Subgroups — #31966493

Order 18176.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597459	C₂	1	1	yes	maximal, characteristic
2	#22597454	C₂	1	1	yes	maximal, characteristic
3	C₄×#14556136	C₂	1	1	yes	maximal, characteristic
4	#22587107	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587106	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587104	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587102	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587101	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587095	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587094	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587091	C₂	1	1	yes	maximal, characteristic, complemented
12	#22587089	C₂	1	1	yes	maximal, characteristic, complemented
13	#22587087	C₂	1	1	yes	maximal, characteristic, complemented
14	#334×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1569	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556136	C₄	1	1	yes	characteristic
17	C₂×#14556136	C₄	1	1	yes	characteristic
18	C₄×#11765865	C₂²	1	1	yes	characteristic
19	#17986128	—	2	1	no	—
20	#17986127	—	2	1	no	—
21	#17986075	—	2	1	no	—
22	#17986074	—	2	1	no	—
23	#17986073	—	2	1	no	—
24	#17986072	—	2	1	no	—
25	#17986069	—	2	1	no	—
26	#17986068	—	2	1	no	—
27	#17986056	C₂²	1	1	yes	characteristic
28	#17986055	C₂²	1	1	yes	characteristic
29	#17986055	C₂²	1	1	yes	characteristic
30	#17986051	C₂²	1	1	yes	characteristic
31	#17986051	C₂²	1	1	yes	characteristic
32	#17986023	C₂²	1	1	yes	characteristic
33	#17986021	C₂²	1	1	yes	characteristic
34	#17986021	C₂²	1	1	yes	characteristic
35	C₄⋊C₈×D₇₁	C₂²	1	1	yes	characteristic
36	C₄⋊C₈×D₇₁	C₂²	1	1	yes	characteristic
37	#17985957	C₄	1	1	yes	characteristic
38	#17985957	C₄	1	1	yes	characteristic
39	#17985956	C₄	1	1	yes	characteristic
40	#17985956	C₄	1	1	yes	characteristic
41	#17985956	C₄	1	1	yes	characteristic
42	#17985956	C₄	1	1	yes	characteristic
43	C₄×#11765848	C₂²	1	1	yes	characteristic
44	C₄×#11765848	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985752	C₂²	1	1	yes	characteristic
49	#17985752	C₂²	1	1	yes	characteristic
50	#17985751	C₂²	1	1	yes	characteristic
51	#17985751	C₂²	1	1	yes	characteristic
52	#17985750	C₂²	1	1	yes	characteristic
53	#17985750	C₂²	1	1	yes	characteristic
54	#17985749	C₂²	1	1	yes	characteristic
55	#17985749	C₂²	1	1	yes	characteristic
56	#17985749	C₂²	1	1	yes	characteristic
57	#17985749	C₂²	1	1	yes	characteristic
58	#17985749	C₂²	1	1	yes	characteristic
59	#17985749	C₂²	1	1	yes	characteristic
60	#432×C₇₁	C₂²	1	1	yes	characteristic
61	#423×C₇₁	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
63	#335×C₇₁	C₂²	1	1	yes	characteristic
64	#335×C₇₁	C₂²	1	1	yes	characteristic
65	#334×C₇₁	C₂²	1	1	yes	characteristic
66	#334×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765865	C₂×C₄	1	1	yes	characteristic
