Subgroups — C₂×C₃⋊D₃×C₁₉×C₄₇ #44565358

Order 32148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₉×C₄₇	—	3	4	no	maximal
4	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₉×C₄₇	—	3	8	no	—
6	C₂×C₃×C₁₉×C₄₇	D₃	1	4	yes	complemented
7	C₂²×C₁₉×C₄₇	—	9	1	no	Hall
8	C₃×C₁₉×C₄₇	C₂×D₃	1	4	yes	complemented
9	C₂×C₁₉×C₄₇	—	9	2	no	—
10	C₂×C₁₉×C₄₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃⋊D₃×C₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₁₉×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃²×C₄₇	C₂×C₁₉	1	1	yes	characteristic, complemented
14	C₃⋊D₃×C₄₇	C₂×C₁₉	1	2	yes	direct product factor
15	C₂×C₃⋊D₃×C₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×D₃×C₄₇	—	3	4	no	—
17	C₃²×C₄₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
19	C₃⋊D₃×C₁₉	C₂×C₄₇	1	2	yes	direct product factor
20	C₂×C₃×C₄₇	D₃×C₁₉	1	4	yes	complemented
21	D₃×C₄₇	—	3	8	no	—
22	C₂×D₃×C₁₉	—	3	4	no	—
23	C₂²×C₄₇	—	9	1	no	Hall
24	C₃²×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	C₂×D₃×C₁₉	1	4	yes	complemented
26	C₂×C₃×C₁₉	D₃×C₄₇	1	4	yes	complemented
27	D₃×C₁₉	—	3	8	no	—
28	C₂×C₄₇	—	9	2	no	—
29	C₂×C₄₇	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
30	C₂²×C₁₉	—	9	1	no	Hall
31	C₃×C₁₉	C₂×D₃×C₄₇	1	4	yes	complemented
32	C₄₇	C₂×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	—	9	2	no	—
34	C₂×C₁₉	C₃⋊D₃×C₄₇	1	1	yes	characteristic, direct product factor
35	C₂×C₃⋊D₃	C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
36	C₁₉	C₂×C₃⋊D₃×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃²	C₂×C₁₉×C₄₇	1	1	yes	characteristic, complemented
38	C₃⋊D₃	C₂×C₁₉×C₄₇	1	2	yes	direct product factor
39	C₂×D₃	—	3	4	no	—
40	C₃²	C₂²×C₁₉×C₄₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₉×C₄₇	1	4	yes	complemented
42	D₃	—	3	8	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₉×C₄₇	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₃⋊D₃×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₉×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₄₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₉×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₁₉×C₄₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₄₇	C₂	semidirect
4. C₃²×C₁₉×C₄₇	C₂²	semidirect
6. C₂×C₃×C₁₉×C₄₇	D₃	semidirect
8. C₃×C₁₉×C₄₇	C₂×D₃	semidirect
10. C₂×C₁₉×C₄₇	C₃⋊D₃	direct (N × H)
11. C₂×C₃⋊D₃×C₄₇	C₁₉	direct (N × H)
12. C₁₉×C₄₇	C₂×C₃⋊D₃	direct (N × H)
13. C₂×C₃²×C₄₇	C₂×C₁₉	semidirect
14. C₃⋊D₃×C₄₇	C₂×C₁₉	direct (N × H)
15. C₂×C₃⋊D₃×C₁₉	C₄₇	direct (N × H)
17. C₃²×C₄₇	C₂²×C₁₉	semidirect
18. C₂×C₃²×C₁₉	C₂×C₄₇	semidirect
19. C₃⋊D₃×C₁₉	C₂×C₄₇	direct (N × H)
20. C₂×C₃×C₄₇	D₃×C₁₉	semidirect
24. C₃²×C₁₉	C₂²×C₄₇	semidirect
25. C₃×C₄₇	C₂×D₃×C₁₉	semidirect
26. C₂×C₃×C₁₉	D₃×C₄₇	semidirect
29. C₂×C₄₇	C₃⋊D₃×C₁₉	direct (N × H)
31. C₃×C₁₉	C₂×D₃×C₄₇	semidirect
32. C₄₇	C₂×C₃⋊D₃×C₁₉	direct (N × H)
34. C₂×C₁₉	C₃⋊D₃×C₄₇	direct (N × H)
35. C₂×C₃⋊D₃	C₁₉×C₄₇	direct (N × H)
36. C₁₉	C₂×C₃⋊D₃×C₄₇	direct (N × H)
37. C₂×C₃²	C₂×C₁₉×C₄₇	semidirect
38. C₃⋊D₃	C₂×C₁₉×C₄₇	direct (N × H)
40. C₃²	C₂²×C₁₉×C₄₇	semidirect
41. C₂×C₃	D₃×C₁₉×C₄₇	semidirect
44. C₃	C₂×D₃×C₁₉×C₄₇	semidirect
46. C₂	C₃⋊D₃×C₁₉×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₁₉×C₄₇	2
C₂×C₃²×C₁₉×C₄₇	2
C₂×D₃×C₁₉×C₄₇	3
C₂×C₃⋊D₃×C₄₇	19
C₂×C₃⋊D₃×C₁₉	47

Subgroups — C2×C3⋊D3×C19×C47 #44565358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₃×C₁₉×C₄₇ #44565358