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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2\wr \SD_{16}$ | 1A | $1$ | $1$ | $C_2\wr \SD_{16}$ | 1A | $()$ |
| $C_2\wr \SD_{16}$ | 2A | $2$ | $1$ | $C_2\wr \SD_{16}$ | 1A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2B | $2$ | $2$ | $C_2^5.D_4^2$ | 1A | $(5,6)(7,8)(9,10)(11,12)$ |
| $C_2\wr \SD_{16}$ | 2C | $2$ | $4$ | $C_2^5.C_2^5$ | 1A | $(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2D | $2$ | $4$ | $C_2^5.C_2^5$ | 1A | $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2E | $2$ | $4$ | $C_2^6.C_2^3.C_2$ | 1A | $(1,2)(3,4)(9,10)(11,12)$ |
| $C_2\wr \SD_{16}$ | 2F | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2G | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2H | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,6)(7,8)(9,11)(10,12)$ |
| $C_2\wr \SD_{16}$ | 2I | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,7)(6,8)(9,12)(10,11)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2J | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,7)(6,8)(9,12)(10,11)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2K | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,7)(6,8)(9,12)(10,11)(13,16)(14,15)$ |
| $C_2\wr \SD_{16}$ | 2L | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2M | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(1,2)(3,4)(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2N | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(1,2)(3,4)(5,7)(6,8)(9,12)(10,11)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2O | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(1,2)(3,4)(5,7)(6,8)(9,12)(10,11)(13,16)(14,15)$ |
| $C_2\wr \SD_{16}$ | 2P | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,7)(6,8)(9,11)(10,12)$ |
| $C_2\wr \SD_{16}$ | 2Q | $2$ | $8$ | $C_2^8.C_2$ | 1A | $(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2R | $2$ | $16$ | $C_2^8$ | 1A | $(9,10)(11,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2S | $2$ | $16$ | $C_2^8$ | 1A | $(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2T | $2$ | $16$ | $C_2^8$ | 1A | $(5,6)(7,8)(9,11)(10,12)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2U | $2$ | $16$ | $C_2^8$ | 1A | $(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2V | $2$ | $16$ | $C_2^8$ | 1A | $(5,6)(7,8)(9,11)(10,12)(13,16)(14,15)$ |
| $C_2\wr \SD_{16}$ | 2W | $2$ | $16$ | $C_2^8$ | 1A | $(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2X | $2$ | $16$ | $C_2^8$ | 1A | $(1,2)(3,4)(5,6)(7,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2Y | $2$ | $16$ | $C_2^8$ | 1A | $(1,2)(3,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2Z | $2$ | $16$ | $C_2^8$ | 1A | $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 2AA | $2$ | $16$ | $C_2^4:\SD_{16}$ | 1A | $(1,2)(5,6)(9,10)(13,14)$ |
| $C_2\wr \SD_{16}$ | 2AB | $2$ | $32$ | $C_2^4:D_4$ | 1A | $(5,9)(6,10)(7,11)(8,12)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2AC | $2$ | $32$ | $C_2^4:D_4$ | 1A | $(3,4)(5,9)(6,10)(7,12)(8,11)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 2AD | $2$ | $64$ | not computed | 1A | $(3,4)(5,9)(6,10)(7,12)(8,11)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 4A | $4$ | $16$ | $C_2^4.\SD_{16}$ | 2A | $(1,4,2,3)(5,7,6,8)(9,12,10,11)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4B | $4$ | $32$ | $C_2^3.C_2^4$ | 2C | $(5,9)(6,10)(7,11)(8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4C | $4$ | $32$ | $C_4^2:C_2^3$ | 2B | $(5,9,6,10)(7,11,8,12)(15,16)$ |
| $C_2\wr \SD_{16}$ | 4D | $4$ | $32$ | $C_2^3.C_2^4$ | 2D | $(5,9,6,10)(7,11,8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4E | $4$ | $32$ | $C_4^2:C_2^3$ | 2B | $(3,4)(5,9,6,10)(7,12,8,11)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 4F | $4$ | $32$ | $C_2^3.C_2^4$ | 2C | $(1,2)(3,4)(5,9)(6,10)(7,11)(8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4G | $4$ | $32$ | $C_2^3.C_2^4$ | 2D | $(1,2)(3,4)(5,9,6,10)(7,11,8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4H | $4$ | $32$ | $C_2^4.D_4$ | 2B | $(1,3,2,4)(5,6)(11,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4I | $4$ | $64$ | not computed | 2P | $(5,9,7,11)(6,10,8,12)(15,16)$ |
| $C_2\wr \SD_{16}$ | 4J | $4$ | $64$ | not computed | 2Q | $(5,9,7,11)(6,10,8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4K | $4$ | $64$ | not computed | 2C | $(3,4)(7,8)(11,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4L | $4$ | $64$ | not computed | 2D | $(3,4)(5,7,6,8)(9,11,10,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4M | $4$ | $64$ | not computed | 2B | $(3,4)(5,9,6,10)(7,12,8,11)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 4N | $4$ | $64$ | not computed | 2P | $(3,4)(5,9,7,12)(6,10,8,11)(13,14)(15,16)$ |
| $C_2\wr \SD_{16}$ | 4O | $4$ | $64$ | not computed | 2P | $(3,4)(5,9,7,12)(6,10,8,11)(13,15)(14,16)$ |
| $C_2\wr \SD_{16}$ | 4P | $4$ | $64$ | not computed | 2P | $(3,4)(5,9,7,12)(6,10,8,11)(13,16)(14,15)$ |
| $C_2\wr \SD_{16}$ | 4Q | $4$ | $64$ | not computed | 2Q | $(1,2)(3,4)(5,9,7,11)(6,10,8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4R | $4$ | $64$ | not computed | 2C | $(1,3)(2,4)(5,9)(6,10)(7,11)(8,12)(13,15,14,16)$ |
| $C_2\wr \SD_{16}$ | 4S | $4$ | $64$ | not computed | 2D | $(1,3)(2,4)(5,9,6,10)(7,11,8,12)(13,15,14,16)$ |