Group #27537389 — subgroups

Subgroups — C₂×#20276586 #27537389

Order 13568.

670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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	C₂×Q₁₆×Dic₅₃	C₂	1	2	yes	maximal
2	#20276586	C₂	1	8	yes	maximal, direct product factor
3	C₂×#16810451	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810427	C₂	1	2	yes	maximal
5	C₂×#16810398	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×Dic₅₃	—	2	2	no	—
8	C₂²×#11719908	C₂²	1	1	yes	characteristic
9	Q₁₆×Dic₅₃	—	2	4	no	—
10	Q₁₆×Dic₅₃	C₂²	1	8	yes	—
11	C₂×#13133151	C₂²	1	2	yes	—
12	C₂×#13133141	—	2	2	no	—
13	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
14	#16810451	C₂²	1	4	yes	—
15	#16810427	C₂²	1	8	yes	—
16	#16810398	C₂²	1	4	yes	—
17	C₂²×Q₁₆×C₅₃	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₅₃	C₄	1	8	yes	complemented
19	C₂×Q₃₂×C₅₃	C₂²	1	4	yes	—
20	C₂²×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
21	C₂²×#88322	D₄	1	1	yes	characteristic
22	Q₈×Dic₅₃	—	2	8	no	—
23	Q₈×Dic₅₃	—	4	4	no	—
24	C₂×C₄⋊Dic₅₃	—	2	2	no	—
25	C₂×C₄⋊Dic₅₃	—	4	2	no	—
26	C₂×C₄×Dic₅₃	—	4	2	no	—
27	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
28	C₂×#11719908	—	2	2	no	—
29	C₂×#11719908	C₂³	1	2	yes	—
30	#13133151	—	2	2	no	—
31	#13133151	C₂³	1	4	yes	—
32	#13133141	—	2	8	no	—
33	C₈×Dic₅₃	D₄	1	2	yes	—
34	C₈×Dic₅₃	C₂³	1	2	yes	—
35	C₂²×Q₈×C₅₃	—	2	2	no	—
36	C₂×Q₁₆×C₅₃	—	2	2	no	—
37	C₂×Q₁₆×C₅₃	—	2	4	no	—
38	C₂×Q₁₆×C₅₃	C₂×C₄	1	8	yes	—
39	C₂×Q₁₆×C₅₃	C₂³	1	4	yes	—
40	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
41	Q₃₂×C₅₃	C₂×C₄	1	16	yes	complemented
42	C₂×C₁₆×C₅₃	C₂×C₄	1	4	yes	—
43	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
44	C₂×Q₈×C₅₃	—	2	8	no	—
45	C₂×Q₈×C₅₃	—	2	4	no	—
46	C₂×Q₈×C₅₃	—	4	2	no	—
47	C₂×Q₈×C₅₃	—	4	4	no	—
48	C₂²×C₄×C₅₃	—	4	2	no	—
49	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₃	—	4	2	no	—
51	C₂²×Dic₅₃	D₈	1	2	yes	—
52	Q₁₆×C₅₃	—	2	8	no	—
53	Q₁₆×C₅₃	—	2	4	no	—
54	Q₁₆×C₅₃	C₂²×C₄	1	8	yes	—
55	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
56	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₅₃	#41	1	2	yes	—
58	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
