Subgroups — #31967352

Order 18176.

634 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598358	C₂	1	1	yes	maximal, characteristic
2	#22597309	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587187	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587180	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587173	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587166	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587144	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587143	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587137	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587132	C₂	1	1	yes	maximal, characteristic, complemented
12	#22587121	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586749	C₂	1	1	yes	maximal, characteristic, complemented
14	#22586624	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1488	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986533	C₂²	1	1	yes	characteristic
17	#17986340	C₄	1	1	yes	characteristic
18	#17986323	C₄	1	1	yes	characteristic
19	#17986306	C₄	1	1	yes	characteristic
20	#17986299	C₄	1	1	yes	characteristic
21	#17986221	C₄	1	1	yes	characteristic
22	#17986214	C₄	1	1	yes	characteristic
23	#17986161	C₄	1	1	yes	characteristic
24	#17986144	C₄	1	1	yes	characteristic
25	#17986126	C₂²	1	1	yes	characteristic
26	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
27	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
28	#17986123	C₂²	1	1	yes	characteristic
29	C₄×#11765855	C₂²	1	1	yes	characteristic
30	C₄×#11765852	C₂²	1	1	yes	characteristic
31	C₄×#11765853	C₂²	1	1	yes	characteristic
32	C₄×#11765850	C₂²	1	1	yes	characteristic
33	#17986076	C₂²	1	1	yes	characteristic
34	#17986067	—	2	1	no	—
35	D₄×C₇₁⋊C₈	—	2	1	no	—
36	D₄×C₇₁⋊C₈	—	2	1	no	—
37	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
38	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
39	#17986064	C₂²	1	1	yes	characteristic
40	(C₂²⋊D₇₁)⋊C₈	—	2	1	no	—
41	#17986061	—	2	1	no	—
42	#17986052	—	2	1	no	—
43	#17986052	C₂²	1	1	yes	characteristic
44	#17986052	C₂²	1	1	yes	characteristic
45	#17985956	—	2	1	no	—
46	C₂×C₄×C₇₁⋊C₈	—	2	1	no	—
47	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
48	#17985751	C₂²	1	1	yes	characteristic
49	#17985751	C₂²	1	1	yes	characteristic
50	#17985749	C₂²	1	1	yes	characteristic
51	#17985749	C₂²	1	1	yes	characteristic
52	#17985731	C₂²	1	1	yes	characteristic
53	#17985731	C₂²	1	1	yes	characteristic
54	#17985728	C₂²	1	1	yes	characteristic
55	#17985728	C₂²	1	1	yes	characteristic
56	#17985721	C₂²	1	1	yes	characteristic
57	#17985721	C₂²	1	1	yes	characteristic
58	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
61	#432×C₇₁	C₂²	1	1	yes	characteristic
62	#431×C₇₁	C₂²	1	1	yes	characteristic
63	Q₈⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
66	D₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
68	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765852	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765850	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765848	—	2	1	no	—
72	C₂²×C₇₁⋊C₈	—	2	1	no	—
73	C₂²×C₇₁⋊C₈	—	2	1	no	—
74	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
75	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
