Group #26134509 — subgroups

Subgroups — #26134509

Order 12032.

590 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 159 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×#15689500	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688923	C₂	1	4	yes	maximal, complemented
3	C₂×#15688899	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₇₆	—	2	1	no	—
6	C₂²×D₃₇₆	C₂²	1	2	yes	—
7	C₂×#13094021	—	2	1	no	—
8	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
9	#15689500	—	2	2	no	—
10	#15689500	C₄	1	4	yes	complemented
11	#15688923	—	2	8	no	—
12	#15688899	—	2	2	no	—
13	C₂×#107×C₄₇	C₂²	1	2	yes	—
14	C₂×#106×C₄₇	—	2	1	no	—
15	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#382	—	2	1	no	—
17	C₂²×D₁₈₈	—	2	2	no	—
18	C₂²×D₁₈₈	—	4	2	no	—
19	C₂×D₃₇₆	—	2	4	no	—
20	C₂×D₃₇₆	—	2	4	no	—
21	C₂×D₃₇₆	—	2	4	no	—
22	C₂×D₃₇₆	—	2	2	no	—
23	C₂×D₃₇₆	—	4	2	no	—
24	C₂×D₃₇₆	—	4	2	no	—
25	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
26	#13094021	—	2	4	no	—
27	#13094021	—	4	2	no	—
28	C₂×C₄₇⋊C₁₆	—	2	2	no	—
29	C₂×C₄₇⋊C₁₆	—	2	2	no	—
30	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	complemented
31	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
34	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
35	#107×C₄₇	—	2	4	no	—
36	#106×C₄₇	—	4	2	no	—
37	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₄₇	D₄	1	2	yes	—
39	#95×C₄₇	—	4	2	no	—
40	C₂³×D₄₇	—	4	2	no	—
41	C₂²×C₄×C₄₇	—	4	2	no	—
42	C₂²×C₄×C₄₇	D₈	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂×D₁₈₈	—	2	4	no	—
45	C₂×D₁₈₈	—	4	2	no	—
46	C₂×D₁₈₈	—	4	2	no	—
47	C₂×D₁₈₈	—	4	2	no	—
48	C₂×D₁₈₈	—	4	2	no	—
49	C₂×D₁₈₈	—	4	8	no	—
50	C₂×D₁₈₈	—	4	2	no	—
51	C₂×D₁₈₈	—	8	8	no	—
52	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
53	C₂×C₈×C₄₇	D₈	1	2	yes	—
54	C₂×C₈×C₄₇	SD₁₆	1	2	yes	—
55	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₄₇	#41	1	2	yes	—
59	C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₄⋊C₄×C₄₇	—	4	2	no	—
61	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₄²×C₄₇	SD₁₆	1	2	yes	—
63	D₃₇₆	—	2	8	no	—
64	D₃₇₆	—	4	8	no	—
65	D₃₇₆	—	4	4	no	—
66	C₄₇⋊C₁₆	—	2	4	no	—
67	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
68	C₂²×D₄₇	—	4	4	no	—
69	C₂²×D₄₇	—	8	2	no	—
70	C₂²×D₄₇	—	8	2	no	—
71	C₂²×D₄₇	—	8	8	no	—
72	C₂×C₄×C₄₇	—	2	4	no	—
73	C₂×C₄×C₄₇	—	8	2	no	—
74	C₂×C₄×C₄₇	—	8	4	no	—
75	C₂×C₄×C₄₇	#102	1	4	yes	—
76	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
78	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
82	D₁₈₈	—	4	4	no	—
83	D₁₈₈	—	4	4	no	—
84	D₁₈₈	—	8	16	no	—
85	D₁₈₈	—	8	2	no	—
86	D₁₈₈	—	8	2	no	—
87	C₈×C₄₇	#102	1	4	yes	—
88	C₈×C₄₇	C₄×D₄	1	2	yes	—
89	C₈×C₄₇	#121	1	2	yes	—
90	#13206	—	47	1	no	maximal, Sylow
91	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
92	C₂²×C₄₇	#486	1	1	yes	characteristic
93	C₂²×C₄₇	#493	1	1	yes	characteristic
94	C₂²×C₄₇	#509	1	4	yes	—
95	C₂×D₄₇	—	8	8	no	—
96	C₂×D₄₇	—	8	4	no	—
97	C₂×D₄₇	—	16	4	no	—
98	C₂×D₄₇	—	16	4	no	—
99	C₄×C₄₇	—	2	4	no	—
100	C₄×C₄₇	—	16	2	no	—
101	C₄×C₄₇	#390	1	1	yes	characteristic
102	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
103	C₄×C₄₇	#486	1	1	yes	characteristic
104	C₄×C₄₇	#492	1	1	yes	characteristic
105	C₂×#493	—	47	1	no	—
106	C₂×#357	—	47	4	no	—
107	C₂×#346	—	47	1	no	—
108	#1846	D₄₇	1	1	yes	characteristic, complemented
