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Label | Subgroup | Ambient | Quotient | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Name | Order | norm | char | cyc | ab | solv | max | perf | cent | Name | Order | Name | Size | cyc | ab | solv | max | |||
1.1.1.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_1$ | $1$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||
2.1.1.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2$ | $2$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ||||
2.1.2.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2$ | $2$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||
3.1.1.a1.a1 | $C_3$ | $3$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_3$ | $3$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ||||
3.1.3.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_3$ | $3$ | $C_3$ | $3$ | ✓ | ✓ | ✓ | |||
4.1.1.a1.a1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_4$ | $2^{2}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | |||||
4.1.2.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_4$ | $2^{2}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | |||
4.1.4.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_4$ | $2^{2}$ | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ||||
4.2.1.a1.a1 | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2^2$ | $2^{2}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||||
4.2.2.a1.c1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2^2$ | $2^{2}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ||||
4.2.2.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2^2$ | $2^{2}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ||||
4.2.2.a1.b1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2^2$ | $2^{2}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ||||
4.2.4.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2^2$ | $2^{2}$ | $C_2^2$ | $2^{2}$ | ✓ | ✓ | |||||
5.1.1.a1.a1 | $C_5$ | $5$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_5$ | $5$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ||||
5.1.5.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_5$ | $5$ | $C_5$ | $5$ | ✓ | ✓ | ✓ | |||
6.1.1.a1.a1 | $S_3$ | $2 \cdot 3$ | ✓ | ✓ | ✓ | $S_3$ | $2 \cdot 3$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||||||
6.1.2.a1.a1 | $C_3$ | $3$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $S_3$ | $2 \cdot 3$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ||||
6.1.3.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | $S_3$ | $2 \cdot 3$ | $3$ | $-$ | $-$ | $-$ | ||||||||
6.1.6.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $S_3$ | $2 \cdot 3$ | $S_3$ | $2 \cdot 3$ | ✓ | ||||||
6.2.1.a1.a1 | $C_6$ | $2 \cdot 3$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_6$ | $2 \cdot 3$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | |||||
6.2.2.a1.a1 | $C_3$ | $3$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_6$ | $2 \cdot 3$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | |||
6.2.3.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_6$ | $2 \cdot 3$ | $C_3$ | $3$ | ✓ | ✓ | ✓ | ✓ | |||
6.2.6.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_6$ | $2 \cdot 3$ | $C_6$ | $2 \cdot 3$ | ✓ | ✓ | ✓ | ||||
7.1.1.a1.a1 | $C_7$ | $7$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_7$ | $7$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ||||
7.1.7.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_7$ | $7$ | $C_7$ | $7$ | ✓ | ✓ | ✓ | |||
8.1.1.a1.a1 | $C_8$ | $2^{3}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_8$ | $2^{3}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | |||||
8.1.2.a1.a1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_8$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ||||
8.1.4.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_8$ | $2^{3}$ | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ||||
8.1.8.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_8$ | $2^{3}$ | $C_8$ | $2^{3}$ | ✓ | ✓ | ✓ | ||||
8.2.1.a1.a1 | $C_2\times C_4$ | $2^{3}$ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||||
8.2.2.b1.a1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||
8.2.2.b1.b1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||
8.2.2.a1.a1 | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||
8.2.4.a1.b1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | |||||
8.2.4.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | |||||
8.2.4.b1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | |||||
8.2.8.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $C_2\times C_4$ | $2^{3}$ | $C_2\times C_4$ | $2^{3}$ | ✓ | ✓ | |||||
8.3.1.a1.a1 | $D_4$ | $2^{3}$ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||||||
8.3.2.b1.a1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||
8.3.2.a1.a1 | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||||
8.3.2.a1.b1 | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | |||||||
8.3.4.b1.b1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $2^{2}$ | $-$ | $-$ | $-$ | |||||||||
8.3.4.b1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $2^{2}$ | $-$ | $-$ | $-$ | |||||||||
8.3.4.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ | |||||
8.3.8.a1.a1 | $C_1$ | $1$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $D_4$ | $2^{3}$ | $D_4$ | $2^{3}$ | ✓ | ||||||
8.4.1.a1.a1 | $Q_8$ | $2^{3}$ | ✓ | ✓ | ✓ | $Q_8$ | $2^{3}$ | $C_1$ | $1$ | ✓ | ✓ | ✓ | ||||||||
8.4.2.a1.c1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | $Q_8$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ||||||
8.4.2.a1.a1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | $Q_8$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ||||||
8.4.2.a1.b1 | $C_4$ | $2^{2}$ | ✓ | ✓ | ✓ | ✓ | ✓ | $Q_8$ | $2^{3}$ | $C_2$ | $2$ | ✓ | ✓ | ✓ | ||||||
8.4.4.a1.a1 | $C_2$ | $2$ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | $Q_8$ | $2^{3}$ | $C_2^2$ | $2^{2}$ | ✓ | ✓ | ✓ |