/usr/include/qt4/ is in libqt4-opengl-dev 4:4.8.7+dfsg-7ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/qt4/Qt/
/usr/include/qt4/Qt/QtOpenGL
/usr/include/qt4/Qt/qgl.h
/usr/include/qt4/Qt/qglbuffer.h
/usr/include/qt4/Qt/qglcolormap.h
/usr/include/qt4/Qt/qglframebufferobject.h
/usr/include/qt4/Qt/qglfunctions.h
/usr/include/qt4/Qt/qglpixelbuffer.h
/usr/include/qt4/Qt/qglscreen_qws.h
/usr/include/qt4/Qt/qglshaderprogram.h
/usr/include/qt4/QtOpenGL/
/usr/include/qt4/QtOpenGL/QGL
/usr/include/qt4/QtOpenGL/QGLBuffer
/usr/include/qt4/QtOpenGL/QGLColormap
/usr/include/qt4/QtOpenGL/QGLContext
/usr/include/qt4/QtOpenGL/QGLFormat
/usr/include/qt4/QtOpenGL/QGLFramebufferObject
/usr/include/qt4/QtOpenGL/QGLFramebufferObjectFormat
/usr/include/qt4/QtOpenGL/QGLFunctions
/usr/include/qt4/QtOpenGL/QGLFunctionsPrivate
/usr/include/qt4/QtOpenGL/QGLPixelBuffer
/usr/include/qt4/QtOpenGL/QGLScreen
/usr/include/qt4/QtOpenGL/QGLScreenSurfaceFunctions
/usr/include/qt4/QtOpenGL/QGLShader
/usr/include/qt4/QtOpenGL/QGLShaderProgram
/usr/include/qt4/QtOpenGL/QGLWidget
/usr/include/qt4/QtOpenGL/QMacCompatGLenum
/usr/include/qt4/QtOpenGL/QMacCompatGLint
/usr/include/qt4/QtOpenGL/QMacCompatGLuint
/usr/include/qt4/QtOpenGL/QMacGLCompatTypes
/usr/include/qt4/QtOpenGL/QtOpenGL
/usr/include/qt4/QtOpenGL/qgl.h
/usr/include/qt4/QtOpenGL/qglbuffer.h
/usr/include/qt4/QtOpenGL/qglcolormap.h
/usr/include/qt4/QtOpenGL/qglframebufferobject.h
/usr/include/qt4/QtOpenGL/qglfunctions.h
/usr/include/qt4/QtOpenGL/qglpixelbuffer.h
/usr/include/qt4/QtOpenGL/qglscreen_qws.h
/usr/include/qt4/QtOpenGL/qglshaderprogram.h