Group #20287699 — subgroups

Subgroups — #20287699

Order 6784.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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	#16811346	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811005	C₂	1	2	yes	maximal
3	#16811002	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810845	C₂	1	2	yes	maximal, complemented
5	#16810842	C₂	1	2	yes	maximal, complemented
6	#16810828	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810825	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×#88322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11719925	C₂	1	2	yes	maximal, complemented
10	C₄×#11719922	C₂	1	1	yes	maximal, characteristic
11	C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719925	C₂²	1	2	yes	—
13	C₂×#11719925	C₂²	1	2	yes	—
14	C₂×#11719923	C₂²	1	2	yes	—
15	C₂×#11719924	C₂²	1	2	yes	—
16	C₂×#11719922	C₂²	1	1	yes	characteristic
17	#13133217	C₂²	1	1	yes	characteristic
18	#13133212	—	2	2	no	—
19	#13133205	C₂²	1	2	yes	—
20	#13133193	—	2	1	no	—
21	C₄×Dic₁₀₆	C₂²	1	2	yes	—
22	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
23	#13133175	—	2	1	no	—
24	#13133150	C₂²	1	1	yes	characteristic
25	C₄⋊#88322	C₂²	1	1	yes	characteristic
26	C₄⋊#88322	C₂²	1	2	yes	—
27	#13133141	C₂²	1	2	yes	—
28	#13133140	C₂²	1	2	yes	—
29	#13133138	C₂²	1	1	yes	characteristic
30	#13133137	C₂²	1	1	yes	characteristic
31	C₄×#88322	C₂²	1	1	yes	characteristic
32	C₄×#88322	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
34	#126×C₅₃	—	2	2	no	—
35	#124×C₅₃	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₅₃	—	2	1	no	—
37	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₅₃	C₂²	1	2	yes	—
39	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	#117×C₅₃	—	2	1	no	—
41	C₂×Q₈×C₅₃	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
43	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₅₃	—	2	1	no	—
45	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
46	C₂×C₄×D₅₃	—	2	1	no	—
47	C₂×Dic₁₀₆	C₂³	1	2	yes	—
48	C₄⋊C₄×C₅₃	—	2	1	no	—
49	C₄⋊C₄×C₅₃	—	2	2	no	—
50	C₄⋊C₄×C₅₃	—	2	1	no	—
51	C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
52	C₄⋊C₄×C₅₃	D₄	1	2	yes	—
53	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
54	C₂²⋊C₄×C₅₃	—	2	2	no	—
55	C₂²⋊C₄×C₅₃	—	2	1	no	—
56	C₂²⋊C₄×C₅₃	—	2	2	no	—
57	C₄²×C₅₃	—	2	2	no	—
58	C₄²×C₅₃	C₂³	1	1	yes	characteristic
59	C₄²×C₅₃	C₂³	1	2	yes	—
60	#11719925	—	2	4	no	—
61	#11719925	—	4	2	no	—
62	#11719924	—	4	2	no	—
63	#11719923	—	4	2	no	—
64	#11719922	—	2	2	no	—
65	#11719921	—	2	2	no	—
66	#11719921	—	2	1	no	—
67	#11719921	—	2	2	no	—
68	C₄⋊Dic₅₃	—	2	1	no	—
69	C₄⋊Dic₅₃	—	2	1	no	—
70	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
71	#11719919	—	2	2	no	—
72	C₄×Dic₅₃	—	2	2	no	—
73	C₂×#88322	C₂³	1	1	yes	characteristic
74	C₂×#88322	C₂³	1	2	yes	—
75	C₂×#88322	C₂³	1	1	yes	characteristic
76	C₂³×C₅₃	—	2	1	no	—
77	C₂²×D₅₃	—	2	1	no	—
78	Q₈×C₅₃	—	2	2	no	—
79	Q₈×C₅₃	—	2	2	no	—
80	Q₈×C₅₃	—	2	2	no	—
81	D₄×C₅₃	—	2	1	no	—
82	D₄×C₅₃	—	2	1	no	—
83	C₂×C₄×C₅₃	—	2	1	no	—
84	C₂×C₄×C₅₃	—	2	2	no	—
85	C₂×C₄×C₅₃	—	4	2	no	—
86	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
87	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₅₃	—	2	2	no	—
92	C₂×Dic₅₃	—	2	1	no	—
93	D₂₁₂	—	2	1	no	—
94	D₂₁₂	—	2	1	no	—
95	C₄×D₅₃	—	4	2	no	—
96	Dic₁₀₆	—	2	2	no	—
97	Dic₁₀₆	—	2	2	no	—
98	#88322	—	2	2	no	—
99	#88322	—	2	1	no	—
100	#88322	#41	1	2	yes	—
101	C₂²×C₅₃	—	4	1	no	—
102	C₂²×C₅₃	—	4	1	no	—
103	C₂²×C₅₃	—	4	1	no	—
104	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₅₃	—	4	1	no	—
106	C₂×D₅₃	—	4	1	no	—
107	C₂×D₅₃	—	4	1	no	—
108	C₄×C₅₃	—	2	2	no	—
