Filtering nested lists while maintaining the list level

Question

some help is needed to address an issue that even though I have been searching around I have not been able to fix it the way I want (I am a novice to Mathematica). I need to filter out sublists of a nested list while maintaining the nested list level. E.g., I have the following list (Matrix) :

Matrix = {
 {
  {
   {O1,2,22,24,28,14,D1},
   {O1,1,21,23,27,13,D1},
   {O1,2,22,24,28,27,13,D1},
   {O1,2,22,24,28,14,13,D1},
   {O1,2,22,24,23,27,13,D1},
   {O1,2,22,21,23,27,13,D1},
   {O1,2,1,21,23,27,13,D1},
   {O1,1,21,23,27,28,14,D1},
   {O1,1,21,23,27,13,14,D1},
   {O1,1,21,23,24,28,14,D1},
   {O1,1,21,22,24,28,14,D1},
   {O1,1,2,22,24,28,14,D1},
   {O1,2,22,24,28,27,13,14,D1},
   {O1,2,22,24,23,27,28,14,D1},
   {O1,1,2,22,21,23,25,9,10,26,24,28,18,17,27,13,14,D1},
   {O1,1,2,22,21,23,25,9,10,26,24,28,16,15,27,13,14,D1},
   {O1,1,2,22,21,23,25,7,8,26,24,28,20,19,27,13,14,D1},
   {O1,1,2,22,21,23,25,7,8,26,24,28,18,PoP2,17,27,13,D1},
   {O1,1,2,22,21,23,25,7,8,26,24,28,18,17,27,13,14,D1},
   {O1,1,2,22,21,23,25,7,8,26,24,28,16,15,27,13,14,D1},
   {O1,1,2,22,21,23,5,PoP1,6,24,28,18,PoP2,17,27,13,14,D1},
   {O1,2,1,21,22,24,26,12,11,25,23,27,17,PoP2,18,28,14,13,D1},
   {O1,2,1,21,22,24,26,10,9,25,23,27,17,PoP2,18,28,14,13,D1},
   {O1,2,1,21,22,24,26,8,7,25,23,27,17,PoP2,18,28,14,13,D1},
   {O1,1,2,22,21,23,25,11,12,26,24,28,18,PoP2,17,27,13,14,D1},
   {O1,1,2,22,21,23,25,9,10,26,24,28,18,PoP2,17,27,13,14,D1},
   {O1,1,2,22,21,23,25,7,8,26,24,28,18,PoP2,17,27,13,14,D1}
  }
 }
}

the point is to select those sublists that contain an ordered sequence of PoP1,PoP2 and exclude the rest while still maintaining the list level, in this case it would be only the following:

{{{{O1,1,2,22,21,23,5,PoP1,6,24,28,18,PoP2,17,27,13,14,D1}}}}

but the actual list is in fact much bigger. I have tried with the following

Select[Flatten[Matrix, {1, 2, 3}], ContainsAll[{PoP1, PoP2}]] 

but this is not correct due to missing orderliness while the other one is not working

Select[Flatten[Matrix, {1, 2, 3}], {PatternSequence[_, (PoP1 & PoP2)]}]

Any help is really appreciated.

Answer 1

DeleteCases deletes patterns without modifying the list structure. So, just apply DeleteCases at level {-2}:

DeleteCases[Matrix, Except@{___,PoP1,___,PoP2,___}, {-2}]

{{{{O1, 1, 2, 22, 21, 23, 5, PoP1, 6, 24, 28, 18, PoP2, 17, 27, 13, 14, D1}}}}

Answer 2

Matrix /. {a_?VectorQ /; FreeQ[a, {___, PoP1, ___, PoP2, ___}] :> 
   Nothing}

{{{{O1, 1, 2, 22, 21, 23, 5, PoP1, 6, 24, 28, 18, PoP2, 17, 27, 13, 14, D1}}}}

Answer 3

m =
  {{{{O1, 2, 22 D1},
     {O1, 1, 21, 13, D1},
     {O1, 1, 2, 22, 21, 18, PoP2, 17, 27, 13, D1},
     {O1, 18, 17, 27, 13, 14, D1},
     {O1, 1, 5, PoP1, 6, 24, 28, PoP2, 17, 27, D1},
     {O1, 2, 1, 27, 17, PoP2, 18, 28, 14, 13, D1},
     {O1, PoP1, PoP2, 17, 27, 13, 14, D1},
     {O1, 1, 2, 22, 18, PoP2, 17, 27, 13, 14, D1}}}};

p = {___, PoP1, ___, PoP2, ___};

d = ArrayDepth[m];

Using Nest and Cases

Nest[List, Cases[m, p, -1], d - 1]

Using Delete and Position

{Delete[m, Position[m, Except[p], {d}]]}

Both return

{{{
{O1, 1, 5, PoP1, 6, 24, 28, PoP2, 17, 27, D1},
{O1, PoP1, PoP2, 17,27, 13, 14, D1}
}}}