Subgroups — #31967147

Order 18176.

626 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597422	C₂	1	1	yes	maximal, characteristic
2	#22597419	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic
4	#22587213	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587212	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587210	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587193	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587190	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587188	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587187	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587085	C₂	1	1	yes	maximal, characteristic
12	#22586733	C₂	1	1	yes	maximal, characteristic
13	#22586733	C₂	1	1	yes	maximal, characteristic
14	#22586631	C₂	1	1	yes	maximal, characteristic
15	C₇₁×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₇₁	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₇₁	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₇₁	C₂²	1	1	yes	characteristic
19	#17986130	C₂²	1	1	yes	characteristic
20	#17986129	C₂²	1	1	yes	characteristic
21	#17986128	—	2	1	no	—
22	#17986127	—	2	1	no	—
23	#17986126	C₂²	1	1	yes	characteristic
24	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₄₂	—	2	1	no	—
26	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
27	#17986123	—	2	1	no	—
28	#17986123	C₂²	1	1	yes	characteristic
29	C₄×Dic₂₈₄	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₇₁	C₄	1	1	yes	characteristic
31	#17986093	C₄	1	1	yes	characteristic
32	C₄×#11765855	C₂²	1	1	yes	characteristic
33	C₄×#11765855	C₂²	1	1	yes	characteristic
34	#17986091	C₄	1	1	yes	characteristic
35	#17986091	C₄	1	1	yes	characteristic
36	#17986055	—	2	1	no	—
37	#17986054	—	2	1	no	—
38	#17986051	—	2	1	no	—
39	#17986051	C₂²	1	1	yes	characteristic
40	#17986051	C₂²	1	1	yes	characteristic
41	#17986050	—	2	1	no	—
42	#17986050	C₂²	1	1	yes	characteristic
43	#17986050	C₂²	1	1	yes	characteristic
44	#107×D₇₁	C₄	1	1	yes	characteristic
45	#103×D₇₁	C₄	1	1	yes	characteristic
46	#103×D₇₁	C₄	1	1	yes	characteristic
47	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
48	#17985751	C₂²	1	1	yes	characteristic
49	#17985751	C₂²	1	1	yes	characteristic
50	#17985750	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×Q₈×D₇₁	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765855	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₇₁	—	2	4	no	—
73	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
75	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₄₂	—	2	1	no	—
78	C₄×Dic₁₄₂	—	2	1	no	—
79	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
81	#14556093	—	2	1	no	—
82	#14556093	—	2	1	no	—
83	#14556093	C₂×C₄	1	1	yes	characteristic
84	#14556093	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₄×D₇₁	—	2	1	no	—
86	C₄⋊C₄×D₇₁	—	2	1	no	—
87	C₄⋊C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₇₁	—	2	1	no	—
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	#14556061	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
96	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
97	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
