Group #31806594 — subgroups

Subgroups — #31806594

Order 17792.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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×C₄⋊Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#17984776	C₂	1	2	yes	maximal, complemented
3	#22580813	C₂	1	1	yes	maximal, characteristic
4	#22580716	C₂	1	2	yes	maximal, complemented
5	C₂×C₂²⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₁₃₉	—	2	1	no	—
7	C₂×C₄⋊Dic₁₃₉	—	2	4	no	—
8	C₂×C₄⋊Dic₁₃₉	—	2	1	no	—
9	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
12	C₂×C₂²⋊Dic₁₃₉	—	2	1	no	—
13	#17984776	—	2	4	no	—
14	C₁₃₉⋊#95	—	2	1	no	—
15	C₂³×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₁₃₉	C₄	1	4	yes	complemented
18	C₂²×Dic₁₃₉	—	2	4	no	—
19	C₂²×Dic₁₃₉	—	2	2	no	—
20	C₂²×Dic₁₃₉	—	2	1	no	—
21	C₂²×Dic₁₃₉	—	2	1	no	—
22	C₂²×Dic₁₃₉	—	4	2	no	—
23	C₂²×Dic₁₃₉	—	4	2	no	—
24	C₄⋊Dic₁₃₉	—	2	4	no	—
25	C₄⋊Dic₁₃₉	—	2	2	no	—
26	C₄⋊Dic₁₃₉	—	2	2	no	—
27	C₄⋊Dic₁₃₉	—	2	2	no	—
28	C₄⋊Dic₁₃₉	D₄	1	4	yes	—
29	C₂²⋊Dic₁₃₉	—	4	2	no	—
30	C₂⁴×C₁₃₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₃₉	—	2	2	no	—
32	C₂²×C₄×C₁₃₉	—	2	2	no	—
33	C₂²×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
34	C₂²×C₄×C₁₃₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃₉	Q₈	1	2	yes	—
36	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂×C₈×C₁₃₉	—	2	2	no	—
38	C₂×C₈×C₁₃₉	—	2	2	no	—
39	C₂×C₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
40	C₂×Dic₁₃₉	—	2	4	no	—
41	C₂×Dic₁₃₉	—	4	8	no	—
42	C₂×Dic₁₃₉	—	4	2	no	—
43	C₂×Dic₁₃₉	—	4	2	no	—
44	C₂×Dic₁₃₉	—	4	1	no	—
45	C₂×Dic₁₃₉	—	4	1	no	—
46	C₂×Dic₁₃₉	—	4	1	no	—
47	C₂×Dic₁₃₉	—	4	1	no	—
48	C₂×Dic₁₃₉	—	4	1	no	—
49	C₂×Dic₁₃₉	—	4	1	no	—
50	C₂³×C₁₃₉	—	2	1	no	—
51	C₂³×C₁₃₉	—	2	1	no	—
52	C₂³×C₁₃₉	—	2	1	no	—
53	C₂³×C₁₃₉	—	2	1	no	—
54	C₂³×C₁₃₉	C₄⋊C₄	1	2	yes	—
55	C₂³×C₁₃₉	D₈	1	2	yes	—
56	C₂³×C₁₃₉	Q₁₆	1	2	yes	—
57	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃₉	—	2	1	no	—
59	C₂×C₄×C₁₃₉	—	2	1	no	—
60	C₂×C₄×C₁₃₉	—	2	4	no	—
61	C₂×C₄×C₁₃₉	—	2	4	no	—
62	C₂×C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
63	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃₉	#41	1	2	yes	—
67	C₈×C₁₃₉	—	2	4	no	—
68	C₂²×C₁₃₉	—	2	2	no	—
69	C₂²×C₁₃₉	—	2	2	no	—
70	C₂²×C₁₃₉	—	2	2	no	—
71	C₂²×C₁₃₉	—	2	2	no	—
72	C₂²×C₁₃₉	—	2	2	no	—
73	C₂²×C₁₃₉	—	2	2	no	—
74	C₂²×C₁₃₉	#107	1	4	yes	complemented
75	C₂²×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₁₃₉	#120	1	1	yes	characteristic
77	C₂²×C₁₃₉	#123	1	1	yes	characteristic
78	C₂²×C₁₃₉	C₂×D₈	1	1	yes	characteristic
79	C₂²×C₁₃₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₂²×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
81	C₂²×C₁₃₉	#137	1	1	yes	characteristic
82	C₄×C₁₃₉	—	2	2	no	—
83	C₄×C₁₃₉	C₄×D₄	1	2	yes	—
84	C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
85	Dic₁₃₉	—	4	4	no	—
86	Dic₁₃₉	—	8	1	no	—
87	Dic₁₃₉	—	8	1	no	—
88	C₂×C₁₃₉	—	2	4	no	—
89	C₂×C₁₃₉	#385	1	1	yes	characteristic
90	C₂×C₁₃₉	C₂×#107	1	1	yes	characteristic
