Group #26230168 — subgroups

Subgroups — #26230168

Order 12032.

810 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 211 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	#20253816	C₂	1	1	yes	maximal, characteristic
2	#20252107	C₂	1	2	yes	maximal, complemented
3	#20244220	C₂	1	2	yes	maximal, complemented
4	#20243714	C₂	1	8	yes	maximal, complemented
5	#20243526	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#13094046	C₂²	1	4	yes	—
8	C₂×#13094030	C₂²	1	4	yes	—
9	#15689673	C₂²	1	2	yes	—
10	#15689507	C₄	1	4	yes	complemented
11	#15689503	C₄	1	1	yes	characteristic, complemented
12	#15689500	C₄	1	1	yes	characteristic, complemented
13	#15689496	C₄	1	2	yes	complemented
14	#15689196	—	2	8	no	—
15	#15689147	C₂²	1	2	yes	—
16	C₂×#13093952	C₂²	1	8	yes	—
17	#15689089	C₂²	1	4	yes	—
18	#15688888	C₂²	1	4	yes	—
19	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#376	C₂²	1	1	yes	characteristic
22	C₄₇×#336	C₂²	1	4	yes	—
23	C₂×#10625350	C₂³	1	4	yes	—
24	#13094046	—	4	8	no	—
25	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
26	C₂×#10625325	C₂×C₄	1	8	yes	—
27	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
28	#13094030	—	4	8	no	—
29	C₂×#10625329	C₂³	1	4	yes	—
30	C₂×#10625324	—	2	4	no	—
31	C₂×C₈×D₄₇	—	2	4	no	—
32	#13094024	C₂×C₄	1	2	yes	—
33	#13094021	C₂×C₄	1	2	yes	—
34	#13094012	C₂×C₄	1	4	yes	—
35	#13093998	—	2	4	no	—
36	C₄×D₁₈₈	—	2	4	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
38	#13093952	—	4	8	no	—
39	(C₂×D₄₇)⋊C₈	—	2	8	no	—
40	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	#97×C₄₇	D₄	1	4	yes	—
45	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
48	#95×C₄₇	—	2	2	no	—
49	C₂²×C₄×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	#41	1	2	yes	—
51	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
52	C₂×C₂²⋊D₄₇	—	2	4	no	—
53	#10625350	—	2	8	no	—
54	#10625350	—	2	8	no	—
55	C₂×D₁₈₈	—	2	4	no	—
56	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
57	C₂×C₄×D₄₇	—	2	4	no	—
58	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
59	C₂×C₈×C₄₇	—	2	4	no	—
60	C₂×C₈×C₄₇	—	2	4	no	—
61	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
63	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
64	C₄²×C₄₇	—	2	4	no	—
65	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₄₇	C₂×D₄	1	2	yes	—
68	(C₂×D₄₇)⋊C₄	—	2	8	no	—
69	C₄⋊Dic₄₇	—	2	4	no	—
70	#10625329	—	2	8	no	—
71	C₂×C₄₇⋊C₈	—	2	4	no	—
72	Dic₁₈₈	—	4	4	no	—
73	D₃₇₆	—	4	4	no	—
74	#10625325	—	4	8	no	—
75	#10625324	—	4	8	no	—
76	C₈×D₄₇	—	4	8	no	—
77	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
78	C₂²×D₄₇	—	2	4	no	—
79	C₂×C₄×C₄₇	—	4	2	no	—
80	C₂×C₄×C₄₇	—	4	4	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
87	C₂²⋊D₄₇	—	4	8	no	—
88	C₂×Dic₄₇	—	2	4	no	—
89	D₁₈₈	—	2	8	no	—
90	D₁₈₈	—	8	4	no	—
91	C₄×D₄₇	—	4	4	no	—
92	C₄×D₄₇	—	4	4	no	—
93	Dic₉₄	—	2	8	no	—
94	C₈×C₄₇	—	2	2	no	—
95	C₈×C₄₇	—	2	2	no	—
96	C₈×C₄₇	—	2	4	no	—
97	C₄₇⋊C₈	—	4	4	no	—
98	#22282	—	47	1	no	maximal, Sylow
99	C₂²×C₄₇	—	2	2	no	—
100	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
101	C₂²×C₄₇	#540	1	2	yes	—
102	C₂×D₄₇	—	4	4	no	—
103	C₂×D₄₇	—	4	8	no	—
104	C₄×C₄₇	—	2	2	no	—
105	C₄×C₄₇	—	2	2	no	—
106	C₄×C₄₇	—	8	2	no	—
107	C₄×C₄₇	#518	1	2	yes	—
108	C₄×C₄₇	#535	1	2	yes	—
109	Dic₄₇	—	4	4	no	—
110	#3147	—	47	1	no	—
111	#2932	—	47	2	no	—
112	#1963	—	47	2	no	—
113	#1876	—	47	8	no	—
