Group #26126258 — subgroups

Subgroups — #26126258

Order 12032.

314 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 115 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	#20253974	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688876	C₂	1	1	yes	maximal, characteristic
3	#20241353	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2162	C₂	1	1	yes	maximal, characteristic
5	#15689680	—	2	1	no	—
6	#15689528	C₄	1	1	yes	characteristic
7	#15689503	C₄	1	1	yes	characteristic
8	#15689474	—	2	1	no	—
9	#15689364	—	2	1	no	—
10	#15689364	C₄	1	2	yes	—
11	C₄×Dic₁₈₈	—	2	1	no	—
12	C₄×Dic₁₈₈	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
14	#15688876	—	2	1	no	—
15	#15688876	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×C₄⋊C₁₆	—	2	1	no	—
18	C₄₇×C₂²⋊C₁₆	—	2	1	no	—
19	C₄×C₁₆×C₄₇	C₂²	1	2	yes	—
20	C₂×Dic₁₈₈	—	2	1	no	—
21	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
22	C₂²×C₄₇⋊C₈	—	4	1	no	—
23	#13094024	—	2	1	no	—
24	#13094024	—	2	1	no	—
25	#13094016	—	4	1	no	—
26	#13094003	—	2	2	no	—
27	#13094003	—	4	1	no	—
28	C₄×Dic₉₄	—	2	2	no	—
29	C₄×Dic₉₄	—	4	1	no	—
30	#13093983	—	4	1	no	—
31	#13093958	—	2	1	no	—
32	#13093958	C₂×C₄	1	2	yes	—
33	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
35	#13093949	—	2	2	no	—
36	#13093949	—	2	2	no	—
37	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₁₆×C₄₇	—	2	2	no	—
41	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
43	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
44	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
48	C₂×Dic₉₄	—	2	2	no	—
49	C₂×Dic₉₄	—	4	1	no	—
50	C₂×C₈×C₄₇	—	2	2	no	—
51	C₂×C₈×C₄₇	—	4	1	no	—
52	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
57	C₄²×C₄₇	D₈	1	1	yes	characteristic
58	C₄²×C₄₇	SD₁₆	1	1	yes	characteristic
59	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂²⋊Dic₄₇	—	4	2	no	—
61	C₄⋊Dic₄₇	—	2	2	no	—
62	C₄⋊Dic₄₇	—	4	1	no	—
63	C₄⋊Dic₄₇	—	4	1	no	—
64	C₄⋊Dic₄₇	—	4	1	no	—
65	Dic₄₇⋊C₄	—	4	2	no	—
66	Dic₄₇⋊C₄	—	4	2	no	—
67	C₄×Dic₄₇	—	4	2	no	—
68	C₂×C₄₇⋊C₈	—	4	2	no	—
69	C₂×C₄₇⋊C₈	—	8	2	no	—
70	Dic₁₈₈	—	2	4	no	—
71	Dic₁₈₈	—	4	2	no	—
72	C₁₆×C₄₇	—	4	2	no	—
73	C₂³×C₄₇	#102	1	1	yes	characteristic
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	4	1	no	—
77	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
78	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
79	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
80	C₂×C₄×C₄₇	SD₃₂	1	2	yes	—
81	C₂×C₄×C₄₇	Q₃₂	1	2	yes	—
82	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×Dic₄₇	—	4	2	no	—
86	C₂×Dic₄₇	—	4	2	no	—
87	Dic₉₄	—	4	2	no	—
88	Dic₉₄	—	4	2	no	—
89	Dic₉₄	—	8	2	no	—
90	C₈×C₄₇	—	2	1	no	—
91	C₈×C₄₇	—	2	1	no	—
92	C₈×C₄₇	—	2	1	no	—
93	C₈×C₄₇	#131	1	2	yes	—
94	C₄₇⋊C₈	—	8	2	no	—
95	#11646	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	—	2	1	no	—
97	C₂²×C₄₇	—	2	1	no	—
98	C₂²×C₄₇	#358	1	2	yes	—
99	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
100	C₄×C₄₇	—	2	1	no	—
101	C₄×C₄₇	—	2	1	no	—
102	C₄×C₄₇	—	2	1	no	—
103	C₄×C₄₇	#358	1	2	yes	—
104	C₄×C₄₇	#408	1	1	yes	characteristic
105	C₄×C₄₇	#421	1	1	yes	characteristic
106	C₄×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
107	C₄×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
108	Dic₄₇	—	8	2	no	—
109	Dic₄₇	—	8	2	no	—
110	#3170	—	47	1	no	—
111	#2162	D₄₇	1	1	yes	characteristic
112	C₂×#335	—	47	1	no	—
113	#1332	—	47	4	no	—
114	C₂×C₄₇	—	2	2	no	—
115	C₂×C₄₇	#1480	1	1	yes	characteristic
