Group #14518040 — subgroups

Subgroups — #11757819⋊C₂ #14518040

Order 1944.

214 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 30 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	#11757819	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#638	—	3	1	no	maximal
3	#10619761	C₃	1	1	yes	maximal, characteristic
4	((C₂²⋊C₉)⋊C₂)⋊C₉	—	3	3	no	maximal
5	#6895⋊C₂	—	4	1	no	maximal
6	C₂²×C₃²×C₉	D₃	1	1	yes	characteristic
7	C₂×C₉×C₃⋊D₃	—	3	1	no	—
8	C₉×C₃⋊Dic₃	—	3	1	no	—
9	C₃²⋊(C₂²⋊C₉)	—	2	1	no	—
10	C₃²⋊(C₂²⋊C₉)	C₂×C₃	1	1	yes	characteristic
11	(C₂²⋊C₉)⋊C₉	—	2	3	no	—
12	(C₂²⋊C₉)⋊C₉	D₃	1	3	yes	complemented
13	#6895	—	4	1	no	Sylow
14	C₃×#638	—	3	1	no	—
15	C₃×(C₂²⋊C₉)⋊C₂	—	3	3	no	—
16	C₉×#67	—	9	3	no	—
17	C₉×#67	—	9	1	no	—
18	C₂×C₃²×C₉	—	3	1	no	—
19	C₉×C₃⋊D₃	—	6	1	no	—
20	#4181	—	4	1	no	—
21	D₉⋊C₉	—	12	3	no	—
22	C₂²×C₃³	C₃×D₃	1	1	yes	characteristic
23	C₂×C₃×C₃⋊D₃	—	3	1	no	—
24	C₃×C₃⋊Dic₃	—	3	1	no	—
25	C₂²×C₃×C₉	—	2	1	no	—
26	C₂²×C₃×C₉	—	3	3	no	—
27	C₂²×C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
28	C₂×D₃×C₉	—	9	3	no	—
29	C₂×D₃×C₉	—	9	1	no	—
30	C₃×C₂²⋊C₉	—	2	3	no	—
31	C₃×C₂²⋊C₉	C₃×D₃	1	3	yes	—
32	C₉×Dic₃	—	9	3	no	—
33	C₉×Dic₃	—	9	1	no	—
34	C₃²×C₉	S₄	1	1	yes	characteristic
35	C₉⋊C₉	—	4	3	no	—
36	C₉⋊C₉	—	8	3	no	—
37	C₃²⋊C₉	—	4	1	no	—
38	C₃²⋊C₉	—	8	1	no	—
39	#638	—	3	1	no	—
40	C₃×#67	—	9	3	no	—
41	C₃×#67	—	9	1	no	—
42	(C₂²⋊C₉)⋊C₂	—	3	3	no	—
43	D₄×C₉	—	27	1	no	—
44	C₂×C₃³	—	3	1	no	—
45	C₃×C₃⋊D₃	—	6	1	no	—
46	C₂×C₃×C₉	—	3	3	no	—
47	C₂×C₃×C₉	—	3	1	no	—
48	C₂×C₃×C₉	—	6	1	no	—
49	C₂×C₃×C₉	—	6	3	no	—
50	D₃×C₉	—	18	3	no	—
51	D₃×C₉	—	18	1	no	—
52	C₃×D₉	—	12	3	no	—
53	C₂²×C₃²	—	3	1	no	—
54	C₂²×C₃²	—	6	1	no	—
55	C₂²×C₃²	AGL(1,ℤ/9)	1	3	yes	—
56	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
57	C₂×C₃⋊D₃	—	3	1	no	—
