Subgroups — C₇₁×#23677 #31844549

Order 18176.

924 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×SD₁₆×C₇₁	C₂	1	2	yes	maximal
2	C₄×C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₁×#2293	C₂	1	1	yes	maximal, characteristic
4	C₇₁×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₁×#2071	C₂	1	1	yes	maximal, characteristic
6	C₇₁×#2066	C₂	1	2	yes	maximal, complemented
7	C₇₁×#2055	C₂	1	2	yes	maximal
8	C₇₁×#2043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2013	C₂	1	1	yes	maximal, characteristic
10	C₄×C₄⋊C₈×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#103×C₇₁	C₂	1	2	yes	maximal, complemented
12	C₂²×SD₁₆×C₇₁	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₁	—	2	1	no	—
17	C₄×SD₁₆×C₇₁	—	2	8	no	—
18	C₂×#106×C₇₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₇₁	C₂²	1	2	yes	—
20	C₂×#103×C₇₁	C₂²	1	2	yes	—
21	C₂×#103×C₇₁	C₂²	1	2	yes	—
22	C₂×#103×C₇₁	C₂²	1	2	yes	—
23	C₂×#102×C₇₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
25	#391×C₇₁	C₂²	1	2	yes	—
26	#390×C₇₁	C₂²	1	1	yes	characteristic
27	#390×C₇₁	C₂²	1	1	yes	characteristic
28	#389×C₇₁	—	2	1	no	—
29	#389×C₇₁	—	2	1	no	—
30	#389×C₇₁	C₂²	1	1	yes	characteristic
31	#389×C₇₁	C₂²	1	1	yes	characteristic
32	#388×C₇₁	—	2	1	no	—
33	#388×C₇₁	—	2	1	no	—
34	#384×C₇₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₇₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₇₁	—	2	1	no	—
39	C₄³×C₇₁	C₂²	1	1	yes	characteristic
40	#340×C₇₁	C₂²	1	2	yes	—
41	#340×C₇₁	C₂²	1	2	yes	—
42	#336×C₇₁	C₂²	1	1	yes	characteristic
43	#336×C₇₁	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₇₁	C₂³	1	2	yes	—
45	C₂²×D₄×C₇₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇₁	—	2	1	no	—
47	C₂×SD₁₆×C₇₁	—	2	4	no	—
48	C₂×SD₁₆×C₇₁	—	2	4	no	—
49	C₂×SD₁₆×C₇₁	—	2	4	no	—
50	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₁	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₇₁	—	2	4	no	—
53	C₄×Q₈×C₇₁	—	2	4	no	—
54	C₄×Q₈×C₇₁	—	2	4	no	—
55	C₄×D₄×C₇₁	—	2	2	no	—
56	C₄×D₄×C₇₁	D₄	1	4	yes	—
57	#117×C₇₁	—	4	4	no	—
58	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
74	C₂×C₄²×C₇₁	—	2	1	no	—
75	C₂×C₄²×C₇₁	—	2	2	no	—
76	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
83	#106×C₇₁	—	2	4	no	—
84	C₄⋊C₈×C₇₁	—	2	4	no	—
85	#103×C₇₁	—	2	4	no	—
86	#103×C₇₁	—	2	4	no	—
87	#103×C₇₁	—	2	4	no	—
88	#102×C₇₁	—	2	4	no	—
89	C₄×C₈×C₇₁	—	2	4	no	—
90	#95×C₇₁	—	2	1	no	—
91	#95×C₇₁	—	2	1	no	—
92	#95×C₇₁	—	2	2	no	—
93	#95×C₇₁	—	2	2	no	—
94	#95×C₇₁	—	2	1	no	—
95	C₂⁴×C₇₁	—	2	1	no	—
96	C₂×Q₈×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	#41	1	4	yes	—
102	C₂×D₄×C₇₁	—	2	2	no	—
103	C₂×D₄×C₇₁	—	2	2	no	—
104	C₂×D₄×C₇₁	—	2	1	no	—
105	C₂×D₄×C₇₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₇₁	—	2	2	no	—
107	C₂²×C₄×C₇₁	—	2	1	no	—
108	C₂²×C₄×C₇₁	—	2	4	no	—
109	C₂²×C₄×C₇₁	—	2	1	no	—
110	C₂²×C₄×C₇₁	—	2	1	no	—
111	C₂²×C₄×C₇₁	—	2	2	no	—
112	C₂²×C₄×C₇₁	—	4	2	no	—
113	C₂²×C₄×C₇₁	—	4	2	no	—
114	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₇₁	—	2	16	no	—
