Group #20243423 — subgroups

Subgroups — #20243423

Order 6016.

292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689086	C₂	1	2	yes	maximal
4	#15688887	C₂	1	2	yes	maximal, complemented
5	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
7	C₂×#10625329	C₂²	1	2	yes	—
8	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₄₇	—	2	2	no	—
10	C₂×C₈×D₄₇	—	2	2	no	—
11	C₂×C₈×D₄₇	C₄	1	4	yes	—
12	#13093960	—	2	2	no	—
13	(C₂×D₄₇)⋊C₈	—	2	4	no	—
14	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	#108×C₄₇	—	2	2	no	—
17	C₂³×D₄₇	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₇	Q₈	1	1	yes	characteristic
20	C₂×C₄×D₄₇	—	2	1	no	—
21	C₂×C₄×D₄₇	—	2	1	no	—
22	C₂×C₄×D₄₇	—	2	1	no	—
23	C₂×C₄×D₄₇	—	2	1	no	—
24	C₂×C₄×D₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₄₇	D₄	1	2	yes	—
26	M₁₆×C₄₇	—	2	2	no	—
27	M₁₆×C₄₇	—	2	2	no	—
28	C₂×C₈×C₄₇	—	2	2	no	—
29	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₄₇	D₄	1	2	yes	—
31	C₂×C₈×C₄₇	D₄	1	2	yes	—
32	#10625329	—	2	2	no	—
33	#10625329	—	2	2	no	—
34	C₂×C₄₇⋊C₈	—	2	1	no	—
35	C₂×C₄₇⋊C₈	—	2	1	no	—
36	C₂×C₄₇⋊C₈	—	2	2	no	—
37	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
38	C₈×D₄₇	—	2	8	no	—
39	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₂²×D₄₇	—	2	1	no	—
41	C₂²×D₄₇	—	2	1	no	—
42	C₂²×D₄₇	—	2	4	no	—
43	C₂²×D₄₇	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
49	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
50	C₂×Dic₄₇	—	2	1	no	—
51	C₂×Dic₄₇	—	2	1	no	—
52	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
53	C₄×D₄₇	—	2	2	no	—
54	C₄×D₄₇	—	2	2	no	—
55	C₄×D₄₇	—	2	2	no	—
56	C₄×D₄₇	—	2	2	no	—
57	C₈×C₄₇	—	4	2	no	—
58	C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
59	C₄₇⋊C₈	—	2	2	no	—
60	C₄₇⋊C₈	—	4	2	no	—
61	C₂²×C₄₇	—	2	2	no	—
62	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
65	C₂×D₄₇	—	2	4	no	—
66	C₂×D₄₇	—	2	4	no	—
67	C₂×D₄₇	—	2	2	no	—
68	C₂×D₄₇	—	2	2	no	—
69	C₂×D₄₇	#108	1	4	yes	complemented
70	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₄×C₄₇	#117	1	1	yes	characteristic
72	C₄×C₄₇	#121	1	1	yes	characteristic
73	C₄×C₄₇	#121	1	1	yes	characteristic
74	Dic₄₇	—	2	2	no	—
75	#1810	—	47	1	no	maximal, Sylow
76	C₂×C₄₇	—	2	1	no	—
77	C₂×C₄₇	—	2	1	no	—
78	C₂×C₄₇	#380	1	1	yes	characteristic
79	C₂×C₄₇	C₂×#108	1	2	yes	—
80	D₄₇	—	2	4	no	—
81	C₂³×C₈	—	47	1	no	—
82	C₂×#108	—	47	1	no	—
83	C₂×#108	D₄₇	1	1	yes	characteristic, complemented
84	#407	—	47	2	no	—
85	#341	—	47	2	no	—
86	C₄₇	#1810	1	1	yes	characteristic, complemented, Sylow
87	C₂³×C₄	—	47	1	no	—
88	C₂×M₁₆	—	47	2	no	—
89	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
90	C₂²×C₈	—	47	1	no	—
91	C₂²×C₈	—	47	4	no	—
92	C₂²×C₈	—	94	2	no	—
93	C₂²×C₈	—	94	2	no	—
94	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
95	#108	—	2	2	no	—
96	#108	—	94	2	no	—
97	C₂²⋊C₈	—	94	4	no	—
98	C₂⁴	—	47	1	no	—
99	C₂²×C₄	—	47	1	no	—
100	C₂²×C₄	—	47	2	no	—
101	C₂²×C₄	—	47	2	no	—
102	C₂²×C₄	—	94	1	no	—
103	C₂²×C₄	—	94	1	no	—
104	C₂²×C₄	—	94	1	no	—
105	C₂²×C₄	—	94	1	no	—
106	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
107	M₁₆	—	2	2	no	—
108	M₁₆	—	2	2	no	—
109	M₁₆	—	94	2	no	—
110	M₁₆	—	94	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	47	2	no	—
113	C₂×C₈	—	94	1	no	—
114	C₂×C₈	—	94	1	no	—
115	C₂×C₈	—	94	8	no	—
116	C₂×C₈	—	94	2	no	—
117	C₂×C₈	C₄×D₄₇	1	2	yes	—
118	C₂×C₈	D₁₈₈	1	2	yes	—
119	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
120	C₂³	—	47	2	no	—
121	C₂³	—	94	4	no	—
122	C₂³	—	94	1	no	—
123	C₂³	—	94	1	no	—
124	C₂³	Q₈×D₄₇	1	1	yes	characteristic
125	C₂×C₄	—	47	2	no	—
126	C₂×C₄	—	94	1	no	—
127	C₂×C₄	—	94	1	no	—
128	C₂×C₄	—	94	2	no	—
129	C₂×C₄	—	94	2	no	—
130	C₂×C₄	—	94	2	no	—
131	C₂×C₄	—	94	2	no	—
132	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
133	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
134	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
135	C₂×C₄	#10625352	1	1	yes	characteristic
136	C₂×C₄	#10625354	1	1	yes	characteristic
137	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₈	—	94	2	no	—
140	C₈	—	188	2	no	—
141	C₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
142	C₂²	—	2	2	no	—
143	C₂²	—	47	4	no	—
144	C₂²	—	94	4	no	—
145	C₂²	—	94	4	no	—
146	C₂²	—	94	2	no	—
147	C₂²	—	94	2	no	—
148	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
149	C₂²	#13094000	1	1	yes	characteristic
150	C₂²	#13094004	1	1	yes	characteristic
151	C₄	—	94	2	no	—
152	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
153	C₄	#13093982	1	1	yes	characteristic
154	C₄	#13093995	1	1	yes	characteristic
155	C₄	#13093999	1	1	yes	characteristic
156	C₂	—	2	1	no	—
157	C₂	—	2	1	no	—
158	C₂	—	94	4	no	—
159	C₂	#15688980	1	1	yes	characteristic
160	C₂	#108×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₄₇

