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We investigate the ground states of spin-1 Bose-Einstein condensates(BECs)with spin-orbit coupling in a radially periodic potential by numerically solving the coupled Gross-Pitaevskii equations.In the radially periodic potential,we first demonstrate that spin-orbit-coupled antiferromagnetic BECs support a multiring petal phase.Polar-core vortex can be observed from phase profiles,which is manifested as circularly symmetric distribution.We further show that spin-orbit coupling can induce multiring soliton structure in ferromagnetic BECs.It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry,and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry.Adjusting the spin-orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs.Finally,we discuss effects of spin-independent and spin-dependent interactions on the ground states.