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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $A_4^2:C_2\wr C_4$ | 1A | $1$ | $1$ | $A_4^2:C_2\wr C_4$ | 1A | 1A | $()$ |
| $A_4^2:C_2\wr C_4$ | 2A | $2$ | $1$ | $A_4^2:C_2\wr C_4$ | 1A | 2A | $(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2B | $2$ | $2$ | $A_4^2.C_2^4.C_2$ | 1A | 2B | $(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2C | $2$ | $4$ | $A_4^2:C_2^4$ | 1A | 2C | $(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2D | $2$ | $6$ | $C_2^5.C_2^3.S_3$ | 1A | 2D | $(3,4)(5,7)$ |
| $A_4^2:C_2\wr C_4$ | 2E | $2$ | $6$ | $C_2^5.C_2^3.S_3$ | 1A | 2E | $(3,4)(5,7)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2F | $2$ | $6$ | $C_2^5.C_2^3.S_3$ | 1A | 2F | $(3,4)(5,7)(9,16)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 2G | $2$ | $6$ | $C_2^5.C_2^3.S_3$ | 1A | 2G | $(3,4)(5,7)(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2H | $2$ | $9$ | $C_2^6.C_2^3.C_2$ | 1A | 2H | $(1,6)(2,8)(3,7)(4,5)(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2I | $2$ | $9$ | $C_2^6.C_2^3.C_2$ | 1A | 2I | $(1,2)(3,4)(5,7)(6,8)$ |
| $A_4^2:C_2\wr C_4$ | 2J | $2$ | $12$ | $C_2^3\times \GL(2,\mathbb{Z}/4)$ | 1A | 2J | $(3,4)(5,7)(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2K | $2$ | $12$ | $C_2^3\times \GL(2,\mathbb{Z}/4)$ | 1A | 2K | $(3,4)(5,7)(10,15)(11,13)$ |
| $A_4^2:C_2\wr C_4$ | 2L | $2$ | $18$ | $C_2^6.C_2^3$ | 1A | 2L | $(1,2)(3,4)(5,7)(6,8)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2M | $2$ | $36$ | $C_2^5:D_4$ | 1A | 2M | $(1,2)(3,4)(5,7)(6,8)(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2N | $2$ | $144$ | $C_2^4:C_4$ | 1A | 2N | $(2,8)(3,4)(9,15)(10,16)(11,14)(12,13)$ |
| $A_4^2:C_2\wr C_4$ | 2O | $2$ | $144$ | $C_2^6$ | 1A | 2O | $(1,6)(4,7)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 2P | $2$ | $144$ | $C_2^6$ | 1A | 2P | $(1,8)(3,4)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 3A | $3$ | $16$ | $C_2^4.C_6^2$ | 3A | 1A | $(4,7,5)$ |
| $A_4^2:C_2\wr C_4$ | 3B | $3$ | $64$ | $C_6^2:C_4$ | 3B | 1A | $(2,8,6)(4,7,5)$ |
| $A_4^2:C_2\wr C_4$ | 4A | $4$ | $8$ | $C_2^5.C_6^2$ | 2B | 4A | $(9,10)(11,14,13,12)(15,16)$ |
| $A_4^2:C_2\wr C_4$ | 4B | $4$ | $24$ | $C_2^5:C_{12}$ | 2B | 4B | $(3,4)(5,7)(9,10)(11,14,13,12)(15,16)$ |
| $A_4^2:C_2\wr C_4$ | 4C | $4$ | $24$ | $C_2^5:C_{12}$ | 2B | 4C | $(3,4)(5,7)(9,15,16,10)(11,12)(13,14)$ |
| $A_4^2:C_2\wr C_4$ | 4D | $4$ | $72$ | $C_2^5\times C_4$ | 2B | 4D | $(1,2)(3,4)(5,7)(6,8)(9,10)(11,12,13,14)(15,16)$ |
| $A_4^2:C_2\wr C_4$ | 4E | $4$ | $144$ | $C_2^2:\OD_{16}$ | 2H | 4E | $(1,2,6,8)(3,5,7,4)(9,15,16,10)(11,12,13,14)$ |
| $A_4^2:C_2\wr C_4$ | 4F | $4$ | $144$ | $C_2^2:\OD_{16}$ | 2I | 4F | $(1,6,2,8)(3,7,4,5)(9,10)(11,14)(12,13)(15,16)$ |
