Subgroups — C₂×C₁₁×C₁₃×C₃⋊D₃ #19104246

Order 5148.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₁×C₁₃	—	3	4	no	maximal
4	C₃²×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×C₁₃	D₃	1	4	yes	complemented
6	D₃×C₁₁×C₁₃	—	3	8	no	—
7	C₂²×C₁₁×C₁₃	—	9	1	no	Hall
8	C₂×C₁₃×C₃⋊D₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁×C₁₃	C₂×D₃	1	4	yes	complemented
10	C₂×C₁₁×C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₁×C₁₃	—	9	2	no	—
12	C₂×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
13	C₂×C₃²×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₁₃×C₃⋊D₃	C₂×C₁₁	1	2	yes	direct product factor
15	C₂×C₃²×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
16	C₁₁×C₃⋊D₃	C₂×C₁₃	1	2	yes	direct product factor
17	C₂×D₃×C₁₃	—	3	4	no	—
18	C₁₁×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×D₃×C₁₁	—	3	4	no	—
20	C₃²×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₃	D₃×C₁₁	1	4	yes	complemented
23	D₃×C₁₃	—	3	8	no	—
24	C₂×C₃×C₁₁	D₃×C₁₃	1	4	yes	complemented
25	D₃×C₁₁	—	3	8	no	—
26	C₂²×C₁₃	—	9	1	no	Hall
27	C₂²×C₁₁	—	9	1	no	Hall
28	C₃×C₁₃	C₂×D₃×C₁₁	1	4	yes	complemented
29	C₂×C₃⋊D₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₁	C₂×D₃×C₁₃	1	4	yes	complemented
31	C₂×C₁₃	—	9	2	no	—
32	C₂×C₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor
33	C₂×C₁₁	—	9	2	no	—
34	C₂×C₁₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
35	C₂×C₃²	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
36	C₃⋊D₃	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
37	C₁₃	C₂×C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×D₃	—	3	4	no	—
39	C₁₁	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
40	C₃²	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₁×C₁₃	1	4	yes	complemented
42	D₃	—	3	8	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₁×C₁₃	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₃⋊D₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₁×C₁₃	C₂	semidirect
4. C₃²×C₁₁×C₁₃	C₂²	semidirect
5. C₂×C₃×C₁₁×C₁₃	D₃	semidirect
8. C₂×C₁₃×C₃⋊D₃	C₁₁	direct (N × H)
9. C₃×C₁₁×C₁₃	C₂×D₃	semidirect
10. C₂×C₁₁×C₃⋊D₃	C₁₃	direct (N × H)
12. C₂×C₁₁×C₁₃	C₃⋊D₃	direct (N × H)
13. C₂×C₃²×C₁₃	C₂×C₁₁	semidirect
14. C₁₃×C₃⋊D₃	C₂×C₁₁	direct (N × H)
15. C₂×C₃²×C₁₁	C₂×C₁₃	semidirect
16. C₁₁×C₃⋊D₃	C₂×C₁₃	direct (N × H)
18. C₁₁×C₁₃	C₂×C₃⋊D₃	direct (N × H)
20. C₃²×C₁₃	C₂²×C₁₁	semidirect
21. C₃²×C₁₁	C₂²×C₁₃	semidirect
22. C₂×C₃×C₁₃	D₃×C₁₁	semidirect
24. C₂×C₃×C₁₁	D₃×C₁₃	semidirect
28. C₃×C₁₃	C₂×D₃×C₁₁	semidirect
29. C₂×C₃⋊D₃	C₁₁×C₁₃	direct (N × H)
30. C₃×C₁₁	C₂×D₃×C₁₃	semidirect
32. C₂×C₁₃	C₁₁×C₃⋊D₃	direct (N × H)
34. C₂×C₁₁	C₁₃×C₃⋊D₃	direct (N × H)
35. C₂×C₃²	C₂×C₁₁×C₁₃	semidirect
36. C₃⋊D₃	C₂×C₁₁×C₁₃	direct (N × H)
37. C₁₃	C₂×C₁₁×C₃⋊D₃	direct (N × H)
39. C₁₁	C₂×C₁₃×C₃⋊D₃	direct (N × H)
40. C₃²	C₂²×C₁₁×C₁₃	semidirect
41. C₂×C₃	D₃×C₁₁×C₁₃	semidirect
44. C₃	C₂×D₃×C₁₁×C₁₃	semidirect
46. C₂	C₁₁×C₁₃×C₃⋊D₃	direct (N × H)

Subgroups — C2×C11×C13×C3⋊D3 #19104246

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁×C₁₃×C₃⋊D₃ #19104246