Group #20287748 — subgroups

Subgroups — #20287748

Order 6784.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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	#16811352	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811346	C₂	1	1	yes	maximal, characteristic
3	#16811017	C₂	1	2	yes	maximal
4	#16811003	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810846	C₂	1	2	yes	maximal
6	#16810834	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810834	C₂	1	2	yes	maximal, complemented
8	#16810829	C₂	1	1	yes	maximal, characteristic
9	#16810731	C₂	1	2	yes	maximal, complemented
10	C₄×#11719913	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₂₁₂	C₂²	1	2	yes	—
13	C₂×Dic₂₁₂	C₂²	1	2	yes	—
14	C₂×Dic₂₁₂	C₂²	1	2	yes	—
15	C₂×#11719913	C₂²	1	1	yes	characteristic
16	C₂×#11719913	C₂²	1	2	yes	—
17	#13133217	C₂²	1	2	yes	—
18	#13133217	C₂²	1	1	yes	characteristic
19	#13133217	C₂²	1	1	yes	characteristic
20	#13133212	—	2	2	no	—
21	#13133208	—	2	1	no	—
22	#13133208	—	2	2	no	—
23	#13133205	C₂²	1	2	yes	—
24	#13133193	—	2	1	no	—
25	Q₈×Dic₅₃	—	2	1	no	—
26	C₄×Dic₁₀₆	C₂²	1	2	yes	—
27	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
28	C₄×Dic₁₀₆	C₂²	1	2	yes	—
29	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
30	#13133175	—	2	1	no	—
31	#13133149	C₂²	1	1	yes	characteristic
32	#13133142	C₂²	1	2	yes	—
33	#13133142	C₂²	1	1	yes	characteristic
34	#13133142	C₂²	1	2	yes	—
35	#13133139	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
39	#97×C₅₃	C₂²	1	2	yes	—
40	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₅₃	D₄	1	1	yes	characteristic
42	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₅₃	—	2	1	no	—
44	C₂×Dic₁₀₆	C₂³	1	2	yes	—
45	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
46	C₂×Dic₁₀₆	C₂³	1	2	yes	—
47	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
48	C₂×C₈×C₅₃	C₂³	1	2	yes	—
49	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
51	C₄⋊C₄×C₅₃	D₄	1	2	yes	—
52	C₄²×C₅₃	C₂³	1	1	yes	characteristic
53	C₄²×C₅₃	C₂³	1	2	yes	—
54	#11719921	—	2	2	no	—
55	#11719921	—	2	1	no	—
56	#11719921	—	2	2	no	—
57	C₄⋊Dic₅₃	—	2	1	no	—
58	C₄⋊Dic₅₃	—	2	2	no	—
59	C₄⋊Dic₅₃	—	2	1	no	—
60	C₄⋊Dic₅₃	—	2	2	no	—
61	C₄⋊Dic₅₃	—	2	1	no	—
62	C₄⋊Dic₅₃	—	2	1	no	—
63	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
