Subgroups — #31968070

Order 18176.

594 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	#22598942	C₂	1	1	yes	maximal, characteristic
2	#22597312	C₂	1	1	yes	maximal, characteristic
3	#22597269	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587236	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587234	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587233	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587231	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587160	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587157	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587152	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587106	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586811	C₂	1	1	yes	maximal, characteristic, complemented
13	#22586802	C₂	1	1	yes	maximal, characteristic
14	#22586619	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986553	C₂²	1	1	yes	characteristic
17	#17986531	C₂²	1	1	yes	characteristic
18	#17986406	C₄	1	1	yes	characteristic
19	#17986390	C₄	1	1	yes	characteristic
20	#17986366	C₄	1	1	yes	characteristic
21	#17986357	C₄	1	1	yes	characteristic
22	#17986258	C₄	1	1	yes	characteristic
23	#17986256	C₄	1	1	yes	characteristic
24	#17986244	C₄	1	1	yes	characteristic
25	#17986242	C₄	1	1	yes	characteristic
26	#17986130	C₂²	1	1	yes	characteristic
27	#17986128	—	2	1	no	—
28	#17986126	C₂²	1	1	yes	characteristic
29	#17986126	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₄₂	—	2	1	no	—
31	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic
34	C₄×#11765855	C₂²	1	1	yes	characteristic
35	C₄×#11765853	C₂²	1	1	yes	characteristic
36	#17986077	C₂²	1	1	yes	characteristic
37	#17986073	—	2	1	no	—
38	C₈×C₂²⋊D₇₁	—	2	1	no	—
39	#17986057	—	2	1	no	—
40	#17986055	C₂²	1	1	yes	characteristic
41	#17986050	C₂²	1	1	yes	characteristic
42	#17986024	—	2	1	no	—
43	#17986021	C₂²	1	1	yes	characteristic
44	#17985954	—	2	1	no	—
45	#17985953	—	2	1	no	—
46	C₄×#11765848	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985751	C₂²	1	1	yes	characteristic
49	#17985750	C₂²	1	1	yes	characteristic
50	#17985749	C₂²	1	1	yes	characteristic
51	#17985731	C₂²	1	1	yes	characteristic
52	#17985731	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
54	#17985729	C₂²	1	1	yes	characteristic
55	#17985729	C₂²	1	1	yes	characteristic
56	D₄⋊(C₇₁⋊C₈)	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	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
62	C₈×D₄×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×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
68	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765849	—	2	1	no	—
71	C₂×#11765848	—	2	1	no	—
72	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
73	C₂×#11765848	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
75	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
76	#14556127	C₂×C₄	1	1	yes	characteristic
77	#14556126	C₂×C₄	1	1	yes	characteristic
78	#14556121	—	2	1	no	—
79	#14556119	C₂×C₄	1	1	yes	characteristic
80	#14556118	—	2	1	no	—
81	#14556115	C₂×C₄	1	1	yes	characteristic
82	#14556110	—	2	1	no	—
83	#14556108	C₂×C₄	1	1	yes	characteristic
84	#14556108	C₂×C₄	1	1	yes	characteristic
