Incomplete multi-view clustering (IMVC) is an unsupervised approach, among which IMVC via contrastive learning has received attention due to its excellent performance. The previous methods have the following problems: 1) Over-reliance on additional projection heads when solving the dimensional collapse problem in which latent features are only valid in lower-dimensional subspaces during clustering. However, many parameters in the projection heads are unnecessary. 2) The recovered view contain inconsistent private information and useless private information will mislead the learning of common semantics due to consistent learning and reconstruction learning on the same feature. To address the above issues, we propose a novel incomplete multi-view contrastive clustering framework. This framework directly optimizes the latent feature subspace, utilizes the learned feature vectors and their sub-vectors for reconstruction learning and consistency learning, thereby effectively avoiding dimensional collapse without relying on projection heads. Since reconstruction loss and contrastive loss are performed on different features, the adverse effect of useless private information is reduced. For the incomplete data, the missing information is recovered by the cross-view prediction mechanism and the inconsistent information from different views is discarded by the minimum conditional entropy to further avoid the influence of private information. Extensive experimental results of the method on 5 public datasets show that the method achieves state-of-the-art clustering results.