The Supremacy was a Mega-class Star Dreadnought built by the First Order that served as the flagship and mobile base of Supreme Leader Snoke. One of the largest starships ever constructed, it was heavily damaged in battle against the Resistance during the events of Star Wars: The Last Jedi.
At a whopping 60 kilometers wide and 13 kilometers long, the Supremacy was the largest starship in the First Order's fleet. Indeed, it was the largest starship ever built, even outclassing the Executor-class Star Dreadnought of the Galactic Empire. The Supremacy had 32 sublight engines for propulsion, and six fusion reactor complexes allowing for increased redundancies and increased damage resistance.
Because the Supremacy served as a mobile capital for the First Order, it was equipped with standard capital features such as shipyards. This was evidenced by its capablity of docking up to eight Resurgent-class Star Destroyers, six externally and another two internally which would either be under repair or under construction. The ship possessed a crew of 2,225,000 Stormtroopers, officers, gunners, engineers, factory workers, technical specialists, and communications staff. The ship also possessed 10 staging areas capable of supporting 36,000 stormtroopers each. The ship also supported factories, trains grounds, research laboratories, repair docks, and even a mining complex for harvesting asteroid ore due to its vast size. This made the ship a truly formidable part of the First Order simply because it could produce extra supplies and resources for its crew and supporting ships.
The true capabilities of the Supremacy, however, were showcased in its lethal armaments and abilities. It could track other ships through hyperspace to ensure there was no escape. It could track enemy ships by way of a frighteningly fast algorithm that had its roots in the Tarkin Initiative. Furthermore, the Supremacy possessed thousands of heavy turbolasers, anti-ship missile batteries, heavy ion cannons, and tractor beam projectors that could decimate entire fleets alone. The bow of the ship further possessed ten heavy turbolaser towers, putting it on par with the Death Stars and Starkiller Base in regards to its abilities.
The Supremacy first appears when Supreme Leader Snoke decides the time has come to reveal himself to the Resistance. The starship appears out of hyperspace and chases the Resistance fleet, tracking them through hyperspace thanks to General Hux's skilled tactical genius. The ship pursues the Resistance fleet relentlessly upon revealing its capabilities, wearing down the starships in a prolonged chase and destroying the enemy star cruisers as they run out of fuel and enter firing range.
As the Supremacy closed in, Vice Admiral Amilyn Holdo evacuated the Resistance flagship, the Raddus, and initiated a hyperspace jump right at the Star Dreadnought. Caught in the Raddus' path, the Supremacy was helpless as the hyperspace jump destroyed the ship, cutting the Supremacy in half. After Kylo Ren killed Snoke and became the new Supreme Leader of the First Order, he ordered the ship scuttled, as it was too damaged to be of use despite remaining fully operational in spite of its bisection.