122	C₂×C₈×C₇₁	—	2	2	no	—
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	2	no	—
127	C₂×C₈×C₇₁	#41	1	4	yes	—
128	C₄⋊C₄×C₇₁	—	2	4	no	—
129	C₄⋊C₄×C₇₁	—	2	4	no	—
130	C₄⋊C₄×C₇₁	—	2	1	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	—	2	2	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	4	no	—
137	C₄⋊C₄×C₇₁	—	4	2	no	—
138	C₄⋊C₄×C₇₁	—	4	2	no	—
139	C₄⋊C₄×C₇₁	—	4	2	no	—
140	C₄⋊C₄×C₇₁	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₇₁	—	2	4	no	—
142	C₂²⋊C₄×C₇₁	—	4	2	no	—
143	C₂²⋊C₄×C₇₁	—	4	2	no	—
144	C₂²⋊C₄×C₇₁	—	4	2	no	—
145	C₂²⋊C₄×C₇₁	—	4	2	no	—
146	C₄²×C₇₁	—	2	2	no	—
147	C₄²×C₇₁	—	2	2	no	—
148	C₄²×C₇₁	—	2	2	no	—
149	C₄²×C₇₁	—	2	2	no	—
150	C₄²×C₇₁	—	4	1	no	—
151	C₄²×C₇₁	—	4	4	no	—
152	C₄²×C₇₁	—	4	2	no	—
153	C₄²×C₇₁	SD₁₆	1	4	yes	complemented
154	C₄²×C₇₁	C₂×D₄	1	2	yes	—
155	C₄²×C₇₁	#41	1	2	yes	—
156	C₂³×C₇₁	—	2	2	no	—
157	C₂³×C₇₁	—	4	1	no	—
158	C₂³×C₇₁	—	4	1	no	—
159	C₂³×C₇₁	—	4	1	no	—
160	C₂³×C₇₁	—	4	1	no	—
161	C₂³×C₇₁	—	4	1	no	—
162	C₂³×C₇₁	—	4	1	no	—
163	C₂³×C₇₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₇₁	—	2	4	no	—
165	Q₈×C₇₁	—	2	4	no	—
166	Q₈×C₇₁	—	4	2	no	—
167	Q₈×C₇₁	—	4	2	no	—
168	D₄×C₇₁	—	2	4	no	—
169	D₄×C₇₁	—	4	2	no	—
170	C₂×C₄×C₇₁	—	2	1	no	—
171	C₂×C₄×C₇₁	—	2	1	no	—
172	C₂×C₄×C₇₁	—	2	1	no	—
173	C₂×C₄×C₇₁	—	2	1	no	—
174	C₂×C₄×C₇₁	—	2	1	no	—
175	C₂×C₄×C₇₁	—	2	1	no	—
176	C₂×C₄×C₇₁	—	2	1	no	—
177	C₂×C₄×C₇₁	—	2	1	no	—
178	C₂×C₄×C₇₁	—	2	2	no	—
179	C₂×C₄×C₇₁	—	2	4	no	—
180	C₂×C₄×C₇₁	—	2	1	no	—
181	C₂×C₄×C₇₁	—	2	1	no	—
182	C₂×C₄×C₇₁	—	2	1	no	—
183	C₂×C₄×C₇₁	—	4	2	no	—
184	C₂×C₄×C₇₁	—	4	2	no	—
185	C₂×C₄×C₇₁	—	4	1	no	—
186	C₂×C₄×C₇₁	—	4	1	no	—
187	C₂×C₄×C₇₁	—	4	8	no	—
188	C₂×C₄×C₇₁	—	4	2	no	—
189	C₂×C₄×C₇₁	—	4	1	no	—
190	C₂×C₄×C₇₁	—	4	1	no	—
191	C₂×C₄×C₇₁	—	4	1	no	—
192	C₂×C₄×C₇₁	—	4	1	no	—
193	C₂×C₄×C₇₁	—	4	1	no	—
194	C₂×C₄×C₇₁	—	4	2	no	—
195	C₂×C₄×C₇₁	—	4	1	no	—
196	C₂×C₄×C₇₁	—	4	2	no	—
197	C₂×C₄×C₇₁	#121	1	2	yes	—
198	C₂×C₄×C₇₁	#121	1	2	yes	—
199	C₂×C₄×C₇₁	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₇₁	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₇₁	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₇₁	#135	1	2	yes	—
203	C₂×C₄×C₇₁	#137	1	2	yes	—
204	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
206	C₂×C₄×C₇₁	C₂×#41	1	2	yes	—
207	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
208	C₈×C₇₁	—	2	4	no	—
209	C₈×C₇₁	—	4	2	no	—
210	C₂²×C₇₁	—	4	2	no	—
211	C₂²×C₇₁	—	4	2	no	—
212	C₂²×C₇₁	—	4	2	no	—
213	C₂²×C₇₁	—	8	1	no	—
214	C₂²×C₇₁	—	8	1	no	—
215	C₂²×C₇₁	—	8	1	no	—
216	C₂²×C₇₁	—	8	1	no	—
217	C₂²×C₇₁	C₂×#121	1	1	yes	characteristic
218	C₂²×C₇₁	#525	1	1	yes	characteristic
219	C₂²×C₇₁	#532	1	1	yes	characteristic
220	C₂²×C₇₁	C₂²×SD₁₆	1	1	yes	characteristic
221	C₂²×C₇₁	C₂×#135	1	1	yes	characteristic
222	C₂²×C₇₁	C₂×#137	1	1	yes	characteristic
223	C₂²×C₇₁	#575	1	1	yes	characteristic
224	C₄×C₇₁	—	2	2	no	—
225	C₄×C₇₁	—	2	2	no	—
226	C₄×C₇₁	—	2	2	no	—
227	C₄×C₇₁	—	2	2	no	—
