Subgroups — C₇₁×#23188 #31844060

Order 18176.

1226 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#442×C₇₁	C₂	1	2	yes	maximal, complemented
3	C₇₁×#2366	C₂	1	2	yes	maximal, complemented
4	C₇₁×#1982	C₂	1	2	yes	maximal, complemented
5	C₇₁×#1972	C₂	1	2	yes	maximal, complemented
6	C₇₁×#1879	C₂	1	4	yes	maximal, complemented
7	C₄×#106×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₇₁	C₂²	1	2	yes	—
10	C₂²×D₈×C₇₁	C₂²	1	2	yes	—
11	C₂×#127×C₇₁	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₇₁	—	2	2	no	—
13	C₂×C₄×D₄×C₇₁	C₂²	1	4	yes	—
14	#493×C₇₁	C₄	1	8	yes	complemented
15	#442×C₇₁	—	2	8	no	—
16	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
17	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
19	C₂×#102×C₇₁	C₂²	1	4	yes	—
20	C₂×#102×C₇₁	C₂²	1	4	yes	—
21	C₂×#97×C₇₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
23	#390×C₇₁	—	2	2	no	—
24	#390×C₇₁	C₂²	1	4	yes	—
25	#386×C₇₁	—	2	4	no	—
26	C₄×C₄⋊C₄×C₇₁	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
28	#340×C₇₁	C₂²	1	2	yes	—
29	#336×C₇₁	C₂²	1	2	yes	—
30	C₂²×D₄×C₇₁	—	2	2	no	—
31	C₂²×D₄×C₇₁	—	2	2	no	—
32	C₂²×D₄×C₇₁	C₂³	1	4	yes	—
33	C₂³×C₄×C₇₁	—	2	4	no	—
34	C₂×D₈×C₇₁	—	2	4	no	—
35	C₂×D₈×C₇₁	—	2	4	no	—
36	C₂×D₈×C₇₁	—	4	2	no	—
37	C₂×D₈×C₇₁	—	4	2	no	—
38	C₂×D₈×C₇₁	C₂×C₄	1	8	yes	complemented
39	C₂×D₈×C₇₁	C₂×C₄	1	8	yes	complemented
40	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
43	#127×C₇₁	—	2	4	no	—
44	#127×C₇₁	C₂×C₄	1	8	yes	complemented
45	C₄×D₄×C₇₁	—	2	8	no	—
46	C₄×D₄×C₇₁	—	4	4	no	—
47	C₄×D₄×C₇₁	—	4	8	no	—
48	C₂×C₄⋊C₄×C₇₁	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
51	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₇₁	—	2	4	no	—
54	C₂×C₄²×C₇₁	—	2	2	no	—
55	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
57	#106×C₇₁	—	2	2	no	—
58	#106×C₇₁	D₄	1	4	yes	complemented
59	C₄⋊C₈×C₇₁	—	2	2	no	—
60	#102×C₇₁	—	2	8	no	—
61	#102×C₇₁	—	4	4	no	—
62	#97×C₇₁	—	2	4	no	—
63	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	complemented
64	#95×C₇₁	—	2	2	no	—
65	#95×C₇₁	D₄	1	2	yes	—
66	C₂⁴×C₇₁	—	2	4	no	—
67	C₂×D₄×C₇₁	—	2	8	no	—
68	C₂×D₄×C₇₁	—	2	8	no	—
69	C₂×D₄×C₇₁	—	2	4	no	—
70	C₂×D₄×C₇₁	—	2	4	no	—
71	C₂×D₄×C₇₁	—	2	4	no	—
72	C₂×D₄×C₇₁	—	2	4	no	—
73	C₂×D₄×C₇₁	—	2	4	no	—
74	C₂×D₄×C₇₁	—	4	4	no	—
75	C₂×D₄×C₇₁	—	4	4	no	—
76	C₂×D₄×C₇₁	—	8	2	no	—
77	C₂×D₄×C₇₁	—	8	2	no	—
78	C₂×D₄×C₇₁	C₂²×C₄	1	8	yes	—
79	C₂²×C₄×C₇₁	—	2	2	no	—
80	C₂²×C₄×C₇₁	—	2	2	no	—
81	C₂²×C₄×C₇₁	—	4	8	no	—
82	C₂²×C₄×C₇₁	—	4	8	no	—
83	C₂²×C₄×C₇₁	—	8	4	no	—
84	C₂²×C₄×C₇₁	C₂×D₄	1	4	yes	—
85	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
88	D₈×C₇₁	—	2	16	no	—
89	D₈×C₇₁	—	4	8	no	—
90	C₂×C₈×C₇₁	—	2	1	no	—
91	C₂×C₈×C₇₁	—	2	1	no	—
92	C₂×C₈×C₇₁	—	2	2	no	—
93	C₂×C₈×C₇₁	—	2	2	no	—
94	C₂×C₈×C₇₁	—	2	2	no	—
95	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₇₁	#41	1	2	yes	—
