Group #24999731 — subgroups

Subgroups — #24999731

Order 11008.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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	#19137888	C₂	1	1	yes	maximal, characteristic
2	#19135576	C₂	1	1	yes	maximal, characteristic
3	#19133095	C₂	1	2	yes	maximal
4	#19132497	C₂	1	2	yes	maximal
5	C₄₃×#1274	C₂	1	1	yes	maximal, characteristic
6	#14583456	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₈₆	—	2	1	no	—
8	#14582923	C₂²	1	1	yes	characteristic
9	#14582831	—	2	2	no	—
10	#14582820	—	2	2	no	—
11	C₄×C₄⋊Dic₄₃	—	2	1	no	—
12	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	#14582659	—	2	1	no	—
14	#14582659	—	2	1	no	—
15	#14582637	—	2	2	no	—
16	#14582637	—	2	2	no	—
17	C₄₃×#431	C₂²	1	2	yes	—
18	C₄₃×#376	C₂²	1	1	yes	characteristic
19	C₂²×Dic₈₆	—	2	1	no	—
20	C₂×#10621877	—	2	1	no	—
21	#13063325	Q₈	1	2	yes	complemented
22	#13063317	—	2	1	no	—
23	#13063304	—	2	2	no	—
24	C₄×Dic₈₆	—	2	2	no	—
25	C₄×Dic₈₆	—	4	2	no	—
26	C₄×Dic₈₆	—	4	2	no	—
27	#13063284	—	2	1	no	—
28	C₂×C₄⋊Dic₄₃	—	2	2	no	—
29	C₂×C₄⋊Dic₄₃	—	2	1	no	—
30	C₂×C₄⋊Dic₄₃	—	2	2	no	—
31	C₂×Dic₄₃⋊C₄	—	2	2	no	—
32	C₂×C₄×Dic₄₃	—	2	2	no	—
33	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
34	C₄₃⋊#95	—	2	1	no	—
35	C₄₃⋊#95	—	2	1	no	—
36	C₄₃⋊#95	D₄	1	2	yes	—
37	C₄₃⋊#95	D₄	1	2	yes	—
38	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
41	C₄⋊C₈×C₄₃	—	2	2	no	—
42	C₂²⋊C₈×C₄₃	—	2	2	no	—
43	C₄×C₈×C₄₃	—	2	2	no	—
44	#95×C₄₃	—	2	2	no	—
45	C₂²×C₄×C₄₃	—	2	1	no	—
46	C₂²×C₄×C₄₃	—	2	1	no	—
47	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
49	C₂²×Dic₄₃	—	2	2	no	—
50	C₂²×Dic₄₃	—	2	2	no	—
51	C₂×Dic₈₆	—	2	2	no	—
52	C₂×Dic₈₆	—	4	4	no	—
53	C₂×Dic₈₆	—	4	2	no	—
54	C₂×C₈×C₄₃	—	4	2	no	—
55	C₄²×C₄₃	—	2	1	no	—
56	C₄²×C₄₃	—	2	1	no	—
57	C₄²×C₄₃	SD₁₆	1	2	yes	—
58	C₄²×C₄₃	Q₁₆	1	2	yes	—
59	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₄₃	#41	1	2	yes	—
61	C₄²×C₄₃	#41	1	1	yes	characteristic
62	C₂²⋊Dic₄₃	—	4	1	no	—
63	C₄⋊Dic₄₃	—	2	2	no	—
64	C₄⋊Dic₄₃	—	2	2	no	—
65	C₄⋊Dic₄₃	—	4	4	no	—
66	C₄⋊Dic₄₃	—	4	4	no	—
67	C₄⋊Dic₄₃	—	4	2	no	—
68	Dic₄₃⋊C₄	—	4	4	no	—
69	Dic₄₃⋊C₄	—	4	2	no	—
70	C₄×Dic₄₃	—	4	1	no	—
71	C₄×Dic₄₃	—	4	2	no	—
72	C₄×Dic₄₃	—	4	2	no	—
