Group #14517549 — subgroups

Subgroups — C₄⋊#92309 #14517549

Order 1944.

324 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 75 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×#92309	C₂	1	2	yes	maximal, complemented
2	C₄×#6896	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊AGL(1,ℤ/9))	—	3	2	no	maximal
4	C₄⋊(C₉⋊D₉)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₄⋊#4169	—	3	2	no	maximal
6	C₂×#6896	C₂²	1	1	yes	characteristic
7	#92309	—	2	2	no	—
8	C₂×C₃⋊AGL(1,ℤ/9)	—	3	4	no	—
9	C₃×C₄×3₋¹⁺²	D₃	1	2	yes	—
10	C₂×C₉⋊D₉	C₂×C₃	1	2	yes	complemented
11	C₂×#4169	—	3	4	no	—
12	C₄×C₉⋊C₉	—	2	2	no	—
13	C₄×C₉⋊C₉	—	2	2	no	—
14	C₄×C₃²⋊C₉	D₃	1	2	yes	—
15	C₄×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
16	#6896	D₄	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₄⋊(C₃⋊D₃)	—	9	1	no	—
18	C₄⋊(C₃⋊D₉)	—	3	2	no	—
19	C₄⋊(C₃⋊D₉)	—	3	2	no	—
20	C₄⋊AGL(1,ℤ/9)	—	9	6	no	—
21	C₂×C₃×3₋¹⁺²	C₂×D₃	1	2	yes	—
22	C₃⋊AGL(1,ℤ/9)	—	6	4	no	—
23	C₂×C₉⋊C₉	—	2	2	no	—
24	C₂×C₉⋊C₉	—	2	2	no	—
25	C₂×C₃²⋊C₉	C₂×D₃	1	2	yes	—
26	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
27	C₉⋊D₉	—	2	2	no	—
28	#4169	—	6	4	no	—
29	C₂×C₃×C₃⋊D₃	—	9	2	no	—
30	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
31	C₂×C₃⋊D₉	—	3	4	no	—
32	C₂×C₃⋊D₉	—	3	4	no	—
33	C₂×AGL(1,ℤ/9)	—	9	12	no	—
34	C₄×3₋¹⁺²	—	3	6	no	—
35	C₃×C₄×C₉	—	2	2	no	—
36	C₃×C₄×C₉	—	2	2	no	—
37	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
38	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
39	C₃×3₋¹⁺²	D₁₂	1	2	yes	—
40	C₉⋊C₉	—	2	2	no	—
41	C₉⋊C₉	—	2	2	no	—
42	C₃²⋊C₉	D₁₂	1	2	yes	—
43	C₉²	C₃×D₄	1	1	yes	characteristic, complemented
44	C₄⋊(C₃⋊D₃)	—	9	1	no	—
45	C₃×D₁₂	—	27	2	no	—
46	C₃×D₁₂	—	27	2	no	—
47	D₃₆	—	9	6	no	—
48	D₃₆	—	27	2	no	—
49	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
50	C₃×C₃⋊D₃	—	18	2	no	—
51	C₂×3₋¹⁺²	—	3	6	no	—
52	C₂×C₃×C₉	—	2	2	no	—
53	C₂×C₃×C₉	—	2	2	no	—
54	C₂×C₃×C₉	C₂×C₃×D₃	1	2	yes	—
55	C₂×C₃×C₉	C₂×C₃×D₃	1	2	yes	—
56	C₃⋊D₉	—	6	4	no	—
57	C₃⋊D₉	—	6	4	no	—
58	AGL(1,ℤ/9)	—	18	12	no	—
59	C₂×C₃⋊D₃	—	9	2	no	—
60	C₂×C₃×D₃	—	27	4	no	—
61	C₂×C₃×D₃	—	27	4	no	—
62	C₃²×C₄	—	3	2	no	—
63	C₃²×C₄	—	3	2	no	—
64	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
65	C₂×D₉	—	9	12	no	—
66	C₂×D₉	—	27	4	no	—
67	C₄×C₉	—	3	2	no	—
68	C₄×C₉	—	6	2	no	—
69	C₄×C₉	—	6	2	no	—
70	C₄×C₉	AGL(1,ℤ/9)	1	6	yes	complemented
71	C₃³	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
72	3₋¹⁺²	—	3	6	no	—
73	C₃×C₉	—	2	2	no	—
74	C₃×C₉	—	2	2	no	—
75	C₃×C₉	C₃×D₁₂	1	2	yes	—
76	C₃×C₉	C₃×D₁₂	1	2	yes	—
77	C₃×D₄	—	81	1	no	—
78	D₁₂	—	27	2	no	—
79	D₁₂	—	27	2	no	—
80	C₂×C₃²	—	3	2	no	—
81	C₂×C₃²	—	3	2	no	—
82	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
83	C₃⋊D₃	—	18	2	no	—
84	C₃×D₃	—	54	4	no	—
85	C₃×D₃	—	54	4	no	—
86	C₂×C₉	—	3	2	no	—
87	C₂×C₉	—	6	2	no	—
88	C₂×C₉	—	6	2	no	—
89	C₂×C₉	C₂×AGL(1,ℤ/9)	1	6	yes	—
90	D₉	—	18	12	no	—
91	D₉	—	54	4	no	—
92	C₂²×C₃	—	81	2	no	—
93	C₂×D₃	—	27	4	no	—
94	C₂×D₃	—	27	4	no	—
95	C₃×C₄	—	9	1	no	—
96	C₃×C₄	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
97	C₃×C₄	#4207	1	2	yes	—
98	C₃²	—	3	2	no	—
99	C₃²	—	3	2	no	—
100	C₃²	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
101	C₉	—	3	2	no	—
102	C₉	—	6	2	no	—
103	C₉	—	6	2	no	—
104	C₉	C₄⋊AGL(1,ℤ/9)	1	6	yes	complemented
105	D₄	—	81	1	no	Sylow
106	C₂×C₃	—	9	1	no	—
107	C₂×C₃	—	162	2	no	—
108	C₂×C₃	C₂×C₃⋊AGL(1,ℤ/9)	1	2	yes	—
109	C₂×C₃	C₂×#4207	1	2	yes	—
110	D₃	—	54	4	no	—
111	D₃	—	54	4	no	—
112	C₂²	—	81	2	no	—
113	C₄	#92309	1	1	yes	characteristic, complemented
114	C₃	—	9	1	no	—
115	C₃	C₄⋊(C₃⋊AGL(1,ℤ/9))	1	2	yes	—
116	C₃	C₄⋊#4207	1	2	yes	—
117	C₂	—	162	2	no	—
118	C₂	C₂×#92309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#92309