58	C₂×C₃×D₃	—	9	3	no	—
59	C₂×C₃×D₃	—	9	1	no	—
60	C₃⋊Dic₃	—	3	1	no	—
61	C₃×Dic₃	—	9	3	no	—
62	C₃×Dic₃	—	9	1	no	—
63	C₂²×C₉	—	3	1	no	—
64	C₂²×C₉	—	6	1	no	—
65	C₂²×C₉	—	27	1	no	—
66	C₂²⋊C₉	—	3	3	no	—
67	C₂²⋊C₉	—	6	3	no	—
68	C₄×C₉	—	27	1	no	—
69	C₃³	C₃×S₄	1	1	yes	characteristic
70	C₃×C₉	—	2	1	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	4	3	no	—
73	C₃×C₉	—	8	3	no	—
74	C₃×C₉	C₃⋊S₄	1	1	yes	characteristic
75	C₃×D₄	—	27	1	no	—
76	#67	—	9	3	no	—
77	#67	—	9	1	no	—
78	C₂×C₃²	—	3	1	no	—
79	C₂×C₃²	—	3	3	no	—
80	C₂×C₃²	—	3	1	no	—
81	C₂×C₃²	—	6	1	no	—
82	C₂×C₃²	—	6	3	no	—
83	C₃⋊D₃	—	6	1	no	—
84	C₃×D₃	—	18	3	no	—
85	C₃×D₃	—	18	1	no	—
86	C₂×C₉	—	3	1	no	—
87	C₂×C₉	—	6	1	no	—
88	C₂×C₉	—	6	3	no	—
89	C₂×C₉	—	54	1	no	—
90	D₉	—	12	3	no	—
91	C₂²×C₃	—	2	1	no	—
92	C₂²×C₃	—	3	3	no	—
93	C₂²×C₃	—	27	1	no	—
94	C₂²×C₃	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
95	C₂²×C₃	#4208	1	1	yes	characteristic
96	C₂×D₃	—	9	3	no	—
97	C₂×D₃	—	9	1	no	—
98	C₃×C₄	—	27	1	no	—
99	Dic₃	—	9	3	no	—
100	Dic₃	—	9	1	no	—
101	C₃²	—	3	1	no	—
102	C₃²	—	6	1	no	—
103	C₃²	((C₂²⋊C₉)⋊C₂)⋊C₃	1	3	yes	—
104	C₃²	C₃×C₃⋊S₄	1	1	yes	characteristic
105	C₉	—	3	1	no	—
106	C₉	—	6	1	no	—
107	C₉	—	12	3	no	—
108	C₉	—	24	3	no	—
109	D₄	—	27	1	no	Sylow
110	C₂×C₃	—	3	3	no	—
111	C₂×C₃	—	3	1	no	—
112	C₂×C₃	—	3	1	no	—
113	C₂×C₃	—	6	1	no	—
114	C₂×C₃	—	6	3	no	—
115	C₂×C₃	—	54	1	no	—
116	D₃	—	18	3	no	—
117	D₃	—	18	1	no	—
118	C₂²	—	27	1	no	—
119	C₂²	#6895⋊C₂	1	1	yes	characteristic, complemented
120	C₄	—	27	1	no	—
121	C₃	—	2	1	no	—
122	C₃	—	3	3	no	—
123	C₃	#10620044	1	1	yes	characteristic
124	C₃	C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)	1	1	yes	characteristic
125	C₂	—	3	1	no	—
126	C₂	—	54	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11757819