68	#14556136	—	2	4	no	—
69	#14556136	—	2	4	no	—
70	C₂×#11765849	—	2	1	no	—
71	C₂×#11765848	—	2	1	no	—
72	C₂×#11765848	—	2	1	no	—
73	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
74	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
75	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
76	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₇₁	—	2	1	no	—
80	C₂×C₈×D₇₁	—	2	1	no	—
81	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₄₂	D₄	1	1	yes	characteristic
86	C₄×Dic₁₄₂	Q₈	1	1	yes	characteristic
87	C₄×D₂₈₄	D₄	1	1	yes	characteristic
88	C₄×D₂₈₄	Q₈	1	1	yes	characteristic
89	C₄×C₂²⋊D₇₁	D₄	1	1	yes	characteristic
90	C₄×C₂²⋊D₇₁	D₄	1	1	yes	characteristic
91	C₄×C₂²⋊D₇₁	Q₈	1	1	yes	characteristic
92	C₄×C₂²⋊D₇₁	Q₈	1	1	yes	characteristic
93	#14556087	C₂×C₄	1	1	yes	characteristic
94	#14556085	C₂×C₄	1	1	yes	characteristic
95	#14556085	C₂×C₄	1	1	yes	characteristic
96	C₄²×D₇₁	C₂³	1	1	yes	characteristic
97	C₄²×D₇₁	C₂³	1	1	yes	characteristic
98	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
99	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₇₁⋊C₈	—	2	1	no	—
104	Dic₇₁⋊C₈	—	2	1	no	—
105	Dic₇₁⋊C₈	—	2	1	no	—
106	Dic₇₁⋊C₈	—	2	1	no	—
107	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
108	(C₂×D₇₁)⋊C₈	—	2	1	no	—
109	(C₂×D₇₁)⋊C₈	—	2	1	no	—
110	(C₂×D₇₁)⋊C₈	—	2	1	no	—
111	(C₂×D₇₁)⋊C₈	—	2	1	no	—
112	#14556039	—	2	1	no	—
113	#14556038	—	2	1	no	—
114	#14556038	—	2	1	no	—
115	#14556038	C₂×C₄	1	1	yes	characteristic
116	#14556038	C₂×C₄	1	1	yes	characteristic
117	#14556038	C₂×C₄	1	1	yes	characteristic
118	#14556038	C₂×C₄	1	1	yes	characteristic
119	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
120	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
121	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₈×Dic₇₁	—	2	1	no	—
124	C₈×Dic₇₁	—	2	1	no	—
125	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
129	C₂×M₁₆×C₇₁	—	2	1	no	—
130	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
132	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₇₁	—	2	1	no	—
134	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₇₁	—	2	1	no	—
139	#97×C₇₁	—	2	1	no	—
140	#97×C₇₁	C₂×C₄	1	1	yes	characteristic
141	#97×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	#11765865	—	2	2	no	—
145	#11765865	—	2	2	no	—
146	C₂×Dic₁₄₂	C₄⋊C₄	1	1	yes	characteristic
147	C₂×D₂₈₄	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₂²⋊D₇₁	C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₂²⋊D₇₁	C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
155	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
156	#11765849	—	8	1	no	—
157	#11765848	—	2	2	no	—
158	#11765848	—	2	2	no	—
159	#11765848	—	2	2	no	—
160	#11765848	—	8	1	no	—
161	#11765848	—	8	1	no	—
162	#11765848	M₁₆	1	4	yes	complemented
163	C₂×C₇₁⋊C₈	—	2	2	no	—
164	C₂×C₇₁⋊C₈	—	2	2	no	—
165	C₂×C₇₁⋊C₈	—	2	1	no	—
