Subgroups — C₂×C₁₇×D₄₃⋊C₃ #22578554

Order 8772.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₄₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₇×D₄₃	C₂×C₃	1	2	yes	complemented
7	C₁₇×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₄₃⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented
10	D₄₃⋊C₃	C₂×C₁₇	1	2	yes	direct product factor
11	C₂²×C₃×C₁₇	—	43	1	no	maximal, Hall
12	C₂×D₄₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₄₃⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₇	—	43	2	no	—
15	C₂×C₃×C₁₇	—	43	1	no	—
16	C₂×C₄₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
17	D₄₃	C₂×C₃×C₁₇	1	2	yes	complemented
18	C₂²×C₁₇	—	43	1	no	Hall
19	C₃×C₁₇	—	43	1	no	Hall
20	C₄₃	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	—	43	2	no	—
22	C₂×C₁₇	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₁₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	43	1	no	Hall
25	C₂×C₃	—	43	2	no	—
26	C₂×C₃	—	43	1	no	—
27	C₂²	—	43	1	no	Sylow
28	C₃	—	43	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	C₁₇×D₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₄₃⋊C₃
commutator, hypocenter	C₄₃	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₄₃	C₂×C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₄₃⋊C₃	C₂	direct (N × H)
2. C₂×C₁₇×C₄₃⋊C₃	C₂	semidirect
3. C₂×C₁₇×D₄₃	C₃	semidirect
4. C₁₇×C₄₃⋊C₃	C₂²	semidirect
5. C₂×C₁₇×C₄₃	C₂×C₃	semidirect
6. C₁₇×D₄₃	C₂×C₃	semidirect
7. C₁₇×C₄₃	C₂²×C₃	semidirect
8. C₂×D₄₃⋊C₃	C₁₇	direct (N × H)
9. C₂×C₄₃⋊C₃	C₂×C₁₇	semidirect
10. D₄₃⋊C₃	C₂×C₁₇	direct (N × H)
12. C₂×D₄₃	C₃×C₁₇	semidirect
13. C₄₃⋊C₃	C₂²×C₁₇	semidirect
16. C₂×C₄₃	C₂×C₃×C₁₇	semidirect
17. D₄₃	C₂×C₃×C₁₇	semidirect
20. C₄₃	C₂²×C₃×C₁₇	semidirect
22. C₂×C₁₇	D₄₃⋊C₃	direct (N × H)
23. C₁₇	C₂×D₄₃⋊C₃	direct (N × H)
30. C₂	C₁₇×D₄₃⋊C₃	direct (N × H)

Subgroups — C2×C17×D43⋊C3 #22578554

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₇×D₄₃⋊C₃ #22578554