Group #20287360 — subgroups

Subgroups — #20287360

Order 6784.

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

normal subgroups only

This group has 350 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	#16811333	C₂	1	1	yes	maximal, characteristic, complemented
2	#16810977	C₂	1	2	yes	maximal, complemented
3	#16810973	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810930	C₂	1	2	yes	maximal, complemented
5	#16810913	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810835	C₂	1	2	yes	maximal
7	#16810825	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×#88322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11719924	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×#11719924	C₂²	1	2	yes	—
13	C₂×#11719922	C₂²	1	1	yes	characteristic
14	#13133217	C₂²	1	1	yes	characteristic
15	#13133209	C₂²	1	2	yes	—
16	#13133195	—	2	2	no	—
17	#13133193	—	2	1	no	—
18	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
19	C₄×D₂₁₂	C₂²	1	2	yes	—
20	C₄⋊C₄×D₅₃	—	2	1	no	—
21	#13133150	C₂²	1	1	yes	characteristic
22	#13133148	C₂²	1	2	yes	—
23	C₄⋊#88322	C₂²	1	1	yes	characteristic
24	C₄⋊#88322	C₂²	1	2	yes	—
25	#13133141	C₂²	1	2	yes	—
26	#13133141	C₂²	1	2	yes	—
27	#13133141	C₂²	1	2	yes	—
28	#13133138	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×C₄×D₅₃	—	2	2	no	—
48	C₂×Dic₁₀₆	—	2	1	no	—
49	C₄⋊C₄×C₅₃	—	2	1	no	—
50	C₄⋊C₄×C₅₃	—	2	2	no	—
51	C₄⋊C₄×C₅₃	—	2	1	no	—
52	C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₅₃	D₄	1	2	yes	—
54	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
55	C₂²⋊C₄×C₅₃	—	2	2	no	—
56	C₂²⋊C₄×C₅₃	—	2	1	no	—
57	C₂²⋊C₄×C₅₃	—	2	2	no	—
58	C₄²×C₅₃	—	2	2	no	—
59	C₄²×C₅₃	C₂³	1	1	yes	characteristic
60	C₄²×C₅₃	C₂³	1	2	yes	—
61	#11719924	—	2	4	no	—
62	#11719922	—	2	2	no	—
63	#11719921	—	2	2	no	—
64	#11719921	—	2	1	no	—
65	C₄⋊Dic₅₃	—	2	1	no	—
66	C₄⋊Dic₅₃	C₂³	1	2	yes	—
67	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
68	#11719919	—	2	2	no	—
69	#11719919	—	2	2	no	—
70	C₂×#88322	C₂³	1	1	yes	characteristic
71	C₂×#88322	C₂³	1	2	yes	—
72	C₂×#88322	C₂³	1	1	yes	characteristic
73	C₂³×C₅₃	—	2	1	no	—
74	C₂²×D₅₃	—	2	1	no	—
75	Q₈×C₅₃	—	2	2	no	—
76	Q₈×C₅₃	—	2	2	no	—
77	Q₈×C₅₃	—	2	2	no	—
78	D₄×C₅₃	—	2	1	no	—
79	D₄×C₅₃	—	2	1	no	—
80	C₂×C₄×C₅₃	—	2	1	no	—
81	C₂×C₄×C₅₃	—	2	2	no	—
82	C₂×C₄×C₅₃	—	4	2	no	—
83	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
86	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₅₃	—	2	2	no	—
89	C₂×Dic₅₃	—	2	1	no	—
90	D₂₁₂	—	2	1	no	—
91	D₂₁₂	#41	1	2	yes	—
92	C₄×D₅₃	—	4	2	no	—
93	C₄×D₅₃	—	8	2	no	—
94	Dic₁₀₆	—	8	1	no	—
95	#88322	—	2	1	no	—
96	#88322	—	2	2	no	—
97	#88322	—	2	1	no	—
98	C₂²×C₅₃	—	4	1	no	—
99	C₂²×C₅₃	—	4	1	no	—
100	C₂²×C₅₃	—	4	1	no	—
101	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₅₃	—	2	2	no	—
103	C₂×D₅₃	—	4	1	no	—
104	C₂×D₅₃	—	4	1	no	—
105	C₄×C₅₃	—	2	2	no	—
106	C₄×C₅₃	—	2	1	no	—
107	C₄×C₅₃	—	2	2	no	—
108	C₄×C₅₃	—	4	2	no	—
109	C₄×C₅₃	—	4	1	no	—
110	C₄×C₅₃	#135	1	2	yes	—
111	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
112	C₄×C₅₃	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₅₃	—	4	1	no	—
114	Dic₅₃	—	4	2	no	—
115	#3360	—	53	1	no	maximal, Sylow
116	C₂×C₅₃	—	8	1	no	—
