Abstract
Hasse constants and their basic properties are introduced to facilitate the connection between the lattice of subalgebras of an algebra \( \mathcal{C} \) and the natural action of the automorphism group Aut( \( \mathcal{C} \)) on \( \mathcal{C} \). These constants are then used to describe the lattice of subloops of the smallest nonassociative simple Moufang loop.
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