q₈×C₇₁	C₂×C₄	semidirect
103. #117×C₇₁	C₂×C₄	semidirect
334. #34324	C₇₁	direct (N × H)
344. #2373	C₂×C₇₁	semidirect
346. #2365	C₂×C₇₁	semidirect
347. #2362	C₂×C₇₁	semidirect
348. #2355	C₂×C₇₁	semidirect
350. Q₈×C₄⋊C₄	C₂×C₇₁	semidirect
351. #2346	C₂×C₇₁	semidirect
352. #2334	C₂×C₇₁	semidirect
354. C₄×C₄⋊Q₈	C₂×C₇₁	semidirect
355. C₄×C₂²⋊Q₈	C₂×C₇₁	semidirect
356. #2296	C₂×C₇₁	semidirect
357. #2295	C₂×C₇₁	semidirect
358. #2276	C₂×C₇₁	semidirect
360. C₇₁	#34324	direct (N × H)
361. #556	C₄×C₇₁	semidirect
433. C₄⋊Q₈	C₂×C₄×C₇₁	semidirect
434. #126	C₂×C₄×C₇₁	semidirect
436. C₂²⋊Q₈	C₂×C₄×C₇₁	semidirect
440. C₄×Q₈	C₂×C₄×C₇₁	semidirect
441. C₄×Q₈	C₂×C₄×C₇₁	semidirect
446. #117	C₂×C₄×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₇₁	2
C₇₁×#2373	2
C₇₁×#2367	2
C₇₁×#2365	2
C₇₁×#2362	2
C₇₁×#2355	2
C₇₁×#2354	2
Q₈×C₄⋊C₄×C₇₁	2
C₇₁×#2346	2
C₇₁×#2334	2
C₇₁×#2326	2
C₄×C₄⋊Q₈×C₇₁	2
C₄×C₂²⋊Q₈×C₇₁	2
C₇₁×#2296	2
C₇₁×#2295	2
C₇₁×#2276	2
C₄²×D₄×C₇₁	2
#34324	71

Subgroups — C71×#34324 #31855196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#34324 #31855196