59	C₄⋊Dic₅₃	—	2	4	no	—
60	C₄⋊Dic₅₃	—	4	2	no	—
61	C₄⋊Dic₅₃	—	4	8	no	—
62	C₄×Dic₅₃	—	4	8	no	—
63	C₄×Dic₅₃	D₈	1	2	yes	—
64	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
65	C₂×#88322	—	2	2	no	—
66	C₂×#88322	C₂×D₄	1	2	yes	—
67	C₁₆×C₅₃	C₂²×C₄	1	4	yes	—
68	#11719908	—	2	2	no	—
69	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
70	Q₈×C₅₃	—	2	8	no	—
71	Q₈×C₅₃	—	4	4	no	—
72	Q₈×C₅₃	—	4	8	no	—
73	C₂×C₄×C₅₃	—	4	4	no	—
74	C₂×C₄×C₅₃	—	4	8	no	—
75	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₅₃	#135	1	2	yes	—
78	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
79	C₂×Dic₅₃	—	2	4	no	—
80	C₂×Dic₅₃	—	4	4	no	—
81	C₂×Dic₅₃	—	8	4	no	—
82	C₂×Dic₅₃	C₂×D₈	1	4	yes	—
83	C₈×C₅₃	C₄×D₄	1	2	yes	—
84	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
85	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
86	#88322	—	2	2	no	—
87	C₂×#2176	—	53	1	no	maximal, Sylow
88	C₂²×C₅₃	C₄×D₈	1	2	yes	—
89	C₂²×C₅₃	#510	1	4	yes	—
90	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
91	C₄×C₅₃	—	4	8	no	—
92	C₄×C₅₃	C₄×D₈	1	2	yes	—
93	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
94	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
95	Dic₅₃	—	2	4	no	—
96	Dic₅₃	—	8	4	no	—
97	C₂²×Q₃₂	D₅₃	1	1	yes	characteristic
98	C₂×C₄×Q₁₆	—	53	2	no	—
99	#2176	—	53	8	no	—
100	C₂×#367	—	53	1	no	—
101	C₂×#358	—	53	2	no	—
102	C₂×#346	—	53	1	no	—
103	C₂×C₅₃	#2176	1	4	yes	complemented
104	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
105	C₂×C₅₃	C₂×#510	1	2	yes	—
106	C₂²×Q₁₆	C₂×D₅₃	1	2	yes	—
107	C₂×C₄×Q₈	—	106	2	no	—
108	C₂×Q₃₂	Dic₅₃	1	8	yes	complemented
109	C₂×Q₃₂	C₂×D₅₃	1	4	yes	—
110	C₂²×C₁₆	—	53	1	no	—
111	C₂²×C₁₆	C₂×D₅₃	1	1	yes	characteristic
112	C₄×Q₁₆	—	53	8	no	—
113	C₄×Q₁₆	—	106	4	no	—
114	C₂×#107	—	53	2	no	—
115	C₂×#103	—	106	2	no	—
116	C₂×C₄×C₈	—	53	1	no	—
117	#367	—	53	4	no	—
118	#358	—	53	8	no	—
119	#346	—	53	4	no	—
120	C₅₃	C₂×#2176	1	1	yes	characteristic, complemented, Sylow
121	C₂²×Q₈	—	2	2	no	—
122	C₂×Q₁₆	—	2	2	no	—
123	C₂×Q₁₆	—	2	4	no	—
124	C₂×Q₁₆	C₂×Dic₅₃	1	8	yes	—
125	C₂×Q₁₆	C₂²×D₅₃	1	4	yes	—
126	C₂²×C₈	—	53	1	no	—
127	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
