Hoechst is a dna stain typically used to identify cell cycle profiles in live cells.  It can and will excite with both a UV and a strong violet laser and will read in a det'r with a 450/50BP filter.  Therefore, do not try to combine it with BV421.  The Ho red emission will probably also cause problems with the BV605 and BUV737 signals.  I'm not sure which lasers you have on your instrument.  But if these are the only fluorophores you are using, I would suggest something simple such as PI or 7AAD as a viability dye.  Both will read off the blue laser.  You should always stain one compensation tube for each color used in your assay.  Think of it this way - it's better to have too many controls than be sorry after the fact that you have too few.  Therefore, stain one tube of cells with your viability dye for compensation purposes (the dyes will not stain beads).  Good luck.

There are a large selection of fixable amine-reactive Viability Dyes to chose from. You can buy them from BD Biosciences, Affymetrix, Life Technologies and Biolegend. Much better than Hoechst for live/dead purposes.

Depending on your flow cytometer's setup it is, in principal, possible and a good option if your panel does not allow to use any other channel. E.g. were using a 379/34BP filter on the UV laser. BV421 needs good compensation indeed. As long as there are other options, for instance the ones mentioned by Lynda and Kerstin, I'd go with these. Good luck!

Thank you very much Lynda, Kerstin and Christoph for this useful information