Group #31897363 — subgroups

Subgroups — #31897363

Order 18176.

454 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22589318	C₂	1	2	yes	maximal
2	C₄×#14556038	C₂	1	1	yes	maximal, characteristic
3	#22587096	C₂	1	1	yes	maximal, characteristic
4	#22586795	C₂	1	2	yes	maximal
5	C₇₁×#3170	C₂	1	1	yes	maximal, characteristic
6	#17986023	C₂²	1	2	yes	—
7	C₂×#14556038	—	2	2	no	—
8	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
9	C₄²×Dic₇₁	C₂²	1	1	yes	characteristic
10	#17985758	—	2	4	no	—
11	#17985750	—	2	2	no	—
12	Q₈⋊(C₇₁⋊C₈)	—	2	4	no	—
13	#533×C₇₁	C₂²	1	2	yes	—
14	#500×C₇₁	C₄	1	1	yes	characteristic, complemented
15	#494×C₇₁	C₄	1	1	yes	characteristic, complemented
16	#487×C₇₁	C₄	1	2	yes	complemented
17	#467×C₇₁	—	2	2	no	—
18	C₄×Q₁₆×C₇₁	—	2	2	no	—
19	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#11765849	—	2	2	no	—
21	C₂²×C₇₁⋊C₈	—	2	1	no	—
22	C₂×C₄×Dic₇₁	—	2	1	no	—
23	C₂×C₄×Dic₇₁	—	2	1	no	—
24	C₂×C₄×Dic₇₁	D₄	1	2	yes	—
25	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
26	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
27	#14556038	—	2	8	no	—
28	C₄×C₇₁⋊C₈	—	2	1	no	—
29	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
30	C₂×Q₁₆×C₇₁	—	2	2	no	—
31	C₂²×C₈×C₇₁	D₄	1	2	yes	—
32	C₄⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
33	C₄⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
34	#125×C₇₁	—	2	2	no	—
35	C₂²⋊Q₈×C₇₁	—	2	2	no	—
36	C₂²⋊Q₈×C₇₁	—	2	2	no	—
37	C₄×Q₈×C₇₁	—	2	2	no	—
38	C₄×Q₈×C₇₁	—	2	2	no	—
39	#117×C₇₁	—	2	2	no	—
40	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
41	#107×C₇₁	—	2	2	no	—
42	#103×C₇₁	—	2	4	no	—
43	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₇₁	D₄	1	2	yes	—
46	C₂²×Dic₇₁	—	2	2	no	—
47	#11765849	—	4	4	no	—
48	C₂×C₇₁⋊C₈	—	2	4	no	—
49	C₂×C₇₁⋊C₈	—	2	2	no	—
50	C₂×C₇₁⋊C₈	—	4	2	no	—
51	C₄×Dic₇₁	—	2	4	no	—
52	C₄×Dic₇₁	—	2	4	no	—
53	C₄×Dic₇₁	—	4	2	no	—
54	C₂×Q₈×C₇₁	—	2	2	no	—
55	C₂×Q₈×C₇₁	—	2	2	no	—
56	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
59	Q₁₆×C₇₁	—	4	4	no	—
60	C₂×C₈×C₇₁	—	2	4	no	—
61	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
63	C₄⋊C₄×C₇₁	—	2	2	no	—
64	C₄⋊C₄×C₇₁	—	2	2	no	—
65	C₄⋊C₄×C₇₁	—	2	2	no	—
66	C₄⋊C₄×C₇₁	—	2	2	no	—
67	C₄⋊C₄×C₇₁	—	4	2	no	—
68	C₄⋊C₄×C₇₁	—	4	2	no	—
69	C₂²⋊C₄×C₇₁	—	4	2	no	—
70	C₄²×C₇₁	—	4	2	no	—
71	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₁	#41	1	1	yes	characteristic
75	C₂³×C₇₁	#121	1	1	yes	characteristic
76	Q₈×C₇₁	—	4	4	no	—
77	Q₈×C₇₁	—	4	4	no	—
78	C₂×C₄×C₇₁	—	2	2	no	—
79	C₂×C₄×C₇₁	—	2	2	no	—
80	C₂×C₄×C₇₁	—	4	2	no	—
81	C₂×C₄×C₇₁	—	4	2	no	—
82	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#137	1	4	yes	—
89	C₂×Dic₇₁	—	2	4	no	—
90	C₂×Dic₇₁	—	4	2	no	—
91	C₂×Dic₇₁	—	4	2	no	—
92	C₈×C₇₁	—	2	2	no	—
93	C₈×C₇₁	#104	1	4	yes	—
94	C₇₁⋊C₈	—	2	4	no	—
95	C₇₁⋊C₈	—	8	2	no	—
96	C₂²×C₇₁	—	2	1	no	—
97	C₂²×C₇₁	—	2	1	no	—
98	C₂²×C₇₁	#390	1	1	yes	characteristic
99	C₂²×C₇₁	#470	1	2	yes	—
100	C₄×C₇₁	—	2	1	no	—
101	C₄×C₇₁	—	2	1	no	—
102	C₄×C₇₁	—	8	2	no	—
103	C₄×C₇₁	—	8	2	no	—
104	C₄×C₇₁	C₂×#104	1	2	yes	—
105	C₄×C₇₁	#441	1	2	yes	—
106	C₄×C₇₁	#444	1	2	yes	—
107	C₄×C₇₁	#497	1	2	yes	—
108	Dic₇₁	—	4	4	no	—
109	#9850	—	71	1	no	maximal, Sylow
110	C₂×C₇₁	—	2	2	no	—
111	C₂×C₇₁	#1962	1	1	yes	characteristic
112	C₂×C₇₁	#1971	1	1	yes	characteristic
