Subgroups — C₂²×C₉×C₁₁×C₁₉ #21418969

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₁₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁×C₁₉	C₂×C₃	1	3	yes	—
5	C₂²×C₁₁×C₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₉×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₁₁×C₁₉	C₂×C₉	1	3	yes	direct product factor
9	C₂²×C₉×C₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉×C₁₉	C₂×C₁₁	1	3	yes	direct product factor
11	C₂²×C₃×C₁₉	C₃×C₁₁	1	1	yes	characteristic
12	C₁₁×C₁₉	C₂²×C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₉×C₁₁	C₂×C₁₉	1	3	yes	direct product factor
14	C₉×C₁₉	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₃×C₁₁	C₃×C₁₉	1	1	yes	characteristic
16	C₂×C₃×C₁₉	C₂×C₃×C₁₁	1	3	yes	—
17	C₉×C₁₁	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₁₉	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₁₁	C₂×C₃×C₁₉	1	3	yes	—
20	C₃×C₁₉	C₂²×C₃×C₁₁	1	1	yes	characteristic
21	C₂²×C₁₁	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₂×C₉×C₁₁	1	3	yes	direct product factor
23	C₂²×C₉	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₁	C₂²×C₃×C₁₉	1	1	yes	characteristic
25	C₂×C₁₁	C₂×C₉×C₁₉	1	3	yes	direct product factor
26	C₁₉	C₂²×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	C₂×C₁₁×C₁₉	1	3	yes	direct product factor
28	C₂²×C₃	C₃×C₁₁×C₁₉	1	1	yes	characteristic
29	C₁₁	C₂²×C₉×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₉	C₂²×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₁₁×C₁₉	1	3	yes	—
32	C₂²	C₉×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₁₁×C₁₉	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₁×C₁₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₃	C₂²×C₃×C₁₁×C₁₉
socle	C₂²×C₃×C₁₁×C₁₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×C₁₁×C₁₉	C₂	direct (N × H)
3. C₉×C₁₁×C₁₉	C₂²	direct (N × H)
5. C₂²×C₁₁×C₁₉	C₉	direct (N × H)
6. C₂²×C₉×C₁₉	C₁₁	direct (N × H)
8. C₂×C₁₁×C₁₉	C₂×C₉	direct (N × H)
9. C₂²×C₉×C₁₁	C₁₉	direct (N × H)
10. C₂×C₉×C₁₉	C₂×C₁₁	direct (N × H)
12. C₁₁×C₁₉	C₂²×C₉	direct (N × H)
13. C₂×C₉×C₁₁	C₂×C₁₉	direct (N × H)
14. C₉×C₁₉	C₂²×C₁₁	direct (N × H)
17. C₉×C₁₁	C₂²×C₁₉	direct (N × H)
18. C₂²×C₁₉	C₉×C₁₁	direct (N × H)
21. C₂²×C₁₁	C₉×C₁₉	direct (N × H)
22. C₂×C₁₉	C₂×C₉×C₁₁	direct (N × H)
23. C₂²×C₉	C₁₁×C₁₉	direct (N × H)
25. C₂×C₁₁	C₂×C₉×C₁₉	direct (N × H)
26. C₁₉	C₂²×C₉×C₁₁	direct (N × H)
27. C₂×C₉	C₂×C₁₁×C₁₉	direct (N × H)
29. C₁₁	C₂²×C₉×C₁₉	direct (N × H)
30. C₉	C₂²×C₁₁×C₁₉	direct (N × H)
32. C₂²	C₉×C₁₁×C₁₉	direct (N × H)
34. C₂	C₂×C₉×C₁₁×C₁₉	direct (N × H)

Subgroups — C22×C9×C11×C19 #21418969

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₉×C₁₁×C₁₉ #21418969