Subgroups — C₇₁×#10271 #31831143

Order 18176.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#498×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#461×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#1954	C₂	1	1	yes	maximal, characteristic
5	C₂×#333×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#332×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₇₁	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
12	#498×C₇₁	—	2	2	no	—
13	#498×C₇₁	—	2	2	no	—
14	#476×C₇₁	—	2	2	no	—
15	#476×C₇₁	—	2	2	no	—
16	#461×C₇₁	—	2	2	no	—
17	#461×C₇₁	—	2	2	no	—
18	C₂×#106×C₇₁	—	2	2	no	—
19	C₂×#106×C₇₁	—	2	1	no	—
20	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₁	—	2	1	no	—
24	C₂×#102×C₇₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₇₁	—	2	2	no	—
26	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
27	#333×C₇₁	—	2	2	no	—
28	#332×C₇₁	—	2	2	no	—
29	C₂²×Q₈×C₇₁	—	2	1	no	—
30	C₂²×Q₈×C₇₁	—	2	1	no	—
31	C₂²×D₄×C₇₁	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₇₁	—	2	1	no	—
33	C₂×SD₁₆×C₇₁	—	2	4	no	—
34	C₂×SD₁₆×C₇₁	—	4	2	no	—
35	C₂×SD₁₆×C₇₁	—	4	2	no	—
36	C₂²×C₈×C₇₁	—	2	1	no	—
37	C₂²×C₈×C₇₁	—	2	1	no	—
38	C₂²×C₈×C₇₁	—	2	1	no	—
39	C₂²×C₈×C₇₁	D₄	1	2	yes	—
40	C₄⋊Q₈×C₇₁	—	2	1	no	—
41	C₄⋊Q₈×C₇₁	—	2	1	no	—
42	C₄⋊Q₈×C₇₁	—	2	1	no	—
43	C₄⋊Q₈×C₇₁	—	2	1	no	—
44	C₄⋊Q₈×C₇₁	—	2	1	no	—
45	C₄⋊Q₈×C₇₁	—	2	1	no	—
46	C₄⋊Q₈×C₇₁	D₄	1	2	yes	—
47	C₄⋊Q₈×C₇₁	D₄	1	2	yes	—
48	C₄×D₄×C₇₁	—	2	1	no	—
49	C₄×D₄×C₇₁	—	2	1	no	—
50	C₄×D₄×C₇₁	—	2	1	no	—
51	C₄×D₄×C₇₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
55	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
58	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
59	#106×C₇₁	—	2	4	no	—
60	#106×C₇₁	—	2	8	no	—
61	C₄⋊C₈×C₇₁	—	2	1	no	—
62	C₄⋊C₈×C₇₁	—	2	1	no	—
63	C₄⋊C₈×C₇₁	—	2	1	no	—
64	C₄⋊C₈×C₇₁	—	2	1	no	—
65	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
66	C₄⋊C₈×C₇₁	D₄	1	2	yes	—
67	#103×C₇₁	—	2	4	no	—
68	#102×C₇₁	—	2	4	no	—
69	C₂²⋊C₈×C₇₁	—	4	4	no	—
70	C₄×C₈×C₇₁	—	2	1	no	—
71	C₄×C₈×C₇₁	—	2	1	no	—
72	C₂⁴×C₇₁	—	2	1	no	—
73	C₂×Q₈×C₇₁	—	2	2	no	—
74	C₂×Q₈×C₇₁	—	2	2	no	—
75	C₂×Q₈×C₇₁	—	4	1	no	—
76	C₂×Q₈×C₇₁	—	4	1	no	—
77	C₂×Q₈×C₇₁	—	4	1	no	—
78	C₂×Q₈×C₇₁	—	4	1	no	—
79	C₂×Q₈×C₇₁	—	4	1	no	—
80	C₂×Q₈×C₇₁	—	4	1	no	—
81	C₂×Q₈×C₇₁	—	8	2	no	—
82	C₂×D₄×C₇₁	—	2	1	no	—
83	C₂×D₄×C₇₁	—	2	1	no	—
84	C₂×D₄×C₇₁	—	2	1	no	—
85	C₂×D₄×C₇₁	—	2	1	no	—
86	C₂×D₄×C₇₁	—	2	1	no	—
87	C₂×D₄×C₇₁	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₇₁	—	2	1	no	—
89	C₂²×C₄×C₇₁	—	4	1	no	—
90	C₂²×C₄×C₇₁	—	4	1	no	—
91	C₂²×C₄×C₇₁	—	4	1	no	—
92	C₂²×C₄×C₇₁	—	4	1	no	—
93	C₂²×C₄×C₇₁	—	4	2	no	—
94	C₂²×C₄×C₇₁	—	4	2	no	—
95	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
98	SD₁₆×C₇₁	—	4	8	no	—
99	C₂×C₈×C₇₁	—	2	2	no	—
100	C₂×C₈×C₇₁	—	2	2	no	—
101	C₂×C₈×C₇₁	—	2	2	no	—
102	C₂×C₈×C₇₁	—	2	2	no	—
103	C₂×C₈×C₇₁	—	4	1	no	—
104	C₂×C₈×C₇₁	—	4	1	no	—
105	C₂×C₈×C₇₁	—	4	1	no	—
106	C₂×C₈×C₇₁	—	4	1	no	—
107	C₂×C₈×C₇₁	—	4	1	no	—
108	C₂×C₈×C₇₁	—	4	2	no	—
109	C₂×C₈×C₇₁	SD₁₆	1	4	yes	complemented
110	C₄⋊C₄×C₇₁	—	2	2	no	—
111	C₄⋊C₄×C₇₁	—	2	1	no	—
112	C₄⋊C₄×C₇₁	—	2	2	no	—
113	C₄⋊C₄×C₇₁	—	2	2	no	—
114	C₄⋊C₄×C₇₁	—	2	1	no	—
115	C₄⋊C₄×C₇₁	—	2	2	no	—
116	C₄⋊C₄×C₇₁	—	4	1	no	—
117	C₄⋊C₄×C₇₁	—	4	1	no	—
