Subgroups — #31968195

Order 18176.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598923	C₂	1	1	yes	maximal, characteristic
2	#22597271	C₂	1	1	yes	maximal, characteristic
3	#22597269	C₂	1	1	yes	maximal, characteristic
4	#22587214	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587213	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587212	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587211	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587210	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587209	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587208	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587094	C₂	1	1	yes	maximal, characteristic
12	#22586793	C₂	1	1	yes	maximal, characteristic
13	#22586793	C₂	1	1	yes	maximal, characteristic
14	#322×D₇₁	C₂	1	1	yes	maximal, characteristic
15	C₇₁×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986553	C₂²	1	1	yes	characteristic
17	#17986553	C₂²	1	1	yes	characteristic
18	#17986403	C₄	1	1	yes	characteristic
19	#17986377	C₄	1	1	yes	characteristic
20	#17986348	C₄	1	1	yes	characteristic
21	#17986348	C₄	1	1	yes	characteristic
22	#17986241	C₄	1	1	yes	characteristic
23	#17986239	C₄	1	1	yes	characteristic
24	#17986239	C₄	1	1	yes	characteristic
25	#17986237	C₄	1	1	yes	characteristic
26	#17986130	C₂²	1	1	yes	characteristic
27	#17986129	C₂²	1	1	yes	characteristic
28	#17986128	—	2	1	no	—
29	#17986127	—	2	1	no	—
30	#17986126	C₂²	1	1	yes	characteristic
31	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₄₂	—	2	1	no	—
33	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
34	#17986123	—	2	1	no	—
35	#17986123	C₂²	1	1	yes	characteristic
36	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic
37	C₄×#11765855	C₂²	1	1	yes	characteristic
38	C₄×#11765855	C₂²	1	1	yes	characteristic
39	#17986024	—	2	1	no	—
40	#17986024	—	2	1	no	—
41	#17986021	C₂²	1	1	yes	characteristic
42	#17986021	C₂²	1	1	yes	characteristic
43	#17985956	—	2	1	no	—
44	#17985953	—	2	1	no	—
45	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985750	C₂²	1	1	yes	characteristic
49	#17985749	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	Q₈⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
55	#17985729	C₂²	1	1	yes	characteristic
56	#17985729	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	#446×C₇₁	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₇₁	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
63	#334×C₇₁	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
65	Q₈⋊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×#11765855	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765848	—	2	1	no	—
71	C₂×#11765848	—	2	1	no	—
72	C₂×C₈×D₇₁	—	2	1	no	—
73	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
76	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
77	#14556127	C₂×C₄	1	1	yes	characteristic
78	#14556127	C₂×C₄	1	1	yes	characteristic
79	#14556126	C₂×C₄	1	1	yes	characteristic
