Subgroups — C₇₁×#23717 #31844589

Order 18176.

752 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#137×C₇₁	C₂	1	2	yes	maximal
2	C₂×C₄×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#2922	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2078	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#2064	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2052	C₂	1	2	yes	maximal
8	C₇₁×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2020	C₂	1	1	yes	maximal, characteristic
10	C₄×#108×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#101×C₇₁	C₂	1	2	yes	maximal, complemented
12	C₂×#137×C₇₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
16	#441×C₇₁	—	2	2	no	—
17	#440×C₇₁	—	2	2	no	—
18	C₄×Q₁₆×C₇₁	—	2	2	no	—
19	C₄×Q₁₆×C₇₁	—	2	2	no	—
20	C₄×Q₁₆×C₇₁	—	2	2	no	—
21	C₄×SD₁₆×C₇₁	—	2	2	no	—
22	#433×C₇₁	—	2	2	no	—
23	#431×C₇₁	—	2	2	no	—
24	C₂×#108×C₇₁	C₂²	1	2	yes	—
25	#428×C₇₁	C₂²	1	2	yes	—
26	C₂×#107×C₇₁	C₂²	1	1	yes	characteristic
27	#424×C₇₁	C₂²	1	1	yes	characteristic
28	#424×C₇₁	C₂²	1	1	yes	characteristic
29	#419×C₇₁	C₂²	1	2	yes	—
30	#417×C₇₁	C₂²	1	2	yes	—
31	C₂×#103×C₇₁	C₂²	1	2	yes	—
32	C₂×#101×C₇₁	C₂²	1	2	yes	—
33	C₂×#101×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×C₄×C₈×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×Q₈×C₇₁	C₂³	1	2	yes	—
45	#137×C₇₁	—	2	4	no	—
46	#137×C₇₁	—	2	4	no	—
47	C₂×Q₁₆×C₇₁	—	2	2	no	—
48	C₂×Q₁₆×C₇₁	—	2	4	no	—
49	C₂×Q₁₆×C₇₁	—	2	2	no	—
50	C₂×SD₁₆×C₇₁	—	2	2	no	—
51	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
54	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₇₁	—	2	2	no	—
58	C₄×Q₈×C₇₁	—	2	2	no	—
59	C₄×Q₈×C₇₁	—	2	2	no	—
60	C₄×Q₈×C₇₁	—	2	2	no	—
61	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
62	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
63	C₄×D₄×C₇₁	—	2	1	no	—
64	C₄×D₄×C₇₁	—	2	1	no	—
65	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
66	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
67	#117×C₇₁	—	2	1	no	—
68	#117×C₇₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₇₁	—	2	1	no	—
72	C₂×C₄²×C₇₁	—	2	2	no	—
73	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
74	#108×C₇₁	—	2	4	no	—
75	#107×C₇₁	—	2	2	no	—
76	#107×C₇₁	—	2	2	no	—
77	#106×C₇₁	—	2	2	no	—
78	C₄⋊C₈×C₇₁	—	2	2	no	—
79	C₄⋊C₈×C₇₁	—	2	2	no	—
80	#103×C₇₁	—	2	2	no	—
81	#103×C₇₁	—	2	4	no	—
82	#103×C₇₁	—	2	2	no	—
83	#103×C₇₁	—	2	2	no	—
84	#102×C₇₁	—	2	2	no	—
85	#101×C₇₁	—	2	4	no	—
86	#101×C₇₁	—	2	4	no	—
87	C₂²⋊C₈×C₇₁	—	2	2	no	—
88	C₂²⋊C₈×C₇₁	—	2	2	no	—
89	#97×C₇₁	—	2	1	no	—
90	#97×C₇₁	—	2	2	no	—
91	C₄×C₈×C₇₁	—	2	1	no	—
92	C₄×C₈×C₇₁	—	2	2	no	—
93	C₄×C₈×C₇₁	D₄	1	2	yes	—
94	C₄×C₈×C₇₁	D₄	1	2	yes	—
95	#41×C₇₁	—	2	2	no	—
