Group #26135031 — subgroups

Subgroups — #26135031

Order 12032.

556 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 99 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	C₂²×D₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689394	C₂	1	2	yes	maximal, complemented
3	C₂×#15688935	C₂	1	2	yes	maximal, complemented
4	#20245001	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094052	—	2	2	no	—
7	C₂²×D₃₇₆	C₂²	1	2	yes	—
8	C₂×#13094030	C₂²	1	1	yes	characteristic
9	C₂×D₇₅₂	—	2	4	no	—
10	C₂×D₇₅₂	—	2	2	no	—
11	C₂×#13093964	C₂²	1	1	yes	characteristic
12	#15689394	—	2	4	no	—
13	#15689394	—	2	4	no	—
14	C₂×#13093940	—	2	2	no	—
15	#15688935	—	2	4	no	—
16	(C₂×D₄₇)⋊C₁₆	—	2	2	no	—
17	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#108×C₄₇	C₂²	1	2	yes	—
19	C₂×#10625350	D₄	1	1	yes	characteristic
20	C₂²×D₁₈₈	—	2	2	no	—
21	#13094052	—	2	8	no	—
22	#13094052	—	4	4	no	—
23	C₂×#10625325	—	4	2	no	—
24	C₂×D₃₇₆	—	2	2	no	—
25	C₂×D₃₇₆	—	2	2	no	—
26	C₂×D₃₇₆	—	2	2	no	—
27	C₂×D₃₇₆	—	2	2	no	—
28	C₂×D₃₇₆	—	2	2	no	—
29	C₂×D₃₇₆	—	4	2	no	—
30	C₂×D₃₇₆	D₄	1	4	yes	—
31	#13094030	—	2	2	no	—
32	#13094030	—	2	2	no	—
33	C₂×#10625329	D₄	1	1	yes	characteristic
34	C₂×#10625324	—	2	1	no	—
35	C₂×C₈×D₄₇	—	2	1	no	—
36	D₇₅₂	—	2	8	no	—
37	#13093964	—	2	2	no	—
38	C₂×C₄₇⋊C₁₆	—	2	1	no	—
39	#13093940	—	2	8	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×C₁₆×C₄₇	—	2	2	no	—
43	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
44	#108×C₄₇	—	2	2	no	—
45	#108×C₄₇	D₄	1	4	yes	—
46	C₂³×D₄₇	—	4	2	no	—
47	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₂²⋊D₄₇	—	2	1	no	—
49	#10625350	—	2	2	no	—
50	#10625350	—	2	2	no	—
51	C₂×D₁₈₈	—	2	4	no	—
52	C₂×D₁₈₈	—	4	2	no	—
53	C₂×D₁₈₈	—	4	2	no	—
54	C₂×D₁₈₈	—	4	2	no	—
55	C₂×D₁₈₈	—	4	2	no	—
56	C₂×D₁₈₈	—	4	2	no	—
57	C₂×D₁₈₈	D₈	1	1	yes	characteristic
58	C₂×C₄×D₄₇	—	2	1	no	—
59	C₂×Dic₉₄	D₈	1	1	yes	characteristic
60	M₁₆×C₄₇	—	2	4	no	—
61	M₁₆×C₄₇	—	4	2	no	—
62	C₂×C₈×C₄₇	—	4	2	no	—
63	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
66	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
67	#10625329	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	2	1	no	—
69	D₃₇₆	—	2	4	no	—
70	D₃₇₆	—	2	4	no	—
71	D₃₇₆	—	4	8	no	—
72	D₃₇₆	—	4	2	no	—
73	D₃₇₆	—	4	2	no	—
74	#10625325	—	4	8	no	—
75	#10625324	—	4	2	no	—
