Group #20243462 — subgroups

Subgroups — #20243462

Order 6016.

504 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 101 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	#15688979	C₂	1	2	yes	maximal
2	#15688890	C₂	1	4	yes	maximal, complemented
3	C₂²×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
5	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
6	C₂⁵×C₄₇	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₄₇	C₄	1	2	yes	complemented
8	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
9	C₂×C₂²⋊C₄×C₄₇	C₄	1	2	yes	complemented
10	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
11	C₂⁴×C₄₇	—	2	4	no	—
12	C₂⁴×C₄₇	—	4	4	no	—
13	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂⁴×C₄₇	D₄	1	4	yes	—
16	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₄₇	—	2	2	no	—
18	C₂²×C₄×C₄₇	—	2	2	no	—
19	C₂²×C₄×C₄₇	—	4	4	no	—
20	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
21	C₂²×Dic₄₇	—	2	4	no	—
22	C₂²⋊C₄×C₄₇	—	2	4	no	—
23	C₂²⋊C₄×C₄₇	—	2	4	no	—
24	C₂²⋊Dic₄₇	—	2	8	no	—
25	C₂²⋊Dic₄₇	—	4	8	no	—
26	C₂³×C₄₇	—	2	4	no	—
27	C₂³×C₄₇	—	2	2	no	—
28	C₂³×C₄₇	—	2	8	no	—
29	C₂³×C₄₇	—	2	2	no	—
30	C₂³×C₄₇	—	2	8	no	—
31	C₂³×C₄₇	—	4	2	no	—
32	C₂³×C₄₇	—	4	4	no	—
33	C₂³×C₄₇	—	4	2	no	—
34	C₂³×C₄₇	—	4	16	no	—
35	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
36	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
37	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
38	C₂³×C₄₇	C₂×D₄	1	2	yes	—
39	C₂³×C₄₇	#41	1	4	yes	—
40	C₂×C₄×C₄₇	—	2	4	no	—
41	C₂×C₄×C₄₇	—	4	4	no	—
42	C₂×C₄×C₄₇	—	4	4	no	—
43	C₂×C₄×C₄₇	—	4	4	no	—
44	C₂×Dic₄₇	—	4	8	no	—
45	C₂×Dic₄₇	—	4	4	no	—
46	C₂²×C₄₇	—	2	8	no	—
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	—	2	4	no	—
49	C₂²×C₄₇	—	2	2	no	—
50	C₂²×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	—	2	2	no	—
52	C₂²×C₄₇	—	2	4	no	—
53	C₂²×C₄₇	—	4	4	no	—
54	C₂²×C₄₇	—	4	16	no	—
55	C₂²×C₄₇	—	4	4	no	—
56	C₂²×C₄₇	#99	1	4	yes	—
57	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄₇	#117	1	2	yes	—
59	C₂²×C₄₇	#123	1	4	yes	—
60	C₄×C₄₇	—	4	4	no	—
61	Dic₄₇	—	8	4	no	—
62	#1819	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	—	2	4	no	—
64	C₂×C₄₇	—	2	4	no	—
65	C₂×C₄₇	—	2	2	no	—
66	C₂×C₄₇	—	4	2	no	—
67	C₂×C₄₇	#381	1	1	yes	characteristic
68	C₂×C₄₇	C₂×#99	1	2	yes	—
69	C₂²×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
70	#379	—	47	2	no	—
71	#342	—	47	4	no	—
72	C₄₇	#1819	1	1	yes	characteristic, complemented, Sylow
73	C₂⁵	C₂×D₄₇	1	1	yes	characteristic
74	C₂³×C₄	Dic₄₇	1	2	yes	complemented
75	C₂×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₂²⋊C₄	—	47	4	no	—
77	C₂×C₂²⋊C₄	—	94	4	no	—
78	C₂×C₂²⋊C₄	Dic₄₇	1	2	yes	complemented
79	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
80	C₂⁴	—	2	4	no	—
81	C₂⁴	—	4	4	no	—
82	C₂⁴	C₂×Dic₄₇	1	1	yes	characteristic
83	C₂⁴	C₂×Dic₄₇	1	1	yes	characteristic
84	C₂⁴	C₂²⋊D₄₇	1	4	yes	—
85	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
86	C₂²×C₄	—	2	2	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	4	4	no	—
89	C₂²×C₄	—	94	4	no	—
90	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
91	C₂²⋊C₄	—	2	4	no	—
92	C₂²⋊C₄	—	2	4	no	—
93	C₂²⋊C₄	—	94	8	no	—
94	C₂²⋊C₄	—	188	8	no	—
95	C₂³	—	2	4	no	—
96	C₂³	—	2	2	no	—
97	C₂³	—	2	8	no	—
98	C₂³	—	2	2	no	—
99	C₂³	—	2	8	no	—
100	C₂³	—	4	2	no	—
101	C₂³	—	4	4	no	—
102	C₂³	—	4	2	no	—
103	C₂³	—	4	16	no	—
104	C₂³	C₂²⋊Dic₄₇	1	2	yes	—
105	C₂³	C₂²⋊Dic₄₇	1	2	yes	—
106	C₂³	#10625350	1	4	yes	—
107	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
108	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
109	C₂×C₄	—	2	4	no	—
110	C₂×C₄	—	4	4	no	—
111	C₂×C₄	—	4	4	no	—
112	C₂×C₄	—	4	4	no	—
113	C₂×C₄	—	188	8	no	—
114	C₂×C₄	—	188	4	no	—
115	C₂²	—	2	8	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	2	2	no	—
119	C₂²	—	2	4	no	—
120	C₂²	—	2	2	no	—
121	C₂²	—	2	4	no	—
122	C₂²	—	4	4	no	—
123	C₂²	—	4	16	no	—
124	C₂²	—	4	4	no	—
125	C₂²	#13093939	1	4	yes	—
126	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
127	C₂²	#13093983	1	2	yes	—
128	C₂²	#13094007	1	4	yes	—
129	C₄	—	4	4	no	—
130	C₄	—	376	4	no	—
131	C₂	—	2	4	no	—
132	C₂	—	2	4	no	—
133	C₂	—	2	2	no	—
134	C₂	—	4	2	no	—
135	C₂	#15688986	1	1	yes	characteristic
136	C₂	C₂×#13093939	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15688979

