Group #31915620 — subgroups

Subgroups — #31915620

Order 18176.

442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 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	#22590096	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17985783	C₂	1	4	yes	maximal, complemented
3	C₂×#17985775	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₁×#2931	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556068	C₂²	1	2	yes	—
6	C₂²×C₇₁⋊C₁₆	C₂²	1	2	yes	—
7	C₄⋊(C₇₁⋊C₁₆)	—	2	2	no	—
8	#17985783	—	2	8	no	—
9	#17985775	—	2	2	no	—
10	C₂×#131×C₇₁	C₂²	1	2	yes	—
11	#532×C₇₁	C₄	1	1	yes	characteristic
12	#436×C₇₁	—	2	2	no	—
13	C₈×D₄×C₇₁	—	2	2	no	—
14	#423×C₇₁	C₄	1	1	yes	characteristic
15	#408×C₇₁	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
17	#14556068	—	2	4	no	—
18	C₂×C₇₁⋊C₁₆	—	2	2	no	—
19	C₂×C₇₁⋊C₁₆	—	2	2	no	—
20	C₂×C₇₁⋊C₁₆	—	2	2	no	—
21	C₂×C₇₁⋊C₁₆	D₄	1	4	yes	complemented
22	C₂×#41×C₇₁	C₂×C₄	1	2	yes	—
23	#131×C₇₁	—	2	4	no	—
24	#131×C₇₁	—	2	4	no	—
25	C₂×M₁₆×C₇₁	—	2	2	no	—
26	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₇₁	—	2	2	no	—
28	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
30	C₄⋊Q₈×C₇₁	C₈	1	1	yes	characteristic
31	#127×C₇₁	C₈	1	1	yes	characteristic
32	#124×C₇₁	C₈	1	2	yes	—
33	#121×C₇₁	—	2	2	no	—
34	C₄×D₄×C₇₁	—	2	2	no	—
35	C₂×C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
36	C₄⋊C₈×C₇₁	—	2	2	no	—
37	C₂²⋊C₈×C₇₁	—	2	4	no	—
38	C₄×C₈×C₇₁	D₄	1	2	yes	—
39	C₄×C₈×C₇₁	D₄	1	2	yes	—
40	C₇₁⋊C₁₆	—	2	4	no	—
41	C₇₁⋊C₁₆	—	4	2	no	—
42	#41×C₇₁	—	2	4	no	—
43	#41×C₇₁	—	2	4	no	—
44	C₂×Q₈×C₇₁	C₂×C₈	1	2	yes	—
45	C₂×D₄×C₇₁	—	2	2	no	—
46	C₂×D₄×C₇₁	—	2	2	no	—
47	C₂×D₄×C₇₁	C₂×C₈	1	2	yes	—
48	C₂²×C₄×C₇₁	—	2	2	no	—
49	C₂²×C₄×C₇₁	M₁₆	1	2	yes	—
50	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
51	M₁₆×C₇₁	—	2	4	no	—
52	M₁₆×C₇₁	—	4	4	no	—
53	C₂×C₈×C₇₁	—	2	2	no	—
54	C₂×C₈×C₇₁	—	2	2	no	—
55	C₂×C₈×C₇₁	—	4	2	no	—
56	C₂×C₈×C₇₁	—	4	2	no	—
57	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₇₁	#41	1	2	yes	—
62	C₄⋊C₄×C₇₁	—	2	2	no	—
63	C₂²⋊C₄×C₇₁	—	2	4	no	—
64	C₄²×C₇₁	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
66	C₄²×C₇₁	C₂×C₈	1	1	yes	characteristic
67	C₂³×C₇₁	—	2	2	no	—
68	C₂³×C₇₁	C₂×M₁₆	1	1	yes	characteristic
69	Q₈×C₇₁	—	2	4	no	—
70	D₄×C₇₁	—	2	4	no	—
71	D₄×C₇₁	—	4	4	no	—
72	D₄×C₇₁	—	4	4	no	—
73	C₂×C₄×C₇₁	—	2	2	no	—
74	C₂×C₄×C₇₁	—	4	2	no	—
75	C₂×C₄×C₇₁	—	4	2	no	—
76	C₂×C₄×C₇₁	—	4	2	no	—
77	C₂×C₄×C₇₁	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₇₁	C₂²⋊C₈	1	2	yes	—
79	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₇₁	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₇₁	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₇₁	#131	1	2	yes	—
83	C₈×C₇₁	—	2	2	no	—
84	C₈×C₇₁	—	4	2	no	—
85	C₈×C₇₁	#121	1	2	yes	—
86	C₈×C₇₁	#124	1	1	yes	characteristic
87	C₈×C₇₁	#127	1	1	yes	characteristic
88	C₂²×C₇₁	—	2	2	no	—
89	C₂²×C₇₁	—	4	4	no	—
90	C₂²×C₇₁	—	4	2	no	—
91	C₂²×C₇₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
92	C₂²×C₇₁	#436	1	2	yes	—
93	C₄×C₇₁	—	2	2	no	—
94	C₄×C₇₁	—	2	2	no	—
95	C₄×C₇₁	—	4	2	no	—
96	C₄×C₇₁	#390	1	1	yes	characteristic
97	C₄×C₇₁	#408	1	1	yes	characteristic
98	C₄×C₇₁	C₈×D₄	1	2	yes	—
99	#13192	—	71	1	no	maximal, Sylow
100	C₂×C₇₁	—	2	2	no	—
101	C₂×C₇₁	—	8	2	no	—
