Subgroups — #31967395

Order 18176.

678 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598369	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#22597049	C₂	1	1	yes	maximal, characteristic
4	#22587220	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587218	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587216	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587155	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₇₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587151	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587149	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587113	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586767	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586737	C₂	1	1	yes	maximal, characteristic
14	#22586631	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1588	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556136	—	2	1	no	—
17	#17986546	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₇₁	C₂²	1	1	yes	characteristic
19	#17986319	C₄	1	1	yes	characteristic
20	#17986316	C₄	1	1	yes	characteristic
21	#17986283	C₄	1	1	yes	characteristic
22	#17986282	C₄	1	1	yes	characteristic
23	#17986198	C₄	1	1	yes	characteristic
24	#17986197	C₄	1	1	yes	characteristic
25	#17986139	C₄	1	1	yes	characteristic
26	#17986136	C₄	1	1	yes	characteristic
27	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₄₂	—	2	1	no	—
29	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
30	#17986123	—	2	1	no	—
31	#17986123	C₂²	1	1	yes	characteristic
32	C₄×#11765854	C₂²	1	1	yes	characteristic
33	C₄×#11765852	C₂²	1	1	yes	characteristic
34	C₄×#11765853	C₂²	1	1	yes	characteristic
35	#17986078	C₂²	1	1	yes	characteristic
36	#17986075	—	2	1	no	—
37	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
38	#17986064	C₂²	1	1	yes	characteristic
39	(C₂²⋊D₇₁)⋊C₈	—	2	1	no	—
40	#17986050	C₂²	1	1	yes	characteristic
41	#17986050	C₂²	1	1	yes	characteristic
42	#17986021	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₇₁	—	2	1	no	—
44	C₄⋊C₈×D₇₁	C₂²	1	1	yes	characteristic
45	#17985964	—	2	1	no	—
46	C₄×C₈×D₇₁	—	2	1	no	—
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985752	C₂²	1	1	yes	characteristic
49	#17985751	C₂²	1	1	yes	characteristic
50	#17985751	C₂²	1	1	yes	characteristic
51	#17985731	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
53	#17985729	C₂²	1	1	yes	characteristic
54	#17985728	C₂²	1	1	yes	characteristic
55	D₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
56	#17985726	C₂²	1	1	yes	characteristic
57	#17985721	C₂²	1	1	yes	characteristic
58	#17985721	C₂²	1	1	yes	characteristic
59	#17985720	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
62	#436×C₇₁	C₂²	1	1	yes	characteristic
63	#335×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	#322×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765865	—	2	1	no	—
