Thanks for any help or comments.

Suppose $G$ is a finite group. Carter subgroup is nilpotent self-normalizing subgroup of $G$. Carter and Vdovin has shown that solvable groups has carter subgroup and in addition, in every group with carter subgroups, its carter subgroups are conjugate see "Carter subgroup of finite group" by Vdovin.

My question is about the structure of groups such that its carter subgroup is 2-Sylow subgroup? I mean, I am intersted about any theorem which guide me toward some classification of this type of groups.

Thanks for any help or comments.

Suppose that $G$ is a finite group. A Carter subgroup of $G$ is a nilpotent self-normalizing subgroup of $G$. Carter and Vdovin have shown that solvable groups have Carter subgroups, and that in addition, in every group with Carter subgroups, the Carter subgroups are conjugate -- see

Carter, R. W. (1961), Nilpotent selfnormalizing subgroups of soluble groups, Mathematische Zeitschrift, 75 (2): 136–139.

Vdovin, E. P. (2006), On the conjugacy problem for Carter subgroups. (Russian.), Sibirsk. Mat. Zh., 47 (4): 725–730. Translation in Siberian Math. J. 47 (2006), no. 4, 597–600

Vdovin, E. P. (2007), Carter subgroups in finite almost simple groups. (Russian.), Algebra i Logika, 46 (2): 157–216.

My question is about the structure of groups whose Carter subgroups are their Sylow $2$-subgroups? I mean, I am interested in any theorem which guides me towards some classification of this type of groups.