Subgroups — C₃²×SD₁₆ #3764

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×SD₁₆	C₃	1	4	yes	maximal, direct product factor
5	C₂²×C₃²	—	2	1	no	—
6	C₃²×C₄	—	2	1	no	—
7	C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×Q₈	C₂×C₃	1	4	yes	complemented
9	C₃×D₄	C₂×C₃	1	4	yes	—
10	C₃×C₈	C₂×C₃	1	4	yes	complemented
11	C₂×C₃²	—	4	1	no	—
12	C₂×C₃²	D₄	1	1	yes	characteristic
13	SD₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃	—	2	4	no	—
15	C₃×C₄	—	2	4	no	—
16	C₃×C₄	C₂²×C₃	1	4	yes	—
17	C₃²	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
18	Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
19	D₄	C₂×C₃²	1	1	yes	characteristic
20	C₈	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₂×C₃	—	4	4	no	—
22	C₂×C₃	C₃×D₄	1	4	yes	—
23	C₂²	—	2	1	no	—
24	C₄	—	2	1	no	—
25	C₄	C₂²×C₃²	1	1	yes	characteristic
26	C₃	C₃×SD₁₆	1	4	yes	direct product factor
27	C₂	—	4	1	no	—
28	C₂	C₃²×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃²	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₃²
prime radical	C₃²×D₄	C₂
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.