Finite groups of order 24 in a special unitary Lie group Here is a list of finite groups of order 24: 
https://groupprops.subwiki.org/wiki/Groups_of_order_24
There are 15 of them.
What constraints and methods can be used to check, among 15 of them, are there some of them can be a subgroup of Lie group SU(3)?
Then, what are these groups of order 24 that are the subgroup of Lie group SU(3)?
 A: In one line : look at the character table of your $15$ groups of order $24$. To be a little more accurate:


*

*a finite group $G$ is isomorphic to a subgroup of $SU(3)$ if and only if it has faithful representation in $\mathbb{C}^3$,

*any representation of $G$ on $\mathbb{C}^3$ will be decomposed as a sum of $3$ $1$-dimensional representations, a sum of $1$-dimensional representation and a $2$-dimensional irreducible representation or will be an irreducible representation,

*if you are given a representation $\rho$ of a finite group $G$ on $\mathbb{C}^d$ then $g\in \ker \rho$ if and only if $tr\rho(g)=d$.
As a result, you can easily construct an algorithm that, given the character table of a group determines if your group is isomorphic to a subgroup of $SU(3)$. 
Remarks:


*

*this  works in any dimension, for any finite group,

*by being slightly more careful I think you can get a conjugacy class classification instead of a isomorphism class classification,

*Among these groups you will probably find $S_4$, $D_{12}$ and $\mathbb{Z}/24$. 
