The Gross-Pitaevskii equation for two-component rotating Bose-Einstein condensates with the Rashba-type spin-orbit (SO) coupling is studied with numerical simulations and variational analyses. A multiquantum vortex state becomes a ground state in a harmonic potential when mutual interaction is absent. When the attractive interaction is strong, the multiquantum vortex state exhibits modulational instability in the azimuthal direction, and a soliton-like state appears. When the repulsive interaction is strong, a vortex lattice state with a multiquantum vortex at the center is created. We find that the vortex lattice state is approximated at a linear combination of multiquantum vortex states.
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