Confused about the Ord class for multi-dimensional lists.

Prelude.max Question on Lists

-- This makes sense
Prelude> max 1 2
2

-- So does this
Prelude> max [1] [2]
[2]

-- Not really sure about this. 
Prelude> max [1,2] [1]
[1,2]

-- At first I assumed that it cuts off the extra dimensions, much like zip
Prelude> max [2,1] [1]
[2,1]

-- But then this doesn't make sense
Prelude> max [1,2] [1,2,4]
[1,2,4]

Prelude> max [1,2,4] [1,2]
[1,2,4]

-- Another example
Prelude> max [[1,2,3],[2,3,4]] [[1,2],[2,3],[2,4]]
[[1,2,3],[2,3,4]]