65	#11719919	—	2	2	no	—
66	#11719919	—	2	2	no	—
67	#11719919	—	2	1	no	—
68	C₄×Dic₅₃	—	2	2	no	—
69	C₄×Dic₅₃	—	2	2	no	—
70	C₄×Dic₅₃	—	2	1	no	—
71	Dic₂₁₂	—	2	4	no	—
72	Dic₂₁₂	—	4	2	no	—
73	Dic₂₁₂	—	4	2	no	—
74	#11719913	—	2	2	no	—
75	#11719913	—	4	2	no	—
76	C₂²×D₅₃	—	2	1	no	—
77	Q₈×C₅₃	—	2	2	no	—
78	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
83	C₂×Dic₅₃	—	2	1	no	—
84	C₂×Dic₅₃	—	2	2	no	—
85	C₂×Dic₅₃	—	2	2	no	—
86	C₂×Dic₅₃	—	2	1	no	—
87	C₂×Dic₅₃	—	2	1	no	—
88	D₂₁₂	—	2	1	no	—
89	D₂₁₂	—	2	1	no	—
90	C₄×D₅₃	—	4	2	no	—
91	Dic₁₀₆	—	2	1	no	—
92	Dic₁₀₆	—	2	2	no	—
93	Dic₁₀₆	—	2	2	no	—
94	Dic₁₀₆	—	2	2	no	—
95	Dic₁₀₆	—	2	2	no	—
96	Dic₁₀₆	—	2	1	no	—
97	C₈×C₅₃	—	2	2	no	—
98	C₈×C₅₃	—	2	1	no	—
99	C₈×C₅₃	#41	1	2	yes	—
100	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₅₃	—	4	1	no	—
102	C₂×D₅₃	—	4	1	no	—
103	C₂×D₅₃	—	4	1	no	—
104	C₄×C₅₃	—	2	2	no	—
105	C₄×C₅₃	—	2	2	no	—
106	C₄×C₅₃	—	2	1	no	—
107	C₄×C₅₃	#137	1	2	yes	—
108	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
109	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
110	Dic₅₃	—	4	1	no	—
111	Dic₅₃	—	4	2	no	—
112	Dic₅₃	—	4	2	no	—
113	Dic₅₃	—	4	1	no	—
114	Dic₅₃	—	4	1	no	—
115	#3398	—	53	1	no	maximal, Sylow
116	C₂×C₅₃	#550	1	1	yes	characteristic
117	C₂×C₅₃	C₂×#137	1	1	yes	characteristic
118	C₂×C₅₃	#578	1	1	yes	characteristic
119	D₅₃	—	8	1	no	—
120	#557	—	53	1	no	—
121	#556	—	53	1	no	—
122	#497	—	53	2	no	—
123	#494	—	53	1	no	—
124	#464	—	53	2	no	—
125	#462	—	53	2	no	—
126	#462	—	53	1	no	—
127	#461	—	53	1	no	—
128	#446	D₅₃	1	1	yes	characteristic, complemented
129	#441	—	53	2	no	—
130	C₄×SD₁₆	—	53	1	no	—
131	C₅₃	#3398	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₁₆	—	53	2	no	—
133	C₂×Q₁₆	—	53	2	no	—
134	C₂×Q₁₆	—	53	2	no	—
135	C₂×SD₁₆	—	53	1	no	—
136	C₂×SD₁₆	—	53	2	no	—
137	C₄⋊Q₈	—	53	1	no	—
138	C₄⋊Q₈	—	53	1	no	—
139	C₄⋊Q₈	—	53	2	no	—
140	#126	—	106	2	no	—
141	#125	—	106	1	no	—
142	#125	—	106	2	no	—
143	#124	—	53	2	no	—
144	C₂²⋊Q₈	—	106	1	no	—
145	C₄×Q₈	—	53	2	no	—
146	C₄×Q₈	—	53	1	no	—
147	C₄×Q₈	—	53	2	no	—
148	C₄×Q₈	—	106	1	no	—
149	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
150	C₄×D₄	—	53	1	no	—
151	#117	—	106	1	no	—
152	#106	—	53	1	no	—
153	C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
154	C₄⋊C₈	C₂×D₅₃	1	2	yes	—
155	#103	—	53	1	no	—
