Group #31917654 — subgroups

Subgroups — #31917654

Order 18176.

290 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂×#17986417	C₂	1	1	yes	maximal, characteristic
2	M₆₄×D₇₁	C₂	1	2	yes	maximal, complemented
3	#22586480	C₂	1	1	yes	maximal, characteristic, complemented
4	#22586479	C₂	1	2	yes	maximal, complemented
5	C₇₁×#1400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14556134	C₄	1	1	yes	characteristic
7	#17986417	—	2	2	no	—
8	#17986417	—	2	2	no	—
9	C₂×#14556067	C₄	1	1	yes	characteristic
10	C₂×#14556067	C₂²	1	1	yes	characteristic
11	C₂²×C₇₁⋊C₁₆	C₄	1	1	yes	characteristic
12	C₂×C₁₆×D₇₁	C₄	1	1	yes	characteristic
13	C₂×C₁₆×D₇₁	C₂²	1	1	yes	characteristic
14	#17985833	C₂²	1	2	yes	—
15	#17985832	—	2	2	no	—
16	C₃₂×D₇₁	—	2	2	no	—
17	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
18	M₆₄×C₇₁	C₂²	1	2	yes	—
19	C₂×#11765865	C₈	1	1	yes	characteristic
20	#14556134	—	2	2	no	—
21	#14556134	—	2	2	no	—
22	C₂×#11765849	C₈	1	1	yes	characteristic
23	C₂×#11765848	C₈	1	1	yes	characteristic
24	C₂×#11765848	C₈	1	1	yes	characteristic
25	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
27	#14556067	—	2	2	no	—
28	#14556067	—	2	2	no	—
29	C₂×C₇₁⋊C₁₆	—	2	1	no	—
30	C₂×C₇₁⋊C₁₆	—	2	1	no	—
31	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
32	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
33	C₁₆×D₇₁	—	2	1	no	—
34	C₁₆×D₇₁	—	2	1	no	—
35	C₁₆×D₇₁	D₄	1	2	yes	—
36	C₁₆×D₇₁	D₄	1	2	yes	—
37	C₇₁⋊C₃₂	—	2	2	no	—
38	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
39	M₃₂×C₇₁	—	2	2	no	—
40	C₂×C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₆×C₇₁	C₂³	1	1	yes	characteristic
42	C₃₂×C₇₁	—	2	2	no	—
43	#11765865	—	2	2	no	—
44	#11765865	—	2	2	no	—
45	C₂×Dic₁₄₂	C₁₆	1	1	yes	characteristic
46	C₂×D₂₈₄	C₁₆	1	1	yes	characteristic
47	C₂×C₂²⋊D₇₁	C₁₆	1	1	yes	characteristic
48	C₂×C₂²⋊D₇₁	C₁₆	1	1	yes	characteristic
49	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
50	C₂×C₄×D₇₁	C₂×C₈	1	1	yes	characteristic
51	#11765849	—	2	2	no	—
52	#11765848	—	2	2	no	—
53	#11765848	—	2	2	no	—
54	C₂×C₇₁⋊C₈	C₂×C₈	1	1	yes	characteristic
55	C₂×C₇₁⋊C₈	C₂×C₈	1	1	yes	characteristic
56	C₈×D₇₁	—	2	1	no	—
57	C₈×D₇₁	—	2	1	no	—
58	C₈×D₇₁	C₂²⋊C₄	1	2	yes	—
59	C₈×D₇₁	M₁₆	1	2	yes	—
60	C₇₁⋊C₁₆	—	2	1	no	—
