Subgroups — C₂×C₃×A₄ #650

Order 72.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×A₄	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃²	—	4	1	no	maximal
5	C₂²×C₃	—	3	1	no	—
6	C₂²×C₃	—	3	1	no	—
7	C₂²×C₃	C₂×C₃	1	1	yes	characteristic, complemented
8	A₄	C₂×C₃	1	3	yes	direct product factor
9	C₃²	—	4	1	no	Sylow
10	C₂³	C₃²	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃	—	3	1	no	—
12	C₂×C₃	—	3	1	no	—
13	C₂×C₃	—	4	3	no	—
14	C₂×C₃	A₄	1	1	yes	characteristic, direct product factor
15	C₂²	—	3	1	no	—
16	C₂²	—	3	1	no	—
17	C₂²	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₃	—	4	3	no	—
19	C₃	C₂×A₄	1	1	yes	characteristic, direct product factor
20	C₂	—	3	1	no	—
21	C₂	—	3	1	no	—
22	C₂	C₃×A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	A₄
commutator, cosocle, hypocenter	C₂²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂³×C₃	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×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.