73	#10621877	—	4	1	no	—
74	#10621877	—	4	1	no	—
75	C₂×C₄₃⋊C₈	—	4	1	no	—
76	C₂³×C₄₃	#120	1	1	yes	characteristic
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	4	2	no	—
80	C₂×C₄×C₄₃	—	4	2	no	—
81	C₂×C₄×C₄₃	—	4	2	no	—
82	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#124	1	2	yes	—
85	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
90	C₂×Dic₄₃	—	2	4	no	—
91	C₂×Dic₄₃	—	4	2	no	—
92	C₂×Dic₄₃	—	4	2	no	—
93	C₂×Dic₄₃	—	4	2	no	—
94	C₂×Dic₄₃	—	4	2	no	—
95	C₂×Dic₄₃	—	4	2	no	—
96	C₂×Dic₄₃	—	4	2	no	—
97	Dic₈₆	—	4	8	no	—
98	Dic₈₆	—	8	2	no	—
99	C₈×C₄₃	—	8	2	no	—
100	C₄₃⋊C₈	—	8	1	no	—
101	#10371	—	43	1	no	maximal, Sylow
102	C₂²×C₄₃	—	2	2	no	—
103	C₂²×C₄₃	#393	1	1	yes	characteristic
104	C₂²×C₄₃	#450	1	1	yes	characteristic
105	C₂²×C₄₃	#451	1	1	yes	characteristic
106	C₄×C₄₃	—	2	2	no	—
107	C₄×C₄₃	—	2	2	no	—
108	C₄×C₄₃	—	4	2	no	—
109	C₄×C₄₃	—	4	2	no	—
110	C₄×C₄₃	#475	1	1	yes	characteristic
111	C₄×C₄₃	#477	1	1	yes	characteristic
112	C₄×C₄₃	#487	1	1	yes	characteristic
113	C₄×C₄₃	#489	1	1	yes	characteristic
114	Dic₄₃	—	4	4	no	—
115	Dic₄₃	—	8	2	no	—
116	Dic₄₃	—	8	2	no	—
117	#2399	—	43	1	no	—
118	#1995	—	43	1	no	—
119	#1503	—	43	2	no	—
120	#1303	—	43	2	no	—
121	#1274	D₄₃	1	1	yes	characteristic
122	C₂×C₄₃	—	2	1	no	—
123	C₂×C₄₃	—	2	1	no	—
124	C₂×C₄₃	#2024	1	1	yes	characteristic
125	C₂×C₄₃	#2031	1	2	yes	—
126	#533	—	43	1	no	—
127	C₂×C₄×Q₈	—	86	1	no	—
128	#431	C₂×D₄₃	1	2	yes	—
129	#423	—	43	1	no	—
130	#398	—	86	2	no	—
131	#395	—	86	2	no	—
132	C₄×C₄⋊C₄	—	43	2	no	—
133	C₄×C₄⋊C₄	—	86	1	no	—
134	#376	C₂×D₄₃	1	1	yes	characteristic
135	#339	—	86	1	no	—
136	#339	—	86	1	no	—
137	#328	—	86	2	no	—
138	#328	—	86	2	no	—
139	C₄₃	#10371	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	86	1	no	—
141	C₂×M₁₆	—	86	1	no	—
142	C₄⋊Q₈	—	43	2	no	—
143	#125	—	86	1	no	—
144	C₂²⋊Q₈	—	86	2	no	—
145	C₄×Q₈	—	86	2	no	—
146	C₄×Q₈	—	172	2	no	—
147	C₄×Q₈	—	172	2	no	—
148	#117	—	86	1	no	—
149	C₂×C₄⋊C₄	—	86	2	no	—
150	C₂×C₄⋊C₄	—	86	1	no	—
151	C₂×C₄⋊C₄	—	86	2	no	—
152	C₂×C₄⋊C₄	—	86	2	no	—
153	C₂×C₄²	—	86	2	no	—
154	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
155	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	86	2	no	—
