Subgroups — C₂×C₃²×D₁₉×C₄₇ #44565352

Order 32148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₉×C₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₉×C₄₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₁₉×C₄₇	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₁₉×C₄₇	C₂×C₃	1	4	yes	complemented
7	C₂×D₁₉×C₄₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₁₉×C₄₇	C₂²×C₃	1	4	yes	complemented
9	C₂×C₁₉×C₄₇	C₂×C₃²	1	1	yes	characteristic, complemented
10	D₁₉×C₄₇	C₂×C₃²	1	2	yes	direct product factor
11	C₂²×C₃²×C₄₇	—	19	1	no	maximal, Hall
12	C₁₉×C₄₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃²×C₄₇	—	19	2	no	—
14	C₂×C₃²×C₄₇	D₁₉	1	1	yes	characteristic, direct product factor
15	C₂×C₃²×D₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃×C₄₇	—	19	4	no	—
17	C₃²×C₄₇	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃²×C₁₉	C₂×C₄₇	1	1	yes	characteristic, complemented
19	C₃²×D₁₉	C₂×C₄₇	1	2	yes	direct product factor
20	C₂×C₃×C₄₇	—	19	8	no	—
21	C₂×C₃×C₄₇	C₃×D₁₉	1	4	yes	direct product factor
22	C₂×C₃×D₁₉	C₃×C₄₇	1	4	yes	direct product factor
23	C₂²×C₄₇	—	19	1	no	Hall
24	C₃²×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	C₂×C₃×D₁₉	1	4	yes	direct product factor
26	C₂×C₃×C₁₉	C₂×C₃×C₄₇	1	4	yes	complemented
27	C₃×D₁₉	C₂×C₃×C₄₇	1	8	yes	direct product factor
28	C₂×C₄₇	—	19	2	no	—
29	C₂×C₄₇	C₃²×D₁₉	1	1	yes	characteristic, direct product factor
30	C₂×D₁₉	C₃²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₁₉	C₂²×C₃×C₄₇	1	4	yes	complemented
32	C₄₇	C₂×C₃²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₁₉	C₂×C₃²×C₄₇	1	1	yes	characteristic, complemented
34	D₁₉	C₂×C₃²×C₄₇	1	2	yes	direct product factor
35	C₂²×C₃²	—	19	1	no	Hall
36	C₁₉	C₂²×C₃²×C₄₇	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²	—	19	2	no	—
38	C₂×C₃²	D₁₉×C₄₇	1	1	yes	characteristic, direct product factor
39	C₂²×C₃	—	19	4	no	—
40	C₃²	C₂×D₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	—	19	8	no	—
42	C₂×C₃	C₃×D₁₉×C₄₇	1	4	yes	direct product factor
43	C₂²	—	19	1	no	Sylow
44	C₃	C₂×C₃×D₁₉×C₄₇	1	4	yes	direct product factor
45	C₂	—	19	2	no	—
46	C₂	C₃²×D₁₉×C₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₄₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃²×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₉×C₄₇	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃²×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₉×C₄₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₉×C₄₇	C₂	semidirect
3. C₂×C₃×D₁₉×C₄₇	C₃	direct (N × H)
4. C₃²×C₁₉×C₄₇	C₂²	semidirect
5. C₃×D₁₉×C₄₇	C₂×C₃	direct (N × H)
6. C₂×C₃×C₁₉×C₄₇	C₂×C₃	semidirect
7. C₂×D₁₉×C₄₇	C₃²	direct (N × H)
8. C₃×C₁₉×C₄₇	C₂²×C₃	semidirect
9. C₂×C₁₉×C₄₇	C₂×C₃²	semidirect
10. D₁₉×C₄₇	C₂×C₃²	direct (N × H)
12. C₁₉×C₄₇	C₂²×C₃²	semidirect
14. C₂×C₃²×C₄₇	D₁₉	direct (N × H)
15. C₂×C₃²×D₁₉	C₄₇	direct (N × H)
17. C₃²×C₄₇	C₂×D₁₉	direct (N × H)
18. C₂×C₃²×C₁₉	C₂×C₄₇	semidirect
19. C₃²×D₁₉	C₂×C₄₇	direct (N × H)
21. C₂×C₃×C₄₇	C₃×D₁₉	direct (N × H)
22. C₂×C₃×D₁₉	C₃×C₄₇	direct (N × H)
24. C₃²×C₁₉	C₂²×C₄₇	semidirect
25. C₃×C₄₇	C₂×C₃×D₁₉	direct (N × H)
26. C₂×C₃×C₁₉	C₂×C₃×C₄₇	semidirect
27. C₃×D₁₉	C₂×C₃×C₄₇	direct (N × H)
29. C₂×C₄₇	C₃²×D₁₉	direct (N × H)
30. C₂×D₁₉	C₃²×C₄₇	direct (N × H)
31. C₃×C₁₉	C₂²×C₃×C₄₇	semidirect
32. C₄₇	C₂×C₃²×D₁₉	direct (N × H)
33. C₂×C₁₉	C₂×C₃²×C₄₇	semidirect
34. D₁₉	C₂×C₃²×C₄₇	direct (N × H)
36. C₁₉	C₂²×C₃²×C₄₇	semidirect
38. C₂×C₃²	D₁₉×C₄₇	direct (N × H)
40. C₃²	C₂×D₁₉×C₄₇	direct (N × H)
42. C₂×C₃	C₃×D₁₉×C₄₇	direct (N × H)
44. C₃	C₂×C₃×D₁₉×C₄₇	direct (N × H)
46. C₂	C₃²×D₁₉×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
C₃²×D₁₉×C₄₇	2
C₂×C₃²×C₁₉×C₄₇	2
C₂×C₃×D₁₉×C₄₇	3
C₂²×C₃²×C₄₇	19
C₂×C₃²×D₁₉	47

Subgroups — C2×C32×D19×C47 #44565352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₁₉×C₄₇ #44565352