166	C₂×C₇₁⋊C₈	—	2	1	no	—
167	C₂×C₇₁⋊C₈	—	2	1	no	—
168	C₂×C₇₁⋊C₈	—	2	1	no	—
169	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₇₁	—	2	2	no	—
174	C₈×D₇₁	—	2	2	no	—
175	C₈×D₇₁	—	2	2	no	—
176	C₈×D₇₁	—	8	1	no	—
177	C₈×D₇₁	—	8	1	no	—
178	C₈×D₇₁	M₁₆	1	4	yes	complemented
179	C₄⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
180	C₄⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
181	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
182	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
184	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
185	C₂²⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
186	C₂²⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
187	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
191	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₇₁	C₂×Q₈	1	1	yes	characteristic
196	C₄×Dic₇₁	C₂×Q₈	1	1	yes	characteristic
197	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
200	M₁₆×C₇₁	—	2	2	no	—
201	M₁₆×C₇₁	—	2	2	no	—
202	M₁₆×C₇₁	—	8	1	no	—
203	C₂×C₈×C₇₁	—	2	1	no	—
204	C₂×C₈×C₇₁	—	2	1	no	—
205	C₂×C₈×C₇₁	—	2	1	no	—
206	C₂×C₈×C₇₁	—	2	1	no	—
207	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
208	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
214	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
215	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₇₁	—	2	1	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	—	4	1	no	—
223	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
229	C₂²⋊D₇₁	—	2	2	no	—
230	C₂²⋊D₇₁	—	2	2	no	—
231	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
237	D₂₈₄	—	2	2	no	—
238	C₄×D₇₁	—	2	1	no	—
239	C₄×D₇₁	—	2	1	no	—
240	C₄×D₇₁	—	2	1	no	—
241	C₄×D₇₁	—	2	1	no	—
242	C₄×D₇₁	—	2	1	no	—
243	C₄×D₇₁	—	2	1	no	—
244	C₄×D₇₁	—	4	1	no	—
245	C₄×D₇₁	—	4	1	no	—
246	C₄×D₇₁	C₂×M₁₆	1	2	yes	—
247	C₄×D₇₁	C₂×M₁₆	1	2	yes	—
248	Dic₁₄₂	—	2	2	no	—
249	C₈×C₇₁	—	2	1	no	—
250	C₈×C₇₁	—	2	1	no	—
251	C₈×C₇₁	—	4	1	no	—
252	C₈×C₇₁	—	4	1	no	—
253	C₈×C₇₁	—	4	1	no	—
254	C₈×C₇₁	—	4	1	no	—
255	C₈×C₇₁	C₂×M₁₆	1	2	yes	—
256	C₈×C₇₁	C₂×M₁₆	1	2	yes	—
257	C₇₁⋊C₈	—	2	1	no	—
258	C₇₁⋊C₈	—	2	1	no	—
259	C₇₁⋊C₈	—	4	1	no	—
260	C₇₁⋊C₈	—	4	1	no	—
261	C₇₁⋊C₈	—	4	1	no	—
262	C₇₁⋊C₈	—	4	1	no	—
263	C₇₁⋊C₈	C₂×M₁₆	1	2	yes	—
264	C₇₁⋊C₈	C₂×M₁₆	1	2	yes	—
265	C₂²×C₇₁	—	2	1	no	—
266	C₂²×C₇₁	—	2	1	no	—
267	C₂²×C₇₁	—	2	1	no	—
268	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₂×D₇₁	—	2	1	no	—
270	C₂×D₇₁	—	2	1	no	—
271	C₂×D₇₁	—	2	1	no	—
272	C₂×D₇₁	—	2	1	no	—
273	C₂×D₇₁	—	2	1	no	—
274	C₂×D₇₁	#423	1	2	yes	—
275	C₄×C₇₁	—	2	1	no	—
276	C₄×C₇₁	—	2	1	no	—
277	C₄×C₇₁	—	2	1	no	—
278	C₄×C₇₁	—	2	1	no	—
279	C₄×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
280	C₄×C₇₁	C₂²×M₁₆	1	1	yes	characteristic
281	C₄×C₇₁	#577	1	1	yes	characteristic
282	C₄×C₇₁	#577	1	1	yes	characteristic
283	Dic₇₁	—	2	1	no	—
284	Dic₇₁	—	2	1	no	—
285	Dic₇₁	—	2	1	no	—