159	C₂²⋊C₈	—	2	2	no	—
160	C₄×C₈	—	2	2	no	—
161	#95	—	2	2	no	—
162	#95	—	43	2	no	—
163	#95	—	43	2	no	—
164	#95	—	86	1	no	—
165	#95	—	86	1	no	—
166	C₂×Q₈	—	86	2	no	—
167	C₂×Q₈	—	172	2	no	—
168	C₂×Q₈	—	172	4	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	86	2	no	—
172	C₂²×C₄	—	86	2	no	—
173	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
174	C₂²×C₄	D₄×D₄₃	1	2	yes	—
175	M₁₆	—	172	1	no	—
176	M₁₆	—	172	1	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	172	1	no	—
179	C₄⋊C₄	—	86	2	no	—
180	C₄⋊C₄	—	86	2	no	—
181	C₄⋊C₄	—	172	4	no	—
182	C₄⋊C₄	—	172	2	no	—
183	C₄⋊C₄	—	172	4	no	—
184	C₄⋊C₄	—	172	4	no	—
185	C₄⋊C₄	—	172	2	no	—
186	C₂²⋊C₄	—	172	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	172	1	no	—
190	C₄²	—	172	2	no	—
191	C₄²	—	172	2	no	—
192	C₄²	#10621873	1	2	yes	—
193	C₄²	Dic₁₇₂	1	2	yes	—
194	C₄²	#10621898	1	2	yes	—
195	C₄²	#10621900	1	1	yes	characteristic
196	C₄²	Q₈×D₄₃	1	1	yes	characteristic
197	C₂³	#13063295	1	1	yes	characteristic
198	Q₈	—	344	2	no	—
199	Q₈	—	172	8	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	86	4	no	—
206	C₂×C₄	—	172	2	no	—
207	C₂×C₄	—	172	2	no	—
208	C₂×C₄	—	172	2	no	—
209	C₂×C₄	—	172	2	no	—
210	C₂×C₄	—	172	2	no	—
211	C₂×C₄	—	172	2	no	—
212	C₂×C₄	#13063303	1	2	yes	—
213	C₂×C₄	#13063305	1	1	yes	characteristic
214	C₂×C₄	#13063311	1	2	yes	—
215	C₂×C₄	#13063313	1	1	yes	characteristic
216	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
217	C₂×C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
218	C₂×C₄	#13063353	1	1	yes	characteristic
219	C₂×C₄	#13063358	1	1	yes	characteristic
220	C₈	—	8	2	no	—
221	C₈	—	344	1	no	—
222	C₂²	—	2	2	no	—
223	C₂²	#14582812	1	1	yes	characteristic
224	C₂²	#14583052	1	1	yes	characteristic
225	C₂²	#14583057	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	344	2	no	—
231	C₄	—	344	2	no	—
232	C₄	—	172	4	no	—
233	C₄	#14583185	1	1	yes	characteristic
234	C₄	#14583195	1	1	yes	characteristic
235	C₄	#14583250	1	1	yes	characteristic
236	C₄	#14583259	1	1	yes	characteristic
237	C₂	—	2	1	no	—
238	C₂	—	2	1	no	—
239	C₂	#19135737	1	1	yes	characteristic
240	C₂	#19135766	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19137888

