Finite Group Databasebeta

← C₁₁×C₁₉×C₄₃⋊C₃ #41004039

Subgroups — C₁₁×C₁₉×C₄₃⋊C₃ #41004039

Order 26961.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₄₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₄₃⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₄₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₁₉	—	43	1	no	maximal, Hall
6	C₁₁×C₄₃	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₁₉	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
8	C₄₃⋊C₃	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₉	—	43	1	no	Hall
10	C₄₃	C₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₁₁	—	43	1	no	Hall
12	C₁₉	C₁₁×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₁₉×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	—	43	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₉×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₄₃	C₃	semidirect
2. C₁₉×C₄₃⋊C₃	C₁₁	direct (N × H)
3. C₁₁×C₄₃⋊C₃	C₁₉	direct (N × H)
4. C₁₉×C₄₃	C₃×C₁₁	semidirect
6. C₁₁×C₄₃	C₃×C₁₉	semidirect
7. C₁₁×C₁₉	C₄₃⋊C₃	direct (N × H)
8. C₄₃⋊C₃	C₁₁×C₁₉	direct (N × H)
10. C₄₃	C₃×C₁₁×C₁₉	semidirect
12. C₁₉	C₁₁×C₄₃⋊C₃	direct (N × H)
13. C₁₁	C₁₉×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₄₃	3
C₁₉×C₄₃⋊C₃	11
C₁₁×C₄₃⋊C₃	19
C₃×C₁₁×C₁₉	43