76	C₈×D₄₇	—	4	1	no	—
77	C₈×D₄₇	—	4	1	no	—
78	C₁₆×C₄₇	—	2	2	no	—
79	C₄₇⋊C₁₆	—	4	1	no	—
80	C₂³×C₄₇	#135	1	1	yes	characteristic
81	C₂²×D₄₇	—	2	1	no	—
82	C₂²×D₄₇	—	4	4	no	—
83	C₂²×D₄₇	—	8	2	no	—
84	C₂²×D₄₇	—	8	2	no	—
85	C₂²×D₄₇	—	16	4	no	—
86	C₂×C₄×C₄₇	#120	1	2	yes	—
87	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
90	C₂²⋊D₄₇	—	4	2	no	—
91	C₂×Dic₄₇	—	2	1	no	—
92	D₁₈₈	—	2	2	no	—
93	D₁₈₈	—	4	4	no	—
94	D₁₈₈	—	4	4	no	—
95	D₁₈₈	—	8	2	no	—
96	D₁₈₈	—	8	2	no	—
97	C₄×D₄₇	—	4	1	no	—
98	C₄×D₄₇	—	4	1	no	—
99	Dic₉₄	—	2	2	no	—
100	C₈×C₄₇	—	4	4	no	—
101	C₈×C₄₇	#120	1	1	yes	characteristic
102	C₈×C₄₇	#121	1	2	yes	—
103	C₈×C₄₇	#127	1	1	yes	characteristic
104	C₄₇⋊C₈	—	4	1	no	—
105	#13313	—	47	1	no	maximal, Sylow
106	C₂²×C₄₇	—	2	2	no	—
107	C₂²×C₄₇	#449	1	2	yes	—
108	C₂²×C₄₇	#466	1	1	yes	characteristic
109	C₂×D₄₇	—	4	2	no	—
110	C₂×D₄₇	—	4	1	no	—
111	C₂×D₄₇	—	8	4	no	—
112	C₂×D₄₇	—	16	4	no	—
113	C₂×D₄₇	—	16	4	no	—
114	C₂×D₄₇	—	16	4	no	—
115	C₄×C₄₇	#392	1	1	yes	characteristic
116	C₄×C₄₇	#447	1	2	yes	—
117	C₄×C₄₇	#469	1	1	yes	characteristic
118	Dic₄₇	—	4	1	no	—
119	C₂²×D₁₆	—	47	1	no	—
120	C₂×#472	—	47	2	no	—
121	C₂×#361	—	47	2	no	—
122	#2113	—	47	1	no	—
123	#1381	D₄₇	1	1	yes	characteristic, complemented
124	C₂×C₄₇	—	2	2	no	—
125	C₂×C₄₇	#1999	1	1	yes	characteristic
126	C₂×C₄₇	#2221	1	2	yes	—
127	D₄₇	—	8	1	no	—
128	D₄₇	—	16	4	no	—
129	C₂×AGL(1,ℤ/8)	—	94	2	no	—
130	C₂²×D₈	—	47	2	no	—
131	C₂×#131	—	47	1	no	—
132	C₂×D₁₆	—	94	4	no	—
133	C₂×D₁₆	—	94	2	no	—
134	C₂×M₃₂	—	47	1	no	—
135	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
136	#472	—	94	4	no	—
137	#472	—	94	4	no	—
138	C₂×#108	C₂×D₄₇	1	2	yes	—
139	C₂×#100	—	94	2	no	—
140	#361	—	94	4	no	—
141	C₂²⋊C₁₆	—	94	2	no	—
142	C₄₇	#13313	1	1	yes	characteristic, complemented, Sylow
143	C₂×#41	—	47	1	no	—
144	C₂²×D₄	—	94	2	no	—
145	AGL(1,ℤ/8)	—	94	8	no	—
146	AGL(1,ℤ/8)	—	188	4	no	—
147	C₂×SD₁₆	—	188	2	no	—
148	C₂×D₈	—	47	4	no	—
149	C₂×D₈	—	94	2	no	—
150	C₂×D₈	—	94	2	no	—
151	C₂×D₈	—	94	2	no	—
152	C₂×D₈	—	94	2	no	—
153	C₂×D₈	—	94	2	no	—
154	C₂×D₈	—	188	2	no	—
155	#131	—	94	2	no	—
156	#131	—	94	2	no	—
157	C₂×M₁₆	—	2	2	no	—
158	C₂×M₁₆	—	47	1	no	—
159	C₂×M₁₆	—	94	1	no	—
160	C₂²×C₈	—	94	1	no	—
161	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
162	D₁₆	—	94	8	no	—
163	M₃₂	—	94	2	no	—
164	C₂×C₁₆	—	2	2	no	—
