Subgroups — C₇₁×#23719 #31844591

Order 18176.

808 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,ℤ/8)×C₇₁	C₂	1	2	yes	maximal, complemented
2	C₂×#442×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₁×#2063	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2051	C₂	1	2	yes	maximal, complemented
8	C₇₁×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2018	C₂	1	1	yes	maximal, characteristic
10	C₇₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#100×C₇₁	C₂	1	2	yes	maximal, complemented
12	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₇₁	C₂²	1	2	yes	—
16	#442×C₇₁	—	2	2	no	—
17	#442×C₇₁	—	2	2	no	—
18	#442×C₇₁	—	2	2	no	—
19	#440×C₇₁	—	2	2	no	—
20	C₄×SD₁₆×C₇₁	—	2	2	no	—
21	C₄×D₈×C₇₁	—	2	2	no	—
22	#433×C₇₁	—	2	2	no	—
23	#432×C₇₁	—	2	2	no	—
24	C₂×#108×C₇₁	C₂²	1	2	yes	—
25	#428×C₇₁	C₂²	1	2	yes	—
26	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
27	#424×C₇₁	C₂²	1	1	yes	characteristic
28	#424×C₇₁	C₂²	1	1	yes	characteristic
29	#418×C₇₁	C₂²	1	2	yes	—
30	#417×C₇₁	C₂²	1	2	yes	—
31	C₂×#102×C₇₁	C₂²	1	2	yes	—
32	C₂×#100×C₇₁	C₂²	1	2	yes	—
33	C₂×#100×C₇₁	C₂²	1	2	yes	—
34	#408×C₇₁	C₂²	1	1	yes	characteristic
35	#408×C₇₁	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
37	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
38	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
39	#343×C₇₁	C₂²	1	2	yes	—
40	#343×C₇₁	C₂²	1	2	yes	—
41	#341×C₇₁	C₂²	1	1	yes	characteristic
42	#341×C₇₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₇₁	—	2	2	no	—
46	AGL(1,ℤ/8)×C₇₁	—	2	4	no	—
47	AGL(1,ℤ/8)×C₇₁	—	2	4	no	—
48	C₂×SD₁₆×C₇₁	—	2	2	no	—
49	C₂×D₈×C₇₁	—	2	2	no	—
50	C₂×D₈×C₇₁	—	2	4	no	—
51	C₂×D₈×C₇₁	—	2	2	no	—
52	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
55	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₇₁	D₄	1	2	yes	—
59	C₄×D₄×C₇₁	—	2	2	no	—
60	C₄×D₄×C₇₁	—	2	2	no	—
61	C₄×D₄×C₇₁	—	2	2	no	—
62	C₄×D₄×C₇₁	—	2	2	no	—
63	C₄×D₄×C₇₁	—	2	2	no	—
64	C₄×D₄×C₇₁	D₄	1	2	yes	—
65	#117×C₇₁	—	2	1	no	—
66	#117×C₇₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₇₁	—	2	2	no	—
69	C₂×C₄²×C₇₁	—	2	1	no	—
70	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
71	#108×C₇₁	—	2	4	no	—
72	#107×C₇₁	—	2	2	no	—
73	#106×C₇₁	—	2	2	no	—
74	#106×C₇₁	—	2	2	no	—
75	C₄⋊C₈×C₇₁	—	2	2	no	—
76	C₄⋊C₈×C₇₁	—	2	2	no	—
77	#103×C₇₁	—	2	2	no	—
78	#102×C₇₁	—	2	2	no	—
79	#102×C₇₁	—	2	4	no	—
80	#102×C₇₁	—	2	2	no	—
81	#102×C₇₁	—	2	2	no	—
82	#100×C₇₁	—	2	4	no	—
83	#100×C₇₁	—	2	4	no	—
84	C₂²⋊C₈×C₇₁	—	2	2	no	—
85	C₂²⋊C₈×C₇₁	—	2	2	no	—
86	#97×C₇₁	—	2	1	no	—
