Group #20291039 — subgroups

Subgroups — D₅₃⋊#361 #20291039

Order 6784.

256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 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	D₅₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₃⋊#108	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811541	C₂	1	4	yes	maximal, complemented
4	C₂×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
5	D₅₃⋊M₁₆	—	2	1	no	—
6	#13133292	C₂²	1	2	yes	complemented
7	#13133291	—	2	1	no	—
8	D₅₃⋊C₁₆	—	2	1	no	—
9	#13133288	—	2	1	no	—
10	#13133287	C₂²	1	2	yes	complemented
11	C₂×D₄×D₅₃	—	2	1	no	—
12	C₂×D₄₂₄	C₄	1	1	yes	characteristic
13	C₂×#11719922	—	2	1	no	—
14	D₈×D₅₃	—	2	1	no	—
15	D₈×D₅₃	—	2	1	no	—
16	D₈×D₅₃	C₄	1	2	yes	—
17	D₈×D₅₃	C₂²	1	2	yes	—
18	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
19	C₂×D₈×C₅₃	C₄	1	1	yes	characteristic
20	C₂³×D₅₃	—	4	1	no	—
21	C₂×D₄×C₅₃	—	2	1	no	—
22	C₂×C₂²⋊D₅₃	—	4	1	no	—
23	D₄×D₅₃	—	2	2	no	—
24	D₄×D₅₃	—	2	2	no	—
25	D₄×D₅₃	—	4	1	no	—
26	D₄×D₅₃	—	4	1	no	—
27	C₂×D₂₁₂	—	2	1	no	—
28	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
29	#11719940	—	4	1	no	—
30	#11719936	—	2	2	no	—
31	D₅₃⋊C₈	—	4	1	no	—
32	D₈×C₅₃	—	2	1	no	—
33	D₈×C₅₃	C₂×C₄	1	2	yes	—
34	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
35	#11719922	—	2	2	no	—
36	#11719922	—	2	2	no	—
37	C₂×#88322	D₄	1	1	yes	characteristic
38	D₄₂₄	—	2	1	no	—
39	D₄₂₄	C₂×C₄	1	2	yes	—
40	C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
41	C₈×D₅₃	D₄	1	1	yes	characteristic
42	C₈×D₅₃	D₄	1	1	yes	characteristic
43	C₈×D₅₃	C₂³	1	1	yes	characteristic
44	#11719910	—	2	2	no	—
45	C₂³×C₅₃	—	4	1	no	—
46	C₂²×D₅₃	—	4	1	no	—
47	C₂²×D₅₃	—	4	2	no	—
48	C₂²×D₅₃	—	4	2	no	—
49	C₂²×D₅₃	—	8	4	no	—
50	C₂²×D₅₃	SD₁₆	1	1	yes	characteristic
51	D₄×C₅₃	—	2	2	no	—
52	D₄×C₅₃	—	4	1	no	—
53	C₂×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²⋊D₅₃	—	4	2	no	—
55	C₂²⋊D₅₃	—	4	2	no	—
56	C₂×Dic₅₃	D₈	1	1	yes	characteristic
57	D₂₁₂	—	2	2	no	—
58	D₂₁₂	—	4	1	no	—
59	C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₄×D₅₃	D₈	1	1	yes	characteristic
61	C₄×D₅₃	SD₁₆	1	1	yes	characteristic
62	C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
63	#88324	—	4	2	no	—
64	C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
66	#88322	C₂²⋊C₄	1	1	yes	characteristic
67	#88322	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₅₃	—	4	2	no	—
69	C₂²×C₅₃	—	8	2	no	—
70	C₂²×C₅₃	#102	1	1	yes	characteristic
71	C₂×D₅₃	—	2	2	no	—
72	C₂×D₅₃	—	4	2	no	—
73	C₂×D₅₃	—	8	4	no	—
74	C₂×D₅₃	—	8	2	no	—
75	C₂×D₅₃	—	8	4	no	—
76	C₂×D₅₃	#102	1	1	yes	characteristic
