Subgroups — C₃⋊(#41⋊C₃) #3784

Order 144.

33 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	#239	C₃	1	1	yes	maximal, characteristic, complemented
3	#41⋊C₃	—	3	1	no	maximal
4	C₃×Dic₃	—	4	1	no	maximal
5	C₃×Q₈	C₂×C₃	1	1	yes	characteristic
6	D₁₂	—	3	1	no	—
7	C₄×D₃	—	3	1	no	—
8	SL(2,𝔽₃)	—	2	1	no	—
9	SL(2,𝔽₃)	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃²	—	4	1	no	—
11	#41	—	3	1	no	Sylow
12	C₂×D₃	—	3	1	no	—
13	C₃×C₄	—	3	1	no	—
14	C₃×C₄	—	12	1	no	—
15	Dic₃	A₄	1	1	yes	characteristic
16	C₃²	—	4	1	no	Sylow
17	Q₈	C₃×D₃	1	1	yes	characteristic
18	D₄	—	9	1	no	—
19	C₂×C₄	—	9	1	no	—
20	C₂×C₃	—	4	1	no	—
21	C₂×C₃	—	8	1	no	—
22	C₂×C₃	C₂×A₄	1	1	yes	characteristic
23	D₃	—	6	1	no	—
24	C₂²	—	9	1	no	—
25	C₄	—	3	1	no	—
26	C₄	—	3	1	no	—
27	C₃	—	4	1	no	—
28	C₃	—	8	1	no	—
29	C₃	#41⋊C₃	1	1	yes	characteristic, complemented
30	C₂	—	18	1	no	—
31	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.