87	#97×C₇₁	—	2	2	no	—
88	#97×C₇₁	D₄	1	2	yes	—
89	#97×C₇₁	D₄	1	2	yes	—
90	C₄×C₈×C₇₁	—	2	1	no	—
91	C₄×C₈×C₇₁	—	2	2	no	—
92	C₂⁴×C₇₁	—	2	2	no	—
93	#41×C₇₁	—	2	2	no	—
94	#41×C₇₁	—	2	2	no	—
95	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₇₁	—	2	1	no	—
97	C₂×D₄×C₇₁	—	2	2	no	—
98	C₂×D₄×C₇₁	—	2	2	no	—
99	C₂×D₄×C₇₁	—	2	2	no	—
100	C₂×D₄×C₇₁	—	2	2	no	—
101	C₂×D₄×C₇₁	—	2	2	no	—
102	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₇₁	#41	1	4	yes	—
104	C₂²×C₄×C₇₁	—	2	1	no	—
105	C₂²×C₄×C₇₁	—	2	2	no	—
106	C₂²×C₄×C₇₁	—	2	2	no	—
107	C₂²×C₄×C₇₁	—	4	2	no	—
108	C₂²×C₄×C₇₁	—	4	2	no	—
109	C₂²×C₄×C₇₁	—	8	4	no	—
110	C₂²×C₄×C₇₁	#41	1	2	yes	—
111	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₇₁	—	2	8	no	—
113	D₈×C₇₁	—	2	8	no	—
114	D₈×C₇₁	—	2	8	no	—
115	M₁₆×C₇₁	—	2	2	no	—
116	M₁₆×C₇₁	—	2	2	no	—
117	M₁₆×C₇₁	—	2	2	no	—
118	M₁₆×C₇₁	—	2	2	no	—
119	M₁₆×C₇₁	—	2	2	no	—
120	M₁₆×C₇₁	#41	1	4	yes	—
121	C₂×C₈×C₇₁	—	2	2	no	—
122	C₂×C₈×C₇₁	—	2	2	no	—
123	C₂×C₈×C₇₁	—	2	2	no	—
124	C₂×C₈×C₇₁	—	2	1	no	—
125	C₂×C₈×C₇₁	—	2	1	no	—
126	C₂×C₈×C₇₁	—	2	2	no	—
127	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₇₁	—	2	2	no	—
130	C₄⋊C₄×C₇₁	—	2	2	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₇₁	—	2	1	no	—
134	C₂²⋊C₄×C₇₁	—	2	2	no	—
135	C₂²⋊C₄×C₇₁	—	4	2	no	—
136	C₂²⋊C₄×C₇₁	—	4	2	no	—
137	C₄²×C₇₁	—	2	2	no	—
138	C₄²×C₇₁	—	2	1	no	—
139	C₄²×C₇₁	C₂×D₄	1	2	yes	—
140	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₇₁	—	2	1	no	—
143	C₂³×C₇₁	—	2	4	no	—
144	C₂³×C₇₁	—	4	2	no	—
145	C₂³×C₇₁	—	4	2	no	—
146	C₂³×C₇₁	—	8	2	no	—
147	C₂³×C₇₁	—	8	2	no	—
148	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
149	Q₈×C₇₁	—	2	2	no	—
150	D₄×C₇₁	—	2	4	no	—
151	D₄×C₇₁	—	2	2	no	—
152	D₄×C₇₁	—	2	4	no	—
153	D₄×C₇₁	—	4	2	no	—
154	D₄×C₇₁	—	4	2	no	—
155	D₄×C₇₁	—	4	2	no	—
156	C₂×C₄×C₇₁	—	2	2	no	—
157	C₂×C₄×C₇₁	—	2	1	no	—
158	C₂×C₄×C₇₁	—	4	2	no	—
159	C₂×C₄×C₇₁	—	4	1	no	—
160	C₂×C₄×C₇₁	—	4	1	no	—
161	C₂×C₄×C₇₁	—	4	2	no	—
162	C₂×C₄×C₇₁	—	8	2	no	—
163	C₂×C₄×C₇₁	—	8	4	no	—
164	C₂×C₄×C₇₁	—	8	4	no	—
165	C₂×C₄×C₇₁	—	8	2	no	—
166	C₂×C₄×C₇₁	#121	1	2	yes	—
167	C₂×C₄×C₇₁	#121	1	2	yes	—
168	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
172	C₈×C₇₁	—	2	2	no	—
173	C₈×C₇₁	—	2	4	no	—
174	C₈×C₇₁	—	2	2	no	—
175	C₈×C₇₁	—	4	1	no	—
176	C₈×C₇₁	—	4	2	no	—
177	C₈×C₇₁	—	4	1	no	—
178	C₂²×C₇₁	—	2	2	no	—
179	C₂²×C₇₁	—	4	1	no	—
180	C₂²×C₇₁	—	4	4	no	—
181	C₂²×C₇₁	—	4	2	no	—
182	C₂²×C₇₁	—	8	4	no	—
183	C₂²×C₇₁	—	8	4	no	—
184	C₂²×C₇₁	—	8	2	no	—
185	C₂²×C₇₁	—	8	2	no	—
186	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