91	C₂×C₁₃₉	#428	1	1	yes	characteristic
92	C₂×C₁₃₉	#447	1	1	yes	characteristic
93	C₂×C₁₃₉	#451	1	1	yes	characteristic
94	C₂×C₁₃₉	#480	1	1	yes	characteristic
95	C₂×C₁₃₉	#484	1	1	yes	characteristic
96	C₁₃₉	#1852	1	1	yes	characteristic, complemented, Sylow
97	#1852	—	139	1	no	maximal, Sylow
98	C₂²×C₄⋊C₄	—	139	1	no	—
99	C₂×#107	—	139	2	no	—
100	C₂×C₂²⋊C₈	D₁₃₉	1	1	yes	characteristic
101	#380	—	139	1	no	—
102	#340	—	139	2	no	—
103	C₂³×C₄	—	278	1	no	—
104	C₂³×C₄	C₂×D₁₃₉	1	1	yes	characteristic
105	C₂²×C₈	C₂×D₁₃₉	1	2	yes	—
106	C₂×C₄⋊C₄	—	278	1	no	—
107	C₂×C₄⋊C₄	—	278	4	no	—
108	C₂×C₄⋊C₄	—	139	1	no	—
109	C₂×C₄⋊C₄	—	139	1	no	—
110	C₂×C₄⋊C₄	—	139	2	no	—
111	C₂×C₂²⋊C₄	—	278	1	no	—
112	#107	—	278	4	no	—
113	C₂²⋊C₈	Dic₁₃₉	1	4	yes	complemented
114	#95	—	278	1	no	—
115	C₂⁴	D₅₅₆	1	1	yes	characteristic
116	C₂²×C₄	—	2	2	no	—
117	C₂²×C₄	—	2	2	no	—
118	C₂²×C₄	—	278	4	no	—
119	C₂²×C₄	—	278	2	no	—
120	C₂²×C₄	—	278	1	no	—
121	C₂²×C₄	—	278	1	no	—
122	C₂²×C₄	—	556	2	no	—
123	C₂²×C₄	—	556	2	no	—
124	C₂²×C₄	C₂×Dic₁₃₉	1	2	yes	—
125	C₂²×C₄	D₅₅₆	1	1	yes	characteristic
126	C₂²×C₄	Dic₂₇₈	1	2	yes	—
127	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	C₂×Dic₁₃₉	1	4	yes	complemented
131	C₄⋊C₄	—	278	4	no	—
132	C₄⋊C₄	—	278	2	no	—
133	C₄⋊C₄	—	278	2	no	—
134	C₄⋊C₄	—	278	2	no	—
135	C₄⋊C₄	—	139	4	no	—
136	C₂²⋊C₄	—	556	2	no	—
137	C₂³	—	2	1	no	—
138	C₂³	—	2	1	no	—
139	C₂³	—	2	1	no	—
140	C₂³	—	2	1	no	—
141	C₂³	C₄⋊Dic₁₃₉	1	2	yes	—
142	C₂³	D₁₁₁₂	1	2	yes	—
143	C₂³	Dic₅₅₆	1	2	yes	—
144	C₂³	C₂×D₅₅₆	1	1	yes	characteristic
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	278	4	no	—
150	C₂×C₄	—	556	8	no	—
151	C₂×C₄	—	556	2	no	—
152	C₂×C₄	—	556	2	no	—
153	C₂×C₄	—	556	1	no	—
154	C₂×C₄	—	556	1	no	—
155	C₂×C₄	—	556	1	no	—
156	C₂×C₄	—	556	1	no	—
157	C₂×C₄	—	556	1	no	—
158	C₂×C₄	—	556	1	no	—
159	C₂×C₄	C₄⋊Dic₁₃₉	1	2	yes	—
160	C₂×C₄	C₂²×Dic₁₃₉	1	1	yes	characteristic
161	C₂×C₄	D₄×D₁₃₉	1	2	yes	—
162	C₂×C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
163	C₂×C₄	#14555784	1	2	yes	—
164	C₈	—	2	4	no	—
165	C₂²	—	2	2	no	—
166	C₂²	—	2	2	no	—
167	C₂²	—	2	2	no	—
168	C₂²	—	2	2	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	2	2	no	—
171	C₂²	#17984776	1	4	yes	complemented
172	C₂²	C₂×C₄⋊Dic₁₃₉	1	1	yes	characteristic
173	C₂²	#17984812	1	1	yes	characteristic
174	C₂²	#17984826	1	1	yes	characteristic
175	C₂²	C₂×D₁₁₁₂	1	1	yes	characteristic
176	C₂²	C₂×Dic₅₅₆	1	1	yes	characteristic
177	C₂²	#17984870	1	1	yes	characteristic
178	C₂²	#17984875	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	556	4	no	—
181	C₄	—	1112	1	no	—
182	C₄	—	1112	1	no	—
183	C₄	D₄×Dic₁₃₉	1	2	yes	—
184	C₄	#17984819	1	2	yes	—
185	C₂	—	2	4	no	—
186	C₂	#22580828	1	1	yes	characteristic
187	C₂	C₂×#17984776	1	1	yes	characteristic
188	C₂	#22580995	1	1	yes	characteristic
189	C₂	#22581089	1	1	yes	characteristic
190	C₂	#22581111	1	1	yes	characteristic
191	C₂	#22581267	1	1	yes	characteristic
192	C₂	#22581289	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₁₃₉