128	C₄×Q₈	—	106	8	no	—
129	C₄×Q₈	—	212	4	no	—
130	C₂×C₄⋊C₄	—	106	2	no	—
131	C₂×C₄⋊C₄	—	212	2	no	—
132	C₂×C₄²	—	53	1	no	—
133	C₂×C₄²	—	212	2	no	—
134	Q₃₂	C₂×Dic₅₃	1	16	yes	complemented
135	C₂×C₁₆	—	53	2	no	—
136	C₂×C₁₆	—	106	2	no	—
137	C₂×C₁₆	C₂×Dic₅₃	1	4	yes	—
138	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
139	#107	—	53	4	no	—
140	#107	—	106	2	no	—
141	#103	—	106	8	no	—
142	C₄×C₈	—	53	2	no	—
143	C₄×C₈	—	53	2	no	—
144	C₂×Q₈	—	2	8	no	—
145	C₂×Q₈	—	2	4	no	—
146	C₂×Q₈	—	4	2	no	—
147	C₂×Q₈	—	4	4	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	53	2	no	—
150	C₂²×C₄	—	212	2	no	—
151	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
152	Q₁₆	—	2	8	no	—
153	Q₁₆	—	2	4	no	—
154	Q₁₆	C₂²×Dic₅₃	1	8	yes	—
155	C₂×C₈	—	53	2	no	—
156	C₂×C₈	—	106	2	no	—
157	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
158	C₂×C₈	#11719947	1	2	yes	—
159	C₂×C₈	C₂²×Dic₅₃	1	2	yes	—
160	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
161	C₄⋊C₄	—	106	4	no	—
162	C₄⋊C₄	—	212	8	no	—
163	C₄⋊C₄	—	212	2	no	—
164	C₄²	—	53	2	no	—
165	C₄²	—	53	2	no	—
166	C₄²	—	212	8	no	—
167	C₁₆	—	106	2	no	—
168	C₁₆	C₂²×Dic₅₃	1	4	yes	—
169	C₂³	D₈×D₅₃	1	1	yes	characteristic
170	Q₈	—	2	8	no	—
171	Q₈	—	4	4	no	—
172	Q₈	—	4	8	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	—	4	8	no	—
175	C₂×C₄	—	53	4	no	—
176	C₂×C₄	—	106	4	no	—
177	C₂×C₄	—	424	4	no	—
178	C₂×C₄	—	212	4	no	—
179	C₂×C₄	D₄×Dic₅₃	1	2	yes	—
180	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
181	C₂×C₄	#13133236	1	2	yes	—
182	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
183	C₈	—	106	2	no	—
184	C₈	D₄×Dic₅₃	1	2	yes	—
185	C₈	C₂³×Dic₅₃	1	1	yes	characteristic
186	C₈	C₂×#11719947	1	1	yes	characteristic
187	C₂²	D₈×Dic₅₃	1	2	yes	—
188	C₂²	#16811065	1	4	yes	—
189	C₂²	C₂×D₈×D₅₃	1	1	yes	characteristic
190	C₄	—	4	8	no	—
191	C₄	—	106	4	no	—
192	C₄	—	424	4	no	—
193	C₄	D₈×Dic₅₃	1	2	yes	—
194	C₄	C₂×D₄×Dic₅₃	1	1	yes	characteristic
195	C₄	C₂×#13133236	1	1	yes	characteristic
196	C₂	#20276586	1	4	yes	direct product factor
197	C₂	C₂×D₈×Dic₅₃	1	1	yes	characteristic
198	C₂	C₂×#16811065	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×Dic₅₃

