D44 SmallGroup(44, 3)

[44 12 4 2]: [f1, f3^2, f2*f3^2, f3^3, f2*f3^4, f2*f3^6, f1*f3^7, f3^8, f1*f3^8, f2*f3^8, f3^9, f1*f3^10]
             [2, 8, 11, 12, 19, 27, 30, 32, 34, 35, 36, 42]

[44 12 4 2]: [f1, f3, f2*f3^2, f3^3, f2*f3^3, f1*f3^7, f2*f3^7, f3^8, f1*f3^8, f2*f3^8, f3^10, f1*f3^10]
             [2, 4, 11, 12, 15, 30, 31, 32, 34, 35, 40, 42]

[44 12 4 2]: [f1, f3, f2*f3, f2*f3^4, f3^5, f3^6, f2*f3^6, f1*f3^8, f1*f3^9, f2*f3^9, f3^10, f1*f3^10]
             [2, 4, 7, 19, 20, 24, 27, 34, 38, 39, 40, 42]

[44 12 4 2]: [f1, f2*f3, f2*f3^2, f3^3, f2*f3^4, f2*f3^6, f3^8, f1*f3^8, f2*f3^8, f1*f2*f3^8, f2*f3^9, f1*f2*f3^10]
             [2, 7, 11, 12, 19, 27, 32, 34, 35, 37, 39, 44]

[44 12 4 2]: [f1, f3, f2*f3^2, f3^3, f3^4, f3^7, f3^8, f1*f3^8, f2*f3^8, f1*f2*f3^8, f3^10, f1*f2*f3^10]
             [2, 4, 11, 12, 16, 28, 32, 34, 35, 37, 40, 44]

[44 12 4 2]: [f1, f2, f2*f3, f2*f3^4, f3^5, f3^6, f2*f3^6, f1*f3^8, f1*f2*f3^8, f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [2, 3, 7, 19, 20, 24, 27, 34, 37, 39, 43, 44]

[44 12 4 2]: [f1, f2, f2*f3, f3^4, f2*f3^4, f2*f3^6, f3^7, f1*f3^9, f2*f3^9, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
             [2, 3, 7, 16, 19, 27, 28, 38, 39, 41, 43, 44]

[44 12 4 2]: [f1, f2*f3, f2*f3^4, f1*f3^5, f1*f2*f3^5, f2*f3^6, f1*f2*f3^6, f1*f3^7, f1*f3^9, f2*f3^9, f1*f2*f3^9, f1*f2*f3^10]
             [2, 7, 19, 22, 25, 27, 29, 30, 38, 39, 41, 44]

[44 13 9 2]: [f1, f3, f3^2, f3^3, f3^4, f3^5, f2*f3^5, f3^6, f1*f2*f3^5, f3^7, f3^8, f3^9, f3^10]
             [2, 4, 8, 12, 16, 20, 23, 24, 25, 28, 32, 36, 40]

[44 23 22 2]: [f1, f1*f2, f1*f3, f1*f2*f3, f1*f3^2, f1*f2*f3^2, f1*f3^3, f1*f2*f3^3, f1*f3^4, f1*f2*f3^4, f1*f3^5, f2*f3^5, f1*f2*f3^5, f1*f3^6, f1*f2*f3^6, f1*f3^7, f1*f2*f3^7, f1*f3^8, f1*f2*f3^8, f1*f3^9, f1*f2*f3^9, f1*f3^10, f1*f2*f3^10]
              [2, 5, 6, 9, 10, 13, 14, 17, 18, 21, 22, 23, 25, 26, 29, 30, 33, 34, 37, 38, 41, 42, 44]

[44 31 27 20]: [f3, f1*f2, f1*f3, f3^2, f1*f2*f3, f1*f3^2, f3^3, f1*f2*f3^2, f1*f3^3, f3^4, f1*f2*f3^3, f1*f3^4, f3^5, f1*f2*f3^4, f1*f3^5, f2*f3^5, f3^6, f1*f3^6, f3^7, f1*f2*f3^6, f1*f3^7, f3^8, f1*f2*f3^7, f1*f3^8, f3^9, f1*f2*f3^8, f1*f3^9, f3^10, f1*f2*f3^9, f1*f3^10, f1*f2*f3^10]
               [4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44]

[44 37 32 30]: [f2, f3, f1*f2, f1*f3, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f2*f3^2, f3^3, f1*f2*f3^2, f1*f3^3, f2*f3^3, f3^4, f1*f2*f3^3, f2*f3^4, f3^5, f1*f2*f3^4, f1*f3^5, f3^6, f1*f2*f3^5, f1*f3^6, f2*f3^6, f3^7, f1*f2*f3^6, f2*f3^7, f3^8, f1*f2*f3^7, f1*f3^8, f2*f3^8, f3^9, f1*f2*f3^8, f2*f3^9, f3^10, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
               [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44]

[44 38 34 32]: [f2, f3, f1*f2, f1*f3, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f2*f3^2, f3^3, f1*f2*f3^2, f1*f3^3, f2*f3^3, f3^4, f1*f2*f3^3, f2*f3^4, f3^5, f1*f2*f3^4, f1*f3^5, f2*f3^5, f3^6, f1*f2*f3^5, f1*f3^6, f2*f3^6, f3^7, f1*f2*f3^6, f2*f3^7, f3^8, f1*f2*f3^7, f1*f3^8, f2*f3^8, f3^9, f1*f2*f3^8, f2*f3^9, f3^10, f1*f2*f3^9, f2*f3^10, f1*f2*f3^10]
               [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44]

[44 41 40 38]: [f2, f3, f1*f2, f1*f3, f2*f3, f3^2, f1*f2*f3, f1*f3^2, f2*f3^2, f3^3, f1*f2*f3^2, f1*f3^3, f2*f3^3, f3^4, f1*f2*f3^3, f1*f3^4, f2*f3^4, f3^5, f1*f2*f3^4, f1*f3^5, f3^6, f1*f2*f3^5, f1*f3^6, f2*f3^6, f3^7, f1*f2*f3^6, f1*f3^7, f2*f3^7, f3^8, f1*f2*f3^7, f1*f3^8, f2*f3^8, f3^9, f1*f2*f3^8, f1*f3^9, f2*f3^9, f3^10, f1*f2*f3^9, f1*f3^10, f2*f3^10, f1*f2*f3^10]
               [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]