Group #26133732 — subgroups

Subgroups — #26133732

Order 12032.

458 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 127 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	#20253043	C₂	1	1	yes	maximal, characteristic
2	#20245109	C₂	1	2	yes	maximal, complemented
3	#20243434	C₂	1	1	yes	maximal, characteristic
4	#20241490	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3407	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	#15689694	—	2	1	no	—
8	#15689381	C₄	1	4	yes	complemented
9	#15689364	—	2	2	no	—
10	#15689161	C₂²	1	2	yes	—
11	#15689161	C₂²	1	1	yes	characteristic
12	#15689133	—	2	1	no	—
13	#15689097	—	2	1	no	—
14	#15688928	—	2	4	no	—
15	#15688880	—	2	1	no	—
16	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#504	—	2	4	no	—
18	C₂×M₃₂×C₄₇	—	2	2	no	—
19	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂×Dic₁₈₈	—	2	2	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×Dic₁₈₈	—	2	1	no	—
24	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
25	#13094022	—	4	1	no	—
26	#13094011	—	4	1	no	—
27	#13094005	—	4	2	no	—
28	#13094003	—	2	4	no	—
29	#13093983	—	2	1	no	—
30	#13093983	—	2	2	no	—
31	#13093958	—	2	1	no	—
32	#13093958	—	2	2	no	—
33	#13093956	—	2	2	no	—
34	#13093956	C₂×C₄	1	2	yes	—
35	#13093949	—	2	4	no	—
36	#13093939	—	4	2	no	—
37	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
38	#131×C₄₇	—	2	2	no	—
39	#131×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	D₄	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	M₃₂×C₄₇	—	2	4	no	—
45	M₃₂×C₄₇	—	2	2	no	—
46	M₃₂×C₄₇	—	2	2	no	—
47	C₂×C₁₆×C₄₇	—	2	4	no	—
48	C₂×C₁₆×C₄₇	D₄	1	4	yes	—
49	#41×C₄₇	—	2	2	no	—
50	#41×C₄₇	—	2	2	no	—
51	C₂×Q₈×C₄₇	SD₁₆	1	1	yes	characteristic
52	C₂×D₄×C₄₇	D₈	1	2	yes	—
53	C₂×D₄×C₄₇	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₄₇	—	4	1	no	—
57	C₂×Dic₉₄	—	2	2	no	—
58	C₂×Dic₉₄	—	4	2	no	—
59	C₂×Dic₉₄	—	4	2	no	—
60	C₂×Dic₉₄	—	4	1	no	—
61	M₁₆×C₄₇	—	2	2	no	—
62	M₁₆×C₄₇	—	2	4	no	—
63	C₂×C₈×C₄₇	—	2	2	no	—
64	C₂×C₈×C₄₇	—	2	2	no	—
65	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₄₇	#41	1	2	yes	—
70	C₂²⋊Dic₄₇	—	4	4	no	—
71	C₂²⋊Dic₄₇	—	4	1	no	—
72	C₂²⋊Dic₄₇	—	4	2	no	—
73	C₄⋊Dic₄₇	—	2	2	no	—
74	C₄⋊Dic₄₇	—	4	2	no	—
75	Dic₄₇⋊C₄	—	4	4	no	—
76	C₄×Dic₄₇	—	4	1	no	—
77	C₄×Dic₄₇	—	4	2	no	—
78	Dic₁₈₈	—	2	4	no	—
79	Dic₁₈₈	—	4	1	no	—
80	Dic₁₈₈	—	4	1	no	—
81	C₁₆×C₄₇	—	2	4	no	—
82	C₂³×C₄₇	#102	1	2	yes	—
83	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
84	Q₈×C₄₇	—	2	2	no	—
85	D₄×C₄₇	—	2	4	no	—
86	D₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	#102	1	2	yes	—
90	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#121	1	2	yes	—
92	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₄₇	#135	1	2	yes	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	8	2	no	—
97	C₂×Dic₄₇	—	8	2	no	—
98	Dic₉₄	—	4	2	no	—
99	Dic₉₄	—	4	2	no	—
100	Dic₉₄	—	8	2	no	—
101	C₈×C₄₇	—	2	2	no	—
102	C₈×C₄₇	C₄×D₄	1	2	yes	—
103	C₈×C₄₇	#120	1	1	yes	characteristic
104	C₈×C₄₇	#123	1	1	yes	characteristic
105	#13075	—	47	1	no	maximal, Sylow
106	C₂²×C₄₇	—	2	2	no	—
107	C₂²×C₄₇	—	4	1	no	—
108	C₂²×C₄₇	—	4	2	no	—
109	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
110	C₂²×C₄₇	#466	1	2	yes	—
111	C₄×C₄₇	—	2	2	no	—
112	C₄×C₄₇	#386	1	1	yes	characteristic
113	C₄×C₄₇	#416	1	1	yes	characteristic
114	C₄×C₄₇	#465	1	2	yes	—
115	Dic₄₇	—	8	2	no	—
116	Dic₄₇	—	8	2	no	—
117	Dic₄₇	—	16	2	no	—
118	#3407	D₄₇	1	1	yes	characteristic
119	#3059	—	47	1	no	—
120	#2141	—	47	2	no	—
121	#1812	—	47	1	no	—
