Subgroups — #31886949

Order 18176.

666 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986052	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986052	C₂	1	1	yes	maximal, characteristic
3	#22586178	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×M₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
5	#17986052	—	2	1	no	—
6	#17986052	—	2	1	no	—
7	#17986052	—	2	1	no	—
8	#17986052	—	2	1	no	—
9	#17986052	C₄	1	2	yes	—
10	#17986052	C₄	1	2	yes	—
11	#17986052	C₄	1	2	yes	—
12	#17986052	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
15	C₂×C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
16	C₂×C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
17	C₂×C₄×C₇₁⋊C₈	—	2	1	no	—
18	C₂×C₄×C₇₁⋊C₈	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₇₁	C₄	1	2	yes	—
20	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₇₁	—	2	1	no	—
22	C₄×M₁₆×C₇₁	—	2	1	no	—
23	C₄×M₁₆×C₇₁	C₄	1	2	yes	—
24	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
25	C₂×#97×C₇₁	—	2	1	no	—
26	C₂×C₄×C₈×C₇₁	—	2	1	no	—
27	C₂²×C₇₁⋊C₈	—	2	2	no	—
28	C₂²×C₇₁⋊C₈	—	2	2	no	—
29	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
30	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
31	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
32	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	4	yes	—
33	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
37	C₄×C₇₁⋊C₈	—	2	2	no	—
38	C₄×C₇₁⋊C₈	—	2	2	no	—
39	C₄×C₇₁⋊C₈	—	2	2	no	—
40	C₄×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇₁	Q₈	1	1	yes	characteristic
44	C₂×M₁₆×C₇₁	—	2	2	no	—
45	C₂×M₁₆×C₇₁	—	2	4	no	—
46	C₂×M₁₆×C₇₁	C₈	1	8	yes	complemented
47	C₂×M₁₆×C₇₁	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₇₁	—	2	2	no	—
49	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₁	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
61	#97×C₇₁	—	2	2	no	—
62	#97×C₇₁	—	2	2	no	—
63	C₄×C₈×C₇₁	—	2	2	no	—
64	C₄×C₈×C₇₁	—	2	2	no	—
65	C₂×C₇₁⋊C₈	—	2	4	no	—
66	C₂×C₇₁⋊C₈	—	2	4	no	—
67	C₂×C₇₁⋊C₈	—	4	4	no	—
68	C₂×C₇₁⋊C₈	—	4	4	no	—
69	C₂⁴×C₇₁	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₇₁	—	4	2	no	—
71	C₂²×C₄×C₇₁	—	4	2	no	—
72	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂×C₈	1	4	yes	—
88	C₂²×C₄×C₇₁	M₁₆	1	4	yes	—
89	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
92	M₁₆×C₇₁	—	2	8	no	—
93	M₁₆×C₇₁	—	2	4	no	—
94	M₁₆×C₇₁	C₂×C₈	1	8	yes	complemented
95	C₂×C₈×C₇₁	—	2	8	no	—
96	C₂×C₈×C₇₁	—	2	4	no	—
97	C₄²×C₇₁	C₄²	1	1	yes	characteristic
98	C₄²×C₇₁	C₄²	1	1	yes	characteristic
99	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₇₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
113	C₂³×C₇₁	—	4	1	no	—
114	C₂³×C₇₁	—	4	1	no	—
115	C₂³×C₇₁	#95	1	1	yes	characteristic
116	C₂³×C₇₁	#95	1	1	yes	characteristic
117	C₂³×C₇₁	C₄⋊C₈	1	4	yes	—
118	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₇₁	—	2	2	no	—
120	C₂×C₄×C₇₁	—	2	2	no	—
121	C₂×C₄×C₇₁	—	2	2	no	—
122	C₂×C₄×C₇₁	—	2	2	no	—
123	C₂×C₄×C₇₁	—	2	2	no	—
124	C₂×C₄×C₇₁	—	2	2	no	—
125	C₂×C₄×C₇₁	—	4	1	no	—
126	C₂×C₄×C₇₁	—	4	1	no	—
127	C₂×C₄×C₇₁	—	4	1	no	—
128	C₂×C₄×C₇₁	—	4	1	no	—
129	C₂×C₄×C₇₁	—	4	1	no	—
130	C₂×C₄×C₇₁	—	4	1	no	—
131	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