116	C₂×C₄₇	C₂×#358	1	1	yes	characteristic
117	C₂×C₄₇	#2143	1	1	yes	characteristic
118	#533	—	94	1	no	—
119	#500	—	47	1	no	—
120	#494	—	47	1	no	—
121	#487	—	94	1	no	—
122	#467	—	47	2	no	—
123	#467	—	94	1	no	—
124	C₄×Q₁₆	—	47	2	no	—
125	C₄×Q₁₆	—	94	1	no	—
126	C₂×C₄⋊C₈	—	94	1	no	—
127	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
128	C₄⋊C₁₆	—	2	1	no	—
129	C₂²⋊C₁₆	—	2	1	no	—
130	C₄×C₁₆	C₂×D₄₇	1	2	yes	—
131	#335	—	47	2	no	—
132	#335	—	94	1	no	—
133	C₄₇	#11646	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₁₆	—	47	2	no	—
135	C₂×Q₁₆	—	94	1	no	—
136	C₂²×C₈	—	188	1	no	—
137	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
138	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
139	C₄⋊Q₈	—	94	1	no	—
140	C₄⋊Q₈	—	94	1	no	—
141	#125	—	188	1	no	—
142	C₂²⋊Q₈	—	94	2	no	—
143	C₂²⋊Q₈	—	188	1	no	—
144	C₄×Q₈	—	94	2	no	—
145	C₄×Q₈	—	188	1	no	—
146	#117	—	188	1	no	—
147	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
148	C₂×C₁₆	—	2	2	no	—
149	#107	—	47	2	no	—
150	#107	—	94	1	no	—
151	C₄⋊C₈	—	94	2	no	—
152	C₄⋊C₈	—	188	1	no	—
153	#103	—	94	2	no	—
154	#103	—	94	2	no	—
155	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
156	C₄×C₈	D₁₈₈	1	1	yes	characteristic
157	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
158	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	C₂×Q₈	—	94	2	no	—
160	C₂×Q₈	—	188	1	no	—
161	C₂²×C₄	#10625325	1	1	yes	characteristic
162	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
163	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
164	Q₁₆	—	94	4	no	—
165	Q₁₆	—	188	2	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	376	2	no	—
169	C₂×C₈	—	188	2	no	—
170	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
171	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
172	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
173	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
174	C₄⋊C₄	—	94	2	no	—
175	C₄⋊C₄	—	188	2	no	—
176	C₄⋊C₄	—	188	1	no	—
177	C₄⋊C₄	—	188	1	no	—
178	C₄⋊C₄	—	188	1	no	—
179	C₄⋊C₄	—	188	2	no	—
180	C₂²⋊C₄	—	188	2	no	—
181	C₄²	—	188	2	no	—
182	C₄²	#10625325	1	1	yes	characteristic
183	C₄²	D₃₇₆	1	1	yes	characteristic
184	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
185	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
186	C₁₆	—	4	2	no	—
187	C₂³	#13093946	1	1	yes	characteristic
188	Q₈	—	376	2	no	—
189	Q₈	—	188	2	no	—
190	Q₈	—	188	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	188	2	no	—
195	C₂×C₄	—	188	2	no	—
196	C₂×C₄	#13093946	1	1	yes	characteristic
197	C₂×C₄	#13093946	1	1	yes	characteristic
198	C₂×C₄	#13093946	1	1	yes	characteristic
199	C₂×C₄	#13093969	1	2	yes	—
200	C₂×C₄	Dic₃₇₆	1	2	yes	—
201	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
202	C₂×C₄	C₂×D₃₇₆	1	1	yes	characteristic
203	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	376	2	no	—
208	C₈	#13094032	1	2	yes	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	#15688928	1	2	yes	—
212	C₂²	C₂×#13093946	1	1	yes	characteristic
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	376	2	no	—
217	C₄	—	376	2	no	—
218	C₄	#15688928	1	2	yes	—
219	C₄	#15689091	1	1	yes	characteristic
220	C₄	#15689141	1	1	yes	characteristic
221	C₄	C₂×#13093969	1	1	yes	characteristic
222	C₄	C₂×Dic₃₇₆	1	1	yes	characteristic
223	C₂	—	2	2	no	—
224	C₂	#20241788	1	1	yes	characteristic
225	C₂	C₂×#15688928	1	1	yes	characteristic
226	C₂	#20245117	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20253974

