Subgroups — D₉⋊SL(2,𝔽₃) #88616

Order 432.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×SL(2,𝔽₃)	—	3	1	no	maximal
3	Q₈×D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×AGL(1,ℤ/9)	—	4	1	no	maximal
5	C₃×SL(2,𝔽₃)	D₃	1	1	yes	characteristic
6	Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₄×D₉	—	3	1	no	—
8	Dic₁₈	—	3	1	no	—
9	Q₈⋊C₉	—	2	1	no	—
10	C₂×3₋¹⁺²	—	4	1	no	—
11	AGL(1,ℤ/9)	—	4	2	no	—
12	D₃×Q₈	—	3	1	no	—
13	C₂×SL(2,𝔽₃)	—	9	1	no	—
14	C₂×C₃×D₃	—	12	1	no	—
15	C₂×D₉	A₄	1	1	yes	characteristic
16	C₄×C₉	—	3	1	no	—
17	Dic₉	—	3	1	no	—
18	3₋¹⁺²	—	4	1	no	Sylow
19	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
20	C₄×D₃	—	9	1	no	—
21	Dic₆	—	9	1	no	—
22	SL(2,𝔽₃)	—	3	1	no	—
23	C₂×C₃²	—	4	1	no	—
24	C₃×D₃	—	12	2	no	—
25	C₂×C₉	—	8	1	no	—
26	C₂×C₉	C₂×A₄	1	1	yes	characteristic
27	D₉	SL(2,𝔽₃)	1	2	yes	complemented
28	C₂×Q₈	—	9	1	no	Sylow
29	C₂²×C₃	—	36	1	no	—
30	C₂×D₃	—	3	1	no	—
31	C₃×C₄	—	3	1	no	—
32	Dic₃	—	9	1	no	—
33	C₃²	—	4	1	no	—
34	C₉	—	8	1	no	—
35	C₉	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, complemented
36	Q₈	—	27	1	no	—
37	Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
38	C₂×C₄	—	27	1	no	—
39	C₂×C₃	—	12	1	no	—
40	C₂×C₃	—	36	2	no	—
41	C₂×C₃	D₃×A₄	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	—
44	C₄	—	3	1	no	—
45	C₄	—	27	1	no	—
46	C₃	—	12	1	no	—
47	C₃	D₃×SL(2,𝔽₃)	1	1	yes	characteristic
48	C₂	—	9	2	no	—
49	C₂	D₉⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉⋊A₄
commutator, Fitting, cosocle, hypocenter	Q₈×C₉	C₂×C₃
Frattini, socle	C₂×C₃	D₃×A₄
LCS	G ▷ Q₈×C₉
UCS	C₁ ◁ C₂

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.