Group #25007031 — subgroups

Subgroups — #25007031

Order 11008.

324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 103 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	#19145181	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063261	C₂	1	1	yes	maximal, characteristic
3	#19132614	C₂	1	4	yes	maximal
4	C₄₃×#2162	C₂	1	1	yes	maximal, characteristic
5	#14583456	—	2	1	no	—
6	#14583304	C₄	1	1	yes	characteristic
7	#14583279	C₄	1	1	yes	characteristic
8	#14583250	—	2	1	no	—
9	#14583140	—	2	1	no	—
10	#14583140	C₂²	1	2	yes	—
11	C₄×Dic₁₇₂	—	2	1	no	—
12	C₄×Dic₁₇₂	C₄	1	2	yes	—
13	C₂×#13063261	—	2	1	no	—
14	C₄×#10621877	—	2	1	no	—
15	#14582664	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×C₄⋊C₁₆	—	2	1	no	—
18	C₄₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
19	C₄×C₁₆×C₄₃	—	2	1	no	—
20	C₂×Dic₁₇₂	—	2	1	no	—
21	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
22	C₂×#10621877	—	2	2	no	—
23	#13063325	—	2	1	no	—
24	#13063325	—	2	1	no	—
25	#13063317	—	4	1	no	—
26	#13063304	—	2	2	no	—
27	#13063304	—	4	1	no	—
28	C₄×Dic₈₆	—	2	2	no	—
29	C₄×Dic₈₆	—	4	1	no	—
30	#13063284	—	4	1	no	—
31	#13063261	—	2	4	no	—
32	#13063259	—	2	1	no	—
33	#13063259	C₂×C₄	1	2	yes	—
34	#13063250	—	2	2	no	—
35	#13063250	—	2	2	no	—
36	#13063236	—	4	1	no	—
37	C₄×C₄₃⋊C₈	—	4	1	no	—
38	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
41	C₂×C₁₆×C₄₃	—	2	2	no	—
42	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
45	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₈₆	—	2	2	no	—
50	C₂×Dic₈₆	—	4	1	no	—
51	C₂×C₈×C₄₃	—	2	2	no	—
52	C₂×C₈×C₄₃	—	4	1	no	—
53	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₄₃	D₈	1	1	yes	characteristic
60	C₄²×C₄₃	D₈	1	1	yes	characteristic
61	C₂²⋊Dic₄₃	—	4	2	no	—
62	C₄⋊Dic₄₃	—	2	2	no	—
63	C₄⋊Dic₄₃	—	4	1	no	—
64	C₄⋊Dic₄₃	—	4	1	no	—
65	C₄⋊Dic₄₃	—	4	1	no	—
66	Dic₄₃⋊C₄	—	4	2	no	—
67	Dic₄₃⋊C₄	—	4	2	no	—
68	C₄×Dic₄₃	—	4	2	no	—
69	#10621877	—	2	4	no	—
70	#10621877	—	4	2	no	—
71	C₂×C₄₃⋊C₈	—	4	2	no	—
72	Dic₁₇₂	—	4	2	no	—
73	Dic₁₇₂	—	4	2	no	—
74	C₁₆×C₄₃	—	4	2	no	—
75	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₄₃	—	2	2	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	1	no	—
79	C₂×C₄×C₄₃	—	2	1	no	—
80	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
81	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
82	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
86	C₂×Dic₄₃	—	4	2	no	—
87	C₂×Dic₄₃	—	4	2	no	—
88	Dic₈₆	—	4	2	no	—
89	Dic₈₆	—	4	2	no	—
90	Dic₈₆	—	8	2	no	—
91	C₈×C₄₃	—	2	1	no	—
92	C₈×C₄₃	—	2	1	no	—
93	C₈×C₄₃	—	2	1	no	—
94	C₈×C₄₃	#104	1	2	yes	—
95	C₄₃⋊C₈	—	4	4	no	—
96	#11748	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	1	no	—
98	C₂²×C₄₃	—	2	1	no	—
99	C₂²×C₄₃	—	2	1	no	—
100	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
101	C₄×C₄₃	—	2	1	no	—
102	C₄×C₄₃	—	2	1	no	—
103	C₄×C₄₃	—	2	1	no	—
104	C₄×C₄₃	#359	1	2	yes	—
105	C₄×C₄₃	#362	1	2	yes	—
106	C₄×C₄₃	#410	1	1	yes	characteristic
107	C₄×C₄₃	C₂×#104	1	1	yes	characteristic
108	Dic₄₃	—	8	2	no	—
109	Dic₄₃	—	8	2	no	—
110	#3170	—	43	1	no	—
111	#2162	D₄₃	1	1	yes	characteristic
112	C₄×#108	—	43	1	no	—
113	#1350	—	43	4	no	—
114	C₂×C₄₃	—	4	1	no	—
115	C₂×C₄₃	#1502	1	1	yes	characteristic
