如图，已知点$C$为线段$\mathit{AB}$的中点，$\mathit{CD}\perp \mathit{AB}$且$\mathit{CD}=\mathit{AB}=4$，连接$\mathit{AD}$，$\mathit{BE}\perp \mathit{AB}$，$\mathit{AE}$是$\angle \mathit{DAB}$的平分线，与$\mathit{DC}$相交于点$F$，$\mathit{EH}\perp \mathit{DC}$于点$G$，交$\mathit{AD}$于点$H$，则$\mathit{HG}$的长为　　．