You can always supress the faction, it'll cost influence and make it unhappy, but it'll be less attractive.
The influence you get from your factions depend on their support, your technologies, and even your ethic (Egalitarian get +15/+30% influence from factions) or civic (Parlementiary System gives +50% influence from factions).
So if you don't have a technology increasing the influence you get from your factions (Adaptive Bureaucracy, The Living State, The Collective Self), the max influence you'll get from your factions is 2.
Let's say you have three of them, the Authoritarian, the Xenophobe, and the Egalitarian.
The Authoritarian has 60% happiness and 50% suppport, the Xenophobe one 55% happiness and 25% support, and the Egalitarian 30% happiness and 25% support.
Then you'll only get influence from the Authoritarian faction, as they are the only have to have 60 or more happiness. Since they have 50% support, they give you 2 * 0.5 Influence, so 1.
So if you don't have much Influence from your factions, check that they have enough happiness (maybe only the Authoritarian or the Xenophobe faction is happy enough, and not both ?), check their support (if a faction has a low support they won't give you much Influence), and try to get the tech giving more Influence from your factions.
So an unhappy faction with a low support level is really not a threat. It's more valuable to make sure your big factions are happy, than trying to completely destroy the unhappy ones - which is not supposed to be possible anyway.