Submission to authority and sadism are often related, but I do not think such was the case in many Milgram's subjects. I read the stuff long time ago, so my recollections may fade a bit, but I recall something about many subjects showing considerable discomfort when pressured by the administrator to proceed with the experiment. Milgram interpreted that as further support that people tend to do what they are told by an authority figure even if that is against their own beliefs.
If memory serves, the point he tried to prove was that democratic traditions, such those in the US, make people less likely to blindly follow orders, as for example the Germans did in WWII - but his experiment failed to produce such evidence. Very few subjects actually refused to go ahead, but among them was a Dutch immigrant who got irked when the administrator recited the formula "you have to proceed, you have no choice," replied that he did have a choice, and quit.
Bur as Miles correctly points out, the experiment was replicated in various different settings, mainly because it produced such uncomfortable results. In one setting, hospital nurses were telephoned by an unknown to them doctor who informed them that he was running late and asked them to administer a certain medication to a patient of his. The dose he ordered was several times the maximum allowed on the medication's (a harmless placebo) label. Most nurses complied with the order - even though no sadism of any sort was involved in this replication.
Wojtek