Saying Takbir collectively after congregational prayer or at other times is impermissible as it is an act of Bid`ah (innovation in religion). It is permissible to remember Allah (Glorified and Exalted be He) sub-vocally and each on his own (Part No. 2; Page No. 237) by Tahlil (saying: "La ilaha illa Allah [There is no God except Allah]"), Tasbih (saying: "Subhan Allah [Glory be to Allah]"), Takbir (saying: "Allahu Akbar [Allah is the Greatest]"), reciting Qur'an, and Istighfar (seeking forgiveness from Allah), acting upon the Saying of Allah (Exalted be He):
O you who believe! Remember Allâh with much remembrance.
And glorify His Praises morning and afternoon [the early morning (Fajr) and ‘Asr prayers].
Therefore remember Me (by praying, glorifying), I will remember you
It is acting according to what the Messenger (peace be upon him) encouraged by his saying:
"Saying: 'Subhan Allah [Glory be to Allah]', 'Alhamdu lillah [All praise is due to Allah]', 'La ilaha illa Allah [There is no God except Allah])', and 'Allahu Akbar [Allah is the Greatest]' is dearer to me than anything over which the sun rises.
(Related by Muslim). He (peace be upon him) also said:
"Whoever says, 'Subhan Allah wa bihamdihi (All praise and glory are due to Allah)' one hundred times, will have his sins forgiven even if they were like the foam of the sea''.
Al-Tirmidhy and the wordings are by him). This is following the guidance of the Salaf (righteous predecessors) as it was not reported from them that they used to make Dhikr (Remembrance of Allah) collectively. This is what the Mubtadi` (people who introduce innovations in religion) do. Dhikr is an act of worship and the basic ruling regarding it is Tawqifiy (bound by a religious text and not amenable to personal opinion). The Prophet (peace be upon him) warned us against (Part No. 2; Page No. 238) innovation in religion when he said:
"Whoever introduces anything into this matter of ours (Islam) that is not part of it, will have it rejected."
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.