113	C₂×C₇₁	#1975	1	1	yes	characteristic
114	#3170	D₇₁	1	1	yes	characteristic
115	#1994	—	71	2	no	—
116	C₄×#97	—	71	1	no	—
117	#1566	—	71	1	no	—
118	#1493	—	71	2	no	—
119	C₇₁	#9850	1	1	yes	characteristic, complemented, Sylow
120	#533	C₂×D₇₁	1	2	yes	—
121	#500	Dic₇₁	1	1	yes	characteristic, complemented
122	#494	Dic₇₁	1	1	yes	characteristic, complemented
123	#487	Dic₇₁	1	2	yes	complemented
124	#467	—	2	2	no	—
125	C₄×Q₁₆	—	2	2	no	—
126	#423	—	71	2	no	—
127	C₂×#97	—	142	2	no	—
128	C₂×C₄×C₈	—	71	1	no	—
129	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
130	C₄³	—	71	1	no	—
131	#339	—	142	4	no	—
132	#334	—	142	2	no	—
133	Q₈⋊C₈	—	142	4	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×M₁₆	—	142	2	no	—
136	C₂²×C₈	—	142	1	no	—
137	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
138	C₄⋊Q₈	C₂×Dic₇₁	1	2	yes	—
139	C₄⋊Q₈	C₂×Dic₇₁	1	2	yes	—
140	#125	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₂²⋊Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	#117	—	2	2	no	—
146	C₂×C₄²	—	71	2	no	—
147	C₂×C₄²	—	142	1	no	—
148	C₂×C₄²	—	142	1	no	—
149	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
150	#107	—	2	2	no	—
151	C₄⋊C₈	—	142	2	no	—
152	C₄⋊C₈	—	142	2	no	—
153	#103	—	2	4	no	—
154	#97	—	142	8	no	—
155	C₄×C₈	—	71	2	no	—
156	C₄×C₈	—	142	1	no	—
157	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
158	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂²×C₄	—	142	2	no	—
163	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
165	C₂²×C₄	#11765864	1	1	yes	characteristic
166	Q₁₆	—	4	4	no	—
167	M₁₆	—	284	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	—	284	2	no	—
170	C₂×C₈	—	142	4	no	—
171	C₂×C₈	—	142	2	no	—
172	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
173	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	2	no	—
181	C₄²	—	4	2	no	—
182	C₄²	—	284	2	no	—
183	C₄²	—	142	4	no	—
184	C₄²	—	142	4	no	—
185	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
186	C₄²	D₄×D₇₁	1	1	yes	characteristic
187	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
188	C₄²	#11765864	1	1	yes	characteristic
189	C₂³	#14556099	1	1	yes	characteristic
190	Q₈	—	4	4	no	—
191	Q₈	—	4	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	284	2	no	—
197	C₂×C₄	—	284	2	no	—
198	C₂×C₄	—	142	4	no	—
199	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
200	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
201	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
202	C₂×C₄	#14556099	1	1	yes	characteristic
203	C₂×C₄	#14556115	1	1	yes	characteristic
204	C₂×C₄	#14556124	1	1	yes	characteristic
205	C₂×C₄	#14556160	1	4	yes	—
206	C₈	—	2	2	no	—
207	C₈	—	568	2	no	—
208	C₈	—	142	4	no	—
209	C₈	#14556055	1	4	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	#17985902	1	1	yes	characteristic
213	C₂²	#17986254	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	8	2	no	—
217	C₄	—	8	2	no	—
218	C₄	—	284	4	no	—
219	C₄	C₂×#14556055	1	2	yes	—
220	C₄	#17986106	1	2	yes	—
221	C₄	#17986121	1	2	yes	—
222	C₄	#17986392	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	#22589169	1	1	yes	characteristic
225	C₂	#22589212	1	1	yes	characteristic
226	C₂	#22589234	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589318