109	C₂×C₄₇	#1957	1	1	yes	characteristic
110	C₂×C₄₇	#2140	1	2	yes	—
111	C₂×C₄₇	#2244	1	2	yes	—
112	C₂×C₄₇	#2250	1	2	yes	—
113	D₄₇	—	16	4	no	—
114	C₂²×D₈	—	47	2	no	—
115	C₂²×D₈	—	94	1	no	—
116	C₂×#127	—	94	1	no	—
117	C₂²×C₁₆	—	47	2	no	—
118	#493	—	47	4	no	—
119	#493	—	94	2	no	—
120	C₂×#107	C₂×D₄₇	1	2	yes	—
121	C₂×#106	—	2	1	no	—
122	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
123	#382	—	2	1	no	—
124	#357	—	94	8	no	—
125	#346	—	94	2	no	—
126	C₄₇	#13206	1	1	yes	characteristic, complemented, Sylow
127	C₂²×D₄	—	94	2	no	—
128	C₂²×D₄	—	188	2	no	—
129	C₂×D₈	—	47	4	no	—
130	C₂×D₈	—	94	4	no	—
131	C₂×D₈	—	94	2	no	—
132	C₂×D₈	—	94	4	no	—
133	C₂×D₈	—	94	4	no	—
134	C₂×D₈	—	188	2	no	—
135	C₂×D₈	—	188	2	no	—
136	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
138	#127	—	94	4	no	—
139	#127	—	188	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
142	C₂×C₁₆	—	47	4	no	—
143	C₂×C₁₆	—	94	2	no	—
144	C₂×C₁₆	—	94	2	no	—
145	#107	—	2	4	no	—
146	#106	—	4	2	no	—
147	C₄×C₈	C₄×D₄₇	1	2	yes	—
148	C₄×C₈	D₁₈₈	1	2	yes	—
149	#95	—	4	2	no	—
150	C₂⁴	—	188	2	no	—
151	C₂×D₄	—	94	4	no	—
152	C₂×D₄	—	376	8	no	—
153	C₂×D₄	—	188	8	no	—
154	C₂×D₄	—	188	2	no	—
155	C₂×D₄	—	188	2	no	—
156	C₂×D₄	—	188	2	no	—
157	C₂×D₄	—	188	2	no	—
158	C₂×D₄	—	188	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	#10625334	1	2	yes	—
161	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
162	D₈	—	94	8	no	—
163	D₈	—	188	8	no	—
164	D₈	—	188	4	no	—
165	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
166	C₂×C₈	#10625334	1	2	yes	—
167	C₂×C₈	#10625336	1	2	yes	—
168	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
169	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
170	C₂×C₈	D₄×D₄₇	1	2	yes	—
171	C₂×C₈	#10625354	1	2	yes	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	2	no	—
174	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
175	C₄²	#10625336	1	2	yes	—
176	C₁₆	—	94	4	no	—
177	C₂³	—	376	2	no	—
178	C₂³	—	376	8	no	—
179	C₂³	—	376	2	no	—
180	C₂³	—	188	4	no	—
181	C₂³	C₂×#10625334	1	1	yes	characteristic
182	D₄	—	376	16	no	—
183	D₄	—	376	2	no	—
184	D₄	—	376	2	no	—
185	D₄	—	188	4	no	—
186	D₄	—	188	4	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	8	2	no	—
189	C₂×C₄	—	8	4	no	—
190	C₂×C₄	#13093944	1	4	yes	—
191	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#13094013	1	1	yes	characteristic
193	C₂×C₄	#13094020	1	1	yes	characteristic
194	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
195	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
196	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
197	C₈	#13093944	1	4	yes	—
198	C₈	#13093986	1	2	yes	—
199	C₈	#13093999	1	2	yes	—
200	C₂²	—	376	8	no	—
201	C₂²	—	376	4	no	—
202	C₂²	—	752	4	no	—
203	C₂²	—	752	4	no	—
204	C₂²	C₂×#13093944	1	1	yes	characteristic
205	C₂²	#15689471	1	1	yes	characteristic
206	C₂²	#15689499	1	1	yes	characteristic
207	C₂²	#15689558	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	16	2	no	—
210	C₄	#15689024	1	1	yes	characteristic
211	C₄	C₂×#13093944	1	1	yes	characteristic
212	C₄	#15689471	1	1	yes	characteristic
213	C₄	#15689497	1	1	yes	characteristic
214	C₂	—	752	4	no	—
215	C₂	#20244193	1	1	yes	characteristic
216	C₂	#20245103	1	2	yes	—
217	C₂	#20245631	1	2	yes	—
218	C₂	#20245655	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689500

