Group #27300259 — subgroups

Subgroups — #27300259

Order 13568.

438 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 139 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×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810448	C₂	1	2	yes	maximal, complemented
3	#20274741	C₂	1	2	yes	maximal
4	#20272807	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1380	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
7	C₂²×#11719908	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×D₅₃	—	2	4	no	—
9	C₂×C₁₆×D₅₃	C₄	1	4	yes	complemented
10	C₂×#13133151	C₂²	1	2	yes	—
11	#16810480	—	2	2	no	—
12	#16810448	—	2	4	no	—
13	#16810385	—	2	2	no	—
14	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×#107×C₅₃	C₂²	1	2	yes	—
16	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
17	C₂²×#88322	D₄	1	1	yes	characteristic
18	C₂×C₈×D₅₃	—	2	2	no	—
19	C₂×C₈×D₅₃	—	2	2	no	—
20	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₅₃	Q₈	1	2	yes	—
22	C₂×C₄⋊Dic₅₃	—	2	2	no	—
23	C₂×#11719921	—	4	2	no	—
24	C₂×#11719908	C₂×C₄	1	2	yes	—
25	C₂×#11719908	D₄	1	4	yes	—
26	C₁₆×D₅₃	—	2	8	no	—
27	#13133151	—	2	2	no	—
28	#13133151	—	2	2	no	—
29	#13133124	—	4	2	no	—
30	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
32	C₂×C₁₆×C₅₃	—	2	2	no	—
33	C₂×C₁₆×C₅₃	C₂×C₄	1	2	yes	—
34	#107×C₅₃	—	2	2	no	—
35	#107×C₅₃	—	2	2	no	—
36	C₂³×D₅₃	D₈	1	1	yes	characteristic
37	C₂²×C₄×C₅₃	—	4	2	no	—
38	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
39	C₂²×Dic₅₃	—	4	2	no	—
40	C₂²×Dic₅₃	D₈	1	1	yes	characteristic
41	C₂×C₄×D₅₃	—	2	2	no	—
42	C₂×C₄×D₅₃	—	2	2	no	—
43	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×D₅₃	Q₁₆	1	2	yes	—
45	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₅₃	#41	1	2	yes	—
49	C₄⋊C₄×C₅₃	—	4	2	no	—
50	C₄⋊C₄×C₅₃	—	4	2	no	—
51	#11719921	—	8	4	no	—
52	C₄⋊Dic₅₃	—	4	2	no	—
53	C₄⋊Dic₅₃	—	4	2	no	—
54	C₂×#88322	—	2	2	no	—
55	C₂×#88322	C₄⋊C₄	1	2	yes	—
56	C₈×D₅₃	—	2	2	no	—
57	C₈×D₅₃	—	2	2	no	—
58	C₈×D₅₃	—	2	4	no	—
59	C₁₆×C₅₃	—	2	2	no	—
60	#11719908	C₂²⋊C₄	1	4	yes	complemented
61	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
62	C₂²×D₅₃	—	2	2	no	—
63	C₂²×D₅₃	—	2	2	no	—
64	C₂²×D₅₃	#107	1	2	yes	—