98	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
104	Dic₇₁⋊C₈	D₄	1	1	yes	characteristic
105	Dic₇₁⋊C₈	D₄	1	1	yes	characteristic
106	#14556053	C₂×C₄	1	1	yes	characteristic
107	#14556053	C₂×C₄	1	1	yes	characteristic
108	#14556052	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	(C₂×D₇₁)⋊C₈	—	2	1	no	—
113	(C₂×D₇₁)⋊C₈	—	2	1	no	—
114	(C₂×D₇₁)⋊C₈	—	2	1	no	—
115	(C₂×D₇₁)⋊C₈	D₄	1	1	yes	characteristic
116	(C₂×D₇₁)⋊C₈	D₄	1	1	yes	characteristic
117	#14556039	—	2	1	no	—
118	#14556038	—	2	1	no	—
119	#14556038	—	2	1	no	—
120	C₄×C₇₁⋊C₈	—	2	1	no	—
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	C₈×Dic₇₁	—	2	1	no	—
126	C₈×Dic₇₁	—	2	1	no	—
127	C₈×Dic₇₁	—	2	1	no	—
128	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
133	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₇₁	—	2	1	no	—
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	#103×C₇₁	C₂×C₄	1	1	yes	characteristic
140	#97×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	C₂×Dic₁₄₂	—	2	1	no	—
146	C₂×Dic₁₄₂	—	2	1	no	—
147	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₇₁	—	2	2	no	—
150	Q₈×D₇₁	—	2	2	no	—
151	Q₈×D₇₁	—	2	2	no	—
152	Q₈×D₇₁	M₁₆	1	4	yes	—
153	C₂×C₄×D₇₁	—	2	1	no	—
154	C₂×C₄×D₇₁	—	2	1	no	—
155	C₂×C₄×D₇₁	—	2	1	no	—
156	C₂×C₄×D₇₁	—	2	1	no	—
157	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
160	Dic₂₈₄	—	2	2	no	—
161	#11765855	—	2	2	no	—
162	#11765855	—	2	2	no	—
163	C₂×C₇₁⋊C₈	—	2	1	no	—
164	C₂×C₇₁⋊C₈	—	2	1	no	—
165	C₂×C₇₁⋊C₈	—	2	1	no	—
166	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₈×D₇₁	—	2	2	no	—
171	C₈×D₇₁	—	2	2	no	—
172	C₄⋊Dic₇₁	—	2	1	no	—
173	C₄⋊Dic₇₁	—	2	1	no	—
174	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊Dic₇₁	C₂²×C₄	1	1	yes	characteristic
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	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	—	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	—	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	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	C₂×M₁₆	1	2	yes	—
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	4	no	—
228	C₄×D₇₁	—	2	1	no	—
229	C₄×D₇₁	—	2	1	no	—
230	C₄×D₇₁	—	4	1	no	—
231	C₄×D₇₁	—	4	2	no	—
232	C₄×D₇₁	—	8	1	no	—
233	C₄×D₇₁	—	8	1	no	—
234	C₄×D₇₁	C₂×M₁₆	1	2	yes	—
235	C₄×D₇₁	#131	1	2	yes	—
236	Dic₁₄₂	—	2	1	no	—
237	Dic₁₄₂	—	2	4	no	—
238	Dic₁₄₂	—	2	1	no	—
239	Dic₁₄₂	—	2	1	no	—
240	Dic₁₄₂	—	4	2	no	—
241	Dic₁₄₂	C₂×M₁₆	1	2	yes	—
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	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	—	4	1	no	—
254	C₇₁⋊C₈	—	4	1	no	—
255	C₇₁⋊C₈	—	4	1	no	—
256	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₇₁	—	2	1	no	—
258	C₂×D₇₁	—	2	1	no	—
259	C₂×D₇₁	#435	1	2	yes	—
260	C₄×C₇₁	—	2	2	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	C₂²×M₁₆	1	1	yes	characteristic
266	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
267	C₄×C₇₁	#578	1	1	yes	characteristic
268	C₄×C₇₁	#578	1	1	yes	characteristic
269	Dic₇₁	—	2	2	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	#435	1	2	yes	—
276	#17880	—	71	1	no	maximal, Sylow
277	C₂×C₇₁	C₂×#435	1	1	yes	characteristic
278	C₂×C₇₁	#2950	1	1	yes	characteristic
279	C₂×C₇₁	#2957	1	1	yes	characteristic
