Adding Catalyst 3850 stack to Prime NCS 22.214.171.124, Prime reports reachability but classifies the stack as an "unsupported device"
Your management system was released in May 2012 - prior to your switch model (which just came out in January / February 2013). Additionally, NCS is designed primarily for wireless management. It's only with the evolution of it into Prime Infrastructure (PI 1.2 and later) that wired devices and associated features started gaining ground.
The Catalyst 3850 is only supported on PI 1.3 or later. See the Compatibility Guide for details.