Subgroups — #31968652

Order 18176.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598418	C₂	1	1	yes	maximal, characteristic
2	#22597501	C₂	1	1	yes	maximal, characteristic
3	#22597426	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587234	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587216	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587210	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587209	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587198	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×Dic₂₈₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587143	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587122	C₂	1	1	yes	maximal, characteristic, complemented
12	#22586797	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#22586622	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#1590	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986531	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₇₁	C₂²	1	1	yes	characteristic
18	#17986331	C₄	1	1	yes	characteristic
19	#17986311	C₄	1	1	yes	characteristic
20	#17986309	C₄	1	1	yes	characteristic
21	#17986308	C₄	1	1	yes	characteristic
22	#17986220	C₄	1	1	yes	characteristic
23	#17986219	C₄	1	1	yes	characteristic
24	#17986156	C₄	1	1	yes	characteristic
25	#17986136	C₄	1	1	yes	characteristic
26	#17986130	C₂²	1	1	yes	characteristic
27	#17986128	—	2	1	no	—
28	#17986127	—	2	1	no	—
29	#17986126	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
31	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
32	#17986123	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	#17986068	—	2	1	no	—
37	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
38	(C₂²⋊D₇₁)⋊C₈	—	2	1	no	—
39	#17986057	—	2	1	no	—
40	#17986055	C₂²	1	1	yes	characteristic
41	#17986054	—	2	1	no	—
42	#17986051	—	2	1	no	—
43	#17986050	C₂²	1	1	yes	characteristic
44	#17986050	C₂²	1	1	yes	characteristic
45	#17986027	—	2	1	no	—
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	#17985751	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	#17985721	C₂²	1	1	yes	characteristic
59	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	#446×C₇₁	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₇₁	C₂²	1	1	yes	characteristic
62	#436×C₇₁	C₂²	1	1	yes	characteristic
63	#334×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	C₈²×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765853	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₇₁⋊C₈	—	2	1	no	—
72	C₂×C₈×D₇₁	—	2	1	no	—
73	C₂×C₈×D₇₁	—	2	1	no	—
74	#14556121	—	2	1	no	—
75	#14556119	C₂×C₄	1	1	yes	characteristic
76	#14556115	C₂×C₄	1	1	yes	characteristic
77	#14556110	—	2	1	no	—
78	#14556108	C₂×C₄	1	1	yes	characteristic
79	#14556099	C₂×C₄	1	1	yes	characteristic
80	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₄₂	—	2	1	no	—
82	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
83	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
84	#14556093	—	2	1	no	—
85	#14556093	C₂×C₄	1	1	yes	characteristic
86	C₄×C₂²⋊D₇₁	—	2	1	no	—
87	#14556087	—	2	1	no	—
88	C₄⋊C₄×D₇₁	—	2	1	no	—
89	C₄⋊C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
90	C₄²×D₇₁	—	2	1	no	—
91	C₄²×D₇₁	C₂³	1	1	yes	characteristic
92	#14556062	C₂×C₄	1	1	yes	characteristic
93	#14556061	C₂×C₄	1	1	yes	characteristic
94	#14556059	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
96	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
97	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
98	Dic₇₁⋊C₈	—	2	1	no	—
99	Dic₇₁⋊C₈	—	2	1	no	—
100	Dic₇₁⋊C₈	—	2	1	no	—
