Subgroups — C₉×D₁₁×D₁₉ #21418974

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₂₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₁₉×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₁×D₁₉	C₃	1	1	yes	maximal, characteristic
5	C₉×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₂₀₉	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₉×D₁₁	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₁×D₁₉	C₂×C₃	1	1	yes	characteristic
9	D₁₁×D₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₉×D₁₉	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic
12	D₂₀₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₁×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₉×D₁₁	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₉×D₁₁	—	19	1	no	maximal, Hall
16	C₂×C₉×C₁₉	—	11	1	no	—
17	C₉×D₁₉	—	11	1	no	—
18	C₉×D₁₉	D₁₁	1	1	yes	characteristic, direct product factor
19	C₂×C₃×D₁₉	—	11	1	no	—
20	C₁₁×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₉×C₁₁	—	19	1	no	—
22	C₉×D₁₁	—	19	1	no	—
23	C₉×D₁₁	D₁₉	1	1	yes	characteristic, direct product factor
24	C₉×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₁₁	—	19	1	no	—
26	C₂×C₃×C₁₉	—	11	1	no	—
27	C₃×D₁₉	—	11	1	no	—
28	C₃×D₁₉	C₃×D₁₁	1	1	yes	characteristic
29	C₉×C₁₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₉	—	11	1	no	Hall
31	C₂×C₃×C₁₁	—	19	1	no	—
32	C₃×D₁₁	—	19	1	no	—
33	C₃×D₁₁	C₃×D₁₉	1	1	yes	characteristic
34	C₃×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic
35	C₂×D₁₁	—	19	1	no	Hall
36	C₂×C₁₉	—	11	1	no	—
37	D₁₉	—	11	1	no	—
38	D₁₉	C₉×D₁₁	1	1	yes	characteristic, direct product factor
39	C₂²×C₉	—	209	1	no	Hall
40	C₃×C₁₁	C₂×C₃×D₁₉	1	1	yes	characteristic
41	C₂×C₁₁	—	19	1	no	—
42	D₁₁	—	19	1	no	—
43	D₁₁	C₉×D₁₉	1	1	yes	characteristic, direct product factor
44	C₁₉	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₉	—	11	1	no	—
46	C₂×C₉	—	19	1	no	—
47	C₂×C₉	—	209	1	no	—
48	C₂²×C₃	—	209	1	no	—
49	C₁₁	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₉	D₁₁×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	11	1	no	—
52	C₂×C₃	—	19	1	no	—
53	C₂×C₃	—	209	1	no	—
54	C₂²	—	209	1	no	Sylow
55	C₃	C₃×D₁₁×D₁₉	1	1	yes	characteristic
56	C₂	—	11	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	209	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₁₁×D₁₉
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₉
Frattini	C₃	C₃×D₁₁×D₁₉
Fitting	C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₁₁×C₁₉	C₂²×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₂₀₉	C₂	semidirect
2. C₉×C₁₉×D₁₁	C₂	semidirect
3. C₉×C₁₁×D₁₉	C₂	semidirect
5. C₉×C₁₁×C₁₉	C₂²	semidirect
9. D₁₁×D₁₉	C₉	direct (N × H)
12. D₂₀₉	C₂×C₉	semidirect
13. C₁₁×D₁₉	C₂×C₉	semidirect
14. C₁₉×D₁₁	C₂×C₉	semidirect
18. C₉×D₁₉	D₁₁	direct (N × H)
20. C₁₁×C₁₉	C₂²×C₉	semidirect
23. C₉×D₁₁	D₁₉	direct (N × H)
24. C₉×C₁₉	C₂×D₁₁	semidirect
29. C₉×C₁₁	C₂×D₁₉	semidirect
38. D₁₉	C₉×D₁₁	direct (N × H)
43. D₁₁	C₉×D₁₉	direct (N × H)
44. C₁₉	C₂×C₉×D₁₁	semidirect
49. C₁₁	C₂×C₉×D₁₉	semidirect
50. C₉	D₁₁×D₁₉	direct (N × H)

Subgroups — C9×D11×D19 #21418974

Conjugacy classes of subgroups

Complements

Subgroups — C₉×D₁₁×D₁₉ #21418974