99	C₄⋊C₄×C₇₁	—	2	4	no	—
100	C₄⋊C₄×C₇₁	—	2	2	no	—
101	C₄⋊C₄×C₇₁	—	2	2	no	—
102	C₄⋊C₄×C₇₁	—	2	2	no	—
103	C₄⋊C₄×C₇₁	C₂×D₄	1	4	yes	—
104	C₂²⋊C₄×C₇₁	—	4	8	no	—
105	C₂²⋊C₄×C₇₁	—	4	8	no	—
106	C₂²⋊C₄×C₇₁	—	8	4	no	—
107	C₄²×C₇₁	—	2	2	no	—
108	C₄²×C₇₁	—	2	2	no	—
109	C₄²×C₇₁	—	4	4	no	—
110	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
111	C₄²×C₇₁	#41	1	2	yes	—
112	C₂³×C₇₁	—	2	8	no	—
113	C₂³×C₇₁	—	4	4	no	—
114	C₂³×C₇₁	—	4	4	no	—
115	C₂³×C₇₁	—	4	4	no	—
116	C₂³×C₇₁	—	4	4	no	—
117	C₂³×C₇₁	—	4	4	no	—
118	C₂³×C₇₁	—	4	4	no	—
119	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
120	D₄×C₇₁	—	2	8	no	—
121	D₄×C₇₁	—	2	8	no	—
122	D₄×C₇₁	—	4	4	no	—
123	D₄×C₇₁	—	4	4	no	—
124	D₄×C₇₁	—	4	16	no	—
125	D₄×C₇₁	—	8	8	no	—
126	C₂×C₄×C₇₁	—	2	2	no	—
127	C₂×C₄×C₇₁	—	2	4	no	—
128	C₂×C₄×C₇₁	—	2	4	no	—
129	C₂×C₄×C₇₁	—	2	4	no	—
130	C₂×C₄×C₇₁	—	2	4	no	—
131	C₂×C₄×C₇₁	—	4	2	no	—
132	C₂×C₄×C₇₁	—	4	2	no	—
133	C₂×C₄×C₇₁	—	4	2	no	—
134	C₂×C₄×C₇₁	—	4	2	no	—
135	C₂×C₄×C₇₁	—	4	2	no	—
136	C₂×C₄×C₇₁	—	8	16	no	—
137	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	4	yes	—
140	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
144	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
146	C₈×C₇₁	—	2	2	no	—
147	C₈×C₇₁	—	4	2	no	—
148	C₈×C₇₁	C₄×D₄	1	4	yes	complemented
149	C₂²×C₇₁	—	4	8	no	—
150	C₂²×C₇₁	—	4	8	no	—
151	C₂²×C₇₁	—	4	8	no	—
152	C₂²×C₇₁	—	8	4	no	—
153	C₂²×C₇₁	—	8	4	no	—
154	C₂²×C₇₁	—	8	4	no	—
155	C₂²×C₇₁	—	8	4	no	—
156	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
157	C₂²×C₇₁	D₄²	1	1	yes	characteristic
158	C₂²×C₇₁	#550	1	1	yes	characteristic
159	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
160	C₂²×C₇₁	#576	1	2	yes	—
161	C₄×C₇₁	—	2	2	no	—
162	C₄×C₇₁	—	4	4	no	—
163	C₄×C₇₁	—	4	4	no	—
164	C₄×C₇₁	—	8	2	no	—
165	C₄×C₇₁	#442	1	4	yes	complemented
166	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
167	C₄×C₇₁	#518	1	1	yes	characteristic
168	C₄×C₇₁	#550	1	1	yes	characteristic
169	C₄×C₇₁	#559	1	1	yes	characteristic
170	#23188	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂×C₇₁	—	8	8	no	—
172	C₂×C₇₁	#2366	1	1	yes	characteristic
173	C₂×C₇₁	C₂×#442	1	1	yes	characteristic
174	C₂×C₇₁	#2948	1	1	yes	characteristic
175	C₂×C₇₁	#3274	1	2	yes	—
176	C₂×C₇₁	#3399	1	2	yes	—
177	C₂×#493	C₂×C₇₁	1	1	yes	characteristic
178	C₂×#442	C₂×C₇₁	1	2	yes	complemented
179	#2366	C₂×C₇₁	1	2	yes	complemented
180	#1982	C₂×C₇₁	1	2	yes	complemented
181	#1972	C₂×C₇₁	1	2	yes	complemented
182	#1879	C₂×C₇₁	1	4	yes	complemented
183	C₄×#106	C₂×C₇₁	1	1	yes	characteristic, complemented
184	#1770	C₂×C₇₁	1	1	yes	characteristic, complemented
185	C₇₁	#23188	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×D₈	C₂²×C₇₁	1	2	yes	—
187	C₂²×D₈	C₂²×C₇₁	1	2	yes	—
188	C₂×#127	C₂²×C₇₁	1	2	yes	—
