Subgroups — #31963111

Order 18176.

836 conjugacy classes of subgroups.

The subgroup lattice has 400 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	#22586637	C₂	1	4	yes	maximal, complemented
4	#22586629	C₂	1	2	yes	maximal, complemented
5	#22586627	C₂	1	2	yes	maximal, complemented
6	C₈×#11765849	C₂	1	2	yes	maximal, complemented
7	M₁₆×C₇₁⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×M₁₆×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×M₁₆×C₇₁	C₄	1	2	yes	—
29	C₂²×C₄²×C₇₁	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₇₁	C₄	1	2	yes	—
31	C₄×M₁₆×C₇₁	C₄	1	2	yes	—
32	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
33	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
34	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
35	C₂×#97×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	C₂×M₁₆×C₇₁	—	2	8	no	—
58	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₇₁	C₂×C₄	1	4	yes	—
60	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₇₁	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
74	#97×C₇₁	C₂×C₄	1	2	yes	—
75	#97×C₇₁	C₂×C₄	1	4	yes	—
76	#97×C₇₁	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₇₁	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₇₁	C₂³	1	2	yes	—
79	C₄×C₈×C₇₁	C₂³	1	2	yes	—
80	#11765849	—	2	8	no	—
81	C₂×C₇₁⋊C₈	—	4	4	no	—
82	C₂×C₇₁⋊C₈	C₂²×C₄	1	4	yes	—
83	C₂×C₇₁⋊C₈	C₂²×C₄	1	4	yes	—
84	C₂×C₇₁⋊C₈	C₂²×C₄	1	8	yes	—
85	C₂⁴×C₇₁	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	—	2	4	no	—
87	C₂²×C₄×C₇₁	—	2	4	no	—
88	C₂²×C₄×C₇₁	—	4	2	no	—
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	C₄²	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	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₇₁	—	2	4	no	—
108	M₁₆×C₇₁	—	2	8	no	—
109	M₁₆×C₇₁	M₁₆	1	8	yes	complemented
110	C₂×C₈×C₇₁	—	2	8	no	—
111	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₇₁	C₂²×C₄	1	4	yes	—
113	C₄²×C₇₁	C₄²	1	1	yes	characteristic
114	C₄²×C₇₁	C₄²	1	1	yes	characteristic
115	C₄²×C₇₁	C₄²	1	1	yes	characteristic
116	C₄²×C₇₁	C₄²	1	1	yes	characteristic
117	C₄²×C₇₁	C₄²	1	1	yes	characteristic
118	C₄²×C₇₁	C₄²	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	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
129	C₂³×C₇₁	—	2	2	no	—
130	C₂³×C₇₁	—	2	2	no	—
131	C₂³×C₇₁	—	4	1	no	—
132	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
133	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
134	C₂³×C₇₁	C₂×C₄²	1	1	yes	characteristic
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	—	2	2	no	—
145	C₂×C₄×C₇₁	—	2	2	no	—
146	C₂×C₄×C₇₁	—	2	2	no	—
147	C₂×C₄×C₇₁	—	2	2	no	—
148	C₂×C₄×C₇₁	—	4	1	no	—
149	C₂×C₄×C₇₁	—	4	1	no	—
150	C₂×C₄×C₇₁	—	4	1	no	—
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	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂×M₁₆	1	4	yes	—
161	C₂×C₄×C₇₁	#131	1	4	yes	—
162	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
165	C₈×C₇₁	—	2	4	no	—
166	C₈×C₇₁	C₂×M₁₆	1	8	yes	—
167	C₇₁⋊C₈	—	2	8	no	—
168	C₇₁⋊C₈	—	2	4	no	—
169	C₇₁⋊C₈	—	2	4	no	—
170	C₂²×C₇₁	—	2	1	no	—
171	C₂²×C₇₁	—	2	1	no	—
172	C₂²×C₇₁	—	2	1	no	—
173	C₂²×C₇₁	—	2	1	no	—
