Group #14517545 — subgroups

Subgroups — #14517545

Order 1944.

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

normal subgroups only

This group has 252 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	C₄×#6896	C₂	1	1	yes	maximal, characteristic
2	#11757613	C₂	1	2	yes	maximal
3	#10619962	—	3	2	no	maximal
4	#10619651	C₃	1	1	yes	maximal, characteristic, complemented
5	#10619590	—	3	2	no	maximal
6	C₂×#6896	C₂²	1	1	yes	characteristic
7	C₃×C₄×3₋¹⁺²	D₃	1	2	yes	—
8	C₃⋊(3₋¹⁺²⋊C₄)	—	3	4	no	—
9	C₄×C₉⋊C₉	—	2	2	no	—
10	C₄×C₉⋊C₉	—	2	2	no	—
11	C₄×C₃²⋊C₉	D₃	1	2	yes	—
12	C₄×C₉²	C₂×C₃	1	1	yes	characteristic
13	C₉⋊Dic₉	C₂×C₃	1	2	yes	—
14	#66316	—	3	4	no	—
15	#6896	Q₈	1	1	yes	characteristic, complemented, Sylow
16	C₃×#634	—	9	1	no	—
17	#6226	—	3	2	no	—
18	#6226	—	3	2	no	—
19	3₋¹⁺²⋊Q₈	—	9	6	no	—
20	C₂×C₃×3₋¹⁺²	C₂×D₃	1	2	yes	—
21	C₂×C₉⋊C₉	—	2	2	no	—
22	C₂×C₉⋊C₉	—	2	2	no	—
23	C₂×C₃²⋊C₉	C₂×D₃	1	2	yes	—
24	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
25	C₃³×C₄	C₃⋊D₃	1	1	yes	characteristic
26	C₃×C₃⋊Dic₃	—	9	2	no	—
27	C₄×3₋¹⁺²	—	3	6	no	—
28	C₃×C₄×C₉	—	2	2	no	—
29	C₃×C₄×C₉	—	2	2	no	—
30	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
31	C₃×C₄×C₉	C₃×D₃	1	2	yes	—
32	C₃⋊Dic₉	—	3	4	no	—
33	C₃⋊Dic₉	—	3	4	no	—
34	3₋¹⁺²⋊C₄	—	9	12	no	—
35	C₃×3₋¹⁺²	Dic₆	1	2	yes	—
36	C₉⋊C₉	—	2	2	no	—
37	C₉⋊C₉	—	2	2	no	—
38	C₃²⋊C₉	Dic₆	1	2	yes	—
39	C₉²	C₃×Q₈	1	1	yes	characteristic, complemented
40	#634	—	9	1	no	—
41	C₃×Dic₆	—	27	2	no	—
42	C₃×Dic₆	—	27	2	no	—
43	Dic₁₈	—	9	6	no	—
44	Dic₁₈	—	27	2	no	—
45	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
46	C₂×3₋¹⁺²	—	3	6	no	—
47	C₂×C₃×C₉	—	2	2	no	—
48	C₂×C₃×C₉	—	2	2	no	—
49	C₂×C₃×C₉	C₂×C₃×D₃	1	2	yes	—
50	C₂×C₃×C₉	C₂×C₃×D₃	1	2	yes	—
51	C₃²×C₄	—	3	2	no	—
52	C₃²×C₄	—	3	2	no	—
53	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
54	C₃⋊Dic₃	—	9	2	no	—
55	C₃×Dic₃	—	27	4	no	—
56	C₃×Dic₃	—	27	4	no	—
57	C₄×C₉	—	3	2	no	—
58	C₄×C₉	—	6	2	no	—
59	C₄×C₉	—	6	2	no	—
60	C₄×C₉	AGL(1,ℤ/9)	1	6	yes	—
61	Dic₉	—	9	12	no	—
62	Dic₉	—	27	4	no	—
63	C₃³	#634	1	1	yes	characteristic
64	3₋¹⁺²	—	3	6	no	—
65	C₃×C₉	—	2	2	no	—
66	C₃×C₉	—	2	2	no	—
67	C₃×C₉	C₃×Dic₆	1	2	yes	—
68	C₃×C₉	C₃×Dic₆	1	2	yes	—
69	C₃×Q₈	—	81	1	no	—
70	Dic₆	—	27	2	no	—
71	Dic₆	—	27	2	no	—
72	C₂×C₃²	—	3	2	no	—
73	C₂×C₃²	—	3	2	no	—
74	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
75	C₂×C₉	—	3	2	no	—
76	C₂×C₉	—	6	2	no	—
77	C₂×C₉	—	6	2	no	—
78	C₂×C₉	C₂×AGL(1,ℤ/9)	1	6	yes	—
79	C₃×C₄	—	9	1	no	—
80	C₃×C₄	—	81	2	no	—
81	C₃×C₄	C₃⋊AGL(1,ℤ/9)	1	2	yes	—
82	C₃×C₄	#4207	1	2	yes	—
83	Dic₃	—	27	4	no	—
84	Dic₃	—	27	4	no	—
85	C₃²	—	3	2	no	—
86	C₃²	—	3	2	no	—
87	C₃²	C₃×#634	1	1	yes	characteristic
88	C₉	—	3	2	no	—
89	C₉	—	6	2	no	—
90	C₉	—	6	2	no	—
91	C₉	3₋¹⁺²⋊Q₈	1	6	yes	complemented
92	Q₈	—	81	1	no	Sylow
93	C₂×C₃	—	9	1	no	—
94	C₂×C₃	C₂×C₃⋊AGL(1,ℤ/9)	1	2	yes	—
95	C₂×C₃	C₂×#4207	1	2	yes	—
96	C₄	—	81	2	no	—
97	C₄	#92309	1	1	yes	characteristic
98	C₃	—	9	1	no	—
99	C₃	#10619962	1	2	yes	—
100	C₃	#10619965	1	2	yes	—
101	C₂	C₂×#92309	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#6896