228	C₄×C₇₁	—	4	4	no	—
229	C₄×C₇₁	—	4	1	no	—
230	C₄×C₇₁	—	4	2	no	—
231	C₄×C₇₁	—	8	1	no	—
232	C₄×C₇₁	—	8	1	no	—
233	C₄×C₇₁	—	8	2	no	—
234	C₄×C₇₁	#461	1	4	yes	—
235	C₄×C₇₁	#525	1	2	yes	—
236	C₄×C₇₁	#529	1	2	yes	—
237	#23677	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂×C₇₁	—	8	2	no	—
239	C₂×C₇₁	#2392	1	1	yes	characteristic
240	C₂×C₇₁	C₂×#461	1	1	yes	characteristic
241	C₂×C₇₁	#3035	1	1	yes	characteristic
242	C₂×C₇₁	#3103	1	1	yes	characteristic
243	C₂×C₇₁	#3108	1	1	yes	characteristic
244	C₂×C₇₁	#3167	1	1	yes	characteristic
245	C₂×C₇₁	#3172	1	1	yes	characteristic
246	C₂×C₄×SD₁₆	C₂×C₇₁	1	2	yes	—
247	C₄×C₄⋊Q₈	C₂×C₇₁	1	1	yes	characteristic, complemented
248	#2293	C₂×C₇₁	1	1	yes	characteristic
249	#2084	C₂×C₇₁	1	1	yes	characteristic, complemented
250	#2071	C₂×C₇₁	1	1	yes	characteristic
251	#2066	C₂×C₇₁	1	2	yes	complemented
252	#2055	C₂×C₇₁	1	2	yes	—
253	#2043	C₂×C₇₁	1	1	yes	characteristic, complemented
254	#2013	C₂×C₇₁	1	1	yes	characteristic
255	C₄×C₄⋊C₈	C₂×C₇₁	1	1	yes	characteristic, complemented
256	C₄×#103	C₂×C₇₁	1	2	yes	complemented
257	C₇₁	#23677	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×SD₁₆	C₂²×C₇₁	1	2	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₇₁	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₇₁	1	2	yes	—
261	C₂×C₄×D₄	C₂²×C₇₁	1	1	yes	characteristic
262	C₂×#117	—	2	1	no	—
263	C₄×SD₁₆	—	2	8	no	—
264	C₂×#106	C₂²×C₇₁	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₇₁	1	2	yes	—
266	C₂×#103	C₂²×C₇₁	1	2	yes	—
267	C₂×#103	C₂²×C₇₁	1	2	yes	—
268	C₂×#103	C₂²×C₇₁	1	2	yes	—
269	C₂×#102	C₂²×C₇₁	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₇₁	1	2	yes	—
271	#391	C₂²×C₇₁	1	2	yes	—
272	#390	C₂²×C₇₁	1	1	yes	characteristic
273	#390	C₂²×C₇₁	1	1	yes	characteristic
274	#389	—	2	1	no	—
275	#389	—	2	1	no	—
276	#389	C₂²×C₇₁	1	1	yes	characteristic
277	#389	C₂²×C₇₁	1	1	yes	characteristic
278	#388	—	2	1	no	—
279	#388	—	2	1	no	—
280	#384	C₂²×C₇₁	1	1	yes	characteristic
281	C₄×C₄⋊C₄	—	2	1	no	—
282	C₄×C₄⋊C₄	—	2	1	no	—
283	C₄×C₄⋊C₄	C₂²×C₇₁	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	C₄³	C₂²×C₇₁	1	1	yes	characteristic
286	#340	C₂²×C₇₁	1	2	yes	—
287	#340	C₂²×C₇₁	1	2	yes	—
288	#336	C₂²×C₇₁	1	1	yes	characteristic
289	#336	C₂²×C₇₁	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₇₁	1	2	yes	—
291	C₂²×D₄	C₂³×C₇₁	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
297	C₂²×C₈	C₂³×C₇₁	1	2	yes	—
298	C₄⋊Q₈	—	2	4	no	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₇₁	1	4	yes	—
303	#117	—	4	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×C₇₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₇₁	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
325	C₂×C₄²	D₄×C₇₁	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₇₁	1	1	yes	characteristic
329	#106	—	2	4	no	—
330	C₄⋊C₈	—	2	4	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#103	—	2	4	no	—
334	#102	—	2	4	no	—
335	C₄×C₈	—	2	4	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	1	no	—