76	C₂×C₈×D₇₁	—	2	1	no	—
77	#14556122	—	2	1	no	—
78	#14556120	C₂×C₄	1	1	yes	characteristic
79	#14556116	C₂×C₄	1	1	yes	characteristic
80	#14556111	—	2	1	no	—
81	#14556107	C₂×C₄	1	1	yes	characteristic
82	#14556102	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
84	C₄×D₂₈₄	C₂³	1	1	yes	characteristic
85	C₄×C₂²⋊D₇₁	—	2	1	no	—
86	#14556085	—	2	1	no	—
87	#14556061	C₂×C₄	1	1	yes	characteristic
88	#14556061	C₂×C₄	1	1	yes	characteristic
89	#14556059	C₂×C₄	1	1	yes	characteristic
90	#14556059	C₂×C₄	1	1	yes	characteristic
91	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
92	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
93	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
97	Dic₇₁⋊C₈	—	2	1	no	—
98	Dic₇₁⋊C₈	—	2	1	no	—
99	#14556052	C₂×C₄	1	1	yes	characteristic
100	#14556052	C₂×C₄	1	1	yes	characteristic
101	#14556051	C₂×C₄	1	1	yes	characteristic
102	#14556051	C₂×C₄	1	1	yes	characteristic
103	#14556049	C₂×C₄	1	1	yes	characteristic
104	#14556049	C₂×C₄	1	1	yes	characteristic
105	#14556048	C₂×C₄	1	1	yes	characteristic
106	#14556048	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₇₁)⋊C₈	—	2	1	no	—
113	(C₂×D₇₁)⋊C₈	—	2	1	no	—
114	#14556038	—	2	1	no	—
115	C₄×C₇₁⋊C₈	—	2	1	no	—
116	C₄×C₇₁⋊C₈	—	2	1	no	—
117	C₄×C₇₁⋊C₈	—	2	1	no	—
118	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
119	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
120	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₇₁	—	2	1	no	—
125	C₂×#41×C₇₁	C₂×C₄	1	1	yes	characteristic
126	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
127	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₇₁	—	2	1	no	—
129	C₄×D₄×C₇₁	—	2	1	no	—
130	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
132	#117×C₇₁	—	2	1	no	—
133	#117×C₇₁	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₇₁	—	2	1	no	—
135	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₁	—	2	1	no	—
137	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
139	C₂²⋊C₈×C₇₁	—	2	1	no	—
140	C₂²⋊C₈×C₇₁	—	2	1	no	—
141	#97×C₇₁	—	2	1	no	—
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₂₈₄	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₂²⋊D₇₁	—	2	1	no	—
147	C₂×C₄×D₇₁	—	2	1	no	—
148	#11765855	—	2	2	no	—
149	#11765853	—	2	2	no	—
150	#11765852	—	2	2	no	—
151	#11765850	—	2	2	no	—
152	#11765848	—	4	2	no	—
153	C₂×C₇₁⋊C₈	—	2	2	no	—
154	C₂×C₇₁⋊C₈	—	2	2	no	—
155	C₂×C₇₁⋊C₈	—	2	1	no	—
156	C₂×C₇₁⋊C₈	—	2	1	no	—
157	C₂×C₇₁⋊C₈	—	4	2	no	—
158	C₂×C₇₁⋊C₈	—	4	2	no	—
159	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₈×D₇₁	—	4	2	no	—
168	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
170	Dic₇₁⋊C₄	—	2	1	no	—
171	Dic₇₁⋊C₄	—	2	1	no	—
172	Dic₇₁⋊C₄	—	2	1	no	—
173	Dic₇₁⋊C₄	—	2	1	no	—
174	C₂²⋊Dic₇₁	—	2	1	no	—
175	(C₂×D₇₁)⋊C₄	—	2	1	no	—
176	(C₂×D₇₁)⋊C₄	—	2	1	no	—
177	(C₂×D₇₁)⋊C₄	—	2	1	no	—
178	(C₂×D₇₁)⋊C₄	—	2	1	no	—
179	C₄×Dic₇₁	—	2	1	no	—
180	#41×C₇₁	—	2	2	no	—
181	#41×C₇₁	—	2	2	no	—
182	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
183	C₂×D₄×C₇₁	—	2	1	no	—
184	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₇₁	—	2	1	no	—
186	C₂²×C₄×C₇₁	—	2	1	no	—
187	C₂²×C₄×C₇₁	—	2	1	no	—
188	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
191	C₂×C₈×C₇₁	—	2	1	no	—
192	C₂×C₈×C₇₁	—	2	1	no	—
