Group #26216894 — subgroups

Subgroups — #26216894

Order 12032.

758 conjugacy classes of subgroups; only the 255 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 255 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	#20252020	C₂	1	2	yes	maximal
2	C₂×#15689075	C₂	1	1	yes	maximal, characteristic
3	#20243562	C₂	1	2	yes	maximal, complemented
4	#20243529	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243429	C₂	1	4	yes	maximal
6	#20243289	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1838	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	C₂²	1	2	yes	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	#15689179	—	2	4	no	—
11	#15689175	—	2	4	no	—
12	C₂×#13093959	C₂²	1	8	yes	—
13	#15689147	C₂²	1	2	yes	—
14	#15689086	C₂²	1	4	yes	—
15	#15689075	C₄	1	8	yes	—
16	M₁₆×Dic₄₇	C₂²	1	4	yes	—
17	C₂×#13093935	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
19	#15688888	C₂²	1	4	yes	—
20	C₄₇×#423	C₂²	1	2	yes	—
21	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#341	C₂²	1	4	yes	—
23	C₂²×C₄×D₄₇	Q₈	1	2	yes	—
24	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
25	C₂×#10625329	C₂³	1	4	yes	—
26	C₂×#10625324	—	2	8	no	—
27	C₂×#10625324	C₂×C₄	1	8	yes	—
28	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
29	C₂×C₄×Dic₄₇	Q₈	1	2	yes	—
30	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
31	C₄²×D₄₇	C₂×C₄	1	4	yes	—
32	C₄²×D₄₇	D₄	1	2	yes	—
33	C₄²×D₄₇	D₄	1	2	yes	—
34	#13093959	—	2	16	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
36	(C₂×D₄₇)⋊C₈	—	2	8	no	—
37	#13093935	C₂×C₄	1	4	yes	—
38	#13093934	—	2	4	no	—
39	C₈×Dic₄₇	—	2	4	no	—
40	C₈×Dic₄₇	C₂×C₄	1	8	yes	—
41	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
42	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₄₇	—	2	4	no	—
45	#97×C₄₇	C₂×C₄	1	4	yes	—
46	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
48	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
50	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
51	C₂×C₄×D₄₇	—	2	4	no	—
52	C₂×C₄×D₄₇	—	4	4	no	—
53	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
54	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
55	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
56	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
57	M₁₆×C₄₇	—	2	8	no	—
58	C₂×C₈×C₄₇	—	2	4	no	—
59	C₂×C₈×C₄₇	—	2	4	no	—
60	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
61	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
62	C₄²×C₄₇	C₂×D₄	1	2	yes	—
63	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
64	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
65	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
66	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
67	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
68	#10625329	—	2	8	no	—
69	C₂×C₄₇⋊C₈	—	2	4	no	—
70	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
71	C₂×C₄₇⋊C₈	#41	1	8	yes	—
72	#10625324	—	2	16	no	—
73	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
74	C₂²×D₄₇	—	2	2	no	—
75	C₂²×D₄₇	—	4	2	no	—
76	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
77	C₂×C₄×C₄₇	—	4	2	no	—
78	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
79	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
80	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
82	C₂×Dic₄₇	—	2	2	no	—
83	C₂×Dic₄₇	—	2	4	no	—
84	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
85	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
86	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
87	C₄×D₄₇	—	2	4	no	—
88	C₄×D₄₇	—	2	4	no	—
89	C₄×D₄₇	—	2	8	no	—
90	C₄×D₄₇	—	4	4	no	—
91	C₈×C₄₇	—	2	4	no	—
