← #72241457
Subgroups — #72241457
Order 4096.
Only the 5227 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 101 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72241424 | C2 | 1 | 45 | yes | maximal, complemented |
| 2 | C2×#6631461 | C22 | 1 | 15 | yes | complemented |
| 3 | #72240972 | C2 | 1 | 3 | yes | maximal |
| 4 | #72240922 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | #72240921 | C22 | 1 | 45 | yes | complemented |
| 6 | #72240920 | C22 | 1 | 180 | yes | complemented |
| 7 | #72240919 | C22 | 1 | 90 | yes | complemented |
| 8 | #72240918 | C22 | 1 | 5 | yes | complemented |
| 9 | #72240911 | C22 | 1 | 45 | yes | — |
| 10 | #72240907 | C22 | 1 | 30 | yes | complemented |
| 11 | #72240529 | C22 | 1 | 15 | yes | complemented |
| 12 | #72240510 | C22 | 1 | 180 | yes | complemented |
| 13 | C2×#392135 | C22 | 1 | 45 | yes | — |
| 14 | C2×H(9,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 15 | H(9,𝔽2) | Q8 | 1 | 16 | yes | complemented |
| 16 | C22×H(7,𝔽2) | C23 | 1 | 15 | yes | — |
| 17 | C22×#2032 | C23 | 1 | 120 | yes | complemented |
| 18 | C2×#23468 | C23 | 1 | 60 | yes | complemented |
| 19 | C2×#20609 | C23 | 1 | 180 | yes | — |
| 20 | C22×#1790 | C23 | 1 | 60 | yes | — |
| 21 | C2×#20585 | C23 | 1 | 45 | yes | — |
| 22 | C2×#20585 | C23 | 1 | 90 | yes | — |
| 23 | #5955332 | C23 | 1 | 45 | yes | complemented |
| 24 | C2×#14873 | C23 | 1 | 15 | yes | complemented |
| 25 | #516323 | C23 | 1 | 30 | yes | — |
| 26 | #516323 | C23 | 1 | 15 | yes | — |
| 27 | #123590 | C23 | 1 | 180 | yes | complemented |
| 28 | #123581 | C23 | 1 | 180 | yes | complemented |
| 29 | #123539 | C23 | 1 | 180 | yes | complemented |
| 30 | #123527 | C23 | 1 | 90 | yes | complemented |
| 31 | #123520 | C23 | 1 | 90 | yes | complemented |
| 32 | C2×H(7,𝔽2) | C2×Q8 | 1 | 120 | yes | — |
| 33 | C23×H(5,𝔽2) | C24 | 1 | 5 | yes | — |
| 34 | C23×H(5,𝔽2) | C24 | 1 | 30 | yes | — |
| 35 | C25×Q8 | C24 | 1 | 1 | yes | characteristic, complemented |
| 36 | C22×#543 | C24 | 1 | 15 | yes | complemented |
| 37 | C23×#99 | C24 | 1 | 180 | yes | — |
| 38 | C2×#2308 | C24 | 1 | 45 | yes | — |
| 39 | C2×#2308 | C24 | 1 | 90 | yes | — |
| 40 | C22×#386 | C24 | 1 | 45 | yes | — |
| 41 | C22×#342 | C24 | 1 | 180 | yes | complemented |
| 42 | #13794 | C24 | 1 | 15 | yes | complemented |
| 43 | C2×C22⋊#95 | C24 | 1 | 45 | yes | complemented |
| 44 | C22×H(5,𝔽2) | C22×Q8 | 1 | 20 | yes | — |
| 45 | C22×H(5,𝔽2) | C22×Q8 | 1 | 120 | yes | — |
| 46 | C22×H(5,𝔽2) | H(5,𝔽2) | 1 | 60 | yes | — |
