Subgroups — C₃×SD₃₂ #855

Order 96.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₈	—	2	1	no	—
6	C₃×D₄	—	2	1	no	—
7	C₃×C₈	C₂²	1	1	yes	characteristic
8	Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
9	D₈	C₂×C₃	1	1	yes	characteristic
10	C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₃	—	4	1	no	—
12	C₃×C₄	—	4	1	no	—
13	C₃×C₄	D₄	1	1	yes	characteristic
14	Q₈	—	2	1	no	—
15	D₄	—	2	1	no	—
16	C₈	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₃	—	8	1	no	—
18	C₂×C₃	D₈	1	1	yes	characteristic
19	C₂²	—	4	1	no	—
20	C₄	—	4	1	no	—
21	C₄	C₃×D₄	1	1	yes	characteristic
22	C₃	SD₃₂	1	1	yes	characteristic, direct product factor, Sylow
23	C₂	—	8	1	no	—
24	C₂	C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₃
prime radical	C₃×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ 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.