101	Dic₇₁⋊C₈	—	2	1	no	—
102	Dic₇₁⋊C₈	—	2	1	no	—
103	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
104	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₇₁⋊C₈	D₄	1	1	yes	characteristic
106	Dic₇₁⋊C₈	D₄	1	1	yes	characteristic
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	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₇₁)⋊C₈	D₄	1	1	yes	characteristic
118	(C₂×D₇₁)⋊C₈	D₄	1	1	yes	characteristic
119	#14556039	—	2	1	no	—
120	#14556038	—	2	1	no	—
121	#14556038	—	2	1	no	—
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	—	2	1	no	—
128	C₈×Dic₇₁	—	2	1	no	—
129	C₂×SD₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
130	C₂×M₁₆×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	#97×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	Q₈×D₇₁	—	2	2	no	—
148	Q₈×D₇₁	—	4	1	no	—
149	C₂×C₂²⋊D₇₁	—	2	1	no	—
150	C₂×C₄×D₇₁	—	2	1	no	—
151	C₂×C₄×D₇₁	—	2	1	no	—
152	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
155	Dic₂₈₄	—	2	2	no	—
156	#11765855	—	4	1	no	—
157	#11765853	—	2	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	—	8	1	no	—
162	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₇₁⋊C₈	C₂²×C₄	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	C₈×D₇₁	—	2	4	no	—
167	C₈×D₇₁	—	8	1	no	—
168	C₄⋊Dic₇₁	—	2	1	no	—
169	C₄⋊Dic₇₁	—	2	1	no	—
170	C₄⋊Dic₇₁	—	2	1	no	—
171	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
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	C₂²⋊Dic₇₁	—	2	1	no	—
179	C₂²⋊Dic₇₁	—	2	1	no	—
180	C₂²⋊Dic₇₁	—	2	1	no	—
181	(C₂×D₇₁)⋊C₄	—	2	1	no	—
182	C₄×Dic₇₁	—	2	1	no	—
183	C₄×Dic₇₁	—	2	1	no	—
184	C₄×Dic₇₁	—	2	1	no	—
185	C₄×Dic₇₁	—	2	1	no	—
186	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
188	C₄×Dic₇₁	#41	1	1	yes	characteristic
189	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
190	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₁	—	2	1	no	—
192	SD₁₆×C₇₁	—	4	1	no	—
193	M₁₆×C₇₁	—	8	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	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₇₁	—	2	1	no	—
205	C₄²×C₇₁	—	2	1	no	—
206	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
207	C₂³×C₇₁	—	2	1	no	—
208	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₇₁	—	2	1	no	—
210	Q₈×C₇₁	—	2	1	no	—
211	D₄×C₇₁	—	2	1	no	—
212	D₄×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	—	4	1	no	—
217	C₂×C₄×C₇₁	—	4	1	no	—
218	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₇₁	—	4	2	no	—
222	C₂×Dic₇₁	—	2	1	no	—
223	C₂×Dic₇₁	—	2	1	no	—
224	C₂×Dic₇₁	—	2	1	no	—
225	C₂×Dic₇₁	—	2	1	no	—
226	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
228	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
229	C₄×D₇₁	—	2	2	no	—
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	2	no	—
235	C₄×D₇₁	—	4	2	no	—
236	Dic₁₄₂	—	2	1	no	—
237	Dic₁₄₂	—	2	1	no	—
238	Dic₁₄₂	—	2	1	no	—
239	Dic₁₄₂	—	4	2	no	—
240	Dic₁₄₂	#131	1	2	yes	—
241	C₈×C₇₁	—	2	2	no	—
242	C₈×C₇₁	—	2	1	no	—
243	C₈×C₇₁	—	2	1	no	—
244	C₈×C₇₁	—	2	1	no	—
245	C₈×C₇₁	—	2	1	no	—
246	C₈×C₇₁	—	4	1	no	—
247	C₈×C₇₁	—	4	1	no	—
248	C₇₁⋊C₈	—	2	2	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	—	4	1	no	—
254	C₇₁⋊C₈	—	4	1	no	—
255	C₂²×C₇₁	—	4	1	no	—
256	C₂²×C₇₁	—	4	1	no	—
257	C₂²×C₇₁	—	4	1	no	—
258	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₇₁	—	2	1	no	—
260	C₂×D₇₁	—	2	1	no	—
261	C₂×D₇₁	#443	1	2	yes	—
262	C₄×C₇₁	—	2	1	no	—
263	C₄×C₇₁	—	4	1	no	—
264	C₄×C₇₁	—	4	1	no	—
265	C₄×C₇₁	—	4	1	no	—
266	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
267	C₄×C₇₁	#568	1	1	yes	characteristic
268	C₄×C₇₁	#577	1	1	yes	characteristic