109	C₄×C₅₃	—	2	2	no	—
110	C₄×C₅₃	—	2	1	no	—
111	C₄×C₅₃	—	4	2	no	—
112	C₄×C₅₃	—	4	1	no	—
113	C₄×C₅₃	#135	1	2	yes	—
114	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
115	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
116	Dic₅₃	—	4	2	no	—
117	Dic₅₃	—	4	1	no	—
118	#3393	—	53	1	no	maximal, Sylow
119	C₂×C₅₃	—	8	1	no	—
120	C₂×C₅₃	#550	1	1	yes	characteristic
121	C₂×C₅₃	C₂×#135	1	1	yes	characteristic
122	C₂×C₅₃	#578	1	1	yes	characteristic
123	D₅₃	—	8	1	no	—
124	#556	—	53	1	no	—
125	#556	D₅₃	1	1	yes	characteristic, complemented
126	#495	—	53	2	no	—
127	#494	—	53	1	no	—
128	#464	—	53	2	no	—
129	#464	—	53	2	no	—
130	#461	—	53	1	no	—
131	#461	—	53	1	no	—
132	C₈×Q₈	—	53	1	no	—
133	C₄×Q₁₆	—	53	2	no	—
134	C₄×D₈	—	53	1	no	—
135	C₅₃	#3393	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	53	2	no	—
137	C₂×Q₁₆	—	53	2	no	—
138	C₂×SD₁₆	—	53	2	no	—
139	C₂×SD₁₆	—	53	2	no	—
140	C₂×D₈	—	53	1	no	—
141	C₄⋊Q₈	—	53	1	no	—
142	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
143	#126	—	2	2	no	—
144	#126	—	106	2	no	—
145	#124	—	53	2	no	—
146	#124	C₂×D₅₃	1	2	yes	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₂²⋊Q₈	—	106	1	no	—
149	C₄×Q₈	—	53	2	no	—
150	C₄×Q₈	C₂×D₅₃	1	2	yes	—
151	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
152	C₄×D₄	—	53	1	no	—
153	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
154	#117	—	2	1	no	—
155	#117	—	106	1	no	—
156	#107	—	53	1	no	—
157	C₄⋊C₈	—	53	1	no	—
158	C₄⋊C₈	—	53	2	no	—
159	#103	—	53	2	no	—
160	#103	—	53	2	no	—
161	#102	—	53	1	no	—
162	#102	—	53	1	no	—
163	C₄×C₈	—	53	1	no	—
164	C₄×C₈	—	53	2	no	—
165	C₂×Q₈	—	53	2	no	—
166	C₂×Q₈	C₂²⋊D₅₃	1	1	yes	characteristic
167	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
168	C₂×D₄	—	53	1	no	—
169	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	106	1	no	—
172	Q₁₆	—	106	4	no	—
173	Q₁₆	—	212	2	no	—
174	SD₁₆	—	212	2	no	—
175	SD₁₆	—	212	2	no	—
176	D₈	—	106	2	no	—
177	C₂×C₈	—	53	1	no	—
178	C₂×C₈	—	53	1	no	—
179	C₂×C₈	—	53	2	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	53	1	no	—
184	C₄⋊C₄	—	106	1	no	—
185	C₄⋊C₄	—	106	2	no	—
186	C₄⋊C₄	—	106	1	no	—
187	C₄⋊C₄	C₂²⋊D₅₃	1	1	yes	characteristic
188	C₄⋊C₄	C₂²⋊D₅₃	1	2	yes	—
189	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	1	no	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	106	2	no	—
194	C₂²⋊C₄	—	106	1	no	—
195	C₂²⋊C₄	—	106	2	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	106	2	no	—
198	C₄²	C₂²×D₅₃	1	1	yes	characteristic
199	C₄²	C₂²×D₅₃	1	2	yes	—
200	C₂³	—	2	1	no	—
201	C₂³	—	106	1	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	2	2	no	—
204	Q₈	—	2	2	no	—
205	Q₈	—	106	2	no	—
206	Q₈	—	106	2	no	—
207	D₄	—	2	1	no	—
208	D₄	—	2	1	no	—
209	D₄	—	106	1	no	—
210	D₄	—	106	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	106	1	no	—
215	C₂×C₄	—	106	2	no	—
216	C₂×C₄	—	212	2	no	—
217	C₂×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
220	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
221	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
222	C₈	—	53	2	no	—
223	C₈	—	106	2	no	—
224	C₈	—	106	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	212	1	no	—
229	C₂²	—	212	1	no	—
230	C₂²	—	212	1	no	—
231	C₂²	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	2	no	—
236	C₄	—	4	1	no	—
237	C₄	—	212	2	no	—
238	C₄	—	212	1	no	—
239	C₄	#13133237	1	2	yes	—
240	C₄	#41×D₅₃	1	1	yes	characteristic
241	C₄	#13133263	1	1	yes	characteristic
242	C₂	—	8	1	no	—
243	C₂	—	424	1	no	—
244	C₂	#16811292	1	1	yes	characteristic
245	C₂	C₂×#13133237	1	1	yes	characteristic
246	C₂	#16811438	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811346

