Group #20243138 — subgroups

Subgroups — #20243138

Order 6016.

240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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×#13093934	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688969	C₂	1	1	yes	maximal, characteristic
4	#15688878	C₂	1	1	yes	maximal, characteristic
5	#15688877	C₂	1	1	yes	maximal, characteristic
6	#15688877	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#336	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄₇⋊C₈	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×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	#13093934	C₄	1	4	yes	complemented
13	C₈×Dic₄₇	C₄	1	4	yes	complemented
14	C₄₇⋊#95	C₄	1	2	yes	—
15	C₄₇⋊#95	C₄	1	2	yes	—
16	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
22	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	—	2	1	no	—
25	C₂×C₈×C₄₇	—	2	1	no	—
26	C₂×C₈×C₄₇	—	2	1	no	—
27	C₂×C₈×C₄₇	—	2	1	no	—
28	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
30	C₄²×C₄₇	—	2	1	no	—
31	C₄²×C₄₇	—	2	1	no	—
32	C₄×Dic₄₇	—	2	1	no	—
33	C₄×Dic₄₇	—	2	1	no	—
34	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
35	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
36	C₂×C₄₇⋊C₈	—	2	1	no	—
37	C₂×C₄₇⋊C₈	—	2	1	no	—
38	C₂×C₄₇⋊C₈	—	2	1	no	—
39	C₂×C₄₇⋊C₈	—	2	1	no	—
40	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
41	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
42	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₄₇	—	2	2	no	—
44	C₂×C₄×C₄₇	—	2	2	no	—
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
49	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
50	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
52	C₂×Dic₄₇	—	2	2	no	—
53	C₂×Dic₄₇	—	2	2	no	—
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	2	2	no	—
57	C₂×Dic₄₇	C₄²	1	2	yes	—
58	C₂×Dic₄₇	C₄²	1	2	yes	—
59	C₈×C₄₇	—	2	2	no	—
60	C₈×C₄₇	—	2	2	no	—
61	C₄₇⋊C₈	—	2	2	no	—
62	C₄₇⋊C₈	—	2	2	no	—
63	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
64	C₂²×C₄₇	#117	1	1	yes	characteristic
65	C₂²×C₄₇	#117	1	1	yes	characteristic
66	C₂²×C₄₇	#131	1	2	yes	—
67	C₂²×C₄₇	#131	1	2	yes	—
68	C₄×C₄₇	—	4	2	no	—
69	C₄×C₄₇	#117	1	1	yes	characteristic
70	C₄×C₄₇	#117	1	1	yes	characteristic
71	C₄×C₄₇	#117	1	1	yes	characteristic
72	C₄×C₄₇	#117	1	1	yes	characteristic
73	Dic₄₇	—	2	2	no	—
74	Dic₄₇	—	2	2	no	—
75	Dic₄₇	—	4	2	no	—
76	#1746	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	#376	1	1	yes	characteristic
78	C₂×C₄₇	#405	1	1	yes	characteristic
79	C₂×C₄₇	#405	1	1	yes	characteristic
80	C₂×C₄₇	#433	1	2	yes	—
81	C₂×C₄₇	#433	1	2	yes	—
82	C₂×#97	—	47	1	no	—
83	C₂×C₄×C₈	—	47	1	no	—
84	#376	—	47	1	no	—
85	#336	—	47	1	no	—
86	#336	—	47	1	no	—
87	#336	—	47	1	no	—
88	#336	D₄₇	1	1	yes	characteristic
89	C₄₇	#1746	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₈	—	47	1	no	—
91	C₂²×C₈	—	47	1	no	—
92	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
93	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
94	C₂×C₄²	—	47	1	no	—
95	C₂×C₄²	—	47	1	no	—
96	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
97	#97	—	47	4	no	—
98	C₄×C₈	—	47	4	no	—
99	#95	—	47	2	no	—
100	#95	—	47	2	no	—
101	C₂²×C₄	—	47	1	no	—
102	C₂²×C₄	—	47	1	no	—
103	C₂²×C₄	—	47	2	no	—
104	C₂²×C₄	C₄×D₄₇	1	2	yes	—
105	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	47	2	no	—
111	C₂×C₈	—	47	2	no	—
112	C₂×C₈	—	94	1	no	—
113	C₂×C₈	—	94	1	no	—
114	C₂×C₈	—	94	1	no	—
115	C₂×C₈	—	94	1	no	—
116	C₂×C₈	C₄×D₄₇	1	2	yes	—
117	C₂×C₈	C₄×D₄₇	1	2	yes	—
118	C₄²	—	2	1	no	—
119	C₄²	—	2	1	no	—
120	C₄²	—	47	2	no	—
121	C₄²	—	47	2	no	—
122	C₄²	—	94	1	no	—
123	C₄²	—	94	1	no	—
124	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	47	2	no	—
129	C₂×C₄	—	47	2	no	—
130	C₂×C₄	—	94	2	no	—
131	C₂×C₄	—	94	2	no	—
132	C₂×C₄	—	94	2	no	—
133	C₂×C₄	—	94	2	no	—
134	C₂×C₄	—	94	2	no	—
135	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
136	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
137	C₂×C₄	#10625352	1	1	yes	characteristic
138	C₂×C₄	#10625352	1	1	yes	characteristic
139	C₂×C₄	#10625352	1	1	yes	characteristic
140	C₂×C₄	#10625354	1	1	yes	characteristic
141	C₈	—	2	2	no	—
142	C₈	—	2	2	no	—
143	C₈	—	94	2	no	—
144	C₈	—	94	2	no	—
145	C₂²	C₄²×D₄₇	1	1	yes	characteristic
146	C₂²	#13093980	1	1	yes	characteristic
147	C₂²	#13093982	1	1	yes	characteristic
148	C₂²	#13094030	1	2	yes	—
149	C₂²	#13094032	1	2	yes	—
150	C₄	—	4	2	no	—
151	C₄	—	94	2	no	—
152	C₄	—	94	2	no	—
153	C₄	—	188	2	no	—
154	C₄	#13093980	1	1	yes	characteristic
155	C₄	#13093980	1	1	yes	characteristic
156	C₄	#13093982	1	1	yes	characteristic
157	C₄	#13093982	1	1	yes	characteristic
158	C₂	#15688968	1	1	yes	characteristic
159	C₂	#15689077	1	1	yes	characteristic
160	C₂	#15689080	1	1	yes	characteristic
161	C₂	#15689181	1	2	yes	—
162	C₂	#15689183	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093934