77	C₂×D₅₃	C₂×SD₁₆	1	1	yes	characteristic
78	C₄×C₅₃	#102	1	1	yes	characteristic
79	C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	Dic₅₃	#102	1	1	yes	characteristic
81	Dic₅₃	C₂×D₈	1	1	yes	characteristic
82	C₂×#361	—	53	1	no	maximal, Sylow
83	C₂×C₅₃	—	2	1	no	—
84	C₂×C₅₃	—	8	2	no	—
85	C₂×C₅₃	C₂×#102	1	1	yes	characteristic
86	D₅₃	—	2	1	no	—
87	D₅₃	—	8	2	no	—
88	D₅₃	#361	1	2	yes	complemented
89	C₂²×D₈	—	53	1	no	—
90	C₂×M₃₂	—	53	1	no	—
91	C₂×#108	—	53	1	no	—
92	#361	—	53	4	no	—
93	C₅₃	C₂×#361	1	1	yes	characteristic, complemented, Sylow
94	C₂²×D₄	—	106	1	no	—
95	C₂×D₈	—	53	2	no	—
96	C₂×D₈	—	53	2	no	—
97	C₂×D₈	—	53	1	no	—
98	C₂×D₈	—	106	1	no	—
99	C₂×D₈	—	106	1	no	—
100	C₂×D₈	—	106	1	no	—
101	C₂×D₈	#6157	1	1	yes	characteristic
102	C₂×M₁₆	—	106	1	no	—
103	C₂²×C₈	—	53	1	no	—
104	M₃₂	—	53	2	no	—
105	M₃₂	—	106	1	no	—
106	C₂×C₁₆	—	106	1	no	—
107	#108	—	53	2	no	—
108	#108	—	106	1	no	—
109	C₂⁴	—	212	1	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	—	106	2	no	—
112	C₂×D₄	—	106	2	no	—
113	C₂×D₄	—	106	1	no	—
114	C₂×D₄	—	212	1	no	—
115	C₂×D₄	—	212	1	no	—
116	C₂×D₄	—	212	1	no	—
117	C₂²×C₄	—	53	1	no	—
118	D₈	—	2	1	no	—
119	D₈	—	53	2	no	—
120	D₈	—	106	2	no	—
121	D₈	—	106	2	no	—
122	D₈	—	106	1	no	—
123	D₈	C₂×#6157	1	2	yes	—
124	M₁₆	—	106	2	no	—
125	M₁₆	—	212	1	no	—
126	C₂×C₈	—	53	1	no	—
127	C₂×C₈	—	53	1	no	—
128	C₂×C₈	—	53	1	no	—
129	C₂×C₈	—	53	1	no	—
130	C₂×C₈	—	53	1	no	—
131	C₂×C₈	—	212	1	no	—
132	C₂×C₈	C₂×#6157	1	1	yes	characteristic
133	C₁₆	—	106	2	no	—
134	C₂³	—	4	1	no	—
135	C₂³	—	53	1	no	—
136	C₂³	—	424	4	no	—
137	C₂³	—	212	2	no	—
138	C₂³	—	212	2	no	—
139	C₂³	—	212	1	no	—
140	D₄	—	2	2	no	—
141	D₄	—	4	1	no	—
142	D₄	—	106	2	no	—
143	D₄	—	212	2	no	—
144	D₄	—	212	2	no	—
145	D₄	—	212	1	no	—
146	C₂×C₄	—	53	1	no	—
147	C₂×C₄	—	53	1	no	—
148	C₂×C₄	—	53	1	no	—
149	C₂×C₄	—	53	1	no	—
150	C₂×C₄	—	53	1	no	—
151	C₂×C₄	C₂²⋊#6157	1	1	yes	characteristic
152	C₈	—	53	1	no	—
153	C₈	—	53	1	no	—
154	C₈	—	212	2	no	—
155	C₈	C₂²⋊#6157	1	1	yes	characteristic
156	C₈	C₂²×#6157	1	1	yes	characteristic
157	C₂²	—	4	2	no	—
158	C₂²	—	8	2	no	—
159	C₂²	—	53	1	no	—
160	C₂²	—	53	1	no	—
161	C₂²	—	106	2	no	—
162	C₂²	—	424	2	no	—
163	C₂²	—	424	4	no	—
164	C₂²	—	424	4	no	—
165	C₂²	—	212	2	no	—
166	C₂²	#13133279	1	1	yes	characteristic
167	C₄	—	53	1	no	—
168	C₄	—	53	1	no	—
169	C₄	#13133279	1	1	yes	characteristic
170	C₄	C₂×C₂²⋊#6157	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	8	2	no	—
173	C₂	—	53	2	no	—
174	C₂	—	106	1	no	—
175	C₂	—	424	2	no	—
176	C₂	C₂×#13133279	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₅₃⋊M₃₂