80	#14556126	C₂×C₄	1	1	yes	characteristic
81	#14556118	—	2	1	no	—
82	#14556118	—	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	#14556106	—	2	1	no	—
87	#14556104	C₂×C₄	1	1	yes	characteristic
88	#14556104	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₄₂	—	2	1	no	—
90	C₄×Dic₁₄₂	—	2	1	no	—
91	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
92	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
93	#14556085	—	2	1	no	—
94	#14556085	—	2	1	no	—
95	C₄²×D₇₁	C₂³	1	1	yes	characteristic
96	#14556062	C₂×C₄	1	1	yes	characteristic
97	#14556061	C₂×C₄	1	1	yes	characteristic
98	#14556061	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
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	—	2	1	no	—
109	#14556053	C₂×C₄	1	1	yes	characteristic
110	#14556053	C₂×C₄	1	1	yes	characteristic
111	#14556052	C₂×C₄	1	1	yes	characteristic
112	#14556052	C₂×C₄	1	1	yes	characteristic
113	#14556051	C₂×C₄	1	1	yes	characteristic
114	#14556051	C₂×C₄	1	1	yes	characteristic
115	#14556039	—	2	1	no	—
116	#14556038	—	2	1	no	—
117	#14556038	—	2	1	no	—
118	C₄×C₇₁⋊C₈	—	2	1	no	—
119	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₈×Dic₇₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
128	C₈×Dic₇₁	D₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
132	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₇₁	—	2	1	no	—
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	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
139	#97×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	—	2	1	no	—
146	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
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	—	4	1	no	—
152	#11765855	—	4	1	no	—
153	#11765855	—	4	1	no	—
154	#11765848	—	4	2	no	—
155	#11765848	—	4	2	no	—
156	C₂×C₇₁⋊C₈	—	2	1	no	—
157	C₂×C₇₁⋊C₈	—	2	1	no	—
158	C₂×C₇₁⋊C₈	—	2	1	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	C₂×D₄	1	1	yes	characteristic
162	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₈×D₇₁	—	2	4	no	—
164	C₈×D₇₁	—	2	2	no	—
165	C₈×D₇₁	—	2	2	no	—
166	C₈×D₇₁	—	4	1	no	—
167	C₈×D₇₁	—	4	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	Dic₇₁⋊C₄	—	2	1	no	—
180	Dic₇₁⋊C₄	—	2	1	no	—
181	Dic₇₁⋊C₄	—	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	(C₂×D₇₁)⋊C₄	—	2	1	no	—
186	C₄×Dic₇₁	—	2	1	no	—
187	C₄×Dic₇₁	—	2	1	no	—
188	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
189	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₇₁	#41	1	1	yes	characteristic
191	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
193	Q₁₆×C₇₁	—	4	1	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	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₇₁	—	2	1	no	—
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	C₄²×C₇₁	—	2	1	no	—
206	C₄²×C₇₁	—	2	1	no	—
207	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
208	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
