Group #31907412 — subgroups

Subgroups — #31907412

Order 18176.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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	#22597274	C₂	1	1	yes	maximal, characteristic
2	#22590139	C₂	1	1	yes	maximal, characteristic
3	#22586323	C₂	1	4	yes	maximal, complemented
4	C₇₁×#2163	C₂	1	1	yes	maximal, characteristic
5	#17986556	C₄	1	1	yes	characteristic
6	#17986129	—	2	1	no	—
7	#17986129	C₂²	1	2	yes	—
8	C₈×Dic₁₄₂	—	2	1	no	—
9	C₈×Dic₁₄₂	C₄	1	2	yes	—
10	#17986025	—	2	1	no	—
11	#17986023	C₄	1	1	yes	characteristic
12	#17985954	—	2	1	no	—
13	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	2	yes	—
14	C₂²⋊(C₇₁⋊C₁₆)	—	2	1	no	—
15	C₄×C₇₁⋊C₁₆	—	2	1	no	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₁	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₁	—	2	1	no	—
19	#346×C₇₁	C₂²	1	2	yes	—
20	C₂×#11765849	—	2	1	no	—
21	#14556128	C₈	1	1	yes	characteristic
22	#14556128	C₈	1	1	yes	characteristic
23	#14556120	—	2	1	no	—
24	#14556107	—	2	1	no	—
25	#14556107	C₈	1	2	yes	—
26	C₄×Dic₁₄₂	—	2	1	no	—
27	C₄×Dic₁₄₂	C₂×C₄	1	2	yes	—
28	#14556087	—	2	1	no	—
29	C₂×C₇₁⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
31	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
32	Dic₇₁⋊C₈	—	2	2	no	—
33	Dic₇₁⋊C₈	—	2	2	no	—
34	#14556038	—	2	2	no	—
35	C₈×Dic₇₁	—	2	2	no	—
36	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₇₁	—	2	2	no	—
40	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₄₂	—	2	1	no	—
45	C₂×Dic₁₄₂	C₂×C₈	1	2	yes	—
46	#11765849	—	4	2	no	—
47	C₂×C₇₁⋊C₈	—	2	2	no	—
48	C₄⋊Dic₇₁	—	2	1	no	—
49	C₄⋊Dic₇₁	—	2	1	no	—
50	C₄⋊Dic₇₁	—	2	1	no	—
51	C₄⋊Dic₇₁	C₂×C₈	1	2	yes	—
52	Dic₇₁⋊C₄	—	2	2	no	—
53	Dic₇₁⋊C₄	—	2	2	no	—
54	C₂²⋊Dic₇₁	—	2	2	no	—
55	C₄×Dic₇₁	—	2	2	no	—
56	C₇₁⋊C₁₆	—	4	2	no	—
57	C₂²×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₄×C₇₁	M₁₆	1	1	yes	characteristic
60	C₂×C₈×C₇₁	—	2	2	no	—
61	C₂×C₈×C₇₁	—	4	1	no	—
62	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
68	C₄²×C₇₁	M₁₆	1	1	yes	characteristic
69	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
70	C₁₆×C₇₁	—	4	2	no	—
71	C₂³×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
72	C₂×C₄×C₇₁	—	2	2	no	—
73	C₂×C₄×C₇₁	—	2	1	no	—
74	C₂×C₄×C₇₁	—	2	1	no	—
75	C₂×C₄×C₇₁	—	4	1	no	—
76	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
77	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
81	C₂×C₄×C₇₁	C₂×M₁₆	1	1	yes	characteristic
82	C₂×Dic₇₁	—	2	2	no	—
83	C₂×Dic₇₁	—	2	2	no	—
84	Dic₁₄₂	—	4	2	no	—
85	Dic₁₄₂	—	4	2	no	—
86	C₈×C₇₁	—	2	1	no	—
87	C₈×C₇₁	—	2	1	no	—
88	C₈×C₇₁	—	2	1	no	—
89	C₈×C₇₁	#137	1	2	yes	—
90	C₇₁⋊C₈	—	4	2	no	—
91	C₂²×C₇₁	—	2	1	no	—
92	C₂²×C₇₁	—	2	1	no	—
93	C₂²×C₇₁	—	2	1	no	—
94	C₂²×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₄×C₇₁	—	2	1	no	—
96	C₄×C₇₁	—	2	1	no	—
97	C₄×C₇₁	—	2	1	no	—
98	C₄×C₇₁	—	2	1	no	—
99	C₄×C₇₁	#350	1	2	yes	—
100	C₄×C₇₁	#419	1	1	yes	characteristic
101	C₄×C₇₁	#421	1	1	yes	characteristic
102	Dic₇₁	—	4	2	no	—
103	Dic₇₁	—	4	2	no	—
104	#11641	—	71	1	no	maximal, Sylow
105	C₂×C₇₁	—	4	1	no	—
106	C₂×C₇₁	#1479	1	1	yes	characteristic
107	C₂×C₇₁	#2115	1	1	yes	characteristic
108	C₂×C₇₁	C₂×#350	1	1	yes	characteristic
109	#2960	—	71	1	no	—