92	C₈×C₄₇	—	4	4	no	—
93	C₄₇⋊C₈	—	4	4	no	—
94	C₄₇⋊C₈	#117	1	8	yes	—
95	#20827	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	—	2	2	no	—
97	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₄₇	#533	1	2	yes	—
99	C₂×D₄₇	—	2	4	no	—
100	C₂×D₄₇	—	2	2	no	—
101	C₂×D₄₇	—	4	4	no	—
102	C₄×C₄₇	—	2	4	no	—
103	C₄×C₄₇	C₂×#117	1	2	yes	—
104	C₄×C₄₇	#532	1	2	yes	—
105	Dic₄₇	—	2	2	no	—
106	Dic₄₇	—	2	2	no	—
107	Dic₄₇	#430	1	4	yes	—
108	#2920	—	47	2	no	—
109	C₂×C₄×M₁₆	—	47	1	no	—
110	#1849	—	47	2	no	—
111	#1838	—	47	1	no	—
112	#1838	D₄₇	1	1	yes	characteristic, complemented
113	#1811	—	47	4	no	—
114	C₄×#108	—	47	4	no	—
115	C₂×C₄₇	—	2	2	no	—
116	C₂×C₄₇	#2285	1	1	yes	characteristic
117	C₂×C₄₇	C₂×#430	1	2	yes	—
118	D₄₇	—	4	2	no	—
119	C₂²×M₁₆	—	47	2	no	—
120	C₂²×C₄²	—	47	1	no	—
121	#432	—	94	4	no	—
122	#431	—	94	4	no	—
123	C₂×#108	—	47	8	no	—
124	#423	—	47	2	no	—
125	#423	C₂×D₄₇	1	2	yes	—
126	#407	—	47	4	no	—
127	C₄×M₁₆	—	47	8	no	—
128	C₄×M₁₆	—	47	4	no	—
129	C₂×#97	—	47	1	no	—
130	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
131	C₂×C₄×C₈	—	47	2	no	—
132	#341	—	47	4	no	—
133	#341	C₂×D₄₇	1	4	yes	—
134	C₄₇	#20827	1	1	yes	characteristic, complemented, Sylow
135	C₂³×C₄	—	47	1	no	—
136	C₂³×C₄	—	47	2	no	—
137	C₂×M₁₆	—	47	8	no	—
138	C₂×M₁₆	—	47	4	no	—
139	C₂×M₁₆	—	94	8	no	—
140	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
141	C₂²×C₈	—	47	2	no	—
142	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
143	C₂×C₄²	—	47	2	no	—
144	C₂×C₄²	—	47	1	no	—
145	C₂×C₄²	—	47	4	no	—
146	C₂×C₄²	—	47	2	no	—
147	C₂×C₄²	—	47	2	no	—
148	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
149	#108	—	94	16	no	—
150	C₄⋊C₈	—	2	4	no	—
151	C₄⋊C₈	—	94	4	no	—
152	C₂²⋊C₈	—	94	8	no	—
153	#97	—	47	4	no	—
154	#97	—	94	4	no	—
155	#97	C₄×D₄₇	1	4	yes	—
156	C₄×C₈	—	47	8	no	—
157	C₄×C₈	—	94	4	no	—
158	C₂⁴	—	47	1	no	—
159	C₂²×C₄	—	47	2	no	—
160	C₂²×C₄	—	47	1	no	—
161	C₂²×C₄	—	47	4	no	—
162	C₂²×C₄	—	47	2	no	—
163	C₂²×C₄	—	47	2	no	—
164	C₂²×C₄	—	47	4	no	—
165	C₂²×C₄	—	94	4	no	—
166	C₂²×C₄	—	188	4	no	—
167	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
168	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
169	M₁₆	—	2	8	no	—
170	M₁₆	—	94	16	no	—
171	M₁₆	—	94	8	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	47	4	no	—
175	C₂×C₈	—	47	8	no	—
176	C₂×C₈	—	94	4	no	—
177	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
178	C₄²	—	47	4	no	—
179	C₄²	—	47	4	no	—
180	C₄²	—	47	2	no	—
181	C₄²	—	47	1	no	—
182	C₄²	—	47	1	no	—
183	C₄²	C₂×C₄×D₄₇	1	2	yes	—
184	C₄²	D₄×D₄₇	1	2	yes	—
185	C₂³	—	47	2	no	—
186	C₂³	—	94	2	no	—
187	C₂³	—	188	2	no	—
188	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	—	47	2	no	—
191	C₂×C₄	—	47	2	no	—
192	C₂×C₄	—	47	2	no	—
193	C₂×C₄	—	94	8	no	—
194	C₂×C₄	—	94	4	no	—
195	C₂×C₄	—	94	2	no	—
196	C₂×C₄	—	94	4	no	—
197	C₂×C₄	—	94	4	no	—
198	C₂×C₄	—	188	4	no	—
199	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
200	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
201	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
202	C₂×C₄	#41×D₄₇	1	4	yes	—
203	C₈	—	2	4	no	—
204	C₈	—	4	4	no	—
205	C₈	—	47	8	no	—
206	C₈	—	188	4	no	—
207	C₂²	—	2	2	no	—
208	C₂²	—	94	2	no	—
209	C₂²	—	94	4	no	—
210	C₂²	—	188	4	no	—
211	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
212	C₂²	#15689679	1	2	yes	—
213	C₄	—	2	4	no	—
214	C₄	—	47	4	no	—
215	C₄	—	94	2	no	—
216	C₄	—	94	2	no	—
217	C₄	#117×D₄₇	1	2	yes	—
218	C₄	#15689672	1	2	yes	—
219	C₂	—	2	2	no	—
220	C₂	—	188	2	no	—
221	C₂	#20245794	1	1	yes	characteristic
222	C₂	#430×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20252020