102	C₂×C₇₁	#1954	1	1	yes	characteristic
103	C₂×C₇₁	#2117	1	2	yes	—
104	#2931	D₇₁	1	1	yes	characteristic
105	#2150	—	71	1	no	—
106	C₂×#350	—	71	4	no	—
107	C₂×#346	—	71	1	no	—
108	C₇₁	#13192	1	1	yes	characteristic, complemented, Sylow
109	C₂×#131	C₂×D₇₁	1	2	yes	—
110	#532	Dic₇₁	1	1	yes	characteristic
111	C₂×M₃₂	—	71	2	no	—
112	C₂²×C₁₆	—	71	2	no	—
113	#436	—	2	2	no	—
114	C₈×D₄	—	2	2	no	—
115	#423	Dic₇₁	1	1	yes	characteristic
116	#408	Dic₇₁	1	2	yes	—
117	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
118	C₄⋊C₁₆	—	142	2	no	—
119	#350	—	142	8	no	—
120	#346	—	142	2	no	—
121	C₂×#41	C₂×Dic₇₁	1	2	yes	—
122	#131	—	2	4	no	—
123	#131	—	2	4	no	—
124	C₂×M₁₆	—	2	2	no	—
125	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
126	C₂²×C₈	—	2	2	no	—
127	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
128	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
129	C₄⋊Q₈	C₇₁⋊C₈	1	1	yes	characteristic
130	#127	C₇₁⋊C₈	1	1	yes	characteristic
131	#124	C₇₁⋊C₈	1	2	yes	—
132	#121	—	2	2	no	—
133	C₄×D₄	—	2	2	no	—
134	C₂×C₄²	C₂×Dic₇₁	1	1	yes	characteristic
135	M₃₂	—	142	4	no	—
136	C₂×C₁₆	—	71	4	no	—
137	C₂×C₁₆	—	142	2	no	—
138	C₂×C₁₆	—	142	2	no	—
139	C₂×C₁₆	—	142	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₂²⋊C₈	—	2	4	no	—
142	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
143	C₄×C₈	C₂²⋊D₇₁	1	2	yes	—
144	#41	—	2	4	no	—
145	#41	—	2	4	no	—
146	C₂×Q₈	C₂×C₇₁⋊C₈	1	2	yes	—
147	C₂×D₄	—	2	2	no	—
148	C₂×D₄	—	2	2	no	—
149	C₂×D₄	C₂×C₇₁⋊C₈	1	2	yes	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	#11765849	1	2	yes	—
152	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
153	M₁₆	—	2	4	no	—
154	M₁₆	—	4	4	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	4	2	no	—
159	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
160	C₂×C₈	D₄×D₇₁	1	2	yes	—
161	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
162	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
163	C₂×C₈	#11765864	1	2	yes	—
164	C₄⋊C₄	—	2	2	no	—
165	C₂²⋊C₄	—	2	4	no	—
166	C₄²	C₂²⋊Dic₇₁	1	2	yes	—
167	C₄²	C₂×C₇₁⋊C₈	1	1	yes	characteristic
168	C₄²	C₂×C₇₁⋊C₈	1	1	yes	characteristic
169	C₁₆	—	284	2	no	—
170	C₁₆	—	142	4	no	—
171	C₂³	—	2	2	no	—
172	C₂³	C₂×#11765849	1	1	yes	characteristic
173	Q₈	—	2	4	no	—
174	D₄	—	2	4	no	—
175	D₄	—	4	4	no	—
176	D₄	—	4	4	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	4	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	C₂²⋊(C₇₁⋊C₈)	1	2	yes	—
182	C₂×C₄	C₂²⋊(C₇₁⋊C₈)	1	2	yes	—
183	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
184	C₂×C₄	D₄×Dic₇₁	1	2	yes	—
185	C₂×C₄	C₂²×C₇₁⋊C₈	1	1	yes	characteristic
186	C₂×C₄	#14556135	1	2	yes	—
187	C₈	—	2	2	no	—
188	C₈	—	4	2	no	—
189	C₈	#14556099	1	2	yes	—
190	C₈	#14556115	1	1	yes	characteristic
191	C₈	#14556124	1	1	yes	characteristic
192	C₂²	—	2	2	no	—
193	C₂²	—	4	4	no	—
194	C₂²	—	4	2	no	—
195	C₂²	C₂×C₂²⋊(C₇₁⋊C₈)	1	1	yes	characteristic
196	C₂²	#17986077	1	2	yes	—
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	4	2	no	—
200	C₄	#17985902	1	1	yes	characteristic
201	C₄	#17985966	1	1	yes	characteristic
202	C₄	D₄×C₇₁⋊C₈	1	2	yes	—
203	C₂	—	2	2	no	—
204	C₂	—	8	2	no	—
205	C₂	#22589135	1	1	yes	characteristic
206	C₂	#22589968	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22590096