110	#2163	D₇₁	1	1	yes	characteristic
111	#2162	—	71	1	no	—
112	#1338	—	71	4	no	—
113	C₇₁	#11641	1	1	yes	characteristic, complemented, Sylow
114	#533	—	71	1	no	—
115	#446	—	71	2	no	—
116	#446	—	142	1	no	—
117	C₈×Q₈	—	71	2	no	—
118	C₈×Q₈	—	142	1	no	—
119	#424	—	142	1	no	—
120	#423	—	71	1	no	—
121	#405	—	142	1	no	—
122	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
123	C₄⋊C₁₆	—	2	1	no	—
124	C₄⋊C₁₆	—	71	2	no	—
125	C₂²⋊C₁₆	—	2	1	no	—
126	C₂²⋊C₁₆	—	142	1	no	—
127	#346	C₂×D₇₁	1	2	yes	—
128	C₄×C₁₆	—	142	1	no	—
129	C₂×M₁₆	—	142	1	no	—
130	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
131	C₂²×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
132	C₄⋊Q₈	—	71	1	no	—
133	C₄⋊Q₈	—	71	1	no	—
134	#125	—	142	1	no	—
135	C₂²⋊Q₈	—	71	2	no	—
136	C₂²⋊Q₈	—	142	1	no	—
137	C₄×Q₈	—	71	2	no	—
138	C₄×Q₈	—	142	1	no	—
139	#117	—	142	1	no	—
140	C₂×C₄²	C₄×D₇₁	1	1	yes	characteristic
141	C₂×C₁₆	—	2	2	no	—
142	C₂×C₁₆	—	142	2	no	—
143	C₄⋊C₈	—	71	2	no	—
144	C₄⋊C₈	—	142	2	no	—
145	C₄⋊C₈	—	142	2	no	—
146	C₄⋊C₈	—	142	1	no	—
147	#97	—	142	2	no	—
148	C₄×C₈	—	142	2	no	—
149	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
150	C₄×C₈	D₂₈₄	1	1	yes	characteristic
151	C₄×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
152	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
153	C₂×Q₈	—	71	2	no	—
154	C₂×Q₈	—	142	1	no	—
155	C₂²×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
157	C₂²×C₄	#11765848	1	1	yes	characteristic
158	M₁₆	—	284	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	—	142	2	no	—
162	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
163	C₂×C₈	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
165	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
166	C₄⋊C₄	—	71	2	no	—
167	C₄⋊C₄	—	142	2	no	—
168	C₄⋊C₄	—	142	1	no	—
169	C₄⋊C₄	—	142	1	no	—
170	C₄⋊C₄	—	142	1	no	—
171	C₄⋊C₄	—	142	2	no	—
172	C₂²⋊C₄	—	142	2	no	—
173	C₄²	—	142	2	no	—
174	C₄²	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
175	C₄²	C₈×D₇₁	1	1	yes	characteristic
176	C₄²	#11765848	1	1	yes	characteristic
177	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
178	C₁₆	—	4	2	no	—
179	C₁₆	—	284	2	no	—
180	C₂³	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
181	Q₈	—	284	2	no	—
182	Q₈	—	284	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	142	2	no	—
188	C₂×C₄	—	142	2	no	—
189	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
190	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
191	C₂×C₄	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
192	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
193	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
194	C₂×C₄	C₂×#11765848	1	1	yes	characteristic
195	C₈	—	2	1	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	284	2	no	—
199	C₈	#14556161	1	2	yes	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	284	2	no	—
209	C₄	—	284	2	no	—
210	C₄	#17985784	1	2	yes	—
211	C₄	#17986009	1	1	yes	characteristic
212	C₄	#17986017	1	1	yes	characteristic
213	C₂	—	4	1	no	—
214	C₂	#22586736	1	1	yes	characteristic
215	C₂	#22589960	1	1	yes	characteristic
216	C₂	C₂×#17985784	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22597274

