Subgroups — AGL(1,𝔽₉)⋊D₃ #89093

Order 432.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊PSU(3,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	#157⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₃×AGL(1,𝔽₉)	C₂	1	1	yes	maximal, characteristic, complemented
4	AΓL(1,𝔽₉)	—	3	1	no	maximal
5	#1113	—	2	1	no	—
6	C₃⋊#157	—	2	1	no	—
7	C₃×#157	C₂²	1	1	yes	characteristic
8	PSU(3,𝔽₂)	—	3	1	no	—
9	GO⁺(4,𝔽₂)	—	3	1	no	—
10	AGL(1,𝔽₉)	D₃	1	1	yes	characteristic, complemented
11	C₃×C₃⋊D₃	—	4	1	no	—
12	C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
13	#204	—	9	1	no	maximal
14	D₃²	—	6	1	no	—
15	D₃²	—	12	1	no	—
16	#157	—	6	1	no	—
17	#157	C₂×D₃	1	1	yes	characteristic
18	C₃³	SD₁₆	1	1	yes	characteristic, complemented, Sylow
19	D₁₂	—	9	1	no	—
20	Dic₆	—	9	1	no	—
21	C₃×C₈	—	9	1	no	—
22	C₃⋊D₃	—	4	1	no	—
23	C₃⋊D₃	D₁₂	1	1	yes	characteristic
24	C₃×D₃	—	12	1	no	—
25	C₃×D₃	—	12	1	no	—
26	C₃×D₃	—	12	1	no	—
27	C₃×D₃	—	24	1	no	—
28	SD₁₆	—	27	1	no	Sylow
29	C₂×D₃	—	18	1	no	—
30	C₂×D₃	—	36	1	no	—
31	C₃×C₄	—	9	1	no	—
32	Dic₃	—	18	1	no	—
33	C₃²	—	4	1	no	—
34	C₃²	—	8	1	no	—
35	C₃²	#204	1	1	yes	characteristic, complemented
36	Q₈	—	27	1	no	—
37	D₄	—	27	1	no	—
38	C₈	—	9	1	no	—
39	C₂×C₃	—	9	1	no	—
40	C₂×C₃	—	36	1	no	—
41	D₃	—	12	1	no	—
42	D₃	—	12	1	no	—
43	D₃	—	12	1	no	—
44	D₃	—	24	1	no	—
45	C₂²	—	54	1	no	—
46	C₄	—	9	1	no	—
47	C₄	—	54	1	no	—
48	C₃	—	4	1	no	—
49	C₃	—	8	1	no	—
50	C₃	AΓL(1,𝔽₉)	1	1	yes	characteristic, complemented
51	C₂	—	9	1	no	—
52	C₂	—	36	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₃×#157	C₂²
Fitting, socle, hypocenter	C₃³	SD₁₆
prime radical	#157⋊D₃	C₂
LCS	G ▷ C₃×#157 ▷ C₃×C₃⋊D₃ ▷ C₃³
UCS	C₁

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

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