Graph neural networks get significant attention for graph representation and classification in machine learning community. Attention mechanism applied on the neighborhood of a node improves the performance of graph neural networks. Typically, it helps to identify a neighbor node which plays more important role to determine the label of the node under consideration. But in real world scenarios, a particular subset of nodes together, but not the individual pairs in the subset, may be important to determine the label of the graph. To address this problem, we introduce the concept of subgraph attention for graphs. On the other hand, hierarchical graph pooling has been shown to be promising in recent literature. But due to noisy hierarchical structure of real world graphs, not all the hierarchies of a graph play equal role for graph classification. Towards this end, we propose a graph classification algorithm called Sub-GattPool which jointly learns the subgraph attention and employs two different types of hierarchical attention mechanisms to find the important nodes in a hierarchy and the importance of individual hierarchies in a graph. Experimental evaluation with different types of graph classification algorithms shows that SubGattPool is able to improve the state-of-the-art or remains competitive on multiple publicly available graph classification datasets. We conduct further experiments on both synthetic and real world graph datasets to justify the usefulness of different components of SubGattPool and to show its consistent performance on other downstream tasks.