96	#41×C₇₁	—	2	2	no	—
97	C₂×Q₈×C₇₁	—	2	2	no	—
98	C₂×Q₈×C₇₁	—	2	2	no	—
99	C₂×Q₈×C₇₁	—	2	2	no	—
100	C₂×Q₈×C₇₁	—	2	2	no	—
101	C₂×Q₈×C₇₁	—	2	2	no	—
102	C₂×Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₇₁	#41	1	4	yes	—
104	C₂×D₄×C₇₁	—	2	1	no	—
105	C₂×D₄×C₇₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₁	—	2	2	no	—
107	C₂²×C₄×C₇₁	—	2	1	no	—
108	C₂²×C₄×C₇₁	—	2	1	no	—
109	C₂²×C₄×C₇₁	—	2	1	no	—
110	C₂²×C₄×C₇₁	—	2	2	no	—
111	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
112	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₇₁	—	2	8	no	—
115	Q₁₆×C₇₁	—	2	8	no	—
116	SD₁₆×C₇₁	—	2	8	no	—
117	M₁₆×C₇₁	—	2	2	no	—
118	M₁₆×C₇₁	—	2	2	no	—
119	M₁₆×C₇₁	—	2	2	no	—
120	M₁₆×C₇₁	—	2	2	no	—
121	M₁₆×C₇₁	—	2	2	no	—
122	M₁₆×C₇₁	#41	1	4	yes	—
123	C₂×C₈×C₇₁	—	2	2	no	—
124	C₂×C₈×C₇₁	—	2	2	no	—
125	C₂×C₈×C₇₁	—	2	2	no	—
126	C₂×C₈×C₇₁	—	2	1	no	—
127	C₂×C₈×C₇₁	—	2	1	no	—
128	C₂×C₈×C₇₁	—	2	2	no	—
129	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₇₁	—	2	1	no	—
132	C₄⋊C₄×C₇₁	—	2	1	no	—
133	C₄⋊C₄×C₇₁	—	2	2	no	—
134	C₄⋊C₄×C₇₁	—	2	2	no	—
135	C₄⋊C₄×C₇₁	—	4	2	no	—
136	C₄⋊C₄×C₇₁	—	4	2	no	—
137	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₇₁	—	2	1	no	—
140	C₂²⋊C₄×C₇₁	—	2	1	no	—
141	C₂²⋊C₄×C₇₁	—	2	1	no	—
142	C₄²×C₇₁	—	2	1	no	—
143	C₄²×C₇₁	—	2	1	no	—
144	C₄²×C₇₁	—	2	1	no	—
145	C₄²×C₇₁	—	4	2	no	—
146	C₄²×C₇₁	—	4	2	no	—
147	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₇₁	—	2	1	no	—
152	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
153	Q₈×C₇₁	—	2	4	no	—
154	Q₈×C₇₁	—	2	4	no	—
155	Q₈×C₇₁	—	2	2	no	—
156	Q₈×C₇₁	—	4	2	no	—
157	Q₈×C₇₁	—	4	2	no	—
158	D₄×C₇₁	—	2	2	no	—
159	D₄×C₇₁	—	4	2	no	—
160	C₂×C₄×C₇₁	—	2	2	no	—
161	C₂×C₄×C₇₁	—	2	1	no	—
162	C₂×C₄×C₇₁	—	2	1	no	—
163	C₂×C₄×C₇₁	—	2	1	no	—
164	C₂×C₄×C₇₁	—	2	4	no	—
165	C₂×C₄×C₇₁	—	4	1	no	—
166	C₂×C₄×C₇₁	—	4	2	no	—
167	C₂×C₄×C₇₁	—	4	2	no	—
168	C₂×C₄×C₇₁	—	4	2	no	—
169	C₂×C₄×C₇₁	—	4	1	no	—
170	C₂×C₄×C₇₁	—	4	1	no	—
171	C₂×C₄×C₇₁	—	4	2	no	—
172	C₂×C₄×C₇₁	—	4	2	no	—
173	C₂×C₄×C₇₁	—	8	2	no	—
174	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
181	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
182	C₈×C₇₁	—	2	2	no	—
183	C₈×C₇₁	—	2	4	no	—
184	C₈×C₇₁	—	2	2	no	—
185	C₈×C₇₁	—	4	1	no	—
186	C₈×C₇₁	—	4	2	no	—
187	C₈×C₇₁	—	4	1	no	—
188	C₂²×C₇₁	—	2	1	no	—
189	C₂²×C₇₁	—	2	1	no	—
190	C₂²×C₇₁	—	4	1	no	—
191	C₂²×C₇₁	—	4	1	no	—
192	C₂²×C₇₁	—	4	1	no	—
193	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
194	C₂²×C₇₁	#529	1	2	yes	—
195	C₄×C₇₁	—	2	1	no	—
196	C₄×C₇₁	—	2	1	no	—
197	C₄×C₇₁	—	2	1	no	—
198	C₄×C₇₁	—	4	1	no	—
199	C₄×C₇₁	—	4	4	no	—
200	C₄×C₇₁	—	4	1	no	—
201	C₄×C₇₁	—	4	1	no	—
202	C₄×C₇₁	—	8	2	no	—