114	#1837	—	47	1	no	—
115	#1746	D₄₇	1	1	yes	characteristic, complemented
116	C₂×C₄₇	—	2	2	no	—
117	C₂×C₄₇	#2328	1	1	yes	characteristic
118	C₂×C₄₇	#2957	1	2	yes	—
119	D₄₇	—	8	4	no	—
120	C₂×#135	—	47	4	no	—
121	C₂×#131	—	47	4	no	—
122	#532	—	47	2	no	—
123	#495	—	47	4	no	—
124	#494	—	47	1	no	—
125	#493	—	47	1	no	—
126	#492	—	47	2	no	—
127	#435	—	94	8	no	—
128	#423	—	47	2	no	—
129	C₂×#104	—	47	8	no	—
130	#408	—	47	4	no	—
131	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
132	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
133	#376	C₂×D₄₇	1	1	yes	characteristic
134	#341	—	47	4	no	—
135	#336	C₂×D₄₇	1	4	yes	—
136	C₄₇	#22282	1	1	yes	characteristic, complemented, Sylow
137	C₂×#41	—	47	4	no	—
138	#135	—	188	8	no	—
139	C₂×Q₁₆	—	47	4	no	—
140	C₂×SD₁₆	—	47	8	no	—
141	C₂×D₈	—	47	4	no	—
142	#131	—	188	8	no	—
143	C₂×M₁₆	—	47	4	no	—
144	C₂×M₁₆	—	94	4	no	—
145	C₂²×C₈	—	94	4	no	—
146	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
147	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
148	C₄⋊Q₈	—	47	2	no	—
149	#127	—	47	2	no	—
150	#124	—	47	4	no	—
151	#121	—	94	4	no	—
152	C₄×D₄	—	94	4	no	—
153	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
154	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
155	C₄⋊C₈	—	94	4	no	—
156	#104	—	188	8	no	—
157	C₂²⋊C₈	—	94	8	no	—
158	#97	D₁₈₈	1	4	yes	—
159	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
160	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
161	C₄×C₈	C₄×D₄₇	1	2	yes	—
162	#95	—	2	2	no	—
163	#41	—	94	8	no	—
164	#41	—	94	8	no	—
165	C₂×Q₈	—	47	4	no	—
166	C₂×D₄	—	47	4	no	—
167	C₂×D₄	—	94	4	no	—
168	C₂×D₄	—	94	4	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	94	4	no	—
171	C₂²×C₄	#10625350	1	2	yes	—
172	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
173	Q₁₆	—	188	4	no	—
174	SD₁₆	—	188	8	no	—
175	D₈	—	188	4	no	—
176	M₁₆	—	94	8	no	—
177	M₁₆	—	188	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	94	4	no	—
181	C₂×C₈	—	188	8	no	—
182	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
183	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
184	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
185	C₄⋊C₄	—	94	4	no	—
186	C₂²⋊C₄	—	94	8	no	—
187	C₄²	—	2	4	no	—
188	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
190	C₄²	C₂×D₁₈₈	1	2	yes	—
191	C₂³	—	94	4	no	—
192	C₂³	C₂×#10625350	1	1	yes	characteristic
193	Q₈	—	94	8	no	—
194	D₄	—	94	8	no	—
195	D₄	—	376	4	no	—
196	D₄	—	188	8	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	94	4	no	—
201	C₂×C₄	—	188	4	no	—
202	C₂×C₄	—	188	4	no	—
203	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
204	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
205	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
206	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
207	C₂×C₄	#13094070	1	4	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	2	4	no	—
211	C₈	—	188	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	188	4	no	—
214	C₂²	—	188	8	no	—
215	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
216	C₂²	#15689728	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	188	4	no	—
221	C₄	#15689597	1	2	yes	—
222	C₄	#15689692	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	376	4	no	—
225	C₂	#20246113	1	1	yes	characteristic
226	C₂	#20252306	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20253816