C₂

yes

maximal, characteristic

#22590139

C₂

yes

maximal, characteristic

#22586323

C₂

yes

maximal, complemented

C₇₁×#2163

C₂

yes

maximal, characteristic

#17986556

C₄

yes

characteristic

#17986129

—

#17986129

C₂²

yes

—

C₈×Dic₁₄₂

—

C₈×Dic₁₄₂

C₄

yes

—

#17986025

—

#17986023

C₄

yes

characteristic

#17985954

—

C₄⋊(C₇₁⋊C₁₆)

C₂²

yes

—

C₂²⋊(C₇₁⋊C₁₆)

—

C₄×C₇₁⋊C₁₆

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

—

C₂²⋊C₁₆×C₇₁

—

#346×C₇₁

C₂²

yes

—

C₂×#11765849

—

#14556128

C₈

yes

characteristic

#14556128

C₈

yes

—

—

C₈

yes

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

C₂×C₄

yes

—

#14556087

—

C₂×C₇₁⋊C₁₆

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

—

Dic₇₁⋊C₈

—

Dic₇₁⋊C₈

—

#14556038

—

C₈×Dic₇₁

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

D₄

yes

characteristic

C₄×C₈×C₇₁

C₂³

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

C₂×C₈

yes

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

C₂×C₈

yes

—

Dic₇₁⋊C₄

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂²×C₄×C₇₁

M₁₆

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄²×C₇₁

C₂²⋊C₄

yes

characteristic

C₄²×C₇₁

C₂×C₈

yes

characteristic

C₄²×C₇₁

M₁₆

yes

characteristic

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂³×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×M₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#137