193	C₂×C₈×C₇₁	—	2	1	no	—
194	C₂×C₈×C₇₁	—	2	1	no	—
195	C₄⋊C₄×C₇₁	—	2	1	no	—
196	C₄⋊C₄×C₇₁	—	2	1	no	—
197	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₇₁	—	2	1	no	—
200	C₂²⋊C₄×C₇₁	—	2	1	no	—
201	C₂²⋊C₄×C₇₁	—	2	1	no	—
202	C₄²×C₇₁	—	2	1	no	—
203	C₄²×C₇₁	—	2	1	no	—
204	C₄²×C₇₁	—	2	1	no	—
205	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₇₁	#41	1	1	yes	characteristic
208	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
209	C₂³×C₇₁	—	2	1	no	—
210	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₇₁	—	2	1	no	—
212	Q₈×C₇₁	—	2	1	no	—
213	Q₈×C₇₁	#131	1	2	yes	—
214	D₄×C₇₁	—	2	4	no	—
215	D₄×C₇₁	—	2	1	no	—
216	D₄×C₇₁	#131	1	2	yes	—
217	C₂×C₄×C₇₁	—	2	4	no	—
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	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	4	1	no	—
226	C₂×C₄×C₇₁	—	4	2	no	—
227	C₂×C₄×C₇₁	—	4	1	no	—
228	C₂×C₄×C₇₁	—	4	1	no	—
229	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
235	C₂²⋊D₇₁	—	4	2	no	—
236	C₂×Dic₇₁	—	2	1	no	—
237	C₂×Dic₇₁	—	2	1	no	—
238	C₂×Dic₇₁	—	2	1	no	—
239	D₂₈₄	—	2	1	no	—
240	D₂₈₄	—	2	1	no	—
241	C₄×D₇₁	—	4	1	no	—
242	C₄×D₇₁	—	4	1	no	—
243	Dic₁₄₂	—	2	1	no	—
244	Dic₁₄₂	—	2	1	no	—
245	C₈×C₇₁	—	4	1	no	—
246	C₈×C₇₁	—	4	1	no	—
247	C₈×C₇₁	—	4	1	no	—
248	C₈×C₇₁	—	4	1	no	—
249	C₇₁⋊C₈	—	2	1	no	—
250	C₇₁⋊C₈	—	2	1	no	—
251	C₇₁⋊C₈	—	2	1	no	—
252	C₇₁⋊C₈	—	2	1	no	—
253	C₇₁⋊C₈	—	2	1	no	—
254	C₇₁⋊C₈	—	2	1	no	—
255	C₇₁⋊C₈	—	4	1	no	—
256	C₇₁⋊C₈	—	4	1	no	—
257	C₇₁⋊C₈	#135	1	2	yes	—
258	C₇₁⋊C₈	#135	1	2	yes	—
259	C₂²×C₇₁	—	2	1	no	—
260	C₂²×C₇₁	—	2	2	no	—
261	C₂²×C₇₁	—	2	1	no	—
262	C₂²×C₇₁	—	2	1	no	—
263	C₂²×C₇₁	—	4	1	no	—
264	C₂²×C₇₁	—	4	1	no	—
265	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂×D₇₁	—	4	1	no	—
267	C₂×D₇₁	—	4	1	no	—
268	C₂×D₇₁	—	4	1	no	—
269	C₄×C₇₁	—	2	1	no	—
270	C₄×C₇₁	—	2	2	no	—
271	C₄×C₇₁	—	2	1	no	—
272	C₄×C₇₁	—	2	1	no	—
273	C₄×C₇₁	—	2	1	no	—
274	C₄×C₇₁	—	4	1	no	—
275	C₄×C₇₁	—	4	1	no	—
276	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
277	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
278	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
279	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
280	Dic₇₁	—	4	1	no	—
281	Dic₇₁	—	4	1	no	—
282	Dic₇₁	—	4	1	no	—
283	#17904	—	71	1	no	maximal, Sylow
284	C₂×C₇₁	—	4	1	no	—
285	C₂×C₇₁	—	4	2	no	—
286	C₂×C₇₁	#2929	1	1	yes	characteristic
287	C₂×C₇₁	C₄×#135	1	1	yes	characteristic
288	C₂×C₇₁	#2955	1	1	yes	characteristic
289	D₇₁	—	8	1	no	—
290	#3102	—	71	1	no	—
291	#2966	—	71	1	no	—
292	C₈×#41	—	71	1	no	—
293	#1584	—	71	1	no	—
294	#1583	—	71	1	no	—
295	#1582	—	71	1	no	—
296	#1581	—	71	1	no	—
297	C₈×Q₁₆	—	71	1	no	—
298	C₈×SD₁₆	—	71	1	no	—
299	C₈×SD₁₆	—	71	1	no	—
300	C₈×D₈	—	71	1	no	—
301	#1572	—	71	1	no	—
302	#1488	D₇₁	1	1	yes	characteristic, complemented
303	#1482	—	71	1	no	—
304	#1450	—	71	1	no	—
305	C₇₁	#17904	1	1	yes	characteristic, complemented, Sylow
306	#529	—	71	1	no	—
307	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
308	#485	—	71	1	no	—
309	#482	—	71	1	no	—
310	#479	—	71	1	no	—
311	#478	—	71	1	no	—
312	#464	—	71	1	no	—
313	#463	—	71	1	no	—
314	#452	—	71	1	no	—
315	#449	—	71	1	no	—
316	#446	—	71	1	no	—
317	C₈×Q₈	—	71	1	no	—
318	C₈×Q₈	—	71	1	no	—
319	C₈×Q₈	—	71	1	no	—
320	C₄×Q₁₆	—	71	1	no	—
