Geodesic
An expression for the number of subgroups of a given order of a finite $p$-group
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 561-568.

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We find an exact expression for the number of subgroups of any (possible) order of an arbitrary finite $p$-group. 
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     author = {V. N. Shokuev},
     title = {An expression for the number of subgroups of a given order of a finite $p$-group},
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V. N. Shokuev. An expression for the number of subgroups of a given order of a finite $p$-group. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 561-568. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a8/