The discrete dipole approximation (DDA) method is used to calculate the scattering matrix elements and optical cross-sections for a wide variety of complex soot aggregates in random orientation at a visible wavelength of 0.628 \mu m. The effects of the material composition and the size of the larger particle that is in touch with soot cluster on scattering and radiative properties of complex soot aggregates are analyzed. It is shown that the material composition and the size of the larger particle can strongly influence or even dominate the overall scattering and radiative properties of the aggregates.