Group #20285957 — subgroups

Subgroups — #20285957

Order 6784.

328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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	#16811180	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811157	C₂	1	1	yes	maximal, characteristic
3	#16811032	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811032	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810983	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810983	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810965	C₂	1	2	yes	maximal, complemented
8	#16810948	C₂	1	2	yes	maximal
9	#16810931	C₂	1	2	yes	maximal, complemented
10	#16810924	C₂	1	2	yes	maximal, complemented
11	C₅₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	#13133217	C₂²	1	1	yes	characteristic
13	#13133217	C₂²	1	1	yes	characteristic
14	#13133211	—	2	1	no	—
15	#13133209	C₂²	1	1	yes	characteristic
16	#13133209	C₂²	1	2	yes	—
17	#13133205	C₂²	1	1	yes	characteristic
18	#13133200	—	2	1	no	—
19	#13133196	—	2	1	no	—
20	#13133196	—	2	1	no	—
21	#13133196	C₂²	1	1	yes	characteristic
22	#13133191	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₀₆	—	2	1	no	—
24	C₄×Dic₁₀₆	—	2	1	no	—
25	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
26	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
27	C₄×C₂²⋊D₅₃	—	2	1	no	—
28	#13133176	C₂²	1	2	yes	—
29	#13133174	—	2	1	no	—
30	#13133151	C₂²	1	2	yes	—
31	#13133151	C₂²	1	2	yes	—
32	#13133149	C₂²	1	2	yes	—
33	#13133149	C₂²	1	2	yes	—
34	#13133142	C₂²	1	2	yes	—
35	#13133142	C₂²	1	2	yes	—
36	#13133139	C₂²	1	2	yes	—
37	#13133139	C₂²	1	2	yes	—
38	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
40	C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
41	#97×C₅₃	C₂²	1	1	yes	characteristic
42	#97×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
44	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
45	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₅₃	—	2	1	no	—
47	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₅₃	—	2	1	no	—
49	C₂×Dic₁₀₆	—	2	1	no	—
50	C₂×Dic₁₀₆	—	2	1	no	—
51	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₅₃	C₂³	1	2	yes	—
53	C₂×C₈×C₅₃	C₂³	1	2	yes	—
54	C₄²×C₅₃	D₄	1	1	yes	characteristic
55	C₄²×C₅₃	D₄	1	1	yes	characteristic
56	C₄²×C₅₃	C₂³	1	1	yes	characteristic
57	C₄²×C₅₃	C₂³	1	1	yes	characteristic
58	C₂²⋊Dic₅₃	—	2	2	no	—
59	C₂²⋊Dic₅₃	—	2	1	no	—
60	#11719921	—	2	1	no	—
61	#11719921	—	2	1	no	—
62	#11719921	—	2	1	no	—
