Group #20243530 — subgroups

Subgroups — #20243530

Order 6016.

240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688878	C₂	1	1	yes	maximal, characteristic
3	#15688877	C₂	1	2	yes	maximal
4	#15688877	C₂	1	2	yes	maximal
5	C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₄₇	—	2	2	no	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₂×C₈×C₄₇	—	2	2	no	—
25	C₄²×C₄₇	—	2	2	no	—
26	C₄×Dic₄₇	—	2	2	no	—
27	C₄×Dic₄₇	—	2	2	no	—
28	C₄×Dic₄₇	—	2	1	no	—
29	C₄×Dic₄₇	—	2	1	no	—
30	C₄×Dic₄₇	—	2	2	no	—
31	C₄×Dic₄₇	—	2	2	no	—
32	C₄×Dic₄₇	C₈	1	4	yes	complemented
33	C₂×C₄₇⋊C₈	—	2	2	no	—
34	C₂×C₄₇⋊C₈	—	2	2	no	—
35	C₂×C₄₇⋊C₈	—	2	2	no	—
36	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	—	2	1	no	—
38	C₂×C₄×C₄₇	—	2	1	no	—
39	C₂×C₄×C₄₇	—	2	1	no	—
40	C₂×C₄×C₄₇	—	2	1	no	—
41	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
42	C₂×C₄×C₄₇	M₁₆	1	2	yes	—
43	C₂×C₄×C₄₇	#41	1	2	yes	—
44	C₂×C₄×C₄₇	#41	1	2	yes	—
45	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
46	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
47	C₂×Dic₄₇	—	2	1	no	—
48	C₂×Dic₄₇	—	2	1	no	—
49	C₂×Dic₄₇	—	2	1	no	—
50	C₂×Dic₄₇	—	2	1	no	—
51	C₂×Dic₄₇	—	2	1	no	—
52	C₂×Dic₄₇	—	2	1	no	—
53	C₂×Dic₄₇	—	2	1	no	—
54	C₂×Dic₄₇	—	2	1	no	—
55	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
56	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
57	C₂×Dic₄₇	M₁₆	1	2	yes	—
58	C₂×Dic₄₇	M₁₆	1	2	yes	—
59	C₈×C₄₇	—	4	2	no	—
60	C₄₇⋊C₈	—	4	2	no	—
61	C₂²×C₄₇	#117	1	1	yes	characteristic
62	C₂²×C₄₇	#117	1	1	yes	characteristic
63	C₂²×C₄₇	#117	1	1	yes	characteristic
64	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
65	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
66	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
67	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
68	C₄×C₄₇	—	2	2	no	—
69	C₄×C₄₇	—	2	2	no	—
70	C₄×C₄₇	#126	1	2	yes	—
71	C₄×C₄₇	#126	1	2	yes	—
72	Dic₄₇	—	2	2	no	—
73	Dic₄₇	—	2	2	no	—
74	Dic₄₇	—	2	2	no	—
75	Dic₄₇	—	2	2	no	—
76	#1839	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	#383	1	1	yes	characteristic
78	C₂×C₄₇	#431	1	1	yes	characteristic
79	C₂×C₄₇	#431	1	1	yes	characteristic
80	C₂×C₄₇	#431	1	1	yes	characteristic
81	C₂×C₄₇	#432	1	1	yes	characteristic
82	C₂×C₄₇	#432	1	1	yes	characteristic
83	C₂×C₄₇	#432	1	1	yes	characteristic
84	C₄³	—	47	1	no	—
85	#336	—	47	2	no	—
86	#336	—	47	2	no	—
87	#336	—	47	1	no	—
88	#336	D₄₇	1	1	yes	characteristic
89	C₄₇	#1839	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₈	—	47	2	no	—
91	C₂²×C₈	C₂×D₄₇	1	2	yes	—
92	C₂×C₄²	—	47	1	no	—
93	C₂×C₄²	—	47	1	no	—
94	C₂×C₄²	—	47	1	no	—
95	C₂×C₄²	—	47	1	no	—
96	C₂×C₄²	—	47	1	no	—
97	C₂×C₄²	—	47	1	no	—
98	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
99	C₂²×C₄	—	47	1	no	—
100	C₂²×C₄	—	47	1	no	—
101	C₂²×C₄	—	47	1	no	—
102	C₂²×C₄	—	47	1	no	—
103	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
104	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	94	2	no	—
110	C₂×C₈	—	94	2	no	—
111	C₂×C₈	—	94	2	no	—
112	C₄²	—	2	2	no	—
113	C₄²	—	47	4	no	—
114	C₄²	—	94	2	no	—
115	C₄²	—	94	2	no	—
116	C₄²	—	94	2	no	—
117	C₄²	—	94	2	no	—
118	C₄²	—	94	1	no	—
119	C₄²	—	94	1	no	—
120	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	47	2	no	—
126	C₂×C₄	—	47	2	no	—
127	C₂×C₄	—	47	2	no	—
128	C₂×C₄	—	47	2	no	—
129	C₂×C₄	—	94	1	no	—
130	C₂×C₄	—	94	1	no	—
131	C₂×C₄	—	94	1	no	—
132	C₂×C₄	—	94	1	no	—
133	C₂×C₄	—	94	1	no	—
134	C₂×C₄	—	94	1	no	—
135	C₂×C₄	—	94	1	no	—
136	C₂×C₄	—	94	1	no	—
137	C₂×C₄	C₈×D₄₇	1	2	yes	—
138	C₂×C₄	#10625324	1	2	yes	—
139	C₂×C₄	#10625350	1	2	yes	—
140	C₂×C₄	#10625352	1	1	yes	characteristic
141	C₂×C₄	#10625352	1	2	yes	—
142	C₂×C₄	#10625354	1	1	yes	characteristic
143	C₈	—	4	2	no	—
144	C₈	—	188	2	no	—
145	C₂²	#13093980	1	1	yes	characteristic
146	C₂²	#13093981	1	1	yes	characteristic
147	C₂²	#13093982	1	1	yes	characteristic
148	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
149	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
150	C₂²	M₁₆×D₄₇	1	1	yes	characteristic
151	C₂²	C₂×#10625324	1	1	yes	characteristic
152	C₄	—	2	2	no	—
153	C₄	—	2	2	no	—
154	C₄	—	94	2	no	—
155	C₄	—	94	2	no	—
156	C₄	—	94	2	no	—
157	C₄	—	94	2	no	—
158	C₄	#13094017	1	2	yes	—
159	C₄	#13094019	1	2	yes	—
160	C₂	#15688990	1	1	yes	characteristic
161	C₂	#15689173	1	1	yes	characteristic
162	C₂	#15689174	1	1	yes	characteristic
163	C₂	#15689175	1	1	yes	characteristic
164	C₂	#15689177	1	1	yes	characteristic
165	C₂	#15689178	1	1	yes	characteristic
166	C₂	#15689179	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

