Subgroups — C₃×GL(2,𝔽₃) #3779

Order 144.

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

	subgroup	G/H
center, socle, hypercenter	C₂×C₃	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂×C₃
Frattini	C₂	C₃×S₄
Fitting	C₃×Q₈	D₃
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

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.