68	C₂×Q₈×D₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765854	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765852	C₂×C₄	1	1	yes	characteristic
72	#14556136	—	4	4	no	—
73	C₂×#11765848	—	2	1	no	—
74	C₂×#11765848	—	2	1	no	—
75	C₂²×C₇₁⋊C₈	—	2	1	no	—
76	C₂×C₈×D₇₁	—	2	1	no	—
77	C₂×C₈×D₇₁	—	2	1	no	—
78	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
79	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
80	#14556127	C₂×C₄	1	1	yes	characteristic
81	#14556124	C₂×C₄	1	1	yes	characteristic
82	#14556114	—	2	1	no	—
83	#14556103	C₂×C₄	1	1	yes	characteristic
84	#14556101	—	2	1	no	—
85	#14556099	C₂×C₄	1	1	yes	characteristic
86	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₁₄₂	—	2	1	no	—
88	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
89	#14556093	—	2	1	no	—
90	#14556093	C₂×C₄	1	1	yes	characteristic
91	C₄×D₂₈₄	C₂³	1	1	yes	characteristic
92	C₄×C₂²⋊D₇₁	—	2	1	no	—
93	C₄⋊C₄×D₇₁	—	2	1	no	—
94	C₄⋊C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
95	C₄²×D₇₁	—	2	1	no	—
96	C₄²×D₇₁	C₂³	1	1	yes	characteristic
97	#14556060	C₂×C₄	1	1	yes	characteristic
98	#14556059	C₂×C₄	1	1	yes	characteristic
99	#14556059	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
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	Dic₇₁⋊C₈	—	2	1	no	—
108	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
109	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
110	#14556053	C₂×C₄	1	1	yes	characteristic
111	#14556052	C₂×C₄	1	1	yes	characteristic
112	#14556051	C₂×C₄	1	1	yes	characteristic
113	#14556050	C₂×C₄	1	1	yes	characteristic
114	#14556049	C₂×C₄	1	1	yes	characteristic
115	#14556048	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
117	(C₂×D₇₁)⋊C₈	—	2	1	no	—
118	(C₂×D₇₁)⋊C₈	—	2	1	no	—
119	(C₂×D₇₁)⋊C₈	—	2	1	no	—
120	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
121	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₄×C₇₁⋊C₈	—	2	1	no	—
123	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₇₁	—	2	1	no	—
127	C₈×Dic₇₁	—	2	1	no	—
128	C₈×Dic₇₁	D₄	1	1	yes	characteristic
129	C₈×Dic₇₁	D₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₂×M₁₆×C₇₁	—	2	1	no	—
132	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
134	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₇₁	—	2	1	no	—
136	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
138	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
139	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₇₁	—	2	1	no	—
141	C₄×C₈×C₇₁	—	2	1	no	—
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
145	#11765865	—	4	2	no	—
146	#11765865	—	4	2	no	—
147	C₂×Dic₁₄₂	—	2	1	no	—
148	C₂×Dic₁₄₂	—	2	1	no	—
149	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
150	Q₈×D₇₁	—	2	2	no	—
151	Q₈×D₇₁	—	2	2	no	—
152	C₂×D₂₈₄	—	2	1	no	—
153	C₂×D₂₈₄	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₂²⋊D₇₁	—	2	1	no	—
155	C₂×C₂²⋊D₇₁	—	2	1	no	—
156	C₂×C₂²⋊D₇₁	—	2	1	no	—
157	C₂×C₄×D₇₁	—	2	1	no	—
158	C₂×C₄×D₇₁	—	2	1	no	—
