Subgroups — C₃×SD₆₄ #4619

Order 192.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₁₆	—	2	1	no	—
6	C₃×D₈	—	2	1	no	—
7	C₃×C₁₆	C₂²	1	1	yes	characteristic
8	Q₃₂	C₂×C₃	1	1	yes	characteristic, complemented
9	D₁₆	C₂×C₃	1	1	yes	characteristic
10	C₃₂	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×Q₈	—	4	1	no	—
12	C₃×D₄	—	4	1	no	—
13	C₃×C₈	D₄	1	1	yes	characteristic
14	Q₁₆	—	2	1	no	—
15	D₈	—	2	1	no	—
16	C₁₆	C₂²×C₃	1	1	yes	characteristic
17	C₂²×C₃	—	8	1	no	—
18	C₃×C₄	—	8	1	no	—
19	C₃×C₄	D₈	1	1	yes	characteristic
20	Q₈	—	4	1	no	—
21	D₄	—	4	1	no	—
22	C₈	C₃×D₄	1	1	yes	characteristic
23	C₂×C₃	—	16	1	no	—
24	C₂×C₃	D₁₆	1	1	yes	characteristic
25	C₂²	—	8	1	no	—
26	C₄	—	8	1	no	—
27	C₄	C₃×D₈	1	1	yes	characteristic
28	C₃	SD₆₄	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	16	1	no	—
30	C₂	C₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂²×C₃
prime radical	C₃×D₁₆	C₂
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.