116	C₂×C₄₃	C₂×#359	1	1	yes	characteristic
117	C₂×C₄₃	C₂×#362	1	1	yes	characteristic
118	#533	—	86	1	no	—
119	#500	—	43	1	no	—
120	#494	—	43	1	no	—
121	#487	—	86	1	no	—
122	#467	—	43	2	no	—
123	#467	—	86	1	no	—
124	C₄×Q₁₆	—	43	2	no	—
125	C₄×Q₁₆	—	86	1	no	—
126	C₂×#108	—	86	1	no	—
127	C₄×M₁₆	—	86	1	no	—
128	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
129	C₄⋊C₁₆	—	2	1	no	—
130	C₂²⋊C₁₆	C₂×D₄₃	1	2	yes	—
131	C₄×C₁₆	—	2	1	no	—
132	#341	—	43	2	no	—
133	C₄₃	#11748	1	1	yes	characteristic, complemented, Sylow
134	C₂×Q₁₆	—	43	2	no	—
135	C₂×Q₁₆	—	86	1	no	—
136	C₂×M₁₆	—	86	2	no	—
137	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
138	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
139	C₄⋊Q₈	—	86	1	no	—
140	C₄⋊Q₈	—	86	1	no	—
141	#125	—	172	1	no	—
142	C₂²⋊Q₈	—	86	2	no	—
143	C₂²⋊Q₈	—	172	1	no	—
144	C₄×Q₈	—	86	2	no	—
145	C₄×Q₈	—	172	1	no	—
146	#117	—	172	1	no	—
147	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
148	C₂×C₁₆	—	2	2	no	—
149	#108	—	86	4	no	—
150	#107	—	43	2	no	—
151	#107	—	86	1	no	—
152	#103	—	86	2	no	—
153	#103	—	86	2	no	—
154	#97	—	172	1	no	—
155	C₄×C₈	—	172	1	no	—
156	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
157	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
158	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
160	C₂×Q₈	—	86	2	no	—
161	C₂×Q₈	—	172	1	no	—
162	C₂²×C₄	#10621873	1	1	yes	characteristic
163	C₂²×C₄	#10621873	1	1	yes	characteristic
164	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
165	Q₁₆	—	172	2	no	—
166	Q₁₆	—	172	2	no	—
167	M₁₆	—	86	4	no	—
168	M₁₆	—	172	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	172	2	no	—
172	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
173	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
174	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
175	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
176	C₄⋊C₄	—	86	2	no	—
177	C₄⋊C₄	—	172	1	no	—
178	C₄⋊C₄	—	172	1	no	—
179	C₄⋊C₄	—	172	2	no	—
180	C₄⋊C₄	—	172	1	no	—
181	C₄⋊C₄	—	172	2	no	—
182	C₂²⋊C₄	—	172	2	no	—
183	C₄²	—	172	2	no	—
184	C₄²	D₃₄₄	1	1	yes	characteristic
185	C₄²	D₃₄₄	1	1	yes	characteristic
186	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
187	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
188	C₁₆	—	4	2	no	—
189	C₂³	C₂×#10621873	1	1	yes	characteristic
190	Q₈	—	344	2	no	—
191	Q₈	—	172	2	no	—
192	Q₈	—	172	2	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	172	2	no	—
198	C₂×C₄	—	172	2	no	—
199	C₂×C₄	#13063247	1	1	yes	characteristic
200	C₂×C₄	#13063247	1	1	yes	characteristic
201	C₂×C₄	#13063247	1	1	yes	characteristic
202	C₂×C₄	#13063247	1	1	yes	characteristic
203	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	172	4	no	—
209	C₈	#13063251	1	2	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	C₂×#13063247	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	344	2	no	—
218	C₄	—	344	2	no	—
219	C₄	#14582707	1	2	yes	—
220	C₄	#14582716	1	2	yes	—
221	C₄	#14582872	1	1	yes	characteristic
222	C₄	C₂×#13063251	1	1	yes	characteristic
223	C₂	—	4	1	no	—
224	C₂	#19133091	1	1	yes	characteristic
225	C₂	C₂×#14582707	1	1	yes	characteristic
226	C₂	C₂×#14582716	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19145181

