Subgroups — #31967342

Order 18176.

618 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22598377	C₂	1	1	yes	maximal, characteristic
2	#22597269	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₇₁	C₂	1	1	yes	maximal, characteristic
4	#22587193	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587191	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587189	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587187	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×Dic₂₈₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11765855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11765855	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587113	C₂	1	1	yes	maximal, characteristic
12	#22586767	C₂	1	1	yes	maximal, characteristic
13	#22586741	C₂	1	1	yes	maximal, characteristic
14	#22586622	C₂	1	1	yes	maximal, characteristic
15	C₈×Q₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#17986553	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₇₁	C₂²	1	1	yes	characteristic
18	#17986336	C₄	1	1	yes	characteristic
19	#17986333	C₄	1	1	yes	characteristic
20	#17986293	C₄	1	1	yes	characteristic
21	#17986292	C₄	1	1	yes	characteristic
22	#17986208	C₄	1	1	yes	characteristic
23	#17986207	C₄	1	1	yes	characteristic
24	#17986156	C₄	1	1	yes	characteristic
25	#17986153	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	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₄₂	—	2	1	no	—
31	C₈×Dic₁₄₂	—	2	1	no	—
32	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
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	#17986050	C₂²	1	1	yes	characteristic
40	#17986050	C₂²	1	1	yes	characteristic
41	#17986024	—	2	1	no	—
42	#17986021	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₇₁	—	2	1	no	—
44	C₄⋊C₈×D₇₁	C₂²	1	1	yes	characteristic
45	#17985953	—	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	#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	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×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	#335×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	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×#11765855	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765848	—	2	1	no	—
72	C₂×C₈×D₇₁	—	2	1	no	—
73	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
75	#14556127	C₂×C₄	1	1	yes	characteristic
76	#14556126	C₂×C₄	1	1	yes	characteristic
77	#14556118	—	2	1	no	—
78	#14556108	C₂×C₄	1	1	yes	characteristic
79	#14556106	—	2	1	no	—
80	#14556104	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₄₂	—	2	1	no	—
83	C₄×Dic₁₄₂	—	2	1	no	—
84	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₄₂	C₂³	1	1	yes	characteristic
86	#14556093	—	2	1	no	—
87	#14556093	C₂×C₄	1	1	yes	characteristic
88	#14556085	—	2	1	no	—
89	C₄⋊C₄×D₇₁	—	2	1	no	—
90	C₄⋊C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₇₁	—	2	1	no	—
92	C₄²×D₇₁	C₂³	1	1	yes	characteristic
93	#14556062	C₂×C₄	1	1	yes	characteristic
94	#14556061	C₂×C₄	1	1	yes	characteristic
95	#14556061	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
97	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
98	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
105	Dic₇₁⋊C₈	—	2	1	no	—