189	C₂×C₄×D₄	—	2	2	no	—
190	C₂×C₄×D₄	C₂²×C₇₁	1	4	yes	—
191	#493	C₄×C₇₁	1	8	yes	complemented
192	#442	—	2	8	no	—
193	C₂×#106	C₂²×C₇₁	1	1	yes	characteristic
194	C₂×#106	C₂²×C₇₁	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
196	C₂×#102	C₂²×C₇₁	1	4	yes	—
197	C₂×#102	C₂²×C₇₁	1	4	yes	—
198	C₂×#97	C₂²×C₇₁	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
200	#390	—	2	2	no	—
201	#390	C₂²×C₇₁	1	4	yes	—
202	#386	—	2	4	no	—
203	C₄×C₄⋊C₄	C₂²×C₇₁	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
205	#340	C₂²×C₇₁	1	2	yes	—
206	#336	C₂²×C₇₁	1	2	yes	—
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	—	2	2	no	—
209	C₂²×D₄	C₂³×C₇₁	1	4	yes	—
210	C₂³×C₄	—	2	4	no	—
211	C₂×D₈	—	2	4	no	—
212	C₂×D₈	—	2	4	no	—
213	C₂×D₈	—	4	2	no	—
214	C₂×D₈	—	4	2	no	—
215	C₂×D₈	C₂×C₄×C₇₁	1	8	yes	complemented
216	C₂×D₈	C₂×C₄×C₇₁	1	8	yes	complemented
217	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
220	#127	—	2	4	no	—
221	#127	C₂×C₄×C₇₁	1	8	yes	complemented
222	C₄×D₄	—	2	8	no	—
223	C₄×D₄	—	4	4	no	—
224	C₄×D₄	—	4	8	no	—
225	C₂×C₄⋊C₄	D₄×C₇₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
228	C₂×C₂²⋊C₄	—	2	4	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	C₂³×C₇₁	1	2	yes	—
233	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
234	#106	—	2	2	no	—
235	#106	D₄×C₇₁	1	4	yes	complemented
236	C₄⋊C₈	—	2	2	no	—
237	#102	—	2	8	no	—
238	#102	—	4	4	no	—
239	#97	—	2	4	no	—
240	C₄×C₈	C₂×C₄×C₇₁	1	4	yes	complemented
241	#95	—	2	2	no	—
242	#95	D₄×C₇₁	1	2	yes	—
243	C₂⁴	—	2	4	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	2	4	no	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	4	4	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	8	2	no	—
254	C₂×D₄	—	8	2	no	—
255	C₂×D₄	C₂²×C₄×C₇₁	1	8	yes	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	—	8	4	no	—
261	C₂²×C₄	C₂×D₄×C₇₁	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
264	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
265	D₈	—	2	16	no	—
266	D₈	—	4	8	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	C₂²×C₄×C₇₁	1	2	yes	—
273	C₂×C₈	C₂²×C₄×C₇₁	1	2	yes	—
274	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
275	C₂×C₈	#41×C₇₁	1	2	yes	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	C₂×D₄×C₇₁	1	4	yes	—
281	C₂²⋊C₄	—	4	8	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	—	8	4	no	—
284	C₄²	—	2	2	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	4	4	no	—
287	C₄²	C₂²×C₄×C₇₁	1	2	yes	—
288	C₄²	#41×C₇₁	1	2	yes	—
289	C₂³	—	2	8	no	—
290	C₂³	—	4	4	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	4	4	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	—	4	4	no	—
296	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
297	D₄	—	2	8	no	—
298	D₄	—	2	8	no	—
299	D₄	—	4	16	no	—
300	D₄	—	4	4	no	—
301	D₄	—	4	4	no	—
