Subgroups — C₈₉×SD₂₅₆ #36385400

Order 22784.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₈₉×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₆₄×C₈₉	—	2	1	no	—
5	D₃₂×C₈₉	—	2	1	no	—
6	C₆₄×C₈₉	C₂²	1	1	yes	characteristic
7	Q₃₂×C₈₉	—	4	1	no	—
8	D₁₆×C₈₉	—	4	1	no	—
9	C₃₂×C₈₉	D₄	1	1	yes	characteristic
10	Q₁₆×C₈₉	—	8	1	no	—
11	D₈×C₈₉	—	8	1	no	—
12	C₁₆×C₈₉	D₈	1	1	yes	characteristic
13	Q₈×C₈₉	—	16	1	no	—
14	D₄×C₈₉	—	16	1	no	—
15	C₈×C₈₉	D₁₆	1	1	yes	characteristic
16	C₂²×C₈₉	—	32	1	no	—
17	C₄×C₈₉	—	32	1	no	—
18	C₄×C₈₉	D₃₂	1	1	yes	characteristic
19	SD₂₅₆	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₈₉	—	64	1	no	—
21	C₂×C₈₉	D₆₄	1	1	yes	characteristic
22	Q₁₂₈	C₂×C₈₉	1	1	yes	characteristic, complemented
23	D₆₄	C₂×C₈₉	1	1	yes	characteristic
24	C₁₂₈	C₂×C₈₉	1	1	yes	characteristic, complemented
25	C₈₉	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
26	Q₆₄	—	2	1	no	—
27	D₃₂	—	2	1	no	—
28	C₆₄	C₂²×C₈₉	1	1	yes	characteristic
29	Q₃₂	—	4	1	no	—
30	D₁₆	—	4	1	no	—
31	C₃₂	D₄×C₈₉	1	1	yes	characteristic
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₈₉	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	D₁₆×C₈₉	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	D₃₂×C₈₉	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₈₉×D₆₄	1	1	yes	characteristic

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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₉×Q₁₂₈	C₂	semidirect
3. C₈₉×C₁₂₈	C₂	semidirect
19. SD₂₅₆	C₈₉	direct (N × H)
22. Q₁₂₈	C₂×C₈₉	semidirect
24. C₁₂₈	C₂×C₈₉	semidirect
25. C₈₉	SD₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×Q₁₂₈	2
C₈₉×D₆₄	2
C₈₉×C₁₂₈	2
SD₂₅₆	89

Subgroups — C89×SD256 #36385400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×SD₂₅₆ #36385400