61	C₇₁⋊C₁₆	C₂²⋊C₄	1	1	yes	characteristic
62	C₇₁⋊C₁₆	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
64	C₂×C₈×C₇₁	—	2	1	no	—
65	C₂×C₈×C₇₁	—	2	1	no	—
66	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
67	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
68	C₁₆×C₇₁	—	2	1	no	—
69	C₁₆×C₇₁	C₂×D₄	1	2	yes	—
70	C₂³×C₇₁	C₂×C₁₆	1	1	yes	characteristic
71	C₂²×D₇₁	C₂×C₁₆	1	1	yes	characteristic
72	C₂²×D₇₁	C₂×C₁₆	1	1	yes	characteristic
73	C₂×C₄×C₇₁	—	2	1	no	—
74	C₂×C₄×C₇₁	—	2	1	no	—
75	C₂×C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
76	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
77	C₂²⋊D₇₁	—	2	2	no	—
78	C₂²⋊D₇₁	—	2	2	no	—
79	C₂×Dic₇₁	C₂×C₁₆	1	1	yes	characteristic
80	C₂×Dic₇₁	C₂×C₁₆	1	1	yes	characteristic
81	D₂₈₄	—	2	2	no	—
82	C₄×D₇₁	—	2	1	no	—
83	C₄×D₇₁	—	2	1	no	—
84	C₄×D₇₁	C₂²⋊C₈	1	2	yes	—
85	C₄×D₇₁	M₃₂	1	2	yes	—
86	Dic₁₄₂	—	2	2	no	—
87	C₈×C₇₁	—	2	1	no	—
88	C₈×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₈×C₇₁	C₂×M₁₆	1	1	yes	characteristic
90	C₇₁⋊C₈	—	2	1	no	—
91	C₇₁⋊C₈	C₂²⋊C₈	1	2	yes	—
92	C₂²×C₇₁	—	2	1	no	—
93	C₂²×C₇₁	—	4	1	no	—
94	C₂²×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
95	C₂×D₇₁	—	2	1	no	—
96	C₂×D₇₁	—	4	1	no	—
97	C₂×D₇₁	—	4	1	no	—
98	C₂×D₇₁	C₂²⋊C₁₆	1	2	yes	—
99	C₄×C₇₁	—	2	1	no	—
100	C₄×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
101	C₄×C₇₁	C₂×M₃₂	1	1	yes	characteristic
102	Dic₇₁	—	2	1	no	—
103	Dic₇₁	C₂²⋊C₁₆	1	2	yes	—
104	#13556	—	71	1	no	maximal, Sylow
105	C₂×C₇₁	—	2	1	no	—
106	C₂×C₇₁	—	4	1	no	—
107	C₂×C₇₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
108	D₇₁	—	2	2	no	—
109	D₇₁	—	4	1	no	—
110	C₂×#504	—	71	1	no	—
111	C₂×M₆₄	—	71	2	no	—
112	#1400	—	71	1	no	—
113	#1400	—	71	2	no	—
114	#1400	D₇₁	1	1	yes	characteristic, complemented
115	C₇₁	#13556	1	1	yes	characteristic, complemented, Sylow
116	C₂×#131	—	71	1	no	—
117	#504	—	142	2	no	—
118	#504	—	142	2	no	—
119	C₂×M₃₂	—	71	1	no	—
120	C₂×M₃₂	—	71	1	no	—
121	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic
122	C₂²×C₁₆	—	71	1	no	—
123	C₂²×C₁₆	—	71	1	no	—
124	C₂²×C₁₆	—	71	1	no	—
125	M₆₄	—	71	2	no	—
126	M₆₄	—	142	2	no	—
127	M₆₄	C₂×D₇₁	1	2	yes	—
128	C₂×C₃₂	—	142	2	no	—
129	C₂×#41	—	71	1	no	—
130	#131	—	142	2	no	—
131	#131	—	142	2	no	—
132	C₂×M₁₆	—	71	1	no	—
