Group #26132490 — subgroups

Subgroups — #26132490

Order 12032.

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

normal subgroups only

This group has 454 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	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#20241465	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	C₄	1	1	yes	characteristic
6	C₂×#13093983	C₄	1	1	yes	characteristic
7	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	#15689078	—	2	2	no	—
9	#15689078	—	2	2	no	—
10	C₂×#13093934	C₄	1	2	yes	—
11	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
12	C₂²⋊(C₄₇⋊C₁₆)	—	2	2	no	—
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₄₇×C₂²⋊C₁₆	—	2	2	no	—
16	C₂×#10625329	—	2	2	no	—
17	C₂×#10625329	—	2	4	no	—
18	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
19	#13093983	—	2	2	no	—
20	#13093983	—	2	2	no	—
21	C₂×C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
22	C₂×C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₄₇	C₈	1	2	yes	—
24	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₄₇⋊C₁₆	—	2	2	no	—
26	C₂×C₄₇⋊C₁₆	—	2	4	no	—
27	#13093934	—	2	4	no	—
28	C₈×Dic₄₇	—	2	2	no	—
29	C₈×Dic₄₇	—	2	2	no	—
30	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₇	—	2	4	no	—
32	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₇	D₄	1	2	yes	—
34	C₂²×C₈×C₄₇	D₄	1	2	yes	—
35	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×C₁₆×C₄₇	—	2	2	no	—
37	C₂×C₁₆×C₄₇	—	2	4	no	—
38	C₂⁴×C₄₇	C₂×C₈	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	—	2	2	no	—
40	C₂²×C₄×C₄₇	—	2	2	no	—
41	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
46	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₄₇	—	2	2	no	—
48	C₂×C₈×C₄₇	—	2	4	no	—
49	C₂×C₈×C₄₇	—	2	4	no	—
50	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₄₇	#41	1	4	yes	—
54	C₂²⋊Dic₄₇	—	2	4	no	—
55	C₄⋊Dic₄₇	—	2	2	no	—
56	C₄⋊Dic₄₇	—	2	2	no	—
57	C₄×Dic₄₇	—	2	2	no	—
58	C₄×Dic₄₇	—	2	2	no	—
59	#10625329	—	2	8	no	—
60	C₂×C₄₇⋊C₈	—	2	2	no	—
61	C₂×C₄₇⋊C₈	—	2	2	no	—
62	C₂×C₄₇⋊C₈	M₁₆	1	4	yes	—
63	C₁₆×C₄₇	—	4	2	no	—
64	C₄₇⋊C₁₆	—	4	2	no	—
65	C₂³×C₄₇	—	2	2	no	—
66	C₂³×C₄₇	—	2	2	no	—
67	C₂³×C₄₇	—	2	2	no	—
68	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
69	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₄×C₄₇	—	2	2	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	4	no	—
74	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₇	#117	1	2	yes	—
77	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
78	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
79	C₂×Dic₄₇	—	2	2	no	—
80	C₂×Dic₄₇	—	2	2	no	—
81	C₂×Dic₄₇	—	2	4	no	—
82	C₂×Dic₄₇	—	2	4	no	—
83	C₈×C₄₇	—	2	2	no	—
84	C₈×C₄₇	#123	1	2	yes	—
85	C₈×C₄₇	#123	1	2	yes	—
86	C₄₇⋊C₈	—	2	4	no	—
87	#12845	—	47	1	no	maximal, Sylow
88	C₂²×C₄₇	—	2	2	no	—
89	C₂²×C₄₇	—	2	2	no	—
90	C₂²×C₄₇	—	2	2	no	—
91	C₂²×C₄₇	—	4	4	no	—
92	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
93	C₂²×C₄₇	#431	1	2	yes	—
94	C₂²×C₄₇	#504	1	2	yes	—
95	C₂²×C₄₇	#504	1	2	yes	—
96	C₄×C₄₇	—	2	2	no	—
97	C₄×C₄₇	#381	1	1	yes	characteristic
98	C₄×C₄₇	#407	1	1	yes	characteristic
99	C₄×C₄₇	#432	1	2	yes	—
100	Dic₄₇	—	4	2	no	—
101	Dic₄₇	—	4	2	no	—
102	C₂×#405	—	47	1	no	—
103	C₂×C₂²⋊C₁₆	—	47	1	no	—
104	C₂×C₂²⋊C₁₆	D₄₇	1	1	yes	characteristic
105	#1374	—	47	4	no	—
