Arguably the biggest irony in Lord of the Flies is the discrepancy between how the boys on the island see themselves and what they're really like in practice. The boys are from an elite social and educational background and are therefore supposed to act like young English gentlemen.
Yet it isn't very long before most of the boys have degenerated into outright savagery, displaying the same kind of behavior that successive generations of British colonialists attributed to Indigenous people.
A further irony arises from this point. Early in the story, Jack states,
We've got to have rules and obey them. After all, we're not savages.
And yet, in a remarkably ironic twist, it is Jack who will show utter contempt for the rules-based order that Ralph tries to establish and becomes, in due course, the leading savage on the island, cementing his dictatorial rule with violence and bloodshed.
Finally, there is the irony that the boys need a grownup to come and help them out of their predicament but that when one eventually arrives, he makes things a whole lot worse.
The adult in question is the dead parachutist, whom most of the boys mistake for a mythical beast that has supposedly been rampaging around the island. Due to the boys' irrational fear of the beast, they turn to Jack for protection, who takes the opportunity to consolidate his power and control.