Finite Group Databasebeta

← D₃×C₁₉×C₁₁₃ #27166262

Subgroups — D₃×C₁₉×C₁₁₃ #27166262

Order 12882.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₉×C₁₁₃	—	3	1	no	maximal, Hall
3	C₁₉×C₁₁₃	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₁₃	—	3	1	no	Hall
7	D₃×C₁₉	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁₃	D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₃×C₁₉	C₂×C₁₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉	—	3	1	no	Hall
11	C₁₉	D₃×C₁₁₃	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₁₉×C₁₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₁₉×C₁₁₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₁₁₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₉×C₁₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₁₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₁₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₁₁₃	C₂	semidirect
3. C₁₉×C₁₁₃	D₃	direct (N × H)
4. D₃×C₁₁₃	C₁₉	direct (N × H)
5. C₃×C₁₁₃	C₂×C₁₉	semidirect
7. D₃×C₁₉	C₁₁₃	direct (N × H)
8. C₁₁₃	D₃×C₁₉	direct (N × H)
9. C₃×C₁₉	C₂×C₁₁₃	semidirect
11. C₁₉	D₃×C₁₁₃	direct (N × H)
12. D₃	C₁₉×C₁₁₃	direct (N × H)
13. C₃	C₂×C₁₉×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×C₁₁₃	2
C₂×C₁₉×C₁₁₃	3
D₃×C₁₁₃	19
D₃×C₁₉	113