C₂

yes

maximal, complemented

C₄×#6896

C₂

yes

maximal, characteristic, complemented

C₄⋊(C₃⋊AGL(1,ℤ/9))

—

maximal

C₄⋊(C₉⋊D₉)

C₃

yes

maximal, characteristic, complemented

C₄⋊#4169

—

maximal

C₂×#6896

C₂²

yes

characteristic

#92309

—

C₂×C₃⋊AGL(1,ℤ/9)

—

C₃×C₄×3₋¹⁺²

D₃

yes

—

C₂×C₉⋊D₉

C₂×C₃

yes

complemented

C₂×#4169

—

C₄×C₉⋊C₉

—

C₄×C₉⋊C₉

—

C₄×C₃²⋊C₉

D₃

yes

—

C₄×C₉²

C₂×C₃

yes

characteristic, complemented

#6896

D₄

yes

characteristic, complemented, Sylow

C₃×C₄⋊(C₃⋊D₃)

—

C₄⋊(C₃⋊D₉)

—

C₄⋊(C₃⋊D₉)

—

C₄⋊AGL(1,ℤ/9)

—

C₂×C₃×3₋¹⁺²

C₂×D₃

yes

—

C₃⋊AGL(1,ℤ/9)

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₃²⋊C₉

C₂×D₃

yes

—

C₂×C₉²

C₂²×C₃

yes

characteristic

C₉⋊D₉

—

#4169

—

C₂×C₃×C₃⋊D₃

—

C₃³×C₄

C₃⋊D₃

yes

characteristic

C₂×C₃⋊D₉

—

C₂×C₃⋊D₉

—

C₂×AGL(1,ℤ/9)

—

C₄×3₋¹⁺²

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

C₃×D₃

yes

—

C₃×C₄×C₉

C₃×D₃

yes

—

C₃×3₋¹⁺²

D₁₂

yes

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

D₁₂

yes

—

C₉²

C₃×D₄

yes

characteristic, complemented

C₄⋊(C₃⋊D₃)