159	C₂×C₄×D₇₁	—	2	1	no	—
160	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
163	#11765854	—	2	2	no	—
164	#11765853	—	2	2	no	—
165	#11765852	—	2	2	no	—
166	#11765848	—	4	2	no	—
167	#11765848	—	4	2	no	—
168	C₂×C₇₁⋊C₈	—	2	1	no	—
169	C₂×C₇₁⋊C₈	—	2	1	no	—
170	C₂×C₇₁⋊C₈	—	2	1	no	—
171	C₂×C₇₁⋊C₈	—	4	2	no	—
172	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
176	C₈×D₇₁	—	2	2	no	—
177	C₈×D₇₁	—	2	2	no	—
178	C₈×D₇₁	—	4	2	no	—
179	C₈×D₇₁	—	4	2	no	—
180	C₄⋊Dic₇₁	—	2	1	no	—
181	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
183	Dic₇₁⋊C₄	—	2	1	no	—
184	Dic₇₁⋊C₄	—	2	1	no	—
185	Dic₇₁⋊C₄	—	2	1	no	—
186	Dic₇₁⋊C₄	—	2	1	no	—
187	C₂²⋊Dic₇₁	—	2	1	no	—
188	(C₂×D₇₁)⋊C₄	—	2	1	no	—
189	(C₂×D₇₁)⋊C₄	—	2	1	no	—
190	C₄×Dic₇₁	—	2	1	no	—
191	C₄×Dic₇₁	—	2	1	no	—
192	C₄×Dic₇₁	—	2	1	no	—
193	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₇₁	#41	1	1	yes	characteristic
196	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₁	—	2	1	no	—
199	SD₁₆×C₇₁	—	2	2	no	—
200	M₁₆×C₇₁	—	4	2	no	—
201	C₂×C₈×C₇₁	—	2	1	no	—
202	C₂×C₈×C₇₁	—	2	1	no	—
203	C₂×C₈×C₇₁	—	2	1	no	—
204	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₇₁	—	2	1	no	—
209	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₇₁	—	2	1	no	—
212	C₄²×C₇₁	—	2	1	no	—
213	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
214	C₂³×C₇₁	—	2	1	no	—
215	C₂²×D₇₁	—	2	1	no	—
216	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
217	Q₈×C₇₁	—	2	1	no	—
218	Q₈×C₇₁	#131	1	2	yes	complemented
219	D₄×C₇₁	—	2	1	no	—
220	D₄×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	—	4	1	no	—
225	C₂×C₄×C₇₁	—	4	1	no	—
226	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
229	C₂²⋊D₇₁	—	4	2	no	—
230	C₂²⋊D₇₁	—	4	2	no	—
231	C₂²⋊D₇₁	—	4	2	no	—
232	C₂×Dic₇₁	—	2	1	no	—
233	C₂×Dic₇₁	—	2	1	no	—
234	C₂×Dic₇₁	—	2	1	no	—
235	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
238	D₂₈₄	—	2	1	no	—
239	D₂₈₄	—	2	1	no	—
240	D₂₈₄	—	4	2	no	—
241	C₄×D₇₁	—	2	4	no	—
242	C₄×D₇₁	—	2	1	no	—
243	C₄×D₇₁	—	2	1	no	—
244	C₄×D₇₁	—	4	1	no	—
245	C₄×D₇₁	—	4	2	no	—
246	C₄×D₇₁	—	4	1	no	—
247	C₄×D₇₁	—	4	1	no	—
248	C₄×D₇₁	AGL(1,ℤ/8)	1	2	yes	—
249	C₄×D₇₁	#137	1	2	yes	—
250	Dic₁₄₂	—	2	4	no	—
251	Dic₁₄₂	—	2	1	no	—
252	Dic₁₄₂	—	4	2	no	—
253	Dic₁₄₂	#131	1	2	yes	complemented
254	C₈×C₇₁	—	2	1	no	—
255	C₈×C₇₁	—	2	1	no	—
256	C₈×C₇₁	—	2	1	no	—
257	C₈×C₇₁	—	2	1	no	—
258	C₈×C₇₁	—	4	1	no	—
259	C₈×C₇₁	—	4	1	no	—
260	C₈×C₇₁	—	4	1	no	—
261	C₇₁⋊C₈	—	2	1	no	—
262	C₇₁⋊C₈	—	2	1	no	—
263	C₇₁⋊C₈	—	2	1	no	—
264	C₇₁⋊C₈	—	2	1	no	—
265	C₇₁⋊C₈	—	4	1	no	—
266	C₇₁⋊C₈	—	4	1	no	—
267	C₇₁⋊C₈	—	4	1	no	—
268	C₂²×C₇₁	—	4	1	no	—
269	C₂²×C₇₁	—	4	1	no	—
270	C₂²×C₇₁	—	4	1	no	—
271	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂×D₇₁	—	2	1	no	—
273	C₂×D₇₁	—	2	1	no	—
274	C₂×D₇₁	—	4	1	no	—
275	C₂×D₇₁	—	4	1	no	—
276	C₂×D₇₁	—	4	1	no	—
277	C₂×D₇₁	#440	1	2	yes	—
278	C₄×C₇₁	—	2	2	no	—
279	C₄×C₇₁	—	2	1	no	—
280	C₄×C₇₁	—	4	1	no	—
281	C₄×C₇₁	—	4	1	no	—
