Subgroups — C₂×C₃×AGL(1,𝔽₉) #89104

Order 432.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#157	C₂	1	1	yes	maximal, characteristic
2	C₃×AGL(1,𝔽₉)	C₂	1	2	yes	maximal, direct product factor
3	C₂×AGL(1,𝔽₉)	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₃×#157	C₄	1	1	yes	characteristic
6	C₃×#157	C₂²	1	1	yes	characteristic
7	C₂×#157	C₂×C₃	1	1	yes	characteristic
8	AGL(1,𝔽₉)	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃³	C₈	1	1	yes	characteristic, complemented
10	C₃×C₃⋊D₃	C₈	1	1	yes	characteristic, complemented
11	C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₈	—	9	1	no	maximal
13	C₂×C₃⋊D₃	C₃×C₄	1	1	yes	characteristic
14	C₂×C₃×D₃	—	12	1	no	—
15	#157	C₃×C₄	1	1	yes	characteristic
16	#157	C₂²×C₃	1	1	yes	characteristic
17	C₃³	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₄	—	9	1	no	—
19	C₃×C₈	—	9	2	no	—
20	C₂×C₃²	—	4	1	no	—
21	C₂×C₃²	—	8	1	no	—
22	C₂×C₃²	C₃×C₈	1	1	yes	characteristic, complemented
23	C₃⋊D₃	C₃×C₈	1	1	yes	characteristic, complemented
24	C₃⋊D₃	C₂×C₃×C₄	1	1	yes	characteristic
25	C₃×D₃	—	12	1	no	—
26	C₃×D₃	—	12	1	no	—
27	C₂×C₈	—	9	1	no	Sylow
28	C₂²×C₃	—	9	1	no	—
29	C₂×D₃	—	12	1	no	—
30	C₃×C₄	—	9	1	no	—
31	C₃×C₄	—	9	1	no	—
32	C₃²	—	4	1	no	—
33	C₃²	—	8	1	no	—
34	C₃²	C₂×C₃×C₈	1	1	yes	characteristic, complemented
35	C₂×C₄	—	9	1	no	—
36	C₈	—	9	2	no	—
37	C₂×C₃	—	4	1	no	—
38	C₂×C₃	—	8	1	no	—
39	C₂×C₃	—	9	1	no	—
40	C₂×C₃	—	9	1	no	—
41	C₂×C₃	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
42	D₃	—	12	1	no	—
43	D₃	—	12	1	no	—
44	C₂²	—	9	1	no	—
45	C₄	—	9	1	no	—
46	C₄	—	9	1	no	—
47	C₃	—	4	1	no	—
48	C₃	—	8	1	no	—
49	C₃	C₂×AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
50	C₂	—	9	1	no	—
51	C₂	—	9	1	no	—
52	C₂	C₃×AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	AGL(1,𝔽₉)
commutator, hypocenter	C₃²	C₂×C₃×C₈
Frattini	C₁	G
Fitting, socle	C₂×C₃³	C₈
prime radical	C₂×C₃×C₃⋊D₃	C₄
cosocle	#157	C₂²×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. C₃×AGL(1,𝔽₉)	C₂	direct (N × H)
3. C₂×AGL(1,𝔽₉)	C₃	direct (N × H)
8. AGL(1,𝔽₉)	C₂×C₃	direct (N × H)
9. C₂×C₃³	C₈	semidirect
10. C₃×C₃⋊D₃	C₈	semidirect
17. C₃³	C₂×C₈	semidirect
22. C₂×C₃²	C₃×C₈	semidirect
23. C₃⋊D₃	C₃×C₈	semidirect
34. C₃²	C₂×C₃×C₈	semidirect
41. C₂×C₃	AGL(1,𝔽₉)	direct (N × H)
49. C₃	C₂×AGL(1,𝔽₉)	direct (N × H)
52. C₂	C₃×AGL(1,𝔽₉)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#157	2
C₃×AGL(1,𝔽₉)	2
C₂×AGL(1,𝔽₉)	3
C₂×C₃×C₈	9

Subgroups — C2×C3×AGL(1,𝔽9) #89104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×AGL(1,𝔽₉) #89104