Subgroups Of Coxeter Group H₃

This paper mainly studies the subgroups of finite Coxeter group H3 and their properties,consisting of four parts.In chapter one,we briefly introduce the definitions and symbols of Coxeter groups,parabolic subgroups,cuspidal classes,etc.In chapter two,we have the relationship between the elements of H3 and the matrixes,as well as the conjugacy classes,conjugacy graphs,and cuspidal classes of H3.In chapter three,for a special subset J(?)S,we have XJJ,XJJJ through the relationship between the elements of H3 and the matrixes,and then calculate XJJJ of H3.In chapter four,we introduce some of related concepts.And we can get that all the subgroups of H3 and their normalizers.