Subgroups — #2168×D₇₁ #32150604

Order 18176.

754 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₇₁	C₂	1	1	yes	maximal, characteristic
4	#22590168	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590167	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590166	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590165	C₂	1	1	yes	maximal, characteristic, complemented
8	#22590164	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590163	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#346×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₇₁	C₄	1	1	yes	characteristic
19	C₂×#14556068	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14556067	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14556067	C₂²	1	1	yes	characteristic, complemented
22	M₃₂×D₇₁	—	2	4	no	—
23	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₆×D₇₁	—	2	4	no	—
25	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
26	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
29	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic, complemented
31	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
32	D₄×C₇₁⋊C₈	C₄	1	1	yes	characteristic
33	#17986064	C₄	1	1	yes	characteristic
34	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₇₁	C₂²	1	1	yes	characteristic
36	(C₂²⋊D₇₁)⋊C₈	C₄	1	1	yes	characteristic
37	(C₂²⋊D₇₁)⋊C₈	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₇₁	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₇₁	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₇₁	C₄	1	1	yes	characteristic
41	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
42	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
43	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
44	Dic₇₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₇₁)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	#17985775	C₂²	1	1	yes	characteristic, complemented
52	#17985774	C₂²	1	1	yes	characteristic, complemented
53	#17985774	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
56	C₈×D₄×C₇₁	C₂²	1	1	yes	characteristic
57	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic, complemented
60	#346×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₄×D₇₁	C₈	1	1	yes	characteristic
62	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₁	—	2	2	no	—
67	C₂×C₈×D₇₁	—	2	2	no	—
68	C₂×C₈×D₇₁	—	2	2	no	—
69	C₂×C₈×D₇₁	—	2	2	no	—
70	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
78	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
79	D₄×Dic₇₁	C₈	1	1	yes	characteristic
80	#14556090	C₈	1	1	yes	characteristic
81	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
83	(C₂²⋊D₇₁)⋊C₄	C₈	1	1	yes	characteristic
84	(C₂²⋊D₇₁)⋊C₄	C₈	1	1	yes	characteristic
85	C₄⋊C₄×D₇₁	C₈	1	1	yes	characteristic
86	C₂²⋊C₄×D₇₁	C₈	1	1	yes	characteristic
87	C₂²⋊C₄×D₇₁	C₈	1	1	yes	characteristic
88	C₄²×D₇₁	C₂×C₄	1	1	yes	characteristic
89	#14556068	—	2	2	no	—
90	#14556067	—	2	2	no	—
91	#14556067	—	2	2	no	—
92	C₂×C₇₁⋊C₁₆	—	2	2	no	—
93	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
97	C₁₆×D₇₁	—	2	2	no	—
98	C₁₆×D₇₁	—	2	2	no	—
99	C₁₆×D₇₁	—	2	2	no	—
