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432 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.8.0 | 4 | 8 | 70 | 40320 | ✓ | all | 9 | rational |
| 4.8.1 | 4 | 8 | 69 | 576 | ✓ | all | 8 | rational |
| 4.8.2 | 4 | 8 | 68 | 1152 | ✓ | all | 7 | rational |
| 4.8.3 | 4 | 8 | 68 | 72 | ✓ | all | 7 | rational |
| 4.8.4 | 4 | 8 | 68 | 32 | ✓ | all | 7 | rational |
| 4.8.5 | 4 | 8 | 67 | 8 | ✓ | all | 6 | rational |
| 4.8.6 | 4 | 8 | 66 | 32 | ✓ | all | 5 | rational |
| 4.8.7 | 4 | 8 | 67 | 32 | ✓ | all | 6 | rational |
| 4.8.8 | 4 | 8 | 66 | 128 | ✓ | all | 5 | rational |
| 4.8.9 | 4 | 8 | 67 | 8 | ✓ | all | 6 | rational |
| 4.8.11 | 4 | 8 | 67 | 8 | ✓ | all | 6 | rational |
| 4.8.12 | 4 | 8 | 66 | 8 | ✓ | all | 5 | rational |
| 4.8.13 | 4 | 8 | 66 | 2 | ✓ | all | 5 | rational |
| 4.8.14 | 4 | 8 | 66 | 4 | ✓ | all | 5 | rational |
| 4.8.18 | 4 | 8 | 67 | 6 | ✓ | all | 6 | rational |
| 4.8.19 | 4 | 8 | 66 | 6 | ✓ | all | 5 | rational |
| 4.8.20 | 4 | 8 | 66 | 1 | ✓ | all | 5 | rational |
| 4.8.24 | 4 | 8 | 66 | 4 | ✓ | all | 5 | rational |
| 4.8.31 | 4 | 8 | 66 | 2 | ✓ | all | 5 | rational |
| 4.8.39 | 4 | 8 | 66 | 24 | ✓ | all | 5 | rational |
| 4.8.41 | 4 | 8 | 66 | 4 | ✓ | all | 5 | rational |
| 4.8.102 | 4 | 8 | 67 | 96 | ✓ | ∅ | -1 | rational |
| 4.8.103 | 4 | 8 | 66 | 8 | ✓ | all | 2 | rational |
| 4.8.112 | 4 | 8 | 66 | 6 | ✓ | all | 3 | rational |
| 4.8.270 | 4 | 8 | 65 | 720 | ✓ | all | 1 | rational |
| 4.8.271 | 4 | 8 | 64 | 144 | ✓ | ∅ | -1 | rational |
| 4.8.272 | 4 | 8 | 64 | 24 | ✓ | all | 0 | rational |
| 4.8.273 | 4 | 8 | 63 | 8 | ✓ | all | 1 | rational |
| 4.8.274 | 4 | 8 | 63 | 8 | ✓ | all but 3 | 0 | rational |
| 4.8.278 | 4 | 8 | 63 | 4 | ✓ | all but 2 | 3 | rational |
| 4.8.313 | 4 | 8 | 60 | 144 | ✓ | {2} | -1 | rational |
| 4.8.317 | 4 | 8 | 55 | 1440 | ✗ | all | 5 | rational |
| 4.8.318 | 4 | 8 | 54 | 96 | ✗ | all | 5 | rational |
| 4.8.321 | 4 | 8 | 35 | 5040 | ✗ | all | 4 | rational |
| 4.8.322 | 4 | 8 | 65 | 720 | ✓ | all | 5 | rational |
| 4.8.323 | 4 | 8 | 64 | 144 | ✓ | all | 4 | rational |
| 4.8.324 | 4 | 8 | 60 | 720 | ✓ | all | 4 | rational |
| 4.8.325 | 4 | 8 | 64 | 24 | ✓ | all | 4 | rational |
| 4.8.326 | 4 | 8 | 63 | 8 | ✓ | all | 4 | rational |
| 4.8.327 | 4 | 8 | 63 | 8 | ✓ | all | 3 | rational |
| 4.8.328 | 4 | 8 | 62 | 8 | ✓ | all | 3 | rational |
| 4.8.329 | 4 | 8 | 63 | 4 | ✓ | all | 4 | rational |
| 4.8.330 | 4 | 8 | 62 | 2 | ✓ | all | 3 | rational |
| 4.8.331 | 4 | 8 | 62 | 4 | ✓ | all | 3 | rational |
| 4.8.332 | 4 | 8 | 62 | 2 | ✓ | all | 3 | rational |
| 4.8.336 | 4 | 8 | 62 | 12 | ✓ | all | 3 | rational |
| 4.8.338 | 4 | 8 | 60 | 144 | ✓ | all | 4 | rational |
| 4.8.339 | 4 | 8 | 63 | 16 | ✓ | all | 3 | rational |
| 4.8.341 | 4 | 8 | 62 | 2 | ✓ | all | 4 | rational |
| 4.8.344 | 4 | 8 | 62 | 2 | ✓ | all | 2 | rational |