Subgroups — #31967479

Order 18176.

624 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597316	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22587191	C₂	1	2	yes	maximal, complemented
4	#22587184	C₂	1	2	yes	maximal, complemented
5	#22587159	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊(C₇₁⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#22587125	C₂	1	1	yes	maximal, characteristic, complemented
8	#22586787	C₂	1	1	yes	maximal, characteristic, complemented
9	#22586753	C₂	1	1	yes	maximal, characteristic
10	#22586630	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3108	C₂	1	1	yes	maximal, characteristic
12	#17986130	C₂²	1	1	yes	characteristic
13	Q₈×C₇₁⋊C₈	—	2	1	no	—
14	Q₈×C₇₁⋊C₈	—	2	1	no	—
15	Q₈×C₇₁⋊C₈	C₂²	1	2	yes	—
16	Q₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
17	Q₈×C₇₁⋊C₈	C₂²	1	2	yes	—
18	#17986077	C₂²	1	1	yes	characteristic
19	#17986071	—	2	1	no	—
20	D₄×C₇₁⋊C₈	—	2	1	no	—
21	D₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
22	#17986060	—	2	1	no	—
23	#17986056	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
25	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
26	#17985955	—	2	1	no	—
27	C₄×#11765849	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₁⋊C₈	—	2	1	no	—
29	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
30	#17985752	C₂²	1	2	yes	—
31	#17985750	C₂²	1	2	yes	—
32	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
33	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
34	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
36	#17985721	C₂²	1	2	yes	—
37	#17985720	C₂²	1	2	yes	—
38	#529×C₇₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
40	#483×C₇₁	C₄	1	1	yes	characteristic
41	#480×C₇₁	C₄	1	1	yes	characteristic
42	#479×C₇₁	C₄	1	2	yes	—
43	#464×C₇₁	C₄	1	2	yes	—
44	#451×C₇₁	C₄	1	1	yes	characteristic
45	#448×C₇₁	C₄	1	1	yes	characteristic
46	C₄×Q₁₆×C₇₁	C₂²	1	2	yes	—
47	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
48	#431×C₇₁	C₂²	1	1	yes	characteristic
49	C₂×#11765849	—	2	1	no	—
50	C₂×#11765849	—	2	1	no	—
51	C₂²×C₇₁⋊C₈	—	2	1	no	—
52	C₂²×C₇₁⋊C₈	—	2	1	no	—
53	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
55	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
56	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
59	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
61	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
63	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
66	#14556039	—	2	1	no	—
67	#14556039	—	2	1	no	—
68	#14556039	—	2	1	no	—
69	C₄×C₇₁⋊C₈	—	2	1	no	—
70	C₄×C₇₁⋊C₈	—	2	2	no	—
71	C₄×C₇₁⋊C₈	—	2	2	no	—
72	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
73	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
74	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
75	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₇₁	C₂×C₄	1	2	yes	—
79	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	—
80	#126×C₇₁	—	2	1	no	—
81	#125×C₇₁	C₂×C₄	1	1	yes	characteristic
82	#124×C₇₁	C₂×C₄	1	1	yes	characteristic
83	#123×C₇₁	—	2	1	no	—
84	C₂²⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