118	C₄⋊C₄×C₇₁	—	4	1	no	—
119	C₄⋊C₄×C₇₁	—	4	1	no	—
120	C₂²⋊C₄×C₇₁	—	4	1	no	—
121	C₂²⋊C₄×C₇₁	—	4	1	no	—
122	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
126	C₂³×C₇₁	—	2	2	no	—
127	C₂³×C₇₁	—	4	1	no	—
128	C₂³×C₇₁	—	4	2	no	—
129	C₂³×C₇₁	—	4	1	no	—
130	C₂³×C₇₁	—	4	2	no	—
131	C₂³×C₇₁	#121	1	1	yes	characteristic
132	Q₈×C₇₁	—	4	2	no	—
133	Q₈×C₇₁	—	4	2	no	—
134	Q₈×C₇₁	—	8	2	no	—
135	Q₈×C₇₁	—	8	2	no	—
136	Q₈×C₇₁	—	8	1	no	—
137	Q₈×C₇₁	—	8	1	no	—
138	D₄×C₇₁	—	2	2	no	—
139	D₄×C₇₁	—	2	2	no	—
140	D₄×C₇₁	—	4	1	no	—
141	D₄×C₇₁	—	4	1	no	—
142	C₂×C₄×C₇₁	—	2	2	no	—
143	C₂×C₄×C₇₁	—	4	1	no	—
144	C₂×C₄×C₇₁	—	4	2	no	—
145	C₂×C₄×C₇₁	—	4	2	no	—
146	C₂×C₄×C₇₁	—	4	2	no	—
147	C₂×C₄×C₇₁	—	8	1	no	—
148	C₂×C₄×C₇₁	—	8	1	no	—
149	C₂×C₄×C₇₁	—	8	2	no	—
150	C₂×C₄×C₇₁	—	8	2	no	—
151	C₂×C₄×C₇₁	—	8	1	no	—
152	C₂×C₄×C₇₁	—	8	1	no	—
153	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
154	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#120	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
162	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
164	C₂×C₄×C₇₁	#137	1	2	yes	—
165	C₈×C₇₁	—	2	4	no	—
166	C₈×C₇₁	—	4	2	no	—
167	C₈×C₇₁	—	4	2	no	—
168	C₈×C₇₁	—	8	1	no	—
169	C₂²×C₇₁	—	4	4	no	—
170	C₂²×C₇₁	—	4	2	no	—
171	C₂²×C₇₁	—	8	2	no	—
172	C₂²×C₇₁	—	8	1	no	—
173	C₂²×C₇₁	—	8	1	no	—
174	C₂²×C₇₁	#392	1	1	yes	characteristic
175	C₂²×C₇₁	#461	1	2	yes	—
176	C₂²×C₇₁	#465	1	1	yes	characteristic
177	C₂²×C₇₁	#468	1	1	yes	characteristic
178	C₂²×C₇₁	#471	1	2	yes	—
179	C₄×C₇₁	—	2	1	no	—
180	C₄×C₇₁	—	2	1	no	—
181	C₄×C₇₁	—	8	2	no	—
182	C₄×C₇₁	—	8	1	no	—
183	C₄×C₇₁	—	8	2	no	—
184	C₄×C₇₁	#448	1	1	yes	characteristic
185	C₄×C₇₁	#448	1	2	yes	—
186	C₄×C₇₁	#449	1	1	yes	characteristic
187	C₄×C₇₁	#450	1	1	yes	characteristic
188	C₄×C₇₁	#452	1	1	yes	characteristic
189	C₄×C₇₁	#492	1	1	yes	characteristic
190	C₄×C₇₁	#497	1	1	yes	characteristic
191	#10271	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₇₁	—	8	2	no	—
193	C₂×C₇₁	#1671	1	2	yes	—
194	C₂×C₇₁	#1691	1	2	yes	—
195	C₂×C₇₁	#2000	1	1	yes	characteristic
196	C₂×C₇₁	#2013	1	1	yes	characteristic
197	C₂×C₇₁	#2019	1	1	yes	characteristic
198	C₂×#498	C₂×C₇₁	1	1	yes	characteristic, complemented
199	C₂×#476	C₂×C₇₁	1	1	yes	characteristic
200	C₂×#461	C₂×C₇₁	1	1	yes	characteristic
201	#1954	C₂×C₇₁	1	1	yes	characteristic
202	C₂×#333	C₂×C₇₁	1	1	yes	characteristic, complemented
203	C₂×#332	C₂×C₇₁	1	1	yes	characteristic, complemented
204	#1277	C₂×C₇₁	1	1	yes	characteristic, complemented
205	C₇₁	#10271	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²×SD₁₆	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
210	#498	—	2	2	no	—
211	#498	—	2	2	no	—
212	#476	—	2	2	no	—
213	#476	—	2	2	no	—
214	#461	—	2	2	no	—
215	#461	—	2	2	no	—
216	C₂×#106	—	2	2	no	—
217	C₂×#106	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₇₁	1	1	yes	characteristic
221	C₂×#103	—	2	1	no	—
222	C₂×#102	—	2	1	no	—
223	C₂×C₂²⋊C₈	—	2	2	no	—
224	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
225	#333	—	2	2	no	—
226	#332	—	2	2	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	D₄×C₇₁	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	—	4	2	no	—
233	C₂×SD₁₆	—	4	2	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	D₄×C₇₁	1	2	yes	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	D₄×C₇₁	1	2	yes	—