C₂

yes

maximal

C₂×#15689075

C₂

yes

maximal, characteristic

#20243562

C₂

yes

maximal, complemented

#20243529

C₂

yes

maximal, characteristic, complemented

#20243429

C₂

yes

maximal

#20243289

C₂

yes

maximal, complemented

C₄₇×#1838

C₂

yes

maximal, characteristic, complemented

C₂²×#10625324

C₂²

yes

—

C₂×C₄²×D₄₇

C₂²

yes

—

—

C₂²

yes

—

#15689147

C₂²

yes

—

#15689086

C₂²

yes

—

#15689075

C₄

yes

—

M₁₆×Dic₄₇

C₂²

yes

—

C₂×#13093935

C₂²

yes

characteristic

C₂×C₈×Dic₄₇

C₂²

yes

—

#15688888

C₂²

yes

—

C₄₇×#423

C₂²

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₄₇×#341

C₂²

yes

—

C₂²×C₄×D₄₇

Q₈

yes

—

C₂²×C₄×D₄₇

C₂³

yes

characteristic

C₂×#10625329

C₂³

yes

—

C₂×#10625324

—

C₂×#10625324

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

C₂³

yes

—

C₂×C₄×Dic₄₇

Q₈

yes

—

C₂×C₄×Dic₄₇

C₂³

yes

characteristic

C₄²×D₄₇

C₂×C₄

yes

—

C₄²×D₄₇

D₄

yes

—

C₄²×D₄₇

D₄

yes

—

#13093959

—

C₄⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

#13093935

C₂×C₄

yes

—

#13093934

—

C₈×Dic₄₇

—

C₈×Dic₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

#97×C₄₇

C₂×C₄

yes

—

C₂³×D₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

—

C₂²×C₄×C₄₇

C₂⁴

yes

characteristic

C₂²×Dic₄₇

C₂×Q₈

yes

characteristic

C₂²×Dic₄₇

C₂×Q₈

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×D₄₇

C₂²×C₄

yes

—

C₂×C₄×D₄₇

C₂×D₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄×Dic₄₇

C₄⋊C₄

yes

—

C₄×Dic₄₇

C₄⋊C₄

yes

—

C₄×Dic₄₇

C₂²×C₄

yes

—

C₄×Dic₄₇

C₂×D₄

yes

characteristic

C₄×Dic₄₇

C₂×D₄

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²×C₄

yes

—

C₂×C₄₇⋊C₈

#41

yes

—

#10625324

—

C₂³×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂³×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₄⋊C₄