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688969

C₂

yes

maximal, characteristic

#15688878

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, characteristic

C₄₇×#336

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093934

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

C₄

yes

—

C₄₇⋊#95

C₄

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

C₂×C₄×C₄₇

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

C₄²

yes

—

C₂×Dic₄₇

C₄²

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄²

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

#131

yes

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#433

yes

—

C₂×#97

—

C₂×C₄×C₈

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1746

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#97

—

C₄×C₈

—

#95

—

100

#95

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₄×D₄₇

yes

—

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

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₄×D₄₇

yes

—

117

C₂×C₈

C₄×D₄₇

yes

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₂³

C₂×C₄×D₄₇

yes

characteristic

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

C₂×C₄×D₄₇

yes

characteristic

136

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

137

C₂×C₄

#10625352

yes

characteristic

138

C₂×C₄

#10625352

yes

characteristic

139

C₂×C₄

#10625352

yes

characteristic

140

C₂×C₄

#10625354

yes

characteristic

141

C₈

—

142

C₈

—

143

C₈

—

144

C₈

—

145

C₂²

C₄²×D₄₇

yes

characteristic

146

C₂²

#13093980

yes

characteristic

147

C₂²

#13093982

yes

characteristic

148

C₂²

#13094030

yes

—

149

C₂²

#13094032

yes

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

188

—

154

C₄

#13093980

yes

characteristic

155

C₄

#13093980

yes

characteristic

156

C₄

#13093982

yes

characteristic

157

C₄

#13093982

yes

characteristic

158

C₂

#15688968

yes

characteristic

159

C₂

#15689077

yes

characteristic

160

C₂

#15689080

yes

characteristic

161

C₂

#15689181

yes

—

162

C₂

#15689183

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂×C₄²
Fitting	C₄₇×#336	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	#336	D₄₇
hypocenter	C₄₇	#1746
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂×C₄²

Fitting

C₄₇×#336

C₂

socle

C₂³×C₄₇

C₂²×C₄

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
12. #13093934	C₄	semidirect
13. C₈×Dic₄₇	C₄	semidirect
89. C₄₇	#1746	semidirect

H ≅ G/N

type

12. #13093934

C₄

semidirect

13. C₈×Dic₄₇

C₄

semidirect

89. C₄₇

#1746

semidirect

Subgroups — #20243138

Conjugacy classes of subgroups

Complements