280	D₇₁	—	2	2	no	—
281	#2983	—	71	1	no	—
282	#2982	—	71	1	no	—
283	C₂×C₄×Q₁₆	—	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	#1584	—	71	1	no	—
289	#1584	—	71	1	no	—
290	#1584	—	71	1	no	—
291	#1584	—	71	1	no	—
292	#1564	—	71	1	no	—
293	#1479	—	71	1	no	—
294	#1479	—	71	1	no	—
295	#1452	—	71	1	no	—
296	C₇₁	#17880	1	1	yes	characteristic, complemented, Sylow
297	C₂²×Q₁₆	—	71	1	no	—
298	C₂×C₄×Q₈	—	71	1	no	—
299	C₂×C₄×Q₈	—	71	1	no	—
300	#446	—	71	1	no	—
301	#446	—	71	1	no	—
302	#446	—	71	1	no	—
303	#446	—	142	1	no	—
304	#446	—	142	1	no	—
305	#446	C₂×D₇₁	1	1	yes	characteristic
306	C₈×Q₈	—	71	1	no	—
307	C₈×Q₈	—	71	1	no	—
308	C₈×Q₈	—	71	1	no	—
309	C₈×Q₈	—	142	1	no	—
310	C₈×Q₈	—	142	1	no	—
311	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
312	C₄×Q₁₆	—	71	1	no	—
313	C₄×Q₁₆	—	71	1	no	—
314	C₄×Q₁₆	—	71	1	no	—
315	C₄×Q₁₆	—	71	1	no	—
316	C₄×Q₁₆	—	71	1	no	—
317	C₄×Q₁₆	—	71	1	no	—
318	C₄×Q₁₆	—	71	1	no	—
319	C₄×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
320	#432	—	142	1	no	—
321	#432	—	142	1	no	—
322	#431	—	71	1	no	—
323	#431	—	71	1	no	—
324	#431	—	71	1	no	—
325	#431	—	71	1	no	—
326	#431	—	142	1	no	—
327	#431	—	142	1	no	—
328	C₂×#107	—	71	1	no	—
329	C₂×#103	—	71	1	no	—
330	C₂×#103	—	71	1	no	—
331	C₂×C₄×C₈	—	71	1	no	—
332	#335	—	71	1	no	—
333	#335	—	71	1	no	—
334	#334	—	71	1	no	—
335	#334	C₂×D₇₁	1	1	yes	characteristic
336	Q₈⋊C₈	—	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	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
344	#322	—	71	1	no	—
345	#322	—	71	1	no	—
346	#322	—	71	1	no	—
347	#322	C₂×D₇₁	1	1	yes	characteristic
348	C₂²×Q₈	—	71	1	no	—
349	C₂²×Q₈	—	71	1	no	—
350	C₂×Q₁₆	—	71	1	no	—
351	C₂×Q₁₆	—	71	1	no	—
352	C₂×Q₁₆	—	71	1	no	—
353	C₂×Q₁₆	—	142	4	no	—
354	C₂×Q₁₆	C₄×D₇₁	1	1	yes	characteristic
355	C₂²×C₈	—	71	1	no	—
356	C₂²×C₈	—	71	1	no	—
357	C₄×Q₈	—	71	1	no	—
358	C₄×Q₈	—	71	1	no	—
359	C₄×Q₈	—	71	1	no	—
360	C₄×Q₈	—	71	1	no	—
361	C₄×Q₈	—	71	1	no	—
362	C₄×Q₈	—	71	1	no	—
363	C₄×Q₈	—	142	1	no	—
364	C₄×Q₈	—	142	1	no	—
365	C₄×Q₈	—	142	1	no	—
366	C₄×Q₈	—	142	1	no	—
367	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
368	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
369	C₂×C₄⋊C₄	—	71	1	no	—
370	C₂×C₄⋊C₄	—	71	1	no	—
371	C₂×C₄⋊C₄	—	142	1	no	—
372	C₂×C₄⋊C₄	—	142	1	no	—
373	C₂×C₄²	—	71	1	no	—
374	C₂×C₄²	—	142	1	no	—
375	C₂×C₄²	—	142	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	—	71	1	no	—
385	C₄⋊C₈	—	71	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	—	142	1	no	—
393	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
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	—	71	1	no	—
401	#103	C₄×D₇₁	1	1	yes	characteristic
402	#103	C₄×D₇₁	1	1	yes	characteristic
403	C₂²⋊C₈	—	71	1	no	—
404	C₂²⋊C₈	—	71	1	no	—
405	C₂²⋊C₈	—	142	1	no	—
406	C₂²⋊C₈	—	142	1	no	—
407	C₂²⋊C₈	—	142	1	no	—
408	#97	—	2	1	no	—
409	#97	—	142	1	no	—
410	#97	—	142	1	no	—
411	#97	—	142	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	71	1	no	—
414	C₄×C₈	—	71	1	no	—
415	C₄×C₈	—	71	1	no	—
416	C₄×C₈	—	71	1	no	—
417	C₄×C₈	—	71	1	no	—
418	C₄×C₈	—	142	1	no	—
419	C₄×C₈	—	142	1	no	—
420	C₄×C₈	—	142	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	4	no	—