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	C₂×C₄×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	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₇₁	—	2	1	no	—
221	C₂×Dic₇₁	—	2	1	no	—
222	C₂×Dic₇₁	—	2	1	no	—
223	C₂×Dic₇₁	—	2	1	no	—
224	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
227	C₄×D₇₁	—	2	1	no	—
228	C₄×D₇₁	—	2	1	no	—
229	C₄×D₇₁	—	2	2	no	—
230	C₄×D₇₁	#137	1	2	yes	—
231	C₄×D₇₁	#137	1	2	yes	—
232	Dic₁₄₂	—	2	1	no	—
233	Dic₁₄₂	—	2	1	no	—
234	Dic₁₄₂	—	2	1	no	—
235	Dic₁₄₂	—	2	1	no	—
236	Dic₁₄₂	—	4	2	no	—
237	Dic₁₄₂	—	4	2	no	—
238	C₈×C₇₁	—	2	2	no	—
239	C₈×C₇₁	—	2	1	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	C₇₁⋊C₈	—	2	2	no	—
246	C₇₁⋊C₈	—	2	1	no	—
247	C₇₁⋊C₈	—	2	1	no	—
248	C₇₁⋊C₈	—	2	1	no	—
249	C₇₁⋊C₈	—	2	1	no	—
250	C₇₁⋊C₈	—	4	1	no	—
251	C₇₁⋊C₈	—	4	1	no	—
252	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×D₇₁	—	2	1	no	—
254	C₂×D₇₁	—	2	1	no	—
255	C₂×D₇₁	#441	1	2	yes	—
256	C₄×C₇₁	—	2	1	no	—
257	C₄×C₇₁	—	4	1	no	—
258	C₄×C₇₁	—	4	1	no	—
259	C₄×C₇₁	—	4	1	no	—
260	C₄×C₇₁	—	4	1	no	—
261	C₄×C₇₁	#568	1	1	yes	characteristic
262	C₄×C₇₁	#568	1	1	yes	characteristic
263	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
264	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
265	Dic₇₁	—	2	1	no	—
266	Dic₇₁	—	4	1	no	—
267	Dic₇₁	—	4	1	no	—
268	Dic₇₁	—	4	1	no	—
269	Dic₇₁	—	4	1	no	—
270	Dic₇₁	#441	1	2	yes	—
271	Dic₇₁	#443	1	2	yes	—
272	#17980	—	71	1	no	maximal, Sylow
273	C₂×C₇₁	#2932	1	1	yes	characteristic
274	C₂×C₇₁	C₂×#441	1	1	yes	characteristic
275	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
276	D₇₁	—	2	2	no	—
277	#3170	—	71	1	no	—
278	#2960	—	71	1	no	—
279	#2960	—	71	1	no	—
280	#1587	—	71	1	no	—
281	#1587	—	71	1	no	—
282	#1587	—	71	1	no	—
283	#1587	—	71	1	no	—
284	#1587	—	71	1	no	—
285	#1587	—	71	1	no	—
286	#1587	—	71	1	no	—
287	#1587	D₇₁	1	1	yes	characteristic, complemented
288	#1566	—	71	1	no	—
289	#1493	—	71	1	no	—
290	#1493	—	71	1	no	—
291	C₂×#322	—	71	1	no	—
292	C₇₁	#17980	1	1	yes	characteristic, complemented, Sylow
293	#533	—	71	1	no	—
294	#533	—	71	1	no	—
295	#500	—	71	1	no	—
296	#494	—	71	1	no	—
297	#487	—	71	1	no	—
298	#487	—	71	1	no	—
299	#467	—	71	1	no	—
300	#467	—	71	1	no	—
301	#467	—	71	1	no	—
302	#467	—	71	1	no	—
303	#446	—	71	1	no	—
304	#446	—	71	1	no	—
305	#446	—	71	1	no	—
306	#446	—	142	1	no	—
307	#446	—	142	1	no	—
308	#446	C₂×D₇₁	1	1	yes	characteristic
309	C₈×Q₈	—	71	1	no	—
310	C₈×Q₈	—	71	1	no	—
311	C₈×Q₈	—	71	1	no	—
312	C₈×Q₈	—	142	1	no	—
313	C₈×Q₈	—	142	1	no	—
314	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
315	C₄×Q₁₆	—	71	1	no	—
316	C₄×Q₁₆	—	71	1	no	—
317	C₄×Q₁₆	—	71	1	no	—
318	C₄×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
319	#424	—	142	1	no	—
320	#424	—	142	1	no	—
321	#423	—	71	1	no	—
322	#423	—	71	1	no	—
323	#405	—	142	1	no	—
324	#405	—	142	1	no	—
325	C₂×C₄×C₈	—	71	1	no	—
326	C₂×C₄×C₈	—	71	1	no	—
327	C₂×C₄×C₈	—	71	1	no	—
328	#334	—	71	1	no	—
329	#334	—	71	1	no	—
330	#334	—	71	1	no	—