C₂

yes

maximal, characteristic

C₂×#17984776

C₂

yes

maximal, complemented

#22580813

C₂

yes

maximal, characteristic

#22580716

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₁₃₉

C₂

yes

maximal, characteristic

C₂³×Dic₁₃₉

—

C₂×C₄⋊Dic₁₃₉

—

C₂×C₄⋊Dic₁₃₉

—

C₂×C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₃₉

—

#17984776

—

C₁₃₉⋊#95

—

C₂³×C₄×C₁₃₉

C₂²

yes

characteristic

C₂²×C₈×C₁₃₉

C₂²

yes

—

C₂²⋊C₈×C₁₃₉

C₄

yes

complemented

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

D₄

yes

—

C₂²⋊Dic₁₃₉

—

C₂⁴×C₁₃₉

D₄

yes

characteristic

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

—

C₂²×C₄×C₁₃₉

C₂×C₄

yes

—

C₂²×C₄×C₁₃₉

D₄

yes

characteristic

C₂²×C₄×C₁₃₉

Q₈

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂×C₄

yes

complemented

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

C₂³×C₁₃₉

C₄⋊C₄

yes

—

C₂³×C₁₃₉

D₈

yes

—

C₂³×C₁₃₉

Q₁₆

yes

—

C₂³×C₁₃₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×D₄

yes

—

C₂×C₄×C₁₃₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃₉

#41

yes

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

#107

yes

complemented

C₂²×C₁₃₉

C₂×C₄⋊C₄

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

C₂×D₈

yes

characteristic

C₂²×C₁₃₉

C₂×Q₁₆

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

yes

C₄×C₁₃₉

—

C₄×C₁₃₉

C₄×D₄

yes

—

C₄×C₁₃₉

C₂²⋊Q₈

yes

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₁₃₉

yes

characteristic, complemented, Sylow

#1852

—

139

maximal, Sylow

C₂²×C₄⋊C₄

—

139

—

C₂×#107

—

139

—

100

C₂×C₂²⋊C₈

D₁₃₉

yes

characteristic

101

#380

—

139

—

102

#340

—

139

—

103

C₂³×C₄

—

278

—

104

C₂³×C₄

C₂×D₁₃₉

yes

characteristic

105

C₂²×C₈

C₂×D₁₃₉

yes

—

106

C₂×C₄⋊C₄

—

278

—

107

C₂×C₄⋊C₄

—

278

—

108

C₂×C₄⋊C₄

—

139

—

109

C₂×C₄⋊C₄

—

139

—

110

C₂×C₄⋊C₄

—

139

—

111

C₂×C₂²⋊C₄

—

278

—

112

#107

—

278

—

113

C₂²⋊C₈

Dic₁₃₉

yes

complemented

114

#95

—

278

—

115

C₂⁴

D₅₅₆

yes

characteristic

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

278

—

119

C₂²×C₄

—

278

—

120

C₂²×C₄

—

278

—

121

C₂²×C₄

—

278

—

122

C₂²×C₄

—

556

—

123

C₂²×C₄

—

556

—

124

C₂²×C₄

C₂×Dic₁₃₉

yes

—

125

C₂²×C₄

D₅₅₆

yes

characteristic

126

C₂²×C₄

Dic₂₇₈

yes

—

127

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

C₂×Dic₁₃₉

yes

complemented

131

C₄⋊C₄

—

278

—

132

C₄⋊C₄

—

278

—

133

C₄⋊C₄

—

278

—

134

C₄⋊C₄

—

278

—

135

C₄⋊C₄

—

139

—

136

C₂²⋊C₄

—

556

—

137

C₂³

—

138

C₂³

—

139

C₂³

—

140

C₂³

—

141

C₂³

C₄⋊Dic₁₃₉

yes

—

142

C₂³

D₁₁₁₂

yes

—

143

C₂³

Dic₅₅₆

yes

—

144

C₂³

C₂×D₅₅₆

yes

characteristic

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

