Subgroups — #31967559

Order 18176.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597451	C₂	1	1	yes	maximal, characteristic
2	#22597435	C₂	1	1	yes	maximal, characteristic, complemented
3	#22587212	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587198	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587191	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587177	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587159	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₇₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₁₆×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587125	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586774	C₂	1	1	yes	maximal, characteristic
13	#22586743	C₂	1	1	yes	maximal, characteristic, complemented
14	#22586640	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#3107	C₂	1	1	yes	maximal, characteristic
16	#17986130	—	2	1	no	—
17	#17986130	—	2	1	no	—
18	#17986130	C₂²	1	1	yes	characteristic
19	#17986130	C₂²	1	1	yes	characteristic
20	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
22	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
23	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
24	D₄×C₇₁⋊C₈	—	2	1	no	—
25	D₄×C₇₁⋊C₈	—	2	1	no	—
26	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
28	#17986060	—	2	1	no	—
29	#17986060	—	2	1	no	—
30	#17986056	C₂²	1	1	yes	characteristic
31	#17986052	—	2	1	no	—
32	#17986052	C₂²	1	1	yes	characteristic
33	#17986052	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
36	#17985752	C₂²	1	1	yes	characteristic
37	#17985752	C₂²	1	1	yes	characteristic
38	#17985750	C₂²	1	1	yes	characteristic
39	#17985750	C₂²	1	1	yes	characteristic
40	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
42	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
43	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
44	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
45	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
46	D₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
48	#17985721	C₂²	1	1	yes	characteristic
49	#17985721	C₂²	1	1	yes	characteristic
50	#17985720	C₂²	1	1	yes	characteristic
51	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
52	#533×C₇₁	C₂²	1	1	yes	characteristic
53	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
54	#485×C₇₁	C₄	1	1	yes	characteristic
55	#485×C₇₁	C₄	1	1	yes	characteristic
56	#475×C₇₁	C₄	1	1	yes	characteristic
57	#474×C₇₁	C₄	1	1	yes	characteristic
58	#462×C₇₁	C₄	1	1	yes	characteristic
59	#461×C₇₁	C₄	1	1	yes	characteristic
60	#452×C₇₁	C₄	1	1	yes	characteristic
61	#452×C₇₁	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
63	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
65	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
66	#431×C₇₁	C₂²	1	1	yes	characteristic
67	C₂²×C₇₁⋊C₈	—	2	1	no	—
68	C₂²×C₇₁⋊C₈	—	2	1	no	—
69	C₂²×C₇₁⋊C₈	—	2	1	no	—
70	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
71	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
72	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
73	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
