Group #20243454 — subgroups

Subgroups — #20243454

Order 6016.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#15688877	C₂	1	4	yes	maximal, complemented
4	C₂×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₇	C₄	1	1	yes	characteristic
6	C₂³×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄×Dic₄₇	—	2	2	no	—
9	C₂×C₄×Dic₄₇	—	2	2	no	—
10	C₂×C₄×Dic₄₇	C₄	1	2	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
12	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
13	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
15	C₂²⋊C₈×C₄₇	—	2	2	no	—
16	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	—	2	4	no	—
18	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	D₄	1	2	yes	—
20	C₂²×C₄×C₄₇	D₄	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	—	2	2	no	—
23	C₂²×Dic₄₇	—	2	2	no	—
24	C₂²×Dic₄₇	—	2	2	no	—
25	C₂²×Dic₄₇	—	2	4	no	—
26	C₂²×Dic₄₇	C₈	1	4	yes	complemented
27	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
28	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₄₇	—	2	2	no	—
30	C₂×C₈×C₄₇	—	2	4	no	—
31	C₄×Dic₄₇	—	2	4	no	—
32	C₄×Dic₄₇	—	2	2	no	—
33	C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄₇⋊C₈	—	2	2	no	—
35	C₂×C₄₇⋊C₈	—	2	4	no	—
36	C₂³×C₄₇	—	2	2	no	—
37	C₂³×C₄₇	—	2	2	no	—
38	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
39	C₂³×C₄₇	C₂×C₈	1	2	yes	—
40	C₂³×C₄₇	M₁₆	1	2	yes	—
41	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	—	2	2	no	—
43	C₂×C₄×C₄₇	—	2	4	no	—
44	C₂×C₄×C₄₇	—	2	4	no	—
45	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	#41	1	4	yes	—
49	C₂×Dic₄₇	—	2	8	no	—
50	C₂×Dic₄₇	—	2	8	no	—
51	C₂×Dic₄₇	—	2	2	no	—
52	C₂×Dic₄₇	—	2	2	no	—
53	C₂×Dic₄₇	—	2	2	no	—
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	C₂×C₈	1	4	yes	—
56	C₂×Dic₄₇	M₁₆	1	4	yes	—
57	C₈×C₄₇	—	4	2	no	—
58	C₄₇⋊C₈	—	4	2	no	—
59	C₂²×C₄₇	—	2	2	no	—
60	C₂²×C₄₇	—	2	2	no	—
61	C₂²×C₄₇	—	2	4	no	—
62	C₂²×C₄₇	—	2	4	no	—
63	C₂²×C₄₇	C₂²⋊C₈	1	4	yes	—
64	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄₇	#117	1	2	yes	—
66	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
67	C₂²×C₄₇	C₂×M₁₆	1	2	yes	—
68	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
69	C₄×C₄₇	—	2	2	no	—
70	C₄×C₄₇	#123	1	2	yes	—
71	C₄×C₄₇	#123	1	2	yes	—
72	Dic₄₇	—	2	4	no	—
73	Dic₄₇	—	2	4	no	—
74	#1817	—	47	1	no	maximal, Sylow
75	C₂×C₄₇	—	2	4	no	—
76	C₂×C₄₇	#381	1	1	yes	characteristic
77	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄₇	#407	1	1	yes	characteristic
79	C₂×C₄₇	#431	1	2	yes	—
80	C₂×C₄₇	#432	1	2	yes	—
81	C₂²×C₄²	—	47	1	no	—
82	C₂×C₂²⋊C₈	—	47	1	no	—
83	C₂×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
84	#336	—	47	4	no	—
85	C₄₇	#1817	1	1	yes	characteristic, complemented, Sylow
86	C₂³×C₄	—	47	1	no	—
87	C₂³×C₄	—	47	1	no	—
88	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
89	C₂²×C₈	—	47	2	no	—
90	C₂²×C₈	C₂×D₄₇	1	2	yes	—
91	C₂×C₄²	—	47	2	no	—
92	C₂×C₄²	—	47	2	no	—
93	C₂×C₄²	—	94	2	no	—
94	C₂×C₄²	—	94	2	no	—
95	C₂²⋊C₈	—	2	2	no	—
96	C₂²⋊C₈	—	94	2	no	—
97	C₂⁴	C₄×D₄₇	1	1	yes	characteristic
98	C₂²×C₄	—	2	4	no	—
99	C₂²×C₄	—	47	4	no	—
100	C₂²×C₄	—	47	2	no	—
101	C₂²×C₄	—	47	2	no	—
102	C₂²×C₄	—	94	4	no	—
103	C₂²×C₄	—	94	2	no	—
104	C₂²×C₄	—	94	2	no	—
105	C₂²×C₄	—	94	2	no	—
106	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
107	C₂²×C₄	D₁₈₈	1	2	yes	—
108	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	94	2	no	—
113	C₂×C₈	—	94	4	no	—
114	C₄²	—	94	4	no	—
115	C₄²	—	94	2	no	—
116	C₄²	—	94	2	no	—
117	C₂³	—	2	2	no	—
118	C₂³	—	2	2	no	—
119	C₂³	C₈×D₄₇	1	2	yes	—
120	C₂³	#10625324	1	2	yes	—
121	C₂³	(C₂×D₄₇)⋊C₄	1	2	yes	—
122	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	47	4	no	—
127	C₂×C₄	—	47	4	no	—
128	C₂×C₄	—	94	8	no	—
129	C₂×C₄	—	94	8	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	(C₂×D₄₇)⋊C₄	1	2	yes	—
135	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
136	C₂×C₄	#10625352	1	4	yes	—
137	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₈	—	188	2	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	4	no	—
143	C₂²	—	2	4	no	—
144	C₂²	(C₂×D₄₇)⋊C₈	1	4	yes	—
145	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
146	C₂²	#13093980	1	2	yes	—
147	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
148	C₂²	M₁₆×D₄₇	1	2	yes	—
149	C₂²	C₂×#10625324	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	94	4	no	—
152	C₄	—	94	4	no	—
153	C₄	#13094005	1	2	yes	—
154	C₄	#13094008	1	2	yes	—
155	C₂	—	2	4	no	—
156	C₂	#15688984	1	1	yes	characteristic
157	C₂	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
158	C₂	#15689086	1	1	yes	characteristic
159	C₂	#15689173	1	2	yes	—
160	C₂	#15689177	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal, complemented

