Group #31909262 — subgroups

Subgroups — #31909262

Order 18176.

232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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	#22590242	C₂	1	1	yes	maximal, characteristic, complemented
2	#22590159	C₂	1	1	yes	maximal, characteristic
3	C₈×#11765854	C₂	1	1	yes	maximal, characteristic
4	#22586318	C₂	1	1	yes	maximal, characteristic, complemented
5	#22586294	C₂	1	1	yes	maximal, characteristic
6	#22586258	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1370	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₆×D₇₁	—	2	1	no	—
9	C₈×Dic₁₄₂	C₂²	1	1	yes	characteristic
10	C₄×#11765854	C₄	1	1	yes	characteristic
11	C₈×D₂₈₄	C₂²	1	1	yes	characteristic
12	Dic₇₁⋊C₁₆	—	2	1	no	—
13	(C₂×D₇₁)⋊C₁₆	—	2	1	no	—
14	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₄×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₁₆×Dic₇₁	—	2	1	no	—
17	#17985750	C₄	1	1	yes	characteristic
18	#17985731	C₄	1	1	yes	characteristic
19	#17985728	C₄	1	1	yes	characteristic
20	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
21	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
22	C₈²×C₇₁	C₂²	1	1	yes	characteristic
23	C₂×#11765854	C₈	1	1	yes	characteristic
24	C₂×C₈×D₇₁	—	2	1	no	—
25	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
26	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
27	C₂×C₇₁⋊C₁₆	—	2	1	no	—
28	C₂×C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
29	C₂×C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
30	C₁₆×D₇₁	—	4	2	no	—
31	#14556060	C₈	1	1	yes	characteristic
32	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
33	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
34	Dic₇₁⋊C₈	—	2	1	no	—
35	#14556053	C₈	1	1	yes	characteristic
36	#14556050	C₈	1	1	yes	characteristic
37	(C₂×D₇₁)⋊C₈	—	2	1	no	—
38	C₈×Dic₇₁	—	2	1	no	—
39	C₂×C₁₆×C₇₁	—	2	1	no	—
40	C₂×C₁₆×C₇₁	—	2	1	no	—
41	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×Dic₁₄₂	C₂×C₈	1	1	yes	characteristic
45	C₂×D₂₈₄	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×D₇₁	—	2	1	no	—
47	#11765854	C₁₆	1	4	yes	complemented
48	C₂×C₇₁⋊C₈	—	2	1	no	—
49	C₂×C₇₁⋊C₈	—	2	1	no	—
50	C₈×D₇₁	—	4	1	no	—
51	C₈×D₇₁	—	4	1	no	—
52	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
53	C₄⋊Dic₇₁	C₂×C₈	1	1	yes	characteristic
54	Dic₇₁⋊C₄	—	2	1	no	—
55	(C₂×D₇₁)⋊C₄	—	2	1	no	—
56	C₄×Dic₇₁	—	2	1	no	—
57	C₇₁⋊C₁₆	—	2	1	no	—
58	C₇₁⋊C₁₆	—	2	1	no	—
59	C₇₁⋊C₁₆	—	4	1	no	—
60	C₂×C₈×C₇₁	—	2	1	no	—
61	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
62	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
63	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
65	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
66	C₁₆×C₇₁	—	4	1	no	—
67	C₁₆×C₇₁	—	4	1	no	—
68	C₂²×D₇₁	—	2	1	no	—
69	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
70	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₇₁	#131	1	1	yes	characteristic
72	C₂×Dic₇₁	—	2	1	no	—
73	C₂×Dic₇₁	—	2	1	no	—
74	C₂×Dic₇₁	—	2	1	no	—
75	D₂₈₄	—	2	1	no	—
76	D₂₈₄	C₂×C₁₆	1	2	yes	—
77	C₄×D₇₁	—	4	1	no	—
78	C₄×D₇₁	—	4	1	no	—
79	Dic₁₄₂	—	2	1	no	—
80	Dic₁₄₂	C₂×C₁₆	1	2	yes	complemented
81	C₈×C₇₁	—	2	1	no	—
82	C₈×C₇₁	—	2	1	no	—
83	C₈×C₇₁	—	4	1	no	—
84	C₈×C₇₁	C₂×C₁₆	1	2	yes	complemented
85	C₈×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₈×C₇₁	#137	1	1	yes	characteristic
87	C₇₁⋊C₈	—	4	1	no	—
88	C₇₁⋊C₈	—	4	1	no	—
89	C₂²×C₇₁	C₈×D₄	1	1	yes	characteristic
90	C₂×D₇₁	—	2	2	no	—
91	C₂×D₇₁	—	4	1	no	—
92	C₂×D₇₁	—	4	1	no	—
93	C₄×C₇₁	—	2	1	no	—
94	C₄×C₇₁	#440	1	1	yes	characteristic