74	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
75	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
76	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
78	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
82	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
84	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
89	C₂²⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
90	#14556039	—	2	1	no	—
91	#14556039	—	2	1	no	—
92	#14556039	—	2	1	no	—
93	C₄×C₇₁⋊C₈	—	2	1	no	—
94	C₄×C₇₁⋊C₈	—	2	1	no	—
95	C₄×C₇₁⋊C₈	—	2	1	no	—
96	C₄×C₇₁⋊C₈	—	2	1	no	—
97	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
103	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
105	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
106	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
107	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
108	#125×C₇₁	—	2	1	no	—
109	C₂²⋊Q₈×C₇₁	—	2	1	no	—
110	C₂²⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₇₁	—	2	1	no	—
113	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₁	—	2	1	no	—
118	C₄×D₄×C₇₁	—	2	1	no	—
119	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
121	#117×C₇₁	—	2	1	no	—
122	#117×C₇₁	—	2	1	no	—
123	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₇₁	—	2	1	no	—
125	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
126	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
127	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
128	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
129	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
132	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
133	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
134	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
135	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
136	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
137	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
138	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
139	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₂×C₇₁⋊C₈	—	2	1	no	—
145	C₂×C₇₁⋊C₈	—	2	1	no	—
146	C₂×C₇₁⋊C₈	—	2	1	no	—
147	C₂×C₇₁⋊C₈	—	2	1	no	—
148	C₂×C₇₁⋊C₈	—	2	1	no	—
149	C₂×C₇₁⋊C₈	—	2	1	no	—
150	C₂×C₇₁⋊C₈	—	8	1	no	—
151	C₂×C₇₁⋊C₈	—	8	1	no	—
152	C₂×C₇₁⋊C₈	—	8	1	no	—
153	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
157	#41×C₇₁	—	2	2	no	—
158	#41×C₇₁	—	2	2	no	—
159	C₂×Q₈×C₇₁	—	2	1	no	—
160	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
162	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₄×C₇₁	—	2	1	no	—
164	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₁	—	2	1	no	—
166	C₂²×C₄×C₇₁	—	2	1	no	—
167	C₂²×C₄×C₇₁	—	2	1	no	—
168	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
171	Q₁₆×C₇₁	—	2	2	no	—
172	Q₁₆×C₇₁	—	2	2	no	—
173	SD₁₆×C₇₁	—	2	2	no	—
174	SD₁₆×C₇₁	—	2	2	no	—
175	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₇₁	—	2	1	no	—
180	C₄⋊C₄×C₇₁	—	2	1	no	—
181	C₄⋊C₄×C₇₁	—	2	1	no	—
182	C₄⋊C₄×C₇₁	—	2	1	no	—
183	C₄⋊C₄×C₇₁	—	2	1	no	—
184	C₄⋊C₄×C₇₁	—	2	1	no	—
185	C₄⋊C₄×C₇₁	—	2	1	no	—
186	C₄⋊C₄×C₇₁	—	2	1	no	—
187	C₄⋊C₄×C₇₁	—	2	1	no	—