#15688878

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal

#15688877

C₂

yes

maximal

C₄₇×#336

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₈

yes

complemented

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

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

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#126

yes

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₄³

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1839

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₄₇

yes

characteristic

104

C₂²×C₄

C₄×D₄₇

yes

characteristic

105

C₂²×C₄

C₂²×D₄₇

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₂³

C₂×C₄×D₄₇

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₈×D₄₇

yes

—

138

C₂×C₄

#10625324

yes

—

139

C₂×C₄

#10625350

yes

—

140

C₂×C₄

#10625352

yes

characteristic

141

C₂×C₄

#10625352

yes

—

142

C₂×C₄

#10625354

yes

characteristic

143

C₈

—

144

C₈

—

188

—

145

C₂²

#13093980

yes

characteristic

146

C₂²

#13093981

yes

characteristic

147

C₂²

#13093982

yes

characteristic

148

C₂²

C₂×C₈×D₄₇

yes

characteristic

149

C₂²

M₁₆×D₄₇

yes

characteristic

150

C₂²

M₁₆×D₄₇

yes

characteristic

151

C₂²

C₂×#10625324

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

#13094017

yes

—

159

C₄

#13094019

yes

—

160

C₂

#15688990

yes

characteristic

161

C₂

#15689173

yes

characteristic

162

C₂

#15689174

yes

characteristic

163

C₂

#15689175

yes

characteristic

164

C₂

#15689177

yes

characteristic

165

C₂

#15689178

yes

characteristic

166

C₂

#15689179

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₈
Fitting	C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	#336	D₄₇
hypocenter	C₄₇	#1839
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂²×C₈

Fitting

C₄₇×#336

C₂

socle

C₂³×C₄₇

C₂²×C₄

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
32. C₄×Dic₄₇	C₈	semidirect
89. C₄₇	#1839	semidirect

H ≅ G/N

type

32. C₄×Dic₄₇

C₈

semidirect

89. C₄₇

#1839

semidirect

Subgroups — #20243530

Conjugacy classes of subgroups

Complements