Patterns driven by buoyancy (e.g., the Rayleigh-Benard system) can be associated with a sequence of bifurcations of the uniform base state. Consequently, methods that exploit the linear instability such as weakly nonlinear analysis are employed to analyse them. In contrast, shear driven patterns (e.g. plane Couette flow) occur even when the associated basic state is linearly stable. Analysis of such subcritical patterns requires a fully nonlinear analysis and thus remains challenging. To investigate the formation of spatio-temporal patterns due to the interaction of buoyancy and a mean shear, we focus on the inclined layer convection (ILC) system. In the ILC cell, the fluid layer is inclined to the horizontal plane and subject to a temperature gradient and generates different patterns due to the interaction of buoyancy and shear. Three relevant parameters characterize this system: the ratio of momentum to thermal diffusivity (Prandtl number, Pr), the ratio of buoyancy to viscous forces (Rayleigh number, R) and the angle of inclination. At small angles of incline, the uniform base state becomes unstable to secondary instabilities in the form of buoyancy dominated longitudinal rolls. There exists a critical angle of incline, a co-dimension 2 point, above which shear driven transverse roll instabilities take over as the secondary instabilities. By varying the thermal driving and the inclination angle for a chosen Prandtl number fluid and computing the location of co-dimension 2 point, all secondary bifurcations and the resulting tertiary states, we characterize the full nonlinear phase diagram of ILC system. The computed phase diagram quantitatively matches previous experimental observations.