Second-harmonic generation (SHG) from centrosymmetric nanostructures originating from the breaking of inversion symmetry at their surfaces is a well-known phenomenon and is extensively used as a surface probe in nonlinear optical microscopy. In recent years, SHG and its subsequent enhancement using plasmonics has been observed from nanostructures such as sharp metallic tips, nanoantennae and nanodimers. However, the process is still inefficient, its mechanism not well understood, and an improvement is required. In order to achieve a higher conversion efficiency, we investigate experimentally a way to minimize the radiative losses at the fundamental frequency. In the present investigation, we use silver heptamer nanostructures and tune the subradiant mode of the Fano resonance to the fundamental of the pump source, while tuning a higher order multipolar term to the second harmonic and in the process we obtain a significant enhancement of the second harmonic signal. A detailed explanation and analysis of this is provided by considering the contribution and effect of varying different parameters, such as gap size and radius, as well as the overall symmetry of the structure. In fact, recently gold heptamers have been studied and have indeed shown strong hybridization of their constituent resonant primitive plasmonic modes, leading to new hybridized superradiant 'bright' and subradiant 'dark' modes(1, 2). The ease of fabrication and possible tunability achievable, make these structures very versatile tools for studying surface SHG in nanostructures.