C₂

yes

maximal, characteristic, complemented

D₅₃⋊#108

C₂

yes

maximal, characteristic, complemented

#16811541

C₂

yes

maximal, complemented

C₂×D₈×D₅₃

C₂

yes

maximal, characteristic

D₅₃⋊M₁₆

—

#13133292

C₂²

yes

complemented

#13133291

—

D₅₃⋊C₁₆

—

#13133288

—

#13133287

C₂²

yes

complemented

C₂×D₄×D₅₃

—

C₂×D₄₂₄

C₄

yes

characteristic

C₂×#11719922

—

D₈×D₅₃

—

D₈×D₅₃

—

D₈×D₅₃

C₄

yes

—

D₈×D₅₃

C₂²

yes

—

C₂×C₈×D₅₃

C₂²

yes

characteristic

C₂×D₈×C₅₃

C₄

yes

characteristic

C₂³×D₅₃

—

C₂×D₄×C₅₃

—

C₂×C₂²⋊D₅₃

—

D₄×D₅₃

—

D₄×D₅₃

—

D₄×D₅₃

—

D₄×D₅₃

—

C₂×D₂₁₂

—

C₂×C₄×D₅₃

D₄

yes

characteristic

#11719940

—

#11719936

—

D₅₃⋊C₈

—

D₈×C₅₃

—

D₈×C₅₃

C₂×C₄

yes

—

C₂×C₈×C₅₃

C₂×C₄

yes

—

—

D₄

yes

characteristic

D₄₂₄

—

D₄₂₄

C₂×C₄

yes

—

C₈×D₅₃

C₂×C₄

yes

characteristic

C₈×D₅₃

D₄

yes

characteristic

C₈×D₅₃

D₄

yes

characteristic

C₈×D₅₃

C₂³

yes

characteristic

#11719910

—

C₂³×C₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

SD₁₆

yes

characteristic

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₅₃

—

C₂²⋊D₅₃

—

C₂×Dic₅₃

D₈

yes

characteristic

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

C₂²⋊C₄

yes

characteristic

C₄×D₅₃

D₈

yes

characteristic

C₄×D₅₃

SD₁₆

yes

characteristic

C₄×D₅₃

C₂×D₄

yes

characteristic

#88324

—

C₈×C₅₃

C₂²⋊C₄

yes

characteristic

C₈×C₅₃

C₂²×C₄

yes

characteristic

#88322

C₂²⋊C₄

yes

characteristic

#88322

C₂×D₄

yes

characteristic

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

#102

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

#102

yes

characteristic

C₂×D₅₃

C₂×SD₁₆

yes

characteristic

C₄×C₅₃

#102

yes

characteristic

C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

Dic₅₃

#102

yes

characteristic

Dic₅₃

C₂×D₈

yes

characteristic

C₂×#361

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

—

C₂×C₅₃

C₂×#102

yes

characteristic

D₅₃

—

D₅₃

—

D₅₃

#361

yes

complemented

C₂²×D₈

—

C₂×M₃₂

—

C₂×#108

—

#361

—

C₅₃

C₂×#361

yes

characteristic, complemented, Sylow

C₂²×D₄

—

106

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

106

—

C₂×D₈

—

106

—

100

C₂×D₈

—

106

—

101

C₂×D₈

#6157

yes

characteristic

102

C₂×M₁₆

—

106

—

103

C₂²×C₈

—

104

M₃₂

—

105

M₃₂

—

106

—

106

C₂×C₁₆

—

106

—