C₂

yes

maximal, characteristic

C₂×#15688923

C₂

yes

maximal, complemented

C₂×#15688899

C₂

yes

maximal, characteristic, complemented

C₄₇×#1846

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₇₆

—

C₂²×D₃₇₆

C₂²

yes

—

C₂×#13094021

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689500

—

#15689500

C₄

yes

complemented

#15688923

—

#15688899

—

C₂×#107×C₄₇

C₂²

yes

—

C₂×#106×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#382

—

C₂²×D₁₈₈

—

C₂²×D₁₈₈

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂×C₄

yes

—

#13094021

—

#13094021

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

complemented

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

#107×C₄₇

—

#106×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

#95×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

D₈

yes

—

C₂×C₈×C₄₇

SD₁₆

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

SD₁₆

yes

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

#102

yes

—

C₈×C₄₇

C₄×D₄

yes

—

C₈×C₄₇

#121

yes

—

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

100

C₄×C₄₇

—

101

C₄×C₄₇

#390

yes

characteristic

102

C₄×C₄₇

C₂×#102

yes

characteristic

103

C₄×C₄₇

#486

yes

characteristic

104

C₄×C₄₇

#492

yes

characteristic

105

C₂×#493

—

106

C₂×#357

—

107

C₂×#346

—

108

#1846

D₄₇

yes

characteristic, complemented

109

C₂×C₄₇

#1957

yes

characteristic

110

C₂×C₄₇

#2140

yes

—

111

C₂×C₄₇

#2244

yes

—

112

C₂×C₄₇

#2250

yes

—

113

D₄₇

—

114

C₂²×D₈

—

115

C₂²×D₈

—

116

C₂×#127

—

117

C₂²×C₁₆

—

118

#493

—

119

#493

—

120

C₂×#107

C₂×D₄₇

yes

—

121

C₂×#106

—

122

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

123

#382

—

124

#357

—

125

#346

—

126

C₄₇

#13206

yes

characteristic, complemented, Sylow

127

C₂²×D₄

—

128

C₂²×D₄

—

188

—

129

C₂×D₈

—

130

C₂×D₈

—

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂×D₈

—

134

C₂×D₈

—

188

—

135

C₂×D₈

—

188

—

136

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

137

C₂²×C₈

C₂²×D₄₇

yes

characteristic

138

#127

—

139

#127

—

188

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

—

145

#107

—

146

#106

—

147

C₄×C₈

C₄×D₄₇

yes

—

148

C₄×C₈

D₁₈₈

yes

—

149

#95

—

150

C₂⁴

—

188

—

151

C₂×D₄

—

152

C₂×D₄

—

376

—

153

C₂×D₄

—

188

—

154

C₂×D₄

—

188

—

155

C₂×D₄

—

188

—

156

C₂×D₄

—

188

—

157

C₂×D₄

—

188

—

158

C₂×D₄

—

188

—

159

C₂²×C₄

—

160

C₂²×C₄

#10625334

yes

—

161

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

162

D₈

—

163

D₈

—

188

—

164

D₈

—

188

—

165

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

166

C₂×C₈

#10625334

