Subgroups — C₂²×C₃²×C₁₉×C₄₇ #44565299

Order 32148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₉×C₄₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₄₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₉×C₄₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₉×C₄₇	C₂×C₃	1	12	yes	direct product factor
5	C₂²×C₁₉×C₄₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₄₇	C₂²×C₃	1	4	yes	direct product factor
7	C₂×C₁₉×C₄₇	C₂×C₃²	1	3	yes	direct product factor
8	C₂²×C₃²×C₄₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₉×C₄₇	C₂²×C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₄₇	C₂×C₁₉	1	3	yes	direct product factor
11	C₂²×C₃²×C₁₉	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×C₄₇	C₃×C₁₉	1	4	yes	direct product factor
13	C₃²×C₄₇	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃²×C₁₉	C₂×C₄₇	1	3	yes	direct product factor
15	C₂×C₃×C₄₇	C₂×C₃×C₁₉	1	12	yes	direct product factor
16	C₂²×C₃×C₁₉	C₃×C₄₇	1	4	yes	direct product factor
17	C₂²×C₄₇	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₁₉	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄₇	C₂²×C₃×C₁₉	1	4	yes	direct product factor
20	C₂×C₃×C₁₉	C₂×C₃×C₄₇	1	12	yes	direct product factor
21	C₂×C₄₇	C₂×C₃²×C₁₉	1	3	yes	direct product factor
22	C₂²×C₁₉	C₃²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₉	C₂²×C₃×C₄₇	1	4	yes	direct product factor
24	C₄₇	C₂²×C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₉	C₂×C₃²×C₄₇	1	3	yes	direct product factor
26	C₂²×C₃²	C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Hall
27	C₁₉	C₂²×C₃²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃²	C₂×C₁₉×C₄₇	1	3	yes	direct product factor
29	C₂²×C₃	C₃×C₁₉×C₄₇	1	4	yes	direct product factor
30	C₃²	C₂²×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₉×C₄₇	1	12	yes	direct product factor
32	C₂²	C₃²×C₁₉×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₁₉×C₄₇	1	4	yes	direct product factor
34	C₂	C₂×C₃²×C₁₉×C₄₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₉×C₄₇	C₂	direct (N × H)
2. C₂²×C₃×C₁₉×C₄₇	C₃	direct (N × H)
3. C₃²×C₁₉×C₄₇	C₂²	direct (N × H)
4. C₂×C₃×C₁₉×C₄₇	C₂×C₃	direct (N × H)
5. C₂²×C₁₉×C₄₇	C₃²	direct (N × H)
6. C₃×C₁₉×C₄₇	C₂²×C₃	direct (N × H)
7. C₂×C₁₉×C₄₇	C₂×C₃²	direct (N × H)
8. C₂²×C₃²×C₄₇	C₁₉	direct (N × H)
9. C₁₉×C₄₇	C₂²×C₃²	direct (N × H)
10. C₂×C₃²×C₄₇	C₂×C₁₉	direct (N × H)
11. C₂²×C₃²×C₁₉	C₄₇	direct (N × H)
12. C₂²×C₃×C₄₇	C₃×C₁₉	direct (N × H)
13. C₃²×C₄₇	C₂²×C₁₉	direct (N × H)
14. C₂×C₃²×C₁₉	C₂×C₄₇	direct (N × H)
15. C₂×C₃×C₄₇	C₂×C₃×C₁₉	direct (N × H)
16. C₂²×C₃×C₁₉	C₃×C₄₇	direct (N × H)
17. C₂²×C₄₇	C₃²×C₁₉	direct (N × H)
18. C₃²×C₁₉	C₂²×C₄₇	direct (N × H)
19. C₃×C₄₇	C₂²×C₃×C₁₉	direct (N × H)
20. C₂×C₃×C₁₉	C₂×C₃×C₄₇	direct (N × H)
21. C₂×C₄₇	C₂×C₃²×C₁₉	direct (N × H)
22. C₂²×C₁₉	C₃²×C₄₇	direct (N × H)
23. C₃×C₁₉	C₂²×C₃×C₄₇	direct (N × H)
24. C₄₇	C₂²×C₃²×C₁₉	direct (N × H)
25. C₂×C₁₉	C₂×C₃²×C₄₇	direct (N × H)
26. C₂²×C₃²	C₁₉×C₄₇	direct (N × H)
27. C₁₉	C₂²×C₃²×C₄₇	direct (N × H)
28. C₂×C₃²	C₂×C₁₉×C₄₇	direct (N × H)
29. C₂²×C₃	C₃×C₁₉×C₄₇	direct (N × H)
30. C₃²	C₂²×C₁₉×C₄₇	direct (N × H)
31. C₂×C₃	C₂×C₃×C₁₉×C₄₇	direct (N × H)
32. C₂²	C₃²×C₁₉×C₄₇	direct (N × H)
33. C₃	C₂²×C₃×C₁₉×C₄₇	direct (N × H)
34. C₂	C₂×C₃²×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
C₂×C₃²×C₁₉×C₄₇	2
C₂²×C₃×C₁₉×C₄₇	3
C₂²×C₃²×C₄₇	19
C₂²×C₃²×C₁₉	47

Subgroups — C22×C32×C19×C47 #44565299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃²×C₁₉×C₄₇ #44565299