Subgroups — C₈₉×D₁₂₈ #36385399

Order 22784.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×D₆₄	C₂	1	2	yes	maximal, complemented
2	C₈₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₂×C₈₉	—	2	2	no	—
4	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
5	D₁₆×C₈₉	—	4	2	no	—
6	C₃₂×C₈₉	D₄	1	1	yes	characteristic
7	D₈×C₈₉	—	8	2	no	—
8	C₁₆×C₈₉	D₈	1	1	yes	characteristic
9	D₄×C₈₉	—	16	2	no	—
10	C₈×C₈₉	D₁₆	1	1	yes	characteristic
11	C₂²×C₈₉	—	32	2	no	—
12	C₄×C₈₉	D₃₂	1	1	yes	characteristic
13	D₁₂₈	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×C₈₉	—	64	2	no	—
15	C₂×C₈₉	D₆₄	1	1	yes	characteristic
16	D₆₄	C₂×C₈₉	1	2	yes	complemented
17	C₁₂₈	C₂×C₈₉	1	1	yes	characteristic, complemented
18	C₈₉	D₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
19	D₃₂	—	2	2	no	—
20	C₆₄	C₂²×C₈₉	1	1	yes	characteristic
21	D₁₆	—	4	2	no	—
22	C₃₂	D₄×C₈₉	1	1	yes	characteristic
23	D₈	—	8	2	no	—
24	C₁₆	D₈×C₈₉	1	1	yes	characteristic
25	D₄	—	16	2	no	—
26	C₈	D₁₆×C₈₉	1	1	yes	characteristic
27	C₂²	—	32	2	no	—
28	C₄	D₃₂×C₈₉	1	1	yes	characteristic
29	C₂	—	64	2	no	—
30	C₂	C₈₉×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₈₉
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₄×C₈₉ ◁ C₈×C₈₉ ◁ C₁₆×C₈₉ ◁ C₃₂×C₈₉ ◁ C₆₄×C₈₉ ◁ 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.