The structure properties for even-even nuclei around 230U, locating on the hexadecapole-deformation island, are investigated by using the potential-energy-surface calculation within the framework of macroscopic-microscopic model. The impact of different deformation degrees of freedom (including axial and nonaxial quadrupole and hexadecapole deformations) on total energy, shell and pairing contributions is analyzed based on the projected energy-maps and -curves. The single-particle structure is presented and briefly discussed. To a large extent, much better agreement with experiment data and other theoretical results was obtained if the hexadecapole deformations, especially the axial one, were taken into account. Present results could provide useful keys to understand the effects of different quadrupole and hexadecapole deformations. Considering the least energy principle, the more reasonable deformation subspace is suggested to simultaneously include the octupole correlation.