| 47 | C23×#41 | H(5,𝔽2) | 1 | 30 | yes | — |
| 48 | C24×D4 | H(5,𝔽2) | 1 | 30 | yes | — |
| 49 | C24×D4 | C25 | 1 | 15 | yes | — |
| 50 | C25×C4 | C25 | 1 | 3 | yes | — |
| 51 | C23×C22⋊C4 | C25 | 1 | 45 | yes | — |
| 52 | C26 | H(3,𝔽4) | 1 | 10 | yes | — |
| 53 | C26 | C2×H(5,𝔽2) | 1 | 15 | yes | — |
| 54 | C26 | C26 | 1 | 1 | yes | characteristic |
| 55 | C22×#41 | #543 | 1 | 120 | yes | — |
| 56 | C22×#41 | H(3,𝔽4) | 1 | 120 | yes | — |
| 57 | C23×Q8 | H(3,𝔽4) | 1 | 10 | yes | — |
| 58 | C23×D4 | #543 | 1 | 120 | yes | — |
| 59 | C23×D4 | H(3,𝔽4) | 1 | 120 | yes | — |
| 60 | C23×D4 | H(3,𝔽4) | 1 | 30 | yes | — |
| 61 | C23×D4 | C23×Q8 | 1 | 30 | yes | — |
| 62 | C23×D4 | C2×H(5,𝔽2) | 1 | 30 | yes | — |
| 63 | C23×D4 | C2×H(5,𝔽2) | 1 | 60 | yes | — |
| 64 | C23×D4 | C2×H(5,𝔽2) | 1 | 60 | yes | — |
| 65 | C24×C4 | H(3,𝔽4) | 1 | 30 | yes | — |
| 66 | C24×C4 | C2×H(5,𝔽2) | 1 | 15 | yes | — |
| 67 | C25 | #2840 | 1 | 40 | yes | complemented |
| 68 | C25 | C2×#543 | 1 | 30 | yes | — |
| 69 | C25 | C2×H(3,𝔽4) | 1 | 30 | yes | — |
| 70 | C25 | C2×H(3,𝔽4) | 1 | 30 | yes | — |
| 71 | C25 | C24×Q8 | 1 | 1 | yes | characteristic |
| 72 | C25 | C22×H(5,𝔽2) | 1 | 15 | yes | — |
| 73 | C25 | C22×H(5,𝔽2) | 1 | 15 | yes | — |
| 74 | C22×Q8 | #2840 | 1 | 40 | yes | complemented |
| 75 | C22×D4 | #2840 | 1 | 120 | yes | complemented |
| 76 | C22×D4 | C2×#543 | 1 | 120 | yes | — |
| 77 | C22×D4 | C2×H(3,𝔽4) | 1 | 120 | yes | — |
| 78 | C23×C4 | #2840 | 1 | 120 | yes | complemented |
| 79 | C23×C4 | C2×#543 | 1 | 30 | yes | — |
| 80 | C23×C4 | C2×H(3,𝔽4) | 1 | 30 | yes | — |
| 81 | C23×C4 | C2×H(3,𝔽4) | 1 | 30 | yes | — |
| 82 | C24 | C2×#2840 | 1 | 60 | yes | — |
| 83 | C24 | C22×#543 | 1 | 15 | yes | — |
| 84 | C24 | C22×H(3,𝔽4) | 1 | 5 | yes | — |
| 85 | C24 | C22×H(3,𝔽4) | 1 | 15 | yes | — |
| 86 | C24 | #62817 | 1 | 90 | yes | — |
| 87 | C24 | #62817 | 1 | 30 | yes | — |
| 88 | C22×C4 | C2×#2840 | 1 | 60 | yes | — |
| 89 | C23 | C22×#2840 | 1 | 5 | yes | — |
| 90 | C23 | #7641846 | 1 | 30 | yes | — |
| 91 | C23 | #8093108 | 1 | 15 | yes | — |
| 92 | C23 | #8093108 | 1 | 90 | yes | — |
| 93 | C23 | #8093108 | 1 | 15 | yes | — |
| 94 | C22 | #72209699 | 1 | 15 | yes | — |
| 95 | C22 | #72209699 | 1 | 1 | yes | characteristic |
| 96 | C22 | #72219811 | 1 | 15 | yes | — |
| 97 | C2 | #72210030 | 1 | 1 | yes | characteristic |
| 98 | C2 | #72210039 | 1 | 1 | yes | characteristic |
| 99 | C2 | #72219812 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta