My first thought was about Dunbar's number too, but Dunbar's number for people is something like 100-120... yet we're still able to field 10,000-man strong divisions, expeditionary forces, etc.
Chains of Command follow the Hub and Spoke model. I'm pretty sure if you break it down the number of people an individual in that structure has to care about is somewhere between 30 & 60...leaving them room for friends and family.