Group #20244923 — subgroups

Subgroups — #20244923

Order 6016.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₂×#13093957	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093949	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093947	C₂	1	1	yes	maximal, characteristic
4	#15689028	C₂	1	1	yes	maximal, characteristic
5	#15688992	C₂	1	1	yes	maximal, characteristic
6	#15688877	C₂	1	1	yes	maximal, characteristic
7	C₂×#107×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₄	—	2	2	no	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	#13093957	—	2	2	no	—
14	#13093949	—	2	2	no	—
15	#13093947	—	2	2	no	—
16	C₄₇⋊#95	—	2	2	no	—
17	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	#107×C₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	—	2	1	no	—
22	C₂²×C₄×C₄₇	—	2	1	no	—
23	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₇	—	2	1	no	—
25	C₂²×Dic₄₇	—	2	1	no	—
26	C₂²×Dic₄₇	D₄	1	2	yes	—
27	C₂×Dic₉₄	—	2	1	no	—
28	C₂×Dic₉₄	—	2	1	no	—
29	C₂×Dic₉₄	—	2	1	no	—
30	C₂×Dic₉₄	—	2	1	no	—
31	C₂×Dic₉₄	—	2	1	no	—
32	C₂×Dic₉₄	Q₈	1	2	yes	—
33	C₂×C₈×C₄₇	—	2	1	no	—
34	C₂×C₈×C₄₇	—	2	1	no	—
35	C₂×C₈×C₄₇	D₄	1	2	yes	—
36	C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₄⋊Dic₄₇	—	2	1	no	—
41	C₄⋊Dic₄₇	—	2	1	no	—
42	Dic₄₇⋊C₄	—	4	4	no	—
43	C₄×Dic₄₇	—	2	1	no	—
44	C₄×Dic₄₇	—	2	1	no	—
45	C₂×C₄₇⋊C₈	—	2	1	no	—
46	C₂×C₄₇⋊C₈	—	2	1	no	—
47	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
48	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	—	4	1	no	—
50	C₂×C₄×C₄₇	—	4	1	no	—
51	C₂×C₄×C₄₇	—	4	2	no	—
52	C₂×C₄×C₄₇	—	4	2	no	—
53	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
57	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
58	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
59	C₂×Dic₄₇	—	2	2	no	—
60	C₂×Dic₄₇	—	2	2	no	—
61	C₂×Dic₄₇	—	2	2	no	—
62	C₂×Dic₄₇	—	4	1	no	—
63	C₂×Dic₄₇	—	4	1	no	—
64	C₂×Dic₄₇	—	4	1	no	—
65	C₂×Dic₄₇	—	4	2	no	—
66	C₂×Dic₄₇	Q₁₆	1	4	yes	—
67	Dic₉₄	—	2	2	no	—
68	Dic₉₄	—	2	2	no	—
69	Dic₉₄	—	4	1	no	—
70	Dic₉₄	—	4	1	no	—
71	C₈×C₄₇	—	2	2	no	—
72	C₄₇⋊C₈	—	2	2	no	—
73	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
74	C₂²×C₄₇	#123	1	1	yes	characteristic
75	C₂²×C₄₇	#127	1	1	yes	characteristic
76	C₂²×C₄₇	C₂×Q₁₆	1	2	yes	—
77	C₂²×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
78	C₄×C₄₇	—	8	1	no	—
79	C₄×C₄₇	—	8	1	no	—
80	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
81	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
82	C₄×C₄₇	#123	1	1	yes	characteristic
83	C₄×C₄₇	#123	1	1	yes	characteristic
84	Dic₄₇	—	2	4	no	—
85	Dic₄₇	—	4	2	no	—
86	Dic₄₇	—	8	1	no	—
87	#2095	—	47	1	no	maximal, Sylow
88	C₂×C₄₇	#399	1	1	yes	characteristic
89	C₂×C₄₇	#477	1	2	yes	—
90	C₂×C₄₇	#484	1	2	yes	—
91	C₂×C₄₇	#494	1	1	yes	characteristic
92	C₂×C₄₇	#496	1	1	yes	characteristic
93	C₂×#107	—	47	1	no	—
94	C₂×#107	D₄₇	1	1	yes	characteristic
95	C₂×#103	—	47	1	no	—
96	C₂×#103	—	47	1	no	—
97	#391	—	47	1	no	—
98	#384	—	47	1	no	—
99	#336	—	47	1	no	—
100	C₄₇	#2095	1	1	yes	characteristic, complemented, Sylow
101	C₂²×Q₈	—	47	1	no	—
102	C₂²×C₈	—	47	1	no	—
103	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
104	C₂×C₄⋊C₄	—	47	1	no	—
105	C₂×C₄⋊C₄	—	94	2	no	—
106	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
107	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
108	C₂×C₄²	—	47	1	no	—
109	#107	—	2	2	no	—
110	#107	—	94	2	no	—
111	#103	—	94	2	no	—
112	#103	—	94	2	no	—
113	#95	—	94	2	no	—
114	C₂×Q₈	—	47	2	no	—
115	C₂×Q₈	—	94	1	no	—
116	C₂×Q₈	—	94	1	no	—
117	C₂×Q₈	—	94	1	no	—
118	C₂×Q₈	—	94	1	no	—
119	C₂×Q₈	—	94	1	no	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	47	2	no	—
123	C₂²×C₄	—	94	1	no	—
124	C₂²×C₄	—	94	1	no	—
125	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	47	2	no	—
129	C₂×C₈	—	94	1	no	—
130	C₂×C₈	—	94	1	no	—
131	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
132	C₄⋊C₄	—	2	1	no	—
133	C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₄	—	2	1	no	—
135	C₄⋊C₄	—	2	1	no	—
136	C₄⋊C₄	—	94	1	no	—
137	C₄⋊C₄	—	94	1	no	—
138	C₄⋊C₄	—	188	4	no	—
139	C₄²	—	94	1	no	—
140	C₄²	—	94	1	no	—
141	C₂³	D₄×D₄₇	1	1	yes	characteristic
142	Q₈	—	94	2	no	—
143	Q₈	—	94	2	no	—
144	Q₈	—	188	1	no	—
145	Q₈	—	188	1	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	4	1	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	47	4	no	—
151	C₂×C₄	—	94	2	no	—
152	C₂×C₄	—	94	2	no	—
153	C₂×C₄	—	94	2	no	—
154	C₂×C₄	—	188	1	no	—
155	C₂×C₄	—	188	2	no	—
156	C₂×C₄	—	188	1	no	—
157	C₂×C₄	—	188	1	no	—
158	C₂×C₄	#10625350	1	1	yes	characteristic
159	C₂×C₄	#10625350	1	1	yes	characteristic
160	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
161	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
162	C₂×C₄	#10625354	1	1	yes	characteristic
163	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	94	2	no	—
166	C₂²	#13094002	1	1	yes	characteristic
167	C₂²	#13094009	1	1	yes	characteristic
168	C₂²	#13094020	1	1	yes	characteristic
169	C₂²	Q₁₆×D₄₇	1	2	yes	—
170	C₂²	#13094048	1	2	yes	—
171	C₄	—	8	1	no	—
172	C₄	—	8	1	no	—
173	C₄	—	94	4	no	—
174	C₄	—	376	1	no	—
175	C₄	—	188	2	no	—
176	C₄	#13094000	1	1	yes	characteristic
177	C₄	#13094002	1	1	yes	characteristic
178	C₄	#13094007	1	1	yes	characteristic
179	C₄	#13094009	1	1	yes	characteristic
180	C₂	#15689058	1	1	yes	characteristic
181	C₂	#15689417	1	2	yes	—
182	C₂	#15689460	1	2	yes	—
183	C₂	#15689501	1	1	yes	characteristic
184	C₂	#15689511	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093957