174	C₂²×C₇₁	—	2	1	no	—
175	C₂²×C₇₁	—	2	1	no	—
176	C₂²×C₇₁	—	2	1	no	—
177	C₂²×C₇₁	—	4	4	no	—
178	C₂²×C₇₁	C₄×M₁₆	1	2	yes	—
179	C₂²×C₇₁	#405	1	2	yes	—
180	C₂²×C₇₁	C₂²×C₄²	1	1	yes	characteristic
181	C₄×C₇₁	—	2	1	no	—
182	C₄×C₇₁	—	2	1	no	—
183	C₄×C₇₁	—	2	1	no	—
184	C₄×C₇₁	—	2	1	no	—
185	C₄×C₇₁	—	2	1	no	—
186	C₄×C₇₁	—	2	1	no	—
187	C₄×C₇₁	—	2	1	no	—
188	C₄×C₇₁	C₄×M₁₆	1	2	yes	—
189	C₄×C₇₁	#405	1	2	yes	—
190	C₄×C₇₁	C₂²×M₁₆	1	2	yes	—
191	C₄×C₇₁	C₂×#131	1	2	yes	—
192	C₄×C₇₁	#568	1	2	yes	—
193	#17327	—	71	1	no	maximal, Sylow
194	C₂×C₇₁	—	2	2	no	—
195	C₂×C₇₁	—	2	2	no	—
196	C₂×C₇₁	—	4	1	no	—
197	C₂×C₇₁	C₂×C₄×M₁₆	1	1	yes	characteristic
198	C₂×C₇₁	C₂×#405	1	1	yes	characteristic
199	C₂×C₇₁	#2873	1	1	yes	characteristic
200	#2920	—	71	1	no	—
201	C₂×#431	—	71	1	no	—
202	C₂×C₄×M₁₆	D₇₁	1	1	yes	characteristic
203	#1453	—	71	4	no	—
204	#1451	—	71	2	no	—
205	#1451	—	71	2	no	—
206	C₈×M₁₆	—	71	2	no	—
207	C₈×M₁₆	—	71	2	no	—
208	C₇₁	#17327	1	1	yes	characteristic, complemented, Sylow
209	C₂²×M₁₆	Dic₇₁	1	2	yes	—
210	C₂²×C₄²	C₂×D₇₁	1	1	yes	characteristic
211	#432	—	71	2	no	—
212	#432	—	71	2	no	—
213	#431	—	71	2	no	—
214	#431	—	71	2	no	—
215	#431	—	71	1	no	—
216	#431	—	71	1	no	—
217	#431	—	71	2	no	—
218	#431	—	71	2	no	—
219	#431	—	71	2	no	—
220	#423	—	71	2	no	—
221	C₂×C₄⋊C₈	—	71	2	no	—
222	#407	—	71	2	no	—
223	C₂×C₂²⋊C₈	—	71	2	no	—
224	C₄×M₁₆	—	71	2	no	—
225	C₄×M₁₆	Dic₇₁	1	2	yes	—
226	C₄×M₁₆	Dic₇₁	1	2	yes	—
227	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
228	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
229	C₄×M₁₆	C₂×D₇₁	1	2	yes	—
230	C₂×#97	Dic₇₁	1	2	yes	—
231	C₂×C₄×C₈	—	71	2	no	—
232	C₂×C₄×C₈	C₂×D₇₁	1	2	yes	—
233	#322	—	71	4	no	—
234	#322	—	71	4	no	—
235	#322	—	71	4	no	—
236	C₈²	—	71	4	no	—
237	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
238	C₂³×C₄	C₄×D₇₁	1	1	yes	characteristic
239	C₂³×C₄	C₂×Dic₇₁	1	1	yes	characteristic
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	—	71	4	no	—
242	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
243	C₂×M₁₆	C₂×Dic₇₁	1	4	yes	—
244	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
245	C₂²×C₈	—	71	4	no	—
246	C₂²×C₈	C₂×Dic₇₁	1	4	yes	—
247	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
249	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
250	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
253	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
254	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
259	C₄⋊C₈	—	71	2	no	—
260	C₄⋊C₈	—	71	2	no	—
261	C₄⋊C₈	—	71	4	no	—
262	C₄⋊C₈	—	71	4	no	—
263	C₄⋊C₈	—	71	4	no	—
264	C₂²⋊C₈	—	71	2	no	—
265	C₂²⋊C₈	—	71	2	no	—
266	C₂²⋊C₈	—	71	4	no	—
267	C₂²⋊C₈	—	71	4	no	—
268	C₂²⋊C₈	—	71	4	no	—
269	#97	—	71	4	no	—
270	#97	C₂×Dic₇₁	1	2	yes	—
271	#97	C₂×Dic₇₁	1	4	yes	—
272	#97	C₂×Dic₇₁	1	2	yes	—
273	C₄×C₈	—	71	4	no	—
274	C₄×C₈	—	71	2	no	—
275	C₄×C₈	—	71	4	no	—
276	C₄×C₈	—	71	2	no	—
277	C₄×C₈	C₂×Dic₇₁	1	4	yes	—
278	C₄×C₈	C₂²×D₇₁	1	2	yes	—
279	C₄×C₈	C₂²×D₇₁	1	2	yes	—
280	C₂⁴	C₄×Dic₇₁	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	2	no	—