95	C₄×C₇₁	#444	1	1	yes	characteristic
96	C₄×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
97	C₄×C₇₁	#504	1	1	yes	characteristic
98	Dic₇₁	—	2	2	no	—
99	Dic₇₁	—	4	1	no	—
100	Dic₇₁	—	4	1	no	—
101	SD₁₆⋊C₁₆	—	71	1	no	maximal, Sylow
102	C₂×C₇₁	SD₁₆⋊C₈	1	1	yes	characteristic
103	C₂×C₇₁	D₄×C₁₆	1	1	yes	characteristic
104	C₂×C₇₁	#2171	1	1	yes	characteristic
105	D₇₁	—	4	2	no	—
106	Q₈×C₁₆	—	71	1	no	—
107	D₄×C₁₆	—	71	1	no	—
108	C₈×SD₁₆	—	71	1	no	—
109	#1370	D₇₁	1	1	yes	characteristic, complemented
110	Q₈⋊C₁₆	—	71	1	no	—
111	D₄⋊C₁₆	—	71	1	no	—
112	#1312	—	71	1	no	—
113	C₇₁	SD₁₆⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
114	C₂²×C₁₆	—	142	1	no	—
115	C₈×Q₈	—	71	1	no	—
116	C₄×SD₁₆	—	71	1	no	—
117	C₈×D₄	—	71	1	no	—
118	C₄⋊C₁₆	—	142	1	no	—
119	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
120	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
121	C₂²⋊C₁₆	—	142	1	no	—
122	C₄×C₁₆	—	71	1	no	—
123	C₄×C₁₆	—	71	1	no	—
124	C₄×C₁₆	—	142	1	no	—
125	#334	—	71	1	no	—
126	Q₈⋊C₈	—	71	1	no	—
127	D₄⋊C₈	—	71	1	no	—
128	C₈²	C₂×D₇₁	1	1	yes	characteristic
129	C₂×SD₁₆	—	71	1	no	—
130	C₂²×C₈	—	142	1	no	—
131	C₄×Q₈	—	71	1	no	—
132	C₄×D₄	—	71	1	no	—
133	C₂×C₁₆	—	2	1	no	—
134	C₂×C₁₆	—	2	1	no	—
135	C₂×C₁₆	—	284	2	no	—
136	C₂×C₁₆	—	71	1	no	—
137	C₂×C₁₆	—	71	1	no	—
138	C₂×C₁₆	—	142	1	no	—
139	#106	—	71	1	no	—
140	C₄⋊C₈	—	71	1	no	—
141	C₄⋊C₈	—	71	1	no	—
142	C₄⋊C₈	—	142	1	no	—
143	#103	—	71	1	no	—
144	#102	—	71	1	no	—
145	C₂²⋊C₈	—	142	1	no	—
146	C₄×C₈	—	142	1	no	—
147	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
148	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
149	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
150	C₂×Q₈	—	71	1	no	—
151	C₂×D₄	—	71	1	no	—
152	C₂²×C₄	—	142	1	no	—
153	SD₁₆	—	71	4	no	—
154	C₂×C₈	—	2	1	no	—
155	C₂×C₈	—	284	1	no	—
156	C₂×C₈	—	284	1	no	—
157	C₂×C₈	—	142	1	no	—
158	C₂×C₈	—	142	1	no	—
159	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
160	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
161	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
162	C₂×C₈	#11765866	1	1	yes	characteristic
163	C₄⋊C₄	—	71	1	no	—
164	C₄⋊C₄	—	71	1	no	—
165	C₄⋊C₄	—	142	1	no	—
166	C₂²⋊C₄	—	142	1	no	—
167	C₄²	—	142	1	no	—
168	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
169	C₁₆	—	4	1	no	—
170	C₁₆	—	4	1	no	—
171	C₁₆	—	284	1	no	—
172	C₁₆	—	142	1	no	—
173	C₁₆	—	142	1	no	—
174	C₂³	—	142	1	no	—
175	Q₈	—	71	2	no	—
176	Q₈	—	142	1	no	—
177	D₄	—	71	2	no	—
178	D₄	—	142	1	no	—
179	C₂×C₄	—	284	1	no	—
180	C₂×C₄	—	284	1	no	—
181	C₂×C₄	—	142	1	no	—
182	C₂×C₄	—	142	1	no	—
183	C₂×C₄	—	142	1	no	—
184	C₂×C₄	#14556090	1	1	yes	characteristic
185	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
186	C₂×C₄	#14556136	1	1	yes	characteristic
187	C₈	—	2	1	no	—
188	C₈	—	2	1	no	—
189	C₈	—	4	1	no	—
190	C₈	—	284	1	no	—
191	C₈	—	284	1	no	—
192	C₈	C₁₆×D₇₁	1	2	yes	complemented
193	C₈	#14556152	1	1	yes	characteristic
194	C₈	#14556160	1	1	yes	characteristic
195	C₂²	—	284	1	no	—
196	C₂²	—	284	1	no	—
197	C₂²	—	142	2	no	—
198	C₂²	#17986064	1	1	yes	characteristic
199	C₄	—	2	1	no	—
200	C₄	—	284	1	no	—
201	C₄	—	284	1	no	—
202	C₄	—	142	2	no	—
203	C₄	#17986098	1	1	yes	characteristic
204	C₄	#17986120	1	1	yes	characteristic
205	C₄	C₂×C₁₆×D₇₁	1	1	yes	characteristic
206	C₄	#17986417	1	1	yes	characteristic
207	C₂	—	284	2	no	—
208	C₂	#22587151	1	1	yes	characteristic
209	C₂	#22590159	1	1	yes	characteristic
210	C₂	#22590181	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22590242

