Subgroups — #31886870

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×C₄×#11765849	C₂	1	1	yes	maximal, characteristic
3	#22586170	C₂	1	4	yes	maximal, complemented
4	C₂×#431×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11765849	C₄	1	2	yes	—
6	#17986052	—	2	1	no	—
7	#17986052	—	2	1	no	—
8	#17986052	C₄	1	2	yes	—
9	#17986052	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
12	C₄×#11765849	—	2	1	no	—
13	C₄×#11765849	—	2	1	no	—
14	C₄×#11765849	—	2	1	no	—
15	C₄×#11765849	—	2	1	no	—
16	C₂×#14556039	C₂²	1	2	yes	—
17	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
18	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
19	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
20	#431×C₇₁	—	2	1	no	—
21	#431×C₇₁	—	2	1	no	—
22	#431×C₇₁	C₄	1	2	yes	—
23	#431×C₇₁	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₇₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₇₁	—	2	1	no	—
26	C₂×C₄×C₈×C₇₁	C₄	1	2	yes	—
27	C₂×#11765849	—	2	2	no	—
28	C₂×#11765849	—	2	2	no	—
29	C₂×#11765849	—	2	4	no	—
30	C₂×#11765849	C₈	1	8	yes	complemented
31	C₂²×C₇₁⋊C₈	—	2	2	no	—
32	C₂²×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
33	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
37	#14556039	—	2	2	no	—
38	#14556039	—	2	2	no	—
39	C₄×C₇₁⋊C₈	—	2	2	no	—
40	C₄×C₇₁⋊C₈	—	2	2	no	—
41	C₄×C₇₁⋊C₈	—	2	2	no	—
42	C₄×C₇₁⋊C₈	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₁	Q₈	1	1	yes	characteristic
46	C₂²×C₈×C₇₁	—	2	2	no	—
47	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₇₁	D₄	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	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₇₁	—	2	2	no	—
60	C₄⋊C₈×C₇₁	—	2	2	no	—
61	C₂²⋊C₈×C₇₁	—	2	2	no	—
62	C₂²⋊C₈×C₇₁	—	2	2	no	—
63	C₄×C₈×C₇₁	—	2	2	no	—
64	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	—
65	#11765849	—	2	8	no	—
66	#11765849	—	2	8	no	—
67	C₂×C₇₁⋊C₈	—	2	4	no	—
68	C₂×C₇₁⋊C₈	—	2	4	no	—
69	C₂×C₇₁⋊C₈	—	2	4	no	—
70	C₂×C₇₁⋊C₈	—	4	4	no	—
71	C₂×C₇₁⋊C₈	C₂×C₈	1	8	yes	complemented
72	C₂⁴×C₇₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₇₁	—	4	2	no	—
74	C₂²×C₄×C₇₁	—	4	2	no	—
75	C₂²×C₄×C₇₁	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₇₁	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇₁	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₂×C₈	1	4	yes	—
91	C₂²×C₄×C₇₁	M₁₆	1	4	yes	—
92	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₈×C₇₁	—	2	4	no	—
96	C₂×C₈×C₇₁	—	4	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	—	4	4	no	—
153	C₇₁⋊C₈	—	2	8	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	H(3,ℤ/4)	1	2	yes	—
175	C₄×C₇₁	#338	1	2	yes	—
176	C₄×C₇₁	C₂×C₄×C₈	1	1	yes	characteristic
177	C₄×C₇₁	C₂×#97	1	1	yes	characteristic
178	C₄×C₇₁	C₂×C₂²⋊C₈	1	2	yes	—
179	#7860	—	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	C₂×H(3,ℤ/4)	1	1	yes	characteristic
185	C₂×C₇₁	C₂×#338	1	1	yes	characteristic
186	C₂×#431	—	71	1	no	—
187	C₂×#431	D₇₁	1	1	yes	characteristic
188	C₂×C₄×M₁₆	—	71	1	no	—
189	#1275	—	71	4	no	—
190	C₇₁	#7860	1	1	yes	characteristic, complemented, Sylow
191	C₂²×M₁₆	—	71	2	no	—
192	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
193	#431	—	2	1	no	—
194	#431	—	2	1	no	—
195	#431	—	71	2	no	—
196	#431	—	71	2	no	—
197	#431	—	142	1	no	—
198	#431	—	142	1	no	—
199	#431	Dic₇₁	1	2	yes	—
200	#431	C₂×D₇₁	1	2	yes	—
201	C₂×C₄⋊C₈	—	2	1	no	—
202	C₂×C₄⋊C₈	—	142	1	no	—
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	C₂×C₂²⋊C₈	—	142	1	no	—
