The Supremacy is a Mega-class Star Dreadnought built by the First Order that serves as the flagship and mobile base of Supreme Leader Snoke during the events of Star Wars: The Last Jedi. One of the largest starships ever constructed, it was heavily damaged in battle against the Resistance when Vice Admiral Amilyn Holdo made a hyperspace jump with the Resistance flaship, the Raddus, aiming directly at the Supremacy, splitting it in half.
At a whopping 60 kilometers wide and 13 kilometers long, the Supremacy is the largest starship in the First Order's fleet. It is the largest starship ever built, even outclassing the Executor-class Star Dreadnought of the Galactic Empire. The Supremacy has 32 sublight engines for propulsion, and six fusion reactor complexes allowing for increased redundancies and increased damage resistance.
Because the Supremacy serves as a mobile capital for the First Order, it is equipped with standard capital features such as shipyards. This is evidenced by its capablity of docking up to eight Resurgent-class Star Destroyers, six externally and another two internally which are either under repair or under construction. The ship possesses a crew of 2,225,000 Stormtroopers, officers, gunners, engineers, factory workers, technical specialists, and communications staff. The ship also possesses 10 staging areas capable of supporting 36,000 stormtroopers each. The ship also supports factories, trains grounds, research laboratories, repair docks, and even a mining complex for harvesting asteroid ore due to its vast size. This makes the ship a truly formidable part of the First Order simply because it can produce extra supplies and resources for its crew and supporting ships.
The true capabilities of the Supremacy, however, are showcased in its lethal armaments and abilities. It can track other ships through hyperspace to ensure there is no escape. It can track enemy ships by way of a frighteningly fast algorithm that has its roots in the Tarkin Initiative. Furthermore, the Supremacy possesses thousands of heavy turbolasers, anti-ship missile batteries, heavy ion cannons, and tractor beam projectors that can decimate entire fleets alone. The bow of the ship further possesses 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 MC85 Star Cruiser Raddus, and initiated a hyperspace jump right at the Mega-Destroyer. 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.