106	Dic₇₁⋊C₈	—	2	1	no	—
107	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
108	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
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	(C₂×D₇₁)⋊C₈	—	2	1	no	—
116	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	#14556039	—	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	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	C₄×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	—	2	1	no	—
146	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₄₂	C₂²×C₄	1	1	yes	characteristic
148	Q₈×D₇₁	—	2	2	no	—
149	Q₈×D₇₁	—	2	2	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	—	2	2	no	—
157	#11765855	—	2	2	no	—
158	#11765848	—	4	2	no	—
159	C₂×C₇₁⋊C₈	—	2	1	no	—
160	C₂×C₇₁⋊C₈	—	2	1	no	—
161	C₂×C₇₁⋊C₈	—	2	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	2	no	—
167	C₈×D₇₁	—	4	2	no	—
168	C₈×D₇₁	Q₁₆	1	4	yes	complemented
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	Dic₇₁⋊C₄	—	2	1	no	—
179	Dic₇₁⋊C₄	—	2	1	no	—
180	Dic₇₁⋊C₄	—	2	1	no	—
181	(C₂×D₇₁)⋊C₄	—	2	1	no	—
182	(C₂×D₇₁)⋊C₄	—	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	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×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	Q₁₆×C₇₁	—	2	2	no	—
193	C₂×C₈×C₇₁	—	2	1	no	—
194	C₂×C₈×C₇₁	—	2	1	no	—
195	C₂×C₈×C₇₁	—	2	1	no	—
196	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₇₁	—	2	1	no	—
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	C₄²×C₇₁	—	2	1	no	—
205	C₄²×C₇₁	—	2	1	no	—
206	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
207	C₂²×D₇₁	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₇₁	—	2	1	no	—
209	Q₈×C₇₁	—	2	1	no	—
210	Q₈×C₇₁	—	2	1	no	—
211	Q₈×C₇₁	#131	1	2	yes	—
212	C₂×C₄×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	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
219	C₂×Dic₇₁	—	2	1	no	—
220	C₂×Dic₇₁	—	2	1	no	—
221	C₂×Dic₇₁	—	2	1	no	—
222	C₂×Dic₇₁	—	2	1	no	—
223	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
224	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₇₁	C₄×D₄	1	1	yes	characteristic
226	C₄×D₇₁	—	2	4	no	—
227	C₄×D₇₁	—	2	1	no	—
228	C₄×D₇₁	—	2	1	no	—
229	C₄×D₇₁	—	4	1	no	—
230	C₄×D₇₁	—	4	2	no	—
231	C₄×D₇₁	C₂×Q₁₆	1	2	yes	—
232	C₄×D₇₁	#135	1	2	yes	—
233	Dic₁₄₂	—	2	4	no	—
234	Dic₁₄₂	—	2	1	no	—
235	Dic₁₄₂	—	2	1	no	—
236	Dic₁₄₂	—	2	1	no	—
237	Dic₁₄₂	—	4	2	no	—
238	Dic₁₄₂	#131	1	2	yes	—
239	C₈×C₇₁	—	2	1	no	—
240	C₈×C₇₁	—	2	1	no	—
241	C₈×C₇₁	—	2	1	no	—
242	C₈×C₇₁	—	4	1	no	—
243	C₈×C₇₁	—	4	1	no	—
244	C₈×C₇₁	—	4	1	no	—
245	C₈×C₇₁	C₂×Q₁₆	1	2	yes	—
246	C₇₁⋊C₈	—	2	1	no	—
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	C₂×Q₁₆	1	2	yes	—
253	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×D₇₁	—	2	1	no	—
255	C₂×D₇₁	—	2	1	no	—
256	C₂×D₇₁	C₄×Q₁₆	1	2	yes	—
257	C₄×C₇₁	—	2	2	no	—
258	C₄×C₇₁	—	2	1	no	—
259	C₄×C₇₁	—	4	1	no	—
260	C₄×C₇₁	—	4	1	no	—
261	C₄×C₇₁	—	4	1	no	—
262	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
263	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
264	C₄×C₇₁	C₂²×Q₁₆	1	1	yes	characteristic
265	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
266	Dic₇₁	—	2	1	no	—
267	Dic₇₁	—	2	2	no	—
268	Dic₇₁	—	2	1	no	—
269	Dic₇₁	—	4	1	no	—
270	Dic₇₁	—	4	1	no	—
271	Dic₇₁	—	4	1	no	—
