Finite Group Databasebeta

← C₁₃×D₁₁×C₆₁ #31775331

Subgroups — C₁₃×D₁₁×C₆₁ #31775331

Order 17446.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₃×C₆₁	—	11	1	no	maximal, Hall
3	D₁₁×C₆₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₆₁	D₁₁	1	1	yes	characteristic, direct product factor, Hall
5	C₁₁×C₆₁	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₁₁	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₁₃	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
8	C₂×C₆₁	—	11	1	no	Hall
9	C₆₁	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₁₃	—	11	1	no	Hall
11	D₁₁	C₁₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃	D₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₂×C₁₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₆₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₁₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₆₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₃×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₆₁	C₂	semidirect
3. D₁₁×C₆₁	C₁₃	direct (N × H)
4. C₁₃×C₆₁	D₁₁	direct (N × H)
5. C₁₁×C₆₁	C₂×C₁₃	semidirect
6. C₁₃×D₁₁	C₆₁	direct (N × H)
7. C₁₁×C₁₃	C₂×C₆₁	semidirect
9. C₆₁	C₁₃×D₁₁	direct (N × H)
11. D₁₁	C₁₃×C₆₁	direct (N × H)
12. C₁₃	D₁₁×C₆₁	direct (N × H)
13. C₁₁	C₂×C₁₃×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₆₁	2
C₂×C₁₃×C₆₁	11
D₁₁×C₆₁	13
C₁₃×D₁₁	61