A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix group. The analogous subgroups where the matrices are taken to be over a finite field (but the group is defined in the same way) are called the Lie-type groups. They are a kind of linear algebraic group.
The Lie-type groups include the Chevalley groups (i.e., 
,
, 
, 
), twisted
Chevalley groups, and the Tits group.
