Subgroups — C₂×C₃²×A₄ #6336

Order 216.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×A₄	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×A₄	C₃	1	12	yes	maximal, direct product factor
4	C₂×C₃³	—	4	1	no	maximal
5	C₂²×C₃²	—	3	1	no	—
6	C₂²×C₃²	—	3	1	no	—
7	C₂²×C₃²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×A₄	C₂×C₃	1	12	yes	direct product factor
9	C₃³	—	4	1	no	Sylow
10	C₂³×C₃	C₃²	1	4	yes	complemented
11	C₂×A₄	C₃²	1	9	yes	direct product factor
12	C₂×C₃²	—	3	1	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₃²	—	4	12	no	—
15	C₂×C₃²	A₄	1	1	yes	characteristic, direct product factor
16	C₂²×C₃	—	3	4	no	—
17	C₂²×C₃	—	3	4	no	—
18	C₂²×C₃	C₂×C₃²	1	4	yes	complemented
19	A₄	C₂×C₃²	1	9	yes	direct product factor
20	C₃²	—	4	12	no	—
21	C₃²	C₂×A₄	1	1	yes	characteristic, direct product factor
22	C₂³	C₃³	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃	—	3	4	no	—
24	C₂×C₃	—	3	4	no	—
25	C₂×C₃	—	4	9	no	—
26	C₂×C₃	C₃×A₄	1	4	yes	direct product factor
27	C₂²	—	3	1	no	—
28	C₂²	—	3	1	no	—
29	C₂²	C₂×C₃³	1	1	yes	characteristic, complemented
30	C₃	—	4	9	no	—
31	C₃	C₂×C₃×A₄	1	4	yes	direct product factor
32	C₂	—	3	1	no	—
33	C₂	—	3	1	no	—
34	C₂	C₃²×A₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	A₄
commutator, cosocle, hypocenter	C₂²	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₂³×C₃²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃²

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.