Subgroups — C₃×SD₁₂₈ #67990

Order 384.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₂	C₂	1	1	yes	maximal, characteristic
3	C₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₂₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×Q₃₂	—	2	1	no	—
6	C₃×D₁₆	—	2	1	no	—
7	C₃×C₃₂	C₂²	1	1	yes	characteristic
8	Q₆₄	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃₂	C₂×C₃	1	1	yes	characteristic
10	C₆₄	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×Q₁₆	—	4	1	no	—
12	C₃×D₈	—	4	1	no	—
13	C₃×C₁₆	D₄	1	1	yes	characteristic
14	Q₃₂	—	2	1	no	—
15	D₁₆	—	2	1	no	—
16	C₃₂	C₂²×C₃	1	1	yes	characteristic
17	C₃×Q₈	—	8	1	no	—
18	C₃×D₄	—	8	1	no	—
19	C₃×C₈	D₈	1	1	yes	characteristic
20	Q₁₆	—	4	1	no	—
21	D₈	—	4	1	no	—
22	C₁₆	C₃×D₄	1	1	yes	characteristic
23	C₂²×C₃	—	16	1	no	—
24	C₃×C₄	—	16	1	no	—
25	C₃×C₄	D₁₆	1	1	yes	characteristic
26	Q₈	—	8	1	no	—
27	D₄	—	8	1	no	—
28	C₈	C₃×D₈	1	1	yes	characteristic
29	C₂×C₃	—	32	1	no	—
30	C₂×C₃	D₃₂	1	1	yes	characteristic
31	C₂²	—	16	1	no	—
32	C₄	—	16	1	no	—
33	C₄	C₃×D₁₆	1	1	yes	characteristic
34	C₃	SD₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
35	C₂	—	32	1	no	—
36	C₂	C₃×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₃
prime radical	C₃×D₃₂	C₂
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.