Leadership-wise I think a corporal might have led a patrol group or work group of about four or so. So, some leadership on a very small, very immediate scale.
Probably more than you want to know, but here goes:
That's about par for the course. A corporal is an E-4 and you won't find an E-4 in charge of any significant amount of people. In general, your entire division will be somewhere in the realm of 100-120 people, with an O-3 (Lt.) in charge. There will be an E-7/8 (Gunny or Master Gunny for Marines, Chief or Senior Chief for Navy) who actually directs the division at the personnel level (the "O" is actually expected to do higher level management, not direct supervision of the troops). Under the E-7/8 will be a number of smaller groups (no idea what the grunts would call it, in the Navy/Marine aviation world we had work centers) of 10-20 people depending on their occupational specialties. Those work centers will have an E-6 (Staff Sergeant or Petty Officer First Class) in charge. As a work center supervisor I had 16 people spread over 2 shifts. My night shift supervisor was an E-5 (Sargeant/P.O. Second Class). So, in general, the E-4s had very little responsibility for the direct supervision of personnel. What you do start getting as an E-4 is collateral duties. These are duties that don't take up enough time to require a single person to do them full-time, so they're parceled out among the people in the work center. You'd have a training P.O. who was responsible for maintaining the training jackets of all the people in the work center and arranging monthly training. You'd have a safety P.O. who made sure that your work center complied with all the various safety regulations. You'd have a publications P.O. who made sure that all your manuals were kept up to date with the latest revisions. You'd have quality assurance inspectors and other things depending on the type of command you were in. So an E-4 might not be in charge of people on a regular basis, but he would have responsibilities above that of just doing his day-to-day job. And, as Anne said, he could be placed in charge of smaller work groups (usually cleaning parties and stuff like that).