133	C₂×M₁₆	—	71	1	no	—
134	C₂×M₁₆	—	71	1	no	—
135	C₂²×C₈	—	71	1	no	—
136	C₂²×C₈	—	71	1	no	—
137	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
138	M₃₂	—	2	2	no	—
139	M₃₂	—	142	2	no	—
140	M₃₂	—	142	2	no	—
141	C₂×C₁₆	—	71	1	no	—
142	C₂×C₁₆	—	71	2	no	—
143	C₂×C₁₆	—	71	2	no	—
144	C₂×C₁₆	—	71	1	no	—
145	C₂×C₁₆	—	142	1	no	—
146	C₂×C₁₆	—	142	1	no	—
147	C₂×C₁₆	—	142	1	no	—
148	C₂×C₁₆	—	142	1	no	—
149	C₂×C₁₆	C₄×D₇₁	1	1	yes	characteristic
150	C₂×C₁₆	C₂²×D₇₁	1	1	yes	characteristic
151	C₃₂	—	2	2	no	—
152	C₃₂	—	142	2	no	—
153	#41	—	142	2	no	—
154	#41	—	142	2	no	—
155	C₂×Q₈	—	71	1	no	—
156	C₂×D₄	—	71	1	no	—
157	C₂×D₄	—	71	1	no	—
158	C₂×D₄	—	71	1	no	—
159	C₂²×C₄	—	71	1	no	—
160	C₂²×C₄	—	71	1	no	—
161	C₂²×C₄	C₈×D₇₁	1	1	yes	characteristic
162	M₁₆	—	142	2	no	—
163	M₁₆	—	142	2	no	—
164	M₁₆	—	142	2	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	71	1	no	—
168	C₂×C₈	—	71	2	no	—
169	C₂×C₈	—	71	2	no	—
170	C₂×C₈	—	71	1	no	—
171	C₂×C₈	—	142	1	no	—
172	C₂×C₈	—	142	1	no	—
173	C₂×C₈	C₈×D₇₁	1	1	yes	characteristic
174	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
175	C₁₆	—	2	1	no	—
176	C₁₆	—	71	1	no	—
177	C₁₆	—	71	1	no	—
178	C₁₆	—	142	1	no	—
179	C₁₆	D₄×D₇₁	1	2	yes	—
180	C₂³	—	71	1	no	—
181	C₂³	—	71	1	no	—
182	C₂³	C₁₆×D₇₁	1	1	yes	characteristic
183	Q₈	—	142	2	no	—
184	D₄	—	142	2	no	—
185	D₄	—	142	2	no	—
186	D₄	—	142	2	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	71	1	no	—
190	C₂×C₄	—	71	2	no	—
191	C₂×C₄	—	71	2	no	—
192	C₂×C₄	—	71	1	no	—
193	C₂×C₄	—	142	1	no	—
194	C₂×C₄	—	142	1	no	—
195	C₂×C₄	C₁₆×D₇₁	1	1	yes	characteristic
196	C₂×C₄	C₂×C₈×D₇₁	1	1	yes	characteristic
197	C₈	—	2	1	no	—
198	C₈	—	71	2	no	—
199	C₈	—	142	1	no	—
200	C₈	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
201	C₈	M₁₆×D₇₁	1	1	yes	characteristic
202	C₂²	—	2	1	no	—
203	C₂²	—	4	1	no	—
204	C₂²	—	284	1	no	—
205	C₂²	—	284	1	no	—
206	C₂²	—	71	2	no	—
207	C₂²	—	142	1	no	—
208	C₂²	C₂×C₁₆×D₇₁	1	1	yes	characteristic
209	C₄	—	2	1	no	—
210	C₄	—	71	2	no	—
211	C₄	—	142	1	no	—
212	C₄	C₂²⋊C₈×D₇₁	1	1	yes	characteristic
213	C₄	M₃₂×D₇₁	1	1	yes	characteristic
214	C₂	—	2	1	no	—
215	C₂	—	4	1	no	—
216	C₂	—	284	1	no	—
217	C₂	—	142	2	no	—
218	C₂	C₂²⋊C₁₆×D₇₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17986417