63	#11719921	—	2	1	no	—
64	C₄⋊Dic₅₃	—	2	1	no	—
65	C₄⋊Dic₅₃	—	2	1	no	—
66	C₄⋊Dic₅₃	C₂³	1	2	yes	—
67	C₄⋊Dic₅₃	C₂³	1	2	yes	—
68	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
69	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
70	#11719919	—	2	1	no	—
71	#11719919	—	2	1	no	—
72	#11719919	—	2	1	no	—
73	#11719919	—	2	2	no	—
74	#11719919	—	2	2	no	—
75	#11719919	—	2	1	no	—
76	C₄×Dic₅₃	—	2	1	no	—
77	C₄×Dic₅₃	—	2	2	no	—
78	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₅₃	—	2	1	no	—
80	C₂×C₄×C₅₃	—	2	2	no	—
81	C₂×C₄×C₅₃	—	4	1	no	—
82	C₂×C₄×C₅₃	—	4	1	no	—
83	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
89	C₂²⋊D₅₃	—	4	2	no	—
90	C₂×Dic₅₃	—	2	2	no	—
91	C₂×Dic₅₃	—	2	2	no	—
92	C₂×Dic₅₃	—	2	1	no	—
93	C₂×Dic₅₃	—	2	1	no	—
94	C₂×Dic₅₃	—	2	1	no	—
95	D₂₁₂	—	2	2	no	—
96	C₄×D₅₃	—	4	2	no	—
97	Dic₁₀₆	—	2	2	no	—
98	Dic₁₀₆	—	4	2	no	—
99	Dic₁₀₆	—	4	2	no	—
100	C₈×C₅₃	—	2	2	no	—
101	C₈×C₅₃	—	2	2	no	—
102	C₂²×C₅₃	—	2	1	no	—
103	C₂²×C₅₃	—	2	1	no	—
104	C₂²×C₅₃	—	2	1	no	—
105	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
106	C₂×D₅₃	—	4	1	no	—
107	C₂×D₅₃	—	4	1	no	—
108	C₂×D₅₃	—	4	1	no	—
109	C₄×C₅₃	—	2	1	no	—
110	C₄×C₅₃	—	2	1	no	—
111	C₄×C₅₃	—	2	1	no	—
112	C₄×C₅₃	—	2	1	no	—
113	C₄×C₅₃	—	2	1	no	—
114	C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
115	Dic₅₃	—	4	1	no	—
116	Dic₅₃	—	4	2	no	—
117	Dic₅₃	—	4	2	no	—
118	Dic₅₃	—	4	1	no	—
119	Dic₅₃	—	4	1	no	—
120	#3240	—	53	1	no	maximal, Sylow
121	C₂×C₅₃	—	4	1	no	—
122	C₂×C₅₃	#536	1	1	yes	characteristic
123	C₂×C₅₃	#575	1	1	yes	characteristic
124	C₂×C₅₃	#575	1	1	yes	characteristic
125	D₅₃	—	8	1	no	—
126	#533	—	53	1	no	—
127	#529	—	53	1	no	—
128	#501	—	53	1	no	—
129	#501	—	53	1	no	—
130	#489	—	53	1	no	—
131	#489	—	53	1	no	—
132	#485	—	53	2	no	—
133	#482	—	53	2	no	—
134	#479	—	53	2	no	—
135	#478	—	53	2	no	—
136	#432	D₅₃	1	1	yes	characteristic, complemented
137	C₅₃	#3240	1	1	yes	characteristic, complemented, Sylow
138	C₄⋊Q₈	—	53	1	no	—
139	C₄⋊Q₈	—	53	1	no	—
140	#126	—	106	1	no	—
141	#125	—	53	1	no	—
142	#125	—	53	2	no	—
143	#124	—	53	1	no	—
144	#123	—	106	1	no	—
145	C₂²⋊Q₈	—	53	1	no	—
146	C₂²⋊Q₈	—	106	1	no	—
147	C₂²⋊Q₈	—	106	1	no	—
148	#121	—	53	1	no	—
149	C₄×Q₈	—	53	1	no	—
150	C₄×Q₈	—	106	1	no	—
151	C₄×Q₈	—	106	1	no	—
152	C₄×D₄	—	53	1	no	—
153	C₄×D₄	—	106	1	no	—
154	#117	—	53	2	no	—
155	#117	—	106	1	no	—
156	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
157	#107	—	53	2	no	—
158	#107	—	53	2	no	—
159	#106	—	53	2	no	—