302	D₄	—	8	8	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	8	16	no	—
314	C₂×C₄	C₄×D₄×C₇₁	1	2	yes	—
315	C₂×C₄	C₄×D₄×C₇₁	1	2	yes	—
316	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	4	yes	—
317	C₂×C₄	C₂³×C₄×C₇₁	1	1	yes	characteristic
318	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
319	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
320	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
321	C₂×C₄	H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
322	C₂×C₄	H(5,𝔽₂)×C₇₁	1	1	yes	characteristic
323	C₈	—	2	2	no	—
324	C₈	—	4	2	no	—
325	C₈	C₄×D₄×C₇₁	1	4	yes	complemented
326	C₂²	—	4	8	no	—
327	C₂²	—	4	8	no	—
328	C₂²	—	4	8	no	—
329	C₂²	—	8	4	no	—
330	C₂²	—	8	4	no	—
331	C₂²	—	8	4	no	—
332	C₂²	—	8	4	no	—
333	C₂²	C₂×C₄×D₄×C₇₁	1	1	yes	characteristic
334	C₂²	D₄²×C₇₁	1	1	yes	characteristic
335	C₂²	#550×C₇₁	1	1	yes	characteristic
336	C₂²	C₂×AGL(1,ℤ/8)×C₇₁	1	2	yes	—
337	C₂²	#576×C₇₁	1	2	yes	—
338	C₄	—	2	2	no	—
339	C₄	—	4	4	no	—
340	C₄	—	4	4	no	—
341	C₄	—	8	2	no	—
342	C₄	#442×C₇₁	1	4	yes	complemented
343	C₄	C₂×C₄×D₄×C₇₁	1	1	yes	characteristic
344	C₄	#518×C₇₁	1	1	yes	characteristic
345	C₄	#550×C₇₁	1	1	yes	characteristic
346	C₄	#559×C₇₁	1	1	yes	characteristic
347	C₂	—	8	8	no	—
348	C₂	C₇₁×#2366	1	1	yes	characteristic
349	C₂	C₂×#442×C₇₁	1	1	yes	characteristic
350	C₂	C₇₁×#2948	1	1	yes	characteristic
351	C₂	C₇₁×#3274	1	2	yes	—
352	C₂	C₇₁×#3399	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
prime radical	C₂×#493×C₇₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₄×C₄⋊C₄×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#442×C₇₁	C₂	semidirect
3. C₇₁×#2366	C₂	semidirect
4. C₇₁×#1982	C₂	semidirect
5. C₇₁×#1972	C₂	semidirect
6. C₇₁×#1879	C₂	semidirect
7. C₄×#106×C₇₁	C₂	semidirect
8. C₇₁×#1770	C₂	semidirect
14. #493×C₇₁	C₄	semidirect
38. C₂×D₈×C₇₁	C₂×C₄	semidirect
39. C₂×D₈×C₇₁	C₂×C₄	semidirect
44. #127×C₇₁	C₂×C₄	semidirect
58. #106×C₇₁	D₄	semidirect
63. C₄×C₈×C₇₁	C₂×C₄	semidirect
148. C₈×C₇₁	C₄×D₄	semidirect
165. C₄×C₇₁	#442	semidirect
170. #23188	C₇₁	direct (N × H)
178. C₂×#442	C₂×C₇₁	semidirect
179. #2366	C₂×C₇₁	semidirect
180. #1982	C₂×C₇₁	semidirect
181. #1972	C₂×C₇₁	semidirect
182. #1879	C₂×C₇₁	semidirect
183. C₄×#106	C₂×C₇₁	semidirect
184. #1770	C₂×C₇₁	semidirect
185. C₇₁	#23188	direct (N × H)
191. #493	C₄×C₇₁	semidirect
215. C₂×D₈	C₂×C₄×C₇₁	semidirect
216. C₂×D₈	C₂×C₄×C₇₁	semidirect
221. #127	C₂×C₄×C₇₁	semidirect
235. #106	D₄×C₇₁	semidirect
240. C₄×C₈	C₂×C₄×C₇₁	semidirect
325. C₈	C₄×D₄×C₇₁	semidirect
342. C₄	#442×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493×C₇₁	2
C₂×#442×C₇₁	2
C₇₁×#2366	2
C₇₁×#1982	2
C₇₁×#1972	2
C₇₁×#1879	2
C₄×#106×C₇₁	2
C₇₁×#1770	2
#23188	71

Subgroups — C71×#23188 #31844060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23188 #31844060