C₂

yes

maximal, characteristic

#20252107

C₂

yes

maximal, complemented

#20244220

C₂

yes

maximal, complemented

#20243714

C₂

yes

maximal, complemented

#20243526

C₂

yes

maximal, characteristic, complemented

C₄₇×#1746

C₂

yes

maximal, characteristic, complemented

C₂×#13094046

C₂²

yes

—

C₂×#13094030

C₂²

yes

—

#15689673

C₂²

yes

—

#15689507

C₄

yes

complemented

#15689503

C₄

yes

characteristic, complemented

#15689500

C₄

yes

characteristic, complemented

#15689496

C₄

yes

complemented

#15689196

—

#15689147

C₂²

yes

—

C₂×#13093952

C₂²

yes

—

#15689089

C₂²

yes

—

#15688888

C₂²

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#376

C₂²

yes

characteristic

C₄₇×#336

C₂²

yes

—

C₂×#10625350

C₂³

yes

—

#13094046

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂×#10625325

C₂×C₄

yes

—

C₂×D₃₇₆

C₂×C₄

yes

—

#13094030

—

C₂×#10625329

C₂³

yes

—

C₂×#10625324

—

C₂×C₈×D₄₇

—

#13094024

C₂×C₄

yes

—

#13094021

C₂×C₄

yes

—

#13094012

C₂×C₄

yes

—

#13093998

—

C₄×D₁₈₈

—

C₄⋊(C₄₇⋊C₈)

—

#13093952

—

(C₂×D₄₇)⋊C₈

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

—

#95×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

#41

yes

—

C₂²×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂²×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₂²×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²×C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

#10625324

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×#41

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₇

H(5,𝔽₂)

