Subgroups — #31963093

Order 18176.

772 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22596973	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986052	C₂	1	1	yes	maximal, characteristic
3	#22586635	C₂	1	4	yes	maximal, complemented
4	#22586633	C₂	1	2	yes	maximal, complemented
5	#22586632	C₂	1	2	yes	maximal, complemented
6	#22586624	C₂	1	2	yes	maximal, complemented
7	#22586623	C₂	1	2	yes	maximal, complemented
8	C₂×#431×C₇₁	C₂	1	1	yes	maximal, characteristic
9	#17986056	C₄	1	2	yes	—
10	#17986056	C₄	1	2	yes	—
11	#17986052	C₄	1	2	yes	—
12	#17986052	C₄	1	2	yes	—
13	#17986052	C₂²	1	2	yes	—
14	#17986052	C₂²	1	1	yes	characteristic
15	#17986052	C₂²	1	2	yes	—
16	#17986052	C₂²	1	2	yes	—
17	#17986052	C₂²	1	1	yes	characteristic
18	#17986023	C₄	1	2	yes	—
19	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
20	#17985963	C₄	1	2	yes	—
21	C₂×C₂²⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
22	C₄×#11765849	C₂²	1	2	yes	—
23	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
24	#17985721	C₂²	1	4	yes	complemented
25	#17985721	C₂²	1	4	yes	complemented
26	#17985720	C₂²	1	4	yes	complemented
27	C₈×C₇₁⋊C₈	C₂²	1	4	yes	complemented
28	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
29	#431×C₇₁	C₄	1	2	yes	—
30	#431×C₇₁	C₄	1	2	yes	—
31	#431×C₇₁	C₂²	1	1	yes	characteristic
32	#431×C₇₁	C₂²	1	1	yes	characteristic
33	#431×C₇₁	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₇₁	C₄	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₁	C₄	1	2	yes	—
36	C₂×C₄×C₈×C₇₁	C₂²	1	2	yes	—
37	C₂×#11765849	C₂×C₄	1	4	yes	—
38	C₂²×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
39	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
40	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
41	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
42	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
43	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
44	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
45	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
46	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
47	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
48	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
49	#14556039	C₂×C₄	1	4	yes	—
50	C₄×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
51	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
52	C₄×C₇₁⋊C₈	C₂³	1	2	yes	—
53	C₄×C₇₁⋊C₈	C₂³	1	4	yes	—
54	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₁	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
71	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
72	C₄⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
73	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
74	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₇₁	C₂×C₄	1	4	yes	—
76	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	—
77	C₄×C₈×C₇₁	C₂³	1	2	yes	—
78	C₄×C₈×C₇₁	C₂³	1	2	yes	—
79	#11765849	—	4	4	no	—
80	C₂×C₇₁⋊C₈	—	2	8	no	—
81	C₂×C₇₁⋊C₈	C₂²×C₄	1	4	yes	—
82	C₂×C₇₁⋊C₈	C₂²×C₄	1	4	yes	—
83	C₂×C₇₁⋊C₈	C₂²×C₄	1	8	yes	—
84	C₂⁴×C₇₁	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₇₁	—	2	4	no	—
86	C₂²×C₄×C₇₁	—	2	4	no	—
87	C₂²×C₄×C₇₁	—	4	2	no	—
88	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₇₁	—	2	8	no	—
107	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
109	C₄²×C₇₁	C₄²	1	1	yes	characteristic
110	C₄²×C₇₁	C₄²	1	1	yes	characteristic
111	C₄²×C₇₁	C₄²	1	1	yes	characteristic
112	C₄²×C₇₁	C₄²	1	1	yes	characteristic
113	C₄²×C₇₁	C₄²	1	1	yes	characteristic
114	C₄²×C₇₁	C₄²	1	1	yes	characteristic