65	C₂²×D₅₃	D₁₆	1	2	yes	—
66	C₂²×D₅₃	Q₃₂	1	2	yes	—
67	C₂×C₄×C₅₃	—	8	2	no	—
68	C₂×C₄×C₅₃	—	8	2	no	—
69	C₂×C₄×C₅₃	—	8	2	no	—
70	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₅₃	#121	1	2	yes	—
72	C₂×C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₅₃	#135	1	2	yes	—
74	C₂×Dic₅₃	—	2	2	no	—
75	C₂×Dic₅₃	—	8	2	no	—
76	C₂×Dic₅₃	—	8	2	no	—
77	C₂×Dic₅₃	—	8	2	no	—
78	C₂×Dic₅₃	#107	1	2	yes	—
79	C₄×D₅₃	—	2	2	no	—
80	C₄×D₅₃	—	2	2	no	—
81	C₄×D₅₃	—	2	4	no	—
82	C₈×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₈×C₅₃	#117	1	1	yes	characteristic
84	C₈×C₅₃	C₂²⋊Q₈	1	2	yes	—
85	#88322	—	2	2	no	—
86	#12834	—	53	1	no	maximal, Sylow
87	C₂²×C₅₃	C₂×#107	1	1	yes	characteristic
88	C₂²×C₅₃	#466	1	2	yes	—
89	C₂²×C₅₃	C₂×D₁₆	1	1	yes	characteristic
90	C₂²×C₅₃	C₂×Q₃₂	1	1	yes	characteristic
91	C₂²×C₅₃	#508	1	2	yes	—
92	C₂×D₅₃	—	2	2	no	—
93	C₂×D₅₃	—	2	2	no	—
94	C₂×D₅₃	—	2	4	no	—
95	C₂×D₅₃	—	2	4	no	—
96	C₂×D₅₃	#366	1	4	yes	complemented
97	C₄×C₅₃	—	16	2	no	—
98	C₄×C₅₃	#380	1	1	yes	characteristic
99	C₄×C₅₃	#427	1	1	yes	characteristic
100	C₄×C₅₃	#467	1	2	yes	—
101	Dic₅₃	—	2	2	no	—
102	Dic₅₃	—	16	2	no	—
103	C₂³×C₁₆	—	53	1	no	—
104	C₂×#366	—	53	2	no	—
105	#1808	—	53	2	no	—
106	#1380	—	53	1	no	—
107	#1380	D₅₃	1	1	yes	characteristic, complemented
108	C₂×C₅₃	#1808	1	1	yes	characteristic
109	C₂×C₅₃	C₂×#366	1	1	yes	characteristic
110	C₂×C₅₃	#2158	1	1	yes	characteristic
111	C₂×C₅₃	#2215	1	2	yes	—
112	C₂×C₅₃	#2216	1	2	yes	—
113	D₅₃	—	2	4	no	—
114	C₂³×C₈	—	53	1	no	—
115	C₂²×C₁₆	—	53	1	no	—
116	C₂²×C₁₆	—	53	4	no	—
117	C₂²×C₁₆	—	106	4	no	—
118	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
119	C₂×#107	—	53	2	no	—
120	C₂×#107	C₂×D₅₃	1	2	yes	—
121	#380	—	106	2	no	—
122	#366	—	106	4	no	—
123	#340	—	106	2	no	—
124	C₅₃	#12834	1	1	yes	characteristic, complemented, Sylow
125	C₂³×C₄	—	53	1	no	—
126	C₂²×C₈	—	53	1	no	—
127	C₂²×C₈	—	53	2	no	—
128	C₂²×C₈	—	53	2	no	—
129	C₂²×C₈	—	106	2	no	—
130	C₂²×C₈	—	106	2	no	—
131	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	106	2	no	—
134	C₂×C₂²⋊C₄	—	212	2	no	—
135	C₂×C₁₆	—	2	2	no	—
136	C₂×C₁₆	—	53	2	no	—
137	C₂×C₁₆	—	53	4	no	—
138	C₂×C₁₆	—	106	8	no	—
139	C₂×C₁₆	C₄×D₅₃	1	2	yes	—
