  A basic problem in constant dimension subspace coding is to determine the
maximal possible size ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces
in ${\bf F}_q^n$ such that the subspace distance satisfies
$\operatorname{dis}(U,V)=2k-2\dim(U \cap V) \geq d$ for any two different
$k$-dimensional subspaces $U$ and $V$ in this set. In this paper we propose new
parameter-controlled inserting constructions of constant dimension subspace
codes. These inserting constructions are flexible because they are controlled
by parameters. Several new better lower bounds which are better than all
previously constructive lower bounds can be derived from our flexible inserting
constructions. $141$ new constant dimension subspace codes of distances $4,6,8$
better than previously best known codes are constructed.