269	C₄×C₇₁	#578	1	1	yes	characteristic
270	Dic₇₁	—	2	2	no	—
271	Dic₇₁	—	2	1	no	—
272	Dic₇₁	—	2	1	no	—
273	Dic₇₁	—	2	1	no	—
274	Dic₇₁	—	4	1	no	—
275	Dic₇₁	—	4	1	no	—
276	Dic₇₁	—	4	1	no	—
277	#18017	—	71	1	no	maximal, Sylow
278	C₂×C₇₁	—	8	1	no	—
279	C₂×C₇₁	#2933	1	1	yes	characteristic
280	C₂×C₇₁	#2947	1	1	yes	characteristic
281	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
282	D₇₁	—	2	2	no	—
283	#3108	—	71	1	no	—
284	#2994	—	71	1	no	—
285	#2984	—	71	1	no	—
286	#1591	—	71	1	no	—
287	#1590	D₇₁	1	1	yes	characteristic, complemented
288	#1588	—	71	1	no	—
289	#1587	—	71	1	no	—
290	#1587	—	71	1	no	—
291	#1585	—	71	1	no	—
292	C₈×Q₁₆	—	71	1	no	—
293	C₈×SD₁₆	—	71	1	no	—
294	#1573	—	71	1	no	—
295	#1494	—	71	1	no	—
296	C₂×Q₈⋊C₈	—	71	1	no	—
297	#1450	—	71	1	no	—
298	C₇₁	#18017	1	1	yes	characteristic, complemented, Sylow
299	#529	—	71	1	no	—
300	C₂×C₄×Q₈	—	71	1	no	—
301	#483	—	71	1	no	—
302	#480	—	71	1	no	—
303	#479	—	71	1	no	—
304	#479	—	71	1	no	—
305	#464	—	71	1	no	—
306	#464	—	71	1	no	—
307	#451	—	71	1	no	—
308	#448	—	71	1	no	—
309	#446	—	71	1	no	—
310	#446	—	71	1	no	—
311	#446	—	142	1	no	—
312	#446	—	142	1	no	—
313	#446	C₂×D₇₁	1	1	yes	characteristic
314	C₈×Q₈	—	71	1	no	—
315	C₈×Q₈	—	71	1	no	—
316	C₈×Q₈	—	71	1	no	—
317	C₄×Q₁₆	—	71	1	no	—
318	C₄×Q₁₆	—	71	1	no	—
319	C₄×SD₁₆	—	71	1	no	—
320	C₄×SD₁₆	C₂×D₇₁	1	1	yes	characteristic
321	#436	C₂×D₇₁	1	1	yes	characteristic
322	#435	—	142	1	no	—
323	C₈×D₄	—	71	1	no	—
324	C₈×D₄	—	142	1	no	—
325	#433	—	142	1	no	—
326	#432	—	71	1	no	—
327	#432	—	142	1	no	—
328	#431	—	71	1	no	—
329	#431	—	71	1	no	—
330	#431	—	142	1	no	—
331	#424	—	142	1	no	—
332	C₂×C₄⋊C₈	—	71	1	no	—
333	C₂×C₄×C₈	—	71	1	no	—
334	#335	—	71	1	no	—
335	#335	—	71	1	no	—
336	#334	—	71	1	no	—
337	#334	C₂×D₇₁	1	1	yes	characteristic
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	—	71	1	no	—
343	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
344	D₄⋊C₈	—	71	1	no	—
345	D₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
346	#322	—	71	1	no	—
347	#322	—	71	1	no	—
348	C₈²	—	71	1	no	—
349	C₈²	C₂×D₇₁	1	1	yes	characteristic
350	C₂²×Q₈	—	71	1	no	—
351	C₂×Q₁₆	—	71	1	no	—
352	C₂×Q₁₆	—	71	1	no	—
353	C₂×SD₁₆	—	71	1	no	—
354	C₂×SD₁₆	C₄×D₇₁	1	1	yes	characteristic
355	C₂×M₁₆	—	2	1	no	—
356	C₂²×C₈	—	142	1	no	—
357	C₂²×C₈	—	142	1	no	—
358	C₂²×C₈	—	142	1	no	—
359	#126	—	142	1	no	—
360	#125	—	71	1	no	—
361	#124	—	71	1	no	—
362	#123	—	142	1	no	—
363	C₂²⋊Q₈	—	71	1	no	—
364	#121	—	71	1	no	—
365	C₄×Q₈	—	71	1	no	—
366	C₄×Q₈	—	71	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×D₄	—	142	1	no	—
373	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
374	#117	—	142	1	no	—
375	C₂×C₄⋊C₄	—	71	1	no	—
376	C₂×C₄⋊C₄	—	142	1	no	—
377	C₂×C₄²	—	71	1	no	—
378	C₂×C₄²	—	142	1	no	—
379	#107	—	71	1	no	—
380	#107	—	71	1	no	—
381	#106	—	71	1	no	—
382	#106	C₄×D₇₁	1	1	yes	characteristic
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	71	1	no	—
385	C₄⋊C₈	—	71	1	no	—
386	C₄⋊C₈	—	71	1	no	—
387	C₄⋊C₈	—	71	1	no	—
388	C₄⋊C₈	—	71	1	no	—
389	C₄⋊C₈	—	71	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	—	142	1	no	—
396	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
398	#103	—	71	1	no	—
399	#103	—	71	1	no	—
400	#103	—	71	1	no	—
401	#103	—	71	1	no	—
402	#103	—	71	1	no	—
403	#103	C₄×D₇₁	1	1	yes	characteristic
404	#102	—	71	1	no	—
405	#102	C₄×D₇₁	1	1	yes	characteristic
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	71	1	no	—
408	C₂²⋊C₈	—	71	1	no	—
409	C₂²⋊C₈	—	71	1	no	—
410	C₂²⋊C₈	—	71	1	no	—
411	C₂²⋊C₈	—	142	1	no	—
412	C₂²⋊C₈	—	142	1	no	—
413	#97	—	2	1	no	—
