:salamext:,
From scholars:
"Ghusl is major purity, and it 'contains' the minor purity of wudu. As such, when you do ghusl, you are on wudu, too."
But make sure you do the minimum of ghusl while showering so that it's countered as major purity and Wudu.
"In response to your first question Sidi, it is enough to have a shower instead of a �full bath� or ablution (wudu) while fulfilling several conditions.
** If having a shower in place of a purificatory bath (ghusl), one must fulfill the three obligatory actions:
Taking water into (1) the nose and (2) the mouth once, (3) And washing the entire body once. (One must wash everything that is possible to wash without hardship, such as the ears, belly button, mustache, eyebrows, inside the beard, and the hair. Women should move their earrings so that water reaches the pierced area) [Ilm al-Hal 11, Faraz Rabbani�s translation].
** If having a shower in place of a wudu,
One must wash the face, arms up to the elbows, and feet up to the anklebones, completely with water, and must wipe a quarter of the head once [Nur al-Idah 1:97-99].
One should not, however, leave the confirmed sunna actions in both the ghusl and wudu. Leaving them is somewhat disliked (makruh tanzihan), and becomes sinful if made a habit."
^The bold part is the relevant bit.
Wassalam.