245	C₄⋊Q₈	D₄×C₇₁	1	2	yes	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	D₄×C₇₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
257	#106	—	2	4	no	—
258	#106	—	2	8	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
264	C₄⋊C₈	D₄×C₇₁	1	2	yes	—
265	#103	—	2	4	no	—
266	#102	—	2	4	no	—
267	C₂²⋊C₈	—	4	4	no	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₂⁴	—	2	1	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	8	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	SD₁₆×C₇₁	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
295	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
296	SD₁₆	—	4	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	SD₁₆×C₇₁	1	4	yes	complemented
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	#121×C₇₁	1	1	yes	characteristic
330	Q₈	—	4	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	8	2	no	—
334	Q₈	—	8	1	no	—
335	Q₈	—	8	1	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	—	8	1	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
352	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
353	C₂×C₄	#120×C₇₁	1	1	yes	characteristic
354	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
355	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
356	C₂×C₄	#127×C₇₁	1	1	yes	characteristic
357	C₂×C₄	C₂×SD₁₆×C₇₁	1	1	yes	characteristic
358	C₂×C₄	C₂×SD₁₆×C₇₁	1	2	yes	—
359	C₂×C₄	#135×C₇₁	1	1	yes	characteristic
360	C₂×C₄	AGL(1,ℤ/8)×C₇₁	1	1	yes	characteristic
361	C₂×C₄	#137×C₇₁	1	1	yes	characteristic
362	C₂×C₄	#137×C₇₁	1	2	yes	—
363	C₈	—	2	4	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	8	1	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	1	no	—
372	C₂²	#392×C₇₁	1	1	yes	characteristic
373	C₂²	#461×C₇₁	1	2	yes	—
374	C₂²	#465×C₇₁	1	1	yes	characteristic
375	C₂²	#468×C₇₁	1	1	yes	characteristic
376	C₂²	#471×C₇₁	1	2	yes	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	#448×C₇₁	1	1	yes	characteristic
383	C₄	#448×C₇₁	1	2	yes	—
384	C₄	#449×C₇₁	1	1	yes	characteristic
385	C₄	#450×C₇₁	1	1	yes	characteristic
386	C₄	#452×C₇₁	1	1	yes	characteristic
387	C₄	#492×C₇₁	1	1	yes	characteristic
388	C₄	#497×C₇₁	1	1	yes	characteristic
389	C₂	—	8	2	no	—
390	C₂	C₇₁×#1671	1	2	yes	—
391	C₂	C₇₁×#1691	1	2	yes	—
392	C₂	C₇₁×#2000	1	1	yes	characteristic
393	C₂	C₇₁×#2013	1	1	yes	characteristic
394	C₂	C₇₁×#2019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₁	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
prime radical	C₂²×D₄×C₇₁	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#498×C₇₁	C₂	semidirect
5. C₂×#333×C₇₁	C₂	semidirect
6. C₂×#332×C₇₁	C₂	semidirect
7. C₇₁×#1277	C₂	semidirect
109. C₂×C₈×C₇₁	SD₁₆	semidirect
191. #10271	C₇₁	direct (N × H)
198. C₂×#498	C₂×C₇₁	semidirect
202. C₂×#333	C₂×C₇₁	semidirect
203. C₂×#332	C₂×C₇₁	semidirect
204. #1277	C₂×C₇₁	semidirect
205. C₇₁	#10271	direct (N × H)
307. C₂×C₈	SD₁₆×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#498×C₇₁	2
C₂×#476×C₇₁	2
C₂×#461×C₇₁	2
C₇₁×#1954	2
C₂×#333×C₇₁	2
C₂×#332×C₇₁	2
C₇₁×#1277	2
#10271	71

Subgroups — C71×#10271 #31831143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#10271 #31831143