414	#97	—	142	1	no	—
415	#97	—	142	1	no	—
416	#97	—	142	1	no	—
417	C₄×C₈	—	71	1	no	—
418	C₄×C₈	—	71	1	no	—
419	C₄×C₈	—	71	1	no	—
420	C₄×C₈	—	142	1	no	—
421	C₄×C₈	—	142	1	no	—
422	C₄×C₈	—	142	1	no	—
423	C₄×C₈	—	142	1	no	—
424	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
427	C₂×Q₈	—	284	1	no	—
428	C₂×Q₈	—	71	1	no	—
429	C₂×Q₈	—	71	1	no	—
430	C₂×Q₈	—	142	1	no	—
431	C₂×Q₈	—	142	2	no	—
432	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
433	C₂×D₄	—	142	1	no	—
434	C₂×D₄	C₂×C₄×D₇₁	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	71	1	no	—
437	C₂²×C₄	—	71	1	no	—
438	C₂²×C₄	—	71	1	no	—
439	C₂²×C₄	—	142	1	no	—
440	C₂²×C₄	—	142	1	no	—
441	Q₁₆	—	284	1	no	—
442	Q₁₆	—	142	2	no	—
443	SD₁₆	—	4	1	no	—
444	SD₁₆	—	142	2	no	—
445	M₁₆	—	8	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	568	1	no	—
450	C₂×C₈	—	568	1	no	—
451	C₂×C₈	—	71	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	71	1	no	—
454	C₂×C₈	—	71	1	no	—
455	C₂×C₈	—	142	4	no	—
456	C₂×C₈	—	142	1	no	—
457	C₂×C₈	—	142	1	no	—
458	C₂×C₈	—	142	1	no	—
459	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
461	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
462	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	71	1	no	—
465	C₄⋊C₄	—	71	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	C₄²	—	2	1	no	—
482	C₄²	—	71	1	no	—
483	C₄²	—	71	1	no	—
484	C₄²	—	71	1	no	—
485	C₄²	—	142	1	no	—
486	C₄²	—	142	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	—	71	2	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	2	no	—
508	C₂×C₄	—	284	2	no	—
509	C₂×C₄	—	71	1	no	—
510	C₂×C₄	—	71	1	no	—
511	C₂×C₄	—	71	1	no	—
512	C₂×C₄	—	142	2	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	—	142	1	no	—
520	C₂×C₄	—	142	1	no	—
521	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
522	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
523	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	284	1	no	—
532	C₈	—	284	1	no	—
533	C₈	—	142	2	no	—
534	C₈	—	142	1	no	—
535	C₈	—	142	1	no	—
536	C₈	—	142	1	no	—
537	C₈	—	142	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	71	2	no	—
542	C₂²	—	142	1	no	—
543	C₂²	—	142	1	no	—
544	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	284	1	no	—
550	C₄	—	284	1	no	—
551	C₄	—	284	1	no	—
552	C₄	—	142	1	no	—
553	C₄	—	142	1	no	—
554	C₄	—	142	2	no	—
555	C₄	—	142	1	no	—
556	C₄	#131×D₇₁	1	1	yes	characteristic
557	C₄	#17986765	1	1	yes	characteristic
558	C₄	#17986805	1	1	yes	characteristic
559	C₄	#17986813	1	1	yes	characteristic
560	C₂	—	8	1	no	—
561	C₂	—	142	2	no	—
562	C₂	#22597069	1	1	yes	characteristic
563	C₂	#22597176	1	1	yes	characteristic
564	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×#1590	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#14556099	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1590	D₇₁
hypocenter	C₇₁	#18017
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
3. #22597426	C₂	semidirect
4. #22587234	C₂	semidirect
5. #22587216	C₂	semidirect
6. #22587210	C₂	semidirect
7. #22587209	C₂	semidirect
8. #22587198	C₂	semidirect
9. C₈×Dic₂₈₄	C₂	semidirect
10. #22587143	C₂	semidirect
11. #22587122	C₂	semidirect
13. Q₈⋊C₈×D₇₁	C₂	semidirect
14. #22586622	C₂	semidirect
15. C₇₁×#1590	C₂	semidirect
287. #1590	D₇₁	semidirect
298. C₇₁	#18017	semidirect

Maximal subgroups

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

subgroup	index
#22598418	2
#22597501	2
#22597426	2
#22587234	2
#22587216	2
#22587210	2
#22587209	2
#22587198	2
C₈×Dic₂₈₄	2
#22587143	2
#22587122	2
#22586797	2
Q₈⋊C₈×D₇₁	2
#22586622	2
C₇₁×#1590	2
#18017	71