272	Dic₇₁	C₄×Q₁₆	1	2	yes	—
273	#17903	—	71	1	no	maximal, Sylow
274	C₂×C₇₁	#2929	1	1	yes	characteristic
275	C₂×C₇₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
276	C₂×C₇₁	#2955	1	1	yes	characteristic
277	D₇₁	—	2	2	no	—
278	#3104	—	71	1	no	—
279	#2960	—	71	1	no	—
280	C₂×C₈×Q₈	—	71	1	no	—
281	#1584	—	71	1	no	—
282	#1584	—	71	1	no	—
283	#1584	—	71	1	no	—
284	#1584	—	71	1	no	—
285	C₈×Q₁₆	—	71	1	no	—
286	C₈×Q₁₆	—	71	1	no	—
287	C₈×Q₁₆	—	71	1	no	—
288	C₈×Q₁₆	D₇₁	1	1	yes	characteristic, complemented
289	#1571	—	71	1	no	—
290	#1487	—	71	1	no	—
291	#1481	—	71	1	no	—
292	#1450	—	71	1	no	—
293	C₇₁	#17903	1	1	yes	characteristic, complemented, Sylow
294	#533	—	71	1	no	—
295	C₂×C₄×Q₈	—	71	1	no	—
296	#484	—	71	1	no	—
297	#484	—	71	1	no	—
298	#477	—	71	1	no	—
299	#477	—	71	1	no	—
300	#462	—	71	1	no	—
301	#462	—	71	1	no	—
302	#451	—	71	1	no	—
303	#451	—	71	1	no	—
304	#446	—	71	1	no	—
305	#446	—	71	1	no	—
306	#446	—	142	1	no	—
307	C₈×Q₈	—	71	1	no	—
308	C₈×Q₈	—	71	1	no	—
309	C₈×Q₈	—	71	1	no	—
310	C₈×Q₈	—	71	1	no	—
311	C₈×Q₈	—	142	1	no	—
312	C₈×Q₈	—	142	1	no	—
313	C₈×Q₈	—	142	1	no	—
314	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
315	C₈×Q₈	C₂×D₇₁	1	1	yes	characteristic
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	#431	—	71	1	no	—
321	#431	—	71	1	no	—
322	#424	—	142	1	no	—
323	#423	—	71	1	no	—
324	C₂×C₄⋊C₈	—	71	1	no	—
325	C₂×C₄⋊C₈	—	142	1	no	—
326	#405	—	142	1	no	—
327	C₂×C₄×C₈	—	71	1	no	—
328	C₂×C₄×C₈	—	142	1	no	—
329	#335	—	71	1	no	—
330	#335	—	71	1	no	—
331	#335	—	71	1	no	—
332	#335	C₂×D₇₁	1	1	yes	characteristic
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	—	71	1	no	—
339	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
340	Q₈⋊C₈	C₂×D₇₁	1	1	yes	characteristic
341	#322	—	71	1	no	—
342	#322	—	71	1	no	—
343	C₈²	—	71	1	no	—
344	C₈²	C₂×D₇₁	1	1	yes	characteristic
345	C₂²×Q₈	—	71	1	no	—
346	C₂×Q₁₆	—	71	1	no	—
347	C₂×Q₁₆	—	71	1	no	—
348	C₂×Q₁₆	—	71	1	no	—
349	C₂×Q₁₆	C₄×D₇₁	1	1	yes	characteristic
350	C₂×M₁₆	—	142	1	no	—
351	C₂²×C₈	—	71	1	no	—
352	C₂²×C₈	—	71	1	no	—
353	C₂²×C₈	—	142	1	no	—
354	C₄⋊Q₈	—	71	1	no	—
355	C₄⋊Q₈	—	71	1	no	—
356	#125	—	142	1	no	—
357	C₂²⋊Q₈	—	71	1	no	—
358	C₂²⋊Q₈	—	71	1	no	—
359	C₂²⋊Q₈	—	142	1	no	—
360	C₄×Q₈	—	71	1	no	—
361	C₄×Q₈	—	71	1	no	—
362	C₄×Q₈	—	71	1	no	—
363	C₄×Q₈	—	71	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	#117	—	142	1	no	—
370	C₂×C₄⋊C₄	—	71	1	no	—
371	C₂×C₄⋊C₄	—	142	1	no	—
372	C₂×C₄²	—	71	1	no	—
373	C₂×C₄²	—	142	1	no	—
374	#107	—	71	1	no	—
375	#107	—	71	1	no	—
376	#107	—	71	1	no	—
377	#107	C₄×D₇₁	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	71	1	no	—
381	C₄⋊C₈	—	71	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	—	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	#97	—	142	1	no	—
407	#97	—	142	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	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	—	71	1	no	—
415	C₄×C₈	—	142	1	no	—
416	C₄×C₈	—	142	1	no	—
417	C₄×C₈	—	142	1	no	—
418	C₄×C₈	—	142	1	no	—
419	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
422	C₂×Q₈	—	71	1	no	—
423	C₂×Q₈	—	71	1	no	—
424	C₂×Q₈	—	142	1	no	—
425	C₂×Q₈	—	142	1	no	—
426	C₂×Q₈	—	142	2	no	—
427	C₂×Q₈	—	142	2	no	—
428	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
