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Elements of the group are displayed as permutations of degree 24.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_2^8.C_2\wr S_4$ | 1A | $1$ | $1$ | $C_2^8.C_2\wr S_4$ | 1A | 1A | $()$ |
| $C_2^8.C_2\wr S_4$ | 2A | $2$ | $1$ | $C_2^8.C_2\wr S_4$ | 1A | 2A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2B | $2$ | $3$ | $C_2^9.C_2^5.C_2^3$ | 1A | 2B | $(5,6)(11,12)(17,18)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2C | $2$ | $3$ | $C_2^9.C_2^5.C_2^3$ | 1A | 2C | $(3,4)(5,6)(9,10)(11,12)(15,16)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2D | $2$ | $4$ | $C_2^6.C_2\wr S_4$ | 1A | 2D | $(1,2)(5,6)(9,10)(13,14)(17,18)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2E | $2$ | $4$ | $C_2^6.C_2\wr S_4$ | 1A | 2E | $(3,4)(7,8)(11,12)(15,16)(19,20)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2F | $2$ | $6$ | $C_2^8.C_2^6.C_2^2$ | 1A | 2F | $(3,4)(5,6)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2G | $2$ | $6$ | $C_2^8.C_2^6.C_2^2$ | 1A | 2G | $(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2H | $2$ | $6$ | $C_2^8.C_2^5.C_2^3$ | 1A | 2H | $(11,12)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2I | $2$ | $6$ | $C_2^8.C_2^5.C_2^3$ | 1A | 2I | $(1,2)(5,6)(7,8)(9,10)(11,12)(13,14)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2J | $2$ | $6$ | $C_2^8.C_2^6.C_2^2$ | 1A | 2J | $(7,8)(13,14)$ |
| $C_2^8.C_2\wr S_4$ | 2K | $2$ | $6$ | $C_2^8.C_2^6.C_2^2$ | 1A | 2K | $(17,18)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2L | $2$ | $8$ | $C_2^5.C_2\wr S_4$ | 1A | 2L | $(3,4)(7,8)(9,10)(11,12)(13,14)(17,18)$ |
| $C_2^8.C_2\wr S_4$ | 2M | $2$ | $8$ | $C_2^5.C_2\wr S_4$ | 1A | 2M | $(9,10)(13,14)(15,16)(17,18)(19,20)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2N | $2$ | $12$ | not computed | 1A | 2N | $(5,17)(6,18)(11,23)(12,24)$ |
| $C_2^8.C_2\wr S_4$ | 2O | $2$ | $12$ | not computed | 1A | 2O | $(1,2)(3,4)(5,17)(6,18)(7,8)(9,10)(11,23)(12,24)(13,14)(15,16)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2P | $2$ | $12$ | not computed | 1A | 2P | $(9,10)(11,12)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2Q | $2$ | $12$ | not computed | 1A | 2Q | $(5,6)(15,16)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2R | $2$ | $12$ | not computed | 1A | 2R | $(3,4)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2S | $2$ | $12$ | not computed | 1A | 2S | $(1,2)(5,6)(11,12)(13,14)(17,18)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2T | $2$ | $12$ | not computed | 1A | 2T | $(1,2)(7,8)(13,14)(15,16)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2U | $2$ | $12$ | not computed | 1A | 2U | $(1,2)(7,8)(13,14)(17,18)(19,20)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2V | $2$ | $12$ | not computed | 1A | 2V | $(3,4)(5,6)(7,8)(9,10)(13,14)(15,16)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2W | $2$ | $12$ | not computed | 1A | 2W | $(1,2)(5,6)(7,8)(9,10)(13,14)(17,18)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2X | $2$ | $12$ | not computed | 1A | 2X | $(1,2)(3,4)(7,8)(9,10)(15,16)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2Y | $2$ | $24$ | not computed | 1A | 2Y | $(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2Z | $2$ | $24$ | not computed | 1A | 2Z | $(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AA | $2$ | $24$ | not computed | 1A | 2AA | $(9,10)(11,12)(13,14)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AB | $2$ | $24$ | not computed | 1A | 2AB | $(7,8)(11,12)(15,16)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AC | $2$ | $24$ | not computed | 1A | 2AC | $(3,4)(5,17)(6,18)(9,10)(11,23)(12,24)(15,16)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AD | $2$ | $24$ | not computed | 1A | 2AD | $(15,16)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AE | $2$ | $24$ | not computed | 1A | 2AE | $(1,2)(5,6)(17,18)(19,20)$ |
| $C_2^8.C_2\wr S_4$ | 2AF | $2$ | $24$ | not computed | 1A | 2AF | $(1,2)(9,10)(13,14)(15,16)(17,18)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AG | $2$ | $24$ | not computed | 1A | 2AG | $(1,2)(5,6)(7,8)(9,10)(13,14)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AH | $2$ | $24$ | not computed | 1A | 2AH | $(1,2)(5,6)(15,16)(17,18)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AI | $2$ | $24$ | not computed | 1A | 2AI | $(9,10)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AJ | $2$ | $24$ | not computed | 1A | 2AJ | $(3,4)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AK | $2$ | $24$ | not computed | 1A | 2AK | $(1,2)(5,6)(7,8)(9,10)(11,12)(17,18)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AL | $2$ | $48$ | not computed | 1A | 2AL | $(11,12)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AM | $2$ | $48$ | not computed | 1A | 2AM | $(11,12)(15,16)(19,20)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AN | $2$ | $48$ | not computed | 1A | 2AN | $(11,12)(13,14)(15,16)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AO | $2$ | $48$ | not computed | 1A | 2AO | $(7,8)(9,10)(11,12)(15,16)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AP | $2$ | $48$ | not computed | 1A | 2AP | $(5,6)(7,8)(9,10)(15,16)(17,18)(19,20)(21,22)(23,24)$ |
| $C_2^8.C_2\wr S_4$ | 2AQ | $2$ | $48$ | not computed | 1A | 2AQ | $(5,17)(6,18)(11,23)(12,24)(15,16)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AR | $2$ | $48$ | not computed | 1A | 2AR | $(5,17)(6,18)(11,23)(12,24)(13,14)(19,20)$ |
| $C_2^8.C_2\wr S_4$ | 2AS | $2$ | $48$ | not computed | 1A | 2AS | $(5,17)(6,18)(9,10)(11,23)(12,24)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AT | $2$ | $48$ | not computed | 1A | 2AT | $(5,17)(6,18)(9,10)(11,23)(12,24)(13,14)(15,16)(19,20)$ |
| $C_2^8.C_2\wr S_4$ | 2AU | $2$ | $48$ | not computed | 1A | 2AU | $(5,17)(6,18)(7,8)(11,23)(12,24)(13,14)(15,16)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AV | $2$ | $48$ | not computed | 1A | 2AV | $(5,17)(6,18)(7,8)(9,10)(11,23)(12,24)(19,20)(21,22)$ |
| $C_2^8.C_2\wr S_4$ | 2AW | $2$ | $48$ | not computed | 1A | 2AW | $(3,4)(5,17)(6,18)(9,10)(11,23)(12,24)(13,14)(15,16)(19,20)(21,22)$ |