Subgroups — C₃×D₆₄ #67989

Order 384.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₂	C₂	1	2	yes	maximal, complemented
2	C₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃×D₁₆	—	2	2	no	—
5	C₃×C₃₂	C₂²	1	1	yes	characteristic
6	D₃₂	C₂×C₃	1	2	yes	complemented
7	C₆₄	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×D₈	—	4	2	no	—
9	C₃×C₁₆	D₄	1	1	yes	characteristic
10	D₁₆	—	2	2	no	—
11	C₃₂	C₂²×C₃	1	1	yes	characteristic
12	C₃×D₄	—	8	2	no	—
13	C₃×C₈	D₈	1	1	yes	characteristic
14	D₈	—	4	2	no	—
15	C₁₆	C₃×D₄	1	1	yes	characteristic
16	C₂²×C₃	—	16	2	no	—
17	C₃×C₄	D₁₆	1	1	yes	characteristic
18	D₄	—	8	2	no	—
19	C₈	C₃×D₈	1	1	yes	characteristic
20	C₂×C₃	—	32	2	no	—
21	C₂×C₃	D₃₂	1	1	yes	characteristic
22	C₂²	—	16	2	no	—
23	C₄	C₃×D₁₆	1	1	yes	characteristic
24	C₃	D₆₄	1	1	yes	characteristic, direct product factor, Sylow
25	C₂	—	32	2	no	—
26	C₂	C₃×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆ ◁ C₃×C₃₂ ◁ 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.