286	Dic₇₁	—	2	1	no	—
287	Dic₇₁	—	2	1	no	—
288	Dic₇₁	#423	1	2	yes	—
289	#17798	—	71	1	no	maximal, Sylow
290	C₂×C₇₁	—	4	1	no	—
291	C₂×C₇₁	C₂×#423	1	1	yes	characteristic
292	C₂×C₇₁	#2912	1	1	yes	characteristic
293	C₂×C₇₁	#2916	1	1	yes	characteristic
294	D₇₁	—	2	2	no	—
295	D₇₁	—	4	1	no	—
296	#2989	—	71	1	no	—
297	#2989	—	71	1	no	—
298	C₄×#131	—	71	1	no	—
299	#1569	—	71	1	no	—
300	#1569	—	71	1	no	—
301	#1569	—	71	1	no	—
302	#1569	D₇₁	1	1	yes	characteristic, complemented
303	#1568	—	71	1	no	—
304	#1568	—	71	1	no	—
305	#1566	—	71	1	no	—
306	#1566	—	71	1	no	—
307	#1565	—	71	1	no	—
308	#1565	—	71	1	no	—
309	#1564	—	71	1	no	—
310	C₂×#334	—	71	1	no	—
311	C₇₁	#17798	1	1	yes	characteristic, complemented, Sylow
312	C₂×#131	—	71	1	no	—
313	C₂×#131	—	71	1	no	—
314	C₄×#41	—	71	1	no	—
315	#446	—	142	1	no	—
316	#446	—	142	1	no	—
317	#436	—	142	1	no	—
318	#436	—	142	1	no	—
319	#435	—	142	1	no	—
320	#435	—	142	1	no	—
321	#435	—	142	1	no	—
322	#435	—	142	1	no	—
323	#432	—	71	1	no	—
324	#432	—	71	1	no	—
325	#432	—	71	1	no	—
326	#432	C₂×D₇₁	1	1	yes	characteristic
327	#431	—	71	1	no	—
328	#431	—	71	1	no	—
329	#423	—	71	1	no	—
330	#423	—	71	1	no	—
331	#423	—	71	1	no	—
332	#423	C₂×D₇₁	1	1	yes	characteristic
333	C₂×C₄⋊C₈	—	71	1	no	—
334	C₂×C₄⋊C₈	—	71	1	no	—
335	#405	—	71	1	no	—
336	#405	—	71	1	no	—
337	#405	—	71	1	no	—
338	#405	—	71	1	no	—
339	#405	—	71	1	no	—
340	#405	—	71	1	no	—
341	C₄×M₁₆	—	71	1	no	—
342	C₄×M₁₆	—	71	1	no	—
343	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
344	C₂×C₄×C₈	—	71	1	no	—
345	C₂×C₄×C₈	—	71	1	no	—
346	C₂×C₄×C₈	—	71	1	no	—
347	#335	—	71	1	no	—
348	#335	—	71	1	no	—
349	#335	—	71	1	no	—
350	#335	—	71	1	no	—
351	#335	C₂×D₇₁	1	1	yes	characteristic
352	#335	C₂×D₇₁	1	1	yes	characteristic
353	#334	—	71	1	no	—
354	#334	—	71	1	no	—
355	#334	—	71	1	no	—
356	#334	—	71	1	no	—
357	#334	—	71	1	no	—
358	#334	—	71	1	no	—
359	#334	—	71	1	no	—
360	#334	—	71	1	no	—
361	#334	C₂×D₇₁	1	1	yes	characteristic
362	#334	C₂×D₇₁	1	1	yes	characteristic
363	C₂×#41	—	71	1	no	—
364	#131	—	142	4	no	—
365	#131	—	142	4	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	71	1	no	—
368	C₂×M₁₆	—	71	1	no	—
369	C₂×M₁₆	—	71	1	no	—
370	C₂×M₁₆	—	71	1	no	—
371	C₂×M₁₆	—	142	1	no	—
372	C₂×M₁₆	—	142	1	no	—
373	C₂×M₁₆	—	142	1	no	—
374	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
375	C₂×M₁₆	C₄×D₇₁	1	1	yes	characteristic
376	C₂²×C₈	—	71	1	no	—
377	C₂²×C₈	—	71	1	no	—
378	C₂²×C₈	—	71	1	no	—
379	C₂²×C₈	—	71	1	no	—
380	C₂²×C₈	—	71	1	no	—
381	C₂²×C₈	—	71	1	no	—
382	C₂²×C₈	—	142	1	no	—
383	C₂²×C₈	—	142	1	no	—
384	C₄×Q₈	—	71	1	no	—
385	C₄×Q₈	—	71	1	no	—
386	C₄×D₄	—	71	1	no	—
387	C₄×D₄	—	71	1	no	—
388	C₄×D₄	—	71	1	no	—
389	C₄×D₄	—	71	1	no	—
390	C₄×D₄	—	71	1	no	—
391	C₄×D₄	—	71	1	no	—
392	#117	—	71	1	no	—
393	#117	—	71	1	no	—
394	#117	—	71	1	no	—
395	C₂×C₄²	—	71	1	no	—
396	C₂×C₄²	—	71	1	no	—