85	#14556106	—	2	1	no	—
86	#14556104	C₂×C₄	1	1	yes	characteristic
87	#14556099	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₄₂	—	2	1	no	—
89	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
90	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
91	C₄×C₂²⋊D₇₁	—	2	1	no	—
92	#14556087	—	2	1	no	—
93	#14556085	—	2	1	no	—
94	C₄²×D₇₁	C₂³	1	1	yes	characteristic
95	#14556062	C₂×C₄	1	1	yes	characteristic
96	#14556061	C₂×C₄	1	1	yes	characteristic
97	#14556059	C₂×C₄	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	Dic₇₁⋊C₈	—	2	1	no	—
102	Dic₇₁⋊C₈	—	2	1	no	—
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	#14556053	C₂×C₄	1	1	yes	characteristic
108	#14556053	C₂×C₄	1	1	yes	characteristic
109	#14556052	C₂×C₄	1	1	yes	characteristic
110	#14556051	C₂×C₄	1	1	yes	characteristic
111	#14556051	C₂×C₄	1	1	yes	characteristic
112	#14556049	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
114	(C₂×D₇₁)⋊C₈	—	2	1	no	—
115	(C₂×D₇₁)⋊C₈	—	2	1	no	—
116	#14556039	—	2	1	no	—
117	#14556038	—	2	1	no	—
118	#14556038	—	2	1	no	—
119	#14556038	—	2	1	no	—
120	#14556038	C₂×C₄	1	1	yes	characteristic
121	#14556038	C₂×C₄	1	1	yes	characteristic
122	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₇₁	—	2	1	no	—
126	C₈×Dic₇₁	—	2	1	no	—
127	C₈×Dic₇₁	D₄	1	1	yes	characteristic
128	C₈×Dic₇₁	D₄	1	1	yes	characteristic
129	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
130	C₂²×C₈×C₇₁	—	2	1	no	—
131	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
133	#106×C₇₁	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₇₁	—	2	1	no	—
135	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
137	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
138	#102×C₇₁	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₇₁	—	2	1	no	—
140	C₄×C₈×C₇₁	—	2	1	no	—
141	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₄₂	—	2	1	no	—
145	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₇₁	—	2	1	no	—
148	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
151	Dic₂₈₄	—	2	2	no	—
152	#11765855	—	2	2	no	—
153	#11765853	—	2	2	no	—
154	#11765849	—	4	2	no	—
155	#11765848	—	2	2	no	—
156	#11765848	—	2	2	no	—
157	#11765848	—	4	2	no	—
158	C₂×C₇₁⋊C₈	—	2	1	no	—
159	C₂×C₇₁⋊C₈	—	2	1	no	—
160	C₂×C₇₁⋊C₈	—	2	1	no	—
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	C₈×D₇₁	—	2	2	no	—
166	C₈×D₇₁	—	4	1	no	—
167	C₄⋊Dic₇₁	—	2	1	no	—
168	C₄⋊Dic₇₁	—	2	1	no	—
169	C₄⋊Dic₇₁	—	2	1	no	—
170	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
172	Dic₇₁⋊C₄	—	2	1	no	—
173	Dic₇₁⋊C₄	—	2	1	no	—
174	Dic₇₁⋊C₄	—	2	1	no	—
175	Dic₇₁⋊C₄	—	2	1	no	—
176	Dic₇₁⋊C₄	—	2	1	no	—
177	Dic₇₁⋊C₄	—	2	1	no	—
178	Dic₇₁⋊C₄	—	2	1	no	—
179	C₂²⋊Dic₇₁	—	2	1	no	—
180	C₂²⋊Dic₇₁	—	2	1	no	—
181	C₂²⋊Dic₇₁	—	2	1	no	—
182	(C₂×D₇₁)⋊C₄	—	2	1	no	—
183	(C₂×D₇₁)⋊C₄	—	2	1	no	—
184	(C₂×D₇₁)⋊C₄	—	2	1	no	—
185	C₄×Dic₇₁	—	2	1	no	—
186	C₄×Dic₇₁	—	2	1	no	—
187	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
189	C₄×Dic₇₁	#41	1	1	yes	characteristic
190	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₁	—	2	1	no	—
193	SD₁₆×C₇₁	—	2	2	no	—
194	C₂×C₈×C₇₁	—	2	1	no	—
195	C₂×C₈×C₇₁	—	2	1	no	—
196	C₂×C₈×C₇₁	—	2	1	no	—
197	C₂×C₈×C₇₁	—	4	2	no	—