117	C₂×C₅₃	#548	1	1	yes	characteristic
118	C₂×C₅₃	C₂×#135	1	1	yes	characteristic
119	C₂×C₅₃	#577	1	1	yes	characteristic
120	D₅₃	—	4	2	no	—
121	#556	D₅₃	1	1	yes	characteristic, complemented
122	#554	—	53	1	no	—
123	#488	—	53	2	no	—
124	#487	—	53	1	no	—
125	#479	—	53	2	no	—
126	#476	—	53	1	no	—
127	#463	—	53	2	no	—
128	#461	—	53	1	no	—
129	C₈×Q₈	—	53	1	no	—
130	C₄×SD₁₆	—	53	2	no	—
131	C₄×D₈	—	53	1	no	—
132	C₅₃	#3360	1	1	yes	characteristic, complemented, Sylow
133	C₂×SD₁₆	—	53	2	no	—
134	C₂×D₈	—	53	1	no	—
135	C₄⋊Q₈	—	53	1	no	—
136	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
137	#126	—	2	2	no	—
138	#125	—	53	2	no	—
139	#124	C₂×D₅₃	1	2	yes	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	106	1	no	—
142	C₂²⋊Q₈	—	106	2	no	—
143	C₄×Q₈	C₂×D₅₃	1	2	yes	—
144	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
145	C₄×D₄	—	53	1	no	—
146	C₄×D₄	—	53	2	no	—
147	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	106	1	no	—
150	#107	—	53	1	no	—
151	#106	—	53	2	no	—
152	C₄⋊C₈	—	53	1	no	—
153	C₄⋊C₈	—	53	2	no	—
154	#103	—	53	2	no	—
155	#103	—	53	2	no	—
156	#103	—	53	2	no	—
157	#102	—	53	1	no	—
158	#102	—	53	2	no	—
159	#102	—	53	1	no	—
160	C₄×C₈	—	53	1	no	—
161	C₄×C₈	—	53	2	no	—
162	C₂×Q₈	—	106	1	no	—
163	C₂×Q₈	C₂²⋊D₅₃	1	1	yes	characteristic
164	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
165	C₂×D₄	—	53	1	no	—
166	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	106	2	no	—
169	C₂²×C₄	—	106	1	no	—
170	SD₁₆	—	106	4	no	—
171	D₈	—	106	2	no	—
172	C₂×C₈	—	53	1	no	—
173	C₂×C₈	—	53	2	no	—
174	C₂×C₈	—	53	1	no	—
175	C₄⋊C₄	—	2	1	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	—	53	2	no	—
179	C₄⋊C₄	—	53	1	no	—
180	C₄⋊C₄	—	106	2	no	—
181	C₄⋊C₄	—	106	1	no	—
182	C₄⋊C₄	—	106	2	no	—
183	C₄⋊C₄	C₂²⋊D₅₃	1	1	yes	characteristic
184	C₄⋊C₄	C₂²⋊D₅₃	1	2	yes	—
185	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	2	no	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	2	2	no	—
189	C₂²⋊C₄	—	106	1	no	—
190	C₂²⋊C₄	—	106	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	C₂²×D₅₃	1	1	yes	characteristic
193	C₄²	C₂²×D₅₃	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	106	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	2	2	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	424	1	no	—
200	D₄	—	2	1	no	—
201	D₄	—	2	1	no	—
202	D₄	—	53	2	no	—
203	D₄	—	106	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	106	1	no	—
208	C₂×C₄	—	106	2	no	—
209	C₂×C₄	—	424	2	no	—
210	C₂×C₄	—	212	2	no	—
211	C₂×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
212	C₂×C₄	C₂×C₂²⋊D₅₃	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
216	C₈	—	106	1	no	—
217	C₈	—	106	2	no	—
218	C₈	—	106	1	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	106	2	no	—
223	C₂²	—	212	1	no	—
224	C₂²	—	212	1	no	—
225	C₂²	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	212	1	no	—
232	C₄	—	212	2	no	—
233	C₄	#13133237	1	2	yes	—
234	C₄	#41×D₅₃	1	1	yes	characteristic
235	C₄	#13133264	1	1	yes	characteristic
236	C₂	—	8	1	no	—
237	C₂	—	212	2	no	—
238	C₂	#16811280	1	1	yes	characteristic
239	C₂	C₂×#13133237	1	1	yes	characteristic
240	C₂	#16811431	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811333

