Group #26116240 — subgroups

Subgroups — #26116240

Order 12032.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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	#20241838	C₂	1	2	yes	maximal, complemented
3	#20241838	C₂	1	2	yes	maximal, complemented
4	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094046	—	2	2	no	—
7	#15689673	C₂²	1	2	yes	—
8	#15689507	—	2	2	no	—
9	#15689503	C₄	1	1	yes	characteristic
10	#15689500	C₄	1	1	yes	characteristic
11	#15689496	C₄	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15688850	—	2	4	no	—
15	#15688850	—	2	4	no	—
16	#15688845	—	2	2	no	—
17	C₄₇×#423	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#341	—	2	2	no	—
20	C₂×#10625350	—	2	2	no	—
21	#13094046	—	4	8	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×#10625325	—	2	4	no	—
24	C₂×D₃₇₆	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	1	no	—
26	C₂²×C₄₇⋊C₈	—	2	1	no	—
27	#13094024	C₂×C₄	1	2	yes	—
28	#13094021	C₂×C₄	1	2	yes	—
29	#13094012	—	2	2	no	—
30	#13093998	—	2	2	no	—
31	#13093998	—	2	2	no	—
32	C₄×D₁₈₈	—	2	2	no	—
33	C₄×D₁₈₈	—	2	2	no	—
34	C₄×C₄₇⋊C₈	—	2	1	no	—
35	C₄×C₄₇⋊C₈	—	2	1	no	—
36	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
37	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₂²×C₈×C₄₇	D₄	1	2	yes	—
40	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₇	—	2	2	no	—
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₄₇	D₄	1	2	yes	—
46	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
49	C₂×C₂²⋊D₄₇	—	4	2	no	—
50	#10625350	—	4	8	no	—
51	C₂×D₁₈₈	—	2	2	no	—
52	C₂×D₁₈₈	—	2	2	no	—
53	C₂×D₁₈₈	—	2	2	no	—
54	C₂×C₄×D₄₇	—	4	2	no	—
55	C₂×Dic₉₄	—	2	2	no	—
56	M₁₆×C₄₇	—	4	4	no	—
57	C₂×C₈×C₄₇	—	2	4	no	—
58	C₂×C₈×C₄₇	—	4	2	no	—
59	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
65	(C₂×D₄₇)⋊C₄	—	4	2	no	—
66	(C₂×D₄₇)⋊C₄	—	4	2	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	2	4	no	—
70	C₂×C₄₇⋊C₈	—	2	2	no	—
71	C₂×C₄₇⋊C₈	—	2	2	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	Dic₁₈₈	—	4	4	no	—
74	D₃₇₆	—	4	4	no	—
75	#10625325	—	4	8	no	—
76	C₂³×C₄₇	#124	1	1	yes	characteristic
77	C₂²×D₄₇	—	4	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
86	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
87	C₂²⋊D₄₇	—	8	4	no	—
88	C₂×Dic₄₇	—	4	2	no	—
89	D₁₈₈	—	4	4	no	—
90	D₁₈₈	—	4	4	no	—
91	D₁₈₈	—	4	4	no	—
92	C₄×D₄₇	—	8	4	no	—
93	Dic₉₄	—	4	4	no	—
94	C₈×C₄₇	—	2	2	no	—
95	C₈×C₄₇	—	2	2	no	—
96	C₈×C₄₇	—	8	2	no	—
97	C₄₇⋊C₈	—	2	4	no	—
98	C₄₇⋊C₈	—	4	2	no	—
99	#9860	—	47	1	no	maximal, Sylow
100	C₂²×C₄₇	—	2	1	no	—
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	#390	1	1	yes	characteristic
103	C₂²×C₄₇	#490	1	2	yes	—
104	C₂×D₄₇	—	8	2	no	—
105	C₂×D₄₇	—	8	2	no	—
106	C₂×D₄₇	—	8	2	no	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	#418	1	2	yes	—
110	C₄×C₄₇	#443	1	2	yes	—
111	C₄×C₄₇	#444	1	2	yes	—
112	C₄×C₄₇	#496	1	2	yes	—
113	Dic₄₇	—	8	2	no	—
114	#3147	—	47	1	no	—
115	#1837	D₄₇	1	1	yes	characteristic, complemented
116	#1492	—	47	2	no	—
117	#1492	—	47	2	no	—
118	C₂×#322	—	47	1	no	—
119	C₂×C₄₇	—	2	2	no	—
120	C₂×C₄₇	#1961	1	1	yes	characteristic
121	C₂×C₄₇	#1974	1	1	yes	characteristic
122	C₂×C₄₇	#1975	1	1	yes	characteristic
123	D₄₇	—	16	2	no	—
124	C₂×#135	—	94	2	no	—
