A swept fin on a slender cone is a canonical geometry relevant to high speed aeronautics. Predicting growth of instabilities and the onset of transition to turbulence on the swept fin/cone flow requires understanding and characterizing the primary flow features of the undisturbed steady state. The fin/cone geometry is topologically complex and involves challenging grid construction and numerical methodology for an accurate flow simulation. In the present study, we compute low-dissipation steady state flow on a blunt (1 mm nose radius), 7° half angle cone with a fin at a sweep angle of 70° in Mach 6 flow with a unit Reynolds number of 9.68 × 106 m−1. While flow separation is minimal due to the highly swept nature of the fin, two steady state primary vortex systems are found to exist: the horse-shoe vortex system on the cone, and the leading edge vortex system on the fin. Multiple streamwise vortices develop in both vortex systems owing to the presence of strong crossflow, both on the fin and the cone. The primary streamwise vortices originate near the fin leading edge junction and require high grid and numerical resolution for accurate spatial evolution. Presence of strong streamwise and cross-stream gradients and streamwise vorticity make the flow susceptible to complex instability mechanisms. This work serves to inform future investigations of flow breakdown on the fin/cone geometry in the presence of disturbances at Mach 6 freestream conditions.