Subgroups — C₂×C₄₇×D₅₇ #24924286

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₉×C₄₇	—	3	1	no	maximal, Hall
4	C₃×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₇	D₃	1	1	yes	characteristic, complemented
6	D₁₉×C₄₇	—	3	2	no	—
7	C₁₉×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃×C₄₇	—	19	1	no	maximal, Hall
9	C₂×C₃×C₄₇	D₁₉	1	1	yes	characteristic, complemented
10	D₃×C₄₇	—	19	2	no	—
11	C₂×D₅₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₄₇	—	57	1	no	Hall
13	C₃×C₄₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
15	D₅₇	C₂×C₄₇	1	2	yes	direct product factor
16	C₂×C₄₇	—	57	2	no	—
17	C₂×C₄₇	D₅₇	1	1	yes	characteristic, direct product factor
18	C₂×D₁₉	—	3	1	no	Hall
19	C₃×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
20	C₄₇	C₂×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₁₉	D₃×C₄₇	1	1	yes	characteristic, complemented
22	D₁₉	—	3	2	no	—
23	C₁₉	C₂×D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	19	1	no	Hall
25	C₂×C₃	D₁₉×C₄₇	1	1	yes	characteristic, complemented
26	D₃	—	19	2	no	—
27	C₂²	—	57	1	no	Sylow
28	C₃	C₂×D₁₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	57	2	no	—
30	C₂	C₄₇×D₅₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₄₇×D₅₇	C₂	direct (N × H)
2. C₂×C₃×C₁₉×C₄₇	C₂	semidirect
4. C₃×C₁₉×C₄₇	C₂²	semidirect
5. C₂×C₁₉×C₄₇	D₃	semidirect
7. C₁₉×C₄₇	C₂×D₃	semidirect
9. C₂×C₃×C₄₇	D₁₉	semidirect
11. C₂×D₅₇	C₄₇	direct (N × H)
13. C₃×C₄₇	C₂×D₁₉	semidirect
14. C₂×C₃×C₁₉	C₂×C₄₇	semidirect
15. D₅₇	C₂×C₄₇	direct (N × H)
17. C₂×C₄₇	D₅₇	direct (N × H)
19. C₃×C₁₉	C₂²×C₄₇	semidirect
20. C₄₇	C₂×D₅₇	direct (N × H)
21. C₂×C₁₉	D₃×C₄₇	semidirect
23. C₁₉	C₂×D₃×C₄₇	semidirect
25. C₂×C₃	D₁₉×C₄₇	semidirect
28. C₃	C₂×D₁₉×C₄₇	semidirect
30. C₂	C₄₇×D₅₇	direct (N × H)

Subgroups — C2×C47×D57 #24924286

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄₇×D₅₇ #24924286