282	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
283	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
284	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
286	Dic₇₁	—	2	1	no	—
287	Dic₇₁	—	2	2	no	—
288	Dic₇₁	—	2	1	no	—
289	Dic₇₁	—	4	1	no	—
290	Dic₇₁	—	4	1	no	—
291	Dic₇₁	#440	1	2	yes	—
292	#17908	—	71	1	no	maximal, Sylow
293	C₂×C₇₁	—	8	1	no	—
294	C₂×C₇₁	#2929	1	1	yes	characteristic
295	C₂×C₇₁	C₂×#440	1	1	yes	characteristic
296	C₂×C₇₁	#2955	1	1	yes	characteristic
297	D₇₁	—	2	2	no	—
298	D₇₁	—	8	1	no	—
299	#3103	—	71	1	no	—
300	C₂×C₈×Q₈	—	71	1	no	—
301	#2931	—	71	1	no	—
302	#1588	—	71	1	no	—
303	#1588	—	71	1	no	—
304	#1588	—	71	1	no	—
305	#1588	D₇₁	1	1	yes	characteristic, complemented
306	SD₁₆⋊C₈	—	71	1	no	—
307	SD₁₆⋊C₈	—	71	1	no	—
308	SD₁₆⋊C₈	—	71	1	no	—
309	SD₁₆⋊C₈	—	71	1	no	—
310	#1571	—	71	1	no	—
311	#1487	—	71	1	no	—
312	#1480	—	71	1	no	—
313	#1452	—	71	1	no	—
314	C₇₁	#17908	1	1	yes	characteristic, complemented, Sylow
315	C₂×#131	—	142	1	no	—
316	#532	—	71	1	no	—
317	C₂×C₄×Q₈	—	71	1	no	—
318	#481	—	71	1	no	—
319	#481	—	71	1	no	—
320	#475	—	71	1	no	—
321	#475	—	71	1	no	—
322	#460	—	71	1	no	—
323	#460	—	71	1	no	—
324	#448	—	71	1	no	—
325	#448	—	71	1	no	—
326	C₈×Q₈	—	71	1	no	—
327	C₈×Q₈	—	71	1	no	—
328	C₈×Q₈	—	71	1	no	—
329	C₈×Q₈	—	142	1	no	—
330	C₈×Q₈	—	142	1	no	—
331	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
332	C₄×SD₁₆	—	71	1	no	—
333	C₄×SD₁₆	—	71	1	no	—
334	C₄×SD₁₆	—	71	1	no	—
335	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
336	#436	—	71	1	no	—
337	#436	—	142	1	no	—
338	#436	C₂×D₇₁	1	1	yes	characteristic
339	C₈×D₄	—	71	1	no	—
340	C₈×D₄	—	71	1	no	—
341	C₈×D₄	—	142	1	no	—
342	#431	—	71	1	no	—
343	#431	—	71	1	no	—
344	#423	—	71	1	no	—
345	C₂×C₄⋊C₈	—	71	1	no	—
346	C₂×C₄⋊C₈	—	142	1	no	—
347	#408	—	142	1	no	—
348	C₂×C₄×C₈	—	71	1	no	—
349	C₂×C₄×C₈	—	142	1	no	—
350	#335	—	71	1	no	—
351	#335	—	71	1	no	—
352	#335	—	71	1	no	—
353	#335	C₂×D₇₁	1	1	yes	characteristic
354	Q₈⋊C₈	—	71	1	no	—
355	Q₈⋊C₈	—	71	1	no	—
356	Q₈⋊C₈	—	71	1	no	—
357	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
358	D₄⋊C₈	—	71	1	no	—
359	D₄⋊C₈	—	71	1	no	—
360	D₄⋊C₈	—	71	1	no	—
361	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
362	#322	—	71	1	no	—
363	#322	—	71	1	no	—
364	#322	—	71	1	no	—
365	#322	C₂×D₇₁	1	1	yes	characteristic
366	C₂×#41	—	142	1	no	—
367	C₂²×Q₈	—	71	1	no	—
368	C₂×SD₁₆	—	71	1	no	—
369	C₂×SD₁₆	—	71	1	no	—
370	C₂×SD₁₆	—	71	1	no	—
371	C₂×SD₁₆	C₄×D₇₁	1	1	yes	characteristic
372	#131	—	284	4	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	142	1	no	—
375	C₂×M₁₆	—	142	1	no	—
376	C₂²×C₈	—	71	1	no	—
377	C₂²×C₈	—	71	1	no	—
378	C₂²×C₈	—	142	1	no	—
379	C₂²×C₈	—	142	1	no	—
380	C₂²×C₈	—	142	1	no	—
381	C₄⋊Q₈	—	71	1	no	—
382	#127	—	71	1	no	—
383	#124	—	142	1	no	—
384	#121	—	71	1	no	—
385	#121	—	71	1	no	—
386	#121	—	142	1	no	—
387	C₄×Q₈	—	71	1	no	—
388	C₄×Q₈	—	71	1	no	—
389	C₄×Q₈	—	71	1	no	—
390	C₄×Q₈	—	142	1	no	—
391	C₄×Q₈	—	142	1	no	—