100	C₁₆×D₇₁	—	2	2	no	—
101	C₁₆×D₇₁	—	2	2	no	—
102	C₁₆×D₇₁	D₄	1	4	yes	complemented
103	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
104	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
108	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₇₁	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
118	M₃₂×C₇₁	—	2	2	no	—
119	C₂×C₁₆×C₇₁	—	2	2	no	—
120	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
122	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
127	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
128	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
129	C₂³×D₇₁	C₂×C₈	1	1	yes	characteristic
130	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
131	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
132	C₂×C₂²⋊D₇₁	C₂×C₈	1	1	yes	characteristic
133	D₄×D₇₁	—	2	4	no	—
134	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
135	C₂²×Dic₇₁	C₂×C₈	1	1	yes	characteristic
136	C₂×C₄×D₇₁	—	2	2	no	—
137	C₂×C₄×D₇₁	—	2	2	no	—
138	C₂×C₄×D₇₁	—	2	2	no	—
139	C₂×C₄×D₇₁	—	2	2	no	—
140	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
143	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₇₁⋊C₈	—	2	2	no	—
150	C₂×C₇₁⋊C₈	—	2	2	no	—
151	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₈×D₇₁	—	2	2	no	—
156	C₈×D₇₁	—	2	2	no	—
157	C₈×D₇₁	—	2	2	no	—
158	C₈×D₇₁	—	2	1	no	—
159	C₈×D₇₁	—	2	1	no	—
160	C₈×D₇₁	—	2	1	no	—
161	C₈×D₇₁	—	2	1	no	—
162	C₈×D₇₁	—	2	2	no	—
163	C₈×D₇₁	—	2	2	no	—
164	C₈×D₇₁	C₂×D₄	1	2	yes	—
165	C₈×D₇₁	#41	1	2	yes	—
166	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
167	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
168	Dic₇₁⋊C₄	C₂×C₈	1	1	yes	characteristic
169	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
170	C₂²⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
171	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
172	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
173	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
174	(C₂×D₇₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
176	C₄×Dic₇₁	C₂×C₈	1	1	yes	characteristic
177	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
178	C₇₁⋊C₁₆	—	2	1	no	—
179	C₇₁⋊C₁₆	—	2	1	no	—
180	C₇₁⋊C₁₆	—	2	1	no	—
181	C₇₁⋊C₁₆	C₂×D₄	1	2	yes	complemented
182	C₂×D₄×C₇₁	C₂×C₈	1	1	yes	characteristic
183	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₇₁	—	2	1	no	—
186	C₂×C₈×C₇₁	—	2	1	no	—
187	C₂×C₈×C₇₁	—	2	1	no	—
188	C₂×C₈×C₇₁	—	2	1	no	—
189	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
193	C₄⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
194	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
195	C₂²⋊C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
196	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
197	C₁₆×C₇₁	—	2	1	no	—
198	C₁₆×C₇₁	—	2	1	no	—
199	C₁₆×C₇₁	—	2	1	no	—
200	C₁₆×C₇₁	C₂×D₄	1	2	yes	complemented
201	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
202	C₂³×C₇₁	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₇₁	—	2	2	no	—
204	C₂²×D₇₁	—	2	2	no	—
205	C₂²×D₇₁	—	2	2	no	—
206	C₂²×D₇₁	—	2	2	no	—
207	C₂²×D₇₁	—	2	2	no	—
208	C₂²×D₇₁	M₃₂	1	4	yes	complemented
