Subgroups — C₃×D₁₁×D₅₃ #20296172

Order 6996.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₁×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅₈₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₁×D₅₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₁×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×D₅₃	—	11	1	no	maximal, Hall
10	C₁₁×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₅₃	—	11	1	no	—
12	C₃×D₅₃	—	11	1	no	—
13	C₃×D₅₃	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×D₅₃	—	11	1	no	Hall
15	C₃×C₅₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×D₁₁	—	53	1	no	maximal, Hall
17	C₂×C₅₃	—	11	1	no	—
18	D₅₃	—	11	1	no	—
19	D₅₃	C₃×D₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₁₁	—	53	1	no	—
21	C₃×D₁₁	—	53	1	no	—
22	C₃×D₁₁	D₅₃	1	1	yes	characteristic, direct product factor
23	C₅₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₁	—	53	1	no	Hall
25	C₃×C₁₁	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁	—	53	1	no	—
27	D₁₁	—	53	1	no	—
28	D₁₁	C₃×D₅₃	1	1	yes	characteristic, direct product factor
29	C₂²×C₃	—	583	1	no	Hall
30	C₁₁	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	11	1	no	—
32	C₂×C₃	—	53	1	no	—
33	C₂×C₃	—	583	1	no	—
34	C₂²	—	583	1	no	Sylow
35	C₃	D₁₁×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	11	1	no	—
37	C₂	—	53	1	no	—
38	C₂	—	583	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₁×D₅₃
commutator, hypocenter	C₁₁×C₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₅₃	C₂²
LCS	G ▷ C₁₁×C₅₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₅₈₃	C₂	semidirect
2. C₃×D₁₁×C₅₃	C₂	semidirect
3. C₃×C₁₁×D₅₃	C₂	semidirect
4. D₁₁×D₅₃	C₃	direct (N × H)
5. C₃×C₁₁×C₅₃	C₂²	semidirect
6. D₅₈₃	C₂×C₃	semidirect
7. C₁₁×D₅₃	C₂×C₃	semidirect
8. D₁₁×C₅₃	C₂×C₃	semidirect
10. C₁₁×C₅₃	C₂²×C₃	semidirect
13. C₃×D₅₃	D₁₁	direct (N × H)
15. C₃×C₅₃	C₂×D₁₁	semidirect
19. D₅₃	C₃×D₁₁	direct (N × H)
22. C₃×D₁₁	D₅₃	direct (N × H)
23. C₅₃	C₂×C₃×D₁₁	semidirect
25. C₃×C₁₁	C₂×D₅₃	semidirect
28. D₁₁	C₃×D₅₃	direct (N × H)
30. C₁₁	C₂×C₃×D₅₃	semidirect
35. C₃	D₁₁×D₅₃	direct (N × H)

Subgroups — C3×D11×D53 #20296172

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₁×D₅₃ #20296172