Group #20242482 — subgroups

Subgroups — #20242482

Order 6016.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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	#15689851	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689469	C₂	1	1	yes	maximal, characteristic
3	#15689320	C₂	1	1	yes	maximal, characteristic
4	#15688870	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688853	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#460	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625335	—	2	1	no	—
9	#13094024	C₂²	1	1	yes	characteristic
10	#13094022	—	2	1	no	—
11	#13094016	—	2	1	no	—
12	#13094014	—	2	2	no	—
13	C₄×Dic₉₄	—	2	1	no	—
14	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#13093989	—	2	1	no	—
16	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	#13093945	—	2	1	no	—
18	#13093945	—	2	2	no	—
19	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₄₇	—	2	1	no	—
21	#127×C₄₇	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	#102×C₄₇	—	2	1	no	—
25	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
26	C₂×D₄×C₄₇	—	2	1	no	—
27	C₂×D₄×C₄₇	—	2	1	no	—
28	C₂×D₄×C₄₇	—	2	1	no	—
29	C₂×Dic₉₄	—	2	1	no	—
30	C₂×Dic₉₄	D₄	1	1	yes	characteristic
31	SD₁₆×C₄₇	—	4	2	no	—
32	C₂×C₈×C₄₇	—	2	1	no	—
33	C₄⋊C₄×C₄₇	—	2	1	no	—
34	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
35	C₄²×C₄₇	—	2	1	no	—
36	C₄²×C₄₇	C₂³	1	1	yes	characteristic
37	#10625335	—	4	2	no	—
38	C₄⋊Dic₄₇	—	2	1	no	—
39	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
40	C₄⋊Dic₄₇	D₄	1	2	yes	—
41	Dic₄₇⋊C₄	—	2	2	no	—
42	Dic₄₇⋊C₄	—	2	2	no	—
43	Dic₄₇⋊C₄	—	2	2	no	—
44	Dic₄₇⋊C₄	—	2	1	no	—
45	C₄×Dic₄₇	—	2	2	no	—
46	C₄×Dic₄₇	—	2	1	no	—
47	C₂×C₄₇⋊C₈	—	2	1	no	—
48	C₂×C₄₇⋊C₈	—	2	1	no	—
49	C₂³×C₄₇	—	4	1	no	—
50	Q₈×C₄₇	—	2	1	no	—
51	Q₈×C₄₇	—	2	1	no	—
52	D₄×C₄₇	—	4	2	no	—
53	D₄×C₄₇	—	4	1	no	—
54	D₄×C₄₇	—	4	1	no	—
55	D₄×C₄₇	—	4	1	no	—
56	D₄×C₄₇	—	4	1	no	—
57	C₂×C₄×C₄₇	—	2	1	no	—
58	C₂×C₄×C₄₇	—	2	1	no	—
59	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂×Dic₄₇	—	2	1	no	—
63	C₂×Dic₄₇	—	2	1	no	—
64	C₂×Dic₄₇	—	2	2	no	—
65	Dic₉₄	—	2	1	no	—
66	Dic₉₄	—	4	1	no	—
67	Dic₉₄	—	4	1	no	—
68	Dic₉₄	SD₁₆	1	2	yes	complemented
69	C₈×C₄₇	—	4	1	no	—
70	C₄₇⋊C₈	—	4	1	no	—
71	C₄₇⋊C₈	—	4	1	no	—
72	C₂²×C₄₇	—	8	1	no	—
73	C₂²×C₄₇	—	8	1	no	—
74	C₂²×C₄₇	—	8	1	no	—
75	C₂²×C₄₇	#120	1	1	yes	characteristic
76	C₄×C₄₇	—	2	1	no	—
77	C₄×C₄₇	—	4	1	no	—
78	C₄×C₄₇	—	4	1	no	—
79	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
80	C₄×C₄₇	#135	1	1	yes	characteristic
81	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₄×C₄₇	#137	1	1	yes	characteristic
83	Dic₄₇	—	2	2	no	—
84	Dic₄₇	—	4	2	no	—
