Group #20243309 — subgroups

Subgroups — #20243309

Order 6016.

820 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13093941	C₂	1	4	yes	maximal, complemented
2	#15689087	C₂	1	2	yes	maximal, complemented
3	C₂³×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	C₂²	1	4	yes	complemented
5	#13093941	—	2	8	no	—
6	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
7	C₂⁵×C₄₇	C₄	1	2	yes	—
8	C₂²×D₄×C₄₇	—	2	8	no	—
9	C₂²×D₄×C₄₇	—	2	4	no	—
10	C₂²×D₄×C₄₇	C₄	1	2	yes	—
11	C₂²×D₄×C₄₇	C₂²	1	2	yes	—
12	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄₇	—	2	8	no	—
14	C₂⁴×C₄₇	—	2	4	no	—
15	C₂⁴×C₄₇	—	4	8	no	—
16	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂⁴×C₄₇	C₂×C₄	1	4	yes	—
18	C₂×D₄×C₄₇	—	2	32	no	—
19	C₂×D₄×C₄₇	—	2	8	no	—
20	C₂×D₄×C₄₇	—	2	4	no	—
21	C₂×D₄×C₄₇	—	2	4	no	—
22	C₂×D₄×C₄₇	—	2	4	no	—
23	C₂×D₄×C₄₇	D₄	1	8	yes	—
24	C₂²×C₄×C₄₇	—	2	4	no	—
25	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₇	D₄	1	4	yes	—
27	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	#10625329	—	2	8	no	—
29	C₂×C₄₇⋊C₈	—	2	4	no	—
30	C₂³×C₄₇	—	2	4	no	—
31	C₂³×C₄₇	—	2	2	no	—
32	C₂³×C₄₇	—	2	16	no	—
33	C₂³×C₄₇	—	2	4	no	—
34	C₂³×C₄₇	—	2	4	no	—
35	C₂³×C₄₇	—	4	8	no	—
36	C₂³×C₄₇	—	4	32	no	—
37	C₂³×C₄₇	—	4	8	no	—
38	C₂³×C₄₇	—	4	8	no	—
39	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
40	C₂³×C₄₇	C₂²⋊C₄	1	8	yes	—
41	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	D₄×C₄₇	—	2	16	no	—
43	D₄×C₄₇	—	2	16	no	—
44	C₂×C₄×C₄₇	—	2	2	no	—
45	C₂×C₄×C₄₇	—	2	8	no	—
46	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
49	C₄₇⋊C₈	—	4	4	no	—
50	C₂²×C₄₇	—	2	8	no	—
51	C₂²×C₄₇	—	2	2	no	—
52	C₂²×C₄₇	—	2	2	no	—
53	C₂²×C₄₇	—	2	2	no	—
54	C₂²×C₄₇	—	2	8	no	—
55	C₂²×C₄₇	—	4	8	no	—
56	C₂²×C₄₇	—	4	32	no	—
57	C₂²×C₄₇	—	4	8	no	—
58	C₂²×C₄₇	—	4	8	no	—
59	C₂²×C₄₇	#100	1	4	yes	complemented
60	C₂²×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₄×C₄₇	—	2	2	no	—
63	C₄×C₄₇	#120	1	4	yes	—
64	#1783	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	—	2	4	no	—
66	C₂×C₄₇	—	2	2	no	—
67	C₂×C₄₇	—	4	8	no	—
68	C₂×C₄₇	#379	1	1	yes	characteristic
69	C₂×C₄₇	C₂×#100	1	2	yes	—
70	C₂³×D₄	D₄₇	1	1	yes	characteristic
71	C₂×#100	—	47	4	no	—
72	#407	—	47	2	no	—
73	C₄₇	#1783	1	1	yes	characteristic, complemented, Sylow
74	C₂⁵	Dic₄₇	1	2	yes	—
75	C₂²×D₄	—	2	8	no	—
76	C₂²×D₄	—	2	4	no	—
77	C₂²×D₄	Dic₄₇	1	2	yes	—
78	C₂²×D₄	C₂×D₄₇	1	2	yes	—
79	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
80	C₂×M₁₆	—	47	4	no	—
81	#100	—	94	8	no	—
82	C₂²⋊C₈	—	94	4	no	—
83	C₂⁴	—	2	8	no	—
84	C₂⁴	—	2	4	no	—
85	C₂⁴	—	4	8	no	—
86	C₂⁴	C₂×Dic₄₇	1	1	yes	characteristic
87	C₂⁴	C₂×Dic₄₇	1	4	yes	—
88	C₂×D₄	—	2	32	no	—
89	C₂×D₄	—	2	8	no	—
90	C₂×D₄	—	2	4	no	—
91	C₂×D₄	—	2	4	no	—
92	C₂×D₄	—	2	4	no	—
93	C₂×D₄	C₂²⋊D₄₇	1	8	yes	—
94	C₂²×C₄	—	2	4	no	—
95	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
96	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
97	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
98	M₁₆	—	94	8	no	—
99	C₂×C₈	—	94	4	no	—
100	C₂³	—	2	4	no	—
101	C₂³	—	2	2	no	—
102	C₂³	—	2	16	no	—
103	C₂³	—	2	4	no	—
104	C₂³	—	2	4	no	—
105	C₂³	—	4	8	no	—
106	C₂³	—	4	32	no	—
107	C₂³	—	4	8	no	—
108	C₂³	—	4	8	no	—
109	C₂³	C₂²⋊Dic₄₇	1	2	yes	—
110	C₂³	C₂²⋊Dic₄₇	1	8	yes	—
111	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
112	D₄	—	2	16	no	—
113	D₄	—	2	16	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	8	no	—
116	C₂×C₄	C₂²⋊Dic₄₇	1	2	yes	—
117	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
118	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
119	C₈	—	188	4	no	—
120	C₂²	—	2	8	no	—
121	C₂²	—	2	2	no	—
122	C₂²	—	2	2	no	—
123	C₂²	—	2	2	no	—
124	C₂²	—	2	8	no	—
125	C₂²	—	4	8	no	—
126	C₂²	—	4	32	no	—
127	C₂²	—	4	8	no	—
128	C₂²	—	4	8	no	—
129	C₂²	#13093941	1	4	yes	complemented
130	C₂²	C₂×C₂²⋊Dic₄₇	1	2	yes	—
131	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
132	C₄	—	2	2	no	—
133	C₄	#13093993	1	4	yes	—
134	C₂	—	2	4	no	—
135	C₂	—	2	2	no	—
136	C₂	—	4	8	no	—
137	C₂	#15688979	1	1	yes	characteristic
138	C₂	C₂×#13093941	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093941