125	#532	—	47	2	no	—
126	#495	—	94	2	no	—
127	#494	—	47	1	no	—
128	#493	—	47	1	no	—
129	#492	—	47	2	no	—
130	#423	C₂×D₄₇	1	2	yes	—
131	C₂×C₄×C₈	—	47	1	no	—
132	C₂×C₄×C₈	—	47	1	no	—
133	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
134	#341	—	2	2	no	—
135	D₄⋊C₈	—	94	4	no	—
136	D₄⋊C₈	—	94	4	no	—
137	#322	—	94	2	no	—
138	C₄₇	#9860	1	1	yes	characteristic, complemented, Sylow
139	C₂×#41	—	94	2	no	—
140	#135	—	188	8	no	—
141	C₂×Q₁₆	—	94	2	no	—
142	C₂×SD₁₆	—	94	4	no	—
143	C₂×D₈	—	94	2	no	—
144	C₂×M₁₆	—	2	2	no	—
145	C₂²×C₈	—	94	1	no	—
146	C₂²×C₈	—	94	1	no	—
147	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
148	C₄⋊Q₈	—	47	2	no	—
149	#127	—	47	2	no	—
150	#124	—	94	2	no	—
151	#121	—	94	2	no	—
152	#121	—	94	2	no	—
153	C₄×D₄	—	94	2	no	—
154	C₄×D₄	—	94	2	no	—
155	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄×C₈	—	47	2	no	—
159	C₄×C₈	—	47	2	no	—
160	C₄×C₈	—	94	1	no	—
161	C₄×C₈	—	94	1	no	—
162	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
163	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
164	C₄×C₈	D₁₈₈	1	2	yes	—
165	#41	—	188	8	no	—
166	C₂×Q₈	—	94	2	no	—
167	C₂×D₄	—	94	2	no	—
168	C₂×D₄	—	94	2	no	—
169	C₂×D₄	—	94	2	no	—
170	C₂×D₄	—	188	2	no	—
171	C₂²×C₄	—	188	2	no	—
172	C₂²×C₄	#10625354	1	1	yes	characteristic
173	C₂²×C₄	#10625354	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
175	Q₁₆	—	188	4	no	—
176	SD₁₆	—	188	8	no	—
177	D₈	—	188	4	no	—
178	M₁₆	—	4	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	4	2	no	—
181	C₂×C₈	—	94	4	no	—
182	C₂×C₈	—	94	2	no	—
183	C₂×C₈	—	94	2	no	—
184	C₂×C₈	—	188	2	no	—
185	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
186	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
187	C₄⋊C₄	—	94	2	no	—
188	C₄⋊C₄	—	94	2	no	—
189	C₂²⋊C₄	—	188	2	no	—
190	C₂²⋊C₄	—	188	2	no	—
191	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
192	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
193	C₄²	D₄×D₄₇	1	1	yes	characteristic
194	C₄²	D₄×D₄₇	1	1	yes	characteristic
195	C₂³	—	188	2	no	—
196	C₂³	#13094013	1	1	yes	characteristic
197	Q₈	—	188	4	no	—
198	D₄	—	376	4	no	—
199	D₄	—	188	4	no	—
200	D₄	—	188	4	no	—
201	D₄	—	188	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	376	4	no	—
205	C₂×C₄	—	188	2	no	—
206	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	#13093986	1	1	yes	characteristic
208	C₂×C₄	#13093986	1	1	yes	characteristic
209	C₂×C₄	#13093999	1	1	yes	characteristic
210	C₂×C₄	#13093999	1	1	yes	characteristic
211	C₂×C₄	#13094020	1	1	yes	characteristic
212	C₂×C₄	#13094049	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	2	2	no	—
215	C₈	—	8	2	no	—
216	C₈	—	94	4	no	—
217	C₈	—	188	2	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	376	2	no	—
221	C₂²	—	376	2	no	—
222	C₂²	—	376	2	no	—
223	C₂²	#15689024	1	1	yes	characteristic
224	C₂²	#15689489	1	2	yes	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	376	2	no	—
228	C₄	#15689127	1	2	yes	—
229	C₄	#15689239	1	2	yes	—
230	C₄	#15689244	1	2	yes	—
231	C₄	#15689513	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	752	2	no	—
234	C₂	#20244211	1	1	yes	characteristic
235	C₂	#20244274	1	1	yes	characteristic
236	C₂	#20244279	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20253816