429	C₂×Q₈	C₂×C₄×D₇₁	1	1	yes	characteristic
430	C₂²×C₄	—	71	1	no	—
431	C₂²×C₄	—	71	1	no	—
432	C₂²×C₄	—	71	1	no	—
433	C₂²×C₄	—	142	1	no	—
434	C₂²×C₄	—	142	1	no	—
435	Q₁₆	—	2	2	no	—
436	Q₁₆	—	142	2	no	—
437	Q₁₆	—	142	2	no	—
438	Q₁₆	—	142	2	no	—
439	M₁₆	—	284	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	284	2	no	—
444	C₂×C₈	—	71	1	no	—
445	C₂×C₈	—	71	4	no	—
446	C₂×C₈	—	71	1	no	—
447	C₂×C₈	—	71	1	no	—
448	C₂×C₈	—	71	1	no	—
449	C₂×C₈	—	142	2	no	—
450	C₂×C₈	—	142	1	no	—
451	C₂×C₈	—	142	1	no	—
452	C₂×C₈	—	142	1	no	—
453	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
455	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
456	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	71	1	no	—
460	C₄⋊C₄	—	71	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	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	71	1	no	—
478	C₄²	—	71	1	no	—
479	C₄²	—	71	1	no	—
480	C₄²	—	142	1	no	—
481	C₄²	—	142	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	—	284	2	no	—
490	Q₈	—	71	2	no	—
491	Q₈	—	142	4	no	—
492	Q₈	—	142	1	no	—
493	Q₈	—	142	1	no	—
494	Q₈	—	142	1	no	—
495	Q₈	#14556134	1	2	yes	—
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	—	284	1	no	—
501	C₂×C₄	—	284	2	no	—
502	C₂×C₄	—	71	1	no	—
503	C₂×C₄	—	71	2	no	—
504	C₂×C₄	—	71	2	no	—
505	C₂×C₄	—	71	1	no	—
506	C₂×C₄	—	71	1	no	—
507	C₂×C₄	—	142	4	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	—	142	1	no	—
513	C₂×C₄	—	142	1	no	—
514	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
516	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
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	—	4	1	no	—
523	C₈	—	284	1	no	—
524	C₈	—	284	1	no	—
525	C₈	—	284	1	no	—
526	C₈	—	71	2	no	—
527	C₈	—	142	1	no	—
528	C₈	—	142	1	no	—
529	C₈	—	142	1	no	—
530	C₈	Q₁₆×D₇₁	1	2	yes	—
531	C₂²	—	71	2	no	—
532	C₂²	—	142	1	no	—
533	C₂²	—	142	1	no	—
534	C₂²	C₄×D₄×D₇₁	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	284	1	no	—
541	C₄	—	284	1	no	—
542	C₄	—	284	1	no	—
543	C₄	—	71	2	no	—
544	C₄	—	142	1	no	—
545	C₄	—	142	1	no	—
546	C₄	—	142	2	no	—
547	C₄	#131×D₇₁	1	1	yes	characteristic
548	C₄	C₂×#14556134	1	1	yes	characteristic
549	C₄	C₂×Q₁₆×D₇₁	1	1	yes	characteristic
550	C₄	#135×D₇₁	1	1	yes	characteristic
551	C₂	—	142	2	no	—
552	C₂	#22597029	1	1	yes	characteristic
553	C₂	C₄×Q₁₆×D₇₁	1	1	yes	characteristic
554	C₂	#22597238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₈×Q₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂²×D₇₁	C₄×D₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₈×Q₁₆	D₇₁
hypocenter	C₇₁	#17903
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #22587193	C₂	semidirect
5. #22587191	C₂	semidirect
6. #22587189	C₂	semidirect
7. #22587187	C₂	semidirect
8. C₈×Dic₂₈₄	C₂	semidirect
9. C₈×#11765855	C₂	semidirect
10. C₈×#11765855	C₂	semidirect
15. C₈×Q₁₆×C₇₁	C₂	semidirect
168. C₈×D₇₁	Q₁₆	semidirect
288. C₈×Q₁₆	D₇₁	semidirect
293. C₇₁	#17903	semidirect

Maximal subgroups

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

subgroup	index
#22598377	2
#22597269	2
C₈×Q₈×D₇₁	2
#22587193	2
#22587191	2
#22587189	2
#22587187	2
C₈×Dic₂₈₄	2
C₈×#11765855	2
#22587113	2
#22586767	2
#22586741	2
#22586622	2
C₈×Q₁₆×C₇₁	2
#17903	71