Subgroups — C₂²⋊SL(2,𝔽₃) #996

Order 96.

41 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂×A₄	—	4	1	no	maximal
3	SL(2,𝔽₃)	—	4	4	no	maximal
4	C₂×Q₈	—	3	4	no	—
5	C₂²×C₄	—	3	1	no	—
6	A₄	—	4	1	no	—
7	C₂³	A₄	1	1	yes	characteristic
8	Q₈	—	3	4	no	—
9	Q₈	A₄	1	4	yes	complemented
10	C₂×C₄	—	3	6	no	—
11	C₂×C₃	—	16	1	no	—
12	C₂²	—	3	1	no	—
13	C₂²	—	3	1	no	—
14	C₂²	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
15	C₄	—	3	4	no	—
16	C₃	—	16	1	no	Sylow
17	C₂	—	3	1	no	—
18	C₂	—	3	1	no	—
19	C₂	C₂²⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₂²⋊A₄
commutator, Fitting, cosocle, hypocenter	C₂²×Q₈	C₃
socle	C₂³	A₄
LCS	G ▷ C₂²×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.