C₂

yes

maximal, characteristic

#20241838

C₂

yes

maximal, complemented

#20241838

C₂

yes

maximal, complemented

C₂×#15688845

C₂

yes

maximal, characteristic, complemented

C₄₇×#1837

C₂

yes

maximal, characteristic, complemented

C₂×#13094046

—

#15689673

C₂²

yes

—

#15689507

—

#15689503

C₄

yes

characteristic

#15689500

C₄

yes

characteristic

#15689496

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₄₇×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#341

—

C₂×#10625350

—

#13094046

—

C₂×Dic₁₈₈

—

C₂×#10625325

—

C₂×D₃₇₆

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

#13094024

C₂×C₄

yes

—

#13094021

C₂×C₄

yes

—

#13094012

—

#13093998

—

#13093998

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

C₂²×C₄×C₄₇

yes

C₂²×C₄×C₄₇

yes

C₂×C₂²⋊D₄₇

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

C₂³×C₄₇

#124

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

#9860

—

maximal, Sylow

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

#390

yes

characteristic

103

C₂²×C₄₇

#490

yes

—

104

C₂×D₄₇

—

105

C₂×D₄₇

—

106

C₂×D₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

#418

yes

—

110

C₄×C₄₇

#443

yes

—

111

C₄×C₄₇

#444

yes

—

112

C₄×C₄₇

#496

yes

—

113

Dic₄₇

—

114

#3147

—

115

#1837

D₄₇

yes

characteristic, complemented

116

#1492

—

117

#1492

—

118

C₂×#322

—

119

C₂×C₄₇

—

120

C₂×C₄₇

#1961

yes

characteristic

121

C₂×C₄₇

#1974

yes

characteristic

122

C₂×C₄₇

#1975

yes

characteristic

123

D₄₇

—

124

C₂×#135

—

125

#532

—

126

#495

—

127

#494

—

128

#493

—

129

#492

—

130

#423

C₂×D₄₇

yes

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

134

#341

—

135

D₄⋊C₈

—

136

D₄⋊C₈

—

137

#322

—

138

C₄₇

#9860

yes

characteristic, complemented, Sylow

139

C₂×#41

—

140

#135

—

188

—

141

C₂×Q₁₆

—

142

C₂×SD₁₆

—

143

C₂×D₈

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₂²⋊D₄₇

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

152

#121

—

153

C₄×D₄

—

154

C₄×D₄

—

155

C₂×C₄²

C₂²×D₄₇

yes

characteristic

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₄×C₈

C₄×D₄₇

yes

characteristic

163

C₄×C₈

C₄×D₄₇

yes

characteristic

164

C₄×C₈

D₁₈₈

yes

—

165

#41

—

188

—

166

C₂×Q₈

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

188

—

171

C₂²×C₄

—

188

—

172

C₂²×C₄

#10625354

yes

characteristic

173

C₂²×C₄

#10625354

yes

characteristic

174

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

175

Q₁₆

—

188

—

176

SD₁₆

—

188

—

177

D₈

—

188

—

178

M₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

188

—

185

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

186

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₂²⋊C₄

—

188

—

190

C₂²⋊C₄

—

188

—

191

C₄²

C₂×C₄×D₄₇

yes

characteristic

192

C₄²

C₂×D₁₈₈

yes

characteristic

193

C₄²

D₄×D₄₇

yes

characteristic

194

C₄²

D₄×D₄₇

yes

characteristic

195

C₂³

—

188

—

196

C₂³

#13094013

yes

characteristic

197

Q₈

—

188

—

198

D₄

—

376

—

199

D₄

—

188

—

200

D₄

—

188

—

201

D₄

—

188

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

376

—

205

C₂×C₄

—

188

—

206

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

207

C₂×C₄

#13093986

yes

characteristic

208

C₂×C₄

#13093986

yes

characteristic

209

C₂×C₄

#13093999

yes

characteristic

210

C₂×C₄

#13093999

yes

characteristic

211

C₂×C₄

#13094020

yes

characteristic

212

C₂×C₄

#13094049

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

188

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

376

—

221

C₂²

—

376

—

222

C₂²

—

376

—

223

C₂²

#15689024

yes

characteristic

224

C₂²

#15689489

yes

—

225

C₄

—

226

C₄

—

227

C₄

—

376

—

228

C₄

#15689127

yes

—

229

C₄

#15689239

yes

—

230

C₄

#15689244

yes

—

231

C₄

#15689513

yes

—

232

C₂

—

233

C₂

—

752

—

234

C₂

#20244211

yes

characteristic

235

C₂

#20244274

yes

characteristic

236

C₂

#20244279

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13094020
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1837	C₂
socle	C₂²×C₄₇	#390
prime radical	#20253816	C₂
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1837	D₄₇
hypocenter	C₄₇	#9860
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

#13094020

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1837

C₂

C₂²×C₄₇

C₂

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. #20241838	C₂	semidirect
3. #20241838	C₂	semidirect
4. C₂×#15688845	C₂	semidirect
5. C₄₇×#1837	C₂	semidirect
115. #1837	D₄₇	semidirect
138. C₄₇	#9860	semidirect

H ≅ G/N

type

2. #20241838

C₂

semidirect

3. #20241838

C₂

semidirect

4. C₂×#15688845

C₂

semidirect

5. C₄₇×#1837

C₂

semidirect

115. #1837

D₄₇

semidirect

138. C₄₇

#9860

semidirect

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

subgroup	index
#20253816	2
#20241838	2
C₂×#15688845	2
C₄₇×#1837	2
#9860	47

subgroup

index

C₄₇×#1837

Subgroups — #26116240

Conjugacy classes of subgroups

Complements

Maximal subgroups