Finite Group Databasebeta

← C₁₁×C₄₇×D₃₁ #44545358

Subgroups — C₁₁×C₄₇×D₃₁ #44545358

Order 32054.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₃₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₇×D₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₄₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₄₇	—	31	1	no	maximal, Hall
5	C₁₁×D₃₁	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₄₇	D₃₁	1	1	yes	characteristic, direct product factor, Hall
7	C₁₁×C₃₁	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₇	—	31	1	no	Hall
9	D₃₁	C₁₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
10	C₄₇	C₁₁×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₃₁	C₂×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₁₁	—	31	1	no	Hall
13	C₁₁	C₄₇×D₃₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₄₇	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₁₁×C₄₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₃₁×C₄₇	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₁×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₃₁×C₄₇	C₂	semidirect
2. C₄₇×D₃₁	C₁₁	direct (N × H)
3. C₃₁×C₄₇	C₂×C₁₁	semidirect
5. C₁₁×D₃₁	C₄₇	direct (N × H)
6. C₁₁×C₄₇	D₃₁	direct (N × H)
7. C₁₁×C₃₁	C₂×C₄₇	semidirect
9. D₃₁	C₁₁×C₄₇	direct (N × H)
10. C₄₇	C₁₁×D₃₁	direct (N × H)
11. C₃₁	C₂×C₁₁×C₄₇	semidirect
13. C₁₁	C₄₇×D₃₁	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×C₃₁×C₄₇	2
C₄₇×D₃₁	11
C₂×C₁₁×C₄₇	31
C₁₁×D₃₁	47