203	C₄×C₇₁	#473	1	2	yes	—
204	C₄×C₇₁	#525	1	1	yes	characteristic
205	C₄×C₇₁	#525	1	2	yes	—
206	C₄×C₇₁	#532	1	1	yes	characteristic
207	#23717	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₁	—	2	2	no	—
209	C₂×C₇₁	—	8	1	no	—
210	C₂×C₇₁	#2392	1	1	yes	characteristic
211	C₂×C₇₁	C₂×#473	1	1	yes	characteristic
212	C₂×C₇₁	#3067	1	1	yes	characteristic
213	C₄×#137	C₂×C₇₁	1	2	yes	—
214	C₂×C₄×Q₁₆	C₂×C₇₁	1	1	yes	characteristic, complemented
215	#2922	C₂×C₇₁	1	1	yes	characteristic
216	#2089	C₂×C₇₁	1	1	yes	characteristic, complemented
217	#2078	C₂×C₇₁	1	1	yes	characteristic
218	#2064	C₂×C₇₁	1	2	yes	complemented
219	#2052	C₂×C₇₁	1	2	yes	—
220	#2047	C₂×C₇₁	1	1	yes	characteristic, complemented
221	#2020	C₂×C₇₁	1	1	yes	characteristic
222	C₄×#108	C₂×C₇₁	1	1	yes	characteristic, complemented
223	C₄×#101	C₂×C₇₁	1	2	yes	complemented
224	C₇₁	#23717	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#137	C₂²×C₇₁	1	2	yes	—
226	C₂²×Q₁₆	C₂²×C₇₁	1	1	yes	characteristic
227	C₄×#41	C₂²×C₇₁	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
229	#441	—	2	2	no	—
230	#440	—	2	2	no	—
231	C₄×Q₁₆	—	2	2	no	—
232	C₄×Q₁₆	—	2	2	no	—
233	C₄×Q₁₆	—	2	2	no	—
234	C₄×SD₁₆	—	2	2	no	—
235	#433	—	2	2	no	—
236	#431	—	2	2	no	—
237	C₂×#108	C₂²×C₇₁	1	2	yes	—
238	#428	C₂²×C₇₁	1	2	yes	—
239	C₂×#107	C₂²×C₇₁	1	1	yes	characteristic
240	#424	C₂²×C₇₁	1	1	yes	characteristic
241	#424	C₂²×C₇₁	1	1	yes	characteristic
242	#419	C₂²×C₇₁	1	2	yes	—
243	#417	C₂²×C₇₁	1	2	yes	—
244	C₂×#103	C₂²×C₇₁	1	2	yes	—
245	C₂×#101	C₂²×C₇₁	1	2	yes	—
246	C₂×#101	C₂²×C₇₁	1	2	yes	—
247	#408	C₂²×C₇₁	1	1	yes	characteristic
248	#408	C₂²×C₇₁	1	1	yes	characteristic
249	C₄×M₁₆	C₂²×C₇₁	1	1	yes	characteristic
250	C₄×M₁₆	C₂²×C₇₁	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
252	#343	C₂²×C₇₁	1	2	yes	—
253	#343	C₂²×C₇₁	1	2	yes	—
254	#341	C₂²×C₇₁	1	1	yes	characteristic
255	#341	C₂²×C₇₁	1	1	yes	characteristic
256	C₂×#41	C₂³×C₇₁	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
258	#137	—	2	4	no	—
259	#137	—	2	4	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×Q₁₆	—	2	4	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
265	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₇₁	1	1	yes	characteristic
267	C₂×M₁₆	C₂³×C₇₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₇₁	1	1	yes	characteristic
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
275	C₄×Q₈	D₄×C₇₁	1	1	yes	characteristic
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
279	C₄×D₄	D₄×C₇₁	1	1	yes	characteristic
280	#117	—	2	1	no	—
281	#117	C₂³×C₇₁	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
287	#108	—	2	4	no	—
288	#107	—	2	2	no	—
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	4	no	—