C₂

yes

maximal, characteristic

#19135576

C₂

yes

maximal, characteristic

#19133095

C₂

yes

maximal

#19132497

C₂

yes

maximal

C₄₃×#1274

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

characteristic

C₂×C₄×Dic₈₆

—

#14582923

C₂²

yes

characteristic

#14582831

—

#14582820

—

C₄×C₄⋊Dic₄₃

—

C₄×C₄⋊Dic₄₃

C₂²

yes

—

—

—

—

—

C₄₃×#431

C₂²

yes

—

C₄₃×#376

C₂²

yes

characteristic

C₂²×Dic₈₆

—

C₂×#10621877

—

#13063325

Q₈

yes

complemented

#13063317

—

#13063304

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

D₄

yes

—

C₄₃⋊#95

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

Q₁₆

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

100

C₄₃⋊C₈

—

101

#10371

—

maximal, Sylow

102

C₂²×C₄₃

—

103

C₂²×C₄₃

#393

yes

characteristic

104

C₂²×C₄₃

#450

yes

characteristic

105

C₂²×C₄₃

#451

yes

characteristic

106

C₄×C₄₃

—

107

C₄×C₄₃

—

108

C₄×C₄₃

—

109

C₄×C₄₃

—

110

C₄×C₄₃

#475

yes

characteristic

111

C₄×C₄₃

#477

yes

characteristic

112

C₄×C₄₃

#487

yes

characteristic

113

C₄×C₄₃

#489

yes

characteristic

114

Dic₄₃

—

115

Dic₄₃

—

116

Dic₄₃

—

117

#2399

—

118

#1995

—

119

#1503

—

120

#1303

—

121

#1274

D₄₃

yes

characteristic

122

C₂×C₄₃

—

123

C₂×C₄₃

—

124

C₂×C₄₃

#2024

yes

characteristic

125

C₂×C₄₃

#2031

yes

—

126

#533

—

127

C₂×C₄×Q₈

—

128

#431

C₂×D₄₃

yes

—

129

#423

—

130

#398

—

131

#395

—

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

—

134

#376

C₂×D₄₃

yes

characteristic

135

#339

—

136

#339

—

137

#328

—

138

#328

—

139

C₄₃

#10371

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

—

143

#125

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

172

—

147

C₄×Q₈

—

172

—

148

#117

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

D₁₇₂

yes

characteristic

155

C₂×C₄²

D₁₇₂

yes

characteristic

156

C₂×C₄²

C₂²×D₄₃

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₂²⋊C₈

—

160

C₄×C₈

—

161

#95

—

162

#95

—

163

#95

—

164

#95

—

165

#95

—

166

C₂×Q₈

—

167

C₂×Q₈

—

172

—

168

C₂×Q₈

—

172

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

174

C₂²×C₄

D₄×D₄₃

yes

—

175

M₁₆

—

172

—

176

M₁₆

—

172

—

177

C₂×C₈

—

178

C₂×C₈

—

172

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

172

—

182

C₄⋊C₄

—

172

—

183

C₄⋊C₄

—

172

—

184

C₄⋊C₄

—

172

—

185

C₄⋊C₄

—

172

—

186

C₂²⋊C₄

—

172

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

172

—

190

C₄²

—

172

—

191

C₄²

—

172

—

192

C₄²

#10621873

yes

—

193

C₄²

Dic₁₇₂

yes

—

194

C₄²

#10621898

yes

—

195

C₄²

#10621900

yes

characteristic

196

C₄²

Q₈×D₄₃

yes

characteristic

197

C₂³

#13063295

yes

characteristic

198

Q₈

—

344

—

199

Q₈

—

172

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

172

—

207

C₂×C₄

—

172

—

208

C₂×C₄

—

172

—

209

C₂×C₄

—

172

—

210

C₂×C₄

—

172

—

211

C₂×C₄

—

172

—

212

C₂×C₄

#13063303

yes

—

213

C₂×C₄

#13063305

yes

characteristic

214

C₂×C₄

#13063311

yes

—

215

C₂×C₄

#13063313

yes

characteristic

216

C₂×C₄

C₂×#10621873

yes

characteristic

217

C₂×C₄

C₂×Dic₁₇₂

yes

characteristic

218

C₂×C₄

#13063353

yes

characteristic

219

C₂×C₄

#13063358

yes

characteristic

220

C₈

—

221

C₈

—

344

—

222

C₂²

—

223

C₂²

#14582812

yes

characteristic

224

C₂²

#14583052

yes

characteristic

225

C₂²

#14583057

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

344

—

231

C₄

—

344

—

232

C₄

—

172

—

233

C₄

#14583185

yes

characteristic

234

C₄

#14583195

yes

characteristic

235

C₄

#14583250

yes

characteristic

236

C₄

#14583259

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#19135737

yes

characteristic

240

C₂

#19135766

yes

—

	subgroup	G/H
center	C₂×C₄	#13063313
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1274	C₂
socle	C₂²×C₄₃	#393
prime radical	C₂³×C₄₃	#120
hypercenter	#1274	D₄₃
hypocenter	C₄₃	#10371
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

subgroup

G/H

center

C₂×C₄

#13063313

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1274

C₂

C₂²×C₄₃

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1274

N	H ≅ G/N	type
21. #13063325	Q₈	semidirect
139. C₄₃	#10371	semidirect

H ≅ G/N

type

21. #13063325

Q₈

semidirect

139. C₄₃

#10371

semidirect

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

subgroup	index
#19137888	2
#19135576	2
#19133095	2
#19132497	2
C₄₃×#1274	2
#10371	43

subgroup

index

C₄₃×#1274

Subgroups — #24999731

Conjugacy classes of subgroups

Complements

Maximal subgroups