Subgroups — C₄₃×SD₂₅₆ #24927569

Order 11008.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×D₆₄	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×Q₆₄	—	2	1	no	—
5	C₄₃×D₃₂	—	2	1	no	—
6	C₄₃×C₆₄	C₂²	1	1	yes	characteristic
7	Q₃₂×C₄₃	—	4	1	no	—
8	D₁₆×C₄₃	—	4	1	no	—
9	C₃₂×C₄₃	D₄	1	1	yes	characteristic
10	Q₁₆×C₄₃	—	8	1	no	—
11	D₈×C₄₃	—	8	1	no	—
12	C₁₆×C₄₃	D₈	1	1	yes	characteristic
13	Q₈×C₄₃	—	16	1	no	—
14	D₄×C₄₃	—	16	1	no	—
15	C₈×C₄₃	D₁₆	1	1	yes	characteristic
16	SD₂₅₆	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₄₃	—	32	1	no	—
18	C₄×C₄₃	—	32	1	no	—
19	C₄×C₄₃	D₃₂	1	1	yes	characteristic
20	Q₁₂₈	C₂×C₄₃	1	1	yes	characteristic, complemented
21	D₆₄	C₂×C₄₃	1	1	yes	characteristic
22	C₁₂₈	C₂×C₄₃	1	1	yes	characteristic, complemented
23	C₂×C₄₃	—	64	1	no	—
24	C₂×C₄₃	D₆₄	1	1	yes	characteristic
25	Q₆₄	—	2	1	no	—
26	D₃₂	—	2	1	no	—
27	C₆₄	C₂²×C₄₃	1	1	yes	characteristic
28	C₄₃	SD₂₅₆	1	1	yes	characteristic, direct product factor, Sylow
29	Q₃₂	—	4	1	no	—
30	D₁₆	—	4	1	no	—
31	C₃₂	D₄×C₄₃	1	1	yes	characteristic
32	Q₁₆	—	8	1	no	—
33	D₈	—	8	1	no	—
34	C₁₆	D₈×C₄₃	1	1	yes	characteristic
35	Q₈	—	16	1	no	—
36	D₄	—	16	1	no	—
37	C₈	D₁₆×C₄₃	1	1	yes	characteristic
38	C₂²	—	32	1	no	—
39	C₄	—	32	1	no	—
40	C₄	C₄₃×D₃₂	1	1	yes	characteristic
41	C₂	—	64	1	no	—
42	C₂	C₄₃×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₃	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂²×C₄₃
prime radical	C₄₃×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₃ ◁ C₄×C₄₃ ◁ C₈×C₄₃ ◁ C₁₆×C₄₃ ◁ C₃₂×C₄₃ ◁ C₄₃×C₆₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×Q₁₂₈	C₂	semidirect
3. C₄₃×C₁₂₈	C₂	semidirect
16. SD₂₅₆	C₄₃	direct (N × H)
20. Q₁₂₈	C₂×C₄₃	semidirect
22. C₁₂₈	C₂×C₄₃	semidirect
28. C₄₃	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
C₄₃×Q₁₂₈	2
C₄₃×D₆₄	2
C₄₃×C₁₂₈	2
SD₂₅₆	43

Subgroups — C43×SD256 #24927569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×SD₂₅₆ #24927569