英语填空题The man in the corner admitted to ___

英语填空题The man in the corner admitted to ___
The man in the corner admitted to ___a lie to the manage of the company.
having told
我想不通.我觉得应该用to have told这个不定式.因为撒谎这个行为是在谓语动作“承认”之前.应该用不定式完成式啊.为什么正确答案会是to having told
admitted 是动词，那么为什么不能接不定式呢？仅仅是固定用法是admit to doing sth /sth？
为什么这个动词不能跟不定式？是不是像admitted这类特定词不能用不定时- 我要记住这些词后面不能用不定式？