C₂

yes

maximal

C₄×#14556038

C₂

yes

maximal, characteristic

#22587096

C₂

yes

maximal, characteristic

#22586795

C₂

yes

maximal

C₇₁×#3170

C₂

yes

maximal, characteristic

#17986023

C₂²

yes

—

C₂×#14556038

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

characteristic

C₄²×Dic₇₁

C₂²

yes

characteristic

#17985758

—

#17985750

—

Q₈⋊(C₇₁⋊C₈)

—

#533×C₇₁

C₂²

yes

—

#500×C₇₁

C₄

yes

characteristic, complemented

#494×C₇₁

C₄

yes

characteristic, complemented

#487×C₇₁

C₄

yes

complemented

#467×C₇₁

—

C₄×Q₁₆×C₇₁

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×#11765849

—

C₂²×C₇₁⋊C₈

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

—

C₂×C₄×Dic₇₁

D₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

#14556038

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂×Q₁₆×C₇₁

—

C₂²×C₈×C₇₁

D₄

yes

—

C₄⋊Q₈×C₇₁

C₂×C₄

yes

—

C₄⋊Q₈×C₇₁

C₂×C₄

yes

—

#125×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

#117×C₇₁

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

#107×C₇₁

—

#103×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

—

C₂²×Dic₇₁

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

#41

yes

characteristic

Q₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#104

yes

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#390

yes

characteristic

C₂²×C₇₁

#470

yes

—

100

C₄×C₇₁

—

101

C₄×C₇₁

—

102

C₄×C₇₁

—

103

C₄×C₇₁

—

104

C₄×C₇₁

C₂×#104

yes

—

105

C₄×C₇₁

#441

yes

—

106

C₄×C₇₁

#444

yes

—

107

C₄×C₇₁

#497

yes

—

108

Dic₇₁

—

109

#9850

—

maximal, Sylow

110

C₂×C₇₁

—

111

C₂×C₇₁

#1962

yes

characteristic

112

C₂×C₇₁

#1971

yes

characteristic

113

C₂×C₇₁

#1975

yes

characteristic

114

#3170

D₇₁

yes

characteristic

115

#1994

—

116

C₄×#97

—

117

#1566

—

118

#1493

—

119

C₇₁

#9850

yes

characteristic, complemented, Sylow

120

#533

C₂×D₇₁

yes

—

121

#500

Dic₇₁

yes

characteristic, complemented

122

#494

Dic₇₁

yes

characteristic, complemented

123

#487

Dic₇₁

yes

complemented

124

#467

—

125

C₄×Q₁₆

—

126

#423

—

127

C₂×#97

—

142

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

130

C₄³

—

131

#339

—

142

—

132

#334

—

142

—

133

Q₈⋊C₈

—

142

—

134

C₂×Q₁₆

—

135

C₂×M₁₆

—

142

—

136

C₂²×C₈

—

142

—

137

C₂²×C₈

C₂²⋊D₇₁

yes

—

138

C₄⋊Q₈

C₂×Dic₇₁

yes

—

139

C₄⋊Q₈

C₂×Dic₇₁

yes

—

140

#125

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

#117

—

146

C₂×C₄²

—

147

C₂×C₄²

—

142

—

148

C₂×C₄²

—

142

—

149

C₂×C₄²

C₂²×D₇₁

yes

characteristic

150

#107

—

151

C₄⋊C₈

—

142

—

152

C₄⋊C₈

—

142

—

153

#103

—

154

#97

—

142

—

155

C₄×C₈

—

156

C₄×C₈

—

142

—

157

C₄×C₈

C₂×Dic₇₁

yes

characteristic

