Group #31917642 — subgroups

Subgroups — C₂×(C₂×D₇₁)⋊C₃₂ #31917642

Order 18176.

342 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂²×C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₇₁)⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₈×D₇₁	C₄	1	1	yes	characteristic
6	C₂²×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₁₆×D₇₁	—	2	2	no	—
8	C₂×C₁₆×D₇₁	—	2	2	no	—
9	C₂×C₁₆×D₇₁	C₄	1	2	yes	—
10	C₂×C₁₆×D₇₁	C₂²	1	2	yes	—
11	C₂×C₇₁⋊C₃₂	—	2	2	no	—
12	C₂×C₇₁⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂²×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₂×C₇₁	—	2	2	no	—
15	C₂×C₃₂×C₇₁	C₂²	1	2	yes	complemented
16	C₂²×C₄×D₇₁	C₈	1	1	yes	characteristic
17	C₂²×C₇₁⋊C₈	C₈	1	1	yes	characteristic
18	C₂×C₈×D₇₁	—	2	2	no	—
19	C₂×C₈×D₇₁	—	2	2	no	—
20	C₂×C₈×D₇₁	C₈	1	2	yes	—
21	C₂×C₈×D₇₁	C₂×C₄	1	2	yes	—
22	C₂×C₇₁⋊C₁₆	—	2	2	no	—
23	C₂×C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
24	C₁₆×D₇₁	—	2	4	no	—
25	C₁₆×D₇₁	—	2	2	no	—
26	C₁₆×D₇₁	—	2	2	no	—
27	C₇₁⋊C₃₂	—	2	2	no	—
28	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
31	C₂×C₁₆×C₇₁	D₄	1	2	yes	—
32	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
33	C₃₂×C₇₁	—	2	2	no	—
34	C₂³×D₇₁	C₁₆	1	1	yes	characteristic
35	C₂²×Dic₇₁	C₁₆	1	1	yes	characteristic
36	C₂×C₄×D₇₁	—	2	2	no	—
37	C₂×C₄×D₇₁	—	2	2	no	—
38	C₂×C₄×D₇₁	C₁₆	1	2	yes	—
39	C₂×C₄×D₇₁	C₂×C₈	1	2	yes	—
40	C₂×C₇₁⋊C₈	—	2	2	no	—
41	C₂×C₇₁⋊C₈	C₂×C₈	1	2	yes	—
42	C₈×D₇₁	—	2	4	no	—
43	C₈×D₇₁	—	2	2	no	—
44	C₈×D₇₁	—	2	2	no	—
45	C₇₁⋊C₁₆	—	2	2	no	—
46	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
48	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
49	C₂×C₈×C₇₁	M₁₆	1	2	yes	—
50	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
51	C₁₆×C₇₁	C₂²⋊C₄	1	2	yes	—
52	C₁₆×C₇₁	C₂×D₄	1	1	yes	characteristic
53	C₁₆×C₇₁	C₂×D₄	1	1	yes	characteristic
54	C₂³×C₇₁	C₂×C₁₆	1	1	yes	characteristic
55	C₂²×D₇₁	—	2	2	no	—
56	C₂²×D₇₁	—	2	2	no	—
57	C₂²×D₇₁	C₃₂	1	4	yes	complemented
58	C₂²×D₇₁	C₂×C₁₆	1	2	yes	—
59	C₂×C₄×C₇₁	C₂²⋊C₈	1	2	yes	—
60	C₂×C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
61	C₂×C₄×C₇₁	M₃₂	1	2	yes	—
62	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
63	C₂×Dic₇₁	—	2	2	no	—
64	C₂×Dic₇₁	C₂×C₁₆	1	2	yes	—
65	C₄×D₇₁	—	2	4	no	—
66	C₄×D₇₁	—	2	2	no	—
67	C₄×D₇₁	—	2	2	no	—
68	C₈×C₇₁	C₂²⋊C₈	1	2	yes	—
69	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₈×C₇₁	C₂×M₁₆	1	1	yes	characteristic
71	C₇₁⋊C₈	—	2	2	no	—
72	C₂²×C₇₁	C₂²⋊C₁₆	1	2	yes	—
73	C₂²×C₇₁	C₂×C₃₂	1	2	yes	—
74	C₂²×C₇₁	M₆₄	1	2	yes	—
75	C₂²×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
76	C₂×D₇₁	—	2	2	no	—
77	C₂×D₇₁	—	2	8	no	—
78	C₂×D₇₁	—	2	2	no	—
79	C₂×D₇₁	C₂×C₃₂	1	4	yes	complemented
80	C₄×C₇₁	C₂²⋊C₁₆	1	2	yes	—
81	C₄×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
82	C₄×C₇₁	C₂×M₃₂	1	1	yes	characteristic
83	Dic₇₁	—	2	2	no	—
84	C₂×C₂²⋊C₃₂	—	71	1	no	maximal, Sylow
85	C₂×C₇₁	C₂²⋊C₃₂	1	4	yes	complemented
86	C₂×C₇₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
