Subgroups — D₃×SL(2,𝔽₃) #3785

Order 144.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×Q₈	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×SL(2,𝔽₃)	—	3	1	no	maximal
4	C₂×C₃×D₃	—	4	1	no	maximal
5	C₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄×D₃	—	3	1	no	—
7	Dic₆	—	3	1	no	—
8	SL(2,𝔽₃)	—	2	1	no	—
9	SL(2,𝔽₃)	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃²	—	4	1	no	—
11	C₃×D₃	—	4	2	no	—
12	C₂×Q₈	—	3	1	no	Sylow
13	C₂²×C₃	—	12	1	no	—
14	C₂×D₃	A₄	1	1	yes	characteristic
15	C₃×C₄	—	3	1	no	—
16	Dic₃	—	3	1	no	—
17	C₃²	—	4	1	no	Sylow
18	Q₈	—	9	1	no	—
19	Q₈	C₃×D₃	1	1	yes	characteristic, complemented
20	C₂×C₄	—	9	1	no	—
21	C₂×C₃	—	4	1	no	—
22	C₂×C₃	—	8	1	no	—
23	C₂×C₃	—	12	2	no	—
24	C₂×C₃	C₂×A₄	1	1	yes	characteristic
25	D₃	SL(2,𝔽₃)	1	2	yes	direct product factor
26	C₂²	—	3	1	no	—
27	C₄	—	3	1	no	—
28	C₄	—	9	1	no	—
29	C₃	—	4	1	no	—
30	C₃	—	8	1	no	—
31	C₃	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, complemented
32	C₂	—	3	2	no	—
33	C₂	D₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×A₄
commutator, Fitting, cosocle, hypocenter	C₃×Q₈	C₂×C₃
socle	C₂×C₃	C₂×A₄
LCS	G ▷ C₃×Q₈
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.