Subgroups — C₃⋊GL(2,𝔽₃) #3782

Order 144.

46 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	GL(2,𝔽₃)	—	3	3	no	maximal
3	#215	—	3	1	no	maximal
4	C₂×C₃⋊D₃	—	4	1	no	maximal
5	C₃×Q₈	D₃	1	1	yes	characteristic, complemented
6	D₁₂	—	3	1	no	—
7	SL(2,𝔽₃)	D₃	1	3	yes	complemented
8	C₃⋊C₈	—	3	1	no	—
9	C₂×C₃²	—	4	1	no	—
10	C₃⋊D₃	—	4	2	no	—
11	SD₁₆	—	9	1	no	Sylow
12	C₂×D₃	—	6	1	no	—
13	C₂×D₃	—	12	3	no	—
14	C₃×C₄	—	3	1	no	—
15	C₃²	—	4	1	no	Sylow
16	Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
17	D₄	—	9	1	no	—
18	C₈	—	9	1	no	—
19	C₂×C₃	—	4	3	no	—
20	C₂×C₃	S₄	1	1	yes	characteristic
21	D₃	—	12	6	no	—
22	D₃	—	12	1	no	—
23	C₂²	—	18	1	no	—
24	C₄	—	3	1	no	—
25	C₃	—	4	3	no	—
26	C₃	GL(2,𝔽₃)	1	1	yes	characteristic, complemented
27	C₂	—	36	1	no	—
28	C₂	C₃⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂
Fitting	C₃×Q₈	D₃
socle	C₂×C₃	S₄
LCS	G ▷ C₃×SL(2,𝔽₃)
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.