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Note: Search results may be incomplete due to uncomputed quantities: Characteristic (9102698 objects)

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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (34 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
85752.b.1.a1.a1 $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_1$ $1$ ✓
85752.b.2.a1.a1 $C_{2382}:C_{18}$ $2^{2} \cdot 3^{3} \cdot 397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2$ $2$ ✓
85752.b.3.a1.a1 $C_{2382}:C_{12}$ $2^{3} \cdot 3^{2} \cdot 397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3$ $3$ ✓
85752.b.4.a1.a1 $C_{1191}:C_{18}$ $2 \cdot 3^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_4$ $2^{2}$ ✓
85752.b.4.b1.a1 $C_{1191}:C_{18}$ $2 \cdot 3^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2^2$ $2^{2}$ ✓
85752.b.4.c1.a1 $C_{1191}:C_{18}$ $2 \cdot 3^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_4$ $2^{2}$ ✓
85752.b.6.a1.a1 $C_{2382}:C_6$ $2^{2} \cdot 3^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_6$ $2 \cdot 3$ ✓
85752.b.8.a1.a1 $C_{1191}:C_9$ $3^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2\times C_4$ $2^{3}$ ✓
85752.b.9.a1.a1 $C_{2382}:C_4$ $2^{3} \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_9$ $3^{2}$ ✓
85752.b.9.b1.a1 $C_{794}:C_{12}$ $2^{3} \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3^2$ $3^{2}$ ✓
85752.b.12.a1.a1 $C_{1191}:C_6$ $2 \cdot 3^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{12}$ $2^{2} \cdot 3$ ✓
85752.b.12.c1.a1 $C_{1191}:C_6$ $2 \cdot 3^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2\times C_6$ $2^{2} \cdot 3$ ✓
85752.b.12.e1.a1 $C_{1191}:C_6$ $2 \cdot 3^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{12}$ $2^{2} \cdot 3$ ✓
85752.b.18.a1.a1 $C_3\times D_{794}$ $2^{2} \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{18}$ $2 \cdot 3^{2}$ ✓
85752.b.18.b1.a1 $C_{794}:C_6$ $2^{2} \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_6$ $2 \cdot 3^{2}$ ✓
85752.b.24.a1.a1 $C_{1191}:C_3$ $3^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2\times C_{12}$ $2^{3} \cdot 3$ ✓
85752.b.27.a1.a1 $C_{794}:C_4$ $2^{3} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_9$ $3^{3}$ ✓
85752.b.36.a1.a1 $C_{2382}$ $2 \cdot 3 \cdot 397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{36}$ $2^{2} \cdot 3^{2}$ ✓
85752.b.36.b1.a1 $C_{397}:C_6$ $2 \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓
85752.b.36.d1.a1 $C_3\times D_{397}$ $2 \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2\times C_{18}$ $2^{2} \cdot 3^{2}$ ✓
85752.b.36.e1.a1 $C_{397}:C_6$ $2 \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_6^2$ $2^{2} \cdot 3^{2}$ ✓
85752.b.36.g1.a1 $C_3\times D_{397}$ $2 \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{36}$ $2^{2} \cdot 3^{2}$ ✓
85752.b.36.h1.a1 $C_{397}:C_6$ $2 \cdot 3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ ✓
85752.b.54.a1.a1 $D_{794}$ $2^{2} \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_{18}$ $2 \cdot 3^{3}$ ✓
85752.b.72.a1.a1 $C_{1191}$ $3 \cdot 397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_2\times C_{36}$ $2^{3} \cdot 3^{2}$ ✓
85752.b.72.b1.a1 $C_{397}:C_3$ $3 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_6\times C_{12}$ $2^{3} \cdot 3^{2}$ ✓
85752.b.108.a1.a1 $C_{794}$ $2 \cdot 397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_{36}$ $2^{2} \cdot 3^{3}$ ✓
85752.b.108.b1.a1 $D_{397}$ $2 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_6\times C_{18}$ $2^{2} \cdot 3^{3}$ ✓
85752.b.108.c1.a1 $D_{397}$ $2 \cdot 397$ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_3\times C_{36}$ $2^{2} \cdot 3^{3}$ ✓
85752.b.216.a1.a1 $C_{397}$ $397$ $397$ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_6\times C_{36}$ $2^{3} \cdot 3^{3}$ ✓ ✓
85752.b.14292.a1.a1 $C_6$ $2 \cdot 3$ ✓ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{397}:C_{36}$ $2^{2} \cdot 3^{2} \cdot 397$
85752.b.28584.a1.a1 $C_3$ $3$ ✓ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{794}:C_{36}$ $2^{3} \cdot 3^{2} \cdot 397$ ✓
85752.b.42876.a1.a1 $C_2$ $2$ ✓ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{1191}:C_{36}$ $2^{2} \cdot 3^{3} \cdot 397$ ✓
85752.b.85752.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$ $C_{2382}:C_{36}$ $2^{3} \cdot 3^{3} \cdot 397$
  displayed columns for results