392	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
393	C₄×D₄	—	71	1	no	—
394	C₄×D₄	—	142	1	no	—
395	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
396	C₂×C₄⋊C₄	—	71	1	no	—
397	C₂×C₄⋊C₄	—	142	1	no	—
398	C₂×C₄²	—	71	1	no	—
399	C₂×C₄²	—	142	1	no	—
400	#106	—	71	1	no	—
401	#106	—	71	1	no	—
402	#106	—	71	1	no	—
403	#106	C₄×D₇₁	1	1	yes	characteristic
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	71	1	no	—
406	C₄⋊C₈	—	71	1	no	—
407	C₄⋊C₈	—	71	1	no	—
408	C₄⋊C₈	—	71	1	no	—
409	C₄⋊C₈	—	142	1	no	—
410	C₄⋊C₈	—	142	1	no	—
411	C₄⋊C₈	—	142	1	no	—
412	C₄⋊C₈	—	142	1	no	—
413	C₄⋊C₈	—	142	1	no	—
414	C₄⋊C₈	—	142	1	no	—
415	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
417	#103	—	71	1	no	—
418	#103	—	71	1	no	—
419	#103	—	71	1	no	—
420	#103	C₄×D₇₁	1	1	yes	characteristic
421	#102	—	71	1	no	—
422	#102	—	71	1	no	—
423	#102	—	71	1	no	—
424	#102	C₄×D₇₁	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	71	1	no	—
427	C₂²⋊C₈	—	71	1	no	—
428	C₂²⋊C₈	—	142	1	no	—
429	C₂²⋊C₈	—	142	1	no	—
430	C₂²⋊C₈	—	142	1	no	—
431	C₂²⋊C₈	—	142	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	71	1	no	—
434	C₄×C₈	—	71	1	no	—
435	C₄×C₈	—	71	1	no	—
436	C₄×C₈	—	71	1	no	—
437	C₄×C₈	—	71	1	no	—
438	C₄×C₈	—	142	1	no	—
439	C₄×C₈	—	142	1	no	—
440	C₄×C₈	—	142	1	no	—
441	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
443	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
444	#41	—	284	2	no	—
445	#41	—	284	2	no	—
446	C₂×Q₈	—	71	1	no	—
447	C₂×Q₈	—	142	1	no	—
448	C₂×Q₈	—	142	1	no	—
449	C₂×Q₈	—	142	2	no	—
450	C₂×Q₈	—	142	2	no	—
451	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
452	C₂×D₄	—	71	1	no	—
453	C₂×D₄	—	142	1	no	—
454	C₂×D₄	—	142	1	no	—
455	C₂×D₄	—	142	1	no	—
456	C₂×D₄	—	142	1	no	—
457	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	71	1	no	—
460	C₂²×C₄	—	71	1	no	—
461	C₂²×C₄	—	71	1	no	—
462	C₂²×C₄	—	142	1	no	—
463	C₂²×C₄	—	142	1	no	—
464	C₂²×C₄	—	142	1	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	142	2	no	—
467	SD₁₆	—	142	2	no	—
468	SD₁₆	—	142	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	284	2	no	—
471	M₁₆	—	284	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	284	2	no	—
476	C₂×C₈	—	284	2	no	—
477	C₂×C₈	—	284	2	no	—
478	C₂×C₈	—	71	1	no	—
479	C₂×C₈	—	71	1	no	—
480	C₂×C₈	—	71	1	no	—
481	C₂×C₈	—	71	1	no	—
482	C₂×C₈	—	142	2	no	—
483	C₂×C₈	—	142	2	no	—
484	C₂×C₈	—	142	1	no	—
485	C₂×C₈	—	142	1	no	—
486	C₂×C₈	—	142	1	no	—
487	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
489	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
490	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	71	1	no	—
493	C₄⋊C₄	—	71	1	no	—
494	C₄⋊C₄	—	142	1	no	—
495	C₄⋊C₄	—	142	1	no	—
496	C₄⋊C₄	—	142	1	no	—
497	C₄⋊C₄	—	142	1	no	—
498	C₄⋊C₄	—	142	1	no	—
499	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
500	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	142	1	no	—
503	C₂²⋊C₄	—	142	1	no	—