160	#106	—	53	2	no	—
161	C₄⋊C₈	C₂×D₅₃	1	2	yes	—
162	#103	—	53	2	no	—
163	#103	—	53	2	no	—
164	#102	—	53	2	no	—
165	#102	—	53	2	no	—
166	C₂²⋊C₈	C₂×D₅₃	1	2	yes	—
167	#97	C₂×D₅₃	1	1	yes	characteristic
168	#97	C₂×D₅₃	1	1	yes	characteristic
169	C₂×Q₈	—	53	1	no	—
170	C₂×Q₈	—	106	1	no	—
171	C₂×Q₈	—	106	1	no	—
172	C₂×D₄	—	53	1	no	—
173	C₂×D₄	—	106	1	no	—
174	C₂²×C₄	—	106	1	no	—
175	C₂²×C₄	D₂₁₂	1	1	yes	characteristic
176	C₂²×C₄	D₂₁₂	1	1	yes	characteristic
177	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
178	C₂×C₈	C₂²×D₅₃	1	2	yes	—
179	C₂×C₈	C₂²×D₅₃	1	2	yes	—
180	C₄⋊C₄	—	53	2	no	—
181	C₄⋊C₄	—	53	2	no	—
182	C₄⋊C₄	—	53	1	no	—
183	C₄⋊C₄	—	53	1	no	—
184	C₄⋊C₄	—	106	1	no	—
185	C₄⋊C₄	—	106	1	no	—
186	C₄⋊C₄	—	106	1	no	—
187	C₄⋊C₄	—	106	1	no	—
188	C₄⋊C₄	—	106	2	no	—
189	C₄⋊C₄	—	106	2	no	—
190	C₄⋊C₄	—	106	1	no	—
191	C₄⋊C₄	—	106	1	no	—
192	C₂²⋊C₄	—	106	2	no	—
193	C₂²⋊C₄	—	106	1	no	—
194	C₂²⋊C₄	—	106	1	no	—
195	C₂²⋊C₄	—	106	1	no	—
196	C₂²⋊C₄	—	106	1	no	—
197	C₂²⋊C₄	—	106	1	no	—
198	C₄²	—	106	2	no	—
199	C₄²	—	106	1	no	—
200	C₄²	D₂₁₂	1	1	yes	characteristic
201	C₄²	D₂₁₂	1	1	yes	characteristic
202	C₄²	C₂²×D₅₃	1	1	yes	characteristic
203	C₄²	C₂²×D₅₃	1	1	yes	characteristic
204	C₂³	—	106	1	no	—
205	C₂³	C₂×D₂₁₂	1	1	yes	characteristic
206	Q₈	—	106	2	no	—
207	Q₈	—	212	2	no	—
208	Q₈	—	212	2	no	—
209	D₄	—	106	2	no	—
210	D₄	—	212	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	4	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	106	1	no	—
215	C₂×C₄	—	106	1	no	—
216	C₂×C₄	—	106	2	no	—
217	C₂×C₄	—	106	2	no	—
218	C₂×C₄	—	106	1	no	—
219	C₂×C₄	—	212	2	no	—
220	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
221	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
222	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
223	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
224	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
225	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	2	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	212	1	no	—
232	C₂²	—	212	1	no	—
233	C₂²	—	212	1	no	—
234	C₂²	C₂²×D₂₁₂	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	1	no	—
240	C₄	—	212	1	no	—
241	C₄	—	212	1	no	—
242	C₄	—	212	2	no	—
243	C₄	—	212	2	no	—
244	C₄	—	212	1	no	—
245	C₄	#13133264	1	2	yes	—
246	C₂	—	4	1	no	—
247	C₂	—	424	1	no	—
248	C₂	#16811199	1	1	yes	characteristic
249	C₂	#16811423	1	1	yes	characteristic
250	C₂	#16811423	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811180