| $A_4^2:C_2\wr C_4$ | 4G | $4$ | $144$ | $C_2^4\times C_4$ | 2D | 4G | $(1,8)(3,4,7,5)(9,16)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 4H | $4$ | $144$ | $C_2^4\times C_4$ | 2I | 4H | $(1,6,8,2)(3,5,7,4)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 4I | $4$ | $144$ | $C_2^4\times C_4$ | 2D | 4I | $(3,5,7,4)(6,8)(9,16)(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 4J | $4$ | $144$ | $C_2^4\times C_4$ | 2D | 4J | $(1,8,6,2)(3,4)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 4K | $4$ | $144$ | $C_2^2:\OD_{16}$ | 2A | 4K | $(4,7)(6,8)(9,10,16,15)(11,14,13,12)$ |
| $A_4^2:C_2\wr C_4$ | 4L | $4$ | $144$ | $C_2^4\times C_4$ | 2D | 4L | $(2,6)(3,5,7,4)(11,13)$ |
| $A_4^2:C_2\wr C_4$ | 4M | $4$ | $144$ | $C_2^4\times C_4$ | 2I | 4M | $(1,2,6,8)(3,7,5,4)(9,16)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 4N | $4$ | $288$ | $C_2^3\times C_4$ | 2D | 4N | $(2,8)(3,4,5,7)(9,15)(10,16)(11,14)(12,13)$ |
| $A_4^2:C_2\wr C_4$ | 4O | $4$ | $288$ | $C_2^3\times C_4$ | 2G | 4O | $(2,8)(3,4,5,7)(9,15,16,10)(11,12,13,14)$ |
| $A_4^2:C_2\wr C_4$ | 4P1 | $4$ | $576$ | $C_2^2\times C_4$ | 2N | 4P-1 | $(1,5)(2,3,8,4)(6,7)(9,11,15,14)(10,12,16,13)$ |
| $A_4^2:C_2\wr C_4$ | 4P-1 | $4$ | $576$ | $C_2^2\times C_4$ | 2N | 4P1 | $(1,5)(2,4,8,3)(6,7)(9,14,15,11)(10,13,16,12)$ |
| $A_4^2:C_2\wr C_4$ | 6A | $6$ | $16$ | $C_2^4.C_6^2$ | 3A | 2A | $(4,5,7)(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6B | $6$ | $16$ | $C_2^4.C_6^2$ | 3A | 2B | $(4,7,5)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6C | $6$ | $16$ | $C_2^4.C_6^2$ | 3A | 2B | $(4,7,5)(9,16)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 6D | $6$ | $32$ | $C_2^3:C_6^2$ | 3A | 2C | $(4,5,7)(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6E | $6$ | $32$ | $C_2^3:C_6^2$ | 3A | 2C | $(4,5,7)(10,15)(11,13)$ |
| $A_4^2:C_2\wr C_4$ | 6F | $6$ | $48$ | $C_2^4:C_{12}$ | 3A | 2D | $(2,6,8)(3,4)(5,7)$ |
| $A_4^2:C_2\wr C_4$ | 6G | $6$ | $48$ | $C_2^4:C_{12}$ | 3A | 2E | $(2,6,8)(3,4)(5,7)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6H | $6$ | $48$ | $C_2^4:C_{12}$ | 3A | 2F | $(2,6,8)(3,4)(5,7)(9,16)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 6I | $6$ | $48$ | $C_2^4:C_{12}$ | 3A | 2G | $(2,6,8)(3,4)(5,7)(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6J | $6$ | $64$ | $C_6^2:C_4$ | 3B | 2A | $(2,6,8)(4,5,7)(9,16)(10,15)(11,13)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6K | $6$ | $64$ | $C_6^2:C_4$ | 3B | 2B | $(1,8,6)(3,4,7)(9,16)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 6L | $6$ | $64$ | $C_6^2:C_4$ | 3B | 2B | $(2,6,8)(3,7,4)(9,16)(10,15)$ |
| $A_4^2:C_2\wr C_4$ | 6M | $6$ | $96$ | $C_2^4\times C_6$ | 3A | 2J | $(2,6,8)(3,4)(5,7)(10,15)(12,14)$ |
| $A_4^2:C_2\wr C_4$ | 6N | $6$ | $96$ | $C_2^4\times C_6$ | 3A | 2K | $(2,6,8)(3,4)(5,7)(10,15)(11,13)$ |