198	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₇₁	—	2	1	no	—
203	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₇₁	—	2	1	no	—
206	C₄²×C₇₁	—	2	1	no	—
207	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
208	C₂³×C₇₁	—	2	1	no	—
209	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₇₁	—	2	1	no	—
211	Q₈×C₇₁	—	2	1	no	—
212	D₄×C₇₁	—	2	1	no	—
213	D₄×C₇₁	—	2	1	no	—
214	C₂×C₄×C₇₁	—	2	1	no	—
215	C₂×C₄×C₇₁	—	2	1	no	—
216	C₂×C₄×C₇₁	—	2	1	no	—
217	C₂×C₄×C₇₁	—	4	1	no	—
218	C₂×C₄×C₇₁	—	4	1	no	—
219	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
222	C₂²⋊D₇₁	—	4	2	no	—
223	C₂×Dic₇₁	—	2	1	no	—
224	C₂×Dic₇₁	—	2	1	no	—
225	C₂×Dic₇₁	—	2	1	no	—
226	C₂×Dic₇₁	—	2	1	no	—
227	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
228	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
230	C₄×D₇₁	—	2	1	no	—
231	C₄×D₇₁	—	2	1	no	—
232	C₄×D₇₁	—	2	1	no	—
233	C₄×D₇₁	—	2	1	no	—
234	C₄×D₇₁	—	4	1	no	—
235	Dic₁₄₂	—	2	1	no	—
236	Dic₁₄₂	—	2	1	no	—
237	Dic₁₄₂	—	2	1	no	—
238	Dic₁₄₂	—	2	1	no	—
239	Dic₁₄₂	—	4	2	no	—
240	C₈×C₇₁	—	2	1	no	—
241	C₈×C₇₁	—	2	1	no	—
242	C₈×C₇₁	—	2	1	no	—
243	C₈×C₇₁	—	4	1	no	—
244	C₈×C₇₁	—	4	1	no	—
245	C₈×C₇₁	—	4	1	no	—
246	C₈×C₇₁	#131	1	2	yes	—
247	C₇₁⋊C₈	—	2	1	no	—
248	C₇₁⋊C₈	—	2	1	no	—
249	C₇₁⋊C₈	—	4	1	no	—
250	C₇₁⋊C₈	—	4	1	no	—
251	C₇₁⋊C₈	—	4	1	no	—
252	C₇₁⋊C₈	#131	1	2	yes	—
253	C₇₁⋊C₈	#137	1	2	yes	—
254	C₂²×C₇₁	—	4	1	no	—
255	C₂²×C₇₁	—	4	1	no	—
256	C₂²×C₇₁	—	4	1	no	—
257	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₇₁	—	2	1	no	—
259	C₂×D₇₁	—	2	1	no	—
260	C₂×D₇₁	—	2	1	no	—
261	C₄×C₇₁	—	2	1	no	—
262	C₄×C₇₁	—	4	1	no	—
263	C₄×C₇₁	—	4	1	no	—
264	C₄×C₇₁	—	4	1	no	—
265	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
266	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
267	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
268	C₄×C₇₁	#575	1	1	yes	characteristic
269	Dic₇₁	—	2	1	no	—
270	Dic₇₁	—	2	1	no	—
271	Dic₇₁	—	2	1	no	—
272	Dic₇₁	—	4	1	no	—
273	Dic₇₁	—	4	1	no	—
274	Dic₇₁	—	4	1	no	—
275	Dic₇₁	—	4	1	no	—
276	#17967	—	71	1	no	maximal, Sylow
277	C₂×C₇₁	—	8	1	no	—
278	C₂×C₇₁	#2931	1	1	yes	characteristic
279	C₂×C₇₁	C₄×#137	1	1	yes	characteristic
280	C₂×C₇₁	#2955	1	1	yes	characteristic
281	D₇₁	—	4	1	no	—
282	#3172	—	71	1	no	—
283	#2966	—	71	1	no	—
284	#2960	—	71	1	no	—
285	#1591	—	71	1	no	—
286	#1591	—	71	1	no	—
287	#1590	—	71	1	no	—
288	#1590	—	71	1	no	—
289	#1579	—	71	1	no	—
290	#1579	—	71	1	no	—
291	SD₁₆⋊C₈	—	71	1	no	—
292	SD₁₆⋊C₈	D₇₁	1	1	yes	characteristic, complemented
293	#1569	—	71	1	no	—
294	#1497	—	71	1	no	—
295	#1495	—	71	1	no	—
296	C₈×M₁₆	—	71	1	no	—
297	C₇₁	#17967	1	1	yes	characteristic, complemented, Sylow
298	#533	—	71	1	no	—
299	#529	—	71	1	no	—
300	#501	—	71	1	no	—
301	#497	—	71	1	no	—
302	#491	—	71	1	no	—
303	#489	—	71	1	no	—
304	#470	—	71	1	no	—
305	#470	—	71	1	no	—
306	#468	—	71	1	no	—
307	#468	—	71	1	no	—
308	#446	—	71	1	no	—
309	#446	—	71	1	no	—
310	#446	—	71	1	no	—
311	#446	—	142	1	no	—
312	C₈×Q₈	—	71	1	no	—
313	C₈×Q₈	—	71	1	no	—
314	C₈×Q₈	—	142	1	no	—
315	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
316	C₄×Q₁₆	—	71	1	no	—
317	C₄×Q₁₆	—	71	1	no	—
318	C₄×SD₁₆	—	71	1	no	—
319	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