C₂

yes

maximal, characteristic, complemented

C₉×#638

—

maximal

#10619761

C₃

yes

maximal, characteristic

((C₂²⋊C₉)⋊C₂)⋊C₉

—

maximal

#6895⋊C₂

—

maximal

C₂²×C₃²×C₉

D₃

yes

characteristic

C₂×C₉×C₃⋊D₃

—

C₉×C₃⋊Dic₃

—

C₃²⋊(C₂²⋊C₉)

—

C₃²⋊(C₂²⋊C₉)

C₂×C₃

yes

characteristic

(C₂²⋊C₉)⋊C₉

—

(C₂²⋊C₉)⋊C₉

D₃

yes

—

—

C₃×(C₂²⋊C₉)⋊C₂

—

C₉×#67

—

C₉×#67

—

C₂×C₃²×C₉

—

C₉×C₃⋊D₃

—

#4181

—

D₉⋊C₉

—

C₂²×C₃³

C₃×D₃

yes

characteristic

C₂×C₃×C₃⋊D₃

—

C₃×C₃⋊Dic₃

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

C₃⋊D₃

yes

characteristic

C₂×D₃×C₉

—

C₂×D₃×C₉

—

C₃×C₂²⋊C₉

—

C₃×C₂²⋊C₉

C₃×D₃

yes

—

C₉×Dic₃

—

C₉×Dic₃

—

C₃²×C₉

S₄

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

#638

—

C₃×#67

—

C₃×#67

—

(C₂²⋊C₉)⋊C₂

—

D₄×C₉

—

C₂×C₃³

—

C₃×C₃⋊D₃

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

D₃×C₉

—

D₃×C₉

—

C₃×D₉

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

AGL(1,ℤ/9)

yes

—

C₂²×C₃²

C₃×C₃⋊D₃

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₃⋊Dic₃

—

C₃×Dic₃

—

C₃×Dic₃

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²⋊C₉

—

C₂²⋊C₉

—

C₄×C₉

—

C₃³

C₃×S₄

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃⋊S₄

yes

characteristic

C₃×D₄

—

#67

—

#67

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

C₃⋊D₃

—

C₃×D₃

—

C₃×D₃

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

D₉

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

yes

C₂²×C₃

yes

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

Dic₃

—

100

Dic₃

—

101

C₃²

—

102

C₃²

—

103

C₃²

((C₂²⋊C₉)⋊C₂)⋊C₃

yes

—

104

C₃²

C₃×C₃⋊S₄

yes

characteristic

105

C₉

—

106

C₉

—

107

C₉

—

108

C₉

—

109

D₄

—

Sylow

110

C₂×C₃

—

111

C₂×C₃

—

112

C₂×C₃

—

113

C₂×C₃

—

114

C₂×C₃

—

115

C₂×C₃

—

116

D₃

—

117

D₃

—

118

C₂²

—

119

C₂²

#6895⋊C₂

yes

characteristic, complemented

120

C₄

—

121

C₃

—

122

C₃

—

123

C₃

#10620044

yes

characteristic

124

C₃

C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)

yes

characteristic

125

C₂

—

126

C₂

—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
commutator, cosocle, hypocenter	C₃²⋊(C₂²⋊C₉)	C₂×C₃
Frattini	C₃²	C₃×C₃⋊S₄
Fitting	C₂²×C₃²×C₉	D₃
socle	C₂²×C₃²	C₃×C₃⋊D₃
prime radical	#10619761	C₃
LCS	G ▷ C₃²⋊(C₂²⋊C₉)
UCS	C₁ ◁ C₃

subgroup

G/H

center, hypercenter

C₃

C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)

commutator, cosocle, hypocenter

C₃²⋊(C₂²⋊C₉)

C₂×C₃

Frattini

C₃²

C₃×C₃⋊S₄

Fitting

C₂²×C₃²×C₉

D₃

socle

C₂²×C₃²

C₃×C₃⋊D₃

C₃

G ▷ C₃²⋊(C₂²⋊C₉)

C₁ ◁ C₃

N	H ≅ G/N	type
1. #11757819	C₂	semidirect
12. (C₂²⋊C₉)⋊C₉	D₃	semidirect
119. C₂²	#6895⋊C₂	semidirect

H ≅ G/N

type

1. #11757819

C₂

semidirect

12. (C₂²⋊C₉)⋊C₉

D₃

semidirect

119. C₂²

#6895⋊C₂

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11757819	2
C₉×#638	3
#10619761	3
((C₂²⋊C₉)⋊C₂)⋊C₉	3
#6895⋊C₂	4

subgroup

index

((C₂²⋊C₉)⋊C₂)⋊C₉

Subgroups — #11757819⋊C₂ #14518040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11757819⋊C2 #14518040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11757819⋊C₂ #14518040