yes

—

C₂×Dic₄₇

C₂×C₄⋊C₄

yes

—

C₂×Dic₄₇

C₂×C₄⋊C₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

#117

yes

—

#20827

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#533

yes

—

C₂×D₄₇

—

100

C₂×D₄₇

—

101

C₂×D₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

C₂×#117

yes

—

104

C₄×C₄₇

#532

yes

—

105

Dic₄₇

—

106

Dic₄₇

—

107

Dic₄₇

#430

yes

—

108

#2920

—

109

C₂×C₄×M₁₆

—

110

#1849

—

111

#1838

—

112

#1838

D₄₇

yes

characteristic, complemented

113

#1811

—

114

C₄×#108

—

115

C₂×C₄₇

—

116

C₂×C₄₇

#2285

yes

characteristic

117

C₂×C₄₇

C₂×#430

yes

—

118

D₄₇

—

119

C₂²×M₁₆

—

120

C₂²×C₄²

—

121

#432

—

122

#431

—

123

C₂×#108

—

124

#423

—

125

#423

C₂×D₄₇

yes

—

126

#407

—

127

C₄×M₁₆

—

128

C₄×M₁₆

—

129

C₂×#97

—

130

C₂×#97

C₂×D₄₇

yes

characteristic

131

C₂×C₄×C₈

—

132

#341

—

133

#341

C₂×D₄₇

yes

—

134

C₄₇

#20827

yes

characteristic, complemented, Sylow

135

C₂³×C₄

—

136

C₂³×C₄

—

137

C₂×M₁₆

—

138

C₂×M₁₆

—

139

C₂×M₁₆

—

140

C₂×M₁₆

C₂²×D₄₇

yes

—

141

C₂²×C₈

—

142

C₂²×C₈

C₂²×D₄₇

yes

—

143

C₂×C₄²

—

144

C₂×C₄²

—

145

C₂×C₄²

—

146

C₂×C₄²

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂²×D₄₇

yes

characteristic

149

#108

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₂²⋊C₈

—

153

#97

—

154

#97

—

155

#97

C₄×D₄₇

yes

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₂⁴

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

188

—

167

C₂²×C₄

Q₈×D₄₇

yes

—

168

C₂²×C₄

C₂³×D₄₇

yes

characteristic

169

M₁₆

—

170

M₁₆

—

171

M₁₆

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

C₂×C₄×D₄₇

yes

—

178

C₄²

—

179

C₄²

—

180

C₄²

—

181

C₄²

—

182

C₄²

—

183

C₄²

C₂×C₄×D₄₇

yes

—

184

C₄²

D₄×D₄₇

yes

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

—

188

C₂³

C₂×Q₈×D₄₇

yes

characteristic

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

188

—

199

C₂×C₄

C₄⋊C₄×D₄₇

yes

—

200

C₂×C₄

C₂²×C₄×D₄₇

yes

characteristic

201

C₂×C₄

C₂×D₄×D₄₇

yes

characteristic

202

C₂×C₄

#41×D₄₇

yes

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

188

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

188

—

211

C₂²

C₂×C₄⋊C₄×D₄₇

yes

characteristic

212

C₂²

#15689679

yes

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

#117×D₄₇

yes

—

218

C₄

#15689672

yes

—

219

C₂

—

220

C₂

—

188

—

221

C₂

#20245794

yes

characteristic

222

C₂

#430×D₄₇

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1838	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₂×Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1838	D₄₇
hypocenter	C₄₇	#20827
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1838

subgroup

G/H

center

C₂×C₄

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₄₇

Fitting

C₄₇×#1838

C₂

socle

C₂²×C₄₇

C₂²×C₄⋊C₄

prime radical

C₂³×D₄₇

C₂×Q₈

cosocle

C₂²×C₄×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1838

N	H ≅ G/N	type
3. #20243562	C₂	semidirect
4. #20243529	C₂	semidirect
6. #20243289	C₂	semidirect
7. C₄₇×#1838	C₂	semidirect
112. #1838	D₄₇	semidirect
134. C₄₇	#20827	semidirect

H ≅ G/N

type

3. #20243562

C₂

semidirect

4. #20243529

C₂

semidirect

6. #20243289

C₂

semidirect

7. C₄₇×#1838

C₂

semidirect

112. #1838

D₄₇

semidirect

134. C₄₇

#20827

semidirect

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

subgroup	index
#20252020	2
C₂×#15689075	2
#20243562	2
#20243529	2
#20243429	2
#20243289	2
C₄₇×#1838	2
#20827	47

subgroup

index

C₄₇×#1838

Subgroups — #26216894

Conjugacy classes of subgroups

Complements

Maximal subgroups