On reflection subgroups of finite Coxeter groups
  Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class of its Coxeter elements to be injective, up to conjugacy. 
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
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