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	C₄×Dic₇₁	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
291	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
292	C₂²×C₄	C₄×Dic₇₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
300	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
302	M₁₆	—	2	4	no	—
303	M₁₆	—	2	8	no	—
304	M₁₆	—	142	8	no	—
305	M₁₆	#11765849	1	8	yes	complemented
306	C₂×C₈	—	2	8	no	—
307	C₂×C₈	—	284	4	no	—
308	C₂×C₈	—	71	4	no	—
309	C₂×C₈	—	71	4	no	—
310	C₂×C₈	—	71	8	no	—
311	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
312	C₂×C₈	C₂²×Dic₇₁	1	4	yes	—
313	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
314	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
315	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
316	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
317	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
318	C₄²	C₄×Dic₇₁	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
320	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
321	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
322	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
324	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
325	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
326	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
327	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
328	C₄²	C₂³×D₇₁	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
333	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
334	C₂³	C₂×C₄×Dic₇₁	1	1	yes	characteristic
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	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#11765849	1	4	yes	—
361	C₂×C₄	#14556136	1	4	yes	—
362	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
364	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	142	8	no	—
367	C₈	—	142	4	no	—
368	C₈	—	142	4	no	—
369	C₈	C₂×#11765849	1	8	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₄×#11765849	1	2	yes	—
379	C₂²	#17985957	1	2	yes	—
380	C₂²	C₂²×C₄×Dic₇₁	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	C₄×#11765849	1	2	yes	—
389	C₄	#17985957	1	2	yes	—
390	C₄	C₂²×#11765849	1	2	yes	—
391	C₄	C₂×#14556136	1	2	yes	—
392	C₄	#17986765	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	—	4	1	no	—
396	C₂	C₂×C₄×#11765849	1	1	yes	characteristic
397	C₂	C₂×#17985957	1	1	yes	characteristic
398	C₂	#22596758	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂²×C₄²
Fitting	C₂×C₄×M₁₆×C₇₁	C₂
prime radical	C₂⁴×C₇₁	C₄²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₇₁
hypocenter	C₇₁	#17327
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22586637	C₂	semidirect
4. #22586629	C₂	semidirect
5. #22586627	C₂	semidirect
6. C₈×#11765849	C₂	semidirect
7. M₁₆×C₇₁⋊C₈	C₂	semidirect
24. #17985721	C₂²	semidirect
25. #17985721	C₂²	semidirect
26. #17985720	C₂²	semidirect
27. C₈×C₇₁⋊C₈	C₂²	semidirect
109. M₁₆×C₇₁	M₁₆	semidirect
208. C₇₁	#17327	semidirect
305. M₁₆	#11765849	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
#22586637	2
#22586629	2
#22586627	2
C₈×#11765849	2
M₁₆×C₇₁⋊C₈	2
C₂×C₄×M₁₆×C₇₁	2
#17327	71