321	C₄×SD₁₆	—	71	1	no	—
322	C₄×SD₁₆	—	71	1	no	—
323	C₄×D₈	—	71	1	no	—
324	#436	—	71	1	no	—
325	#435	—	142	1	no	—
326	C₈×D₄	—	71	1	no	—
327	C₈×D₄	—	71	1	no	—
328	C₈×D₄	—	71	1	no	—
329	C₈×D₄	—	142	1	no	—
330	C₈×D₄	—	142	1	no	—
331	C₈×D₄	—	142	1	no	—
332	#433	—	142	1	no	—
333	#432	C₂×D₇₁	1	1	yes	characteristic
334	#431	—	71	1	no	—
335	#431	—	71	1	no	—
336	#431	—	142	1	no	—
337	#431	C₂×D₇₁	1	1	yes	characteristic
338	#405	—	142	1	no	—
339	C₂×C₄×C₈	—	71	1	no	—
340	C₂×C₄×C₈	—	142	1	no	—
341	#335	—	71	1	no	—
342	#335	—	71	1	no	—
343	#334	—	71	1	no	—
344	#334	—	71	1	no	—
345	Q₈⋊C₈	—	71	1	no	—
346	Q₈⋊C₈	—	71	1	no	—
347	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
348	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
349	D₄⋊C₈	—	71	1	no	—
350	D₄⋊C₈	—	71	1	no	—
351	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
352	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
353	#322	—	71	1	no	—
354	#322	—	71	1	no	—
355	C₈²	—	71	1	no	—
356	C₈²	—	71	1	no	—
357	C₂×#41	C₄×D₇₁	1	1	yes	characteristic
358	C₂×Q₁₆	—	71	1	no	—
359	C₂×SD₁₆	—	71	1	no	—
360	C₂×SD₁₆	—	71	1	no	—
361	C₂×D₈	—	71	1	no	—
362	C₂×M₁₆	—	142	1	no	—
363	C₂²×C₈	—	71	1	no	—
364	C₂²×C₈	—	71	1	no	—
365	C₂²×C₈	—	142	1	no	—
366	C₂²×C₈	—	142	1	no	—
367	C₂²×C₈	—	142	1	no	—
368	#126	—	142	1	no	—
369	#125	—	71	1	no	—
370	#124	—	71	1	no	—
371	#123	—	142	1	no	—
372	C₂²⋊Q₈	—	71	1	no	—
373	#121	—	71	1	no	—
374	C₄×Q₈	—	71	1	no	—
375	C₄×Q₈	C₄×D₇₁	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	71	1	no	—
380	C₄×D₄	—	142	1	no	—
381	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	142	1	no	—
385	#117	C₄×D₇₁	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
388	#107	—	71	1	no	—
389	#107	—	71	1	no	—
390	#106	—	71	1	no	—
391	#106	—	71	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	71	1	no	—
394	C₄⋊C₈	—	71	1	no	—
395	C₄⋊C₈	—	71	1	no	—
396	C₄⋊C₈	—	71	1	no	—
397	C₄⋊C₈	—	142	1	no	—
398	C₄⋊C₈	—	142	1	no	—
399	C₄⋊C₈	—	142	1	no	—
400	C₄⋊C₈	—	142	1	no	—
401	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
403	#103	—	71	1	no	—
404	#103	—	71	1	no	—
405	#103	—	71	1	no	—
406	#103	—	71	1	no	—
407	#102	—	71	1	no	—
408	#102	—	71	1	no	—
409	#102	—	71	1	no	—
410	#102	—	71	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	71	1	no	—
414	C₂²⋊C₈	—	71	1	no	—
415	C₂²⋊C₈	—	142	1	no	—
416	C₂²⋊C₈	—	142	1	no	—
417	C₂²⋊C₈	—	142	1	no	—
418	C₂²⋊C₈	—	142	1	no	—
419	C₂²⋊C₈	—	142	1	no	—
420	#97	—	2	1	no	—
421	#97	—	142	1	no	—
422	C₄×C₈	—	71	1	no	—
423	C₄×C₈	—	71	1	no	—
424	C₄×C₈	—	71	1	no	—
425	C₄×C₈	—	71	1	no	—
426	C₄×C₈	—	71	1	no	—
427	C₄×C₈	—	71	1	no	—
428	C₄×C₈	—	142	1	no	—
429	C₄×C₈	—	142	1	no	—
430	C₄×C₈	—	142	1	no	—
431	C₄×C₈	—	142	1	no	—
432	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	—	71	1	no	—
437	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	71	1	no	—
440	C₂×D₄	—	142	1	no	—
441	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	142	1	no	—
446	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
448	C₂²×C₄	#11765864	1	1	yes	characteristic
449	Q₁₆	—	142	2	no	—
450	SD₁₆	—	142	2	no	—
451	SD₁₆	—	142	2	no	—
452	D₈	—	142	2	no	—
453	M₁₆	—	284	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	284	2	no	—
459	C₂×C₈	—	284	2	no	—
460	C₂×C₈	—	284	2	no	—