C₂

yes

maximal, characteristic, complemented

#22590159

C₂

yes

maximal, characteristic

C₈×#11765854

C₂

yes

maximal, characteristic

#22586318

C₂

yes

maximal, characteristic, complemented

#22586294

C₂

yes

maximal, characteristic

#22586258

C₂

yes

maximal, characteristic, complemented

C₇₁×#1370

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₇₁

—

C₈×Dic₁₄₂

C₂²

yes

characteristic

C₄×#11765854

C₄

yes

characteristic

C₈×D₂₈₄

C₂²

yes

characteristic

Dic₇₁⋊C₁₆

—

(C₂×D₇₁)⋊C₁₆

—

C₄×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₄×C₇₁⋊C₁₆

C₂²

yes

characteristic

C₁₆×Dic₇₁

—

#17985750

C₄

yes

characteristic

#17985731

C₄

yes

characteristic

#17985728

C₄

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

C₈²×C₇₁

C₂²

yes

characteristic

C₂×#11765854

C₈

yes

characteristic

C₂×C₈×D₇₁

—

C₄×Dic₁₄₂

C₂×C₄

yes

characteristic

C₄×D₂₈₄

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

D₄

yes

characteristic

C₂×C₇₁⋊C₁₆

D₄

yes

characteristic

C₁₆×D₇₁

—

#14556060

C₈

yes

characteristic

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

characteristic

C₄⋊(C₇₁⋊C₈)