115	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
125	C₂³×C₇₁	—	2	2	no	—
126	C₂³×C₇₁	—	2	2	no	—
127	C₂³×C₇₁	—	4	1	no	—
128	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
129	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
130	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
131	C₂×C₄×C₇₁	—	2	2	no	—
132	C₂×C₄×C₇₁	—	2	2	no	—
133	C₂×C₄×C₇₁	—	2	2	no	—
134	C₂×C₄×C₇₁	—	2	2	no	—
135	C₂×C₄×C₇₁	—	2	2	no	—
136	C₂×C₄×C₇₁	—	2	2	no	—
137	C₂×C₄×C₇₁	—	2	2	no	—
138	C₂×C₄×C₇₁	—	2	2	no	—
139	C₂×C₄×C₇₁	—	2	2	no	—
140	C₂×C₄×C₇₁	—	2	2	no	—
141	C₂×C₄×C₇₁	—	2	2	no	—
142	C₂×C₄×C₇₁	—	2	2	no	—
143	C₂×C₄×C₇₁	—	2	2	no	—
144	C₂×C₄×C₇₁	—	4	1	no	—
145	C₂×C₄×C₇₁	—	4	1	no	—
146	C₂×C₄×C₇₁	—	4	1	no	—
147	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#131	1	4	yes	—
157	C₂×C₄×C₇₁	#131	1	4	yes	—
158	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
161	C₈×C₇₁	—	2	4	no	—
162	C₈×C₇₁	—	2	4	no	—
163	C₇₁⋊C₈	—	2	4	no	—
164	C₇₁⋊C₈	—	2	4	no	—
165	C₇₁⋊C₈	—	2	8	no	—
166	C₂²×C₇₁	—	2	1	no	—
167	C₂²×C₇₁	—	2	1	no	—
168	C₂²×C₇₁	—	2	1	no	—
169	C₂²×C₇₁	—	2	1	no	—
170	C₂²×C₇₁	—	2	1	no	—
171	C₂²×C₇₁	—	2	1	no	—
172	C₂²×C₇₁	—	2	1	no	—
173	C₂²×C₇₁	—	4	4	no	—
174	C₂²×C₇₁	#405	1	2	yes	—
175	C₂²×C₇₁	#405	1	2	yes	—
176	C₂²×C₇₁	C₂²×C₄²	1	1	yes	characteristic
177	C₄×C₇₁	—	2	1	no	—
178	C₄×C₇₁	—	2	1	no	—
179	C₄×C₇₁	—	2	1	no	—
180	C₄×C₇₁	—	2	1	no	—
181	C₄×C₇₁	—	2	1	no	—
182	C₄×C₇₁	—	2	1	no	—
183	C₄×C₇₁	—	2	1	no	—
184	C₄×C₇₁	#405	1	2	yes	—
185	C₄×C₇₁	#405	1	2	yes	—
186	C₄×C₇₁	C₂×#131	1	2	yes	—
187	C₄×C₇₁	C₂×#131	1	2	yes	—
188	C₄×C₇₁	#568	1	2	yes	—
189	#17325	—	71	1	no	maximal, Sylow
190	C₂×C₇₁	—	2	2	no	—
191	C₂×C₇₁	—	2	2	no	—
192	C₂×C₇₁	—	4	1	no	—
193	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
194	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
195	C₂×C₇₁	#2873	1	1	yes	characteristic
196	#2920	—	71	1	no	—
197	C₂×#431	—	71	1	no	—
198	C₂×#431	D₇₁	1	1	yes	characteristic
199	#1453	—	71	4	no	—
200	#1452	—	71	2	no	—
201	#1452	—	71	2	no	—
202	#1450	—	71	2	no	—
203	#1450	—	71	2	no	—
204	C₇₁	#17325	1	1	yes	characteristic, complemented, Sylow
205	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
206	#432	—	71	2	no	—
207	#432	—	71	2	no	—
208	#431	—	71	2	no	—
209	#431	—	71	2	no	—
210	#431	—	71	1	no	—
211	#431	—	71	1	no	—
212	#431	—	71	2	no	—
213	#431	—	71	2	no	—
214	#431	—	71	2	no	—
215	#431	Dic₇₁	1	2	yes	—
216	#431	Dic₇₁	1	2	yes	—
217	#431	C₂×D₇₁	1	1	yes	characteristic
218	#431	C₂×D₇₁	1	1	yes	characteristic
219	#431	C₂×D₇₁	1	2	yes	—
220	#423	—	71	2	no	—
221	C₂×C₄⋊C₈	—	71	2	no	—
222	C₂×C₄⋊C₈	Dic₇₁	1	2	yes	—
223	#407	—	71	2	no	—
224	C₂×C₂²⋊C₈	—	71	2	no	—
225	C₂×C₂²⋊C₈	Dic₇₁	1	2	yes	—
226	C₄×M₁₆	—	71	2	no	—
227	C₂×C₄×C₈	—	71	2	no	—
228	C₂×C₄×C₈	C₂×D₇₁	1	2	yes	—
229	#322	—	71	4	no	—
230	#322	—	71	4	no	—
231	#322	—	71	4	no	—
232	C₈²	—	71	4	no	—
233	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
234	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
235	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
236	C₂×M₁₆	—	71	4	no	—
237	C₂²×C₈	—	71	4	no	—
238	C₂²×C₈	C₂×Dic₇₁	1	4	yes	—
239	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
251	C₄⋊C₈	—	71	2	no	—
252	C₄⋊C₈	—	71	2	no	—
253	C₄⋊C₈	—	71	4	no	—
254	C₄⋊C₈	—	71	4	no	—
255	C₄⋊C₈	—	71	4	no	—
256	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
257	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
258	C₄⋊C₈	C₂×Dic₇₁	1	4	yes	—
259	C₂²⋊C₈	—	71	2	no	—
260	C₂²⋊C₈	—	71	2	no	—
261	C₂²⋊C₈	—	71	4	no	—
262	C₂²⋊C₈	—	71	4	no	—
263	C₂²⋊C₈	—	71	4	no	—