132	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
133	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
134	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
135	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
136	C₂×C₄×C₇₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₇₁	C₄×C₈	1	2	yes	—
138	C₂×C₄×C₇₁	C₄×C₈	1	2	yes	—
139	C₂×C₄×C₇₁	#97	1	2	yes	—
140	C₂×C₄×C₇₁	#97	1	2	yes	—
141	C₂×C₄×C₇₁	C₂²⋊C₈	1	4	yes	—
142	C₂×C₄×C₇₁	C₂²⋊C₈	1	4	yes	—
143	C₂×C₄×C₇₁	C₄⋊C₈	1	4	yes	—
144	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²×C₈	1	2	yes	—
151	C₂×C₄×C₇₁	C₂×M₁₆	1	2	yes	—
152	C₈×C₇₁	—	2	8	no	—
153	C₇₁⋊C₈	—	4	4	no	—
154	C₇₁⋊C₈	—	4	4	no	—
155	C₂²×C₇₁	—	2	1	no	—
156	C₂²×C₇₁	—	2	1	no	—
157	C₂²×C₇₁	—	2	1	no	—
158	C₂²×C₇₁	—	2	1	no	—
159	C₂²×C₇₁	—	2	1	no	—
160	C₂²×C₇₁	—	2	1	no	—
161	C₂²×C₇₁	—	4	4	no	—
162	C₂²×C₇₁	#336	1	2	yes	—
163	C₂²×C₇₁	#336	1	2	yes	—
164	C₂²×C₇₁	C₂×#95	1	1	yes	characteristic
165	C₂²×C₇₁	C₂×C₄⋊C₈	1	2	yes	—
166	C₄×C₇₁	—	2	1	no	—
167	C₄×C₇₁	—	2	1	no	—
168	C₄×C₇₁	—	2	1	no	—
169	C₄×C₇₁	—	2	1	no	—
170	C₄×C₇₁	—	2	1	no	—
171	C₄×C₇₁	—	2	1	no	—
172	C₄×C₇₁	#336	1	2	yes	—
173	C₄×C₇₁	#336	1	2	yes	—
174	C₄×C₇₁	C₂×C₄×C₈	1	1	yes	characteristic
175	C₄×C₇₁	C₂×#97	1	1	yes	characteristic
176	C₄×C₇₁	C₂×C₂²⋊C₈	1	2	yes	—
177	C₄×C₇₁	#421	1	2	yes	—
178	C₄×C₇₁	#430	1	2	yes	—
179	#7882	—	71	1	no	maximal, Sylow
180	C₂×C₇₁	—	2	2	no	—
181	C₂×C₇₁	—	2	2	no	—
182	C₂×C₇₁	—	2	2	no	—
183	C₂×C₇₁	C₂×#336	1	1	yes	characteristic
184	C₂×C₇₁	#1733	1	1	yes	characteristic
185	C₂×C₇₁	#1738	1	1	yes	characteristic
186	C₂×#431	—	71	1	no	—
187	C₂×#431	—	71	1	no	—
188	C₂×C₄×M₁₆	D₇₁	1	1	yes	characteristic
189	#1278	—	71	4	no	—
190	C₇₁	#7882	1	1	yes	characteristic, complemented, Sylow
191	C₂²×M₁₆	Dic₇₁	1	2	yes	—
192	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
193	#431	—	71	2	no	—
194	#431	—	71	2	no	—
195	#431	—	71	2	no	—
196	#431	—	71	2	no	—
197	#431	—	142	1	no	—
198	#431	—	142	1	no	—
199	#431	—	142	1	no	—
200	#431	—	142	1	no	—
201	C₂×C₄⋊C₈	—	71	2	no	—
202	C₂×C₄⋊C₈	—	142	1	no	—
203	C₂×C₂²⋊C₈	—	142	1	no	—
204	C₂×C₂²⋊C₈	—	142	1	no	—
205	C₄×M₁₆	—	2	1	no	—
206	C₄×M₁₆	—	2	1	no	—
207	C₄×M₁₆	Dic₇₁	1	2	yes	—
208	C₄×M₁₆	C₂×D₇₁	1	2	yes	—
209	C₂×#97	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	C₂×C₄×C₈	—	71	2	no	—
212	C₂×C₄×C₈	—	142	1	no	—
213	C₂³×C₄	Dic₁₄₂	1	1	yes	characteristic
214	C₂³×C₄	D₂₈₄	1	1	yes	characteristic
215	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	4	no	—
218	C₂×M₁₆	C₇₁⋊C₈	1	8	yes	complemented
219	C₂×M₁₆	C₂×Dic₇₁	1	4	yes	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	142	2	no	—
222	C₂²×C₈	—	142	2	no	—
223	C₂×C₄²	Dic₁₄₂	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
228	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
235	C₄⋊C₈	—	71	4	no	—
236	C₄⋊C₈	—	142	2	no	—
237	C₄⋊C₈	—	142	2	no	—
238	C₄⋊C₈	—	142	2	no	—
239	C₂²⋊C₈	—	142	2	no	—
240	C₂²⋊C₈	—	142	2	no	—
241	C₂²⋊C₈	—	142	2	no	—
242	C₂²⋊C₈	—	142	2	no	—
243	#97	—	2	2	no	—
244	#97	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	71	4	no	—
248	C₄×C₈	—	142	2	no	—
249	C₄×C₈	—	142	2	no	—
250	C₄×C₈	—	142	2	no	—
251	C₂⁴	C₄⋊Dic₇₁	1	1	yes	characteristic