C₂×C₄

yes

characteristic

Dic₇₁⋊C₈

—

#14556053

C₈

yes

characteristic

#14556050

C₈

yes

characteristic

(C₂×D₇₁)⋊C₈

—

C₈×Dic₇₁

—

C₂×C₁₆×C₇₁

—

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂×C₄

yes

characteristic

C₄×C₈×C₇₁

C₂³

yes

characteristic

C₂×Dic₁₄₂

C₂×C₈

yes

characteristic

C₂×D₂₈₄

C₂×C₈

yes

characteristic

C₂×C₄×D₇₁

—

#11765854

C₁₆

yes

complemented

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

C₂×C₈

yes

characteristic

C₄⋊Dic₇₁

C₂×C₈

yes

characteristic

Dic₇₁⋊C₄

—

(C₂×D₇₁)⋊C₄

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

#41

yes

characteristic

C₄²×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

—

C₂²×D₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

#131

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

C₂×C₁₆

yes

—

C₄×D₇₁

—

C₄×D₇₁

—

Dic₁₄₂

—

Dic₁₄₂

C₂×C₁₆

yes

complemented

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

C₂×C₁₆

yes

C₈×C₇₁

yes

C₈×C₇₁

yes

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₂²×C₇₁

C₈×D₄

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₂²×C₁₆

yes

characteristic

C₄×C₇₁

#504

yes

characteristic

Dic₇₁

—

Dic₇₁

—

100

Dic₇₁

—

101

SD₁₆⋊C₁₆

—

maximal, Sylow

102

C₂×C₇₁

SD₁₆⋊C₈

yes

characteristic

103

C₂×C₇₁

D₄×C₁₆

yes

characteristic

104

C₂×C₇₁

#2171

yes

characteristic

105

D₇₁

—

106

Q₈×C₁₆

—

107

D₄×C₁₆

—

108

C₈×SD₁₆

—

109

#1370

D₇₁

yes

characteristic, complemented

110

Q₈⋊C₁₆

—

111

D₄⋊C₁₆

—

112

#1312

—

113

C₇₁

SD₁₆⋊C₁₆

yes

characteristic, complemented, Sylow

114

C₂²×C₁₆

—

142

—

115

C₈×Q₈

—

116

C₄×SD₁₆

—

117

C₈×D₄

—

118

C₄⋊C₁₆

—

142

—

119

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

120

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

121

C₂²⋊C₁₆

—

142

—

122

C₄×C₁₆

—

123

C₄×C₁₆

—

124

C₄×C₁₆

—

142

—

125

#334

—

126

Q₈⋊C₈

—

127

D₄⋊C₈

—

128

C₈²

C₂×D₇₁

yes

characteristic

129

C₂×SD₁₆

—

130

C₂²×C₈

—

142

—

131

C₄×Q₈

—

132

C₄×D₄

—

133

C₂×C₁₆

—

134

C₂×C₁₆

—

135

C₂×C₁₆

—

284

—

136

C₂×C₁₆

—

137

C₂×C₁₆

—

138

C₂×C₁₆

—

142

—

139

#106

—

140

C₄⋊C₈

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

142

—

143

#103

—

144

#102

—

145

C₂²⋊C₈

—

142

—

146

C₄×C₈

—

142

—

147

C₄×C₈

C₄×D₇₁

yes

characteristic

148

C₄×C₈

C₄×D₇₁

yes

characteristic

149

C₄×C₈

C₂²×D₇₁

yes

characteristic

150

C₂×Q₈

—

151

C₂×D₄

—

152

C₂²×C₄

—

142

—

153

SD₁₆

—

154

C₂×C₈

—

155

C₂×C₈

—

284

—

156

C₂×C₈

—

284

—

157

C₂×C₈

—

142

—

158

C₂×C₈

—

142

—

159

C₂×C₈

C₈×D₇₁

yes

characteristic

160

C₂×C₈

C₈×D₇₁

yes

characteristic

161

C₂×C₈

D₄×D₇₁

yes

characteristic

162

C₂×C₈

#11765866

yes