C₂×C₂²⋊C₈×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₄

yes

characteristic

C₂³×Dic₄₇

C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₈

yes

complemented

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₈

yes

—

C₂³×C₄₇

M₁₆

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#123

yes

—

C₄×C₄₇

#123

yes

—

Dic₄₇

—

Dic₄₇

—

#1817

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#381

yes

characteristic

C₂×C₄₇

C₂×C₂²⋊C₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#432

yes

—

C₂²×C₄²

—

C₂×C₂²⋊C₈

—

C₂×C₂²⋊C₈

D₄₇

yes

characteristic

#336

—

C₄₇

#1817

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

C₄×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₄×D₄₇

yes

characteristic

107

C₂²×C₄

D₁₈₈

yes

—

108

C₂²×C₄

C₂²⋊D₄₇

yes

—

109

C₂²×C₄

C₂²×D₄₇

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄²

—

115

C₄²

—

116

C₄²

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₈×D₄₇

yes

—

120

C₂³

#10625324

yes

—

121

C₂³

(C₂×D₄₇)⋊C₄

yes

—

122

C₂³

C₂×C₄×D₄₇

yes

characteristic

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

(C₂×D₄₇)⋊C₄

yes

—

135

C₂×C₄

C₂×D₁₈₈

yes

characteristic

136

C₂×C₄

#10625352

yes

—

137

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

138

C₈

—

139

C₈

—

188

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

(C₂×D₄₇)⋊C₈

yes

—

145

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

146

C₂²

#13093980

yes

—

147

C₂²

C₂×C₈×D₄₇

yes

characteristic

148

C₂²

M₁₆×D₄₇

yes

—

149

C₂²

C₂×#10625324

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

#13094005

yes

—

154

C₄

#13094008

yes

—

155

C₂

—

156

C₂

#15688984

yes

characteristic

157

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

158

C₂

#15689086

yes

characteristic

159

C₂

#15689173

yes

—

160

C₂

#15689177

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₈
Fitting	C₂×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#1817
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂²×C₈

Fitting

C₂×C₂²⋊C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂×C₂²⋊C₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. #15688877	C₂	semidirect
26. C₂²×Dic₄₇	C₈	semidirect
85. C₄₇	#1817	semidirect

H ≅ G/N

type

3. #15688877

C₂

semidirect

26. C₂²×Dic₄₇

C₈

semidirect

85. C₄₇

#1817

semidirect

Subgroups — #20243454

Conjugacy classes of subgroups

Complements