Subgroups — C₂²×SL(2,𝔽₃) #991

Order 96.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, hypercenter	C₂³	A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃
Frattini	C₂	C₂²×A₄
Fitting	C₂²×Q₈	C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂³

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.