156	#103	—	53	2	no	—
157	#103	—	53	2	no	—
158	#102	—	53	1	no	—
159	#97	C₂×D₅₃	1	2	yes	—
160	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
161	C₂×Q₈	—	53	2	no	—
162	C₂×Q₈	—	53	1	no	—
163	C₂×Q₈	—	53	2	no	—
164	C₂×Q₈	D₂₁₂	1	1	yes	characteristic
165	C₂×D₄	—	53	1	no	—
166	C₂²×C₄	—	106	1	no	—
167	Q₁₆	—	106	4	no	—
168	Q₁₆	—	212	2	no	—
169	Q₁₆	—	212	2	no	—
170	SD₁₆	—	106	2	no	—
171	SD₁₆	—	212	2	no	—
172	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₅₃	1	2	yes	—
174	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
175	C₄⋊C₄	—	53	1	no	—
176	C₄⋊C₄	—	53	1	no	—
177	C₄⋊C₄	—	106	1	no	—
178	C₄⋊C₄	—	106	2	no	—
179	C₄⋊C₄	—	106	2	no	—
180	C₄⋊C₄	—	106	1	no	—
181	C₄⋊C₄	—	106	2	no	—
182	C₄⋊C₄	—	106	1	no	—
183	C₄⋊C₄	—	106	2	no	—
184	C₄⋊C₄	—	106	1	no	—
185	C₄⋊C₄	—	106	1	no	—
186	C₄⋊C₄	D₂₁₂	1	1	yes	characteristic
187	C₄⋊C₄	D₂₁₂	1	2	yes	—
188	C₂²⋊C₄	—	106	2	no	—
189	C₂²⋊C₄	—	106	1	no	—
190	C₂²⋊C₄	—	106	2	no	—
191	C₄²	—	106	2	no	—
192	C₄²	—	106	2	no	—
193	C₄²	—	106	1	no	—
194	C₄²	C₂²×D₅₃	1	1	yes	characteristic
195	C₄²	C₂²×D₅₃	1	2	yes	—
196	C₂³	—	106	1	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	106	1	no	—
199	Q₈	—	106	2	no	—
200	Q₈	—	106	2	no	—
201	Q₈	—	106	2	no	—
202	Q₈	—	106	2	no	—
203	Q₈	—	106	1	no	—
204	D₄	—	106	1	no	—
205	D₄	—	106	1	no	—
206	C₂×C₄	—	106	1	no	—
207	C₂×C₄	—	106	1	no	—
208	C₂×C₄	—	106	2	no	—
209	C₂×C₄	—	106	1	no	—
210	C₂×C₄	—	106	2	no	—
211	C₂×C₄	—	212	2	no	—
212	C₂×C₄	C₂×D₂₁₂	1	2	yes	—
213	C₂×C₄	C₂×D₂₁₂	1	2	yes	—
214	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
215	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
216	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
217	C₈	—	2	2	no	—
218	C₈	—	2	1	no	—
219	C₈	#11719949	1	2	yes	—
220	C₂²	—	212	1	no	—
221	C₂²	—	212	1	no	—
222	C₂²	—	212	1	no	—
223	C₂²	C₂²×D₂₁₂	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	2	no	—
226	C₄	—	2	1	no	—
227	C₄	—	212	2	no	—
228	C₄	—	212	1	no	—
229	C₄	—	212	2	no	—
230	C₄	—	212	1	no	—
231	C₄	—	212	1	no	—
232	C₄	#13133250	1	2	yes	—
233	C₄	C₂×#11719949	1	1	yes	characteristic
234	C₄	#13133263	1	1	yes	characteristic
235	C₂	—	424	1	no	—
236	C₂	#16811295	1	1	yes	characteristic
237	C₂	C₂×#13133250	1	1	yes	characteristic
238	C₂	#16811440	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811352

