Which classification algorithms can handle 24000 features Which classification algorithms can handle 24000 features? What are their pros and cons?
Deep Learning Algorithms and Graphical model algorithms can handle that scale of features.

For example a typical parsing algorithm using CRF++ computes millions of features. 
In case of Deep Learning, A typical image of 256*256*3 has to deal with 196608 number of features where each pixel in image is a feature.