C₂

yes

maximal, characteristic, complemented

#16811157

C₂

yes

maximal, characteristic

#16811032

C₂

yes

maximal, characteristic, complemented

#16811032

C₂

yes

maximal, characteristic, complemented

#16810983

C₂

yes

maximal, characteristic, complemented

#16810983

C₂

yes

maximal, characteristic, complemented

#16810965

C₂

yes

maximal, complemented

#16810948

C₂

yes

maximal

#16810931

C₂

yes

maximal, complemented

#16810924

C₂

yes

maximal, complemented

C₅₃×#432

C₂

yes

maximal, characteristic, complemented

#13133217

C₂²

yes

characteristic

#13133217

C₂²

yes

characteristic

#13133211

—

#13133209

C₂²

yes

characteristic

#13133209

C₂²

yes

—

#13133205

C₂²

yes

—

—

—

C₂²

yes

characteristic

#13133191

C₂²

yes

characteristic

C₄×Dic₁₀₆

—

C₄×Dic₁₀₆

—

C₄×Dic₁₀₆

C₂²

yes

characteristic

C₄×D₂₁₂

C₂²

yes

characteristic

C₄×C₂²⋊D₅₃

—

#13133176

C₂²

yes

—

#13133174

—

#13133151

C₂²

yes

—

#13133151

C₂²

yes

—

#13133149

C₂²

yes

—

#13133149

C₂²

yes

—

#13133142

C₂²

yes

—

#13133142

C₂²

yes

—

#13133139

C₂²

yes

—

#13133139

C₂²

yes

—

C₂×C₄²×C₅₃

C₂²

yes

characteristic

C₄⋊C₈×C₅₃

C₂²

yes

—

C₂²⋊C₈×C₅₃

C₂²

yes

—

#97×C₅₃

C₂²

yes

characteristic

#97×C₅₃

C₂²

yes

characteristic

C₂²×C₄×C₅₃

D₄

yes

characteristic

C₂²×C₄×C₅₃

D₄

yes

characteristic

C₂²×C₄×C₅₃

C₂³

yes

characteristic

C₂×C₂²⋊D₅₃

—

C₂×D₂₁₂

C₂³

yes

characteristic

C₂×C₄×D₅₃

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

C₂³

yes

characteristic

C₂×C₈×C₅₃

C₂³

yes

—

C₂×C₈×C₅₃

C₂³

yes

—

C₄²×C₅₃

D₄

yes

characteristic

C₄²×C₅₃

D₄

yes

characteristic

C₄²×C₅₃

C₂³

yes

characteristic

C₄²×C₅₃

C₂³

yes

characteristic

C₂²⋊Dic₅₃

—

C₂²⋊Dic₅₃

—

—

—

—

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

C₂³

yes

—

C₄⋊Dic₅₃

C₂³

yes

—

C₄⋊Dic₅₃

C₂³

yes

characteristic

C₄⋊Dic₅₃

C₂³

yes

—

—

—

—

—

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₂³×C₅₃

C₂×D₄

yes

characteristic

C₂²×D₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂⁴

yes

characteristic

C₂²⋊D₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

C₄×D₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

100

C₈×C₅₃

—

101

C₈×C₅₃

—

102

C₂²×C₅₃

—

103

C₂²×C₅₃

—

104

C₂²×C₅₃

—

105

C₂²×C₅₃

C₂²×D₄

yes

characteristic

106

C₂×D₅₃

—

107

C₂×D₅₃

—

108

C₂×D₅₃

—

109

C₄×C₅₃

—

110

C₄×C₅₃

—

111

C₄×C₅₃

—

112

C₄×C₅₃

—

113

C₄×C₅₃

—

114

C₄×C₅₃

2₋¹⁺⁴

yes

—

115

Dic₅₃

—

116

Dic₅₃

—

117

Dic₅₃

—

118

Dic₅₃

—

119

Dic₅₃

—

120

#3240

—

maximal, Sylow

121

C₂×C₅₃

—

122

C₂×C₅₃

#536

yes

characteristic

123

C₂×C₅₃

#575

yes

characteristic

124

C₂×C₅₃

#575

yes

characteristic

125

D₅₃

—

126

#533

—

127

#529

—

128

#501

—

129

#501

—

130

#489

—

131

#489

—

132

#485

—

133

#482

—

134

#479

—

135

#478

—

136

#432

D₅₃

yes

characteristic, complemented

137

C₅₃

#3240

yes

characteristic, complemented, Sylow

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

#126

—

106

—

141

#125

—

142

#125

—

143

#124

—

144

#123

—

106

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

106

—

147

C₂²⋊Q₈

—

106

—

148

#121

—

149

C₄×Q₈

—

150

C₄×Q₈

—

106

—

151

C₄×Q₈

—

106

—

152

C₄×D₄

—

153

C₄×D₄

—

106

—

154

#117