C₂

yes

maximal

#20276586

C₂

yes

maximal, direct product factor

C₂×#16810451

C₂

yes

maximal, characteristic

C₂×#16810427

C₂

yes

maximal

C₂×#16810398

C₂

yes

maximal, characteristic

C₂²×Q₃₂×C₅₃

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₅₃

—

C₂²×#11719908

C₂²

yes

characteristic

Q₁₆×Dic₅₃

—

Q₁₆×Dic₅₃

C₂²

yes

—

C₂×#13133151

C₂²

yes

—

C₂×#13133141

—

C₂×C₈×Dic₅₃

C₂²

yes

characteristic

#16810451

C₂²

yes

—

#16810427

C₂²

yes

—

#16810398

C₂²

yes

—

C₂²×Q₁₆×C₅₃

C₂²

yes

—

C₂×Q₃₂×C₅₃

C₄

yes

complemented

C₂×Q₃₂×C₅₃

C₂²

yes

—

C₂²×C₁₆×C₅₃

C₂²

yes

characteristic

C₂²×#88322

D₄

yes

characteristic

Q₈×Dic₅₃

—

Q₈×Dic₅₃

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

D₄

yes

characteristic

C₂×#11719908

—

C₂×#11719908

C₂³

yes

—

#13133151

—

#13133151

C₂³

yes

—

#13133141

—

C₈×Dic₅₃

D₄

yes

—

C₈×Dic₅₃

C₂³

yes

—

C₂²×Q₈×C₅₃

—

C₂×Q₁₆×C₅₃

—

C₂×Q₁₆×C₅₃

—

C₂×Q₁₆×C₅₃

C₂×C₄

yes

—

C₂×Q₁₆×C₅₃

C₂³

yes

—

C₂²×C₈×C₅₃

C₂³

yes

characteristic

Q₃₂×C₅₃

C₂×C₄

yes

complemented

C₂×C₁₆×C₅₃

C₂×C₄

yes

—

C₂×C₁₆×C₅₃

C₂³

yes

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

D₈

yes

—

Q₁₆×C₅₃

—

Q₁₆×C₅₃

—

Q₁₆×C₅₃

C₂²×C₄

yes

—

C₂×C₈×C₅₃

C₂²×C₄

yes

—

C₂×C₈×C₅₃

C₂×D₄

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₂×C₈×C₅₃

C₂⁴

yes

characteristic

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

D₈

yes

—

C₄×Dic₅₃

C₂×D₄

yes

—

C₂×#88322

—

C₂×#88322

C₂×D₄

yes

—

C₁₆×C₅₃

C₂²×C₄

yes

—

#11719908

—

C₂³×C₅₃

C₂×D₈

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₈

yes

characteristic

C₂×C₄×C₅₃

#135

yes

—

C₂×C₄×C₅₃

C₂²×D₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×D₈

yes

—

C₈×C₅₃

C₄×D₄

yes

—

C₈×C₅₃

C₂³×C₄

yes

characteristic

C₈×C₅₃

C₂×#41

yes

—

—

C₂²×C₅₃

C₄×D₈

yes

—

C₂²×C₅₃

#510

yes

—

C₂²×C₅₃

C₂²×D₈

yes

characteristic

C₄×C₅₃

—

C₄×C₅₃

C₄×D₈

yes

—

C₄×C₅₃

C₂×C₄×D₄

yes

characteristic

C₄×C₅₃

C₂×#135

yes

characteristic

Dic₅₃

—

Dic₅₃

—

C₂²×Q₃₂

D₅₃

yes

characteristic

C₂×C₄×Q₁₆

—

#2176

—

100

C₂×#367

—

101

C₂×#358

—

102

C₂×#346

—

103

C₂×C₅₃

#2176

yes

complemented

104

C₂×C₅₃

C₂×C₄×D₈

yes

characteristic

105

C₂×C₅₃

C₂×#510

yes

—

106

C₂²×Q₁₆

C₂×D₅₃

yes

—

107

C₂×C₄×Q₈

—

106

—

108

C₂×Q₃₂

Dic₅₃

yes

complemented

109

C₂×Q₃₂

C₂×D₅₃

yes

—

110

C₂²×C₁₆

—

111

C₂²×C₁₆

C₂×D₅₃

yes

characteristic

112

C₄×Q₁₆

—

113

C₄×Q₁₆

—

106

—

114

C₂×#107

—

115

C₂×#103

—

106

—

116

C₂×C₄×C₈

—

117

#367

—

118

#358

—

119

#346

—

120

C₅₃

C₂×#2176

yes

characteristic, complemented, Sylow

121

C₂²×Q₈

—

122

C₂×Q₁₆

—

123

C₂×Q₁₆

—

124

C₂×Q₁₆

C₂×Dic₅₃

yes

—

125

C₂×Q₁₆

C₂²×D₅₃

yes

—

126

C₂²×C₈

—

127

C₂²×C₈

C₂²×D₅₃

yes

characteristic

128

C₄×Q₈

—

106

—

129

C₄×Q₈

—

212

—

130

C₂×C₄⋊C₄

—

106

—

131

C₂×C₄⋊C₄

—

212

—

132

C₂×C₄²

—

133

C₂×C₄²