187	C₂²×C₇₁	#529	1	2	yes	—
188	C₄×C₇₁	—	2	2	no	—
189	C₄×C₇₁	—	2	2	no	—
190	C₄×C₇₁	—	4	1	no	—
191	C₄×C₇₁	—	4	2	no	—
192	C₄×C₇₁	—	8	2	no	—
193	C₄×C₇₁	#525	1	1	yes	characteristic
194	C₄×C₇₁	#525	1	2	yes	—
195	C₄×C₇₁	#532	1	1	yes	characteristic
196	#23719	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₇₁	—	2	2	no	—
198	C₂×C₇₁	—	8	1	no	—
199	C₂×C₇₁	—	8	4	no	—
200	C₂×C₇₁	#2392	1	1	yes	characteristic
201	C₂×C₇₁	#3068	1	2	yes	—
202	C₄×AGL(1,ℤ/8)	C₂×C₇₁	1	2	yes	complemented
203	C₂×#442	C₂×C₇₁	1	1	yes	characteristic, complemented
204	#2923	C₂×C₇₁	1	1	yes	characteristic, complemented
205	#2090	C₂×C₇₁	1	1	yes	characteristic, complemented
206	#2079	C₂×C₇₁	1	1	yes	characteristic, complemented
207	#2063	C₂×C₇₁	1	2	yes	complemented
208	#2051	C₂×C₇₁	1	2	yes	complemented
209	#2045	C₂×C₇₁	1	1	yes	characteristic, complemented
210	#2018	C₂×C₇₁	1	1	yes	characteristic
211	#1778	C₂×C₇₁	1	1	yes	characteristic, complemented
212	C₄×#100	C₂×C₇₁	1	2	yes	complemented
213	C₇₁	#23719	1	1	yes	characteristic, direct product factor, Sylow
214	C₂×AGL(1,ℤ/8)	C₂²×C₇₁	1	2	yes	—
215	C₂²×D₈	C₂²×C₇₁	1	1	yes	characteristic
216	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₇₁	1	2	yes	—
218	#442	—	2	2	no	—
219	#442	—	2	2	no	—
220	#442	—	2	2	no	—
221	#440	—	2	2	no	—
222	C₄×SD₁₆	—	2	2	no	—
223	C₄×D₈	—	2	2	no	—
224	#433	—	2	2	no	—
225	#432	—	2	2	no	—
226	C₂×#108	C₂²×C₇₁	1	2	yes	—
227	#428	C₂²×C₇₁	1	2	yes	—
228	C₂×#106	C₂²×C₇₁	1	1	yes	characteristic
229	#424	C₂²×C₇₁	1	1	yes	characteristic
230	#424	C₂²×C₇₁	1	1	yes	characteristic
231	#418	C₂²×C₇₁	1	2	yes	—
232	#417	C₂²×C₇₁	1	2	yes	—
233	C₂×#102	C₂²×C₇₁	1	2	yes	—
234	C₂×#100	C₂²×C₇₁	1	2	yes	—
235	C₂×#100	C₂²×C₇₁	1	2	yes	—
236	#408	C₂²×C₇₁	1	1	yes	characteristic
237	#408	C₂²×C₇₁	1	1	yes	characteristic
238	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
239	C₄×M₁₆	C₂²×C₇₁	1	2	yes	—
240	C₂×#97	C₂²×C₇₁	1	1	yes	characteristic
241	#343	C₂²×C₇₁	1	2	yes	—
242	#343	C₂²×C₇₁	1	2	yes	—
243	#341	C₂²×C₇₁	1	1	yes	characteristic
244	#341	C₂²×C₇₁	1	1	yes	characteristic
245	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₇₁	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	AGL(1,ℤ/8)	—	2	4	no	—
249	AGL(1,ℤ/8)	—	2	4	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
255	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
257	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
260	C₄×Q₈	D₄×C₇₁	1	2	yes	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	D₄×C₇₁	1	2	yes	—
267	#117	—	2	1	no	—