C₂

yes

maximal, characteristic, complemented

#16810977

C₂

yes

maximal, complemented

#16810973

C₂

yes

maximal, characteristic, complemented

#16810930

C₂

yes

maximal, complemented

#16810913

C₂

yes

maximal, characteristic, complemented

#16810835

C₂

yes

maximal

#16810825

C₂

yes

maximal, characteristic, complemented

Q₈×#88322

C₂

yes

maximal, characteristic, complemented

C₄×#11719924

C₂

yes

maximal, complemented

C₄×#11719922

C₂

yes

maximal, characteristic

C₅₃×#556

C₂

yes

maximal, characteristic, complemented

C₂×#11719924

C₂²

yes

—

C₂×#11719922

C₂²

yes

characteristic

#13133217

C₂²

yes

characteristic

#13133209

C₂²

yes

—

#13133195

—

#13133193

—

C₄×D₂₁₂

C₂²

yes

characteristic

C₄×D₂₁₂

C₂²

yes

—

C₄⋊C₄×D₅₃

—

#13133150

C₂²

yes

characteristic

#13133148

C₂²

yes

—

C₄⋊#88322

C₂²

yes

characteristic

C₄⋊#88322

C₂²

yes

—

#13133141

C₂²

yes

—

#13133141

C₂²

yes

—

#13133141

C₂²

yes

—

#13133138

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×C₄×D₅₃

—

C₂×Dic₁₀₆

—

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

C₂³

yes

—

C₄⋊Dic₅₃

C₂³

yes

—

—

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

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂⁴

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

#41

yes

—

C₄×D₅₃

—

C₄×D₅₃

—

Dic₁₀₆

—

#88322

—

#88322

—

#88322

—

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

—

101

C₂²×C₅₃

C₂²×D₄

yes

characteristic

102

C₂×D₅₃

—

103

C₂×D₅₃

—

104

C₂×D₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

—

107

C₄×C₅₃

—

108

C₄×C₅₃

—

109

C₄×C₅₃

—

110

C₄×C₅₃

#135

yes

—

111

C₄×C₅₃

C₂×#41

yes

characteristic

112

C₄×C₅₃

2₋¹⁺⁴

yes

characteristic

113

Dic₅₃

—

114

Dic₅₃

—

115

#3360

—

maximal, Sylow

116

C₂×C₅₃

—

117

C₂×C₅₃

#548

yes

characteristic

118

C₂×C₅₃

C₂×#135

yes

characteristic

119

C₂×C₅₃

#577

yes

characteristic

120

D₅₃

—

121

#556

D₅₃

yes

characteristic, complemented

122

#554

—

123

#488

—

124

#487

—

125

#479

—

126

#476

—

127

#463

—

128

#461

—

129

C₈×Q₈

—

130

C₄×SD₁₆

—

131

C₄×D₈

—

132

C₅₃

#3360

yes

characteristic, complemented, Sylow

133

C₂×SD₁₆

—

134

C₂×D₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×D₅₃

yes

characteristic

137

#126

—

138

#125

—

139

#124

C₂×D₅₃

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

106

—

142

C₂²⋊Q₈

—

106

—

143

C₄×Q₈

C₂×D₅₃

yes

—

144

C₄×Q₈

C₂×D₅₃

yes

characteristic

145

C₄×D₄

—

146

C₄×D₄

—

147

C₄×D₄

C₂×D₅₃

yes

characteristic