87	C₂×C₇₁	C₂²×C₃₂	1	1	yes	characteristic
88	C₂×C₇₁	C₂×M₆₄	1	1	yes	characteristic
89	D₇₁	—	2	4	no	—
90	C₂³×C₁₆	—	71	1	no	—
91	C₂²×C₃₂	—	71	1	no	—
92	C₂²×C₃₂	D₇₁	1	1	yes	characteristic, complemented
93	C₂²⋊C₃₂	—	71	4	no	—
94	C₇₁	C₂×C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₈	—	71	1	no	—
96	C₂²×C₁₆	—	71	1	no	—
97	C₂²×C₁₆	—	71	2	no	—
98	C₂²×C₁₆	—	71	2	no	—
99	C₂²×C₁₆	—	142	2	no	—
100	C₂²×C₁₆	—	142	2	no	—
101	C₂²×C₁₆	C₂×D₇₁	1	1	yes	characteristic
102	C₂×C₃₂	—	2	2	no	—
103	C₂×C₃₂	—	71	2	no	—
104	C₂×C₃₂	—	142	2	no	—
105	C₂×C₃₂	C₂×D₇₁	1	2	yes	complemented
106	C₂³×C₄	—	71	1	no	—
107	C₂²×C₈	—	71	1	no	—
108	C₂²×C₈	—	71	2	no	—
109	C₂²×C₈	—	71	2	no	—
110	C₂²×C₈	—	142	2	no	—
111	C₂²×C₈	—	142	2	no	—
112	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
113	C₂×C₁₆	—	71	2	no	—
114	C₂×C₁₆	—	142	2	no	—
115	C₂×C₁₆	—	142	4	no	—
116	C₂×C₁₆	—	142	2	no	—
117	C₂×C₁₆	—	142	2	no	—
118	C₂×C₁₆	C₄×D₇₁	1	1	yes	characteristic
119	C₂×C₁₆	D₂₈₄	1	2	yes	—
120	C₂×C₁₆	C₂²⋊D₇₁	1	2	yes	—
121	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
122	C₃₂	—	2	2	no	—
123	C₃₂	—	142	2	no	—
124	C₂⁴	—	71	1	no	—
125	C₂²×C₄	—	71	1	no	—
126	C₂²×C₄	—	71	2	no	—
127	C₂²×C₄	—	71	2	no	—
128	C₂²×C₄	—	142	2	no	—
129	C₂²×C₄	—	142	2	no	—
130	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
131	C₂×C₈	—	71	2	no	—
132	C₂×C₈	—	142	2	no	—
133	C₂×C₈	—	142	4	no	—
134	C₂×C₈	—	142	2	no	—
135	C₂×C₈	—	142	2	no	—
136	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
137	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
138	C₂×C₈	#11765848	1	2	yes	—
139	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
140	C₁₆	—	142	2	no	—
141	C₁₆	(C₂×D₇₁)⋊C₄	1	2	yes	—
142	C₁₆	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
143	C₁₆	C₂×D₂₈₄	1	1	yes	characteristic
144	C₂³	—	71	4	no	—
145	C₂³	—	71	2	no	—
146	C₂³	—	142	2	no	—
147	C₂³	—	142	2	no	—
148	C₂³	C₁₆×D₇₁	1	1	yes	characteristic
149	C₂×C₄	—	71	2	no	—
150	C₂×C₄	—	142	2	no	—
151	C₂×C₄	—	142	2	no	—
152	C₂×C₄	—	142	2	no	—
153	C₂×C₄	—	142	4	no	—
154	C₂×C₄	(C₂×D₇₁)⋊C₈	1	2	yes	—
155	C₂×C₄	C₁₆×D₇₁	1	1	yes	characteristic
156	C₂×C₄	#14556067	1	2	yes	—
157	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
158	C₈	—	142	2	no	—
159	C₈	(C₂×D₇₁)⋊C₈	1	2	yes	—
160	C₈	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
161	C₈	C₂×#11765848	1	1	yes	characteristic
162	C₂²	—	71	4	no	—
163	C₂²	—	142	8	no	—
164	C₂²	—	142	2	no	—
165	C₂²	—	142	2	no	—
166	C₂²	(C₂×D₇₁)⋊C₁₆	1	2	yes	—
167	C₂²	C₃₂×D₇₁	1	2	yes	—
168	C₂²	#17985832	1	2	yes	—
169	C₂²	C₂×C₁₆×D₇₁	1	1	yes	characteristic
170	C₄	—	142	2	no	—
171	C₄	(C₂×D₇₁)⋊C₁₆	1	2	yes	—
172	C₄	C₂×(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
173	C₄	C₂×#14556067	1	1	yes	characteristic
174	C₂	—	142	4	no	—
175	C₂	(C₂×D₇₁)⋊C₃₂	1	4	yes	direct product factor
176	C₂	C₂×(C₂×D₇₁)⋊C₁₆	1	1	yes	characteristic
177	C₂	C₂×C₃₂×D₇₁	1	1	yes	characteristic
178	C₂	C₂×#17985832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₆×D₇₁