504	C₂²⋊C₄	—	142	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	71	1	no	—
507	C₄²	—	71	1	no	—
508	C₄²	—	71	1	no	—
509	C₄²	—	142	1	no	—
510	C₄²	—	142	1	no	—
511	C₄²	—	142	1	no	—
512	C₄²	C₂³×D₇₁	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	71	1	no	—
515	C₂³	—	142	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	284	2	no	—
518	Q₈	—	71	2	no	—
519	Q₈	—	142	4	no	—
520	Q₈	—	142	1	no	—
521	Q₈	#14556136	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	284	2	no	—
525	D₄	—	284	2	no	—
526	D₄	—	284	2	no	—
527	D₄	—	284	2	no	—
528	D₄	—	142	1	no	—
529	D₄	—	142	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	284	1	no	—
536	C₂×C₄	—	284	2	no	—
537	C₂×C₄	—	284	1	no	—
538	C₂×C₄	—	284	1	no	—
539	C₂×C₄	—	71	1	no	—
540	C₂×C₄	—	71	2	no	—
541	C₂×C₄	—	71	2	no	—
542	C₂×C₄	—	71	1	no	—
543	C₂×C₄	—	71	1	no	—
544	C₂×C₄	—	142	4	no	—
545	C₂×C₄	—	142	1	no	—
546	C₂×C₄	—	142	1	no	—
547	C₂×C₄	—	142	1	no	—
548	C₂×C₄	—	142	1	no	—
549	C₂×C₄	—	142	1	no	—
550	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
552	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	284	1	no	—
561	C₈	—	284	1	no	—
562	C₈	—	284	1	no	—
563	C₈	—	142	1	no	—
564	C₈	—	142	1	no	—
565	C₈	—	142	1	no	—
566	C₈	—	142	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	284	1	no	—
571	C₂²	—	284	1	no	—
572	C₂²	—	284	1	no	—
573	C₂²	—	71	2	no	—
574	C₂²	—	142	1	no	—
575	C₂²	—	142	1	no	—
576	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	284	1	no	—
582	C₄	—	284	1	no	—
583	C₄	—	71	2	no	—
584	C₄	—	142	1	no	—
585	C₄	—	142	1	no	—
586	C₄	—	142	2	no	—
587	C₄	#131×D₇₁	1	1	yes	characteristic
588	C₄	C₂×#14556136	1	1	yes	characteristic
589	C₄	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
590	C₄	#137×D₇₁	1	1	yes	characteristic
591	C₂	—	8	1	no	—
592	C₂	—	568	1	no	—
593	C₂	—	142	2	no	—
594	C₂	#22597031	1	1	yes	characteristic
595	C₂	#440×D₇₁	1	1	yes	characteristic
596	C₂	#22597238	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×#1588	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#17986546	C₂²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1588	D₇₁
hypocenter	C₇₁	#17908
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₇₁	C₂	semidirect
4. #22587220	C₂	semidirect
5. #22587218	C₂	semidirect
6. #22587216	C₂	semidirect
7. #22587155	C₂	semidirect
8. SD₁₆⋊(C₇₁⋊C₈)	C₂	semidirect
9. #22587151	C₂	semidirect
10. #22587149	C₂	semidirect
11. #22587113	C₂	semidirect
12. #22586767	C₂	semidirect
14. #22586631	C₂	semidirect
15. C₇₁×#1588	C₂	semidirect
218. Q₈×C₇₁	#131	semidirect
253. Dic₁₄₂	#131	semidirect
305. #1588	D₇₁	semidirect
314. C₇₁	#17908	semidirect
521. Q₈	#14556136	semidirect

Maximal subgroups

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

subgroup	index
#22598369	2
C₈×Q₈×D₇₁	2
#22597049	2
#22587220	2
#22587218	2
#22587216	2
#22587155	2
SD₁₆⋊(C₇₁⋊C₈)	2
#22587151	2
#22587149	2
#22587113	2
#22586767	2
#22586737	2
#22586631	2
C₇₁×#1588	2
#17908	71