—

155

#117

—

106

—

156

C₂×C₄²

C₂×D₅₃

yes

characteristic

157

#107

—

158

#107

—

159

#106

—

160

#106

—

161

C₄⋊C₈

C₂×D₅₃

yes

—

162

#103

—

163

#103

—

164

#102

—

165

#102

—

166

C₂²⋊C₈

C₂×D₅₃

yes

—

167

#97

C₂×D₅₃

yes

characteristic

168

#97

C₂×D₅₃

yes

characteristic

169

C₂×Q₈

—

170

C₂×Q₈

—

106

—

171

C₂×Q₈

—

106

—

172

C₂×D₄

—

173

C₂×D₄

—

106

—

174

C₂²×C₄

—

106

—

175

C₂²×C₄

D₂₁₂

yes

characteristic

176

C₂²×C₄

D₂₁₂

yes

characteristic

177

C₂²×C₄

C₂²×D₅₃

yes

characteristic

178

C₂×C₈

C₂²×D₅₃

yes

—

179

C₂×C₈

C₂²×D₅₃

yes

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

106

—

185

C₄⋊C₄

—

106

—

186

C₄⋊C₄

—

106

—

187

C₄⋊C₄

—

106

—

188

C₄⋊C₄

—

106

—

189

C₄⋊C₄

—

106

—

190

C₄⋊C₄

—

106

—

191

C₄⋊C₄

—

106

—

192

C₂²⋊C₄

—

106

—

193

C₂²⋊C₄

—

106

—

194

C₂²⋊C₄

—

106

—

195

C₂²⋊C₄

—

106

—

196

C₂²⋊C₄

—

106

—

197

C₂²⋊C₄

—

106

—

198

C₄²

—

106

—

199

C₄²

—

106

—

200

C₄²

D₂₁₂

yes

characteristic

201

C₄²

D₂₁₂

yes

characteristic

202

C₄²

C₂²×D₅₃

yes

characteristic

203

C₄²

C₂²×D₅₃

yes

characteristic

204

C₂³

—

106

—

205

C₂³

C₂×D₂₁₂

yes

characteristic

206

Q₈

—

106

—

207

Q₈

—

212

—

208

Q₈

—

212

—

209

D₄

—

106

—

210

D₄

—

212

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

106

—

215

C₂×C₄

—

106

—

216

C₂×C₄

—

106

—

217

C₂×C₄

—

106

—

218

C₂×C₄

—

106

—

219

C₂×C₄

—

212

—

220

C₂×C₄

C₂×D₂₁₂

yes

characteristic

221

C₂×C₄

C₂×D₂₁₂

yes

characteristic

222

C₂×C₄

C₂×D₂₁₂

yes

characteristic

223

C₂×C₄

C₂×D₂₁₂

yes

characteristic

224

C₂×C₄

C₂×D₂₁₂

yes

characteristic

225

C₂×C₄

C₂³×D₅₃

yes

characteristic

226

C₈

—

227

C₈

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

212

—

232

C₂²

—

212

—

233

C₂²

—

212

—

234

C₂²

C₂²×D₂₁₂

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

212

—

241

C₄

—

212

—

242

C₄

—

212

—

243

C₄

—

212

—

244

C₄

—

212

—

245

C₄

#13133264

yes

—

246

C₂

—

247

C₂

—

424

—

248

C₂

#16811199

yes

characteristic

249

C₂

#16811423

yes

characteristic

250

C₂

#16811423

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₁₂
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#432	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#432	D₅₃
hypocenter	C₅₃	#3240
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₂²×D₂₁₂

commutator

C₂×C₄×C₅₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₃

Fitting

C₅₃×#432

C₂

socle

C₂²×C₅₃

C₂²×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
1. #16811180	C₂	semidirect
3. #16811032	C₂	semidirect
4. #16811032	C₂	semidirect
5. #16810983	C₂	semidirect
6. #16810983	C₂	semidirect
7. #16810965	C₂	semidirect
9. #16810931	C₂	semidirect
10. #16810924	C₂	semidirect
11. C₅₃×#432	C₂	semidirect
136. #432	D₅₃	semidirect
137. C₅₃	#3240	semidirect

H ≅ G/N

type

1. #16811180

C₂

semidirect

3. #16811032

C₂

semidirect

4. #16811032

C₂

semidirect

5. #16810983

C₂

semidirect

6. #16810983

C₂

semidirect

7. #16810965

C₂

semidirect

9. #16810931

C₂

semidirect

10. #16810924

C₂

semidirect

11. C₅₃×#432

C₂

semidirect

136. #432

D₅₃

semidirect

137. C₅₃

#3240

semidirect

Subgroups — #20285957

Conjugacy classes of subgroups

Complements