Let
p
p
be a prime. In this paper we investigate finite
K
{
2
,
p
}
\mathcal K_{\{2,p\}}
-groups
G
G
which have a subgroup
H
≤
G
H \le G
such that
K
≤
H
=
N
G
(
K
)
≤
Aut
(
K
)
K \le H = N_G(K) \le \operatorname {Aut}(K)
for
K
K
a simple group of Lie type in characteristic
p
p
, and
|
G
:
H
|
|G:H|
is coprime to
p
p
. If
G
G
is of local characteristic
p
p
, then
G
G
is called almost of Lie type in characteristic
p
p
. Here
G
G
is of local characteristic
p
p
means that for all nontrivial
p
p
-subgroups
P
P
of
G
G
, and
Q
Q
the largest normal
p
p
-subgroup in
N
G
(
P
)
N_G(P)
we have the containment
C
G
(
Q
)
≤
Q
C_G(Q)\le Q
. We determine details of the structure of groups which are almost of Lie type in characteristic
p
p
. In particular, in the case that the rank of
K
K
is at least
3
3
we prove that
G
=
H
G = H
. If
H
H
has rank
2
2
and
K
K
is not
PSL
3
(
p
)
\operatorname {PSL}_3(p)
we determine all the examples where
G
≠
H
G \ne H
. We further investigate the situation above in which
G
G
is of parabolic characteristic
p
p
. This is a weaker assumption than local characteristic
p
p
. In this case, especially when
p
∈
{
2
,
3
}
p \in \{2,3\}
, many more examples appear.
In the appendices we compile a catalogue of results about the simple groups with proofs. These results may be of independent interest.