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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2^6.C_2\wr C_4$ | 1A | $1$ | $1$ | $C_2^6.C_2\wr C_4$ | 1A | $()$ |
| $C_2^6.C_2\wr C_4$ | 2A | $2$ | $1$ | $C_2^6.C_2\wr C_4$ | 1A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2B | $2$ | $2$ | $C_2^5.C_2^5.C_2$ | 1A | $(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2C | $2$ | $4$ | $C_2^5.C_2^5$ | 1A | $(11,12)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2D | $2$ | $4$ | $C_2^5.C_2^5$ | 1A | $(1,2)(3,4)(5,6)(7,8)(11,12)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2E | $2$ | $4$ | $C_2^7.D_4$ | 1A | $(3,4)(7,8)(9,10)(13,14)$ |
| $C_2^6.C_2\wr C_4$ | 2F | $2$ | $8$ | $C_2^6:D_4$ | 1A | $(13,14)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2G | $2$ | $8$ | $C_2^6:D_4$ | 1A | $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2H | $2$ | $8$ | $C_2^4.C_2^5$ | 1A | $(1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 2I | $2$ | $8$ | $C_2^4.C_2^5$ | 1A | $(3,4)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 2J | $2$ | $8$ | $C_2^4.C_2^5$ | 1A | $(3,4)(7,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2^6.C_2\wr C_4$ | 2K | $2$ | $8$ | $C_2^4.C_2^5$ | 1A | $(9,14)(10,13)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 2L | $2$ | $16$ | $C_2^5:D_4$ | 1A | $(5,6)(7,8)(11,12)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2M | $2$ | $16$ | $C_2^6:C_4$ | 1A | $(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 2N | $2$ | $16$ | $C_2^6:C_4$ | 1A | $(3,8)(4,7)(11,16)(12,15)$ |
| $C_2^6.C_2\wr C_4$ | 2O | $2$ | $16$ | $C_2^5:D_4$ | 1A | $(1,2)(7,8)(9,10)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2P | $2$ | $16$ | $C_2^6:C_4$ | 1A | $(1,6)(2,5)(3,4)(7,8)(9,14)(10,13)(11,12)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 2Q | $2$ | $32$ | $D_4\times C_2^4$ | 1A | $(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^6.C_2\wr C_4$ | 2R | $2$ | $32$ | $D_4\times C_2^4$ | 1A | $(7,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^6.C_2\wr C_4$ | 2S | $2$ | $32$ | $D_4\times C_2^4$ | 1A | $(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 2T | $2$ | $32$ | $D_4\times C_2^4$ | 1A | $(3,4)(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2^6.C_2\wr C_4$ | 2U | $2$ | $32$ | $D_4\times C_2^4$ | 1A | $(3,4)(5,6)(7,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2^6.C_2\wr C_4$ | 2V | $2$ | $32$ | $C_2^7$ | 1A | $(3,7)(4,8)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2^6.C_2\wr C_4$ | 4A | $4$ | $8$ | $C_2^4.C_2^4.C_2$ | 2B | $(9,13,10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4B | $4$ | $8$ | $C_2^4.C_2^4.C_2$ | 2B | $(1,2)(3,4)(5,6)(7,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4C | $4$ | $16$ | $C_2^3.C_2^5$ | 2B | $(3,4)(7,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4D | $4$ | $16$ | $C_4^2.\OD_{16}$ | 2A | $(1,5,2,6)(3,7,4,8)(9,14,10,13)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4E | $4$ | $32$ | $D_4:C_2^4$ | 2B | $(7,8)(9,11,10,12)(13,15,14,16)$ |