C₂

yes

maximal, characteristic

M₆₄×D₇₁

C₂

yes

maximal, complemented

#22586480

C₂

yes

maximal, characteristic, complemented

#22586479

C₂

yes

maximal, complemented

C₇₁×#1400

C₂

yes

maximal, characteristic, complemented

C₂×#14556134

C₄

yes

—

—

C₄

yes

characteristic

C₂×#14556067

C₂²

yes

characteristic

C₂²×C₇₁⋊C₁₆

C₄

yes

characteristic

C₂×C₁₆×D₇₁

C₄

yes

characteristic

C₂×C₁₆×D₇₁

C₂²

yes

characteristic

#17985833

C₂²

yes

—

#17985832

—

C₃₂×D₇₁

—

C₂×M₃₂×C₇₁

C₂²

yes

characteristic

M₆₄×C₇₁

C₂²

yes

—

C₂×#11765865

C₈

yes

—

—

C₈

yes

characteristic

C₂×#11765848

C₈

yes

characteristic

C₂×#11765848

C₈

yes

characteristic

C₂×C₈×D₇₁

C₂×C₄

yes

characteristic

C₂×C₈×D₇₁

C₂×C₄

yes

characteristic

#14556067

—

#14556067

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

characteristic

C₁₆×D₇₁

—

C₁₆×D₇₁

—

C₁₆×D₇₁

D₄

yes

—

C₁₆×D₇₁

D₄

yes

—

C₇₁⋊C₃₂

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

M₃₂×C₇₁

—

C₂×C₁₆×C₇₁

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₁

C₂³

yes

characteristic

C₃₂×C₇₁

—

#11765865

—

#11765865

—

C₂×Dic₁₄₂

C₁₆

yes

characteristic

C₂×D₂₈₄

C₁₆

yes

characteristic

C₂×C₂²⋊D₇₁

C₁₆

yes

characteristic

C₂×C₂²⋊D₇₁

C₁₆

yes

characteristic

C₂×C₄×D₇₁

C₂×C₈

yes

characteristic

C₂×C₄×D₇₁

C₂×C₈

yes

—

—

—

C₂×C₇₁⋊C₈

C₂×C₈

yes

characteristic

C₂×C₇₁⋊C₈

C₂×C₈

yes

characteristic

C₈×D₇₁

—

C₈×D₇₁

—

C₈×D₇₁

C₂²⋊C₄

yes

—

C₈×D₇₁

M₁₆

yes

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

C₂²⋊C₄

yes

characteristic

C₇₁⋊C₁₆

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂×C₈

yes

characteristic

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

C₂×D₄

yes

—

C₂³×C₇₁

C₂×C₁₆

yes

characteristic

C₂²×D₇₁

C₂×C₁₆

yes

characteristic

C₂²×D₇₁

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂²⋊D₇₁

—

C₂²⋊D₇₁

—

C₂×Dic₇₁

C₂×C₁₆

yes

characteristic

C₂×Dic₇₁

C₂×C₁₆

yes

characteristic

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

C₂²⋊C₈

yes

—

C₄×D₇₁

M₃₂

yes

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₇₁

C₂×M₁₆

yes

characteristic

C₇₁⋊C₈

—

C₇₁⋊C₈

C₂²⋊C₈

yes

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂²×C₁₆

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

C₂²⋊C₁₆

yes

—

C₄×C₇₁

—

100

C₄×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

101

C₄×C₇₁

C₂×M₃₂

yes

characteristic

102

Dic₇₁

—

103

Dic₇₁

C₂²⋊C₁₆

yes

—

104

#13556

—

maximal, Sylow

105

C₂×C₇₁

—

106

C₂×C₇₁

—

107

C₂×C₇₁

C₂×C₂²⋊C₁₆

yes

characteristic

108

D₇₁

—

109

D₇₁

—

110

C₂×#504

—

111

C₂×M₆₄

—

112

#1400

—

113

#1400

—

114

#1400

D₇₁

yes

characteristic, complemented

115

C₇₁

#13556

yes

characteristic, complemented, Sylow

116

C₂×#131

—

117

#504

—

142

—

118

#504

—

142

—

119

C₂×M₃₂

—

120

C₂×M₃₂

—

121

C₂×M₃₂

C₂×D₇₁

yes

characteristic

122

C₂²×C₁₆

—

123

C₂²×C₁₆

—

124

C₂²×C₁₆

—

125

M₆₄

—

126

M₆₄

—

142

—

127

M₆₄

C₂×D₇₁

yes

—

128

