Finite Group Databasebeta

← D₃×C₁₁×C₅₅₇ #49145261

Subgroups — D₃×C₁₁×C₅₅₇ #49145261

Order 36762.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₅₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁×C₅₅₇	—	3	1	no	maximal, Hall
3	C₁₁×C₅₅₇	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₅₅₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅₅₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅₅₇	—	3	1	no	Hall
7	C₅₅₇	D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
8	D₃×C₁₁	C₅₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×C₅₅₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁	—	3	1	no	Hall
11	C₁₁	D₃×C₅₅₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₁₁×C₅₅₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₁₁×C₅₅₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₅₅₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₁×C₅₅₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₅₅₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₁×C₅₅₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₅₅₇	C₂	semidirect
3. C₁₁×C₅₅₇	D₃	direct (N × H)
4. D₃×C₅₅₇	C₁₁	direct (N × H)
5. C₃×C₅₅₇	C₂×C₁₁	semidirect
7. C₅₅₇	D₃×C₁₁	direct (N × H)
8. D₃×C₁₁	C₅₅₇	direct (N × H)
9. C₃×C₁₁	C₂×C₅₅₇	semidirect
11. C₁₁	D₃×C₅₅₇	direct (N × H)
12. D₃	C₁₁×C₅₅₇	direct (N × H)
13. C₃	C₂×C₁₁×C₅₅₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁×C₅₅₇	2
C₂×C₁₁×C₅₅₇	3
D₃×C₅₅₇	11
D₃×C₁₁	557