Subgroups — C₂³×AGL(1,ℤ/9) #88912

Order 432.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/9)	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃×D₃	—	3	1	no	maximal
4	C₂³×D₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂²×3₋¹⁺²	C₂²	1	7	yes	complemented
6	C₂×AGL(1,ℤ/9)	C₂²	1	28	yes	direct product factor
7	C₂³×C₃²	D₃	1	1	yes	characteristic
8	C₂²×C₃×D₃	—	3	14	no	—
9	C₂³×C₉	—	2	1	no	—
10	C₂³×C₉	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×D₉	C₂×C₃	1	14	yes	complemented
12	C₂×3₋¹⁺²	C₂³	1	7	yes	complemented
13	AGL(1,ℤ/9)	C₂³	1	8	yes	direct product factor
14	C₂⁴×C₃	—	9	1	no	—
15	C₂³×D₃	—	3	1	no	—
16	C₂²×C₃²	C₂×D₃	1	7	yes	—
17	C₂×C₃×D₃	—	3	28	no	—
18	C₂²×C₉	—	2	7	no	—
19	C₂²×C₉	C₂²×C₃	1	7	yes	complemented
20	C₂×D₉	C₂²×C₃	1	28	yes	complemented
21	3₋¹⁺²	C₂⁴	1	1	yes	characteristic, complemented, Sylow
22	C₂³×C₃	—	3	1	no	—
23	C₂³×C₃	—	9	14	no	—
24	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
25	C₂²×D₃	—	3	14	no	—
26	C₂×C₃²	C₂²×D₃	1	7	yes	—
27	C₃×D₃	—	3	8	no	—
28	C₂×C₉	—	2	7	no	—
29	C₂×C₉	C₂³×C₃	1	7	yes	complemented
30	D₉	C₂³×C₃	1	8	yes	complemented
31	C₂⁴	—	9	1	no	Sylow
32	C₂²×C₃	—	3	7	no	—
33	C₂²×C₃	—	9	28	no	—
34	C₂²×C₃	C₂×C₃×D₃	1	7	yes	—
35	C₂×D₃	—	3	28	no	—
36	C₃²	C₂³×D₃	1	1	yes	characteristic
37	C₉	—	2	1	no	—
38	C₉	C₂⁴×C₃	1	1	yes	characteristic, complemented
39	C₂³	—	9	14	no	—
40	C₂³	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
41	C₂×C₃	—	3	7	no	—
42	C₂×C₃	—	9	8	no	—
43	C₂×C₃	C₂²×C₃×D₃	1	7	yes	—
44	D₃	—	3	8	no	—
45	C₂²	—	9	28	no	—
46	C₂²	C₂×AGL(1,ℤ/9)	1	7	yes	direct product factor
47	C₃	—	3	1	no	—
48	C₃	C₂³×C₃×D₃	1	1	yes	characteristic
49	C₂	—	9	8	no	—
50	C₂	C₂²×AGL(1,ℤ/9)	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉	C₂⁴×C₃
Frattini	C₃	C₂³×C₃×D₃
Fitting	C₂³×3₋¹⁺²	C₂
socle	C₂³×C₃	C₃×D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂³×3₋¹⁺²	C₂	semidirect
2. C₂²×AGL(1,ℤ/9)	C₂	direct (N × H)
4. C₂³×D₉	C₃	semidirect
5. C₂²×3₋¹⁺²	C₂²	semidirect
6. C₂×AGL(1,ℤ/9)	C₂²	direct (N × H)
10. C₂³×C₉	C₂×C₃	semidirect
11. C₂²×D₉	C₂×C₃	semidirect
12. C₂×3₋¹⁺²	C₂³	semidirect
13. AGL(1,ℤ/9)	C₂³	direct (N × H)
19. C₂²×C₉	C₂²×C₃	semidirect
20. C₂×D₉	C₂²×C₃	semidirect
21. 3₋¹⁺²	C₂⁴	semidirect
29. C₂×C₉	C₂³×C₃	semidirect
30. D₉	C₂³×C₃	semidirect
38. C₉	C₂⁴×C₃	semidirect
40. C₂³	AGL(1,ℤ/9)	direct (N × H)
46. C₂²	C₂×AGL(1,ℤ/9)	direct (N × H)
50. C₂	C₂²×AGL(1,ℤ/9)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×3₋¹⁺²	2
C₂²×AGL(1,ℤ/9)	2
C₂³×C₃×D₃	3
C₂³×D₉	3

Subgroups — C23×AGL(1,ℤ/9) #88912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×AGL(1,ℤ/9) #88912