C₂×C₃₂

—

142

—

129

C₂×#41

—

130

#131

—

142

—

131

#131

—

142

—

132

C₂×M₁₆

—

133

C₂×M₁₆

—

134

C₂×M₁₆

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

C₄×D₇₁

yes

characteristic

138

M₃₂

—

139

M₃₂

—

142

—

140

M₃₂

—

142

—

141

C₂×C₁₆

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

—

145

C₂×C₁₆

—

142

—

146

C₂×C₁₆

—

142

—

147

C₂×C₁₆

—

142

—

148

C₂×C₁₆

—

142

—

149

C₂×C₁₆

C₄×D₇₁

yes

characteristic

150

C₂×C₁₆

C₂²×D₇₁

yes

characteristic

151

C₃₂

—

152

C₃₂

—

142

—

153

#41

—

142

—

154

#41

—

142

—

155

C₂×Q₈

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

C₈×D₇₁

yes

characteristic

162

M₁₆

—

142

—

163

M₁₆

—

142

—

164

M₁₆

—

142

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

142

—

172

C₂×C₈

—

142

—

173

C₂×C₈

C₈×D₇₁

yes

characteristic

174

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

175

C₁₆

—

176

C₁₆

—

177

C₁₆

—

178

C₁₆

—

142

—

179

C₁₆

D₄×D₇₁

yes

—

180

C₂³

—

181

C₂³

—

182

C₂³

C₁₆×D₇₁

yes

characteristic

183

Q₈

—

142

—

184

D₄

—

142

—

185

D₄

—

142

—

186

D₄

—

142

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

142

—

194

C₂×C₄

—

142

—

195

C₂×C₄

C₁₆×D₇₁

yes

characteristic

196

C₂×C₄

C₂×C₈×D₇₁

yes

characteristic

197

C₈

—

198

C₈

—

199

C₈

—

142

—

200

C₈

C₂²⋊C₄×D₇₁

yes

characteristic

201

C₈

M₁₆×D₇₁

yes

characteristic

202

C₂²

—

203

C₂²

—

204

C₂²

—

284

—

205

C₂²

—

284

—

206

C₂²

—

207

C₂²

—

142

—

208

C₂²

C₂×C₁₆×D₇₁

yes

characteristic

209

C₄

—

210

C₄

—

211

C₄

—

142

—

212

C₄

C₂²⋊C₈×D₇₁

yes

characteristic

213

C₄

M₃₂×D₇₁

yes

characteristic

214

C₂

—

215

C₂

—

216

C₂

—

284

—

217

C₂

—

142

—

218

C₂

C₂²⋊C₁₆×D₇₁

yes

characteristic

	subgroup	G/H
center	C₈	C₂²⋊C₄×D₇₁
commutator	C₂²×C₇₁	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₇₁
Fitting	C₇₁×#1400	C₂
socle	C₂×C₇₁	C₂×C₂²⋊C₁₆
prime radical	C₂×#11765865	C₈
cosocle	C₂×C₁₆×C₇₁	C₂³
hypercenter	#1400	D₇₁
hypocenter	C₇₁	#13556
LCS	G ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #1400

subgroup

G/H

center

C₈

C₂²⋊C₄×D₇₁

commutator

C₂²×C₇₁

C₂²×C₁₆

Frattini

C₂×C₁₆

C₂²×D₇₁

Fitting

C₇₁×#1400

C₂

socle

C₂×C₇₁

C₂×C₂²⋊C₁₆

prime radical

C₂×#11765865

C₈

cosocle

C₂×C₁₆×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #1400

N	H ≅ G/N	type
2. M₆₄×D₇₁	C₂	semidirect
3. #22586480	C₂	semidirect
4. #22586479	C₂	semidirect
5. C₇₁×#1400	C₂	semidirect
114. #1400	D₇₁	semidirect
115. C₇₁	#13556	semidirect

H ≅ G/N

type

2. M₆₄×D₇₁

C₂

semidirect

3. #22586480

C₂

semidirect

4. #22586479

C₂

semidirect

5. C₇₁×#1400

C₂

semidirect

114. #1400

D₇₁

semidirect

115. C₇₁

#13556

semidirect

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

subgroup	index
C₂×#17986417	2
M₆₄×D₇₁	2
#22586480	2
#22586479	2
C₇₁×#1400	2
#13556	71

subgroup

index

M₆₄×D₇₁

C₇₁×#1400

Subgroups — #31917654

Conjugacy classes of subgroups

Complements

Maximal subgroups