165	C₂×C₁₆	—	94	1	no	—
166	C₂×C₁₆	D₁₈₈	1	2	yes	—
167	#108	—	2	2	no	—
168	#108	D₁₈₈	1	4	yes	—
169	#100	—	94	8	no	—
170	C₂⁴	—	188	2	no	—
171	#41	—	94	2	no	—
172	#41	—	94	2	no	—
173	C₂×Q₈	—	47	1	no	—
174	C₂×D₄	—	47	1	no	—
175	C₂×D₄	—	94	1	no	—
176	C₂×D₄	—	94	4	no	—
177	C₂×D₄	—	188	2	no	—
178	C₂×D₄	—	188	2	no	—
179	C₂×D₄	—	188	2	no	—
180	C₂×D₄	—	188	2	no	—
181	C₂×D₄	—	188	2	no	—
182	C₂²×C₄	—	94	1	no	—
183	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
184	SD₁₆	—	188	8	no	—
185	D₈	—	94	4	no	—
186	D₈	—	94	4	no	—
187	D₈	—	188	8	no	—
188	D₈	—	188	2	no	—
189	D₈	—	188	2	no	—
190	M₁₆	—	2	4	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	94	2	no	—
193	M₁₆	—	188	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	94	1	no	—
196	C₂×C₈	—	188	1	no	—
197	C₂×C₈	—	188	1	no	—
198	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
199	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
200	C₂×C₈	D₄×D₄₇	1	2	yes	—
201	C₂×C₈	#10625354	1	1	yes	characteristic
202	C₁₆	—	2	2	no	—
203	C₁₆	—	188	1	no	—
204	C₂³	—	94	1	no	—
205	C₂³	—	376	2	no	—
206	C₂³	—	376	2	no	—
207	C₂³	—	188	4	no	—
208	C₂³	—	752	4	no	—
209	C₂³	#13094047	1	1	yes	characteristic
210	Q₈	—	94	2	no	—
211	D₄	—	94	2	no	—
212	D₄	—	376	2	no	—
213	D₄	—	376	2	no	—
214	D₄	—	188	2	no	—
215	D₄	—	188	4	no	—
216	D₄	—	188	4	no	—
217	C₂×C₄	—	94	1	no	—
218	C₂×C₄	—	188	1	no	—
219	C₂×C₄	—	188	1	no	—
220	C₂×C₄	#13093994	1	2	yes	—
221	C₂×C₄	#13093999	1	1	yes	characteristic
222	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
223	C₂×C₄	#13094051	1	2	yes	—
224	C₈	—	4	4	no	—
225	C₈	—	188	1	no	—
226	C₈	#13093994	1	1	yes	characteristic
227	C₈	#13093999	1	2	yes	—
228	C₈	#13094021	1	1	yes	characteristic
229	C₂²	—	2	2	no	—
230	C₂²	—	376	4	no	—
231	C₂²	—	188	2	no	—
232	C₂²	—	188	1	no	—
233	C₂²	—	752	4	no	—
234	C₂²	—	752	4	no	—
235	C₂²	—	752	4	no	—
236	C₂²	#15689271	1	2	yes	—
237	C₂²	#15689360	1	1	yes	characteristic
238	C₄	—	188	1	no	—
239	C₄	#15689033	1	1	yes	characteristic
240	C₄	#15689258	1	2	yes	—
241	C₄	#15689377	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	376	1	no	—
244	C₂	—	752	4	no	—
245	C₂	#20244387	1	1	yes	characteristic
246	C₂	#20245509	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₇₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#15689394