122	#1384	—	47	2	no	—
123	C₂×C₄₇	—	2	1	no	—
124	C₂×C₄₇	—	2	2	no	—
125	C₂×C₄₇	—	4	2	no	—
126	C₂×C₄₇	#1893	1	1	yes	characteristic
127	C₂²×Q₁₆	—	47	1	no	—
128	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
129	#536	—	94	1	no	—
130	#504	—	2	4	no	—
131	C₂×M₃₂	—	2	2	no	—
132	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
133	#470	—	47	4	no	—
134	#467	—	94	2	no	—
135	#427	—	47	1	no	—
136	#427	—	47	2	no	—
137	#419	—	94	1	no	—
138	#410	—	94	1	no	—
139	#358	—	94	4	no	—
140	H(3,ℤ/4)	—	94	1	no	—
141	C₄₇	#13075	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	D₁₈₈	1	1	yes	characteristic
143	C₂²×Q₈	—	94	1	no	—
144	C₂×Q₁₆	—	47	2	no	—
145	C₂×Q₁₆	—	94	2	no	—
146	C₂×Q₁₆	—	94	2	no	—
147	C₂×Q₁₆	—	94	1	no	—
148	#131	—	2	2	no	—
149	#131	—	2	2	no	—
150	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
151	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
152	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
153	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
154	C₄⋊Q₈	—	188	1	no	—
155	#124	—	188	1	no	—
156	#123	—	188	2	no	—
157	C₂²⋊Q₈	—	94	4	no	—
158	#117	—	94	1	no	—
159	#117	—	94	2	no	—
160	M₃₂	—	2	4	no	—
161	M₃₂	—	2	2	no	—
162	M₃₂	—	2	2	no	—
163	C₂×C₁₆	—	2	4	no	—
164	C₂×C₁₆	C₂²⋊D₄₇	1	4	yes	—
165	#107	—	94	1	no	—
166	#107	—	94	2	no	—
167	#106	—	47	2	no	—
168	#106	—	94	2	no	—
169	#103	—	94	4	no	—
170	#99	—	188	2	no	—
171	#41	—	2	2	no	—
172	#41	—	2	2	no	—
173	C₂×Q₈	—	94	2	no	—
174	C₂×Q₈	—	188	2	no	—
175	C₂×Q₈	—	188	2	no	—
176	C₂×Q₈	—	188	1	no	—
177	C₂×Q₈	#10625325	1	1	yes	characteristic
178	C₂×D₄	#10625325	1	1	yes	characteristic
179	C₂×D₄	D₃₇₆	1	2	yes	—
180	C₂²×C₄	—	188	1	no	—
181	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
182	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
183	Q₁₆	—	94	4	no	—
184	Q₁₆	—	188	1	no	—
185	Q₁₆	—	188	1	no	—
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
191	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
192	C₂×C₈	#10625350	1	2	yes	—
193	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
194	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
195	C₄⋊C₄	—	94	2	no	—
196	C₄⋊C₄	—	188	2	no	—
197	C₄⋊C₄	—	188	4	no	—
198	C₂²⋊C₄	—	188	2	no	—
199	C₂²⋊C₄	—	188	4	no	—
200	C₂²⋊C₄	—	188	1	no	—
201	C₄²	—	188	2	no	—
202	C₄²	—	188	1	no	—
203	C₁₆	—	2	4	no	—
204	C₂³	#13093946	1	2	yes	—
205	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
206	Q₈	—	2	2	no	—
207	Q₈	—	376	2	no	—
208	Q₈	—	188	2	no	—
209	Q₈	—	188	2	no	—
210	D₄	—	2	4	no	—
211	D₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	376	2	no	—
215	C₂×C₄	—	376	2	no	—
216	C₂×C₄	—	188	2	no	—
217	C₂×C₄	—	188	2	no	—
218	C₂×C₄	#13093946	1	2	yes	—
219	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
220	C₂×C₄	#13093998	1	2	yes	—
221	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
222	C₂×C₄	#13094046	1	2	yes	—
223	C₈	—	2	2	no	—
224	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
225	C₈	#13093993	1	1	yes	characteristic
226	C₈	#13094007	1	1	yes	characteristic
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	2	no	—
230	C₂²	C₂×#13093946	1	1	yes	characteristic
231	C₂²	#15689359	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	376	2	no	—
234	C₄	—	376	2	no	—
235	C₄	—	752	2	no	—
236	C₄	#15689002	1	1	yes	characteristic
237	C₄	#15689120	1	1	yes	characteristic
238	C₄	#15689352	1	2	yes	—
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	2	no	—
242	C₂	#20243816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20253043

