They're supposed to be powerful so they can be behind anything.

It would be anyone's guess at this point. If you go with the argument that the Illuminati is such a powerful secret organization, then it would be not strange to find a cover-up of the real happenings or reasons behind the JFK assassination. One can speculate about it, but without facts, it would be difficult to make a case. The investigation has gone through several committees, so it would be difficult to make heads or tails out of the investigation. You may find suspicious things such as missing facts and documents, but without proof, it's just another conspiracy theory on top of others.

It is believed that the Kennedys were part of the Illuminati organization, and that JFK did something that made the group unhappy. And so, JFK was ordered to be killed. It sounds nice in theory, like some form of suspense and intrigue novel, but in the real world, it takes more than that. The facts are missing, and one can point fingers at virtually anyone but without any evidence, nothing will come out of it. Though the Illuminati is shrouded in mystery and intrigue, those are not enough to establish a solid connection between the group and the assassination of JFK.

This is one theory that would be hard to prove. The only thing that can be said at this point is that the angle of a possible conspiracy was not explored exhaustively by the investigating committees assigned to the JFK assassination case. The issue is, how can one really connect the Illuminati to the assassination? Can you find any reliable evidence that implicates the group? At best, all you can get is an eye-witness account, and even that is not fool-proof in the courts. You can always make insinuations, but can you actually prosecute anyone? That would hardly be the case.

If you grant all the powers associated by conspiracy theorists to the Illuminati, then the group being behind the assassination is possible. If this group truly holds a lot of power and influence, the assassination of even the President of the United States is not hard to imagine. The real question is, is it really them? Can anyone come up with any evidence that would implicate the Illuminati? Though the conspiracy angle was not sufficiently explored by the investigating committees assigned to the JFK assassination, can any proof be acquired? If one wants to implicate the Illuminati, one would have one's task cut out for him or her.