Group #26121297 — subgroups

Subgroups — #26121297

Order 12032.

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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	#20244368	C₂	1	1	yes	maximal, characteristic
2	#20243541	C₂	1	1	yes	maximal, characteristic
3	#20242164	C₂	1	1	yes	maximal, characteristic
4	#20241792	C₂	1	1	yes	maximal, characteristic
5	#20241790	C₂	1	1	yes	maximal, characteristic
6	#20241216	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1571	C₂	1	1	yes	maximal, characteristic
8	#15689680	C₂²	1	1	yes	characteristic
9	#15689176	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₈	—	2	2	no	—
12	#15688969	C₂²	1	1	yes	characteristic
13	#15688884	—	2	2	no	—
14	#15688875	—	2	2	no	—
15	#15688855	—	2	2	no	—
16	#15688853	—	2	2	no	—
17	C₄₇×#431	C₂²	1	1	yes	characteristic
18	C₄₇×#423	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#335	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	#13094024	Q₈	1	1	yes	characteristic
23	#13094024	Q₈	1	1	yes	characteristic
24	#13094016	—	2	1	no	—
25	#13094003	—	2	1	no	—
26	#13094003	—	2	1	no	—
27	C₄×Dic₉₄	—	2	1	no	—
28	C₄×Dic₉₄	—	2	1	no	—
29	#13093983	—	2	1	no	—
30	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
33	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
34	Dic₄₇⋊C₈	—	4	4	no	—
35	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
36	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
37	C₄₇⋊#95	—	2	1	no	—
38	C₄₇⋊#95	—	2	1	no	—
39	C₂×M₁₆×C₄₇	—	2	1	no	—
40	C₂²×C₈×C₄₇	—	2	1	no	—
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	1	no	—
43	C₄⋊C₈×C₄₇	—	2	1	no	—
44	C₄⋊C₈×C₄₇	—	2	1	no	—
45	C₄⋊C₈×C₄₇	—	2	1	no	—
46	C₄⋊C₈×C₄₇	—	2	1	no	—
47	C₂²⋊C₈×C₄₇	—	2	1	no	—
48	C₄×C₈×C₄₇	D₄	1	2	yes	—
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
52	C₂²×Dic₄₇	—	2	2	no	—
53	C₂×Dic₉₄	—	2	1	no	—
54	C₂×Dic₉₄	—	2	1	no	—
55	M₁₆×C₄₇	—	4	2	no	—
56	C₂×C₈×C₄₇	—	2	2	no	—
57	C₂×C₈×C₄₇	—	4	1	no	—
58	C₂×C₈×C₄₇	—	4	1	no	—
59	C₂×C₈×C₄₇	—	4	2	no	—
60	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₄₇	#41	1	1	yes	characteristic
64	C₂²⋊Dic₄₇	—	4	1	no	—
65	C₄⋊Dic₄₇	—	2	1	no	—
66	C₄⋊Dic₄₇	—	2	1	no	—
67	C₄⋊Dic₄₇	—	2	1	no	—
68	C₄⋊Dic₄₇	—	2	1	no	—
69	Dic₄₇⋊C₄	—	4	1	no	—
70	Dic₄₇⋊C₄	—	4	1	no	—
71	C₄×Dic₄₇	—	2	2	no	—
72	C₄×Dic₄₇	—	4	1	no	—
73	C₄×Dic₄₇	Q₁₆	1	4	yes	—
74	C₂×C₄₇⋊C₈	—	2	2	no	—
75	C₂×C₄₇⋊C₈	—	4	1	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₂³×C₄₇	#123	1	1	yes	characteristic
78	C₂×C₄×C₄₇	—	4	1	no	—
79	C₂×C₄×C₄₇	—	4	1	no	—
80	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
88	C₂×Dic₄₇	—	2	4	no	—
89	C₂×Dic₄₇	—	4	2	no	—
90	C₂×Dic₄₇	—	4	2	no	—
91	C₂×Dic₄₇	—	4	1	no	—
92	C₂×Dic₄₇	—	4	1	no	—
93	Dic₉₄	—	4	2	no	—
94	Dic₉₄	—	4	2	no	—
95	C₈×C₄₇	—	4	2	no	—
96	C₈×C₄₇	—	8	1	no	—
97	C₈×C₄₇	—	8	1	no	—
98	C₄₇⋊C₈	—	4	2	no	—
99	C₄₇⋊C₈	—	8	1	no	—
100	#10668	—	47	1	no	maximal, Sylow
101	C₂²×C₄₇	—	2	1	no	—
102	C₂²×C₄₇	—	2	1	no	—
103	C₂²×C₄₇	#399	1	1	yes	characteristic
104	C₂²×C₄₇	#484	1	2	yes	—
105	C₄×C₄₇	—	2	1	no	—
106	C₄×C₄₇	—	2	1	no	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	#477	1	2	yes	—
110	C₄×C₄₇	#494	1	1	yes	characteristic
111	C₄×C₄₇	#496	1	1	yes	characteristic
112	Dic₄₇	—	4	4	no	—
113	Dic₄₇	—	8	1	no	—
114	Dic₄₇	—	8	1	no	—
115	#1995	—	47	1	no	—
116	#1843	—	47	1	no	—
117	#1571	—	47	1	no	—
