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$N_\infty$ operads for 
$C_{qp^n}$ and 
$D_{p^n}$
We provide a general recursive method for constructing transfer systems on finite lattices. Using this, we calculate the number of homotopically distinct 
$N_{\infty} $ operads for dihedral groups 
$D_{p^n}$, 
$p \gt 2$ prime, and cyclic groups 
$C_{qp^n}$, 
$p \neq q$ prime. We then further display some of the beautiful combinatorics obtained by restricting to certain homotopically meaningful 
$N_\infty$ operads for these groups.