C₂

yes

maximal

#15688890

C₂

yes

maximal, complemented

C₂²×C₂²⋊C₄×C₄₇

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂⁵×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂⁴×C₄₇

D₄

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

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

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#99

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

#123

yes

—

C₄×C₄₇

—

Dic₄₇

—

#1819

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#381

yes

characteristic

C₂×C₄₇

C₂×#99

yes

—

C₂²×C₂²⋊C₄

D₄₇

yes

characteristic

#379

—

#342

—

C₄₇

#1819

yes

characteristic, complemented, Sylow

C₂⁵

C₂×D₄₇

yes

characteristic

C₂³×C₄

Dic₄₇

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

Dic₄₇

yes

complemented

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂×Dic₄₇

yes

characteristic

C₂⁴

C₂×Dic₄₇

yes

characteristic

C₂⁴

C₂²⋊D₄₇

yes

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

188

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

C₂²⋊Dic₄₇

yes

—

105

C₂³

C₂²⋊Dic₄₇

yes

—

106

C₂³

#10625350

yes

—

107

C₂³

C₂²×Dic₄₇

yes

characteristic

108

C₂³

C₂×C₂²⋊D₄₇

yes

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

188

—

114

C₂×C₄

—

188

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

#13093939

yes

—

126

C₂²

C₂×C₂²⋊Dic₄₇

yes

characteristic

127

C₂²

#13093983

yes

—

128

C₂²

#13094007

yes

—

129

C₄

—

130

C₄

—

376

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

—

135

C₂

#15688986

yes

characteristic

136

C₂

C₂×#13093939

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Frattini	C₂⁴	C₂²×D₄₇
Fitting	C₂²×C₂²⋊C₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	C₂²×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#1819
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×C₂²⋊C₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₄₇

commutator

C₂³×C₄₇

C₂²×C₄

Frattini

C₂⁴

C₂²×D₄₇

Fitting

C₂²×C₂²⋊C₄×C₄₇

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

hypercenter

C₂²×C₂²⋊C₄

D₄₇

hypocenter

C₄₇

#1819

LCS

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂²×C₂²⋊C₄

N	H ≅ G/N	type
2. #15688890	C₂	semidirect
7. C₂³×C₄×C₄₇	C₄	semidirect
9. C₂×C₂²⋊C₄×C₄₇	C₄	semidirect
72. C₄₇	#1819	semidirect
74. C₂³×C₄	Dic₄₇	semidirect
78. C₂×C₂²⋊C₄	Dic₄₇	semidirect

H ≅ G/N

type

2. #15688890

C₂

semidirect

7. C₂³×C₄×C₄₇

C₄

semidirect

9. C₂×C₂²⋊C₄×C₄₇

C₄

semidirect

72. C₄₇

#1819

semidirect

74. C₂³×C₄

Dic₄₇

semidirect

78. C₂×C₂²⋊C₄

Dic₄₇

semidirect

Subgroups — #20243462

Conjugacy classes of subgroups

Complements