C₂

yes

maximal, characteristic, complemented

#16811005

C₂

yes

maximal

#16811002

C₂

yes

maximal, characteristic, complemented

#16810845

C₂

yes

maximal, complemented

#16810842

C₂

yes

maximal, complemented

#16810828

C₂

yes

maximal, characteristic, complemented

#16810825

C₂

yes

maximal, characteristic, complemented

Q₈×#88322

C₂

yes

maximal, characteristic, complemented

C₄×#11719925

C₂

yes

maximal, complemented

C₄×#11719922

C₂

yes

maximal, characteristic

C₅₃×#556

C₂

yes

maximal, characteristic, complemented

C₂×#11719925

C₂²

yes

—

C₂×#11719925

C₂²

yes

—

C₂×#11719923

C₂²

yes

—

C₂×#11719924

C₂²

yes

—

C₂×#11719922

C₂²

yes

characteristic

#13133217

C₂²

yes

characteristic

#13133212

—

#13133205

C₂²

yes

—

#13133193

—

C₄×Dic₁₀₆

C₂²

yes

—

C₄×D₂₁₂

C₂²

yes

characteristic

#13133175

—

#13133150

C₂²

yes

characteristic

C₄⋊#88322

C₂²

yes

characteristic

C₄⋊#88322

C₂²

yes

—

#13133141

C₂²

yes

—

#13133140

C₂²

yes

—

#13133138

C₂²

yes

characteristic

#13133137

C₂²

yes

characteristic

C₄×#88322

C₂²

yes

characteristic

C₄×#88322

C₂²

yes

—

C₄⋊Q₈×C₅₃

C₂²

yes

characteristic

#126×C₅₃

—

#124×C₅₃

C₂²

yes

—

C₂²⋊Q₈×C₅₃

—

C₄×Q₈×C₅₃

C₂²

yes

characteristic

C₄×Q₈×C₅₃

C₂²

yes

—

C₄×D₄×C₅₃

C₂²

yes

characteristic

#117×C₅₃

—

C₂×Q₈×C₅₃

D₄

yes

characteristic

C₂×Q₈×C₅₃

C₂³

yes

—

C₂×D₄×C₅₃

C₂³

yes

characteristic

C₂²×C₄×C₅₃

—

C₂×D₂₁₂

C₂³

yes

characteristic

C₂×C₄×D₅₃

—

C₂×Dic₁₀₆

C₂³

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

D₄

yes

characteristic

C₄⋊C₄×C₅₃

D₄

yes

—

C₄⋊C₄×C₅₃

C₂³

yes

characteristic

C₂²⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂³

yes

characteristic

C₄²×C₅₃

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

C₂³

yes

characteristic

#11719919

—

C₄×Dic₅₃

—

C₂×#88322

C₂³

yes

characteristic

C₂×#88322

C₂³

yes

—

C₂×#88322

C₂³

yes

characteristic

C₂³×C₅₃

—

C₂²×D₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×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

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

#88322

—

#88322

—

100

#88322

#41

yes

—

101

C₂²×C₅₃

—

102

C₂²×C₅₃

—

103

C₂²×C₅₃

—

104

C₂²×C₅₃

C₂²×D₄

yes

characteristic

105

C₂×D₅₃

—

106

C₂×D₅₃

—

107

C₂×D₅₃

—

108

C₄×C₅₃

—

109

C₄×C₅₃

—

110

C₄×C₅₃

—

111

C₄×C₅₃

—

112

C₄×C₅₃

—

113

C₄×C₅₃

#135

yes

—

114

C₄×C₅₃

C₂×#41

yes

characteristic

115

C₄×C₅₃

H(5,𝔽₂)

yes

characteristic

116

Dic₅₃

—

117

Dic₅₃

—

118

#3393

—

maximal, Sylow

119

C₂×C₅₃

—

120

C₂×C₅₃

#550

yes

characteristic

121

C₂×C₅₃

C₂×#135

yes

characteristic

122

C₂×C₅₃

#578

yes

characteristic

123

D₅₃

—

124

#556

—

125

#556

D₅₃

yes

characteristic, complemented

126

#495

—

127

#494

—

128

#464

—

129

#464

—

130

#461

—

131

#461

—

132

C₈×Q₈

—

133

C₄×Q₁₆

—

134

C₄×D₈

—

135

C₅₃

#3393

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×D₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