C₂

yes

maximal, characteristic

C₂×#15688876

C₂

yes

maximal, characteristic

#20241353

C₂

yes

maximal, complemented

C₄₇×#2162

C₂

yes

maximal, characteristic

#15689680

—

#15689528

C₄

yes

characteristic

#15689503

C₄

yes

—

—

C₄

yes

—

C₄×Dic₁₈₈

—

C₄×Dic₁₈₈

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

—

#15688876

—

#15688876

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×C₄⋊C₁₆

—

C₄₇×C₂²⋊C₁₆

—

C₄×C₁₆×C₄₇

C₂²

yes

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

—

—

—

—

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

#13093983

—

#13093958

—

#13093958

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093949

—

#13093949

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂²⋊C₄

yes

characteristic

C₄²×C₄₇

D₈

yes

characteristic

C₄²×C₄₇

SD₁₆

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

#102

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

SD₃₂

yes

—

C₂×C₄×C₄₇

Q₃₂

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#131

yes

—

C₄₇⋊C₈

—

#11646

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#358

yes

—

C₂²×C₄₇

C₂×#102

yes

characteristic

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

#358

yes

—

104

C₄×C₄₇

#408

yes

characteristic

105

C₄×C₄₇

#421

yes

characteristic

106

C₄×C₄₇

C₂×SD₃₂

yes

characteristic

107

C₄×C₄₇

C₂×Q₃₂

yes

characteristic

108

Dic₄₇

—

109

Dic₄₇

—

110

#3170

—

111

#2162

D₄₇

yes

characteristic

112

C₂×#335

—

113

#1332

—

114

C₂×C₄₇

—

115

C₂×C₄₇

#1480

yes

characteristic

116

C₂×C₄₇

C₂×#358

yes

characteristic

117

C₂×C₄₇

#2143

yes

characteristic

118

#533

—

119

#500

—

120

#494

—

121

#487

—

122

#467

—

123

#467

—

124

C₄×Q₁₆

—

125

C₄×Q₁₆

—

126

C₂×C₄⋊C₈

—

127

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

128

C₄⋊C₁₆

—

129

C₂²⋊C₁₆

—

130

C₄×C₁₆

C₂×D₄₇

yes

—

131

#335

—

132

#335

—

133

C₄₇

#11646

yes

characteristic, complemented, Sylow

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂²×C₈

—

188

—

137

C₂²×C₈

C₄×D₄₇

yes

characteristic

138

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

#125

—

188

—

142

C₂²⋊Q₈

—

143

C₂²⋊Q₈

—

188

—

144

C₄×Q₈

—

145

C₄×Q₈

—

188

—

146

#117

—

188

—

147

C₂×C₄²

D₁₈₈

yes

characteristic

148

C₂×C₁₆

—

149

#107

—

150

#107

—

151

C₄⋊C₈

—

152

C₄⋊C₈

—

188

—

153

#103

—

154

#103

—

155

C₄×C₈

C₄×D₄₇

yes

characteristic

156

C₄×C₈

D₁₈₈

yes

characteristic

157

C₄×C₈

C₂²⋊D₄₇

yes

characteristic

158

C₄×C₈

C₂²×D₄₇

yes

characteristic

159

C₂×Q₈

—

160

C₂×Q₈

—

188

—

161

C₂²×C₄

#10625325

yes

characteristic