397	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	71	1	no	—
400	C₄⋊C₈	—	71	1	no	—
401	C₄⋊C₈	—	71	1	no	—
402	C₄⋊C₈	—	71	1	no	—
403	C₄⋊C₈	—	142	1	no	—
404	C₄⋊C₈	—	142	1	no	—
405	C₄⋊C₈	—	142	1	no	—
406	C₄⋊C₈	—	142	1	no	—
407	C₄⋊C₈	—	142	1	no	—
408	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
409	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
410	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
411	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	142	1	no	—
414	C₂²⋊C₈	—	142	1	no	—
415	C₂²⋊C₈	—	142	1	no	—
416	C₂²⋊C₈	—	142	1	no	—
417	C₂²⋊C₈	—	142	1	no	—
418	#97	—	2	1	no	—
419	#97	—	71	1	no	—
420	#97	—	71	1	no	—
421	#97	—	71	1	no	—
422	#97	—	71	1	no	—
423	#97	—	142	1	no	—
424	#97	—	142	1	no	—
425	#97	—	142	1	no	—
426	#97	C₄×D₇₁	1	1	yes	characteristic
427	#97	C₄×D₇₁	1	1	yes	characteristic
428	C₄×C₈	—	71	1	no	—
429	C₄×C₈	—	71	1	no	—
430	C₄×C₈	—	71	1	no	—
431	C₄×C₈	—	71	1	no	—
432	C₄×C₈	—	71	1	no	—
433	C₄×C₈	—	71	1	no	—
434	C₄×C₈	—	71	1	no	—
435	C₄×C₈	—	71	1	no	—
436	C₄×C₈	—	142	1	no	—
437	C₄×C₈	—	142	1	no	—
438	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
439	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
440	#41	—	142	2	no	—
441	#41	—	142	2	no	—
442	C₂×Q₈	—	71	1	no	—
443	C₂×D₄	—	71	1	no	—
444	C₂×D₄	—	71	1	no	—
445	C₂×D₄	—	71	1	no	—
446	C₂²×C₄	—	71	1	no	—
447	C₂²×C₄	—	71	1	no	—
448	C₂²×C₄	—	71	1	no	—
449	C₂²×C₄	—	71	1	no	—
450	C₂²×C₄	—	71	1	no	—
451	C₂²×C₄	—	71	1	no	—
452	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
454	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
455	M₁₆	—	2	2	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	8	1	no	—
458	M₁₆	—	568	1	no	—
459	M₁₆	—	568	1	no	—
460	M₁₆	—	568	1	no	—
461	M₁₆	—	71	4	no	—
462	M₁₆	—	142	2	no	—
463	M₁₆	—	142	2	no	—
464	M₁₆	—	142	2	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	568	1	no	—
470	C₂×C₈	—	568	1	no	—
471	C₂×C₈	—	71	1	no	—
472	C₂×C₈	—	71	1	no	—
473	C₂×C₈	—	71	4	no	—
474	C₂×C₈	—	71	1	no	—
475	C₂×C₈	—	71	1	no	—
476	C₂×C₈	—	142	2	no	—
477	C₂×C₈	—	142	2	no	—
478	C₂×C₈	—	142	1	no	—
479	C₂×C₈	—	142	1	no	—
480	C₂×C₈	—	142	1	no	—
481	C₂×C₈	—	142	1	no	—
482	C₂×C₈	—	142	2	no	—
483	C₂×C₈	—	142	2	no	—
484	C₂×C₈	—	142	2	no	—
485	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
486	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
487	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
489	C₄⋊C₄	—	71	1	no	—
490	C₄⋊C₄	—	71	1	no	—
491	C₄⋊C₄	—	71	1	no	—
492	C₄⋊C₄	—	71	1	no	—
493	C₄⋊C₄	—	71	1	no	—
494	C₄⋊C₄	—	71	1	no	—
495	C₂²⋊C₄	—	71	1	no	—
496	C₂²⋊C₄	—	71	1	no	—
497	C₂²⋊C₄	—	71	1	no	—
498	C₂²⋊C₄	—	71	1	no	—
499	C₂²⋊C₄	—	71	1	no	—
500	C₂²⋊C₄	—	71	1	no	—
501	C₄²	—	71	1	no	—
502	C₄²	—	71	1	no	—
503	C₄²	—	71	1	no	—
504	C₄²	—	71	1	no	—
505	C₄²	—	71	1	no	—
506	C₄²	—	71	1	no	—
507	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