C₂

yes

maximal, characteristic

C₂²×C₇₁⋊C₃₂

C₂

yes

maximal, characteristic, complemented

(C₂×D₇₁)⋊C₃₂

C₂

yes

maximal, direct product factor

C₂²×C₃₂×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₇₁

C₄

yes

characteristic

C₂²×C₇₁⋊C₁₆

C₄

yes

characteristic

C₂×C₁₆×D₇₁

—

C₂×C₁₆×D₇₁

—

C₂×C₁₆×D₇₁

C₄

yes

—

C₂×C₁₆×D₇₁

C₂²

yes

—

C₂×C₇₁⋊C₃₂

—

C₂×C₇₁⋊C₃₂

C₂²

yes

complemented

C₂²×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₃₂×C₇₁

—

C₂×C₃₂×C₇₁

C₂²

yes

complemented

C₂²×C₄×D₇₁

C₈

yes

characteristic

C₂²×C₇₁⋊C₈

C₈

yes

characteristic

C₂×C₈×D₇₁

—

C₂×C₈×D₇₁

—

C₂×C₈×D₇₁

C₈

yes

—

C₂×C₈×D₇₁

C₂×C₄

yes

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

—

C₁₆×D₇₁

—

C₁₆×D₇₁

—

C₁₆×D₇₁

—

C₇₁⋊C₃₂

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

C₂³

yes

characteristic

C₃₂×C₇₁

—

C₂³×D₇₁

C₁₆

yes

characteristic

C₂²×Dic₇₁

C₁₆

yes

characteristic

C₂×C₄×D₇₁

—

C₂×C₄×D₇₁

—

C₂×C₄×D₇₁

C₁₆

yes

—

C₂×C₄×D₇₁

C₂×C₈

yes

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂×C₈

yes

—

C₈×D₇₁

—

C₈×D₇₁

—

C₈×D₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

M₁₆

yes

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

C₂²⋊C₄

yes

—

C₁₆×C₇₁

C₂×D₄

yes

characteristic

C₁₆×C₇₁

C₂×D₄

yes

characteristic

C₂³×C₇₁

C₂×C₁₆

yes

characteristic

C₂²×D₇₁

—

C₂²×D₇₁

—

C₂²×D₇₁

C₃₂

yes

complemented

C₂²×D₇₁

C₂×C₁₆

yes

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

—

C₂×C₄×C₇₁

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₁

M₃₂

yes

—

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

C₂×C₁₆

yes

—

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

C₂²⋊C₈

yes

—

C₈×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₁

C₂×M₁₆

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

C₂²⋊C₁₆

yes

—

C₂²×C₇₁

C₂×C₃₂

yes

—

C₂²×C₇₁

M₆₄

yes

—

C₂²×C₇₁

C₂²×C₁₆

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

C₂×C₃₂

yes

complemented

C₄×C₇₁

C₂²⋊C₁₆

yes

—

C₄×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₇₁

C₂×M₃₂

yes

characteristic

Dic₇₁

—

C₂×C₂²⋊C₃₂

—

maximal, Sylow

C₂×C₇₁

C₂²⋊C₃₂

yes