264	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
265	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
266	C₂²⋊C₈	C₂×Dic₇₁	1	4	yes	—
267	#97	—	71	4	no	—
268	C₄×C₈	—	71	4	no	—
269	C₄×C₈	—	71	2	no	—
270	C₄×C₈	—	71	4	no	—
271	C₄×C₈	—	71	2	no	—
272	C₄×C₈	C₂×Dic₇₁	1	4	yes	—
273	C₄×C₈	C₂²×D₇₁	1	2	yes	—
274	C₄×C₈	C₂²×D₇₁	1	2	yes	—
275	C₂⁴	C₄×Dic₇₁	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
280	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
281	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
282	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
283	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
295	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
296	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
297	M₁₆	—	284	4	no	—
298	C₂×C₈	—	2	8	no	—
299	C₂×C₈	—	71	4	no	—
300	C₂×C₈	—	71	4	no	—
301	C₂×C₈	—	71	8	no	—
302	C₂×C₈	—	142	8	no	—
303	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
304	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
305	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
306	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
307	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
308	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
309	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
310	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
311	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
312	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
313	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
314	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
315	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
316	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
317	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
318	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
319	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
320	C₄²	C₂³×D₇₁	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
325	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
326	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
352	C₂×C₄	#14556134	1	4	yes	—
353	C₂×C₄	#14556135	1	4	yes	—
354	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
356	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	2	4	no	—
359	C₈	—	142	4	no	—
360	C₈	—	142	4	no	—
361	C₈	—	142	8	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	4	4	no	—
370	C₂²	#17985954	1	2	yes	—
371	C₂²	#17985955	1	2	yes	—
372	C₂²	C₂²×C₄×Dic₇₁	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	#17985954	1	2	yes	—
381	C₄	#17985955	1	2	yes	—
382	C₄	C₂×#14556134	1	2	yes	—
383	C₄	C₂×#14556135	1	2	yes	—
384	C₄	#17986765	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	C₂×#17985954	1	1	yes	characteristic
389	C₂	C₂×#17985955	1	1	yes	characteristic
390	C₂	#22596758	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂²×C₄²
Fitting	C₂×#431×C₇₁	C₂
prime radical	C₂⁴×C₇₁	C₄²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₂×#431	D₇₁
hypocenter	C₇₁	#17325
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #22586635	C₂	semidirect
4. #22586633	C₂	semidirect
5. #22586632	C₂	semidirect
6. #22586624	C₂	semidirect
7. #22586623	C₂	semidirect
24. #17985721	C₂²	semidirect
25. #17985721	C₂²	semidirect
26. #17985720	C₂²	semidirect
27. C₈×C₇₁⋊C₈	C₂²	semidirect
204. C₇₁	#17325	semidirect

Maximal subgroups

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

subgroup	index
#22596973	2
C₂×#17986052	2
#22586635	2
#22586633	2
#22586632	2
#22586624	2
#22586623	2
C₂×#431×C₇₁	2
#17325	71