C₂

yes

maximal, characteristic

C₄×#13063261

C₂

yes

maximal, characteristic

#19132614

C₂

yes

maximal

C₄₃×#2162

C₂

yes

maximal, characteristic

#14583456

—

#14583304

C₄

yes

characteristic

#14583279

C₄

yes

—

—

C₂²

yes

—

C₄×Dic₁₇₂

—

C₄×Dic₁₇₂

C₄

yes

—

C₂×#13063261

—

C₄×#10621877

—

#14582664

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×C₄⋊C₁₆

—

C₄₃×C₂²⋊C₁₆

C₂²

yes

—

C₄×C₁₆×C₄₃

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

—

—

—

—

—

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

—

—

—

C₂×C₄

yes

—

#13063250

—

#13063250

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

SD₁₆

yes

characteristic

C₂²×C₄×C₄₃

SD₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

C₂²⋊C₄

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

C₄²×C₄₃

D₈

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

#104

yes

—

C₄₃⋊C₈

—

#11748

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

100

C₂²×C₄₃

C₂×#102

yes

characteristic

101

C₄×C₄₃

—

102

C₄×C₄₃

—

103

C₄×C₄₃

—

104

C₄×C₄₃

#359

yes

—

105

C₄×C₄₃

#362

yes

—

106

C₄×C₄₃

#410

yes

characteristic

107

C₄×C₄₃

C₂×#104

yes

characteristic

108

Dic₄₃

—

109

Dic₄₃

—

110

#3170

—

111

#2162

D₄₃

yes

characteristic

112

C₄×#108

—

113

#1350

—

114

C₂×C₄₃

—

115

C₂×C₄₃

#1502

yes

characteristic

116

C₂×C₄₃

C₂×#359

yes

characteristic

117

C₂×C₄₃

C₂×#362

yes

characteristic

118

#533

—

119

#500

—

120

#494

—

121

#487

—

122

#467

—

123

#467

—

124

C₄×Q₁₆

—

125

C₄×Q₁₆

—

126

C₂×#108

—

127

C₄×M₁₆

—

128

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

129

C₄⋊C₁₆

—

130

C₂²⋊C₁₆

C₂×D₄₃

yes

—

131

C₄×C₁₆

—

132

#341

—

133

C₄₃

#11748

yes

characteristic, complemented, Sylow

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

D₁₇₂

yes

characteristic

138

C₂²×C₈

C₂²×D₄₃

yes

characteristic

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

#125

—

172

—

142

C₂²⋊Q₈

—

143

C₂²⋊Q₈

—

172

—

144

C₄×Q₈

—

145

C₄×Q₈

—

172

—

146

#117

—

172

—

147

C₂×C₄²

D₁₇₂

yes

characteristic

148

C₂×C₁₆

—

149

#108

—

150

#107

—

151

#107

—

152

#103

—

153

#103

—

154

#97

—

172

—

155

C₄×C₈

—

172

—

156

C₄×C₈

C₄×D₄₃

yes

characteristic

157

C₄×C₈

C₄×D₄₃

yes

characteristic

158

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

159

C₄×C₈

C₂²⋊D₄₃

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

172

—

162

C₂²×C₄

#10621873

yes

characteristic

163

C₂²×C₄

#10621873

yes

characteristic

164

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

165

Q₁₆

—

172

—

166

Q₁₆

—

172

—

167

M₁₆

—

168

M₁₆

—

172

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

—

172

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

173

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

174

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

175

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

176

C₄⋊C₄

—

177

C₄⋊C₄

—

172

—

178

C₄⋊C₄

—

172

—

179

C₄⋊C₄

—

172

—

180

C₄⋊C₄

—

172

—

181

C₄⋊C₄

—

172

—

182

C₂²⋊C₄

—

172

—

183

C₄²

—

172

—

184

C₄²

D₃₄₄

yes

characteristic

185

C₄²

D₃₄₄

yes

characteristic

186

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

187

C₄²

(C₂×D₄₃)⋊C₄

yes

characteristic

188

C₁₆

—

189

C₂³

C₂×#10621873

yes

characteristic

190

Q₈

—

344

—

191

Q₈

—

172

—

192

Q₈

—

172

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

172

—

198

C₂×C₄

—

172

—

199

C₂×C₄

#13063247

yes

characteristic

200

C₂×C₄

#13063247

yes

characteristic

201

C₂×C₄

#13063247

yes

characteristic

202

C₂×C₄

#13063247

yes

characteristic

203

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

204

C₂×C₄

C₂×D₃₄₄

yes

characteristic

205

C₈

—

206

C₈

—

207

C₈

—

208

C₈

—

172

—

209

C₈

#13063251

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

C₂×#13063247

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

344

—

218

C₄

—

344

—

219

C₄

#14582707

yes

—

220

C₄

#14582716

yes

—

221

C₄

#14582872

yes

characteristic

222

C₄

C₂×#13063251

yes

characteristic

223

C₂

—

224

C₂

#19133091

yes

characteristic

225

C₂

C₂×#14582707

yes

characteristic

226

C₂

C₂×#14582716

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13063247
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#2162	C₂
socle	C₂²×C₄₃	C₂×#102
prime radical	C₂³×C₄₃	C₂×SD₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#2162	D₄₃
hypocenter	C₄₃	#11748
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₄

#13063247

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₄₃×#2162

C₂

socle

C₂²×C₄₃

C₂×#102

prime radical

C₂³×C₄₃

C₂×SD₁₆

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

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

N	H ≅ G/N	type
133. C₄₃	#11748	semidirect

H ≅ G/N

type

133. C₄₃

#11748

semidirect

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

subgroup	index
#19145181	2
C₄×#13063261	2
#19132614	2
C₄₃×#2162	2
#11748	43

subgroup

index

C₄₃×#2162

Subgroups — #25007031

Conjugacy classes of subgroups

Complements

Maximal subgroups