complemented

C₂×C₇₁

C₂×C₂²⋊C₁₆

yes

characteristic

C₂×C₇₁

C₂²×C₃₂

yes

characteristic

C₂×C₇₁

C₂×M₆₄

yes

characteristic

D₇₁

—

C₂³×C₁₆

—

C₂²×C₃₂

—

C₂²×C₃₂

D₇₁

yes

characteristic, complemented

C₂²⋊C₃₂

—

C₇₁

C₂×C₂²⋊C₃₂

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂²×C₁₆

—

142

—

100

C₂²×C₁₆

—

142

—

101

C₂²×C₁₆

C₂×D₇₁

yes

characteristic

102

C₂×C₃₂

—

103

C₂×C₃₂

—

104

C₂×C₃₂

—

142

—

105

C₂×C₃₂

C₂×D₇₁

yes

complemented

106

C₂³×C₄

—

107

C₂²×C₈

—

108

C₂²×C₈

—

109

C₂²×C₈

—

110

C₂²×C₈

—

142

—

111

C₂²×C₈

—

142

—

112

C₂²×C₈

C₄×D₇₁

yes

characteristic

113

C₂×C₁₆

—

114

C₂×C₁₆

—

142

—

115

C₂×C₁₆

—

142

—

116

C₂×C₁₆

—

142

—

117

C₂×C₁₆

—

142

—

118

C₂×C₁₆

C₄×D₇₁

yes

characteristic

119

C₂×C₁₆

D₂₈₄

yes

—

120

C₂×C₁₆

C₂²⋊D₇₁

yes

—

121

C₂×C₁₆

C₂²×D₇₁

yes

characteristic

122

C₃₂

—

123

C₃₂

—

142

—

124

C₂⁴

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

142

—

129

C₂²×C₄

—

142

—

130

C₂²×C₄

C₈×D₇₁

yes

characteristic

131

C₂×C₈

—

132

C₂×C₈

—

142

—

133

C₂×C₈

—

142

—

134

C₂×C₈

—

142

—

135

C₂×C₈

—

142

—

136

C₂×C₈

(C₂×D₇₁)⋊C₄

yes

—

137

C₂×C₈

C₈×D₇₁

yes

characteristic

138

C₂×C₈

#11765848

yes

—

139

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

140

C₁₆

—

142

—

141

C₁₆

(C₂×D₇₁)⋊C₄

yes

—

142

C₁₆

C₂×C₂²⋊D₇₁

yes

characteristic

143

C₁₆

C₂×D₂₈₄

yes

characteristic

144

C₂³

—

145

C₂³

—

146

C₂³

—

142

—

147

C₂³

—

142

—

148

C₂³

C₁₆×D₇₁

yes

characteristic

149

C₂×C₄

—

150

C₂×C₄

—

142

—

151

C₂×C₄

—

142

—

152

C₂×C₄

—

142

—

153

C₂×C₄

—

142

—

154

C₂×C₄

(C₂×D₇₁)⋊C₈

yes

—

155

C₂×C₄

C₁₆×D₇₁

yes

characteristic

156

C₂×C₄

#14556067

yes

—

157

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

158

C₈

—

142

—

159

C₈

(C₂×D₇₁)⋊C₈

yes

—

160

C₈

C₂×(C₂×D₇₁)⋊C₄

yes

characteristic

161

C₈

C₂×#11765848

yes

characteristic

162

C₂²

—

163

C₂²

—

142

—

164

C₂²

—

142

—

165

C₂²

—

142

—

166

C₂²

(C₂×D₇₁)⋊C₁₆

yes

—

167

C₂²

C₃₂×D₇₁

yes

—

168

C₂²

#17985832

yes

—

169

C₂²

C₂×C₁₆×D₇₁

yes