341	C₂⁴	—	2	1	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	#41×C₇₁	1	4	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	C₂×D₄×C₇₁	1	2	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₇₁	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₇₁	1	1	yes	characteristic
367	SD₁₆	—	2	16	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	#41×C₇₁	1	4	yes	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	C₂×D₄×C₇₁	1	2	yes	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	4	4	no	—
398	C₄²	—	4	2	no	—
399	C₄²	SD₁₆×C₇₁	1	4	yes	complemented
400	C₄²	C₂×D₄×C₇₁	1	2	yes	—
401	C₄²	#41×C₇₁	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₂²×D₄×C₇₁	1	1	yes	characteristic
410	Q₈	—	2	4	no	—
411	Q₈	—	2	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	4	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	#121×C₇₁	1	2	yes	—
444	C₂×C₄	#121×C₇₁	1	2	yes	—
445	C₂×C₄	C₂×SD₁₆×C₇₁	1	2	yes	—
446	C₂×C₄	C₂×SD₁₆×C₇₁	1	2	yes	—
447	C₂×C₄	C₂×SD₁₆×C₇₁	1	2	yes	—
448	C₂×C₄	#135×C₇₁	1	2	yes	—
449	C₂×C₄	#137×C₇₁	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₇₁	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
452	C₂×C₄	C₂×#41×C₇₁	1	2	yes	—
453	C₂×C₄	C₂×#41×C₇₁	1	1	yes	characteristic
454	C₈	—	2	4	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	C₂×#121×C₇₁	1	1	yes	characteristic
464	C₂²	#525×C₇₁	1	1	yes	characteristic
465	C₂²	#532×C₇₁	1	1	yes	characteristic
466	C₂²	C₂²×SD₁₆×C₇₁	1	1	yes	characteristic
467	C₂²	C₂×#135×C₇₁	1	1	yes	characteristic
468	C₂²	C₂×#137×C₇₁	1	1	yes	characteristic
469	C₂²	#575×C₇₁	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	#461×C₇₁	1	4	yes	—
481	C₄	#525×C₇₁	1	2	yes	—
482	C₄	#529×C₇₁	1	2	yes	—
483	C₂	—	8	2	no	—
484	C₂	C₇₁×#2392	1	1	yes	characteristic
485	C₂	C₂×#461×C₇₁	1	1	yes	characteristic
486	C₂	C₇₁×#3035	1	1	yes	characteristic
487	C₂	C₇₁×#3103	1	1	yes	characteristic
488	C₂	C₇₁×#3108	1	1	yes	characteristic
489	C₂	C₇₁×#3167	1	1	yes	characteristic
490	C₂	C₇₁×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
socle	C₂³×C₇₁	C₂²×D₄
prime radical	C₂²×D₄×C₇₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₁ ◁ C₄³×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₄⋊Q₈×C₇₁	C₂	semidirect
4. C₇₁×#2084	C₂	semidirect
6. C₇₁×#2066	C₂	semidirect
8. C₇₁×#2043	C₂	semidirect
10. C₄×C₄⋊C₈×C₇₁	C₂	semidirect
11. C₄×#103×C₇₁	C₂	semidirect
153. C₄²×C₇₁	SD₁₆	semidirect
237. #23677	C₇₁	direct (N × H)
247. C₄×C₄⋊Q₈	C₂×C₇₁	semidirect
249. #2084	C₂×C₇₁	semidirect
251. #2066	C₂×C₇₁	semidirect
253. #2043	C₂×C₇₁	semidirect
255. C₄×C₄⋊C₈	C₂×C₇₁	semidirect
256. C₄×#103	C₂×C₇₁	semidirect
257. C₇₁	#23677	direct (N × H)
399. C₄²	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×C₄×SD₁₆×C₇₁	2
C₄×C₄⋊Q₈×C₇₁	2
C₇₁×#2293	2
C₇₁×#2084	2
C₇₁×#2071	2
C₇₁×#2066	2
C₇₁×#2055	2
C₇₁×#2043	2
C₇₁×#2013	2
C₄×C₄⋊C₈×C₇₁	2
C₄×#103×C₇₁	2
#23677	71

Subgroups — C71×#23677 #31844549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#23677 #31844549