C₂

yes

maximal, complemented

C₂×#15688935

C₂

yes

maximal, complemented

#20245001

C₂

yes

maximal, characteristic, complemented

C₄₇×#1381

C₂

yes

maximal, characteristic, complemented

C₂×#13094052

—

C₂²×D₃₇₆

C₂²

yes

—

C₂×#13094030

C₂²

yes

characteristic

C₂×D₇₅₂

—

C₂×D₇₅₂

—

C₂×#13093964

C₂²

yes

—

—

—

—

(C₂×D₄₇)⋊C₁₆

—

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×#108×C₄₇

C₂²

yes

—

C₂×#10625350

D₄

yes

characteristic

C₂²×D₁₈₈

—

#13094052

—

#13094052

—

C₂×#10625325

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

D₄

yes

—

#13094030

—

#13094030

—

C₂×#10625329

D₄

yes

characteristic

C₂×#10625324

—

C₂×C₈×D₄₇

—

D₇₅₂

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093940

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

—

#108×C₄₇

—

#108×C₄₇

D₄

yes

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

D₈

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

#10625325

—

#10625324

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

#135

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

#121

yes

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

100

C₈×C₄₇

—

101

C₈×C₄₇

#120

yes

characteristic

102

C₈×C₄₇

#121

yes

—

103

C₈×C₄₇

#127

yes

characteristic

104

C₄₇⋊C₈

—

105

#13313

—

maximal, Sylow

106

C₂²×C₄₇

—

107

C₂²×C₄₇

#449

yes

—

108

C₂²×C₄₇

#466

yes

characteristic

109

C₂×D₄₇

—

110

C₂×D₄₇

—

111

C₂×D₄₇

—

112

C₂×D₄₇

—

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₄×C₄₇

#392

yes

characteristic

116

C₄×C₄₇

#447

yes

—

117

C₄×C₄₇

#469

yes

characteristic

118

Dic₄₇

—

119

C₂²×D₁₆

—

120

C₂×#472

—

121

C₂×#361

—

122

#2113

—

123

#1381

D₄₇

yes

characteristic, complemented

124

C₂×C₄₇

—

125

C₂×C₄₇

#1999

yes

characteristic

126

C₂×C₄₇

#2221

yes

—

127

D₄₇

—

128

D₄₇

—

129

C₂×AGL(1,ℤ/8)

—

130

C₂²×D₈

—

131

C₂×#131

—

132

C₂×D₁₆

—

133

C₂×D₁₆

—

134

C₂×M₃₂

—

135

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

136

#472

—

137

#472

—

138

C₂×#108

C₂×D₄₇

yes

—

139

C₂×#100

—

140

#361

—

141

C₂²⋊C₁₆

—

142

C₄₇

#13313

yes

characteristic, complemented, Sylow

143

C₂×#41

—

144

C₂²×D₄

—

145

AGL(1,ℤ/8)

—

146

AGL(1,ℤ/8)