320	#436	—	71	1	no	—
321	#435	—	142	1	no	—
322	C₈×D₄	—	142	1	no	—
323	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
324	#433	—	142	1	no	—
325	#432	—	71	1	no	—
326	#431	—	71	1	no	—
327	#424	—	142	1	no	—
328	#423	—	71	1	no	—
329	#405	—	142	1	no	—
330	#405	—	142	1	no	—
331	C₄×M₁₆	—	71	1	no	—
332	C₂×C₄×C₈	—	71	1	no	—
333	#335	—	71	1	no	—
334	#335	C₂×D₇₁	1	1	yes	characteristic
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	C₂×D₇₁	1	1	yes	characteristic
343	D₄⋊C₈	—	71	1	no	—
344	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
345	#322	—	71	1	no	—
346	#322	C₂×D₇₁	1	1	yes	characteristic
347	C₈²	—	71	1	no	—
348	C₈²	—	71	1	no	—
349	C₂×Q₁₆	—	71	1	no	—
350	C₂×Q₁₆	—	71	1	no	—
351	C₂×SD₁₆	—	71	1	no	—
352	C₂×SD₁₆	C₄×D₇₁	1	1	yes	characteristic
353	C₂×M₁₆	—	71	1	no	—
354	C₂×M₁₆	—	71	1	no	—
355	C₂×M₁₆	—	142	1	no	—
356	C₂×M₁₆	—	142	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	71	1	no	—
359	C₂²×C₈	—	71	1	no	—
360	C₄⋊Q₈	—	71	1	no	—
361	C₄⋊Q₈	—	71	1	no	—
362	#126	—	142	1	no	—
363	#125	—	71	1	no	—
364	#125	—	142	1	no	—
365	#124	—	71	1	no	—
366	#123	—	142	1	no	—
367	C₂²⋊Q₈	—	71	1	no	—
368	C₂²⋊Q₈	—	71	1	no	—
369	C₂²⋊Q₈	—	71	1	no	—
370	C₂²⋊Q₈	—	142	1	no	—
371	#121	—	71	1	no	—
372	C₄×Q₈	—	71	1	no	—
373	C₄×Q₈	—	71	1	no	—
374	C₄×Q₈	—	142	1	no	—
375	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
376	C₄×D₄	—	142	1	no	—
377	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
378	#117	—	142	1	no	—
379	#117	—	142	1	no	—
380	C₂×C₄²	—	71	1	no	—
381	#107	—	71	1	no	—
382	#107	—	71	1	no	—
383	#106	—	71	1	no	—
384	#106	C₄×D₇₁	1	1	yes	characteristic
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	71	1	no	—
387	C₄⋊C₈	—	71	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	C₂²×D₇₁	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
397	#103	—	71	1	no	—
398	#103	—	71	1	no	—
399	#103	—	71	1	no	—
400	#103	—	71	1	no	—
401	#103	—	71	1	no	—
402	#103	C₄×D₇₁	1	1	yes	characteristic
403	#102	—	71	1	no	—
404	#102	C₄×D₇₁	1	1	yes	characteristic
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	142	1	no	—
407	C₂²⋊C₈	—	142	1	no	—
408	C₂²⋊C₈	—	142	1	no	—
409	#97	—	71	1	no	—
410	#97	—	71	1	no	—
411	#97	—	142	1	no	—
412	#97	—	142	1	no	—
413	#97	—	142	1	no	—
414	#97	—	142	1	no	—
415	C₄×C₈	—	2	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	—	71	1	no	—
421	C₄×C₈	—	142	1	no	—
422	C₄×C₈	—	142	1	no	—
423	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
426	C₂×Q₈	—	71	1	no	—
427	C₂×Q₈	—	71	1	no	—
428	C₂×Q₈	—	142	1	no	—
429	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
430	C₂×D₄	—	142	1	no	—
431	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	71	1	no	—
434	C₂²×C₄	—	71	1	no	—
435	C₂²×C₄	—	71	1	no	—
436	Q₁₆	—	142	2	no	—
437	Q₁₆	—	142	2	no	—
438	SD₁₆	—	2	2	no	—
439	SD₁₆	—	142	2	no	—
440	M₁₆	—	284	2	no	—
441	M₁₆	—	284	2	no	—
442	M₁₆	—	142	2	no	—
443	M₁₆	—	142	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	4	2	no	—
448	C₂×C₈	—	284	1	no	—
449	C₂×C₈	—	71	1	no	—
450	C₂×C₈	—	71	1	no	—
451	C₂×C₈	—	71	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	142	2	no	—
454	C₂×C₈	—	142	1	no	—
455	C₂×C₈	—	142	1	no	—
456	C₂×C₈	—	142	1	no	—