106	C₂×C₄₇	—	4	2	no	—
107	C₂×C₄₇	#1817	1	1	yes	characteristic
108	C₂×C₄₇	#2113	1	1	yes	characteristic
109	C₂×C₄₇	#2113	1	1	yes	characteristic
110	C₂×C₄₇	#2164	1	4	yes	—
111	C₂²×M₁₆	—	47	1	no	—
112	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
113	C₂×#117	—	47	1	no	—
114	C₂²×C₁₆	—	47	2	no	—
115	C₂²×C₁₆	C₂×D₄₇	1	2	yes	—
116	#405	—	94	2	no	—
117	#405	—	94	2	no	—
118	C₂×#97	—	47	2	no	—
119	C₂×C₄×C₈	—	47	2	no	—
120	C₂²⋊C₁₆	—	2	2	no	—
121	C₂²⋊C₁₆	—	94	2	no	—
122	C₄₇	#12845	1	1	yes	characteristic, complemented, Sylow
123	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
124	C₂×M₁₆	—	94	4	no	—
125	C₂×M₁₆	—	94	2	no	—
126	C₂²×C₈	—	2	4	no	—
127	C₂²×C₈	—	47	2	no	—
128	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
129	C₂²×C₈	D₁₈₈	1	2	yes	—
130	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
131	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
132	#117	—	94	2	no	—
133	#117	—	94	2	no	—
134	C₂×C₄⋊C₄	—	47	1	no	—
135	C₂×C₄⋊C₄	—	47	1	no	—
136	C₂×C₂²⋊C₄	—	47	2	no	—
137	C₂×C₄²	—	47	2	no	—
138	C₂×C₁₆	—	2	4	no	—
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	94	2	no	—
141	C₂×C₁₆	—	94	4	no	—
142	#97	—	94	4	no	—
143	C₄×C₈	—	94	2	no	—
144	C₄×C₈	—	94	2	no	—
145	C₂⁴	C₈×D₄₇	1	1	yes	characteristic
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	47	2	no	—
149	C₂²×C₄	—	47	2	no	—
150	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
151	C₂²×C₄	#10625324	1	2	yes	—
152	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
153	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
154	M₁₆	—	94	8	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	2	4	no	—
158	C₂×C₈	—	47	4	no	—
159	C₂×C₈	—	94	2	no	—
160	C₂×C₈	—	94	2	no	—
161	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
162	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
163	C₂×C₈	#10625352	1	4	yes	—
164	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
165	C₄⋊C₄	—	94	2	no	—
166	C₄⋊C₄	—	94	2	no	—
167	C₂²⋊C₄	—	94	4	no	—
168	C₄²	—	94	2	no	—
169	C₄²	—	94	2	no	—
170	C₁₆	—	4	2	no	—
171	C₁₆	—	188	2	no	—
172	C₂³	—	2	2	no	—
173	C₂³	—	2	2	no	—
174	C₂³	—	2	2	no	—
175	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
176	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	94	4	no	—
182	C₂×C₄	—	94	4	no	—
183	C₂×C₄	—	94	2	no	—
184	C₂×C₄	—	94	2	no	—
185	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
186	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
187	C₂×C₄	#13093980	1	2	yes	—
188	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
189	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
190	C₈	—	2	2	no	—
191	C₈	—	94	4	no	—
192	C₈	#13094005	1	2	yes	—
193	C₈	#13094008	1	2	yes	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	4	4	no	—
198	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
199	C₂²	#15689173	1	2	yes	—
200	C₂²	#15689539	1	2	yes	—
201	C₂²	#15689541	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	188	2	no	—
204	C₄	—	188	2	no	—
205	C₄	#15688984	1	1	yes	characteristic
206	C₄	#15689086	1	1	yes	characteristic
207	C₄	#15689177	1	2	yes	—
208	C₂	—	4	2	no	—
209	C₂	#20243454	1	1	yes	characteristic
210	C₂	#20245001	1	1	yes	characteristic
211	C₂	#20245003	1	1	yes	characteristic
212	C₂	#20245192	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689078

