Subgroups — C₁₁×C₁₉×Dic₉ #21418965

Order 7524.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₃×C₁₉	—	3	1	no	maximal
3	C₉×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₁₉	D₃	1	1	yes	characteristic
5	C₄×C₁₁×C₁₉	—	9	1	no	Hall
6	C₁₉×Dic₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₁₉	Dic₃	1	1	yes	characteristic
8	C₂×C₁₁×C₁₉	D₉	1	1	yes	characteristic
9	C₁₁×Dic₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₉×C₁₉	C₂×C₁₁	1	1	yes	characteristic
11	Dic₃×C₁₉	—	3	1	no	—
12	C₁₁×C₁₉	Dic₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₉×C₁₁	C₂×C₁₉	1	1	yes	characteristic
14	C₉×C₁₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×Dic₃	—	3	1	no	—
16	C₂×C₃×C₁₉	D₃×C₁₁	1	1	yes	characteristic
17	C₉×C₁₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₄×C₁₉	—	9	1	no	Hall
19	C₂×C₃×C₁₁	D₃×C₁₉	1	1	yes	characteristic
20	C₃×C₁₉	C₁₁×Dic₃	1	1	yes	characteristic
21	C₄×C₁₁	—	9	1	no	Hall
22	C₂×C₁₉	C₁₁×D₉	1	1	yes	characteristic
23	Dic₉	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₁	Dic₃×C₁₉	1	1	yes	characteristic
25	C₂×C₁₁	D₉×C₁₉	1	1	yes	characteristic
26	C₁₉	C₁₁×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₉	C₂×C₁₁×C₁₉	1	1	yes	characteristic
28	Dic₃	—	3	1	no	—
29	C₁₁	C₁₉×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₉	C₄×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₃×C₁₁×C₁₉	1	1	yes	characteristic
32	C₄	—	9	1	no	Sylow
33	C₃	C₁₁×Dic₃×C₁₉	1	1	yes	characteristic
34	C₂	C₁₁×D₉×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₉	D₉
commutator, hypocenter	C₉	C₄×C₁₁×C₁₉
Frattini	C₂×C₃	D₃×C₁₁×C₁₉
Fitting	C₂×C₉×C₁₁×C₁₉	C₂
socle	C₂×C₃×C₁₁×C₁₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁×C₁₉	C₄	semidirect
6. C₁₉×Dic₉	C₁₁	direct (N × H)
9. C₁₁×Dic₉	C₁₉	direct (N × H)
12. C₁₁×C₁₉	Dic₉	direct (N × H)
14. C₉×C₁₉	C₄×C₁₁	semidirect
17. C₉×C₁₁	C₄×C₁₉	semidirect
23. Dic₉	C₁₁×C₁₉	direct (N × H)
26. C₁₉	C₁₁×Dic₉	direct (N × H)
29. C₁₁	C₁₉×Dic₉	direct (N × H)
30. C₉	C₄×C₁₁×C₁₉	semidirect

Subgroups — C11×C19×Dic9 #21418965

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×C₁₉×Dic₉ #21418965