C₂

yes

maximal, characteristic, complemented

C₂×#17985783

C₂

yes

maximal, complemented

C₂×#17985775

C₂

yes

maximal, characteristic, complemented

C₇₁×#2931

C₂

yes

maximal, characteristic

C₂×#14556068

C₂²

yes

—

C₂²×C₇₁⋊C₁₆

C₂²

yes

—

C₄⋊(C₇₁⋊C₁₆)

—

#17985783

—

#17985775

—

C₂×#131×C₇₁

C₂²

yes

—

#532×C₇₁

C₄

yes

characteristic

#436×C₇₁

—

C₈×D₄×C₇₁

—

#423×C₇₁

C₄

yes

characteristic

#408×C₇₁

C₄

yes

—

C₂×C₄×C₈×C₇₁

C₂²

yes

characteristic

#14556068

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

—

C₂×C₇₁⋊C₁₆

D₄

yes

complemented

C₂×#41×C₇₁

C₂×C₄

yes

—

#131×C₇₁

—

#131×C₇₁

—

C₂×M₁₆×C₇₁

—

C₂×M₁₆×C₇₁

C₂×C₄

yes

—

C₂²×C₈×C₇₁

—

C₂²×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊Q₈×C₇₁

C₈

yes

characteristic

#127×C₇₁

C₈

yes

characteristic

#124×C₇₁

C₈

yes

—

#121×C₇₁

—

C₄×D₄×C₇₁

—

C₂×C₄²×C₇₁

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₄×C₈×C₇₁

D₄

yes

—

C₄×C₈×C₇₁

D₄

yes

—

C₇₁⋊C₁₆

—

C₇₁⋊C₁₆

—

#41×C₇₁

—

#41×C₇₁

—

C₂×Q₈×C₇₁

C₂×C₈

yes

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

—

C₂×D₄×C₇₁

C₂×C₈

yes

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

M₁₆

yes

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²⋊C₄

yes

—

C₂×C₈×C₇₁

C₂×D₄

yes

—

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

#41

yes

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

C₂²⋊C₄

yes

—

C₄²×C₇₁

C₂×C₈

yes

characteristic

C₄²×C₇₁

C₂×C₈

yes

characteristic

C₂³×C₇₁

—

C₂³×C₇₁

C₂×M₁₆

yes

characteristic

Q₈×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

—

C₂×C₄×C₇₁

C₂²⋊C₈

yes

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₄×D₄

yes

—

C₂×C₄×C₇₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₇₁

#131

yes

—

C₈×C₇₁

—

C₈×C₇₁

—

C₈×C₇₁

#121

yes

—

C₈×C₇₁

yes

C₈×C₇₁

yes

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₇₁

#436

yes

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₈×D₄

yes

—

#13192

—

maximal, Sylow

100

C₂×C₇₁

—

101

C₂×C₇₁

—

102

C₂×C₇₁

#1954

yes

characteristic

103

C₂×C₇₁

#2117

yes

—

104

#2931

D₇₁

yes

characteristic

105

#2150

—

106

C₂×#350

—

107

C₂×#346

—

108

C₇₁

#13192

yes

characteristic, complemented, Sylow

109

C₂×#131

C₂×D₇₁

yes

—

110

#532

Dic₇₁

yes

characteristic

111

C₂×M₃₂

—

112

C₂²×C₁₆

—

113

#436

—

114

C₈×D₄

—

115

#423

Dic₇₁

yes

characteristic

116

#408

Dic₇₁

yes

—

117

C₂×C₄×C₈

C₂×D₇₁

yes

characteristic

118

C₄⋊C₁₆

—

142

—

119

#350

—

142

—

120

#346

—

142

—

121

C₂×#41

C₂×Dic₇₁

yes

—

122

#131

—

123

#131

—

124

C₂×M₁₆

—

125

C₂×M₁₆

C₂×Dic₇₁

yes

—

126

C₂²×C₈

—

127

C₂²×C₈

C₂×Dic₇₁

yes

characteristic

128

C₂²×C₈

C₂²×D₇₁

yes

characteristic

129

C₄⋊Q₈

C₇₁⋊C₈

yes

characteristic

130

#127

C₇₁⋊C₈

yes

characteristic