508	C₄²	D₄×D₇₁	1	1	yes	characteristic
509	C₄²	Q₈×D₇₁	1	1	yes	characteristic
510	C₄²	C₂³×D₇₁	1	1	yes	characteristic
511	C₂³	—	71	1	no	—
512	C₂³	—	71	1	no	—
513	C₂³	C₄⋊C₄×D₇₁	1	1	yes	characteristic
514	Q₈	—	142	2	no	—
515	D₄	—	142	2	no	—
516	D₄	—	142	2	no	—
517	D₄	—	142	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	284	1	no	—
524	C₂×C₄	—	284	1	no	—
525	C₂×C₄	—	71	1	no	—
526	C₂×C₄	—	71	2	no	—
527	C₂×C₄	—	71	2	no	—
528	C₂×C₄	—	71	1	no	—
529	C₂×C₄	—	71	1	no	—
530	C₂×C₄	—	71	1	no	—
531	C₂×C₄	—	71	1	no	—
532	C₂×C₄	—	71	1	no	—
533	C₂×C₄	—	142	1	no	—
534	C₂×C₄	—	142	1	no	—
535	C₂×C₄	—	142	1	no	—
536	C₂×C₄	—	142	1	no	—
537	C₂×C₄	—	142	1	no	—
538	C₂×C₄	—	142	1	no	—
539	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
540	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
541	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
543	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
544	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	284	1	no	—
552	C₈	—	284	1	no	—
553	C₈	—	284	1	no	—
554	C₈	—	284	1	no	—
555	C₈	—	71	2	no	—
556	C₈	—	71	2	no	—
557	C₈	—	142	1	no	—
558	C₈	—	142	1	no	—
559	C₈	M₁₆×D₇₁	1	2	yes	—
560	C₈	M₁₆×D₇₁	1	2	yes	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	71	2	no	—
565	C₂²	—	142	1	no	—
566	C₂²	—	142	1	no	—
567	C₂²	—	142	1	no	—
568	C₂²	—	142	1	no	—
569	C₂²	—	142	1	no	—
570	C₂²	C₂×C₄⋊C₄×D₇₁	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	71	2	no	—
576	C₄	—	142	1	no	—
577	C₄	—	142	1	no	—
578	C₄	—	142	1	no	—
579	C₄	—	142	1	no	—
580	C₄	—	142	1	no	—
581	C₄	C₂×M₁₆×D₇₁	1	1	yes	characteristic
582	C₄	C₂×M₁₆×D₇₁	1	1	yes	characteristic
583	C₄	#17986808	1	1	yes	characteristic
584	C₄	#17986809	1	1	yes	characteristic
585	C₂	—	4	1	no	—
586	C₂	—	284	1	no	—
587	C₂	—	142	2	no	—
588	C₂	#423×D₇₁	1	1	yes	characteristic
589	C₂	#22596934	1	1	yes	characteristic
590	C₂	#22596950	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×#1569	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#11765865	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1569	D₇₁
hypocenter	C₇₁	#17798
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #22587107	C₂	semidirect
5. #22587106	C₂	semidirect
6. #22587104	C₂	semidirect
7. #22587102	C₂	semidirect
8. #22587101	C₂	semidirect
9. #22587095	C₂	semidirect
10. #22587094	C₂	semidirect
11. #22587091	C₂	semidirect
12. #22587089	C₂	semidirect
13. #22587087	C₂	semidirect
14. #334×D₇₁	C₂	semidirect
15. C₇₁×#1569	C₂	semidirect
162. #11765848	M₁₆	semidirect
178. C₈×D₇₁	M₁₆	semidirect
302. #1569	D₇₁	semidirect
311. C₇₁	#17798	semidirect

Maximal subgroups

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

subgroup	index
#22597459	2
#22597454	2
C₄×#14556136	2
#22587107	2
#22587106	2
#22587104	2
#22587102	2
#22587101	2
#22587095	2
#22587094	2
#22587091	2
#22587089	2
#22587087	2
#334×D₇₁	2
C₇₁×#1569	2
#17798	71