158

C₄×C₈

C₂×Dic₇₁

yes

characteristic

159

C₄×C₈

C₂²⋊D₇₁

yes

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂²×C₄

—

142

—

163

C₂²×C₄

D₄×D₇₁

yes

characteristic

164

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

165

C₂²×C₄

#11765864

yes

characteristic

166

Q₁₆

—

167

M₁₆

—

284

—

168

C₂×C₈

—

169

C₂×C₈

—

284

—

170

C₂×C₈

—

142

—

171

C₂×C₈

—

142

—

172

C₂×C₈

C₂²⋊Dic₇₁

yes

—

173

C₂×C₈

C₂²⋊Dic₇₁

yes

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

—

182

C₄²

—

284

—

183

C₄²

—

142

—

184

C₄²

—

142

—

185

C₄²

C₂²×Dic₇₁

yes

characteristic

186

C₄²

D₄×D₇₁

yes

characteristic

187

C₄²

C₂×C₂²⋊D₇₁

yes

characteristic

188

C₄²

#11765864

yes

characteristic

189

C₂³

#14556099

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

284

—

197

C₂×C₄

—

284

—

198

C₂×C₄

—

142

—

199

C₂×C₄

C₂×C₂²⋊Dic₇₁

yes

characteristic

200

C₂×C₄

D₄×Dic₇₁

yes

characteristic

201

C₂×C₄

D₄×Dic₇₁

yes

characteristic

202

C₂×C₄

#14556099

yes

characteristic

203

C₂×C₄

#14556115

yes

characteristic

204

C₂×C₄

#14556124

yes

characteristic

205

C₂×C₄

#14556160

yes

—

206

C₈

—

207

C₈

—

568

—

208

C₈

—

142

—

209

C₈

#14556055

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

#17985902

yes

characteristic

213

C₂²

#17986254

yes

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

284

—

219

C₄

C₂×#14556055

yes

—

220

C₄

#17986106

yes

—

221

C₄

#17986121

yes

—

222

C₄

#17986392

yes

—

223

C₂

—

224

C₂

#22589169

yes

characteristic

225

C₂

#22589212

yes

characteristic

226

C₂

#22589234

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556124
commutator	C₄²×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#3170	C₂
socle	C₂²×C₇₁	#390
prime radical	C₂³×C₇₁	#121
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#3170	D₇₁
hypocenter	C₇₁	#9850
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#14556124

commutator

C₄²×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#3170

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. #500×C₇₁	C₄	semidirect
15. #494×C₇₁	C₄	semidirect
16. #487×C₇₁	C₄	semidirect
119. C₇₁	#9850	semidirect
121. #500	Dic₇₁	semidirect
122. #494	Dic₇₁	semidirect
123. #487	Dic₇₁	semidirect

H ≅ G/N

type

14. #500×C₇₁

C₄

semidirect

15. #494×C₇₁

C₄

semidirect

16. #487×C₇₁

C₄

semidirect

119. C₇₁

#9850

semidirect

121. #500

Dic₇₁

semidirect

122. #494

Dic₇₁

semidirect

123. #487

Dic₇₁

semidirect

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

subgroup	index
#22589318	2
C₄×#14556038	2
#22587096	2
#22586795	2
C₇₁×#3170	2
#9850	71

subgroup

index

C₇₁×#3170

Subgroups — #31897363

Conjugacy classes of subgroups

Complements

Maximal subgroups