C₂

yes

maximal, characteristic, complemented

#16811346

C₂

yes

maximal, characteristic

#16811017

C₂

yes

maximal

#16811003

C₂

yes

maximal, characteristic, complemented

#16810846

C₂

yes

maximal

#16810834

C₂

yes

maximal, characteristic, complemented

#16810834

C₂

yes

maximal, complemented

#16810829

C₂

yes

maximal, characteristic

#16810731

C₂

yes

maximal, complemented

C₄×#11719913

C₂

yes

maximal, characteristic

C₅₃×#446

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₁₂

C₂²

yes

—

C₂×Dic₂₁₂

C₂²

yes

—

C₂×Dic₂₁₂

C₂²

yes

—

C₂×#11719913

C₂²

yes

characteristic

C₂×#11719913

C₂²

yes

—

#13133217

C₂²

yes

—

#13133217

C₂²

yes

characteristic

#13133217

C₂²

yes

—

—

—

C₂²

yes

—

#13133193

—

Q₈×Dic₅₃

—

C₄×Dic₁₀₆

C₂²

yes

—

C₄×Dic₁₀₆

C₂²

yes

characteristic

C₄×Dic₁₀₆

C₂²

yes

—

C₄×D₂₁₂

C₂²

yes

characteristic

#13133175

—

#13133149

C₂²

yes

characteristic

#13133142

C₂²

yes

—

#13133142

C₂²

yes

characteristic

#13133142

C₂²

yes

—

#13133139

C₂²

yes

characteristic

C₄×Q₈×C₅₃

C₂²

yes

characteristic

C₄⋊C₈×C₅₃

C₂²

yes

characteristic

C₄⋊C₈×C₅₃

C₂²

yes

—

#97×C₅₃

C₂²

yes

—

C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×Q₈×C₅₃

D₄

yes

characteristic

C₂×D₂₁₂

C₂³

yes

characteristic

C₂×C₄×D₅₃

—

C₂×Dic₁₀₆

C₂³

yes

—

C₂×Dic₁₀₆

C₂³

yes

characteristic

C₂×Dic₁₀₆

C₂³

yes

—

C₂×C₈×C₅₃

C₂³

yes

characteristic

C₂×C₈×C₅₃

C₂³

yes

—

C₂×C₈×C₅₃

C₂³

yes

characteristic

C₄⋊C₄×C₅₃

D₄

yes

characteristic

C₄⋊C₄×C₅₃

D₄

yes

—

C₄²×C₅₃

C₂³

yes

characteristic

C₄²×C₅₃

C₂³

yes

—

#11719921

—

#11719921

—

#11719921

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

C₂³

yes

characteristic

C₄⋊Dic₅₃

C₂³

yes

—

—

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

Dic₂₁₂

—

Dic₂₁₂

—

Dic₂₁₂

—

#11719913

—

#11719913

—

C₂²×D₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂⁴

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

#41

yes

—

100

C₂²×C₅₃

C₂²×D₄

yes

characteristic

101

C₂×D₅₃

—

102

C₂×D₅₃

—

103

C₂×D₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

—

107

C₄×C₅₃

#137

yes

—

108

C₄×C₅₃

C₂×#41

yes

characteristic

109

C₄×C₅₃

H(5,𝔽₂)