331	#334	C₂×D₇₁	1	1	yes	characteristic
332	Q₈⋊C₈	—	71	1	no	—
333	Q₈⋊C₈	—	71	1	no	—
334	Q₈⋊C₈	—	71	1	no	—
335	Q₈⋊C₈	—	71	1	no	—
336	Q₈⋊C₈	—	71	1	no	—
337	Q₈⋊C₈	—	71	1	no	—
338	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
339	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
340	#322	—	71	1	no	—
341	#322	—	71	1	no	—
342	#322	—	71	1	no	—
343	#322	C₂×D₇₁	1	1	yes	characteristic
344	C₂×Q₁₆	—	71	1	no	—
345	C₂×Q₁₆	—	71	1	no	—
346	C₂×Q₁₆	—	71	1	no	—
347	C₂×Q₁₆	C₄×D₇₁	1	1	yes	characteristic
348	C₂×M₁₆	—	142	1	no	—
349	C₂×M₁₆	—	142	1	no	—
350	C₂²×C₈	—	71	1	no	—
351	C₂²×C₈	—	71	1	no	—
352	C₂²×C₈	—	71	1	no	—
353	C₂²×C₈	—	71	1	no	—
354	C₂²×C₈	—	142	1	no	—
355	C₄⋊Q₈	—	71	1	no	—
356	C₄⋊Q₈	—	71	1	no	—
357	C₄⋊Q₈	—	71	1	no	—
358	C₄⋊Q₈	—	71	1	no	—
359	#125	—	142	1	no	—
360	#125	—	142	1	no	—
361	C₂²⋊Q₈	—	71	1	no	—
362	C₂²⋊Q₈	—	71	1	no	—
363	C₂²⋊Q₈	—	71	1	no	—
364	C₂²⋊Q₈	—	71	1	no	—
365	C₂²⋊Q₈	—	142	1	no	—
366	C₂²⋊Q₈	—	142	1	no	—
367	C₄×Q₈	—	71	1	no	—
368	C₄×Q₈	—	71	1	no	—
369	C₄×Q₈	—	142	1	no	—
370	C₄×Q₈	—	142	1	no	—
371	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
372	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
373	#117	—	142	1	no	—
374	#117	—	142	1	no	—
375	C₂×C₄²	—	71	1	no	—
376	#107	—	71	1	no	—
377	#107	—	71	1	no	—
378	#107	—	71	1	no	—
379	#107	C₄×D₇₁	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	71	1	no	—
383	C₄⋊C₈	—	71	1	no	—
384	C₄⋊C₈	—	142	1	no	—
385	C₄⋊C₈	—	142	1	no	—
386	C₄⋊C₈	—	142	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	C₂²×D₇₁	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
394	#103	—	71	1	no	—
395	#103	—	71	1	no	—
396	#103	—	71	1	no	—
397	#103	—	71	1	no	—
398	#103	—	71	1	no	—
399	#103	—	71	1	no	—
400	#103	C₄×D₇₁	1	1	yes	characteristic
401	#103	C₄×D₇₁	1	1	yes	characteristic
402	#97	—	2	1	no	—
403	#97	—	142	1	no	—
404	#97	—	142	1	no	—
405	#97	—	142	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	71	1	no	—
408	C₄×C₈	—	71	1	no	—
409	C₄×C₈	—	71	1	no	—
410	C₄×C₈	—	71	1	no	—
411	C₄×C₈	—	71	1	no	—
412	C₄×C₈	—	71	1	no	—
413	C₄×C₈	—	71	1	no	—
414	C₄×C₈	—	142	1	no	—
415	C₄×C₈	—	142	1	no	—
416	C₄×C₈	—	142	1	no	—
417	C₄×C₈	—	142	1	no	—
418	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
421	C₂×Q₈	—	71	1	no	—
422	C₂×Q₈	—	71	1	no	—
423	C₂×Q₈	—	142	1	no	—
424	C₂×Q₈	—	142	1	no	—
425	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
426	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
427	C₂²×C₄	—	71	1	no	—
428	C₂²×C₄	—	71	1	no	—
429	C₂²×C₄	—	71	1	no	—
430	Q₁₆	—	4	1	no	—
431	Q₁₆	—	284	1	no	—
432	Q₁₆	—	284	1	no	—
433	Q₁₆	—	284	1	no	—
434	M₁₆	—	284	2	no	—
435	M₁₆	—	284	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	284	1	no	—
440	C₂×C₈	—	284	1	no	—
441	C₂×C₈	—	71	1	no	—
442	C₂×C₈	—	71	1	no	—
443	C₂×C₈	—	71	1	no	—
444	C₂×C₈	—	71	1	no	—
445	C₂×C₈	—	142	2	no	—
446	C₂×C₈	—	142	2	no	—
447	C₂×C₈	—	142	4	no	—
448	C₂×C₈	—	142	1	no	—
449	C₂×C₈	—	142	1	no	—
450	C₂×C₈	—	142	1	no	—
