Subgroups — C₃×D₃₂ #4618

Order 192.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃×D₈	—	2	2	no	—
5	C₃×C₁₆	C₂²	1	1	yes	characteristic
6	D₁₆	C₂×C₃	1	2	yes	complemented
7	C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₄	—	4	2	no	—
9	C₃×C₈	D₄	1	1	yes	characteristic
10	D₈	—	2	2	no	—
11	C₁₆	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	—	8	2	no	—
13	C₃×C₄	D₈	1	1	yes	characteristic
14	D₄	—	4	2	no	—
15	C₈	C₃×D₄	1	1	yes	characteristic
16	C₂×C₃	—	16	2	no	—
17	C₂×C₃	D₁₆	1	1	yes	characteristic
18	C₂²	—	8	2	no	—
19	C₄	C₃×D₈	1	1	yes	characteristic
20	C₃	D₃₂	1	1	yes	characteristic, direct product factor, Sylow
21	C₂	—	16	2	no	—
22	C₂	C₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆ ◁ 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.