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

#22282

—

maximal, Sylow

C₂²×C₄₇

—

100

C₂²×C₄₇

C₂×C₄×D₄

yes

characteristic

101

C₂²×C₄₇

#540

yes

—

102

C₂×D₄₇

—

103

C₂×D₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

#518

yes

—

108

C₄×C₄₇

#535

yes

—

109

Dic₄₇

—

110

#3147

—

111

#2932

—

112

#1963

—

113

#1876

—

114

#1837

—

115

#1746

D₄₇

yes

characteristic, complemented

116

C₂×C₄₇

—

117

C₂×C₄₇

#2328

yes

characteristic

118

C₂×C₄₇

#2957

yes

—

119

D₄₇

—

120

C₂×#135

—

121

C₂×#131

—

122

#532

—

123

#495

—

124

#494

—

125

#493

—

126

#492

—

127

#435

—

128

#423

—

129

C₂×#104

—

130

#408

—

131

C₂×#97

C₂×D₄₇

yes

characteristic

132

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

133

#376

C₂×D₄₇

yes

characteristic

134

#341

—

135

#336

C₂×D₄₇

yes

—

136

C₄₇

#22282

yes

characteristic, complemented, Sylow

137

C₂×#41

—

138

#135

—

188

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×D₈

—

142

#131

—

188

—

143

C₂×M₁₆

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

C₂²×D₄₇

yes

—

147

C₂²×C₈

C₂²×D₄₇

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

152

C₄×D₄

—

153

C₂×C₄²

C₂²×D₄₇

yes

—

154

C₂×C₄²

C₂²×D₄₇

yes

characteristic

155

C₄⋊C₈

—

156

#104

—

188

—

157

C₂²⋊C₈

—

158

#97

D₁₈₈

yes

—

159

C₄×C₈

C₄×D₄₇

yes

characteristic

160

C₄×C₈

C₄×D₄₇

yes

characteristic

161

C₄×C₈

C₄×D₄₇

yes

—

162

#95

—

163

#41

—

164

#41

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

#10625350

yes

—

172

C₂²×C₄

C₂³×D₄₇

yes

characteristic

173

Q₁₆

—

188

—

174

SD₁₆

—

188

—

175

D₈

—

188

—

176

M₁₆

—

177

M₁₆

—

188

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

188

—

182

C₂×C₈

C₂×C₄×D₄₇

yes

—

183

C₂×C₈

C₂×C₄×D₄₇

yes

—

184

C₂×C₈

C₂×D₁₈₈

yes

—

185

C₄⋊C₄

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

C₂×C₄×D₄₇

yes

characteristic

189

C₄²

C₂×C₄×D₄₇

yes

characteristic

190

C₄²

C₂×D₁₈₈

yes

—

191

C₂³

—

192

C₂³

C₂×#10625350

yes

characteristic

193

Q₈

—

194

D₄

—

195

D₄

—

376

—

196

D₄

—

188

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

188

—

202

C₂×C₄

—

188

—

203

C₂×C₄

C₄×D₁₈₈

yes

—

204

C₂×C₄

C₄×D₁₈₈

yes

—

205

C₂×C₄

C₂²×C₄×D₄₇

yes

characteristic

206

C₂×C₄

C₂²×D₁₈₈

yes

characteristic

207

C₂×C₄

#13094070

yes

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

188

—

212

C₂²

—

213

C₂²

—

188

—

214

C₂²

—

188

—

215

C₂²

C₂×C₄×D₁₈₈

yes

characteristic

216

C₂²

#15689728

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

188

—

221

C₄

#15689597

yes

—

222

C₄

#15689692

yes

—

223

C₂

—

224

C₂

—

376

—

225

C₂

#20246113

yes

characteristic

226

C₂

#20252306

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1746	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253816	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1746	D₄₇
hypocenter	C₄₇	#22282
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂²×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₄₇

Fitting

C₄₇×#1746

C₂

socle

C₂²×C₄₇

C₂×C₄×D₄

prime radical

#20253816

C₂

cosocle

C₂²×C₄×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

N	H ≅ G/N	type
2. #20252107	C₂	semidirect
3. #20244220	C₂	semidirect
4. #20243714	C₂	semidirect
5. #20243526	C₂	semidirect
6. C₄₇×#1746	C₂	semidirect
10. #15689507	C₄	semidirect
11. #15689503	C₄	semidirect
12. #15689500	C₄	semidirect
13. #15689496	C₄	semidirect
115. #1746	D₄₇	semidirect
136. C₄₇	#22282	semidirect

H ≅ G/N

type

2. #20252107

C₂

semidirect

3. #20244220

C₂

semidirect

4. #20243714

C₂

semidirect

5. #20243526

C₂

semidirect

6. C₄₇×#1746

C₂

semidirect

10. #15689507

C₄

semidirect

11. #15689503

C₄

semidirect

12. #15689500

C₄

semidirect

13. #15689496

C₄

semidirect

115. #1746

D₄₇

semidirect

136. C₄₇

#22282

semidirect

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

subgroup	index
#20253816	2
#20252107	2
#20244220	2
#20243714	2
#20243526	2
C₄₇×#1746	2
#22282	47

subgroup

index

C₄₇×#1746

Subgroups — #26230168

Conjugacy classes of subgroups

Complements

Maximal subgroups