209	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
210	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
211	C₂²×D₇₁	C₂²×C₈	1	1	yes	characteristic
212	D₄×C₇₁	—	2	2	no	—
213	C₂×C₄×C₇₁	—	2	1	no	—
214	C₂×C₄×C₇₁	—	2	1	no	—
215	C₂×C₄×C₇₁	—	2	1	no	—
216	C₂×C₄×C₇₁	—	2	1	no	—
217	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
218	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
219	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
220	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
221	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
222	C₂²⋊D₇₁	—	2	2	no	—
223	C₂²⋊D₇₁	—	2	2	no	—
224	C₂×Dic₇₁	—	2	2	no	—
225	C₂×Dic₇₁	—	2	2	no	—
226	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
227	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
228	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
229	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
230	C₂×Dic₇₁	C₂²×C₈	1	1	yes	characteristic
231	D₂₈₄	—	2	2	no	—
232	C₄×D₇₁	—	2	2	no	—
233	C₄×D₇₁	—	2	2	no	—
234	C₄×D₇₁	—	2	2	no	—
235	C₄×D₇₁	—	2	2	no	—
236	C₄×D₇₁	—	2	1	no	—
237	C₄×D₇₁	—	2	1	no	—
238	C₄×D₇₁	—	2	1	no	—
239	C₄×D₇₁	—	2	1	no	—
240	C₄×D₇₁	—	2	2	no	—
241	C₄×D₇₁	—	2	2	no	—
242	C₄×D₇₁	C₄×D₄	1	2	yes	—
243	C₄×D₇₁	#131	1	2	yes	—
244	C₈×C₇₁	—	2	1	no	—
245	C₈×C₇₁	—	2	1	no	—
246	C₈×C₇₁	—	2	1	no	—
247	C₈×C₇₁	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
249	C₇₁⋊C₈	—	2	1	no	—
250	C₇₁⋊C₈	—	2	1	no	—
251	C₇₁⋊C₈	—	2	1	no	—
252	C₇₁⋊C₈	C₄×D₄	1	2	yes	—
253	C₂²×C₇₁	—	2	1	no	—
254	C₂²×C₇₁	—	2	1	no	—
255	C₂²×C₇₁	—	2	1	no	—
256	C₂²×C₇₁	—	2	1	no	—
257	C₂²×C₇₁	—	2	1	no	—
258	C₂²×C₇₁	C₂×M₃₂	1	2	yes	complemented
259	C₂²×C₇₁	C₂³×C₈	1	1	yes	characteristic
260	C₂×D₇₁	—	2	1	no	—
261	C₂×D₇₁	—	2	1	no	—
262	C₂×D₇₁	—	2	8	no	—
263	C₂×D₇₁	—	2	1	no	—
264	C₂×D₇₁	—	2	1	no	—
265	C₂×D₇₁	—	2	1	no	—
266	C₂×D₇₁	—	4	4	no	—
267	C₂×D₇₁	C₈×D₄	1	2	yes	—
268	C₂×D₇₁	C₂×M₃₂	1	2	yes	—
269	C₂×D₇₁	C₂×M₃₂	1	2	yes	complemented
270	C₂×D₇₁	#504	1	2	yes	—
271	C₄×C₇₁	—	2	1	no	—
272	C₄×C₇₁	—	2	1	no	—
273	C₄×C₇₁	—	2	1	no	—
274	C₄×C₇₁	—	2	1	no	—
275	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
276	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
277	Dic₇₁	—	2	1	no	—
278	Dic₇₁	—	2	1	no	—
279	Dic₇₁	—	2	1	no	—
280	Dic₇₁	—	2	1	no	—
281	Dic₇₁	C₈×D₄	1	2	yes	—
282	C₂×#2168	—	71	1	no	maximal, Sylow
283	C₂×C₇₁	—	2	2	no	—
284	C₂×C₇₁	—	4	1	no	—
285	C₂×C₇₁	C₂×C₈×D₄	1	1	yes	characteristic
286	C₂×C₇₁	C₂²×M₃₂	1	1	yes	characteristic
287	C₂×C₇₁	C₂×#504	1	1	yes	characteristic
288	D₇₁	—	2	2	no	—
289	D₇₁	—	4	1	no	—
290	D₇₁	#2168	1	4	yes	direct product factor
291	C₂²×M₃₂	—	71	1	no	—
292	C₂³×C₁₆	—	71	1	no	—
293	C₂×C₈×D₄	—	71	1	no	—
294	#2168	—	71	1	no	—
295	#2168	—	71	1	no	—
296	#2168	—	71	1	no	—
297	#2168	—	71	1	no	—
298	#2168	—	71	1	no	—
299	#2168	—	71	1	no	—
300	#2168	—	71	1	no	—
301	#2168	D₇₁	1	1	yes	characteristic, direct product factor
302	C₂×C₄⋊C₁₆	—	71	1	no	—
303	C₂×C₂²⋊C₁₆	—	71	1	no	—
304	C₂×C₂²⋊C₁₆	—	71	1	no	—
305	C₂×#346	—	71	1	no	—
306	C₇₁	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
307	C₂³×C₈	—	71	1	no	—
308	C₂³×C₈	—	71	1	no	—