C₂

yes

maximal, characteristic

C₂×#13093949

C₂

yes

maximal, characteristic

C₂×#13093947

C₂

yes

maximal, characteristic

#15689028

C₂

yes

maximal, characteristic

#15688992

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, characteristic

C₂×#107×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

C₂²

yes

—

—

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

#107×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

Q₁₆

yes

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²⋊Q₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×Q₁₆

yes

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

C₂²⋊Q₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#484

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

yes

—

—

—

—

—

100

C₄₇

#2095

yes

characteristic, complemented, Sylow

101

C₂²×Q₈

—

102

C₂²×C₈

—

103

C₂²×C₈

C₂×D₄₇

yes

characteristic

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

107

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

108

C₂×C₄²

—

109

#107

—

110

#107

—

111

#103

—

112

#103

—

113

#95

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

C₂²×D₄₇

yes

characteristic

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

C₂²⋊D₄₇

yes

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

188

—

139

C₄²

—

140

C₄²

—

141

C₂³

D₄×D₄₇

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

188

—

145

Q₈

—

188

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

188

—

155

C₂×C₄

—

188

—

156

C₂×C₄

—

188

—

157

C₂×C₄

—

188

—

158

C₂×C₄

#10625350

yes

characteristic

159

C₂×C₄

#10625350

yes

characteristic

160

C₂×C₄

D₄×D₄₇

yes

characteristic

161

C₂×C₄

Q₈×D₄₇

yes

characteristic

162

C₂×C₄

#10625354

yes

characteristic

163

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

164

C₈

—

165

C₈

—

166

C₂²

#13094002

yes

characteristic

167

C₂²

#13094009

yes

characteristic

168

C₂²

#13094020

yes

characteristic

169

C₂²

Q₁₆×D₄₇

yes

—

170

C₂²

#13094048

yes

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

376

—

175

C₄

—

188

—

176

C₄

#13094000

yes

characteristic

177

C₄

#13094002

yes

characteristic

178

C₄

#13094007

yes

characteristic

179

C₄

#13094009

yes

characteristic

180

C₂

#15689058

yes

characteristic

181

C₂

#15689417

yes

—

182

C₂

#15689460

yes

—

183

C₂

#15689501

yes

characteristic

184

C₂

#15689511

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#107	D₄₇
hypocenter	C₄₇	#2095
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#107×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
100. C₄₇	#2095	semidirect

H ≅ G/N

type

100. C₄₇

#2095

semidirect

Subgroups — #20244923

Conjugacy classes of subgroups

Complements