205	C₄×M₁₆	—	142	1	no	—
206	C₄×M₁₆	—	142	1	no	—
207	C₄×M₁₆	—	142	1	no	—
208	C₄×M₁₆	—	142	1	no	—
209	C₂×#97	—	71	2	no	—
210	C₂×C₄×C₈	—	71	2	no	—
211	C₂×C₄×C₈	—	71	2	no	—
212	C₂×C₄×C₈	Dic₇₁	1	2	yes	—
213	C₂³×C₄	Dic₁₄₂	1	1	yes	characteristic
214	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₇₁	1	1	yes	characteristic
216	C₂×M₁₆	—	71	8	no	—
217	C₂×M₁₆	—	142	2	no	—
218	C₂×M₁₆	—	142	2	no	—
219	C₂×M₁₆	—	142	4	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	71	4	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	D₂₈₄	1	1	yes	characteristic
228	C₂×C₄²	D₂₈₄	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₇₁	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	—	2	2	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	142	2	no	—
238	C₄⋊C₈	—	142	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	142	2	no	—
242	C₂²⋊C₈	—	142	2	no	—
243	#97	—	142	2	no	—
244	#97	—	142	2	no	—
245	C₄×C₈	—	2	2	no	—
246	C₄×C₈	—	71	4	no	—
247	C₄×C₈	—	142	2	no	—
248	C₄×C₈	—	142	2	no	—
249	C₄×C₈	—	142	2	no	—
250	C₄×C₈	C₂×Dic₇₁	1	4	yes	—
251	C₂⁴	Dic₇₁⋊C₄	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	Dic₇₁⋊C₄	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	C₈×D₇₁	1	4	yes	—
270	C₂²×C₄	#11765848	1	4	yes	—
271	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
274	M₁₆	—	142	8	no	—
275	M₁₆	—	142	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	4	4	no	—
278	C₂×C₈	—	284	4	no	—
279	C₂×C₈	—	71	8	no	—
280	C₂×C₈	—	142	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	C₄⋊Dic₇₁	1	1	yes	characteristic
294	C₄²	C₄⋊Dic₇₁	1	1	yes	characteristic
295	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
296	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
298	C₄²	C₂×D₂₈₄	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	Dic₇₁⋊C₈	1	4	yes	—
304	C₂³	C₂×Dic₇₁⋊C₄	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	C₈×Dic₇₁	1	2	yes	—
324	C₂×C₄	C₈×Dic₇₁	1	2	yes	—
325	C₂×C₄	#14556038	1	2	yes	—
326	C₂×C₄	#14556038	1	2	yes	—
327	C₂×C₄	(C₂×D₇₁)⋊C₈	1	4	yes	—
328	C₂×C₄	(C₂×D₇₁)⋊C₈	1	4	yes	—
329	C₂×C₄	Dic₇₁⋊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×C₄⋊Dic₇₁	1	1	yes	characteristic
336	C₂×C₄	C₂×C₈×D₇₁	1	2	yes	—
337	C₂×C₄	C₂×#11765848	1	2	yes	—
338	C₈	—	4	4	no	—
339	C₈	—	284	4	no	—
340	C₈	—	142	8	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	#17985753	1	2	yes	—
349	C₂²	#17985753	1	2	yes	—
350	C₂²	C₂×C₇₁⋊#95	1	1	yes	characteristic
351	C₂²	C₂×Dic₇₁⋊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	#17985753	1	2	yes	—
359	C₄	#17985753	1	2	yes	—
360	C₄	#17985755	1	2	yes	—
361	C₄	C₇₁⋊#338	1	2	yes	—
362	C₄	C₂×C₈×Dic₇₁	1	1	yes	characteristic
363	C₄	C₂×#14556038	1	1	yes	characteristic
364	C₄	C₂×(C₂×D₇₁)⋊C₈	1	2	yes	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	—	2	2	no	—
368	C₂	C₂×#17985753	1	1	yes	characteristic
369	C₂	C₂×#17985755	1	1	yes	characteristic
370	C₂	C₂×C₇₁⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₇₁
commutator	C₄×C₇₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₂×#431×C₇₁	C₂
socle	C₂²×C₇₁	C₂×#95
prime radical	C₂⁴×C₇₁	C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	C₂×#431	D₇₁
hypocenter	C₇₁	#7860
LCS	G ▷ C₄×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #22586170	C₂	semidirect
30. C₂×#11765849	C₈	semidirect
71. C₂×C₇₁⋊C₈	C₂×C₈	semidirect
190. C₇₁	#7860	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
C₂×C₄×#11765849	2
#22586170	2
C₂×#431×C₇₁	2
#7860	71