C₂×D₅₃

yes

characteristic

143

#126

—

144

#126

—

106

—

145

#124

—

146

#124

C₂×D₅₃

yes

—

147

C₂²⋊Q₈

—

148

C₂²⋊Q₈

—

106

—

149

C₄×Q₈

—

150

C₄×Q₈

C₂×D₅₃

yes

—

151

C₄×Q₈

C₂×D₅₃

yes

characteristic

152

C₄×D₄

—

153

C₄×D₄

C₂×D₅₃

yes

characteristic

154

#117

—

155

#117

—

106

—

156

#107

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#103

—

160

#103

—

161

#102

—

162

#102

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₂×Q₈

—

166

C₂×Q₈

C₂²⋊D₅₃

yes

characteristic

167

C₂×Q₈

C₂²×D₅₃

yes

—

168

C₂×D₄

—

169

C₂×D₄

C₂²×D₅₃

yes

characteristic

170

C₂²×C₄

—

171

C₂²×C₄

—

106

—

172

Q₁₆

—

106

—

173

Q₁₆

—

212

—

174

SD₁₆

—

212

—

175

SD₁₆

—

212

—

176

D₈

—

106

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

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

C₂²⋊D₅₃

yes

characteristic

188

C₄⋊C₄

C₂²⋊D₅₃

yes

—

189

C₄⋊C₄

C₂²×D₅₃

yes

characteristic

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

106

—

194

C₂²⋊C₄

—

106

—

195

C₂²⋊C₄

—

106

—

196

C₄²

—

197

C₄²

—

106

—

198

C₄²

C₂²×D₅₃

yes

characteristic

199

C₄²

C₂²×D₅₃

yes

—

200

C₂³

—

201

C₂³

—

106

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

106

—

206

Q₈

—

106

—

207

D₄

—

208

D₄

—

209

D₄

—

106

—

210

D₄

—

106

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

106

—

215

C₂×C₄

—

106

—

216

C₂×C₄

—

212

—

217

C₂×C₄

C₂×C₂²⋊D₅₃

yes

—

218

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

219

C₂×C₄

C₂×C₂²⋊D₅₃

yes

—

220

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

221

C₂×C₄

C₂³×D₅₃

yes

characteristic

222

C₈

—

223

C₈

—

106

—

224

C₈

—

106

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

212

—

229

C₂²

—

212

—

230

C₂²

—

212

—

231

C₂²

C₂²×C₂²⋊D₅₃

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

212

—

238

C₄

—

212

—

239

C₄

#13133237

yes

—

240

C₄

#41×D₅₃

yes

characteristic

241

C₄

#13133263

yes

characteristic

242

C₂

—

243

C₂

—

424

—

244

C₂

#16811292

yes

characteristic

245

C₂

C₂×#13133237

yes

characteristic

246

C₂

#16811438

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#556	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#556	D₅₃
hypocenter	C₅₃	#3393
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₃

commutator

C₂×C₄×C₅₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₃

Fitting

C₅₃×#556

C₂

socle

C₂²×C₅₃

C₂²×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #16811346	C₂	semidirect
3. #16811002	C₂	semidirect
4. #16810845	C₂	semidirect
5. #16810842	C₂	semidirect
6. #16810828	C₂	semidirect
7. #16810825	C₂	semidirect
8. Q₈×#88322	C₂	semidirect
9. C₄×#11719925	C₂	semidirect
11. C₅₃×#556	C₂	semidirect
125. #556	D₅₃	semidirect
135. C₅₃	#3393	semidirect

H ≅ G/N

type

1. #16811346

C₂

semidirect

3. #16811002

C₂

semidirect

4. #16810845

C₂

semidirect

5. #16810842

C₂

semidirect

6. #16810828

C₂

semidirect

7. #16810825

C₂

semidirect

8. Q₈×#88322

C₂

semidirect

9. C₄×#11719925

C₂

semidirect

11. C₅₃×#556

C₂

semidirect

125. #556

D₅₃

semidirect

135. C₅₃

#3393

semidirect

Subgroups — #20287699

Conjugacy classes of subgroups

Complements