118	#1571	D₄₇	1	1	yes	characteristic
119	#1481	—	47	1	no	—
120	#1481	—	47	1	no	—
121	#1274	—	47	1	no	—
122	C₂×C₄₇	—	2	2	no	—
123	C₂×C₄₇	#2095	1	1	yes	characteristic
124	C₂×C₄₇	#2098	1	1	yes	characteristic
125	C₂×C₄₇	#2098	1	1	yes	characteristic
126	#533	—	47	1	no	—
127	#431	—	47	1	no	—
128	#431	C₂×D₄₇	1	1	yes	characteristic
129	#423	C₂×D₄₇	1	1	yes	characteristic
130	C₂×C₄⋊C₈	—	47	1	no	—
131	C₂×C₄⋊C₈	—	94	2	no	—
132	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
133	#376	—	47	1	no	—
134	#339	—	94	2	no	—
135	#335	—	2	2	no	—
136	#335	—	94	2	no	—
137	Q₈⋊C₈	—	94	2	no	—
138	Q₈⋊C₈	—	94	2	no	—
139	C₄₇	#10668	1	1	yes	characteristic, complemented, Sylow
140	C₂×M₁₆	—	2	1	no	—
141	C₂²×C₈	—	2	1	no	—
142	C₂²×C₈	—	94	1	no	—
143	C₄⋊Q₈	—	47	1	no	—
144	C₄⋊Q₈	—	47	1	no	—
145	#125	—	94	1	no	—
146	C₂²⋊Q₈	—	94	1	no	—
147	C₂²⋊Q₈	—	94	1	no	—
148	C₄×Q₈	—	94	1	no	—
149	C₄×Q₈	—	94	1	no	—
150	#117	—	94	1	no	—
151	C₂×C₄²	—	47	2	no	—
152	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	—	2	1	no	—
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	94	1	no	—
159	C₄⋊C₈	—	94	1	no	—
160	C₄⋊C₈	—	94	1	no	—
161	C₄⋊C₈	—	188	4	no	—
162	C₂²⋊C₈	—	2	1	no	—
163	C₂²⋊C₈	—	94	1	no	—
164	C₄×C₈	—	47	2	no	—
165	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
166	#95	—	94	1	no	—
167	#95	—	94	1	no	—
168	C₂×Q₈	—	94	1	no	—
169	C₂×Q₈	—	94	1	no	—
170	C₂²×C₄	—	94	2	no	—
171	C₂²×C₄	#10625350	1	1	yes	characteristic
172	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
173	C₂²×C₄	#10625354	1	1	yes	characteristic
174	M₁₆	—	4	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	4	2	no	—
179	C₂×C₈	—	94	2	no	—
180	C₂×C₈	—	188	1	no	—
181	C₂×C₈	—	188	2	no	—
182	C₄⋊C₄	—	94	1	no	—
183	C₄⋊C₄	—	94	1	no	—
184	C₄⋊C₄	—	94	1	no	—
185	C₄⋊C₄	—	94	1	no	—
186	C₄⋊C₄	—	188	1	no	—
187	C₄⋊C₄	—	188	1	no	—
188	C₂²⋊C₄	—	188	1	no	—
189	C₄²	—	47	4	no	—
190	C₄²	—	94	2	no	—
191	C₄²	—	188	1	no	—
192	C₄²	#10625350	1	1	yes	characteristic
193	C₄²	D₄×D₄₇	1	1	yes	characteristic
194	C₄²	Q₈×D₄₇	1	1	yes	characteristic
195	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
196	C₂³	#13094009	1	1	yes	characteristic
197	Q₈	—	188	2	no	—
198	Q₈	—	188	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	94	4	no	—
202	C₂×C₄	—	188	1	no	—
203	C₂×C₄	—	188	1	no	—
204	C₂×C₄	—	188	2	no	—
205	C₂×C₄	—	188	2	no	—
206	C₂×C₄	#13094000	1	1	yes	characteristic
207	C₂×C₄	#13094002	1	1	yes	characteristic
208	C₂×C₄	#13094002	1	1	yes	characteristic
209	C₂×C₄	#13094007	1	1	yes	characteristic
210	C₂×C₄	#13094009	1	1	yes	characteristic
211	C₂×C₄	#13094020	1	1	yes	characteristic
212	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
213	C₂×C₄	#13094048	1	2	yes	—
214	C₈	—	4	2	no	—
215	C₈	—	8	1	no	—
216	C₈	—	8	1	no	—
217	C₈	—	376	1	no	—
218	C₈	—	188	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#15689058	1	1	yes	characteristic
222	C₂²	#15689460	1	2	yes	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	376	1	no	—
228	C₄	—	376	1	no	—
229	C₄	—	188	4	no	—
230	C₄	#15689417	1	2	yes	—
231	C₄	#15689501	1	1	yes	characteristic
232	C₄	#15689511	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	#20244923	1	1	yes	characteristic
235	C₂	#20244940	1	1	yes	characteristic
236	C₂	#20244944	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20244368

