Author: Ian J Leary 
Affiliation: The Ohio State University and University of Southampton 

Abstract:  A group is of type F if it has a finite classifying space. 
A group is type VF if it contains a finite-index subgroup of type F.  
For each finite group $Q$ not of prime power order, we construct a 
group $G$ that is type VF, contains infinitely many conjugacy 
classes of subgroups isomorphic to $Q$, and contains only 
finitely many conjugacy classes of other finite subgroups.  
(K. S. Brown has shown that a group of type VF contains only 
finitely many conjugacy classes of subgroup of prime power order. 
B. E. A. Nucinkis and the author have constructed groups of type VF 
containing infinitely many conjugacy classes of `sufficiently 
complicated' finite subgroups.  This paper fills the gap between 
these results.)  

Status: preprint