427	C₂×Q₈	—	71	1	no	—
428	C₂×Q₈	—	71	1	no	—
429	C₂×Q₈	—	142	1	no	—
430	C₂×Q₈	—	142	1	no	—
431	C₂×Q₈	—	142	2	no	—
432	C₂×Q₈	—	142	2	no	—
433	C₂×Q₈	—	142	2	no	—
434	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
435	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
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	C₂²×C₄	—	142	1	no	—
442	C₂²×C₄	—	142	1	no	—
443	Q₁₆	—	2	2	no	—
444	Q₁₆	—	142	2	no	—
445	Q₁₆	—	142	2	no	—
446	Q₁₆	—	142	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	71	1	no	—
451	C₂×C₈	—	71	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	71	1	no	—
454	C₂×C₈	—	142	2	no	—
455	C₂×C₈	—	142	2	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	—	2	1	no	—
465	C₄⋊C₄	—	71	1	no	—
466	C₄⋊C₄	—	71	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	—	142	1	no	—
475	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
476	C₄⋊C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
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	—	142	1	no	—
485	C₄²	—	142	1	no	—
486	C₄²	—	142	1	no	—
487	C₄²	—	142	1	no	—
488	C₄²	C₂³×D₇₁	1	1	yes	characteristic
489	C₂³	—	71	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	284	2	no	—
494	Q₈	—	71	2	no	—
495	Q₈	—	142	4	no	—
496	Q₈	—	142	1	no	—
497	Q₈	—	142	1	no	—
498	Q₈	—	142	1	no	—
499	Q₈	M₁₆×D₇₁	1	2	yes	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	284	1	no	—
505	C₂×C₄	—	284	2	no	—
506	C₂×C₄	—	568	1	no	—
507	C₂×C₄	—	568	1	no	—
508	C₂×C₄	—	71	1	no	—
509	C₂×C₄	—	71	2	no	—
510	C₂×C₄	—	71	2	no	—
511	C₂×C₄	—	71	1	no	—
512	C₂×C₄	—	71	1	no	—
513	C₂×C₄	—	142	4	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	C₂²×C₄×D₇₁	1	1	yes	characteristic
521	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
522	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	284	1	no	—
531	C₈	—	284	1	no	—
532	C₈	—	284	1	no	—
533	C₈	—	142	1	no	—
534	C₈	—	142	1	no	—
535	C₈	—	142	1	no	—
536	C₈	—	142	1	no	—
537	C₂²	—	71	2	no	—
538	C₂²	—	142	1	no	—
539	C₂²	—	142	1	no	—
540	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	284	1	no	—
547	C₄	—	284	1	no	—
548	C₄	—	284	1	no	—
549	C₄	—	71	2	no	—
550	C₄	—	142	1	no	—
551	C₄	—	142	1	no	—
552	C₄	—	142	2	no	—
553	C₄	C₂×M₁₆×D₇₁	1	1	yes	characteristic
554	C₄	#131×D₇₁	1	1	yes	characteristic
555	C₄	#17986815	1	1	yes	characteristic
556	C₄	#17986815	1	1	yes	characteristic
557	C₂	—	142	2	no	—
558	C₂	#435×D₇₁	1	1	yes	characteristic
559	C₂	#22597205	1	1	yes	characteristic
560	C₂	#22597252	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	#17880
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. #22587213	C₂	semidirect
5. #22587212	C₂	semidirect
6. #22587210	C₂	semidirect
7. #22587193	C₂	semidirect
8. #22587190	C₂	semidirect
9. #22587188	C₂	semidirect
10. #22587187	C₂	semidirect
15. C₇₁×#1587	C₂	semidirect
287. #1587	D₇₁	semidirect
296. C₇₁	#17880	semidirect

Maximal subgroups

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

subgroup	index
#22597422	2
#22597419	2
C₄×Q₁₆×D₇₁	2
#22587213	2
#22587212	2
#22587210	2
#22587193	2
#22587190	2
#22587188	2
#22587187	2
#22587085	2
#22586733	2
#22586631	2
C₇₁×#1587	2
#17880	71