What are the disadvantages of agglomerative hierarchical clustering?

Objective function: SSE is the objective function for K-means. Likewise, there exists no global objective function for hierarchical clustering. It considers proximity locally before merging two clusters.

Time and space complexity: The time and space complexity of agglomerative clustering is more than K-means clustering, and in some cases, it is prohibitive.

Final merging decisions: The merging decisions, once given by the algorithm, cannot be undone at a later point in time. Due to this, a local optimisation criteria cannot become global criteria. Note that there are some advanced approaches available to overcome this problem.