C₂

yes

maximal, characteristic

C₂×#13093960

C₂

yes

maximal, characteristic, complemented

#15689086

C₂

yes

maximal

#15688887

C₂

yes

maximal, complemented

C₂×#108×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

C₄

yes

—

#13093960

—

(C₂×D₄₇)⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

C₂³×D₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

Q₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#108

yes

complemented

C₄×C₄₇

C₂×C₂²⋊C₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1810

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#380

yes

characteristic

C₂×C₄₇

C₂×#108

yes

—

D₄₇

—

C₂³×C₈

—

C₂×#108

—

C₂×#108

D₄₇

yes

characteristic, complemented

#407

—

#341

—

C₄₇

#1810

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#108

—

#108

—

C₂²⋊C₈

—

C₂⁴

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂²×D₄₇

yes

characteristic

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₄×D₄₇

yes

—

118

C₂×C₈

D₁₈₈

yes

—

119

C₂×C₈

C₂²⋊D₄₇

yes

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

Q₈×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

C₂×C₄×D₄₇

yes

characteristic

133

C₂×C₄

C₂×D₁₈₈

yes

characteristic

134

C₂×C₄

D₄×D₄₇

yes

characteristic

135

C₂×C₄

#10625352

yes

characteristic

136

C₂×C₄

#10625354

yes

characteristic

137

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

138

C₈

—

139

C₈

—

140

C₈

—

188

—

141

C₈

(C₂×D₄₇)⋊C₄

yes

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

149

C₂²

#13094000

yes

characteristic

150

C₂²

#13094004

yes

characteristic

151

C₄

—

152

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

153

C₄

#13093982

yes

characteristic

154

C₄

#13093995

yes

characteristic

155

C₄

#13093999

yes

characteristic

156

C₂

—

157

C₂

—

158

C₂

—

159

C₂

#15688980

yes

characteristic

160

C₂

#108×D₄₇

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1810
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#108×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₄⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. C₂×#13093960	C₂	semidirect
4. #15688887	C₂	semidirect
5. C₂×#108×C₄₇	C₂	semidirect
69. C₂×D₄₇	#108	semidirect
83. C₂×#108	D₄₇	semidirect
86. C₄₇	#1810	semidirect

H ≅ G/N

type

2. C₂×#13093960

C₂

semidirect

4. #15688887

C₂

semidirect

5. C₂×#108×C₄₇

C₂

semidirect

69. C₂×D₄₇

#108

semidirect

83. C₂×#108

D₄₇

semidirect

86. C₄₇

#1810

semidirect

Subgroups — #20243423

Conjugacy classes of subgroups

Complements