characteristic

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

142

—

166

C₂²⋊C₄

—

142

—

167

C₄²

—

142

—

168

C₄²

C₂×C₄×D₇₁

yes

characteristic

169

C₁₆

—

170

C₁₆

—

171

C₁₆

—

284

—

172

C₁₆

—

142

—

173

C₁₆

—

142

—

174

C₂³

—

142

—

175

Q₈

—

176

Q₈

—

142

—

177

D₄

—

178

D₄

—

142

—

179

C₂×C₄

—

284

—

180

C₂×C₄

—

284

—

181

C₂×C₄

—

142

—

182

C₂×C₄

—

142

—

183

C₂×C₄

—

142

—

184

C₂×C₄

#14556090

yes

characteristic

185

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

186

C₂×C₄

#14556136

yes

characteristic

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

284

—

191

C₈

—

284

—

192

C₈

C₁₆×D₇₁

yes

complemented

193

C₈

#14556152

yes

characteristic

194

C₈

#14556160

yes

characteristic

195

C₂²

—

284

—

196

C₂²

—

284

—

197

C₂²

—

142

—

198

C₂²

#17986064

yes

characteristic

199

C₄

—

200

C₄

—

284

—

201

C₄

—

284

—

202

C₄

—

142

—

203

C₄

#17986098

yes

characteristic

204

C₄

#17986120

yes

characteristic

205

C₄

C₂×C₁₆×D₇₁

yes

characteristic

206

C₄

#17986417

yes

characteristic

207

C₂

—

284

—

208

C₂

#22587151

yes

characteristic

209

C₂

#22590159

yes

characteristic

210

C₂

#22590181

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₇₁
commutator	C₄×C₇₁	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#1370	C₂
socle	C₂²×C₇₁	C₈×D₄
prime radical	C₂×D₂₈₄	C₂×C₈
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#1370	D₇₁
hypocenter	C₇₁	SD₁₆⋊C₁₆
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₇₁

commutator

C₄×C₇₁

C₂²×C₁₆

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#1370

C₂

socle

C₂²×C₇₁

C₈×D₄

prime radical

C₂×D₂₈₄

C₂×C₈

cosocle

C₄×C₈×C₇₁

C₂³

hypercenter

#1370

D₇₁

hypocenter

C₇₁

SD₁₆⋊C₁₆

LCS

G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
1. #22590242	C₂	semidirect
4. #22586318	C₂	semidirect
6. #22586258	C₂	semidirect
7. C₇₁×#1370	C₂	semidirect
47. #11765854	C₁₆	semidirect
80. Dic₁₄₂	C₂×C₁₆	semidirect
84. C₈×C₇₁	C₂×C₁₆	semidirect
109. #1370	D₇₁	semidirect
113. C₇₁	SD₁₆⋊C₁₆	semidirect
192. C₈	C₁₆×D₇₁	semidirect

H ≅ G/N

type

1. #22590242

C₂

semidirect

4. #22586318

C₂

semidirect

6. #22586258

C₂

semidirect

7. C₇₁×#1370

C₂

semidirect

47. #11765854

C₁₆

semidirect

80. Dic₁₄₂

C₂×C₁₆

semidirect

84. C₈×C₇₁

C₂×C₁₆

semidirect

109. #1370

D₇₁

semidirect

113. C₇₁

SD₁₆⋊C₁₆

semidirect

192. C₈

C₁₆×D₇₁

semidirect

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

subgroup	index
#22590242	2
#22590159	2
C₈×#11765854	2
#22586318	2
#22586294	2
#22586258	2
C₇₁×#1370	2
SD₁₆⋊C₁₆	71

subgroup

index

C₇₁×#1370

SD₁₆⋊C₁₆

Subgroups — #31909262

Conjugacy classes of subgroups

Complements

Maximal subgroups