yes

—

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#350

yes

—

100

C₄×C₇₁

#419

yes

characteristic

101

C₄×C₇₁

#421

yes

characteristic

102

Dic₇₁

—

103

Dic₇₁

—

104

#11641

—

maximal, Sylow

105

C₂×C₇₁

—

106

C₂×C₇₁

#1479

yes

characteristic

107

C₂×C₇₁

#2115

yes

characteristic

108

C₂×C₇₁

C₂×#350

yes

characteristic

109

#2960

—

110

#2163

D₇₁

yes

characteristic

111

#2162

—

112

#1338

—

113

C₇₁

#11641

yes

characteristic, complemented, Sylow

114

#533

—

115

#446

—

116

#446

—

142

—

117

C₈×Q₈

—

118

C₈×Q₈

—

142

—

119

#424

—

142

—

120

#423

—

121

#405

—

142

—

122

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

125

C₂²⋊C₁₆

—

126

C₂²⋊C₁₆

—

142

—

127

#346

C₂×D₇₁

yes

—

128

C₄×C₁₆

—

142

—

129

C₂×M₁₆

—

142

—

130

C₂²×C₈

D₂₈₄

yes

characteristic

131

C₂²×C₈

C₂²⋊D₇₁

yes

characteristic

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

142

—

135

C₂²⋊Q₈

—

136

C₂²⋊Q₈

—

142

—

137

C₄×Q₈

—

138

C₄×Q₈

—

142

—

139

#117

—

142

—

140

C₂×C₄²

C₄×D₇₁

yes

characteristic

141

C₂×C₁₆

—

142

C₂×C₁₆

—

142

—

143

C₄⋊C₈

—

144

C₄⋊C₈

—

142

—

145

C₄⋊C₈

—

142

—

146

C₄⋊C₈

—

142

—

147

#97

—

142

—

148

C₄×C₈

—

142

—

149

C₄×C₈

C₄×D₇₁

yes

characteristic

150

C₄×C₈

D₂₈₄

yes

characteristic

151

C₄×C₈

C₂²⋊D₇₁

yes

characteristic

152

C₄×C₈

C₂²×D₇₁

yes

characteristic

153

C₂×Q₈

—

154

C₂×Q₈

—

142

—

155

C₂²×C₄

(C₂×D₇₁)⋊C₄

yes

characteristic

156

C₂²×C₄

C₈×D₇₁

yes

characteristic

157

C₂²×C₄

#11765848

yes

characteristic

158

M₁₆

—

284

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

142

—

162

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

163

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

characteristic

164

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

165

C₂×C₈

C₂×D₂₈₄

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

142

—

168

C₄⋊C₄

—

142

—

169

C₄⋊C₄

—

142

—

170

C₄⋊C₄

—

142

—

171

C₄⋊C₄

—

142

—

172

C₂²⋊C₄

—

142

—

173

C₄²

—

142

—

174

C₄²

(C₂×D₇₁)⋊C₄

yes

characteristic

175

C₄²

C₈×D₇₁

yes

characteristic

176

C₄²

#11765848

yes

characteristic

177

C₄²

C₂×C₄×D₇₁

yes

characteristic

178

C₁₆

—

179

C₁₆

—

284

—

180

C₂³

(C₂×D₇₁)⋊C₈

yes

characteristic

181

Q₈

—

284

—

182

Q₈

—

284

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

142

—

188

C₂×C₄

—

142

—

189

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

190

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

191

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

characteristic

192

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

193

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

194

C₂×C₄

C₂×#11765848

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

—

198

C₈

—

284

—

199

C₈

#14556161

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

284

—

209

C₄

—

284

—

210

C₄

#17985784

yes

—

211

C₄

#17986009

yes

characteristic

212

C₄

#17986017

yes

characteristic

213

C₂

—

214

C₂

#22586736

yes

characteristic

215

C₂

#22589960

yes

characteristic

216

C₂

C₂×#17985784

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄
commutator	C₂×C₄×C₇₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#2163	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₇₁	C₂²⋊C₈
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#2163	D₇₁
hypocenter	C₇₁	#11641
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

subgroup

G/H

center

C₂×C₄

C₂×(C₂×D₇₁)⋊C₄

commutator

C₂×C₄×C₇₁

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#2163

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₈

prime radical

C₂³×C₇₁

C₂²⋊C₈

cosocle

C₄×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2163

N	H ≅ G/N	type
3. #22586323	C₂	semidirect
113. C₇₁	#11641	semidirect

H ≅ G/N

type

3. #22586323

C₂

semidirect

113. C₇₁

#11641

semidirect

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

subgroup	index
#22597274	2
#22590139	2
#22586323	2
C₇₁×#2163	2
#11641	71

subgroup

index

C₇₁×#2163

Subgroups — #31907412

Conjugacy classes of subgroups

Complements

Maximal subgroups