openGL SubTexturing

Question

I have image data and i want to get a sub image of that to use as an opengl texture.

glGenTextures(1, &m_name);
glGetIntegerv(GL_TEXTURE_BINDING_2D, &oldName);
glBindTexture(GL_TEXTURE_2D, m_name);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, m_width, m_height, 0, GL_RGBA, GL_UNSIGNED_BYTE, m_data);

How can i get a sub image of that image loaded as a texture. I think it has something to do with using glTexSubImage2D, but i have no clue how to use it to create a new texture that i can load. Calling:

glTexSubImage2D(GL_TEXTURE_2D, 0, xOffset, yOffset, xWidth, yHeight, GL_RGBA, GL_UNSIGNED_BYTE, m_data);

does nothing that i can see, and calling glCopyTexSubImage2D just takes part of my framebuffer. Thanks