188	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₇₁	—	2	1	no	—
193	C₂²⋊C₄×C₇₁	—	2	1	no	—
194	C₂²⋊C₄×C₇₁	—	2	1	no	—
195	C₂²⋊C₄×C₇₁	—	2	1	no	—
196	C₂²⋊C₄×C₇₁	—	2	1	no	—
197	C₄²×C₇₁	—	2	1	no	—
198	C₄²×C₇₁	—	2	1	no	—
199	C₄²×C₇₁	—	2	1	no	—
200	C₄²×C₇₁	—	2	1	no	—
201	C₄²×C₇₁	—	2	1	no	—
202	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₇₁	#41	1	1	yes	characteristic
205	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
206	C₂³×C₇₁	—	2	1	no	—
207	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₇₁	—	2	1	no	—
209	Q₈×C₇₁	—	2	1	no	—
210	Q₈×C₇₁	—	2	1	no	—
211	Q₈×C₇₁	—	2	1	no	—
212	Q₈×C₇₁	—	2	1	no	—
213	Q₈×C₇₁	—	8	1	no	—
214	Q₈×C₇₁	#131	1	2	yes	—
215	D₄×C₇₁	—	2	4	no	—
216	D₄×C₇₁	—	2	1	no	—
217	D₄×C₇₁	#131	1	2	yes	—
218	C₂×C₄×C₇₁	—	2	4	no	—
219	C₂×C₄×C₇₁	—	2	1	no	—
220	C₂×C₄×C₇₁	—	2	1	no	—
221	C₂×C₄×C₇₁	—	2	1	no	—
222	C₂×C₄×C₇₁	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	2	1	no	—
227	C₂×C₄×C₇₁	—	2	1	no	—
228	C₂×C₄×C₇₁	—	2	1	no	—
229	C₂×C₄×C₇₁	—	2	1	no	—
230	C₂×C₄×C₇₁	—	4	1	no	—
231	C₂×C₄×C₇₁	—	4	1	no	—
232	C₂×C₄×C₇₁	—	4	1	no	—
233	C₂×C₄×C₇₁	—	8	1	no	—
234	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
240	C₈×C₇₁	—	2	1	no	—
241	C₈×C₇₁	—	2	1	no	—
242	C₈×C₇₁	—	2	1	no	—
243	C₈×C₇₁	—	2	1	no	—
244	C₇₁⋊C₈	—	2	1	no	—
245	C₇₁⋊C₈	—	2	1	no	—
246	C₇₁⋊C₈	—	2	1	no	—
247	C₇₁⋊C₈	—	2	1	no	—
248	C₇₁⋊C₈	—	4	1	no	—
249	C₇₁⋊C₈	—	4	1	no	—
250	C₇₁⋊C₈	—	4	1	no	—
251	C₇₁⋊C₈	—	4	1	no	—
252	C₇₁⋊C₈	—	4	1	no	—
253	C₇₁⋊C₈	—	4	1	no	—
254	C₂²×C₇₁	—	2	1	no	—
255	C₂²×C₇₁	—	2	2	no	—
256	C₂²×C₇₁	—	2	1	no	—
257	C₂²×C₇₁	—	2	1	no	—
258	C₂²×C₇₁	—	4	1	no	—
259	C₂²×C₇₁	—	4	1	no	—
260	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
261	C₄×C₇₁	—	2	1	no	—
262	C₄×C₇₁	—	2	2	no	—
263	C₄×C₇₁	—	2	1	no	—
264	C₄×C₇₁	—	2	1	no	—
265	C₄×C₇₁	—	2	1	no	—
266	C₄×C₇₁	—	4	1	no	—
267	C₄×C₇₁	—	4	1	no	—
268	C₄×C₇₁	—	4	1	no	—
269	C₄×C₇₁	—	4	1	no	—
270	C₄×C₇₁	—	4	1	no	—
271	C₄×C₇₁	—	4	1	no	—
272	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
273	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
274	C₄×C₇₁	#577	1	1	yes	characteristic
275	C₄×C₇₁	#578	1	1	yes	characteristic
276	#17921	—	71	1	no	maximal, Sylow
277	C₂×C₇₁	—	4	1	no	—
278	C₂×C₇₁	—	4	2	no	—
279	C₂×C₇₁	#2929	1	1	yes	characteristic
280	C₂×C₇₁	#2947	1	1	yes	characteristic
281	C₂×C₇₁	#2957	1	1	yes	characteristic
282	#3107	D₇₁	1	1	yes	characteristic
283	#2988	—	71	1	no	—
284	#2985	—	71	1	no	—
285	#1587	—	71	1	no	—
286	#1585	—	71	1	no	—
287	#1584	—	71	1	no	—
288	#1582	—	71	1	no	—
289	#1579	—	71	1	no	—
290	SD₁₆⋊C₈	—	71	1	no	—
291	C₈×Q₁₆	—	71	1	no	—
292	C₈×SD₁₆	—	71	1	no	—
293	#1573	—	71	1	no	—
294	#1488	—	71	1	no	—
295	#1481	—	71	1	no	—
296	#1454	—	71	1	no	—
297	C₇₁	#17921	1	1	yes	characteristic, complemented, Sylow
298	#533	C₂×D₇₁	1	1	yes	characteristic
299	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
300	#485	Dic₇₁	1	1	yes	characteristic
301	#485	Dic₇₁	1	1	yes	characteristic
302	#475	Dic₇₁	1	1	yes	characteristic
303	#474	Dic₇₁	1	1	yes	characteristic
304	#462	Dic₇₁	1	1	yes	characteristic
305	#461	Dic₇₁	1	1	yes	characteristic
306	#452	Dic₇₁	1	1	yes	characteristic
307	#452	Dic₇₁	1	1	yes	characteristic
