Subgroups — C₂×C₃×SL(2,𝔽₃) #3813

Order 144.

50 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, direct product factor
2	C₂×C₃×Q₈	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×SL(2,𝔽₃)	C₃	1	3	yes	maximal, direct product factor
4	C₂²×C₃²	—	4	1	no	maximal
5	C₃×Q₈	—	3	1	no	—
6	C₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₄	—	3	1	no	—
8	SL(2,𝔽₃)	C₂×C₃	1	3	yes	direct product factor
9	C₂×C₃²	—	4	2	no	—
10	C₂×C₃²	—	4	1	no	—
11	C₂×Q₈	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃	—	4	3	no	—
13	C₂²×C₃	A₄	1	1	yes	characteristic
14	C₃×C₄	—	3	1	no	—
15	C₃×C₄	—	3	1	no	—
16	C₃²	—	4	1	no	Sylow
17	Q₈	—	3	1	no	—
18	Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₂×C₄	—	3	1	no	—
20	C₂×C₃	—	4	6	no	—
21	C₂×C₃	—	4	3	no	—
22	C₂×C₃	SL(2,𝔽₃)	1	2	yes	direct product factor
23	C₂×C₃	C₂×A₄	1	1	yes	characteristic
24	C₂²	C₃×A₄	1	1	yes	characteristic
25	C₄	—	3	1	no	—
26	C₄	—	3	1	no	—
27	C₃	—	4	3	no	—
28	C₃	C₂×SL(2,𝔽₃)	1	1	yes	characteristic, direct product factor
29	C₂	C₃×SL(2,𝔽₃)	1	2	yes	direct product factor
30	C₂	C₂×C₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, hypercenter	C₂²×C₃	A₄
commutator, cosocle, hypocenter	Q₈	C₂×C₃²
Frattini	C₂	C₂×C₃×A₄
Fitting	C₂×C₃×Q₈	C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂²×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.