140	#107	—	2	2	no	—
141	#107	—	2	2	no	—
142	#107	—	106	2	no	—
143	#107	—	106	2	no	—
144	#95	—	212	2	no	—
145	C₂⁴	—	53	1	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	53	1	no	—
148	C₂²×C₄	—	53	2	no	—
149	C₂²×C₄	—	53	2	no	—
150	C₂²×C₄	—	106	2	no	—
151	C₂²×C₄	—	106	2	no	—
152	C₂²×C₄	—	212	2	no	—
153	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
154	C₂×C₈	—	53	2	no	—
155	C₂×C₈	—	106	2	no	—
156	C₂×C₈	—	106	2	no	—
157	C₂×C₈	—	106	2	no	—
158	C₂×C₈	—	106	4	no	—
159	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
160	C₂×C₈	#11719945	1	2	yes	—
161	C₂×C₈	D₄×D₅₃	1	2	yes	—
162	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	212	2	no	—
166	C₄⋊C₄	—	212	2	no	—
167	C₂²⋊C₄	—	424	4	no	—
168	C₁₆	—	2	2	no	—
169	C₁₆	—	53	4	no	—
170	C₂³	—	53	2	no	—
171	C₂³	—	53	2	no	—
172	C₂³	—	53	2	no	—
173	C₂³	—	106	2	no	—
174	C₂³	—	106	2	no	—
175	C₂³	D₈×D₅₃	1	1	yes	characteristic
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	53	2	no	—
180	C₂×C₄	—	106	2	no	—
181	C₂×C₄	—	106	4	no	—
182	C₂×C₄	—	106	2	no	—
183	C₂×C₄	—	106	2	no	—
184	C₂×C₄	—	424	2	no	—
185	C₂×C₄	—	424	2	no	—
186	C₂×C₄	—	424	2	no	—
187	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
188	C₂×C₄	#13133190	1	2	yes	—
189	C₂×C₄	Q₁₆×D₅₃	1	1	yes	characteristic
190	C₂×C₄	#13133238	1	2	yes	—
191	C₈	—	106	2	no	—
192	C₈	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
193	C₈	#13133174	1	1	yes	characteristic
194	C₈	#13133195	1	2	yes	—
195	C₂²	—	53	4	no	—
196	C₂²	—	106	2	no	—
197	C₂²	—	106	2	no	—
198	C₂²	—	106	4	no	—
199	C₂²	—	106	4	no	—
200	C₂²	#107×D₅₃	1	1	yes	characteristic
201	C₂²	#16810858	1	2	yes	—
202	C₂²	D₁₆×D₅₃	1	1	yes	characteristic
203	C₂²	Q₃₂×D₅₃	1	1	yes	characteristic
204	C₂²	#16811054	1	2	yes	—
205	C₄	—	16	2	no	—
206	C₄	—	848	2	no	—
207	C₄	—	106	2	no	—
208	C₄	#16810482	1	1	yes	characteristic
209	C₄	#16810658	1	1	yes	characteristic
210	C₄	#16810863	1	2	yes	—
211	C₂	—	106	4	no	—
212	C₂	#20274743	1	1	yes	characteristic
213	C₂	#366×D₅₃	1	1	yes	characteristic
214	C₂	#20276498	1	1	yes	characteristic
215	C₂	#20276800	1	2	yes	—
216	C₂	#20276805	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₆×D₅₃