461	C₂×C₈	—	71	1	no	—
462	C₂×C₈	—	71	1	no	—
463	C₂×C₈	—	71	1	no	—
464	C₂×C₈	—	71	1	no	—
465	C₂×C₈	—	71	1	no	—
466	C₂×C₈	—	71	1	no	—
467	C₂×C₈	—	71	1	no	—
468	C₂×C₈	—	71	1	no	—
469	C₂×C₈	—	142	1	no	—
470	C₂×C₈	—	142	1	no	—
471	C₂×C₈	—	142	2	no	—
472	C₂×C₈	—	142	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	71	1	no	—
476	C₄⋊C₄	—	71	1	no	—
477	C₄⋊C₄	—	142	1	no	—
478	C₄⋊C₄	—	142	1	no	—
479	C₄⋊C₄	—	142	1	no	—
480	C₄⋊C₄	—	142	1	no	—
481	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	142	1	no	—
487	C₂²⋊C₄	—	142	1	no	—
488	C₂²⋊C₄	—	142	1	no	—
489	C₂²⋊C₄	—	142	1	no	—
490	C₂²⋊C₄	—	142	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	142	1	no	—
495	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
496	C₄²	D₄×D₇₁	1	1	yes	characteristic
497	C₄²	#11765864	1	1	yes	characteristic
498	C₄²	C₂³×D₇₁	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	142	1	no	—
501	C₂³	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	142	1	no	—
504	Q₈	—	142	1	no	—
505	Q₈	#14556136	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	284	2	no	—
509	D₄	—	142	1	no	—
510	D₄	—	142	1	no	—
511	D₄	#14556136	1	2	yes	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	284	1	no	—
525	C₂×C₄	—	284	1	no	—
526	C₂×C₄	—	142	1	no	—
527	C₂×C₄	—	142	1	no	—
528	C₂×C₄	—	142	1	no	—
529	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
534	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	284	1	no	—
540	C₈	—	284	1	no	—
541	C₈	—	71	2	no	—
542	C₈	—	71	2	no	—
543	C₈	—	142	1	no	—
544	C₈	—	142	1	no	—
545	C₈	—	142	1	no	—
546	C₈	—	142	1	no	—
547	C₈	—	142	1	no	—
548	C₈	—	142	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	284	1	no	—
556	C₂²	—	284	1	no	—
557	C₂²	—	284	1	no	—
558	C₂²	C₂×(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	284	1	no	—
567	C₄	—	284	1	no	—
568	C₄	—	284	1	no	—
569	C₄	C₂×#14556136	1	1	yes	characteristic
570	C₄	C₂×#14556136	1	1	yes	characteristic
571	C₄	#135×D₇₁	1	1	yes	characteristic
572	C₄	#135×D₇₁	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	568	1	no	—
576	C₂	#22597030	1	1	yes	characteristic
577	C₂	#22597108	1	1	yes	characteristic
578	C₂	#22597239	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×#1488	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#17986144	C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1488	D₇₁
hypocenter	C₇₁	#17904
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1488

Complements

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

N	H ≅ G/N	type
2. #22597309	C₂	semidirect
3. #41×C₇₁⋊C₈	C₂	semidirect
4. #22587187	C₂	semidirect
5. #22587180	C₂	semidirect
6. #22587173	C₂	semidirect
7. #22587166	C₂	semidirect
8. #22587144	C₂	semidirect
9. #22587143	C₂	semidirect
10. #22587137	C₂	semidirect
11. #22587132	C₂	semidirect
12. #22587121	C₂	semidirect
13. #22586749	C₂	semidirect
14. #22586624	C₂	semidirect
15. C₇₁×#1488	C₂	semidirect
302. #1488	D₇₁	semidirect
305. C₇₁	#17904	semidirect

Maximal subgroups

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

subgroup	index
#22598358	2
#22597309	2
#41×C₇₁⋊C₈	2
#22587187	2
#22587180	2
#22587173	2
#22587166	2
#22587144	2
#22587143	2
#22587137	2
#22587132	2
#22587121	2
#22586749	2
#22586624	2
C₇₁×#1488	2
#17904	71