The bandgaps of the twodimensional Archimedes (4,82) lattice consisting of different dielectric circular and square rods were calculated with the plane wave expansion method. The bandgaps of the lattice with dielectric rods were investigated as the refractive index, dielectric rods shape, filling fraction and rotational symmetry changing. It was found that the width of the complete photonic bandgaps is not always increasing with the difference of the refractive index. The widest complete photonic bandgaps could be achieved in the (4,82) structure when the refractive index is between 2.60 and 5.40. For the Archimedes (4,82) lattice of circular dielectric rod, the width of complete bandgap reaches the maximum when the dielectric refractive index of rod is equal to 2.80. Also, the complete bandgap of square dielectric rod reaches the maximum when the dielectric refractive index equals 2.80 and 4.40. In addition, the rotation angle of square dielectric rods can significantly increase the width of complete bandgap. The results demonstrate that the quantity, width and frequency position of bandgaps can be modulated by changing the refractive index, the filling fraction and other structural parameters.