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Subgroup label Subgroup order Cyclic Abelian Solvable
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Results (1-50 of 766 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
4608.ti.1.a1.a1 $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_1$ $1$ ✓
4608.ti.2._.A $(D_6\times C_2^4):C_{12}$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.B $C_{12}.D_4\times S_4$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.C $(C_2^2\times C_6).\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.D $C_2^4.D_6^2$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.E $(C_2\times C_{12}).\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.F $C_2^3:C_{12}\times S_4$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.2._.G $(C_2\times C_{12}).\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2}$ ✓ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2$ $2$ ✓
4608.ti.3._.A $(C_2\times C_{12}).D_4^2$ $2^{9} \cdot 3$ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $3$ $-$
4608.ti.3._.B $C_2\wr C_4\times S_4$ $2^{9} \cdot 3$ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $3$ $-$
4608.ti.4._.A $C_6\times D_4\times S_4$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.B $A_4\times D_6:D_4$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.C $C_2^5.C_6^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.D $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.E $(C_2\times C_6):\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.F $A_4\times C_{12}.D_4$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.G $C_3\times C_2^2.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_2^2$ $2^{2}$ ✓
4608.ti.4._.H $C_2^3:D_6^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
4608.ti.4._.I $C_2^5.S_3^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
4608.ti.4._.J $C_2^5.S_3^2$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
4608.ti.4._.K $D_6:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $C_4$ $2^{2}$ ✓
4608.ti.4._.L $C_2^5:S_3^2$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.M $D_6:\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.N $D_6:C_4\times S_4$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.O $(C_6\times S_4):D_4$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.P $C_3:\OD_{16}\times S_4$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.Q $C_{12}.\GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.R $C_2^2:C_{12}\times S_4$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.S $(C_2^2\times S_4):C_{12}$ $2^{7} \cdot 3^{2}$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.4._.T $(C_2\times D_6^2):C_4$ $2^{7} \cdot 3^{2}$ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2^{2}$ $-$
4608.ti.6._.A $C_2^3:C_4\times S_4$ $2^{8} \cdot 3$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
4608.ti.6._.B $(D_6\times C_2^4):C_4$ $2^{8} \cdot 3$ ✓ ✓ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $S_3$ $2 \cdot 3$
4608.ti.6._.C $D_6:D_4^2$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.D $C_2^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.E $C_{12}.D_4^2$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.F $S_4\times \OD_{16}:C_2$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.G $C_2^6:D_6$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.H $C_2^6:C_{12}$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.I $D_4\times C_2^3:C_{12}$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.J $(C_2^3\times C_{12}).D_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.K $(D_6\times C_2^4):C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.L $C_2^3.\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.M $(C_2^3\times C_{12}).D_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.N $C_2^5.D_{12}$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.O $(C_2^3\times C_{12}).D_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.P $C_{12}:C_2\wr C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.Q $(C_2^3\times D_{12}):C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.R $(D_6\times C_2^4):C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.S $(D_6\times C_2^4):C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
4608.ti.6._.T $(C_2^3\times D_{12}):C_4$ $2^{8} \cdot 3$ $(C_6\times \GL(2,\mathbb{Z}/4)).D_4$ $2^{9} \cdot 3^{2}$ $2 \cdot 3$ $-$
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