C₂

yes

maximal, characteristic

#20245109

C₂

yes

maximal, complemented

#20243434

C₂

yes

maximal, characteristic

#20241490

C₂

yes

maximal, complemented

C₄₇×#3407

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

C₂²

yes

characteristic

#15689694

—

#15689381

C₄

yes

complemented

#15689364

—

#15689161

C₂²

yes

—

#15689161

C₂²

yes

—

—

—

—

C₂×#131×C₄₇

C₂²

yes

characteristic

C₄₇×#504

—

C₂×M₃₂×C₄₇

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#13093949

—

#13093939

—

C₂×#41×C₄₇

D₄

yes

characteristic

#131×C₄₇

—

#131×C₄₇

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

SD₁₆

yes

characteristic

C₂×D₄×C₄₇

D₈

yes

—

C₂×D₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

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

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

100

Dic₉₄

—

101

C₈×C₄₇

—

102

C₈×C₄₇

C₄×D₄

yes

—

103

C₈×C₄₇

#120

yes

characteristic

104

C₈×C₄₇

yes

105

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

C₂×#102

yes

characteristic

110

C₂²×C₄₇

#466

yes

—

111

C₄×C₄₇

—

112

C₄×C₄₇

#386

yes

characteristic

113

C₄×C₄₇

#416

yes

characteristic

114

C₄×C₄₇

#465

yes

—

115

Dic₄₇

—

116

Dic₄₇

—

117

Dic₄₇

—

118

#3407

D₄₇

yes

characteristic

119

#3059

—

120

#2141

—

121

#1812

—

122

#1384

—

123

C₂×C₄₇

—

124

C₂×C₄₇

—

125

C₂×C₄₇

—

126

C₂×C₄₇

#1893

yes

characteristic

127

C₂²×Q₁₆

—

128

C₂×#131

C₂×D₄₇

yes

characteristic

129

#536

—

130

#504

—

131

C₂×M₃₂

—

132

C₂×M₃₂

C₂×D₄₇

yes

—

133

#470

—

134

#467

—

135

#427

—

136

#427

—

137

#419

—

138

#410

—

139

#358

—

140

H(3,ℤ/4)