309	C₂×C₄×D₄	—	71	1	no	—
310	C₂×M₃₂	—	71	1	no	—
311	C₂×M₃₂	—	71	1	no	—
312	C₂×M₃₂	—	71	1	no	—
313	C₂×M₃₂	—	142	4	no	—
314	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic, complemented
315	C₂²×C₁₆	—	71	1	no	—
316	C₂²×C₁₆	—	71	1	no	—
317	C₂²×C₁₆	—	71	1	no	—
318	C₂²×C₁₆	—	71	1	no	—
319	C₂²×C₁₆	—	71	1	no	—
320	C₂²×C₁₆	—	71	1	no	—
321	C₂²×C₁₆	—	71	1	no	—
322	C₂²×C₁₆	—	142	4	no	—
323	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
324	C₈×D₄	—	71	1	no	—
325	C₈×D₄	—	71	1	no	—
326	C₈×D₄	—	71	1	no	—
327	C₈×D₄	—	71	1	no	—
328	C₈×D₄	—	71	1	no	—
329	C₈×D₄	—	71	1	no	—
330	C₈×D₄	—	71	1	no	—
331	C₈×D₄	C₂×D₇₁	1	1	yes	characteristic
332	C₂×C₄⋊C₈	—	71	1	no	—
333	C₂×C₂²⋊C₈	—	71	1	no	—
334	C₂×C₂²⋊C₈	—	71	1	no	—
335	C₂×C₄×C₈	—	71	1	no	—
336	C₄⋊C₁₆	—	71	1	no	—
337	C₄⋊C₁₆	—	71	1	no	—
338	C₄⋊C₁₆	—	71	1	no	—
339	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
340	C₂²⋊C₁₆	—	71	1	no	—
341	C₂²⋊C₁₆	—	71	1	no	—
342	C₂²⋊C₁₆	—	71	1	no	—
343	C₂²⋊C₁₆	—	71	1	no	—
344	C₂²⋊C₁₆	—	71	1	no	—
345	C₂²⋊C₁₆	—	71	1	no	—
346	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
347	C₂²⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic, complemented
348	#346	—	71	1	no	—
349	#346	—	71	1	no	—
350	#346	—	71	1	no	—
351	#346	C₂×D₇₁	1	1	yes	characteristic, complemented
352	C₂²×D₄	—	71	1	no	—
353	C₂³×C₄	—	71	1	no	—
354	C₂³×C₄	—	71	1	no	—
355	C₂²×C₈	—	71	1	no	—
356	C₂²×C₈	—	71	1	no	—
357	C₂²×C₈	—	71	1	no	—
358	C₂²×C₈	—	71	1	no	—
359	C₂²×C₈	—	71	1	no	—
360	C₂²×C₈	—	71	1	no	—
361	C₂²×C₈	—	71	1	no	—
362	C₂²×C₈	—	71	1	no	—
363	C₂²×C₈	—	71	1	no	—
364	C₂²×C₈	—	71	1	no	—
365	C₂²×C₈	—	142	2	no	—
366	C₂²×C₈	—	142	2	no	—
367	C₂²×C₈	—	142	2	no	—
368	C₂²×C₈	—	142	2	no	—
369	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
370	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
371	C₄×D₄	—	71	1	no	—
372	C₄×D₄	—	71	1	no	—
373	C₄×D₄	—	71	1	no	—
374	C₄×D₄	—	71	1	no	—
375	C₄×D₄	—	71	1	no	—
376	C₄×D₄	—	71	1	no	—
377	C₄×D₄	—	71	1	no	—
378	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	71	1	no	—
380	C₂×C₂²⋊C₄	—	71	1	no	—
381	C₂×C₂²⋊C₄	—	71	1	no	—
382	C₂×C₄²	—	71	1	no	—
383	M₃₂	—	2	2	no	—
384	M₃₂	—	142	2	no	—
385	M₃₂	—	142	2	no	—
386	M₃₂	—	142	2	no	—
387	C₂×C₁₆	—	2	2	no	—
388	C₂×C₁₆	—	71	1	no	—
389	C₂×C₁₆	—	71	4	no	—
390	C₂×C₁₆	—	71	1	no	—
391	C₂×C₁₆	—	71	1	no	—
392	C₂×C₁₆	—	71	1	no	—
393	C₂×C₁₆	—	142	2	no	—
394	C₂×C₁₆	—	142	2	no	—
395	C₂×C₁₆	—	142	2	no	—
396	C₂×C₁₆	—	142	2	no	—
397	C₂×C₁₆	—	142	2	no	—
398	C₂×C₁₆	—	142	2	no	—
399	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
400	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
401	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
402	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
403	C₄⋊C₈	—	71	1	no	—
404	C₄⋊C₈	—	71	1	no	—
405	C₄⋊C₈	—	71	1	no	—
406	C₄⋊C₈	C₄×D₇₁	1	1	yes	characteristic
407	C₂²⋊C₈	—	71	1	no	—
408	C₂²⋊C₈	—	71	1	no	—
409	C₂²⋊C₈	—	71	1	no	—
410	C₂²⋊C₈	—	71	1	no	—
411	C₂²⋊C₈	—	71	1	no	—
412	C₂²⋊C₈	—	71	1	no	—
413	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
414	C₂²⋊C₈	C₄×D₇₁	1	1	yes	characteristic
415	C₄×C₈	—	71	1	no	—
416	C₄×C₈	—	71	1	no	—