268	#117	C₂³×C₇₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
273	#108	—	2	4	no	—
274	#107	—	2	2	no	—
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	4	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#100	—	2	4	no	—
285	#100	—	2	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#97	—	2	1	no	—
289	#97	—	2	2	no	—
290	#97	D₄×C₇₁	1	2	yes	—
291	#97	D₄×C₇₁	1	2	yes	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
305	C₂×D₄	#41×C₇₁	1	4	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	8	4	no	—
312	C₂²×C₄	#41×C₇₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
314	SD₁₆	—	2	8	no	—
315	D₈	—	2	8	no	—
316	D₈	—	2	8	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	#41×C₇₁	1	4	yes	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	C₂×D₄×C₇₁	1	2	yes	—
342	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₂×#41×C₇₁	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	#121×C₇₁	1	2	yes	—
369	C₂×C₄	#121×C₇₁	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
373	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
374	C₈	—	2	2	no	—
375	C₈	—	2	4	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
389	C₂²	#529×C₇₁	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	#525×C₇₁	1	1	yes	characteristic
396	C₄	#525×C₇₁	1	2	yes	—
397	C₄	#532×C₇₁	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	8	1	no	—
400	C₂	—	8	4	no	—
401	C₂	C₇₁×#2392	1	1	yes	characteristic
402	C₂	C₇₁×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
prime radical	C₇₁×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×AGL(1,ℤ/8)×C₇₁	C₂	semidirect
2. C₂×#442×C₇₁	C₂	semidirect
3. C₇₁×#2923	C₂	semidirect
4. C₇₁×#2090	C₂	semidirect
5. C₇₁×#2079	C₂	semidirect
6. C₇₁×#2063	C₂	semidirect
7. C₇₁×#2051	C₂	semidirect
8. C₇₁×#2045	C₂	semidirect
10. C₇₁×#1778	C₂	semidirect
11. C₄×#100×C₇₁	C₂	semidirect
196. #23719	C₇₁	direct (N × H)
202. C₄×AGL(1,ℤ/8)	C₂×C₇₁	semidirect
203. C₂×#442	C₂×C₇₁	semidirect
204. #2923	C₂×C₇₁	semidirect
205. #2090	C₂×C₇₁	semidirect
206. #2079	C₂×C₇₁	semidirect
207. #2063	C₂×C₇₁	semidirect
208. #2051	C₂×C₇₁	semidirect
209. #2045	C₂×C₇₁	semidirect
211. #1778	C₂×C₇₁	semidirect
212. C₄×#100	C₂×C₇₁	semidirect
213. C₇₁	#23719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×AGL(1,ℤ/8)×C₇₁	2
C₂×#442×C₇₁	2
C₇₁×#2923	2
C₇₁×#2090	2
C₇₁×#2079	2
C₇₁×#2063	2
C₇₁×#2051	2
C₇₁×#2045	2
C₇₁×#2018	2
C₇₁×#1778	2
C₄×#100×C₇₁	2
#23719	71

Subgroups — C71×#23719 #31844591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23719 #31844591