I think it should be $17$ (with at least one vertex)
And asked about exactly with $3$ vertices then $2^{n(n-1)/2} =8$
But here at least $1$ vertex so
- $3$ subgraph as consider single - vertices ( question does not mention about distinct so we will consider all cases )
- $3$ subgraph consider $2$ vertices
- $1$ subgraph consider $3$ vertices
- $3$ subgraph consider $2$ vertices, one edge
- $3$ subgraph consider $3$ vertices, $2$ edges
- $3$ subgraph consider $3$ vertices, $1$ edge
- $1$ subgraph consider $3$ vertices, $3$ edges
So, total $17$