—

141

C₄₇

#13075

yes

characteristic, complemented, Sylow

142

C₂×#41

D₁₈₈

yes

characteristic

143

C₂²×Q₈

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

#131

—

149

#131

—

150

C₂×M₁₆

C₄×D₄₇

yes

—

151

C₂×M₁₆

D₁₈₈

yes

characteristic

152

C₂²×C₈

C₂²⋊D₄₇

yes

—

153

C₂²×C₈

C₂²×D₄₇

yes

characteristic

154

C₄⋊Q₈

—

188

—

155

#124

—

188

—

156

#123

—

188

—

157

C₂²⋊Q₈

—

158

#117

—

159

#117

—

160

M₃₂

—

161

M₃₂

—

162

M₃₂

—

163

C₂×C₁₆

—

164

C₂×C₁₆

C₂²⋊D₄₇

yes

—

165

#107

—

166

#107

—

167

#106

—

168

#106

—

169

#103

—

170

#99

—

188

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

188

—

175

C₂×Q₈

—

188

—

176

C₂×Q₈

—

188

—

177

C₂×Q₈

#10625325

yes

characteristic

178

C₂×D₄

#10625325

yes

characteristic

179

C₂×D₄

D₃₇₆

yes

—

180

C₂²×C₄

—

188

—

181

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

182

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

183

Q₁₆

—

184

Q₁₆

—

188

—

185

Q₁₆

—

188

—

186

M₁₆

—

187

M₁₆

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

191

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

192

C₂×C₈

#10625350

yes

—

193

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

194

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

195

C₄⋊C₄

—

196

C₄⋊C₄

—

188

—

197

C₄⋊C₄

—

188

—

198

C₂²⋊C₄

—

188

—

199

C₂²⋊C₄

—

188

—

200

C₂²⋊C₄

—

188

—

201

C₄²

—

188

—

202

C₄²

—

188

—

203

C₁₆

—

204

C₂³

#13093946

yes

—

205

C₂³

C₂×D₃₇₆

yes

characteristic

206

Q₈

—

207

Q₈

—

376

—

208

Q₈

—

188

—

209

Q₈

—

188

—

210

D₄

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

376

—

215

C₂×C₄

—

376

—

216

C₂×C₄

—

188

—

217

C₂×C₄

—

188

—

218

C₂×C₄

#13093946

yes

—

219

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

220

C₂×C₄

#13093998

yes

—

221

C₂×C₄

C₂×#10625325

yes

characteristic

222

C₂×C₄

#13094046

yes

—

223

C₈

—

224

C₈

C₄×C₂²⋊D₄₇

yes

—

225

C₈

#13093993

yes

characteristic

226

C₈

#13094007

yes

characteristic

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

C₂×#13093946

yes

characteristic

231

C₂²

#15689359

yes

—

232

C₄

—

233

C₄

—

376

—

234

C₄

—

376

—

235

C₄

—

752

—

236

C₄

#15689002

yes

characteristic

237

C₄

#15689120

yes

characteristic

238

C₄

#15689352

yes

—

239

C₂

—

240

C₂

—

241

C₂

—

242

C₂

#20243816

yes

characteristic

	subgroup	G/H
center	C₂	#20243816
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#3407	C₂
socle	C₂×C₄₇	#1893
prime radical	C₂×#41×C₄₇	D₄
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#3407	D₄₇
hypocenter	C₄₇	#13075
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#20243816

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#3407

C₂

socle

C₂×C₄₇

#1893

prime radical

C₂×#41×C₄₇

D₄

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #20245109	C₂	semidirect
4. #20241490	C₂	semidirect
8. #15689381	C₄	semidirect
141. C₄₇	#13075	semidirect

H ≅ G/N

type

2. #20245109

C₂

semidirect

4. #20241490

C₂

semidirect

8. #15689381

C₄

semidirect

141. C₄₇

#13075

semidirect

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

subgroup	index
#20253043	2
#20245109	2
#20243434	2
#20241490	2
C₄₇×#3407	2
#13075	47

subgroup

index

C₄₇×#3407

Subgroups — #26133732

Conjugacy classes of subgroups

Complements

Maximal subgroups