—

188

—

147

C₂×SD₁₆

—

188

—

148

C₂×D₈

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

188

—

155

#131

—

156

#131

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂²×C₈

—

161

C₂²×C₈

C₂²×D₄₇

yes

characteristic

162

D₁₆

—

163

M₃₂

—

164

C₂×C₁₆

—

165

C₂×C₁₆

—

166

C₂×C₁₆

D₁₈₈

yes

—

167

#108

—

168

#108

D₁₈₈

yes

—

169

#100

—

170

C₂⁴

—

188

—

171

#41

—

172

#41

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

188

—

178

C₂×D₄

—

188

—

179

C₂×D₄

—

188

—

180

C₂×D₄

—

188

—

181

C₂×D₄

—

188

—

182

C₂²×C₄

—

183

C₂²×C₄

D₄×D₄₇

yes

characteristic

184

SD₁₆

—

188

—

185

D₈

—

186

D₈

—

187

D₈

—

188

—

188

D₈

—

188

—

189

D₈

—

188

—

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

193

M₁₆

—

188

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

188

—

197

C₂×C₈

—

188

—

198

C₂×C₈

C₂×D₁₈₈

yes

characteristic

199

C₂×C₈

C₂×D₁₈₈

yes

—

200

C₂×C₈

D₄×D₄₇

yes

—

201

C₂×C₈

#10625354

yes

characteristic

202

C₁₆

—

203

C₁₆

—

188

—

204

C₂³

—

205

C₂³

—

376

—

206

C₂³

—

376

—

207

C₂³

—

188

—

208

C₂³

—

752

—

209

C₂³

#13094047

yes

characteristic

210

Q₈

—

211

D₄

—

212

D₄

—

376

—

213

D₄

—

376

—

214

D₄

—

188

—

215

D₄

—

188

—

216

D₄

—

188

—

217

C₂×C₄

—

218

C₂×C₄

—

188

—

219

C₂×C₄

—

188

—

220

C₂×C₄

#13093994

yes

—

221

C₂×C₄

#13093999

yes

characteristic

222

C₂×C₄

D₈×D₄₇

yes

characteristic

223

C₂×C₄

#13094051

yes

—

224

C₈

—

225

C₈

—

188

—

226

C₈

#13093994

yes

characteristic

227

C₈

#13093999

yes

—

228

C₈

#13094021

yes

characteristic

229

C₂²

—

230

C₂²

—

376

—

231

C₂²

—

188

—

232

C₂²

—

188

—

233

C₂²

—

752

—

234

C₂²

—

752

—

235

C₂²

—

752

—

236

C₂²

#15689271

yes

—

237

C₂²

#15689360

yes

characteristic

238

C₄

—

188

—

239

C₄

#15689033

yes

characteristic

240

C₄

#15689258

yes

—

241

C₄

#15689377

yes

characteristic

242

C₂

—

243

C₂

—

376

—

244

C₂

—

752

—

245

C₂

#20244387

yes

characteristic

246

C₂

#20245509

yes

—

	subgroup	G/H
center	C₂²	#15689360
commutator, cosocle	C₂²×C₈×C₄₇	C₂³
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1381	C₂
socle	C₂²×C₄₇	#466
hypercenter	#1381	D₄₇
hypocenter	C₄₇	#13313
LCS	G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

subgroup

G/H

center

C₂²

#15689360

commutator, cosocle

C₂²×C₈×C₄₇

C₂³

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1381

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1381

N	H ≅ G/N	type
1. C₂²×D₇₅₂	C₂	semidirect
2. C₂×#15689394	C₂	semidirect
3. C₂×#15688935	C₂	semidirect
4. #20245001	C₂	semidirect
5. C₄₇×#1381	C₂	semidirect
123. #1381	D₄₇	semidirect
142. C₄₇	#13313	semidirect

H ≅ G/N

type

1. C₂²×D₇₅₂

C₂

semidirect

2. C₂×#15689394

C₂

semidirect

3. C₂×#15688935

C₂

semidirect

4. #20245001

C₂

semidirect

5. C₄₇×#1381

C₂

semidirect

123. #1381

D₄₇

semidirect

142. C₄₇

#13313

semidirect

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

subgroup	index
C₂²×D₇₅₂	2
C₂×#15689394	2
C₂×#15688935	2
#20245001	2
C₄₇×#1381	2
#13313	47

subgroup

index

C₂²×D₇₅₂

C₄₇×#1381

Subgroups — #26135031

Conjugacy classes of subgroups

Complements

Maximal subgroups