85	#121×C₇₁	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₇₁	—	2	1	no	—
87	C₄×Q₈×C₇₁	—	2	1	no	—
88	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
90	C₄×Q₈×C₇₁	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₇₁	—	2	1	no	—
92	C₄×D₄×C₇₁	C₂³	1	1	yes	characteristic
93	#117×C₇₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₁	—	2	1	no	—
97	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
98	#107×C₇₁	C₂×C₄	1	2	yes	—
99	#106×C₇₁	C₂×C₄	1	2	yes	—
100	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
101	#103×C₇₁	C₂×C₄	1	2	yes	—
102	#103×C₇₁	C₂×C₄	1	2	yes	—
103	#103×C₇₁	C₂×C₄	1	2	yes	—
104	#102×C₇₁	C₂×C₄	1	2	yes	—
105	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₇₁	C₂³	1	2	yes	—
108	#11765849	—	4	2	no	—
109	#11765849	—	4	2	no	—
110	C₂×C₇₁⋊C₈	—	2	2	no	—
111	C₂×C₇₁⋊C₈	—	2	2	no	—
112	C₂×C₇₁⋊C₈	—	2	1	no	—
113	C₂×C₇₁⋊C₈	—	2	1	no	—
114	C₂×C₇₁⋊C₈	—	2	2	no	—
115	C₂×C₇₁⋊C₈	—	4	1	no	—
116	C₂×C₇₁⋊C₈	—	4	2	no	—
117	C₂×C₇₁⋊C₈	—	4	2	no	—
118	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₇₁	—	2	4	no	—
123	C₂×Q₈×C₇₁	—	2	1	no	—
124	C₂×Q₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
126	C₂×D₄×C₇₁	—	2	1	no	—
127	C₂×D₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₁	—	2	1	no	—
129	C₂²×C₄×C₇₁	—	2	1	no	—
130	C₂²×C₄×C₇₁	—	2	1	no	—
131	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
134	Q₁₆×C₇₁	—	2	4	no	—
135	SD₁₆×C₇₁	—	2	4	no	—
136	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₇₁	—	2	2	no	—
139	C₄⋊C₄×C₇₁	—	2	1	no	—
140	C₄⋊C₄×C₇₁	—	2	1	no	—
141	C₄⋊C₄×C₇₁	—	2	1	no	—
142	C₄⋊C₄×C₇₁	—	2	1	no	—
143	C₄⋊C₄×C₇₁	—	2	2	no	—
144	C₄⋊C₄×C₇₁	—	2	1	no	—
145	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
146	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
147	C₄⋊C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₇₁	—	2	1	no	—
149	C₂²⋊C₄×C₇₁	—	2	1	no	—
150	C₂²⋊C₄×C₇₁	—	2	1	no	—
151	C₂²⋊C₄×C₇₁	—	2	1	no	—
152	C₂²⋊C₄×C₇₁	—	2	1	no	—
153	C₄²×C₇₁	—	2	2	no	—
154	C₄²×C₇₁	—	2	2	no	—
155	C₄²×C₇₁	—	2	1	no	—
156	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₁	#41	1	1	yes	characteristic
159	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇₁	—	2	1	no	—
161	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
162	Q₈×C₇₁	—	2	4	no	—
163	Q₈×C₇₁	—	2	2	no	—
164	Q₈×C₇₁	—	2	2	no	—
165	Q₈×C₇₁	#131	1	4	yes	—
166	D₄×C₇₁	—	2	2	no	—
167	D₄×C₇₁	—	4	2	no	—
168	C₂×C₄×C₇₁	—	2	4	no	—
169	C₂×C₄×C₇₁	—	2	2	no	—
170	C₂×C₄×C₇₁	—	2	2	no	—
171	C₂×C₄×C₇₁	—	2	2	no	—
172	C₂×C₄×C₇₁	—	2	1	no	—
173	C₂×C₄×C₇₁	—	2	1	no	—
174	C₂×C₄×C₇₁	—	2	2	no	—
175	C₂×C₄×C₇₁	—	2	1	no	—
176	C₂×C₄×C₇₁	—	2	1	no	—
177	C₂×C₄×C₇₁	—	2	1	no	—
178	C₂×C₄×C₇₁	—	4	2	no	—
179	C₂×C₄×C₇₁	—	4	1	no	—
180	C₂×C₄×C₇₁	—	4	1	no	—
181	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₇₁	—	2	2	no	—
188	C₈×C₇₁	—	2	2	no	—
189	C₇₁⋊C₈	—	2	1	no	—
190	C₇₁⋊C₈	—	2	1	no	—
191	C₇₁⋊C₈	—	2	1	no	—
192	C₇₁⋊C₈	—	4	2	no	—
193	C₇₁⋊C₈	—	4	1	no	—
194	C₇₁⋊C₈	—	4	2	no	—
195	C₇₁⋊C₈	—	4	1	no	—
196	C₇₁⋊C₈	#137	1	2	yes	—
197	C₂²×C₇₁	—	2	1	no	—
198	C₂²×C₇₁	—	2	1	no	—
199	C₂²×C₇₁	—	4	1	no	—
200	C₂²×C₇₁	—	4	1	no	—
201	C₂²×C₇₁	—	4	1	no	—
202	C₂²×C₇₁	#444	1	2	yes	—
203	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₇₁	—	2	4	no	—