85	Dic₄₇	—	4	1	no	—
86	#1626	—	47	1	no	maximal, Sylow
87	C₂×C₄₇	—	16	1	no	—
88	C₂×C₄₇	#448	1	1	yes	characteristic
89	C₂×C₄₇	#449	1	1	yes	characteristic
90	C₂×C₄₇	#454	1	1	yes	characteristic
91	#557	—	47	1	no	—
92	#486	—	47	1	no	—
93	#460	—	47	1	no	—
94	#460	D₄₇	1	1	yes	characteristic
95	#332	—	47	1	no	—
96	Q₈⋊C₈	—	47	1	no	—
97	Q₈⋊C₈	—	47	1	no	—
98	C₄₇	#1626	1	1	yes	characteristic, complemented, Sylow
99	C₂×SD₁₆	—	2	1	no	—
100	C₂×SD₁₆	—	94	1	no	—
101	C₄⋊Q₈	—	47	1	no	—
102	C₄⋊Q₈	—	94	1	no	—
103	#127	C₂×D₄₇	1	1	yes	characteristic
104	#125	—	94	1	no	—
105	#125	—	94	2	no	—
106	C₄×Q₈	—	47	1	no	—
107	C₄×Q₈	—	94	1	no	—
108	C₄×Q₈	—	94	1	no	—
109	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
110	C₄⋊C₈	—	47	1	no	—
111	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
112	#102	—	2	1	no	—
113	#102	—	94	1	no	—
114	#102	—	94	2	no	—
115	C₄×C₈	—	47	1	no	—
116	C₂×Q₈	—	47	1	no	—
117	C₂×Q₈	—	94	1	no	—
118	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
119	C₂×D₄	—	2	1	no	—
120	C₂×D₄	—	2	1	no	—
121	C₂×D₄	—	2	1	no	—
122	SD₁₆	—	4	2	no	—
123	SD₁₆	—	188	2	no	—
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	94	1	no	—
126	C₂×C₈	—	94	1	no	—
127	C₄⋊C₄	—	2	1	no	—
128	C₄⋊C₄	—	47	1	no	—
129	C₄⋊C₄	—	47	2	no	—
130	C₄⋊C₄	—	94	2	no	—
131	C₄⋊C₄	—	94	2	no	—
132	C₄⋊C₄	—	94	2	no	—
133	C₄⋊C₄	—	94	1	no	—
134	C₄⋊C₄	—	94	1	no	—
135	C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
136	C₄²	—	2	1	no	—
137	C₄²	—	94	2	no	—
138	C₄²	—	94	1	no	—
139	C₄²	C₂²×D₄₇	1	1	yes	characteristic
140	C₂³	—	4	1	no	—
141	Q₈	—	2	1	no	—
142	Q₈	—	2	1	no	—
143	Q₈	—	47	2	no	—
144	Q₈	—	94	1	no	—
145	Q₈	—	188	1	no	—
146	Q₈	—	188	1	no	—
147	D₄	—	4	2	no	—
148	D₄	—	4	1	no	—
149	D₄	—	4	1	no	—
150	D₄	—	4	1	no	—
151	D₄	—	4	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	94	1	no	—
155	C₂×C₄	—	94	1	no	—
156	C₂×C₄	—	94	2	no	—
157	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
158	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
159	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
160	C₈	—	4	1	no	—
161	C₈	—	188	1	no	—
162	C₈	—	188	1	no	—
163	C₂²	—	8	1	no	—
164	C₂²	—	8	1	no	—
165	C₂²	—	8	1	no	—
166	C₂²	#13093992	1	1	yes	characteristic
167	C₄	—	2	1	no	—
168	C₄	—	4	1	no	—
169	C₄	—	4	1	no	—
170	C₄	—	94	2	no	—
171	C₄	—	188	2	no	—
172	C₄	—	188	1	no	—
173	C₄	SD₁₆×D₄₇	1	1	yes	characteristic
174	C₄	#13094044	1	1	yes	characteristic
175	C₄	#13094050	1	1	yes	characteristic
176	C₄	#13094053	1	1	yes	characteristic
177	C₂	—	16	1	no	—
178	C₂	#15689260	1	1	yes	characteristic
179	C₂	#15689266	1	1	yes	characteristic
180	C₂	#15689294	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689851