107

#108

—

108

#108

—

106

—

109

C₂⁴

—

212

—

110

C₂×D₄

—

111

C₂×D₄

—

106

—

112

C₂×D₄

—

106

—

113

C₂×D₄

—

106

—

114

C₂×D₄

—

212

—

115

C₂×D₄

—

212

—

116

C₂×D₄

—

212

—

117

C₂²×C₄

—

118

D₈

—

119

D₈

—

120

D₈

—

106

—

121

D₈

—

106

—

122

D₈

—

106

—

123

D₈

C₂×#6157

yes

—

124

M₁₆

—

106

—

125

M₁₆

—

212

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

212

—

132

C₂×C₈

C₂×#6157

yes

characteristic

133

C₁₆

—

106

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

424

—

137

C₂³

—

212

—

138

C₂³

—

212

—

139

C₂³

—

212

—

140

D₄

—

141

D₄

—

142

D₄

—

106

—

143

D₄

—

212

—

144

D₄

—

212

—

145

D₄

—

212

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

C₂²⋊#6157

yes

characteristic

152

C₈

—

153

C₈

—

154

C₈

—

212

—

155

C₈

C₂²⋊#6157

yes

characteristic

156

C₈

C₂²×#6157

yes

characteristic

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

106

—

162

C₂²

—

424

—

163

C₂²

—

424

—

164

C₂²

—

424

—

165

C₂²

—

212

—

166

C₂²

#13133279

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

#13133279

yes

characteristic

170

C₄

C₂×C₂²⋊#6157

yes

characteristic

171

C₂

—

172

C₂

—

173

C₂

—

174

C₂

—

106

—

175

C₂

—

424

—

176

C₂

C₂×#13133279

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#13133279
commutator	C₈×C₅₃	C₂²×C₄
Frattini	C₈	C₂²×#6157
Fitting	C₂×D₈×C₅₃	C₄
socle	C₂×C₅₃	C₂×#102
hypercenter	C₂×D₈	#6157
hypocenter	C₅₃	C₂×#361
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂

C₂×#13133279

commutator

C₈×C₅₃

C₂²×C₄

Frattini

C₈

C₂²×#6157

Fitting

C₂×D₈×C₅₃

C₄

C₂×C₅₃

C₂×D₈

C₅₃

G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. D₅₃⋊M₃₂	C₂	semidirect
2. D₅₃⋊#108	C₂	semidirect
3. #16811541	C₂	semidirect
6. #13133292	C₂²	semidirect
10. #13133287	C₂²	semidirect
88. D₅₃	#361	semidirect
93. C₅₃	C₂×#361	semidirect

H ≅ G/N

type

1. D₅₃⋊M₃₂

C₂

semidirect

2. D₅₃⋊#108

C₂

semidirect

3. #16811541

C₂

semidirect

6. #13133292

C₂²

semidirect

10. #13133287

C₂²

semidirect

88. D₅₃

#361

semidirect

93. C₅₃

C₂×#361

semidirect

Subgroups — D₅₃⋊#361 #20291039

Conjugacy classes of subgroups

Complements

Subgroups — D53⋊#361 #20291039

Conjugacy classes of subgroups

Complements

Subgroups — D₅₃⋊#361 #20291039