205	C₄×C₇₁	—	2	1	no	—
206	C₄×C₇₁	—	2	1	no	—
207	C₄×C₇₁	—	2	1	no	—
208	C₄×C₇₁	—	2	1	no	—
209	C₄×C₇₁	—	4	1	no	—
210	C₄×C₇₁	—	4	1	no	—
211	C₄×C₇₁	—	4	2	no	—
212	C₄×C₇₁	—	4	1	no	—
213	C₄×C₇₁	C₂×#131	1	2	yes	—
214	C₄×C₇₁	C₂×#137	1	1	yes	characteristic
215	C₄×C₇₁	#575	1	1	yes	characteristic
216	#17915	—	71	1	no	maximal, Sylow
217	C₂×C₇₁	—	2	2	no	—
218	C₂×C₇₁	—	8	1	no	—
219	C₂×C₇₁	#2929	1	1	yes	characteristic
220	C₂×C₇₁	C₄×#137	1	1	yes	characteristic
221	C₂×C₇₁	C₂×#444	1	1	yes	characteristic
222	#3108	D₇₁	1	1	yes	characteristic
223	#2966	—	71	1	no	—
224	C₂×C₈×Q₈	—	71	1	no	—
225	#1584	—	71	2	no	—
226	#1583	—	71	2	no	—
227	#1579	—	71	2	no	—
228	SD₁₆⋊C₈	—	71	2	no	—
229	#1573	—	71	1	no	—
230	#1491	—	71	1	no	—
231	#1483	—	71	1	no	—
232	#1451	—	71	1	no	—
233	C₇₁	#17915	1	1	yes	characteristic, complemented, Sylow
234	#529	C₂×D₇₁	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
236	#483	Dic₇₁	1	1	yes	characteristic
237	#480	Dic₇₁	1	1	yes	characteristic
238	#479	Dic₇₁	1	2	yes	—
239	#464	Dic₇₁	1	2	yes	—
240	#451	Dic₇₁	1	1	yes	characteristic
241	#448	Dic₇₁	1	1	yes	characteristic
242	#446	—	71	1	no	—
243	C₈×Q₈	—	71	2	no	—
244	C₈×Q₈	—	71	1	no	—
245	C₈×Q₈	—	71	2	no	—
246	C₈×Q₈	—	142	1	no	—
247	C₈×Q₈	—	142	1	no	—
248	C₄×Q₁₆	C₂×D₇₁	1	2	yes	—
249	C₄×SD₁₆	C₂×D₇₁	1	2	yes	—
250	#436	—	71	1	no	—
251	#435	—	142	1	no	—
252	C₈×D₄	—	71	1	no	—
253	C₈×D₄	—	142	1	no	—
254	#433	—	142	1	no	—
255	#432	—	71	1	no	—
256	#431	C₂×D₇₁	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	71	1	no	—
258	C₂×C₄⋊C₈	—	142	1	no	—
259	#405	—	142	1	no	—
260	C₄×M₁₆	—	71	1	no	—
261	C₂×C₄×C₈	—	71	1	no	—
262	C₂×C₄×C₈	—	142	1	no	—
263	#335	—	71	2	no	—
264	#334	—	71	2	no	—
265	Q₈⋊C₈	—	71	2	no	—
266	Q₈⋊C₈	—	71	2	no	—
267	Q₈⋊C₈	—	71	2	no	—
268	D₄⋊C₈	—	71	2	no	—
269	#322	—	71	2	no	—
270	#322	—	71	2	no	—
271	C₂²×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
272	C₂×Q₁₆	C₂×Dic₇₁	1	2	yes	—
273	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	—
274	C₂×M₁₆	—	142	1	no	—
275	C₂×M₁₆	—	142	1	no	—
276	C₂²×C₈	—	71	1	no	—
277	C₂²×C₈	—	71	1	no	—
278	C₂²×C₈	—	142	1	no	—
279	C₂²×C₈	—	142	1	no	—
280	#126	—	2	1	no	—
281	#125	C₂×Dic₇₁	1	1	yes	characteristic
282	#124	C₂×Dic₇₁	1	1	yes	characteristic
283	#123	—	2	1	no	—
284	C₂²⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
285	#121	C₂×Dic₇₁	1	1	yes	characteristic
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	C₂×Dic₇₁	1	2	yes	—
289	C₄×Q₈	C₂²×D₇₁	1	2	yes	—
290	C₄×Q₈	C₂²×D₇₁	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂²×D₇₁	1	1	yes	characteristic
293	#117	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂×Dic₇₁	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
298	#107	C₂×Dic₇₁	1	2	yes	—
299	#106	C₂×Dic₇₁	1	2	yes	—
300	C₄⋊C₈	—	71	2	no	—
301	C₄⋊C₈	—	71	1	no	—
302	C₄⋊C₈	—	71	1	no	—
303	C₄⋊C₈	—	142	2	no	—
304	C₄⋊C₈	—	142	2	no	—
305	C₄⋊C₈	—	142	1	no	—
306	C₄⋊C₈	—	142	1	no	—
307	C₄⋊C₈	—	142	1	no	—
308	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
309	#103	C₂×Dic₇₁	1	2	yes	—
310	#103	C₂×Dic₇₁	1	2	yes	—
311	#103	C₂×Dic₇₁	1	2	yes	—
312	#102	C₂×Dic₇₁	1	2	yes	—
313	C₂²⋊C₈	—	142	1	no	—
314	C₂²⋊C₈	—	142	1	no	—