C₂

yes

maximal, characteristic

C₂×#16810448

C₂

yes

maximal, complemented

#20274741

C₂

yes

maximal

#20272807

C₂

yes

maximal, characteristic, complemented

C₅₃×#1380

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₅₃

C₂²

yes

characteristic

C₂²×#11719908

C₂²

yes

characteristic

C₂×C₁₆×D₅₃

—

C₂×C₁₆×D₅₃

C₄

yes

complemented

C₂×#13133151

C₂²

yes

—

#16810480

—

#16810448

—

#16810385

—

C₂²×C₁₆×C₅₃

C₂²

yes

characteristic

C₂×#107×C₅₃

C₂²

yes

—

C₂²×C₄×D₅₃

D₄

yes

characteristic

C₂²×#88322

D₄

yes

characteristic

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

—

C₂×C₈×D₅₃

C₂×C₄

yes

—

C₂×C₈×D₅₃

Q₈

yes

—

C₂×C₄⋊Dic₅₃

—

C₂×#11719921

—

C₂×#11719908

C₂×C₄

yes

—

C₂×#11719908

D₄

yes

—

C₁₆×D₅₃

—

#13133151

—

#13133151

—

#13133124

—

C₂²×C₈×C₅₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₅₃

—

C₂×C₁₆×C₅₃

—

C₂×C₁₆×C₅₃

C₂×C₄

yes

—

#107×C₅₃

—

#107×C₅₃

—

C₂³×D₅₃

D₈

yes

characteristic

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

D₈

yes

characteristic

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

C₄⋊C₄

yes

—

C₂×C₄×D₅₃

Q₁₆

yes

—

C₂×C₈×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×D₄

yes

—

C₂×C₈×C₅₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

#11719921

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₂×#88322

—

C₂×#88322

C₄⋊C₄

yes

—

C₈×D₅₃

—

C₈×D₅₃

—

C₈×D₅₃

—

C₁₆×C₅₃

—

#11719908

C₂²⋊C₄

yes

complemented

C₂³×C₅₃

C₂×D₈

yes

characteristic

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

#107

yes

—

C₂²×D₅₃

D₁₆

yes

—

C₂²×D₅₃

Q₃₂

yes

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₃

#121

yes

—

C₂×C₄×C₅₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅₃

#135

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

#107

yes

—

C₄×D₅₃

—

C₄×D₅₃

—

C₄×D₅₃

—

C₈×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₅₃

#117

yes

characteristic

C₈×C₅₃

C₂²⋊Q₈

yes

—

—

—

C₂²×C₅₃

yes

C₂²×C₅₃

yes

—

C₂²×C₅₃

C₂×D₁₆

yes

characteristic

C₂²×C₅₃

C₂×Q₃₂

yes

characteristic

C₂²×C₅₃

#508

yes

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

#366

yes

complemented

C₄×C₅₃

—

C₄×C₅₃

yes

C₄×C₅₃

yes

100

C₄×C₅₃

#467

yes

—

101

Dic₅₃

—

102

Dic₅₃

—

103

C₂³×C₁₆

—

104

C₂×#366

—

105

#1808

—

106

#1380

—

107

#1380

D₅₃

yes

characteristic, complemented

108

C₂×C₅₃

#1808

yes

characteristic

109

C₂×C₅₃

C₂×#366

yes

characteristic

110

C₂×C₅₃

#2158

yes

characteristic

111

C₂×C₅₃

#2215

yes

—

112

C₂×C₅₃

#2216

yes

—

113

D₅₃

—

114

C₂³×C₈

—

115

C₂²×C₁₆

—

116

C₂²×C₁₆

—

117

C₂²×C₁₆

—

106

—

118

C₂²×C₁₆

C₂×D₅₃

yes

characteristic

119

C₂×#107

—

120

C₂×#107

C₂×D₅₃

yes

—

121

#380

—

106

—

122

#366

—

106

—

123

#340

—

106

—

124

C₅₃

#12834

yes

characteristic, complemented, Sylow

125

C₂³×C₄

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₂²×C₈

—

106

—

130

C₂²×C₈

—

106

—

131

C₂²×C₈

C₂²×D₅₃

yes

characteristic

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

106

—

134

C₂×C₂²⋊C₄

—

212

—

135

C₂×C₁₆

—

136

C₂×C₁₆

—

137

C₂×C₁₆

—

138

C₂×C₁₆

—

106

—

139

C₂×C₁₆

C₄×D₅₃

