The idiom 'Under the thumb' means -

• The idiom 'Under the thumb' means - Under full control.

• Under one's thumb or under the thumb (Idiom)
- English Meaning: Under full control; to be controlled or dominated by someone.
- Bangla Meaning: পুরোপুরি বাধ্য; কারও কর্তৃত্বাধীনে।

• Ex. Sentence: He’s always been under the thumb of his overbearing boss.
- Bangla Meaning: সে সবসময় তার কর্তৃত্বপরায়ণ বসের অধীনে ছিল।

• অন্যদিকে,
- All thumbs: Extremely awkward or clumsy.
- Thumb one's nose: To express disdain or defiance.

Source:
1. Accessible Dictionary by Bangla Academy.
2. Cambridge Dictionary.
3. Merriam-Webster Dictionary.