417	C₄×C₈	—	71	1	no	—
418	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
419	C₂⁴	—	71	1	no	—
420	C₂⁴	—	71	1	no	—
421	C₂×D₄	—	71	1	no	—
422	C₂×D₄	—	71	1	no	—
423	C₂×D₄	—	71	1	no	—
424	C₂×D₄	—	142	4	no	—
425	C₂×D₄	C₈×D₇₁	1	1	yes	characteristic
426	C₂²×C₄	—	71	1	no	—
427	C₂²×C₄	—	71	1	no	—
428	C₂²×C₄	—	71	1	no	—
429	C₂²×C₄	—	71	1	no	—
430	C₂²×C₄	—	71	1	no	—
431	C₂²×C₄	—	71	1	no	—
432	C₂²×C₄	—	71	1	no	—
433	C₂²×C₄	—	71	1	no	—
434	C₂²×C₄	—	71	1	no	—
435	C₂²×C₄	—	71	1	no	—
436	C₂²×C₄	—	71	1	no	—
437	C₂²×C₄	—	142	2	no	—
438	C₂²×C₄	—	142	2	no	—
439	C₂²×C₄	—	142	2	no	—
440	C₂²×C₄	—	142	2	no	—
441	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	71	1	no	—
448	C₂×C₈	—	71	2	no	—
449	C₂×C₈	—	71	2	no	—
450	C₂×C₈	—	71	1	no	—
451	C₂×C₈	—	71	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	142	2	no	—
454	C₂×C₈	—	142	2	no	—
455	C₂×C₈	—	142	2	no	—
456	C₂×C₈	—	142	2	no	—
457	C₂×C₈	—	142	2	no	—
458	C₂×C₈	—	142	2	no	—
459	C₂×C₈	—	142	2	no	—
460	C₂×C₈	—	142	1	no	—
461	C₂×C₈	—	142	1	no	—
462	C₂×C₈	—	142	1	no	—
463	C₂×C₈	—	142	1	no	—
464	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
467	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
468	C₄⋊C₄	—	71	1	no	—
469	C₄⋊C₄	—	71	1	no	—
470	C₄⋊C₄	—	71	1	no	—
471	C₄⋊C₄	C₈×D₇₁	1	1	yes	characteristic
472	C₂²⋊C₄	—	71	1	no	—
473	C₂²⋊C₄	—	71	1	no	—
474	C₂²⋊C₄	—	71	1	no	—
475	C₂²⋊C₄	—	71	1	no	—
476	C₂²⋊C₄	—	71	1	no	—
477	C₂²⋊C₄	—	71	1	no	—
478	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
479	C₂²⋊C₄	C₈×D₇₁	1	1	yes	characteristic
480	C₄²	—	71	1	no	—
481	C₄²	—	71	1	no	—
482	C₄²	—	71	1	no	—
483	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
484	C₁₆	—	2	1	no	—
485	C₁₆	—	2	1	no	—
486	C₁₆	—	2	1	no	—
487	C₁₆	—	71	2	no	—
488	C₁₆	—	142	1	no	—
489	C₁₆	—	142	1	no	—
490	C₁₆	—	142	1	no	—
491	C₁₆	D₄×D₇₁	1	2	yes	complemented
492	C₂³	—	71	1	no	—
493	C₂³	—	71	4	no	—
494	C₂³	—	71	1	no	—
495	C₂³	—	71	1	no	—
496	C₂³	—	142	2	no	—
497	C₂³	—	142	2	no	—
498	C₂³	—	142	2	no	—
499	C₂³	—	142	2	no	—
500	C₂³	—	142	2	no	—
501	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
502	C₂³	C₂×C₈×D₇₁	1	1	yes	characteristic
503	D₄	—	2	2	no	—
504	D₄	—	142	2	no	—
505	D₄	—	142	2	no	—
506	D₄	—	142	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	71	1	no	—
512	C₂×C₄	—	71	2	no	—
513	C₂×C₄	—	71	2	no	—
514	C₂×C₄	—	71	1	no	—
515	C₂×C₄	—	71	1	no	—
516	C₂×C₄	—	71	1	no	—
517	C₂×C₄	—	71	1	no	—
518	C₂×C₄	—	142	2	no	—
519	C₂×C₄	—	142	2	no	—
520	C₂×C₄	—	142	2	no	—
521	C₂×C₄	—	142	2	no	—
522	C₂×C₄	—	142	2	no	—
523	C₂×C₄	—	142	2	no	—
524	C₂×C₄	—	142	2	no	—
525	C₂×C₄	—	142	2	no	—
526	C₂×C₄	—	142	1	no	—
527	C₂×C₄	—	142	1	no	—
528	C₂×C₄	—	142	1	no	—
529	C₂×C₄	—	142	1	no	—
530	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
531	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
532	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
533	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	71	2	no	—
539	C₈	—	142	1	no	—
540	C₈	—	142	1	no	—
541	C₈	—	142	1	no	—
542	C₈	C₂×D₄×D₇₁	1	1	yes	characteristic
543	C₈	#41×D₇₁	1	1	yes	characteristic
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	284	4	no	—