C₂

yes

maximal, characteristic, complemented

#15689469

C₂

yes

maximal, characteristic

#15689320

C₂

yes

maximal, characteristic

#15688870

C₂

yes

maximal, characteristic, complemented

Q₈⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic, complemented

#15688853

C₂

yes

maximal, characteristic, complemented

C₄₇×#460

C₂

yes

maximal, characteristic

C₂×#10625335

—

#13094024

C₂²

yes

—

—

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂²

yes

characteristic

#13093989

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

#13093945

—

#13093945

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×SD₁₆×C₄₇

—

#127×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

#102×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

characteristic

SD₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

D₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×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×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

SD₁₆

yes

complemented

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#1626

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

D₄₇

yes

characteristic

#332

—

Q₈⋊C₈

—

Q₈⋊C₈

—

C₄₇

#1626

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

100

C₂×SD₁₆

—

101

C₄⋊Q₈

—

102

C₄⋊Q₈

—

103

#127

C₂×D₄₇

yes

characteristic

104

#125

—

105

#125

—

106

C₄×Q₈

—

107

C₄×Q₈

—

108

C₄×Q₈

—

109

C₄×Q₈

C₂×D₄₇

yes

characteristic

110

C₄⋊C₈

—

111

C₄⋊C₈

C₂×D₄₇

yes

characteristic

112

#102

—

113

#102

—

114

#102

—

115

C₄×C₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

C₂²⋊D₄₇

yes

characteristic

119

C₂×D₄

—

120

C₂×D₄

—

121

C₂×D₄

—

122

SD₁₆

—

123

SD₁₆

—

188

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

136

C₄²

—

137

C₄²

—

138

C₄²

—

139

C₄²

C₂²×D₄₇

yes

characteristic

140

C₂³

—

141

Q₈

—

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

188

—

146

Q₈

—

188

—

147

D₄

—

148

D₄

—

149

D₄

—

150

D₄

—

151

D₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

D₄×D₄₇

yes

characteristic

158

C₂×C₄

D₄×D₄₇

yes

characteristic

159

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

160

C₈

—

161

C₈

—

188

—

162

C₈

—

188

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

#13093992

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

188

—

172

C₄

—

188

—

173

C₄

SD₁₆×D₄₇

yes

characteristic

174

C₄

#13094044

yes

characteristic

175

C₄

#13094050

yes

characteristic

176

C₄

#13094053

yes

characteristic

177

C₂

—

178

C₂

#15689260

yes

characteristic

179

C₂

#15689266

yes

characteristic

180

C₂

#15689294

yes

characteristic

	subgroup	G/H
center	C₂²	#13093992
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#460	C₂
socle	C₂²×C₄₇	#120
hypercenter	#460	D₄₇
hypocenter	C₄₇	#1626
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #460

subgroup

G/H

center

C₂²

#13093992

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#460

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #460

N	H ≅ G/N	type
1. #15689851	C₂	semidirect
4. #15688870	C₂	semidirect
5. Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
6. #15688853	C₂	semidirect
68. Dic₉₄	SD₁₆	semidirect
98. C₄₇	#1626	semidirect

H ≅ G/N

type

1. #15689851

C₂

semidirect

4. #15688870

C₂

semidirect

5. Q₈⋊(C₄₇⋊C₈)

C₂

semidirect

6. #15688853

C₂

semidirect

68. Dic₉₄

SD₁₆

semidirect

98. C₄₇

#1626

semidirect

Subgroups — #20242482

Conjugacy classes of subgroups

Complements