yes

characteristic

110

Dic₅₃

—

111

Dic₅₃

—

112

Dic₅₃

—

113

Dic₅₃

—

114

Dic₅₃

—

115

#3398

—

maximal, Sylow

116

C₂×C₅₃

#550

yes

characteristic

117

C₂×C₅₃

C₂×#137

yes

characteristic

118

C₂×C₅₃

#578

yes

characteristic

119

D₅₃

—

120

#557

—

121

#556

—

122

#497

—

123

#494

—

124

#464

—

125

#462

—

126

#462

—

127

#461

—

128

#446

D₅₃

yes

characteristic, complemented

129

#441

—

130

C₄×SD₁₆

—

131

C₅₃

#3398

yes

characteristic, complemented, Sylow

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×SD₁₆

—

136

C₂×SD₁₆

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#126

—

106

—

141

#125

—

106

—

142

#125

—

106

—

143

#124

—

144

C₂²⋊Q₈

—

106

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

106

—

149

C₄×Q₈

C₂×D₅₃

yes

characteristic

150

C₄×D₄

—

151

#117

—

106

—

152

#106

—

153

C₄⋊C₈

C₂×D₅₃

yes

characteristic

154

C₄⋊C₈

C₂×D₅₃

yes

—

155

#103

—

156

#103

—

157

#103

—

158

#102

—

159

#97

C₂×D₅₃

yes

—

160

C₄×C₈

C₂×D₅₃

yes

characteristic

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

D₂₁₂

yes

characteristic

165

C₂×D₄

—

166

C₂²×C₄

—

106

—

167

Q₁₆

—

106

—

168

Q₁₆

—

212

—

169

Q₁₆

—

212

—

170

SD₁₆

—

106

—

171

SD₁₆

—

212

—

172

C₂×C₈

C₂²×D₅₃

yes

characteristic

173

C₂×C₈

C₂²×D₅₃

yes

—

174

C₂×C₈

C₂²×D₅₃

yes

characteristic

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

106

—

178

C₄⋊C₄

—

106

—

179

C₄⋊C₄

—

106

—

180

C₄⋊C₄

—

106

—

181

C₄⋊C₄

—

106

—

182

C₄⋊C₄

—

106

—

183

C₄⋊C₄

—

106

—

184

C₄⋊C₄

—

106

—

185

C₄⋊C₄

—

106

—

186

C₄⋊C₄

D₂₁₂

yes

characteristic

187

C₄⋊C₄

D₂₁₂

yes

—

188

C₂²⋊C₄

—

106

—

189

C₂²⋊C₄

—

106

—

190

C₂²⋊C₄

—

106

—

191

C₄²

—

106

—

192

C₄²

—

106

—

193

C₄²

—

106

—

194

C₄²

C₂²×D₅₃

yes

characteristic

195

C₄²

C₂²×D₅₃

yes

—

196

C₂³

—

106

—

197

Q₈

—

198

Q₈

—

106

—

199

Q₈

—

106

—

200

Q₈

—

106

—

201

Q₈

—

106

—

202

Q₈

—

106

—

203

Q₈

—

106

—

204

D₄

—

106

—

205

D₄

—

106

—

206

C₂×C₄

—

106

—

207

C₂×C₄

—

106

—

208

C₂×C₄

—

106

—

209

C₂×C₄

—

106

—

210

C₂×C₄

—

106

—

211

C₂×C₄

—

212

—

212

C₂×C₄

C₂×D₂₁₂

yes

—

213

C₂×C₄

C₂×D₂₁₂

yes

—

214

C₂×C₄

C₂×D₂₁₂

yes

characteristic

215

C₂×C₄

C₂×D₂₁₂

yes

characteristic

216

C₂×C₄

C₂³×D₅₃

yes

characteristic

217

C₈

—

218

C₈

—

219

C₈

#11719949

yes

—

220

C₂²

—

212

—

221

C₂²

—

212

—

222

C₂²

—

212

—

223

C₂²

C₂²×D₂₁₂

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

212

—

228

C₄

—

212

—

229

C₄

—

212

—

230

C₄

—

212

—

231

C₄

—

212

—

232

C₄

#13133250

yes

—

233

C₄

C₂×#11719949

yes

characteristic

234

C₄

#13133263

yes

characteristic

235

C₂

—

424

—

236

C₂

#16811295

yes

characteristic

237

C₂

C₂×#13133250

yes

characteristic

238

C₂

#16811440

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#446	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#446	D₅₃
hypocenter	C₅₃	#3398
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

subgroup

G/H

center

C₂²

C₂²×D₂₁₂

commutator

C₂×C₄×C₅₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₃

Fitting

C₅₃×#446

C₂

socle

C₂²×C₅₃

C₂²×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

N	H ≅ G/N	type
1. #16811352	C₂	semidirect
4. #16811003	C₂	semidirect
6. #16810834	C₂	semidirect
7. #16810834	C₂	semidirect
9. #16810731	C₂	semidirect
11. C₅₃×#446	C₂	semidirect
128. #446	D₅₃	semidirect
131. C₅₃	#3398	semidirect

H ≅ G/N

type

1. #16811352

C₂

semidirect

4. #16811003

C₂

semidirect

6. #16810834

C₂

semidirect

7. #16810834

C₂

semidirect

9. #16810731

C₂

semidirect

11. C₅₃×#446

C₂

semidirect

128. #446

D₅₃

semidirect

131. C₅₃

#3398

semidirect

Subgroups — #20287748

Conjugacy classes of subgroups

Complements