457	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
459	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
460	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	71	1	no	—
463	C₄⋊C₄	—	71	1	no	—
464	C₄⋊C₄	—	142	1	no	—
465	C₄⋊C₄	—	142	1	no	—
466	C₄⋊C₄	—	142	1	no	—
467	C₄⋊C₄	—	142	1	no	—
468	C₄⋊C₄	—	142	1	no	—
469	C₄⋊C₄	—	142	1	no	—
470	C₄⋊C₄	—	142	1	no	—
471	C₄⋊C₄	—	142	1	no	—
472	C₄⋊C₄	—	142	1	no	—
473	C₄⋊C₄	—	142	1	no	—
474	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	142	1	no	—
478	C₂²⋊C₄	—	142	1	no	—
479	C₂²⋊C₄	—	142	1	no	—
480	C₂²⋊C₄	—	142	1	no	—
481	C₂²⋊C₄	—	142	1	no	—
482	C₂²⋊C₄	—	142	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	71	1	no	—
485	C₄²	—	71	1	no	—
486	C₄²	—	71	1	no	—
487	C₄²	—	142	1	no	—
488	C₄²	—	142	1	no	—
489	C₄²	C₂³×D₇₁	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	71	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	284	2	no	—
495	Q₈	—	142	1	no	—
496	Q₈	—	142	1	no	—
497	Q₈	—	142	1	no	—
498	Q₈	—	142	1	no	—
499	D₄	—	2	1	no	—
500	D₄	—	2	1	no	—
501	D₄	—	284	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	284	1	no	—
508	C₂×C₄	—	71	1	no	—
509	C₂×C₄	—	71	1	no	—
510	C₂×C₄	—	71	1	no	—
511	C₂×C₄	—	142	1	no	—
512	C₂×C₄	—	142	1	no	—
513	C₂×C₄	—	142	1	no	—
514	C₂×C₄	—	142	1	no	—
515	C₂×C₄	—	142	1	no	—
516	C₂×C₄	—	142	1	no	—
517	C₂×C₄	—	142	1	no	—
518	C₂×C₄	—	142	1	no	—
519	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
521	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	284	1	no	—
529	C₈	—	284	1	no	—
530	C₈	—	284	1	no	—
531	C₈	—	71	2	no	—
532	C₈	—	71	2	no	—
533	C₈	—	142	1	no	—
534	C₈	—	142	1	no	—
535	C₈	#14556134	1	2	yes	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	142	1	no	—
540	C₂²	—	142	1	no	—
541	C₂²	—	142	1	no	—
542	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	284	1	no	—
548	C₄	—	284	1	no	—
549	C₄	—	284	1	no	—
550	C₄	—	284	1	no	—
551	C₄	—	142	1	no	—
552	C₄	—	142	1	no	—
553	C₄	—	142	1	no	—
554	C₄	#131×D₇₁	1	1	yes	characteristic
555	C₄	C₂×#14556134	1	1	yes	characteristic
556	C₄	#137×D₇₁	1	1	yes	characteristic
557	C₄	#17986795	1	1	yes	characteristic
558	C₂	—	8	1	no	—
559	C₂	—	284	1	no	—
560	C₂	#22597047	1	1	yes	characteristic
561	C₂	#22597162	1	1	yes	characteristic
562	C₂	#22597240	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×SD₁₆⋊C₈	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#14556099	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	SD₁₆⋊C₈	D₇₁
hypocenter	C₇₁	#17967
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
3. #22597269	C₂	semidirect
4. #22587236	C₂	semidirect
5. #22587234	C₂	semidirect
6. #22587233	C₂	semidirect
7. #22587231	C₂	semidirect
8. #22587160	C₂	semidirect
9. #22587157	C₂	semidirect
10. #22587152	C₂	semidirect
11. #22587106	C₂	semidirect
12. #22586811	C₂	semidirect
14. #22586619	C₂	semidirect
15. C₇₁×SD₁₆⋊C₈	C₂	semidirect
292. SD₁₆⋊C₈	D₇₁	semidirect
297. C₇₁	#17967	semidirect

Maximal subgroups

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

subgroup	index
#22598942	2
#22597312	2
#22597269	2
#22587236	2
#22587234	2
#22587233	2
#22587231	2
#22587160	2
#22587157	2
#22587152	2
#22587106	2
#22586811	2
#22586802	2
#22586619	2
C₇₁×SD₁₆⋊C₈	2
#17967	71