Finite subgroups of integral linear group GL(3,Z) It seems it is a classical result to list all the finite subgroups of $GL(3,\mathbb{Z})$, up to conjugation. But I was not able to find this list anywhere.
I found, however, the list of what is called all irreducible maximal finite integral matrix groups; there are three of them, all isomorphic as groups, with $48$ elements.
I understood first that the maximallity here means that all finite subgroups of $GL(3,\mathbb{Z})$ is conjugate to (at least) one of the three groups, but I have found an order $6$ matrix whose conjugates are not in any of this groups.
Can someone give me some reference or explanation of how to get this list?
Added The paper by Ken-Ichi Tahara from 1971, ON THE FINITE SUBGROUPS OF GL (3, Z), apart from being difficult to read, it seems it has errors. At least the group of order 24 that he calls $W_5$, has in fact order $12$.
It will be very nice to have the list in some computer system so we can be sure it is without errors.
Aside, in the paper by Plesken and Pohst On maximal ... they say this list was already known in the XIX century...
 A: I explain what I have found during these last days about the question, but for $GL(n,\mathbb{Z})$.
The key point is that the maximal irreducible finite subgroups of $GL(n,\mathbb{Z})$, which is what you find easily in GAP or in Magma, are not the maximal finite subgroups of $GL(n,\mathbb{Z})$, in the sense that any finite subgroup of $GL(n,\mathbb{Z})$ is conjugate to a subgroup of one of the maximal finite subgroups (I understand that they are the ones we are looking for that are irreducible). These last ones are called Dade subgroups because of the paper
E.C. Dade, The maximal finite groups of $4\times 4$ integral matrices, Illinois J. Math. 9(1): 99-122
where the author finds the list of such maximal groups for $GL(4,\mathbb{Z})$. So considering all the subgroups of this subgroups one gets all the possible finite subgroups of $GL(4,\mathbb{Z})$ up to conjugation (and with a lot of repetitions, of course).
I don't know if the same result is known for $n=5$. Also I don't know if one can obtain them from the list of  the maximal finite subgroups of $GL(n,\mathbb{Z})$ for $n\le 5$.