—

C₃×D₁₂

—

C₃×D₁₂

—

D₃₆

—

D₃₆

—

C₂×C₃³

C₂×C₃⋊D₃

yes

characteristic

C₃×C₃⋊D₃

—

C₂×3₋¹⁺²

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₃⋊D₉

—

C₃⋊D₉

—

AGL(1,ℤ/9)

—

C₂×C₃⋊D₃

—

C₂×C₃×D₃

—

C₂×C₃×D₃

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

C₃×C₃⋊D₃

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

AGL(1,ℤ/9)

yes

complemented

C₃³

C₄⋊(C₃⋊D₃)

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×D₁₂

yes

—

C₃×C₉

C₃×D₁₂

yes

—

C₃×D₄

—

D₁₂

—

D₁₂

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

C₂×C₃×C₃⋊D₃

yes

characteristic

C₃⋊D₃

—

C₃×D₃

—

C₃×D₃

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

C₂×AGL(1,ℤ/9)

yes

—

D₉

—

D₉

—

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

C₃×C₄

C₃⋊AGL(1,ℤ/9)

yes

—

C₃×C₄

#4207

yes

—

C₃²

—

C₃²

—

100

C₃²

C₃×C₄⋊(C₃⋊D₃)

yes

characteristic

101

C₉

—

102

C₉

—

103

C₉

—

104

C₉

C₄⋊AGL(1,ℤ/9)

yes

complemented

105

D₄

—

Sylow

106

C₂×C₃

—

107

C₂×C₃

—

162

—

108

C₂×C₃

C₂×C₃⋊AGL(1,ℤ/9)

yes

—

109

C₂×C₃

C₂×#4207

yes

—

110

D₃

—

111

D₃

—

112

C₂²

—

113

C₄

#92309

yes

characteristic, complemented

114

C₃

—

115

C₃

C₄⋊(C₃⋊AGL(1,ℤ/9))

yes

—

116

C₃

C₄⋊#4207

yes

—

117

C₂

—

162

—

118

C₂

C₂×#92309

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#92309
commutator, cosocle	C₂×C₉²	C₂²×C₃
Frattini, socle	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₄×#6896	C₂
hypercenter	C₄	#92309
hypocenter	C₉²	C₃×D₄
LCS	G ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄

subgroup

G/H

center

C₂

C₂×#92309

commutator, cosocle

C₂×C₉²

C₂²×C₃

Frattini, socle

C₂×C₃²

C₂×C₃×C₃⋊D₃

C₂

C₄

C₉²

C₃×D₄

LCS

G ▷ C₂×C₉² ▷ C₉²

UCS

C₁ ◁ C₂ ◁ C₄

N	H ≅ G/N	type
1. C₂×#92309	C₂	semidirect
2. C₄×#6896	C₂	semidirect
4. C₄⋊(C₉⋊D₉)	C₃	semidirect
10. C₂×C₉⋊D₉	C₂×C₃	semidirect
15. C₄×C₉²	C₂×C₃	semidirect
16. #6896	D₄	semidirect
43. C₉²	C₃×D₄	semidirect
70. C₄×C₉	AGL(1,ℤ/9)	semidirect
104. C₉	C₄⋊AGL(1,ℤ/9)	semidirect
113. C₄	#92309	semidirect

H ≅ G/N

type

1. C₂×#92309

C₂

semidirect

2. C₄×#6896

C₂

semidirect

4. C₄⋊(C₉⋊D₉)

C₃

semidirect

10. C₂×C₉⋊D₉

C₂×C₃

semidirect

15. C₄×C₉²

C₂×C₃

semidirect

16. #6896

D₄

semidirect

43. C₉²

C₃×D₄

semidirect

70. C₄×C₉

AGL(1,ℤ/9)

semidirect

104. C₉

C₄⋊AGL(1,ℤ/9)

semidirect

113. C₄

#92309

semidirect

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

subgroup	index
C₂×#92309	2
C₄×#6896	2
C₄⋊(C₃⋊AGL(1,ℤ/9))	3
C₄⋊(C₉⋊D₉)	3
C₄⋊#4169	3

subgroup

index

C₄⋊(C₉⋊D₉)

Subgroups — C₄⋊#92309 #14517549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4⋊#92309 #14517549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#92309 #14517549