REDUCED FUSION SYSTEMS OVER 2-GROUPS OF SMALL ORDER KASPER K. S. ANDERSEN, BOB OLIVER, AND JOANA VENTURA Abstract. We prove, when S is a 2-group of order at most 29 , that each reduced fusion system over S is the fusion

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• Finite groups
• Focal subgroup theorem
• Sylow theorems
• P-group
• Index of a subgroup
• Abelian group
• XTR
• Simple group
• Center
• Quasidihedral group
• PSL
• Normal p-complement