550	C₂²	—	71	2	no	—
551	C₂²	—	71	2	no	—
552	C₂²	—	71	2	no	—
553	C₂²	—	71	2	no	—
554	C₂²	—	142	8	no	—
555	C₂²	—	142	1	no	—
556	C₂²	—	142	1	no	—
557	C₂²	—	142	1	no	—
558	C₂²	—	142	1	no	—
559	C₂²	—	142	1	no	—
560	C₂²	M₃₂×D₇₁	1	2	yes	complemented
561	C₂²	C₂²×C₈×D₇₁	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	71	2	no	—
567	C₄	—	142	1	no	—
568	C₄	—	142	1	no	—
569	C₄	—	142	1	no	—
570	C₄	—	142	1	no	—
571	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
572	C₄	#131×D₇₁	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	1	no	—
575	C₂	—	284	1	no	—
576	C₂	—	71	4	no	—
577	C₂	—	142	2	no	—
578	C₂	C₈×D₄×D₇₁	1	1	yes	characteristic
579	C₂	C₂×M₃₂×D₇₁	1	1	yes	characteristic
580	C₂	#504×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₇₁
commutator, socle	C₂²×C₇₁	C₂³×C₈
Fitting	C₇₁×#2168	C₂
prime radical	C₂×D₄×D₇₁	C₈
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2168	D₇₁
hypocenter	C₇₁	C₂×#2168
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₇₁	C₂	semidirect
2. C₂²×C₁₆×D₇₁	C₂	semidirect
4. #22590168	C₂	semidirect
5. #22590167	C₂	semidirect
6. #22590166	C₂	semidirect
7. #22590165	C₂	semidirect
8. #22590164	C₂	semidirect
9. #22590163	C₂	semidirect
10. #22590162	C₂	semidirect
11. C₄⋊C₁₆×D₇₁	C₂	semidirect
12. C₂²⋊C₁₆×D₇₁	C₂	semidirect
13. C₂²⋊C₁₆×D₇₁	C₂	semidirect
14. #346×D₇₁	C₂	semidirect
15. C₇₁×#2168	C₂	semidirect
19. C₂×#14556068	C₂²	semidirect
20. C₂×#14556067	C₂²	semidirect
21. C₂×#14556067	C₂²	semidirect
23. C₂²×C₇₁⋊C₁₆	C₂²	semidirect
29. C₂×C₁₆×D₇₁	C₂²	semidirect
30. C₂×C₁₆×D₇₁	C₂²	semidirect
42. C₄⋊(C₇₁⋊C₁₆)	C₂²	semidirect
43. Dic₇₁⋊C₁₆	C₂²	semidirect
44. Dic₇₁⋊C₁₆	C₂²	semidirect
45. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
46. C₂²⋊(C₇₁⋊C₁₆)	C₂²	semidirect
47. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
48. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
49. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
50. (C₂×D₇₁)⋊C₁₆	C₂²	semidirect
51. #17985775	C₂²	semidirect
52. #17985774	C₂²	semidirect
53. #17985774	C₂²	semidirect
54. C₂×M₃₂×C₇₁	C₂²	semidirect
55. C₂²×C₁₆×C₇₁	C₂²	semidirect
57. C₄⋊C₁₆×C₇₁	C₂²	semidirect
58. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
59. C₂²⋊C₁₆×C₇₁	C₂²	semidirect
60. #346×C₇₁	C₂²	semidirect
102. C₁₆×D₇₁	D₄	semidirect
181. C₇₁⋊C₁₆	C₂×D₄	semidirect
200. C₁₆×C₇₁	C₂×D₄	semidirect
208. C₂²×D₇₁	M₃₂	semidirect
258. C₂²×C₇₁	C₂×M₃₂	semidirect
269. C₂×D₇₁	C₂×M₃₂	semidirect
290. D₇₁	#2168	direct (N × H)
301. #2168	D₇₁	direct (N × H)
306. C₇₁	C₂×#2168	semidirect
314. C₂×M₃₂	C₂×D₇₁	semidirect
323. C₂²×C₁₆	C₂×D₇₁	semidirect
339. C₄⋊C₁₆	C₂×D₇₁	semidirect
346. C₂²⋊C₁₆	C₂×D₇₁	semidirect
347. C₂²⋊C₁₆	C₂×D₇₁	semidirect
351. #346	C₂×D₇₁	semidirect
491. C₁₆	D₄×D₇₁	semidirect
560. C₂²	M₃₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₇₁	2
C₂²×C₁₆×D₇₁	2
C₈×D₄×D₇₁	2
#22590168	2
#22590167	2
#22590166	2
#22590165	2
#22590164	2
#22590163	2
#22590162	2
C₄⋊C₁₆×D₇₁	2
C₂²⋊C₁₆×D₇₁	2
#346×D₇₁	2
C₇₁×#2168	2
C₂×#2168	71

Subgroups — #2168×D71 #32150604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2168×D₇₁ #32150604