Finite Group Databasebeta

← C₃×C₁₁×C₁₉×C₄₃ #41004038

Subgroups — C₃×C₁₁×C₁₉×C₄₃ #41004038

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, direct product factor, Hall
2	C₃×C₁₉×C₄₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁×C₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₄₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₁×C₁₉	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
7	C₁₁×C₁₉	C₃×C₄₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄₃	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₉	C₁₁×C₄₃	1	1	yes	characteristic, direct product factor, Hall
10	C₄₃	C₃×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₃×C₁₁	C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₉	C₃×C₁₁×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₃×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₃	C₁₁×C₁₉×C₄₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×C₄₃	C₃	direct (N × H)
2. C₃×C₁₉×C₄₃	C₁₁	direct (N × H)
3. C₃×C₁₁×C₄₃	C₁₉	direct (N × H)
4. C₁₉×C₄₃	C₃×C₁₁	direct (N × H)
5. C₃×C₁₁×C₁₉	C₄₃	direct (N × H)
6. C₁₁×C₄₃	C₃×C₁₉	direct (N × H)
7. C₁₁×C₁₉	C₃×C₄₃	direct (N × H)
8. C₃×C₄₃	C₁₁×C₁₉	direct (N × H)
9. C₃×C₁₉	C₁₁×C₄₃	direct (N × H)
10. C₄₃	C₃×C₁₁×C₁₉	direct (N × H)
11. C₃×C₁₁	C₁₉×C₄₃	direct (N × H)
12. C₁₉	C₃×C₁₁×C₄₃	direct (N × H)
13. C₁₁	C₃×C₁₉×C₄₃	direct (N × H)
14. C₃	C₁₁×C₁₉×C₄₃	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
C₃×C₁₉×C₄₃	11
C₃×C₁₁×C₄₃	19
C₃×C₁₁×C₁₉	43