characteristic

170

C₄

—

142

—

171

C₄

(C₂×D₇₁)⋊C₁₆

yes

—

172

C₄

C₂×(C₂×D₇₁)⋊C₈

yes

characteristic

173

C₄

C₂×#14556067

yes

characteristic

174

C₂

—

142

—

175

C₂

(C₂×D₇₁)⋊C₃₂

yes

direct product factor

176

C₂

C₂×(C₂×D₇₁)⋊C₁₆

yes

characteristic

177

C₂

C₂×C₃₂×D₇₁

yes

characteristic

178

C₂

C₂×#17985832

yes

characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂×D₇₁
commutator	C₂×C₇₁	C₂²×C₃₂
Frattini	C₂×C₁₆	C₂²×D₇₁
Fitting	C₂²×C₃₂×C₇₁	C₂
socle	C₂³×C₇₁	C₂×C₁₆
prime radical	C₂³×D₇₁	C₁₆
cosocle	C₂×C₁₆×C₇₁	C₂³
hypercenter	C₂²×C₃₂	D₇₁
hypocenter	C₇₁	C₂×C₂²⋊C₃₂
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

subgroup

G/H

center

C₂²×C₁₆

C₂×D₇₁

commutator

C₂×C₇₁

C₂²×C₃₂

Frattini

C₂×C₁₆

C₂²×D₇₁

Fitting

C₂²×C₃₂×C₇₁

C₂

socle

C₂³×C₇₁

C₂×C₁₆

prime radical

C₂³×D₇₁

C₁₆

cosocle

C₂×C₁₆×C₇₁

C₂³

hypercenter

C₂²×C₃₂

D₇₁

hypocenter

C₇₁

C₂×C₂²⋊C₃₂

LCS

G ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

N	H ≅ G/N	type
2. C₂²×C₇₁⋊C₃₂	C₂	semidirect
3. (C₂×D₇₁)⋊C₃₂	C₂	direct (N × H)
4. C₂²×C₃₂×C₇₁	C₂	semidirect
12. C₂×C₇₁⋊C₃₂	C₂²	semidirect
15. C₂×C₃₂×C₇₁	C₂²	semidirect
57. C₂²×D₇₁	C₃₂	semidirect
79. C₂×D₇₁	C₂×C₃₂	semidirect
85. C₂×C₇₁	C₂²⋊C₃₂	semidirect
92. C₂²×C₃₂	D₇₁	semidirect
94. C₇₁	C₂×C₂²⋊C₃₂	semidirect
105. C₂×C₃₂	C₂×D₇₁	semidirect
175. C₂	(C₂×D₇₁)⋊C₃₂	direct (N × H)

H ≅ G/N

type

2. C₂²×C₇₁⋊C₃₂

C₂

semidirect

3. (C₂×D₇₁)⋊C₃₂

C₂

direct (N × H)

4. C₂²×C₃₂×C₇₁

C₂

semidirect

12. C₂×C₇₁⋊C₃₂

C₂²

semidirect

15. C₂×C₃₂×C₇₁

C₂²

semidirect

57. C₂²×D₇₁

C₃₂

semidirect

79. C₂×D₇₁

C₂×C₃₂

semidirect

85. C₂×C₇₁

C₂²⋊C₃₂

semidirect

92. C₂²×C₃₂

D₇₁

semidirect

94. C₇₁

C₂×C₂²⋊C₃₂

semidirect

105. C₂×C₃₂

C₂×D₇₁

semidirect

175. C₂

(C₂×D₇₁)⋊C₃₂

direct (N × H)

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

subgroup	index
C₂²×C₁₆×D₇₁	2
C₂²×C₇₁⋊C₃₂	2
(C₂×D₇₁)⋊C₃₂	2
C₂²×C₃₂×C₇₁	2
C₂×C₂²⋊C₃₂	71

subgroup

index

C₂²×C₁₆×D₇₁

C₂²×C₇₁⋊C₃₂

(C₂×D₇₁)⋊C₃₂

C₂²×C₃₂×C₇₁

C₂×C₂²⋊C₃₂

Subgroups — C₂×(C₂×D₇₁)⋊C₃₂ #31917642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×(C2×D71)⋊C32 #31917642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₂×D₇₁)⋊C₃₂ #31917642