Subgroups — D₃×AGL(1,𝔽₉) #89089

Order 432.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#157	C₂	1	1	yes	maximal, characteristic
2	C₃⋊AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×AGL(1,𝔽₉)	—	3	1	no	maximal
5	D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
6	C₃⋊#157	C₄	1	1	yes	characteristic
7	C₃×#157	C₂²	1	1	yes	characteristic
8	C₂×#157	—	3	1	no	—
9	AGL(1,𝔽₉)	—	3	1	no	—
10	AGL(1,𝔽₉)	D₃	1	1	yes	characteristic, direct product factor
11	C₃⋊(C₃⋊D₃)	C₈	1	1	yes	characteristic, complemented
12	C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
13	C₃²×D₃	C₈	1	1	yes	characteristic, complemented
14	D₃×C₈	—	9	1	no	maximal
15	C₂×C₃⋊D₃	—	3	1	no	—
16	D₃²	—	12	1	no	—
17	#157	—	3	1	no	—
18	#157	C₂×D₃	1	1	yes	characteristic
19	C₃³	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
20	C₄×D₃	—	9	1	no	—
21	C₃×C₈	—	9	1	no	—
22	C₃⋊C₈	—	9	1	no	—
23	C₂×C₃²	—	3	1	no	—
24	C₃⋊D₃	—	3	1	no	—
25	C₃⋊D₃	—	12	1	no	—
26	C₃⋊D₃	—	24	1	no	—
27	C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
28	C₃×D₃	—	4	1	no	—
29	C₃×D₃	—	12	1	no	—
30	C₂×C₈	—	27	1	no	Sylow
31	C₂×D₃	—	9	1	no	—
32	C₂×D₃	—	36	1	no	—
33	C₃×C₄	—	9	1	no	—
34	Dic₃	—	9	1	no	—
35	C₃²	—	4	1	no	—
36	C₃²	—	8	1	no	—
37	C₃²	D₃×C₈	1	1	yes	characteristic, complemented
38	C₂×C₄	—	27	1	no	—
39	C₈	—	9	1	no	—
40	C₈	—	27	1	no	—
41	C₂×C₃	—	9	1	no	—
42	C₂×C₃	—	12	1	no	—
43	D₃	—	9	1	no	—
44	D₃	—	12	1	no	—
45	D₃	—	36	1	no	—
46	D₃	—	72	1	no	—
47	D₃	AGL(1,𝔽₉)	1	1	yes	characteristic, direct product factor
48	C₂²	—	27	1	no	—
49	C₄	—	9	1	no	—
50	C₄	—	27	1	no	—
51	C₃	—	4	1	no	—
52	C₃	—	8	1	no	—
53	C₃	C₂×AGL(1,𝔽₉)	1	1	yes	characteristic, complemented
54	C₂	—	3	1	no	—
55	C₂	—	9	1	no	—
56	C₂	—	27	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃⋊AGL(1,𝔽₉)	C₂	semidirect
3. C₃×AGL(1,𝔽₉)	C₂	semidirect
10. AGL(1,𝔽₉)	D₃	direct (N × H)
11. C₃⋊(C₃⋊D₃)	C₈	semidirect
13. C₃²×D₃	C₈	semidirect
19. C₃³	C₂×C₈	semidirect
37. C₃²	D₃×C₈	semidirect
47. D₃	AGL(1,𝔽₉)	direct (N × H)
53. C₃	C₂×AGL(1,𝔽₉)	semidirect

Maximal subgroups

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

subgroup	index
D₃×#157	2
C₃⋊AGL(1,𝔽₉)	2
C₃×AGL(1,𝔽₉)	2
C₂×AGL(1,𝔽₉)	3
D₃×C₈	9

Subgroups — D3×AGL(1,𝔽9) #89089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×AGL(1,𝔽₉) #89089