131

#124

C₇₁⋊C₈

yes

—

132

#121

—

133

C₄×D₄

—

134

C₂×C₄²

C₂×Dic₇₁

yes

characteristic

135

M₃₂

—

142

—

136

C₂×C₁₆

—

137

C₂×C₁₆

—

142

—

138

C₂×C₁₆

—

142

—

139

C₂×C₁₆

—

142

—

140

C₄⋊C₈

—

141

C₂²⋊C₈

—

142

C₄×C₈

C₂²⋊D₇₁

yes

—

143

C₄×C₈

C₂²⋊D₇₁

yes

—

144

#41

—

145

#41

—

146

C₂×Q₈

C₂×C₇₁⋊C₈

yes

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

C₂×C₇₁⋊C₈

yes

—

150

C₂²×C₄

—

151

C₂²×C₄

#11765849

yes

—

152

C₂²×C₄

C₂²×Dic₇₁

yes

characteristic

153

M₁₆

—

154

M₁₆

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

C₂²⋊Dic₇₁

yes

—

160

C₂×C₈

D₄×D₇₁

yes

—

161

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

162

C₂×C₈

C₂×C₂²⋊D₇₁

yes

characteristic

163

C₂×C₈

#11765864

yes

—

164

C₄⋊C₄

—

165

C₂²⋊C₄

—

166

C₄²

C₂²⋊Dic₇₁

yes

—

167

C₄²

C₂×C₇₁⋊C₈

yes

characteristic

168

C₄²

C₂×C₇₁⋊C₈

yes

characteristic

169

C₁₆

—

284

—

170

C₁₆

—

142

—

171

C₂³

—

172

C₂³

C₂×#11765849

yes

characteristic

173

Q₈

—

174

D₄

—

175

D₄

—

176

D₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

C₂²⋊(C₇₁⋊C₈)

yes

—

182

C₂×C₄

C₂²⋊(C₇₁⋊C₈)

yes

—

183

C₂×C₄

C₂×C₂²⋊Dic₇₁

yes

characteristic

184

C₂×C₄

D₄×Dic₇₁

yes

—

185

C₂×C₄

C₂²×C₇₁⋊C₈

yes

characteristic

186

C₂×C₄

#14556135

yes

—

187

C₈

—

188

C₈

—

189

C₈

#14556099

yes

—

190

C₈

#14556115

yes

characteristic

191

C₈

#14556124

yes

characteristic

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

C₂×C₂²⋊(C₇₁⋊C₈)

yes

characteristic

196

C₂²

#17986077

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

#17985902

yes

characteristic

201

C₄

#17985966

yes

characteristic

202

C₄

D₄×C₇₁⋊C₈

yes

—

203

C₂

—

204

C₂

—

205

C₂

#22589135

yes

characteristic

206

C₂

#22589968

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₇₁×#2931	C₂
socle	C₂²×C₇₁	C₂×C₂²⋊C₈
prime radical	#532×C₇₁	C₄
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	#2931	D₇₁
hypocenter	C₇₁	#13192
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₇₁

commutator

C₂×C₄×C₇₁

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₇₁×#2931

C₂

socle

C₂²×C₇₁

C₂×C₂²⋊C₈

prime radical

#532×C₇₁

C₄

cosocle

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

N	H ≅ G/N	type
1. #22590096	C₂	semidirect
2. C₂×#17985783	C₂	semidirect
3. C₂×#17985775	C₂	semidirect
21. C₂×C₇₁⋊C₁₆	D₄	semidirect
108. C₇₁	#13192	semidirect

H ≅ G/N

type

1. #22590096

C₂

semidirect

2. C₂×#17985783

C₂

semidirect

3. C₂×#17985775

C₂

semidirect

21. C₂×C₇₁⋊C₁₆

D₄

semidirect

108. C₇₁

#13192

semidirect

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

subgroup	index
#22590096	2
C₂×#17985783	2
C₂×#17985775	2
C₇₁×#2931	2
#13192	71

subgroup

index

C₇₁×#2931

Subgroups — #31915620

Conjugacy classes of subgroups

Complements

Maximal subgroups