451	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
452	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
453	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
454	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	71	1	no	—
458	C₄⋊C₄	—	71	1	no	—
459	C₄⋊C₄	—	142	1	no	—
460	C₄⋊C₄	—	142	1	no	—
461	C₄⋊C₄	—	142	1	no	—
462	C₄⋊C₄	—	142	1	no	—
463	C₄⋊C₄	—	142	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	C₂×C₄×D₇₁	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
473	C₂²⋊C₄	—	142	1	no	—
474	C₂²⋊C₄	—	142	1	no	—
475	C₂²⋊C₄	—	142	1	no	—
476	C₂²⋊C₄	—	142	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	71	1	no	—
480	C₄²	—	71	1	no	—
481	C₄²	—	71	1	no	—
482	C₄²	—	142	1	no	—
483	C₄²	—	142	1	no	—
484	C₄²	C₂³×D₇₁	1	1	yes	characteristic
485	C₂³	—	71	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	284	2	no	—
491	Q₈	—	284	2	no	—
492	Q₈	—	142	1	no	—
493	Q₈	—	142	1	no	—
494	Q₈	—	142	1	no	—
495	Q₈	—	142	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	71	1	no	—
501	C₂×C₄	—	71	1	no	—
502	C₂×C₄	—	71	2	no	—
503	C₂×C₄	—	71	2	no	—
504	C₂×C₄	—	71	1	no	—
505	C₂×C₄	—	142	2	no	—
506	C₂×C₄	—	142	1	no	—
507	C₂×C₄	—	142	1	no	—
508	C₂×C₄	—	142	1	no	—
509	C₂×C₄	—	142	1	no	—
510	C₂×C₄	—	142	1	no	—
511	C₂×C₄	—	142	1	no	—
512	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
513	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
514	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	284	1	no	—
523	C₈	—	284	1	no	—
524	C₈	—	142	2	no	—
525	C₈	—	142	1	no	—
526	C₈	—	142	1	no	—
527	C₈	—	142	1	no	—
528	C₈	—	142	1	no	—
529	C₂²	—	71	2	no	—
530	C₂²	—	142	1	no	—
531	C₂²	—	142	1	no	—
532	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	284	1	no	—
539	C₄	—	284	1	no	—
540	C₄	—	284	1	no	—
541	C₄	—	284	1	no	—
542	C₄	—	71	2	no	—
543	C₄	—	71	2	no	—
544	C₄	—	142	1	no	—
545	C₄	#17986764	1	1	yes	characteristic
546	C₄	#17986765	1	1	yes	characteristic
547	C₄	#137×D₇₁	1	1	yes	characteristic
548	C₄	#137×D₇₁	1	1	yes	characteristic
549	C₂	—	142	2	no	—
550	C₂	#22597054	1	1	yes	characteristic
551	C₂	#441×D₇₁	1	1	yes	characteristic
552	C₂	#443×D₇₁	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×#1587	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂²×D₇₁	C₄×D₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1587	D₇₁
hypocenter	C₇₁	#17980
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
4. #22587214	C₂	semidirect
5. #22587213	C₂	semidirect
6. #22587212	C₂	semidirect
7. #22587211	C₂	semidirect
8. #22587210	C₂	semidirect
9. #22587209	C₂	semidirect
10. #22587208	C₂	semidirect
15. C₇₁×#1587	C₂	semidirect
287. #1587	D₇₁	semidirect
292. C₇₁	#17980	semidirect

Maximal subgroups

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

subgroup	index
#22598923	2
#22597271	2
#22597269	2
#22587214	2
#22587213	2
#22587212	2
#22587211	2
#22587210	2
#22587209	2
#22587208	2
#22587094	2
#22586793	2
#322×D₇₁	2
C₇₁×#1587	2
#17980	71