Subgroups — C₃×Q₆₄ #4620

Order 192.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₃₂	C₂	1	2	yes	maximal
2	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Q₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃×Q₁₆	—	2	2	no	—
5	C₃×C₁₆	C₂²	1	1	yes	characteristic
6	Q₃₂	C₂×C₃	1	2	yes	—
7	C₃₂	C₂×C₃	1	1	yes	characteristic
8	C₃×Q₈	—	4	2	no	—
9	C₃×C₈	D₄	1	1	yes	characteristic
10	Q₁₆	—	2	2	no	—
11	C₁₆	C₂²×C₃	1	1	yes	characteristic
12	C₃×C₄	—	8	2	no	—
13	C₃×C₄	D₈	1	1	yes	characteristic
14	Q₈	—	4	2	no	—
15	C₈	C₃×D₄	1	1	yes	characteristic
16	C₂×C₃	D₁₆	1	1	yes	characteristic
17	C₄	—	8	2	no	—
18	C₄	C₃×D₈	1	1	yes	characteristic
19	C₃	Q₆₄	1	1	yes	characteristic, direct product factor, Sylow
20	C₂	C₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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.

N	H ≅ G/N	type
3. Q₆₄	C₃	direct (N × H)
19. C₃	Q₆₄	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.