—

212

—

134

Q₃₂

C₂×Dic₅₃

yes

complemented

135

C₂×C₁₆

—

136

C₂×C₁₆

—

106

—

137

C₂×C₁₆

C₂×Dic₅₃

yes

—

138

C₂×C₁₆

C₂²×D₅₃

yes

—

139

#107

—

140

#107

—

106

—

141

#103

—

106

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

212

—

151

C₂²×C₄

D₄×D₅₃

yes

characteristic

152

Q₁₆

—

153

Q₁₆

—

154

Q₁₆

C₂²×Dic₅₃

yes

—

155

C₂×C₈

—

156

C₂×C₈

—

106

—

157

C₂×C₈

D₄×D₅₃

yes

characteristic

158

C₂×C₈

#11719947

yes

—

159

C₂×C₈

C₂²×Dic₅₃

yes

—

160

C₂×C₈

C₂³×D₅₃

yes

characteristic

161

C₄⋊C₄

—

106

—

162

C₄⋊C₄

—

212

—

163

C₄⋊C₄

—

212

—

164

C₄²

—

165

C₄²

—

166

C₄²

—

212

—

167

C₁₆

—

106

—

168

C₁₆

C₂²×Dic₅₃

yes

—

169

C₂³

D₈×D₅₃

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

106

—

177

C₂×C₄

—

424

—

178

C₂×C₄

—

212

—

179

C₂×C₄

D₄×Dic₅₃

yes

—

180

C₂×C₄

D₈×D₅₃

yes

characteristic

181

C₂×C₄

#13133236

yes

—

182

C₂×C₄

C₂×D₄×D₅₃

yes

characteristic

183

C₈

—

106

—

184

C₈

D₄×Dic₅₃

yes

—

185

C₈

C₂³×Dic₅₃

yes

characteristic

186

C₈

C₂×#11719947

yes

characteristic

187

C₂²

D₈×Dic₅₃

yes

—

188

C₂²

#16811065

yes

—

189

C₂²

C₂×D₈×D₅₃

yes

characteristic

190

C₄

—

191

C₄

—

106

—

192

C₄

—

424

—

193

C₄

D₈×Dic₅₃

yes

—

194

C₄

C₂×D₄×Dic₅₃

yes

characteristic

195

C₄

C₂×#13133236

yes

characteristic

196

C₂

#20276586

yes

direct product factor

197

C₂

C₂×D₈×Dic₅₃

yes

characteristic

198

C₂

C₂×#16811065

yes

—

	subgroup	G/H
center	C₂³	D₈×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₂²×Q₃₂×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	C₂×D₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₂²×Q₃₂	D₅₃
hypocenter	C₅₃	C₂×#2176
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₅₃

commutator

C₈×C₅₃

C₂³×C₄

Frattini

C₂×C₈

C₂³×D₅₃

Fitting

C₂²×Q₃₂×C₅₃

C₂

socle, prime radical

C₂³×C₅₃

C₂×D₈

cosocle

C₂×C₈×C₅₃

C₂⁴

hypercenter

C₂²×Q₃₂

D₅₃

hypocenter

C₅₃

C₂×#2176

LCS

G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
2. #20276586	C₂	direct (N × H)
18. C₂×Q₃₂×C₅₃	C₄	semidirect
41. Q₃₂×C₅₃	C₂×C₄	semidirect
103. C₂×C₅₃	#2176	semidirect
108. C₂×Q₃₂	Dic₅₃	semidirect
120. C₅₃	C₂×#2176	semidirect
134. Q₃₂	C₂×Dic₅₃	semidirect
196. C₂	#20276586	direct (N × H)

H ≅ G/N

type

2. #20276586

C₂

direct (N × H)

18. C₂×Q₃₂×C₅₃

C₄

semidirect

41. Q₃₂×C₅₃

C₂×C₄

semidirect

103. C₂×C₅₃

#2176

semidirect

108. C₂×Q₃₂

Dic₅₃

semidirect

120. C₅₃

C₂×#2176

semidirect

134. Q₃₂

C₂×Dic₅₃

semidirect

196. C₂

#20276586

direct (N × H)

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

subgroup	index
C₂×Q₁₆×Dic₅₃	2
#20276586	2
C₂×#16810451	2
C₂×#16810427	2
C₂×#16810398	2
C₂²×Q₃₂×C₅₃	2
C₂×#2176	53

subgroup

index

C₂×Q₁₆×Dic₅₃

C₂²×Q₃₂×C₅₃

Subgroups — C₂×#20276586 #27537389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#20276586 #27537389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20276586 #27537389