Subgroups — C₃²×C₁₉×Dic₁₁ #21419005

Order 7524.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×Dic₁₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₁₉	C₂×C₃	1	4	yes	—
5	C₁₉×Dic₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₄×C₁₉	—	11	1	no	maximal, Hall
7	C₃×C₁₁×C₁₉	C₃×C₄	1	4	yes	complemented
8	C₂×C₁₁×C₁₉	C₂×C₃²	1	1	yes	characteristic
9	C₃²×Dic₁₁	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₁₉	D₁₁	1	1	yes	characteristic
11	C₃×C₄×C₁₉	—	11	4	no	—
12	C₁₁×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃²×C₁₁	C₂×C₁₉	1	1	yes	characteristic
14	C₃²×C₁₉	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
15	C₃×Dic₁₁	C₃×C₁₉	1	4	yes	direct product factor
16	C₂×C₃×C₁₉	C₃×D₁₁	1	4	yes	—
17	C₃²×C₁₁	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₄×C₁₉	—	11	1	no	Hall
19	C₂×C₃×C₁₁	C₂×C₃×C₁₉	1	4	yes	—
20	C₃×C₁₉	C₃×Dic₁₁	1	4	yes	direct product factor
21	Dic₁₁	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₉	C₃²×D₁₁	1	1	yes	characteristic
23	C₃²×C₄	—	11	1	no	Hall
24	C₃×C₁₁	C₃×C₄×C₁₉	1	4	yes	complemented
25	C₂×C₁₁	C₂×C₃²×C₁₉	1	1	yes	characteristic
26	C₁₉	C₃²×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃²	C₁₉×D₁₁	1	1	yes	characteristic
28	C₃×C₄	—	11	4	no	—
29	C₁₁	C₃²×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
30	C₃²	C₁₉×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₁₉×D₁₁	1	4	yes	—
32	C₄	—	11	1	no	Sylow
33	C₃	C₃×C₁₉×Dic₁₁	1	4	yes	direct product factor
34	C₂	C₃²×C₁₉×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	D₁₁
commutator, hypocenter	C₁₁	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×D₁₁
Fitting, socle	C₂×C₃²×C₁₁×C₁₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×Dic₁₁	C₃	direct (N × H)
3. C₃²×C₁₁×C₁₉	C₄	semidirect
5. C₁₉×Dic₁₁	C₃²	direct (N × H)
7. C₃×C₁₁×C₁₉	C₃×C₄	semidirect
9. C₃²×Dic₁₁	C₁₉	direct (N × H)
12. C₁₁×C₁₉	C₃²×C₄	semidirect
14. C₃²×C₁₉	Dic₁₁	direct (N × H)
15. C₃×Dic₁₁	C₃×C₁₉	direct (N × H)
17. C₃²×C₁₁	C₄×C₁₉	semidirect
20. C₃×C₁₉	C₃×Dic₁₁	direct (N × H)
21. Dic₁₁	C₃²×C₁₉	direct (N × H)
24. C₃×C₁₁	C₃×C₄×C₁₉	semidirect
26. C₁₉	C₃²×Dic₁₁	direct (N × H)
29. C₁₁	C₃²×C₄×C₁₉	semidirect
30. C₃²	C₁₉×Dic₁₁	direct (N × H)
33. C₃	C₃×C₁₉×Dic₁₁	direct (N × H)

Subgroups — C32×C19×Dic11 #21419005

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₉×Dic₁₁ #21419005