Subgroups — C₃²×D₈ #3763

Order 144.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₄	C₂	1	2	yes	maximal, complemented
2	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₈	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²	—	2	2	no	—
5	C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₃×D₄	C₂×C₃	1	8	yes	complemented
7	C₃×C₈	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²	—	4	2	no	—
9	C₂×C₃²	D₄	1	1	yes	characteristic
10	D₈	C₃²	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₃	—	2	8	no	—
12	C₃×C₄	C₂²×C₃	1	4	yes	—
13	C₃²	D₈	1	1	yes	characteristic, direct product factor, Sylow
14	D₄	C₂×C₃²	1	2	yes	complemented
15	C₈	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₂×C₃	—	4	8	no	—
17	C₂×C₃	C₃×D₄	1	4	yes	—
18	C₂²	—	2	2	no	—
19	C₄	C₂²×C₃²	1	1	yes	characteristic
20	C₃	C₃×D₈	1	4	yes	direct product factor
21	C₂	—	4	2	no	—
22	C₂	C₃²×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₃²×C₄ ◁ G

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.