278

—

150

C₂×C₄

—

556

—

151

C₂×C₄

—

556

—

152

C₂×C₄

—

556

—

153

C₂×C₄

—

556

—

154

C₂×C₄

—

556

—

155

C₂×C₄

—

556

—

156

C₂×C₄

—

556

—

157

C₂×C₄

—

556

—

158

C₂×C₄

—

556

—

159

C₂×C₄

C₄⋊Dic₁₃₉

yes

—

160

C₂×C₄

C₂²×Dic₁₃₉

yes

characteristic

161

C₂×C₄

D₄×D₁₃₉

yes

—

162

C₂×C₄

C₂×Dic₂₇₈

yes

characteristic

163

C₂×C₄

#14555784

yes

—

164

C₈

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

#17984776

yes

complemented

172

C₂²

C₂×C₄⋊Dic₁₃₉

yes

characteristic

173

C₂²

#17984812

yes

characteristic

174

C₂²

#17984826

yes

characteristic

175

C₂²

C₂×D₁₁₁₂

yes

characteristic

176

C₂²

C₂×Dic₅₅₆

yes

characteristic

177

C₂²

#17984870

yes

characteristic

178

C₂²

#17984875

yes

characteristic

179

C₄

—

180

C₄

—

556

—

181

C₄

—

1112

—

182

C₄

—

1112

—

183

C₄

D₄×Dic₁₃₉

yes

—

184

C₄

#17984819

yes

—

185

C₂

—

186

C₂

#22580828

yes

characteristic

187

C₂

C₂×#17984776

yes

characteristic

188

C₂

#22580995

yes

characteristic

189

C₂

#22581089

yes

characteristic

190

C₂

#22581111

yes

characteristic

191

C₂

#22581267

yes

characteristic

192

C₂

#22581289

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₅₆
commutator	C₂×C₄×C₁₃₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃₉
Fitting	C₂×C₂²⋊C₈×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂×D₄
prime radical	C₂⁴×C₁₃₉	D₄
cosocle	C₂²×C₄×C₁₃₉	C₂³
hypercenter	C₂×C₂²⋊C₈	D₁₃₉
hypocenter	C₁₃₉	#1852
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂³

C₂×D₅₅₆

commutator

C₂×C₄×C₁₃₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₃₉

Fitting

C₂×C₂²⋊C₈×C₁₃₉

C₂

socle

C₂³×C₁₃₉

C₂×D₄

prime radical

C₂⁴×C₁₃₉

D₄

cosocle

C₂²×C₄×C₁₃₉

C₂³

hypercenter

C₂×C₂²⋊C₈

D₁₃₉

hypocenter

C₁₃₉

#1852

LCS

G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
2. C₂×#17984776	C₂	semidirect
4. #22580716	C₂	semidirect
17. C₂²⋊C₈×C₁₃₉	C₄	semidirect
39. C₂×C₈×C₁₃₉	C₂×C₄	semidirect
74. C₂²×C₁₃₉	#107	semidirect
96. C₁₃₉	#1852	semidirect
113. C₂²⋊C₈	Dic₁₃₉	semidirect
130. C₂×C₈	C₂×Dic₁₃₉	semidirect
171. C₂²	#17984776	semidirect

H ≅ G/N

type

2. C₂×#17984776

C₂

semidirect

4. #22580716

C₂

semidirect

17. C₂²⋊C₈×C₁₃₉

C₄

semidirect

39. C₂×C₈×C₁₃₉

C₂×C₄

semidirect

74. C₂²×C₁₃₉

#107

semidirect

96. C₁₃₉

#1852

semidirect

113. C₂²⋊C₈

Dic₁₃₉

semidirect

130. C₂×C₈

C₂×Dic₁₃₉

semidirect

171. C₂²

#17984776

semidirect

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

subgroup	index
C₂²×C₄⋊Dic₁₃₉	2
C₂×#17984776	2
#22580813	2
#22580716	2
C₂×C₂²⋊C₈×C₁₃₉	2
#1852	139

subgroup

index

C₂²×C₄⋊Dic₁₃₉

C₂×C₂²⋊C₈×C₁₃₉

139

Subgroups — #31806594

Conjugacy classes of subgroups

Complements

Maximal subgroups