308	#446	—	71	1	no	—
309	#446	—	71	1	no	—
310	#446	—	142	1	no	—
311	#446	—	142	1	no	—
312	C₈×Q₈	—	71	1	no	—
313	C₈×Q₈	—	71	1	no	—
314	C₈×Q₈	—	71	1	no	—
315	C₈×Q₈	—	71	1	no	—
316	C₄×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
317	C₄×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
318	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
319	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
320	C₈×D₄	—	71	1	no	—
321	C₈×D₄	—	71	1	no	—
322	C₈×D₄	—	142	1	no	—
323	C₈×D₄	—	142	1	no	—
324	#433	—	142	1	no	—
325	#433	—	142	1	no	—
326	#432	—	71	1	no	—
327	#431	—	71	1	no	—
328	#431	—	71	1	no	—
329	#431	—	142	1	no	—
330	#431	C₂×D₇₁	1	1	yes	characteristic
331	C₂×C₄⋊C₈	—	71	1	no	—
332	C₂×C₄⋊C₈	—	142	1	no	—
333	#335	—	71	1	no	—
334	#335	—	71	1	no	—
335	#334	—	71	1	no	—
336	#334	—	71	1	no	—
337	Q₈⋊C₈	—	71	1	no	—
338	Q₈⋊C₈	—	71	1	no	—
339	Q₈⋊C₈	—	71	1	no	—
340	Q₈⋊C₈	—	71	1	no	—
341	Q₈⋊C₈	—	71	1	no	—
342	Q₈⋊C₈	—	71	1	no	—
343	D₄⋊C₈	—	71	1	no	—
344	D₄⋊C₈	—	71	1	no	—
345	#322	—	71	1	no	—
346	#322	—	71	1	no	—
347	#322	—	71	1	no	—
348	C₈²	—	71	1	no	—
349	C₂×#41	C₂×Dic₇₁	1	1	yes	characteristic
350	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic
351	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic
352	C₂×SD₁₆	C₂×Dic₇₁	1	1	yes	characteristic
353	C₂×SD₁₆	C₂×Dic₇₁	1	1	yes	characteristic
354	C₂²×C₈	—	142	1	no	—
355	C₂²×C₈	—	142	1	no	—
356	C₂²×C₈	—	142	1	no	—
357	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
358	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
359	#125	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
365	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
366	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
367	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
371	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	C₂×Dic₇₁	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
377	#107	C₂×Dic₇₁	1	1	yes	characteristic
378	#107	C₂×Dic₇₁	1	1	yes	characteristic
379	#106	C₂×Dic₇₁	1	1	yes	characteristic
380	#106	C₂×Dic₇₁	1	1	yes	characteristic
381	C₄⋊C₈	—	71	1	no	—
382	C₄⋊C₈	—	71	1	no	—
383	C₄⋊C₈	—	71	1	no	—
384	C₄⋊C₈	—	71	1	no	—
385	C₄⋊C₈	—	71	1	no	—
386	C₄⋊C₈	—	71	1	no	—
387	C₄⋊C₈	—	142	1	no	—
388	C₄⋊C₈	—	142	1	no	—
389	C₄⋊C₈	—	142	1	no	—
390	C₄⋊C₈	—	142	1	no	—
391	C₄⋊C₈	—	142	1	no	—
392	C₄⋊C₈	—	142	1	no	—
393	C₄⋊C₈	—	142	1	no	—
394	C₄⋊C₈	—	142	1	no	—
395	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
396	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
397	#103	C₂×Dic₇₁	1	1	yes	characteristic
398	#103	C₂×Dic₇₁	1	1	yes	characteristic
399	#103	C₂×Dic₇₁	1	1	yes	characteristic
400	#103	C₂×Dic₇₁	1	1	yes	characteristic
401	#103	C₂×Dic₇₁	1	1	yes	characteristic
402	#103	C₂×Dic₇₁	1	1	yes	characteristic
403	#102	C₂×Dic₇₁	1	1	yes	characteristic
404	#102	C₂×Dic₇₁	1	1	yes	characteristic
405	C₂²⋊C₈	—	71	1	no	—
406	C₂²⋊C₈	—	71	1	no	—
407	C₂²⋊C₈	—	142	1	no	—
408	C₂²⋊C₈	—	142	1	no	—
409	C₂²⋊C₈	—	142	1	no	—
410	C₂²⋊C₈	—	142	1	no	—
411	C₂²⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
412	C₂²⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