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₇₁	1	1	yes	characteristic
262	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₇₁⋊C₈	1	4	yes	—
270	C₂²×C₄	#11765849	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
274	M₁₆	—	2	8	no	—
275	M₁₆	—	2	4	no	—
276	M₁₆	C₂×C₇₁⋊C₈	1	8	yes	complemented
277	C₂×C₈	—	2	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	284	4	no	—
280	C₂×C₈	—	284	4	no	—
281	C₂×C₈	—	142	4	no	—
282	C₂×C₈	—	142	4	no	—
283	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
284	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
285	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
287	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
288	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
289	C₄²	C₂²⋊Dic₇₁	1	1	yes	characteristic
290	C₄²	C₂²⋊Dic₇₁	1	1	yes	characteristic
291	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₇₁⋊C₄	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
296	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
299	C₂³	—	4	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₇₁⋊#95	1	1	yes	characteristic
302	C₂³	C₇₁⋊#95	1	1	yes	characteristic
303	C₂³	C₄⋊(C₇₁⋊C₈)	1	4	yes	—
304	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
318	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
319	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
320	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
321	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₇₁⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₄×C₇₁⋊C₈	1	2	yes	—
324	C₂×C₄	C₄×C₇₁⋊C₈	1	2	yes	—
325	C₂×C₄	#14556039	1	2	yes	—
326	C₂×C₄	#14556039	1	2	yes	—
327	C₂×C₄	C₂²⋊(C₇₁⋊C₈)	1	4	yes	—
328	C₂×C₄	C₂²⋊(C₇₁⋊C₈)	1	4	yes	—
329	C₂×C₄	C₄⋊(C₇₁⋊C₈)	1	4	yes	—
330	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
331	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₇₁⋊C₈	1	2	yes	—
337	C₂×C₄	C₂×#11765849	1	2	yes	—
338	C₈	—	2	8	no	—
339	C₈	—	284	4	no	—
340	C₈	—	284	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	4	4	no	—
348	C₂²	#17985754	1	2	yes	—
349	C₂²	#17985754	1	2	yes	—
350	C₂²	C₂×C₇₁⋊#95	1	1	yes	characteristic
351	C₂²	C₂×C₄⋊(C₇₁⋊C₈)	1	2	yes	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	#17985754	1	2	yes	—
359	C₄	#17985754	1	2	yes	—
360	C₄	C₂×C₄×C₇₁⋊C₈	1	1	yes	characteristic
361	C₄	C₂×#14556039	1	1	yes	characteristic
362	C₄	C₂×C₂²⋊(C₇₁⋊C₈)	1	2	yes	—
363	C₄	#17986015	1	2	yes	—
364	C₄	#17986047	1	2	yes	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	—	2	2	no	—
368	C₂	C₂×#17985754	1	1	yes	characteristic
369	C₂	#22588051	1	1	yes	characteristic
370	C₂	#22588066	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₇₁
commutator	C₄×C₇₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₂×C₄×M₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×#95
prime radical	C₂⁴×C₇₁	C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₂×C₄×M₁₆	D₇₁
hypocenter	C₇₁	#7882
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22586178	C₂	semidirect
46. C₂×M₁₆×C₇₁	C₈	semidirect
94. M₁₆×C₇₁	C₂×C₈	semidirect
190. C₇₁	#7882	semidirect
218. C₂×M₁₆	C₇₁⋊C₈	semidirect
276. M₁₆	C₂×C₇₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986052	2
#22586178	2
C₂×C₄×M₁₆×C₇₁	2
#7882	71