Orderings on Set with 4 Elements

Examples of Orderings
Let $S$ be an arbitrary set with $4$ elements.

The following are the Hasse diagrams for the $15$ isomorphism classes of all the possible orderings on $S$:


 * Ordering-4-Elements.png

Of the above, $\text{(l)}$ and $\text{(o)}$ are lattice orderings.