Subgroups — GU(2,𝔽₃) #860

Order 96.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#104	—	3	1	no	maximal, Sylow
3	SL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
4	C₃⋊C₈	—	4	1	no	maximal
5	#41	D₃	1	1	yes	characteristic
6	M₁₆	—	3	1	no	—
7	C₄²	—	3	1	no	—
8	C₃×C₄	—	4	1	no	—
9	Q₈	Dic₃	1	1	yes	characteristic
10	D₄	—	3	1	no	—
11	C₂×C₄	—	3	1	no	—
12	C₂×C₄	—	6	1	no	—
13	C₈	—	6	1	no	—
14	C₂×C₃	—	4	1	no	—
15	C₂²	—	3	1	no	—
16	C₄	—	3	1	no	—
17	C₄	—	6	2	no	—
18	C₄	S₄	1	1	yes	characteristic
19	C₃	—	4	1	no	Sylow
20	C₂	—	6	1	no	—
21	C₂	SL(2,ℤ/4)	1	1	yes	characteristic

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

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. SL(2,𝔽₃)	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.