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Elements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{2}=c^{44}=[a,b]=1, a^{2}=c^{22}, c^{a}=c^{23}, c^{b}=c^{21} \rangle$ .

Group Label Order Size Centralizer Powers Representative
2P 11P
$Q_8\times D_{11}$ 1A $1$ $1$ $Q_8\times D_{11}$ 1A 1A $1$
$Q_8\times D_{11}$ 2A $2$ $1$ $Q_8\times D_{11}$ 1A 2A $c^{22}$
$Q_8\times D_{11}$ 2B $2$ $11$ $C_2\times Q_8$ 1A 2B $b$
$Q_8\times D_{11}$ 2C $2$ $11$ $C_2\times Q_8$ 1A 2C $bc^{2}$
$Q_8\times D_{11}$ 4A $4$ $2$ $C_4\times D_{11}$ 2A 4A $c^{11}$
$Q_8\times D_{11}$ 4B $4$ $2$ $C_4\times D_{11}$ 2A 4B $ac^{22}$
$Q_8\times D_{11}$ 4C $4$ $2$ $C_4\times D_{11}$ 2A 4C $ac^{11}$
$Q_8\times D_{11}$ 4D $4$ $22$ $C_2\times C_4$ 2A 4D $bc^{39}$
$Q_8\times D_{11}$ 4E $4$ $22$ $C_2\times C_4$ 2A 4E $abc^{12}$
$Q_8\times D_{11}$ 4F $4$ $22$ $C_2\times C_4$ 2A 4F $abc^{31}$
$Q_8\times D_{11}$ 11A1 $11$ $2$ $Q_8\times C_{11}$ 11A2 11A5 $c^{4}$
$Q_8\times D_{11}$ 11A2 $11$ $2$ $Q_8\times C_{11}$ 11A4 11A1 $c^{8}$
$Q_8\times D_{11}$ 11A3 $11$ $2$ $Q_8\times C_{11}$ 11A5 11A4 $c^{12}$
$Q_8\times D_{11}$ 11A4 $11$ $2$ $Q_8\times C_{11}$ 11A3 11A2 $c^{16}$
$Q_8\times D_{11}$ 11A5 $11$ $2$ $Q_8\times C_{11}$ 11A1 11A3 $c^{20}$
$Q_8\times D_{11}$ 22A1 $22$ $2$ $Q_8\times C_{11}$ 11A1 22A5 $c^{2}$
$Q_8\times D_{11}$ 22A3 $22$ $2$ $Q_8\times C_{11}$ 11A3 22A7 $c^{6}$
$Q_8\times D_{11}$ 22A5 $22$ $2$ $Q_8\times C_{11}$ 11A5 22A3 $c^{10}$
$Q_8\times D_{11}$ 22A7 $22$ $2$ $Q_8\times C_{11}$ 11A4 22A9 $c^{14}$
$Q_8\times D_{11}$ 22A9 $22$ $2$ $Q_8\times C_{11}$ 11A2 22A1 $c^{18}$
$Q_8\times D_{11}$ 44A1 $44$ $4$ $C_{44}$ 22A1 44A5 $c$
$Q_8\times D_{11}$ 44A3 $44$ $4$ $C_{44}$ 22A3 44A7 $c^{3}$
$Q_8\times D_{11}$ 44A5 $44$ $4$ $C_{44}$ 22A5 44A3 $c^{5}$
$Q_8\times D_{11}$ 44A7 $44$ $4$ $C_{44}$ 22A7 44A9 $c^{29}$
$Q_8\times D_{11}$ 44A9 $44$ $4$ $C_{44}$ 22A9 44A1 $c^{9}$
$Q_8\times D_{11}$ 44B1 $44$ $4$ $C_{44}$ 22A7 44B5 $ac^{4}$
$Q_8\times D_{11}$ 44B3 $44$ $4$ $C_{44}$ 22A1 44B7 $ac^{12}$
$Q_8\times D_{11}$ 44B5 $44$ $4$ $C_{44}$ 22A9 44B3 $ac^{2}$
$Q_8\times D_{11}$ 44B7 $44$ $4$ $C_{44}$ 22A5 44B9 $ac^{16}$
$Q_8\times D_{11}$ 44B9 $44$ $4$ $C_{44}$ 22A3 44B1 $ac^{8}$
$Q_8\times D_{11}$ 44C1 $44$ $4$ $C_{44}$ 22A1 44C5 $ac$
$Q_8\times D_{11}$ 44C3 $44$ $4$ $C_{44}$ 22A3 44C7 $ac^{3}$
$Q_8\times D_{11}$ 44C5 $44$ $4$ $C_{44}$ 22A5 44C3 $ac^{5}$
$Q_8\times D_{11}$ 44C7 $44$ $4$ $C_{44}$ 22A7 44C9 $ac^{29}$
$Q_8\times D_{11}$ 44C9 $44$ $4$ $C_{44}$ 22A9 44C1 $ac^{9}$
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