Apples to apples is great, but would be hard for a 4 year old because you have to be able to read.
Group games that could include a four year old, maybe pictionary or charades.
You could try something like Jenga, but I'm not sure it would be great for a large group. You might have to divide up your group into smaller groups.
It's a card game, but Spoons might fit your criteria.
https://en.m.wikipedia.org/wiki/Spoons