Subgroups — D₃×#19149919 #45686813

Order 33330.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19149919	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×#19149919	—	3	1	no	maximal, Hall
3	D₃×C₁₁×C₁₀₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	#19149919	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₁×C₁₀₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₀₁⋊C₅	—	11	1	no	maximal, Hall
7	C₂×C₁₁×C₁₀₁	—	3	1	no	Hall
8	C₃×C₁₀₁⋊C₅	—	11	1	no	Hall
9	C₁₁×C₁₀₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₀₁⋊C₅	—	33	1	no	Hall
11	D₃×C₁₀₁	C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
12	C₁₀₁⋊C₅	—	11	1	no	Hall
13	D₃×C₁₁⋊C₅	—	101	1	no	maximal, Hall
14	C₃×C₁₀₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₀₁	—	3	1	no	Hall
16	C₃×C₁₁⋊C₅	—	101	1	no	Hall
17	C₂×C₁₁⋊C₅	—	303	1	no	Hall
18	C₁₀₁	D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	D₃×C₁₁	C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Hall
20	C₁₁⋊C₅	—	101	1	no	Hall
21	C₃×C₁₁	C₂×C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	1111	1	no	Hall
23	C₂×C₁₁	—	3	1	no	Hall
24	C₃×C₅	—	1111	1	no	Hall
25	C₁₁	D₃×C₁₀₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	3333	1	no	Hall
27	D₃	#19149919	1	1	yes	characteristic, direct product factor, Hall
28	C₅	—	1111	1	no	Sylow
29	C₃	C₂×#19149919	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₀₁	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₁₀₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#19149919	C₂	semidirect
3. D₃×C₁₁×C₁₀₁	C₅	semidirect
4. #19149919	D₃	direct (N × H)
5. C₃×C₁₁×C₁₀₁	C₂×C₅	semidirect
9. C₁₁×C₁₀₁	C₅×D₃	semidirect
11. D₃×C₁₀₁	C₁₁⋊C₅	semidirect
14. C₃×C₁₀₁	C₂×C₁₁⋊C₅	semidirect
18. C₁₀₁	D₃×C₁₁⋊C₅	semidirect
19. D₃×C₁₁	C₁₀₁⋊C₅	semidirect
21. C₃×C₁₁	C₂×C₁₀₁⋊C₅	semidirect
25. C₁₁	D₃×C₁₀₁⋊C₅	semidirect
27. D₃	#19149919	direct (N × H)
29. C₃	C₂×#19149919	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#19149919	2
C₂×#19149919	3
D₃×C₁₁×C₁₀₁	5
D₃×C₁₀₁⋊C₅	11
D₃×C₁₁⋊C₅	101

Subgroups — D3×#19149919 #45686813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#19149919 #45686813