295	#103	—	2	2	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#101	—	2	4	no	—
299	#101	—	2	4	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	#97	—	2	1	no	—
303	#97	—	2	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	D₄×C₇₁	1	2	yes	—
307	C₄×C₈	D₄×C₇₁	1	2	yes	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	C₂×D₄×C₇₁	1	1	yes	characteristic
316	C₂×Q₈	#41×C₇₁	1	4	yes	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂×D₄×C₇₁	1	1	yes	characteristic
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
325	C₂²×C₄	#41×C₇₁	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
327	Q₁₆	—	2	8	no	—
328	Q₁₆	—	2	8	no	—
329	SD₁₆	—	2	8	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	#41×C₇₁	1	4	yes	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₇₁	1	2	yes	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
351	C₄⋊C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	—	4	2	no	—
360	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₇₁	1	1	yes	characteristic
364	C₂³	—	2	1	no	—
365	C₂³	C₂×#41×C₇₁	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
388	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
389	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
390	C₂×C₄	#121×C₇₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
394	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
395	C₈	—	2	2	no	—
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
407	C₂²	#529×C₇₁	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	#473×C₇₁	1	2	yes	—
417	C₄	#525×C₇₁	1	1	yes	characteristic
418	C₄	#525×C₇₁	1	2	yes	—
419	C₄	#532×C₇₁	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	8	1	no	—
422	C₂	C₇₁×#2392	1	1	yes	characteristic
423	C₂	C₂×#473×C₇₁	1	1	yes	characteristic
424	C₂	C₇₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
socle	C₂²×C₇₁	C₂×#121
prime radical	C₂×#41×C₇₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₇₁	C₂	semidirect
4. C₇₁×#2089	C₂	semidirect
6. C₇₁×#2064	C₂	semidirect
8. C₇₁×#2047	C₂	semidirect
10. C₄×#108×C₇₁	C₂	semidirect
11. C₄×#101×C₇₁	C₂	semidirect
207. #23717	C₇₁	direct (N × H)
214. C₂×C₄×Q₁₆	C₂×C₇₁	semidirect
216. #2089	C₂×C₇₁	semidirect
218. #2064	C₂×C₇₁	semidirect
220. #2047	C₂×C₇₁	semidirect
222. C₄×#108	C₂×C₇₁	semidirect
223. C₄×#101	C₂×C₇₁	semidirect
224. C₇₁	#23717	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×#137×C₇₁	2
C₂×C₄×Q₁₆×C₇₁	2
C₇₁×#2922	2
C₇₁×#2089	2
C₇₁×#2078	2
C₇₁×#2064	2
C₇₁×#2052	2
C₇₁×#2047	2
C₇₁×#2020	2
C₄×#108×C₇₁	2
C₄×#101×C₇₁	2
#23717	71

Subgroups — C71×#23717 #31844589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23717 #31844589