Subgroups — C₂²×C₃×A₄ #3850

Order 144.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×A₄	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×A₄	C₃	1	3	yes	maximal, direct product factor
4	C₂²×C₃²	—	4	1	no	maximal
5	C₃×A₄	C₂²	1	1	yes	characteristic, direct product factor
6	C₂³×C₃	—	3	3	no	—
7	C₂³×C₃	—	3	1	no	—
8	C₂³×C₃	C₂×C₃	1	3	yes	complemented
9	C₂×A₄	C₂×C₃	1	9	yes	direct product factor
10	C₂×C₃²	—	4	3	no	—
11	C₂⁴	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃	—	3	3	no	—
13	C₂²×C₃	—	3	2	no	—
14	C₂²×C₃	—	3	3	no	—
15	C₂²×C₃	—	3	3	no	—
16	C₂²×C₃	—	4	3	no	—
17	C₂²×C₃	A₄	1	1	yes	characteristic, direct product factor
18	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic, complemented
19	A₄	C₂²×C₃	1	3	yes	direct product factor
20	C₃²	—	4	1	no	Sylow
21	C₂³	—	3	3	no	—
22	C₂³	—	3	1	no	—
23	C₂³	C₂×C₃²	1	3	yes	complemented
24	C₂×C₃	—	3	3	no	—
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	—	4	9	no	—
27	C₂×C₃	C₂×A₄	1	3	yes	direct product factor
28	C₂²	—	3	3	no	—
29	C₂²	—	3	2	no	—
30	C₂²	—	3	3	no	—
31	C₂²	—	3	3	no	—
32	C₂²	C₃×A₄	1	1	yes	characteristic, direct product factor
33	C₂²	C₂²×C₃²	1	1	yes	characteristic, complemented
34	C₃	—	4	3	no	—
35	C₃	C₂²×A₄	1	1	yes	characteristic, direct product factor
36	C₂	—	3	1	no	—
37	C₂	—	3	3	no	—
38	C₂	C₂×C₃×A₄	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	A₄
commutator, cosocle, hypocenter	C₂²	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₃
LCS	G ▷ C₂²
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.