413	#97	—	142	1	no	—
414	#97	—	142	1	no	—
415	#97	—	142	1	no	—
416	C₄×C₈	—	71	1	no	—
417	C₄×C₈	—	71	1	no	—
418	C₄×C₈	—	71	1	no	—
419	C₄×C₈	—	71	1	no	—
420	C₄×C₈	—	142	1	no	—
421	C₄×C₈	—	142	1	no	—
422	C₄×C₈	—	142	1	no	—
423	C₄×C₈	—	142	1	no	—
424	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
430	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
431	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
439	C₂²×C₄	#11765864	1	1	yes	characteristic
440	Q₁₆	—	2	2	no	—
441	Q₁₆	—	2	2	no	—
442	SD₁₆	—	2	2	no	—
443	SD₁₆	—	2	2	no	—
444	C₂×C₈	—	568	1	no	—
445	C₂×C₈	—	568	1	no	—
446	C₂×C₈	—	568	1	no	—
447	C₂×C₈	—	71	1	no	—
448	C₂×C₈	—	71	1	no	—
449	C₂×C₈	—	71	1	no	—
450	C₂×C₈	—	71	1	no	—
451	C₂×C₈	—	142	1	no	—
452	C₂×C₈	—	142	1	no	—
453	C₂×C₈	—	142	1	no	—
454	C₂×C₈	—	142	1	no	—
455	C₂×C₈	—	142	1	no	—
456	C₂×C₈	—	142	1	no	—
457	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
458	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
459	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
460	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
485	C₄²	D₄×D₇₁	1	1	yes	characteristic
486	C₄²	#11765864	1	1	yes	characteristic
487	C₄²	C₂³×D₇₁	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	D₄×Dic₇₁	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	#14556135	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	#14556135	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
517	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
518	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
519	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
521	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	284	1	no	—
527	C₈	—	284	1	no	—
528	C₈	—	284	1	no	—
529	C₈	—	284	1	no	—
530	C₈	—	284	1	no	—
531	C₈	—	284	1	no	—
532	C₈	—	142	1	no	—
533	C₈	—	142	1	no	—
534	C₈	—	142	1	no	—
535	C₈	—	142	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	C₂×#14556135	1	1	yes	characteristic
555	C₄	C₂×#14556135	1	1	yes	characteristic
556	C₄	#17986808	1	1	yes	characteristic
557	C₄	#17986815	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	#22597035	1	1	yes	characteristic
561	C₂	#22597184	1	1	yes	characteristic
562	C₂	#22597257	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#3107	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂×#41×C₇₁	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#3107	D₇₁
hypocenter	C₇₁	#17921
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #22597435	C₂	semidirect
3. #22587212	C₂	semidirect
4. #22587198	C₂	semidirect
5. #22587191	C₂	semidirect
6. #22587177	C₂	semidirect
7. #22587159	C₂	semidirect
8. SD₁₆⋊(C₇₁⋊C₈)	C₂	semidirect
9. Q₁₆×C₇₁⋊C₈	C₂	semidirect
10. SD₁₆×C₇₁⋊C₈	C₂	semidirect
11. #22587125	C₂	semidirect
13. #22586743	C₂	semidirect
14. #22586640	C₂	semidirect
297. C₇₁	#17921	semidirect

Maximal subgroups

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

subgroup	index
#22597451	2
#22597435	2
#22587212	2
#22587198	2
#22587191	2
#22587177	2
#22587159	2
SD₁₆⋊(C₇₁⋊C₈)	2
Q₁₆×C₇₁⋊C₈	2
SD₁₆×C₇₁⋊C₈	2
#22587125	2
#22586774	2
#22586743	2
#22586640	2
C₇₁×#3107	2
#17921	71