How much control did the First Order have by the time of The Last Jedi?

Question

So we know that in The Force Awakens, the First Order

uses Starkiller Base to blow up several planets of political importance in the new Republic.

But we're not really told how much power and control the First Order has over the galaxy. In TFA, we're led to believe they're a peer on the same or even a smaller level than the Republic with less political influence but perhaps more firepower.

In The Last Jedi, however, it appears that the Resistance (now being called "The Rebellion" again) is on the run and a handful of ships are all that's left of the good guys.

Does the First Order have more control over the galaxy than TFA suggests (like at the magnitude of the Galactic Empire) or do they just seem to have more control due to another factor (like no Republic military presence outside the Resistence)?

Answer 1

The Last Jedi Visual Dictionary says this about the First Order Fleet (relevant parts are bold):

The discovery of the Resistance base's location leads to the dramatic arrival of the First Order fleet at D'Qar. Spearheading the assault is the Finalizer, the Resurgent-class Star Destroyer under General Hux's direct command. Even this overwhelming force is merely the first wave of a larger offensive. The true scale of the First Order military is beyond even General Organa's worst-case projections. In the shadowy corners of uncharted space - and within the hidden ledgers of scheming weapons manufacturers - the First Order has been secretly building for war. With the New Republic fleet vaporized by the Starkiller, it now stands unopposed.

So, there's no army big enough to challenge the First Order now that the New Republic's fleet is gone. It's also significant that this attack is only the first wave. So even the overwhelming force that arrives at D'Qar is just a piece of the entire First Order's army.

For some extra perspective, The Last Jedi: Incredible Cross-Sections says that the Dreadnought has a crew of 215,000 (53,000 officers, 140,000 enlisted, and 22,000 stormtroopers). Poe says "We have a chance to destroy a Dreadnought", implying that there are others - so there's at least 400k+ people fighting with the First Order, compared to the 400 people that make up the Resistance (according to a line from Vice-Admiral Holdo).

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This is related and interesting, but not actually part of the answer to this question:

The Force Awakens opening crawl says:

Luke Skywalker has vanished. In his absence, the sinister FIRST ORDER has risen from the ashes of the Empire and will not rest until Skywalker, the last Jedi, has been destroyed.

This tells that The First Order did not arise immediately after the Empire fell. Rather, it came into existence after Luke went into hiding. We know he didn't leave until after his conflict with Ben Solo, so it was at least 16-ish years later (the age of Ben Solo when he turned on Luke).

Answer 2

The backstory of The Force Awakens is that the New Republic, to resist the effects of centralizing too much power, only had a modest fleet and other naval forces were primarily planetary defense squadrons. The First Order built up their forces, but was still somewhat limited in scope and the Republic probably could have at least matched them in a straight showdown, but the majority of their fleet was destroyed with the planets in the Hossnian system.

The Resistance was an unofficial, unsanctioned, but covertly supported small force that opposed the First Order. Think of them like, say, American-sponsored Mujahedeen fighting against the Soviets in Afghanistan, or Soviet-backed North Vietnamese fighting Americans in Vietnam.

To continue the analogy, the First Order gutting the Republic political and military command structure and taking out most of their assets would be like the Soviets suddenly taking out the NATO military and political leadership and a large portion of the American military. Suddenly the mujahedeen are really screwed because now there's no support and nothing preventing the Red Army from chasing them down. It doesn't mean the Soviets have conquered the entire world, it just means there's no longer a single unified force large enough to prevent them from attempting to do so, and it will take time to organize.