Subgroups — D₃×D₁₉×C₄₇ #24924278

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₄₇	D₃×D₁₉
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₄₇	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₄₇

Complements

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

N	H ≅ G/N	type
1. C₄₇×D₅₇	C₂	semidirect
2. D₃×C₁₉×C₄₇	C₂	semidirect
3. C₃×D₁₉×C₄₇	C₂	semidirect
5. C₃×C₁₉×C₄₇	C₂²	semidirect
8. D₁₉×C₄₇	D₃	direct (N × H)
9. C₁₉×C₄₇	C₂×D₃	semidirect
13. D₃×C₄₇	D₁₉	direct (N × H)
14. D₃×D₁₉	C₄₇	direct (N × H)
16. C₃×C₄₇	C₂×D₁₉	semidirect
17. D₅₇	C₂×C₄₇	semidirect
18. C₃×D₁₉	C₂×C₄₇	semidirect
19. D₃×C₁₉	C₂×C₄₇	semidirect
24. C₃×C₁₉	C₂²×C₄₇	semidirect
25. C₄₇	D₃×D₁₉	direct (N × H)
28. D₁₉	D₃×C₄₇	direct (N × H)
29. C₁₉	C₂×D₃×C₄₇	semidirect
33. D₃	D₁₉×C₄₇	direct (N × H)
35. C₃	C₂×D₁₉×C₄₇	semidirect

Subgroups — D3×D19×C47 #24924278

Conjugacy classes of subgroups

Complements

Subgroups — D₃×D₁₉×C₄₇ #24924278