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic

#20241465

C₂

yes

maximal, complemented

C₂×C₄₇×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×#10625329

C₄

yes

characteristic

C₂×#13093983

C₄

yes

characteristic

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689078

—

#15689078

—

C₂×#13093934

C₄

yes

—

C₂×C₈×Dic₄₇

C₂²

yes

—

C₂²⋊(C₄₇⋊C₁₆)

—

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₁₆×C₄₇

C₂²

yes

—

C₄₇×C₂²⋊C₁₆

—

C₂×#10625329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

#13093983

—

#13093983

—

C₂×C₄⋊Dic₄₇

C₈

yes

characteristic

C₂×C₄⋊Dic₄₇

C₈

yes

characteristic

C₂×C₂²⋊Dic₄₇

C₈

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

#13093934

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂⁴×C₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₈

yes

—

C₂²×Dic₄₇

C₂×C₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

M₁₆

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₈

yes

—

C₂³×C₄₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#117

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#123

yes

—

C₈×C₄₇

#123

yes

—

C₄₇⋊C₈

—

#12845

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₄₇

#431

yes

—

C₂²×C₄₇

#504

yes

—

C₂²×C₄₇

#504

yes

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

100

Dic₄₇

—

101

Dic₄₇

—

102

C₂×#405

—

103

C₂×C₂²⋊C₁₆

—

104

C₂×C₂²⋊C₁₆

D₄₇

yes

characteristic

105

#1374

—

106

C₂×C₄₇

—

107

C₂×C₄₇

#1817

yes

characteristic

108

C₂×C₄₇

#2113

yes

characteristic

109

C₂×C₄₇

#2113

yes

characteristic

110

C₂×C₄₇

#2164

yes

—

111

C₂²×M₁₆

—

112

C₂³×C₈

C₂×D₄₇

yes

characteristic

113

C₂×#117

—

114

C₂²×C₁₆

—

115

C₂²×C₁₆

C₂×D₄₇

yes

—

116

#405

—

117

#405

—

118

C₂×#97

—

119

C₂×C₄×C₈

—

120

C₂²⋊C₁₆

—

121

C₂²⋊C₁₆

—

122

C₄₇

#12845

yes

characteristic, complemented, Sylow

123

C₂³×C₄

C₄×D₄₇

yes

characteristic

124

C₂×M₁₆

—

125

C₂×M₁₆

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

C₄×D₄₇

yes

characteristic

129

C₂²×C₈

D₁₈₈

yes

—

130

C₂²×C₈

C₂²⋊D₄₇

yes

—

131

C₂²×C₈

C₂²×D₄₇

yes

characteristic

132

#117

—

133

#117

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

#97

—

143

C₄×C₈

—

144

C₄×C₈

—

145

C₂⁴

C₈×D₄₇

yes

characteristic

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

C₈×D₄₇

yes

characteristic

151

C₂²×C₄

#10625324

yes

—

152

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

153

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

154

M₁₆

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

162

C₂×C₈

C₂×D₁₈₈

yes

characteristic

163

C₂×C₈

#10625352

yes

—

164

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

—

170

C₁₆

—

171

C₁₆

—

188

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

(C₂×D₄₇)⋊C₈

yes

—

176

C₂³

C₂×C₈×D₄₇

yes

characteristic

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

186

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

187

C₂×C₄

#13093980

yes

—

188

C₂×C₄

M₁₆×D₄₇

yes

—

189

C₂×C₄

C₂×#10625324

yes

characteristic

190

C₈

—

191

C₈

—

192

C₈

#13094005

yes

—

193

C₈

#13094008

yes

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

199

C₂²

#15689173

yes

—

200

C₂²

#15689539

yes

—

201

C₂²

#15689541

yes

—

202

C₄

—

203

C₄

—

188

—

204

C₄

—

188

—

205

C₄

#15688984

yes

characteristic

206

C₄

#15689086

yes

characteristic

207

C₄

#15689177

yes

—

208

C₂

—

209

C₂

#20243454

yes

characteristic

210

C₂

#20245001

yes

characteristic

211

C₂

#20245003

yes

characteristic

212

C₂

#20245192

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂²×C₈
Fitting	C₂×C₄₇×C₂²⋊C₁₆	C₂
prime radical	C₂⁴×C₄₇	C₂×C₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×C₂²⋊C₁₆	D₄₇
hypocenter	C₄₇	#12845
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₄₇

commutator, socle

C₂³×C₄₇

C₂²×C₈

Fitting

C₂×C₄₇×C₂²⋊C₁₆

C₂

prime radical

C₂⁴×C₄₇

C₂×C₈

cosocle

C₂²×C₈×C₄₇

C₂³

hypercenter

C₂×C₂²⋊C₁₆

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₈ ◁ C₂×C₂²⋊C₁₆

N	H ≅ G/N	type
3. #20241465	C₂	semidirect
122. C₄₇	#12845	semidirect

H ≅ G/N

type

3. #20241465

C₂

semidirect

122. C₄₇

#12845

semidirect

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

subgroup	index
C₂×#15689078	2
C₂×C₂²⋊(C₄₇⋊C₁₆)	2
#20241465	2
C₂×C₄₇×C₂²⋊C₁₆	2
#12845	47

subgroup

index

C₂×#15689078

C₂×C₂²⋊(C₄₇⋊C₁₆)

#20241465

C₂×C₄₇×C₂²⋊C₁₆

#12845

Subgroups — #26132490

Conjugacy classes of subgroups

Complements

Maximal subgroups