| $C_2^6.C_2\wr C_4$ | 4F | $4$ | $32$ | $D_4:C_2^4$ | 2B | $(7,8)(9,11,10,12)(13,16,14,15)$ |
| $C_2^6.C_2\wr C_4$ | 4G | $4$ | $32$ | $D_4:C_2^4$ | 2B | $(5,6)(7,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4H | $4$ | $32$ | $D_4:C_2^4$ | 2B | $(3,4)(5,6)(7,8)(9,11,10,12)(13,15,14,16)$ |
| $C_2^6.C_2\wr C_4$ | 4I | $4$ | $32$ | $D_4:C_2^4$ | 2B | $(3,4)(5,6)(7,8)(9,11,10,12)(13,16,14,15)$ |
| $C_2^6.C_2\wr C_4$ | 4J | $4$ | $32$ | $C_2^3:C_4^2$ | 2B | $(1,5)(2,6)(3,7)(4,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4K | $4$ | $64$ | $C_2^4\times C_4$ | 2C | $(3,7)(4,8)(11,15,12,16)(13,14)$ |
| $C_2^6.C_2\wr C_4$ | 4L | $4$ | $64$ | $C_2^2\times C_4^2$ | 2I | $(3,7,4,8)(9,11,13,15)(10,12,14,16)$ |
| $C_2^6.C_2\wr C_4$ | 4M | $4$ | $64$ | $C_2^2\times C_4^2$ | 2J | $(3,7,4,8)(9,11,13,16)(10,12,14,15)$ |
| $C_2^6.C_2\wr C_4$ | 4N | $4$ | $64$ | $C_2^4\times C_4$ | 2C | $(3,7,4,8)(5,6)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2^6.C_2\wr C_4$ | 4O | $4$ | $64$ | $C_2^2\times C_4^2$ | 2I | $(1,2)(3,7,4,8)(5,6)(9,11,13,15)(10,12,14,16)$ |
| $C_2^6.C_2\wr C_4$ | 4P | $4$ | $64$ | $C_2^2\times C_4^2$ | 2J | $(1,2)(3,7,4,8)(5,6)(9,11,13,16)(10,12,14,15)$ |
| $C_2^6.C_2\wr C_4$ | 4Q | $4$ | $64$ | $C_4^2:C_2^2$ | 2C | $(1,3)(2,4)(5,7)(6,8)(9,13)(10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4R | $4$ | $64$ | $C_4^2:C_2^2$ | 2C | $(1,3)(2,4)(5,7)(6,8)(9,13,10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4S | $4$ | $64$ | $C_4^2:C_2^2$ | 2D | $(1,3,2,4)(5,7,6,8)(9,13)(10,14)(11,15,12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4T | $4$ | $64$ | $C_4^2:C_2^2$ | 2D | $(1,3,2,4)(5,7,6,8)(9,13,10,14)(11,15)(12,16)$ |
| $C_2^6.C_2\wr C_4$ | 4U | $4$ | $64$ | $C_2^2:\OD_{16}$ | 2E | $(1,2)(3,8,4,7)(9,13,10,14)(15,16)$ |
| $C_2^6.C_2\wr C_4$ | 4V | $4$ | $128$ | $C_2^3\times C_4$ | 2O | $(1,8,2,7)(3,5)(4,6)(9,16,10,15)(11,13)(12,14)$ |
| $C_2^6.C_2\wr C_4$ | 4W | $4$ | $128$ | $C_2^3\times C_4$ | 2K | $(1,2)(3,7)(4,8)(9,11,14,15)(10,12,13,16)$ |
| $C_2^6.C_2\wr C_4$ | 4X | $4$ | $128$ | $C_2^3\times C_4$ | 2O | $(1,4,2,3)(5,8)(6,7)(9,15)(10,16)(11,13,12,14)$ |
| $C_2^6.C_2\wr C_4$ | 4Y | $4$ | $128$ | $C_2^3\times C_4$ | 2K | $(1,3,5,8)(2,4,6,7)(11,16)(12,15)(13,14)$ |
| $C_2^6.C_2\wr C_4$ | 4Z1 | $4$ | $128$ | $C_2^3\times C_4$ | 2N | $(1,10)(2,9)(3,15,8,12)(4,16,7,11)(5,13)(6,14)$ |
| $C_2^6.C_2\wr C_4$ | 4Z-1 | $4$ | $128$ | $C_2^3\times C_4$ | 2N | $(1,10)(2,9)(3,12,8,15)(4,11,7,16)(5,13)(6,14)$ |