yes

—

140

#107

—

141

#107

—

142

#107

—

106

—

143

#107

—

106

—

144

#95

—

212

—

145

C₂⁴

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

106

—

151

C₂²×C₄

—

106

—

152

C₂²×C₄

—

212

—

153

C₂²×C₄

D₄×D₅₃

yes

characteristic

154

C₂×C₈

—

155

C₂×C₈

—

106

—

156

C₂×C₈

—

106

—

157

C₂×C₈

—

106

—

158

C₂×C₈

—

106

—

159

C₂×C₈

C₂×C₄×D₅₃

yes

characteristic

160

C₂×C₈

#11719945

yes

—

161

C₂×C₈

D₄×D₅₃

yes

—

162

C₂×C₈

Q₈×D₅₃

yes

characteristic

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

212

—

166

C₄⋊C₄

—

212

—

167

C₂²⋊C₄

—

424

—

168

C₁₆

—

169

C₁₆

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

106

—

174

C₂³

—

106

—

175

C₂³

D₈×D₅₃

yes

characteristic

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

106

—

181

C₂×C₄

—

106

—

182

C₂×C₄

—

106

—

183

C₂×C₄

—

106

—

184

C₂×C₄

—

424

—

185

C₂×C₄

—

424

—

186

C₂×C₄

—

424

—

187

C₂×C₄

C₄⋊C₄×D₅₃

yes

characteristic

188

C₂×C₄

#13133190

yes

—

189

C₂×C₄

Q₁₆×D₅₃

yes

characteristic

190

C₂×C₄

#13133238

yes

—

191

C₈

—

106

—

192

C₈

C₂²⋊C₄×D₅₃

yes

characteristic

193

C₈

#13133174

yes

characteristic

194

C₈

#13133195

yes

—

195

C₂²

—

196

C₂²

—

106

—

197

C₂²

—

106

—

198

C₂²

—

106

—

199

C₂²

—

106

—

200

C₂²

#107×D₅₃

yes

characteristic

201

C₂²

#16810858

yes

—

202

C₂²

D₁₆×D₅₃

yes

characteristic

203

C₂²

Q₃₂×D₅₃

yes

characteristic

204

C₂²

#16811054

yes

—

205

C₄

—

206

C₄

—

848

—

207

C₄

—

106

—

208

C₄

#16810482

yes

characteristic

209

C₄

#16810658

yes

characteristic

210

C₄

#16810863

yes

—

211

C₂

—

106

—

212

C₂

#20274743

yes

characteristic

213

C₂

#366×D₅₃

yes

characteristic

214

C₂

#20276498

yes

characteristic

215

C₂

#20276800

yes

—

216

C₂

#20276805

yes

—

	subgroup	G/H
center	C₂³	D₈×D₅₃
commutator	C₂×C₈×C₅₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₃
Fitting	C₅₃×#1380	C₂
socle	C₂³×C₅₃	C₂×D₈
prime radical	C₂³×D₅₃	D₈
cosocle	C₂²×C₈×C₅₃	C₂³
hypercenter	#1380	D₅₃
hypocenter	C₅₃	#12834
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

subgroup

G/H

center

C₂³

D₈×D₅₃

commutator

C₂×C₈×C₅₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₃

Fitting

C₅₃×#1380

C₂

socle

C₂³×C₅₃

C₂×D₈

prime radical

C₂³×D₅₃

D₈

cosocle

C₂²×C₈×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

N	H ≅ G/N	type
2. C₂×#16810448	C₂	semidirect
4. #20272807	C₂	semidirect
5. C₅₃×#1380	C₂	semidirect
9. C₂×C₁₆×D₅₃	C₄	semidirect
60. #11719908	C₂²⋊C₄	semidirect
96. C₂×D₅₃	#366	semidirect
107. #1380	D₅₃	semidirect
124. C₅₃	#12834	semidirect

H ≅ G/N

type

2. C₂×#16810448

C₂

semidirect

4. #20272807

C₂

semidirect

5. C₅₃×#1380

C₂

semidirect

9. C₂×C₁₆×D₅₃

C₄

semidirect

60. #11719908

C₂²⋊C₄

semidirect

96. C₂×D₅₃

#366

semidirect

107. #1380

D₅₃

semidirect

124. C₅₃

#12834

semidirect

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

subgroup	index
C₂²×C₁₆×D₅₃	2
C₂×#16810448	2
#20274741	2
#20272807	2
C₅₃×#1380	2
#12834	53

subgroup

index

C₂²×C₁₆×D₅₃

C₅₃×#1380

Subgroups — #27300259

Conjugacy classes of subgroups

Complements

Maximal subgroups