315	C₂²⋊C₈	—	142	1	no	—
316	C₂²⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
317	C₂²⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
318	#97	—	142	1	no	—
319	#97	—	142	1	no	—
320	#97	—	142	1	no	—
321	C₄×C₈	—	71	1	no	—
322	C₄×C₈	—	71	1	no	—
323	C₄×C₈	—	71	1	no	—
324	C₄×C₈	—	71	1	no	—
325	C₄×C₈	—	71	2	no	—
326	C₄×C₈	—	142	2	no	—
327	C₄×C₈	—	142	2	no	—
328	C₄×C₈	—	142	1	no	—
329	C₄×C₈	C₂²×D₇₁	1	2	yes	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	C₂²×Dic₇₁	1	1	yes	characteristic
333	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂²×Dic₇₁	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
341	C₂²×C₄	#11765864	1	1	yes	characteristic
342	Q₁₆	—	2	4	no	—
343	SD₁₆	—	2	4	no	—
344	M₁₆	—	284	2	no	—
345	M₁₆	—	284	2	no	—
346	C₂×C₈	—	284	2	no	—
347	C₂×C₈	—	284	2	no	—
348	C₂×C₈	—	284	1	no	—
349	C₂×C₈	—	71	1	no	—
350	C₂×C₈	—	71	1	no	—
351	C₂×C₈	—	71	1	no	—
352	C₂×C₈	—	71	1	no	—
353	C₂×C₈	—	142	2	no	—
354	C₂×C₈	—	142	1	no	—
355	C₂×C₈	—	142	1	no	—
356	C₂×C₈	—	142	2	no	—
357	C₂×C₈	—	142	2	no	—
358	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
359	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
368	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×Dic₇₁	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	2	no	—
378	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
379	C₄²	D₄×D₇₁	1	1	yes	characteristic
380	C₄²	#11765864	1	1	yes	characteristic
381	C₄²	C₂³×D₇₁	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	D₄×Dic₇₁	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	Q₈	#14556135	1	4	yes	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
404	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
405	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
406	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
408	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	284	2	no	—
412	C₈	—	284	1	no	—
413	C₈	—	284	2	no	—
414	C₈	—	284	1	no	—
415	C₈	—	71	2	no	—
416	C₈	—	142	1	no	—
417	C₈	—	142	1	no	—
418	C₈	—	142	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	#17986121	1	2	yes	—
425	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	C₂×#14556135	1	2	yes	—
436	C₄	#137×D₇₁	1	1	yes	characteristic
437	C₄	#17986798	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	#22597035	1	1	yes	characteristic
441	C₂	#137×Dic₇₁	1	1	yes	characteristic
442	C₂	C₂×#17986121	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×#3108	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#121×C₇₁	C₂×C₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#3108	D₇₁
hypocenter	C₇₁	#17915
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₇₁⋊C₈	C₂	semidirect
3. #22587191	C₂	semidirect
4. #22587184	C₂	semidirect
5. #22587159	C₂	semidirect
6. SD₁₆⋊(C₇₁⋊C₈)	C₂	semidirect
7. #22587125	C₂	semidirect
8. #22586787	C₂	semidirect
10. #22586630	C₂	semidirect
233. C₇₁	#17915	semidirect

Maximal subgroups

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

subgroup	index
#22597316	2
C₂×Q₈×C₇₁⋊C₈	2
#22587191	2
#22587184	2
#22587159	2
SD₁₆⋊(C₇₁⋊C₈)	2
#22587125	2
#22586787	2
#22586753	2
#22586630	2
C₇₁×#3108	2
#17915	71