162

C₂²×C₄

D₃₇₆

yes

characteristic

163

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

188

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

376

—

169

C₂×C₈

—

188

—

170

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

171

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

172

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

173

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

174

C₄⋊C₄

—

175

C₄⋊C₄

—

188

—

176

C₄⋊C₄

—

188

—

177

C₄⋊C₄

—

188

—

178

C₄⋊C₄

—

188

—

179

C₄⋊C₄

—

188

—

180

C₂²⋊C₄

—

188

—

181

C₄²

—

188

—

182

C₄²

#10625325

yes

characteristic

183

C₄²

D₃₇₆

yes

characteristic

184

C₄²

(C₂×D₄₇)⋊C₄

yes

characteristic

185

C₄²

C₂×D₁₈₈

yes

characteristic

186

C₁₆

—

187

C₂³

#13093946

yes

characteristic

188

Q₈

—

376

—

189

Q₈

—

188

—

190

Q₈

—

188

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

188

—

195

C₂×C₄

—

188

—

196

C₂×C₄

#13093946

yes

characteristic

197

C₂×C₄

#13093946

yes

characteristic

198

C₂×C₄

#13093946

yes

characteristic

199

C₂×C₄

#13093969

yes

—

200

C₂×C₄

Dic₃₇₆

yes

—

201

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

202

C₂×C₄

C₂×D₃₇₆

yes

characteristic

203

C₂×C₄

C₂×#10625325

yes

characteristic

204

C₈

—

205

C₈

—

206

C₈

—

207

C₈

—

376

—

208

C₈

#13094032

yes

—

209

C₂²

—

210

C₂²

—

211

C₂²

#15688928

yes

—

212

C₂²

C₂×#13093946

yes

characteristic

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

376

—

217

C₄

—

376

—

218

C₄

#15688928

yes

—

219

C₄

#15689091

yes

characteristic

220

C₄

#15689141

yes

characteristic

221

C₄

C₂×#13093969

yes

characteristic

222

C₄

C₂×Dic₃₇₆

yes

characteristic

223

C₂

—

224

C₂

#20241788

yes

characteristic

225

C₂

C₂×#15688928

yes

characteristic

226

C₂

#20245117

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₄₇
Fitting	C₄₇×#2162	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	C₂³×C₄₇	#102
cosocle	C₄×C₈×C₄₇	C₂³
hypercenter	#2162	D₄₇
hypocenter	C₄₇	#11646
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₄

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₄₇

Fitting

C₄₇×#2162

C₂

C₂²×C₄₇

C₂³×C₄₇

C₄×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
3. #20241353	C₂	semidirect
133. C₄₇	#11646	semidirect

H ≅ G/N

type

3. #20241353

C₂

semidirect

133. C₄₇

#11646

semidirect

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

subgroup	index
#20253974	2
C₂×#15688876	2
#20241353	2
C₄₇×#2162	2
#11646	47

subgroup

index

C₄₇×#2162

Subgroups — #26126258

Conjugacy classes of subgroups

Complements

Maximal subgroups