Subgroups — C₃⋊GU(2,𝔽₃) #63756

Order 288.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	GU(2,𝔽₃)	—	3	3	no	maximal
3	#837	—	3	1	no	maximal
4	C₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
5	C₃⋊(C₃⋊C₈)	—	4	1	no	maximal
6	C₃×#41	D₃	1	1	yes	characteristic
7	#41⋊C₃	D₃	1	3	yes	—
8	C₄×Dic₃	—	3	1	no	—
9	#208	—	3	1	no	—
10	C₃²×C₄	—	4	1	no	—
11	#104	—	9	1	no	Sylow
12	C₃×Q₈	Dic₃	1	1	yes	characteristic
13	C₃×D₄	—	3	1	no	—
14	C₂×C₃×C₄	—	3	1	no	—
15	C₂×Dic₃	—	6	1	no	—
16	SL(2,𝔽₃)	Dic₃	1	3	yes	complemented
17	C₃⋊C₈	—	6	1	no	—
18	C₃⋊C₈	—	12	3	no	—
19	C₂×C₃²	—	4	1	no	—
20	#41	C₃⋊D₃	1	1	yes	characteristic
21	M₁₆	—	9	1	no	—
22	C₄²	—	9	1	no	—
23	C₂²×C₃	—	3	1	no	—
24	C₃×C₄	—	3	1	no	—
25	C₃×C₄	—	4	3	no	—
26	C₃×C₄	S₄	1	1	yes	characteristic
27	Dic₃	—	6	2	no	—
28	C₃²	—	4	1	no	Sylow
29	Q₈	C₃⋊Dic₃	1	1	yes	characteristic
30	D₄	—	3	1	no	—
31	C₂×C₄	—	3	1	no	—
32	C₂×C₄	—	18	1	no	—
33	C₈	—	18	1	no	—
34	C₂×C₃	—	4	3	no	—
35	C₂×C₃	—	6	1	no	—
36	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
37	C₂²	—	3	1	no	—
38	C₄	—	3	1	no	—
39	C₄	—	18	2	no	—
40	C₄	C₃⋊S₄	1	1	yes	characteristic
41	C₃	—	4	3	no	—
42	C₃	GU(2,𝔽₃)	1	1	yes	characteristic, complemented
43	C₂	—	6	1	no	—
44	C₂	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₄
Fitting	C₃×#41	D₃
socle	C₂×C₃	SL(2,ℤ/4)
prime radical, cosocle	C₃×#41⋊C₃	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₄

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.