yes

—

167

C₂×C₈

#10625336

yes

—

168

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

169

C₂×C₈

C₂×D₁₈₈

yes

characteristic

170

C₂×C₈

D₄×D₄₇

yes

—

171

C₂×C₈

#10625354

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄²

(C₂×D₄₇)⋊C₄

yes

—

175

C₄²

#10625336

yes

—

176

C₁₆

—

177

C₂³

—

376

—

178

C₂³

—

376

—

179

C₂³

—

376

—

180

C₂³

—

188

—

181

C₂³

C₂×#10625334

yes

characteristic

182

D₄

—

376

—

183

D₄

—

376

—

184

D₄

—

376

—

185

D₄

—

188

—

186

D₄

—

188

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

#13093944

yes

—

191

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

192

C₂×C₄

#13094013

yes

characteristic

193

C₂×C₄

#13094020

yes

characteristic

194

C₂×C₄

C₂×#10625334

yes

characteristic

195

C₂×C₄

C₂×#10625336

yes

characteristic

196

C₂×C₄

C₂×#10625336

yes

characteristic

197

C₈

#13093944

yes

—

198

C₈

#13093986

yes

—

199

C₈

#13093999

yes

—

200

C₂²

—

376

—

201

C₂²

—

376

—

202

C₂²

—

752

—

203

C₂²

—

752

—

204

C₂²

C₂×#13093944

yes

characteristic

205

C₂²

#15689471

yes

characteristic

206

C₂²

#15689499

yes

characteristic

207

C₂²

#15689558

yes

—

208

C₄

—

209

C₄

—

210

C₄

#15689024

yes

characteristic

211

C₄

C₂×#13093944

yes

characteristic

212

C₄

#15689471

yes

characteristic

213

C₄

#15689497

yes

characteristic

214

C₂

—

752

—

215

C₂

#20244193

yes

characteristic

216

C₂

#20245103

yes

—

217

C₂

#20245631

yes

—

218

C₂

#20245655

yes

—

	subgroup	G/H
center	C₂³	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1846	C₂
socle	C₂³×C₄₇	C₂×D₈
prime radical	C₂×#15689500	C₂
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1846	D₄₇
hypocenter	C₄₇	#13206
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

subgroup

G/H

center

C₂³

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1846

C₂

socle

C₂³×C₄₇

C₂×D₈

prime radical

C₂×#15689500

C₂

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

N	H ≅ G/N	type
2. C₂×#15688923	C₂	semidirect
3. C₂×#15688899	C₂	semidirect
4. C₄₇×#1846	C₂	semidirect
10. #15689500	C₄	semidirect
30. C₂×C₄₇⋊C₁₆	D₄	semidirect
108. #1846	D₄₇	semidirect
126. C₄₇	#13206	semidirect

H ≅ G/N

type

2. C₂×#15688923

C₂

semidirect

3. C₂×#15688899

C₂

semidirect

4. C₄₇×#1846

C₂

semidirect

10. #15689500

C₄

semidirect

30. C₂×C₄₇⋊C₁₆

D₄

semidirect

108. #1846

D₄₇

semidirect

126. C₄₇

#13206

semidirect

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

subgroup	index
C₂×#15689500	2
C₂×#15688923	2
C₂×#15688899	2
C₄₇×#1846	2
#13206	47

subgroup

index

C₄₇×#1846

Subgroups — #26134509

Conjugacy classes of subgroups

Complements

Maximal subgroups