C₂

yes

maximal, characteristic

#11757613

C₂

yes

—

C₃

yes

maximal, characteristic, complemented

#10619590

—

maximal

C₂×#6896

C₂²

yes

characteristic

C₃×C₄×3₋¹⁺²

D₃

yes

—

C₃⋊(3₋¹⁺²⋊C₄)

—

C₄×C₉⋊C₉

—

C₄×C₉⋊C₉

—

C₄×C₃²⋊C₉

D₃

yes

—

C₄×C₉²

C₂×C₃

yes

characteristic

C₉⋊Dic₉

C₂×C₃

yes

—

#66316

—

#6896

Q₈

yes

characteristic, complemented, Sylow

C₃×#634

—

#6226

—

#6226

—

3₋¹⁺²⋊Q₈

—

C₂×C₃×3₋¹⁺²

C₂×D₃

yes

—

C₂×C₉⋊C₉

—

C₂×C₉⋊C₉

—

C₂×C₃²⋊C₉

C₂×D₃

yes

—

C₂×C₉²

C₂²×C₃

yes

characteristic

C₃³×C₄

C₃⋊D₃

yes

characteristic

C₃×C₃⋊Dic₃

—

C₄×3₋¹⁺²

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

C₃×D₃

yes

—

C₃×C₄×C₉

C₃×D₃

yes

—

C₃⋊Dic₉

—

C₃⋊Dic₉

—

3₋¹⁺²⋊C₄

—

C₃×3₋¹⁺²

Dic₆

yes

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

Dic₆

yes

—

C₉²

C₃×Q₈

yes

characteristic, complemented

#634

—

C₃×Dic₆

—

C₃×Dic₆

—

Dic₁₈

—

Dic₁₈

—

C₂×C₃³

C₂×C₃⋊D₃

yes

characteristic

C₂×3₋¹⁺²

—

C₂×C₃×C₉

—

C₂×C₃×C₉

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₂×C₃×C₉

C₂×C₃×D₃

yes

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

C₃×C₃⋊D₃

yes

characteristic

C₃⋊Dic₃

—

C₃×Dic₃

—

C₃×Dic₃

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

—

C₄×C₉

AGL(1,ℤ/9)

yes

—

Dic₉

—

Dic₉

—

C₃³

#634

yes

characteristic

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃×Dic₆

yes

—

C₃×C₉

C₃×Dic₆

yes

—

C₃×Q₈

—

Dic₆

—

Dic₆

—

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

C₂×C₃×C₃⋊D₃

yes

characteristic

C₂×C₉

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

C₂×AGL(1,ℤ/9)

yes

—

C₃×C₄

—

C₃×C₄

—

C₃×C₄

C₃⋊AGL(1,ℤ/9)

yes

—

C₃×C₄

#4207

yes

—

Dic₃

—

Dic₃

—

C₃²

—

C₃²

—

C₃²

C₃×#634

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

3₋¹⁺²⋊Q₈

yes

complemented

Q₈

—

Sylow

C₂×C₃

—

C₂×C₃

C₂×C₃⋊AGL(1,ℤ/9)

yes

—

C₂×C₃

C₂×#4207

yes

—

C₄

—

C₄

#92309

yes

characteristic

C₃

—

C₃

#10619962

yes

—

100

C₃

#10619965

yes

—

101

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
prime radical	C₂×C₃³	C₂×C₃⋊D₃
hypercenter	C₄	#92309
hypocenter	C₉²	C₃×Q₈
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

Fitting

C₄×#6896

C₂

prime radical

C₂×C₃³

C₂×C₃⋊D₃

hypercenter

C₄

#92309

hypocenter

C₉²

C₃×Q₈

LCS

G ▷ C₂×C₉² ▷ C₉²

UCS

C₁ ◁ C₂ ◁ C₄

N	H ≅ G/N	type
4. #10619651	C₃	semidirect
15. #6896	Q₈	semidirect
39. C₉²	C₃×Q₈	semidirect
91. C₉	3₋¹⁺²⋊Q₈	semidirect

H ≅ G/N

type

4. #10619651

C₃

semidirect

15. #6896

Q₈

semidirect

39. C₉²

C₃×Q₈

semidirect

91. C₉

3₋¹⁺²⋊Q₈

semidirect

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

subgroup	index
C₄×#6896	2
#11757613	2
#10619962	3
#10619651	3
#10619590	3

subgroup

index

Subgroups — #14517545

Conjugacy classes of subgroups

Complements

Maximal subgroups