Is there a way to calculate the total number of subgroups of a group?
I can imagine that for example if $G=D_n$ is the dihedral group or $G=S_n$ the symmetric group then there exists a formula to calculate the total number of subgroups.
The reason why I started to think about this question is because I was trying to find all subgroups of $D_4$ (the square).
And I found some but I want to prove that I found all of them.
So if the answer is no to the question above then I'd be equally happy with a way of being sure that given a collection of subgroups to determine that there cannot be more.