C₂

yes

maximal, characteristic

#20243541

C₂

yes

maximal, characteristic

#20242164

C₂

yes

maximal, characteristic

#20241792

C₂

yes

maximal, characteristic

#20241790

C₂

yes

maximal, characteristic

#20241216

C₂

yes

maximal, characteristic

C₄₇×#1571

C₂

yes

maximal, characteristic

#15689680

C₂²

yes

characteristic

#15689176

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₈

—

#15688969

C₂²

yes

—

—

—

—

C₄₇×#431

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#335

—

C₂²×C₄₇⋊C₈

—

#13094024

Q₈

yes

characteristic

#13094024

Q₈

yes

—

—

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

#13093983

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

C₂²×C₄×C₄₇

yes

C₂²×C₄×C₄₇

yes

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

characteristic

C₄²×C₄₇

#41

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

Q₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

100

#10668

—

maximal, Sylow

101

C₂²×C₄₇

—

102

C₂²×C₄₇

—

103

C₂²×C₄₇

#399

yes

characteristic

104

C₂²×C₄₇

#484

yes

—

105

C₄×C₄₇

—

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

#477

yes

—

110

C₄×C₄₇

#494

yes

characteristic

111

C₄×C₄₇

#496

yes

characteristic

112

Dic₄₇

—

113

Dic₄₇

—

114

Dic₄₇

—

115

#1995

—

116

#1843

—

117

#1571

—

118

#1571

D₄₇

yes

characteristic

119

#1481

—

120

#1481

—

121

#1274

—

122

C₂×C₄₇

—

123

C₂×C₄₇

#2095

yes

characteristic

124

C₂×C₄₇

#2098

yes

characteristic

125

C₂×C₄₇

#2098

yes

characteristic

126

#533

—

127

#431

—

128

#431

C₂×D₄₇

yes

characteristic

129

#423

C₂×D₄₇

yes

characteristic

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

132

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

133

#376

—

134

#339

—

135

#335

—

136

#335

—

137

Q₈⋊C₈

—

138

Q₈⋊C₈

—

139

C₄₇

#10668

yes

characteristic, complemented, Sylow

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

#125

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₄₇

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

188

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

C₄×C₈

—

165

C₄×C₈

C₂²⋊D₄₇

yes

—

166

#95

—

167

#95

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂²×C₄

—

171

C₂²×C₄

#10625350

yes

characteristic

172

C₂²×C₄

D₄×D₄₇

yes

characteristic

173

C₂²×C₄

#10625354

yes

characteristic

174

M₁₆

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

188

—

181

C₂×C₈

—

188

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

188

—

187

C₄⋊C₄

—

188

—

188

C₂²⋊C₄

—

188

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

188

—

192

C₄²

#10625350

yes

characteristic

193

C₄²

D₄×D₄₇

yes

characteristic

194

C₄²

Q₈×D₄₇

yes

characteristic

195

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

196

C₂³

#13094009

yes

characteristic

197

Q₈

—

188

—

198

Q₈

—

188

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

188

—

203

C₂×C₄

—

188

—

204

C₂×C₄

—

188

—

205

C₂×C₄

—

188

—

206

C₂×C₄

#13094000

yes

characteristic

207

C₂×C₄

#13094002

yes

characteristic

208

C₂×C₄

#13094002

yes

characteristic

209

C₂×C₄

#13094007

yes

characteristic

210

C₂×C₄

#13094009

yes

characteristic

211

C₂×C₄

#13094020

yes

characteristic

212

C₂×C₄

Q₁₆×D₄₇

yes

—

213

C₂×C₄

#13094048

yes

—

214

C₈

—

215

C₈

—

216

C₈

—

217

C₈

—

376

—

218

C₈

—

188

—

219

C₂²

—

220

C₂²

—

221

C₂²

#15689058

yes

characteristic

222

C₂²

#15689460

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

376

—

228

C₄

—

376

—

229

C₄

—

188

—

230

C₄

#15689417

yes

—

231

C₄

#15689501

yes

characteristic

232

C₄

#15689511

yes

characteristic

233

C₂

—

234

C₂

#20244923

yes

characteristic

235

C₂

#20244940

yes

characteristic

236

C₂

#20244944

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13094020
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1571	C₂
socle	C₂²×C₄₇	#399
prime radical	C₂³×C₄₇	#123
hypercenter	#1571	D₄₇
hypocenter	C₄₇	#10668
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

subgroup

G/H

center

C₂×C₄

#13094020

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1571

C₂

C₂²×C₄₇

C₂³×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

N	H ≅ G/N	type
139. C₄₇	#10668	semidirect

H ≅ G/N

type

139. C₄₇

#10668

semidirect

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

subgroup	index
#20244368	2
#20243541	2
#20242164	2
#20241792	2
#20241790	2
#20241216	2
C₄₇×#1571	2
#10668	47

subgroup

index

C₄₇×#1571

Subgroups — #26121297

Conjugacy classes of subgroups

Complements

Maximal subgroups