148

#117

—

149

C₂×C₄⋊C₄

—

106

—

150

#107

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

#102

—

158

#102

—

159

#102

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×Q₈

—

106

—

163

C₂×Q₈

C₂²⋊D₅₃

yes

characteristic

164

C₂×Q₈

C₂²×D₅₃

yes

—

165

C₂×D₄

—

166

C₂×D₄

C₂²×D₅₃

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

106

—

169

C₂²×C₄

—

106

—

170

SD₁₆

—

106

—

171

D₈

—

106

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

106

—

181

C₄⋊C₄

—

106

—

182

C₄⋊C₄

—

106

—

183

C₄⋊C₄

C₂²⋊D₅₃

yes

characteristic

184

C₄⋊C₄

C₂²⋊D₅₃

yes

—

185

C₄⋊C₄

C₂²×D₅₃

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

106

—

190

C₂²⋊C₄

—

106

—

191

C₄²

—

192

C₄²

C₂²×D₅₃

yes

characteristic

193

C₄²

C₂²×D₅₃

yes

—

194

C₂³

—

195

C₂³

—

106

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

Q₈

—

424

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

106

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

106

—

208

C₂×C₄

—

106

—

209

C₂×C₄

—

424

—

210

C₂×C₄

—

212

—

211

C₂×C₄

C₂×C₂²⋊D₅₃

yes

—

212

C₂×C₄

C₂×C₂²⋊D₅₃

yes

—

213

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

215

C₂×C₄

C₂³×D₅₃

yes

characteristic

216

C₈

—

106

—

217

C₈

—

106

—

218

C₈

—

106

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

106

—

223

C₂²

—

212

—

224

C₂²

—

212

—

225

C₂²

C₂²×C₂²⋊D₅₃

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

212

—

232

C₄

—

212

—

233

C₄

#13133237

yes

—

234

C₄

#41×D₅₃

yes

characteristic

235

C₄

#13133264

yes

characteristic

236

C₂

—

237

C₂

—

212

—

238

C₂

#16811280

yes

characteristic

239

C₂

C₂×#13133237

yes

characteristic

240

C₂

#16811431

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	#3360
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. #16811333	C₂	semidirect
2. #16810977	C₂	semidirect
3. #16810973	C₂	semidirect
4. #16810930	C₂	semidirect
5. #16810913	C₂	semidirect
7. #16810825	C₂	semidirect
8. Q₈×#88322	C₂	semidirect
9. C₄×#11719924	C₂	semidirect
11. C₅₃×#556	C₂	semidirect
121. #556	D₅₃	semidirect
132. C₅₃	#3360	semidirect

H ≅ G/N

type

1. #16811333

C₂

semidirect

2. #16810977

C₂

semidirect

3. #16810973

C₂

semidirect

4. #16810930

C₂

semidirect

5. #16810913

C₂

semidirect

7. #16810825

C₂

semidirect

8. Q₈×#88322

C₂

semidirect

9. C₄×#11719924

C₂

semidirect

11. C₅₃×#556

C₂

semidirect

121. #556

D₅₃

semidirect

132. C₅₃

#3360

semidirect

Subgroups — #20287360

Conjugacy classes of subgroups

Complements