Allah T'ala says in the Holy Quran:
إِنَّ اللّهَ لاَ يَأْمُرُ بِالْفَحْشَاء
Indded, Allah does not command indecency.
This sentence appears in Ayat 7:28:
وَإِذَا فَعَلُواْ فَاحِشَةً قَالُواْ وَجَدْنَا عَلَيْهَا آبَاءنَا وَاللّهُ أَمَرَنَا بِهَا قُلْ إِنَّ اللّهَ لاَ يَأْمُرُ بِالْفَحْشَاء أَتَقُولُونَ عَلَى اللّهِ مَا لاَ تَعْلَمُونَ
The word fawahish applies to all those acts whose abominable character is self-evident. In the Qur'an all extra-marital sexual relationships, sodomy, nudity, false accusations of unchastity, and taking as one's wife a woman who had been married to one's father, are specifically reckoned as 'shameful deeds' (fawahish).
In Hadith, theft, taking intoxicating drinks and begging have been characterized as fawahish, as have many other brazenly indecent acts. Man is required to abstain from them both openly and in secret.
In fact, Allah T'ala says:
قُلْ إِنَّمَا حَرَّمَ رَبِّيَ الْفَوَاحِشَ مَا ظَهَرَ مِنْهَا وَمَا بَطَنَ وَالإِثْمَ وَالْبَغْيَ بِغَيْرِ الْحَقِّ وَأَن تُشْرِكُواْ بِاللّهِ مَا لَمْ يُنَزِّلْ بِهِ سُلْطَانًا وَأَن تَقُولُواْ عَلَى اللّهِ مَا لاَ تَعْلَمُونَ
Tell them (0 Muhammad): 'My Lord has only forbidden indecent acts, whether overt or hidden; all manner of sin; wrongful transgression; and [He has forbidden] that you associate with Allah in His divinity that for which He has sent down no sanction; and that you ascribe to Allah things of which you have no sure knowledge that they are from Him.'