C₂

yes

maximal, complemented

#15689087

C₂

yes

maximal, complemented

C₂³×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

complemented

#13093941

—

C₂²⋊(C₄₇⋊C₈)

—

C₂⁵×C₄₇

C₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₄

yes

—

C₂²×D₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂⁴×C₄₇

C₂×C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#100

yes

complemented

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#120

yes

—

#1783

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#379

yes

characteristic

C₂×C₄₇

C₂×#100

yes

—

C₂³×D₄

D₄₇

yes

characteristic

C₂×#100

—

#407

—

C₄₇

#1783

yes

characteristic, complemented, Sylow

C₂⁵

Dic₄₇

yes

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

Dic₄₇

yes

—

C₂²×D₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

#100

—

C₂²⋊C₈

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂×Dic₄₇

yes

characteristic

C₂⁴

C₂×Dic₄₇

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

C₂×C₈

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₂²⋊Dic₄₇

yes

—

110

C₂³

C₂²⋊Dic₄₇

yes

—

111

C₂³

C₂²×Dic₄₇

yes

characteristic

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₂²⋊Dic₄₇

yes

—

117

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

118

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

119

C₈

—

188

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#13093941

yes

complemented

130

C₂²

C₂×C₂²⋊Dic₄₇

yes

—

131

C₂²

C₂×C₂²⋊Dic₄₇

yes

characteristic

132

C₄

—

133

C₄

#13093993

yes

—

134

C₂

—

135

C₂

—

136

C₂

—

137

C₂

#15688979

yes

characteristic

138

C₂

C₂×#13093941

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂³×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂³×D₄	D₄₇
hypocenter	C₄₇	#1783
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×D₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂³×D₄×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

hypercenter

C₂³×D₄

D₄₇

hypocenter

C₄₇

#1783

LCS

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×D₄

N	H ≅ G/N	type
1. C₂×#13093941	C₂	semidirect
2. #15689087	C₂	semidirect
4. C₂×#10625329	C₂²	semidirect
59. C₂²×C₄₇	#100	semidirect
73. C₄₇	#1783	semidirect
129. C₂²	#13093941	semidirect

H ≅ G/N

type

1. C₂×#13093941

C₂

semidirect

2. #15689087

C₂

semidirect

4. C₂×#10625329

C₂²

semidirect

59. C₂²×C₄₇

#100

semidirect

73. C₄₇

#1783

semidirect

129. C₂²

#13093941

semidirect

Subgroups — #20243309

Conjugacy classes of subgroups

Complements