← #72337574
Subgroups — #72337574
Order 2048.
Only the 306 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 106 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72337559 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72311606 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72310930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72284724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72238013 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #72236925 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72227731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72210025 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | H(9,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #8928621 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #6628902 | C22 | 1 | 1 | yes | characteristic |
| 12 | #6628896 | C22 | 1 | 2 | yes | — |
| 13 | #6628896 | C22 | 1 | 4 | yes | — |
| 14 | #6628873 | C22 | 1 | 2 | yes | — |
| 15 | #496240 | C22 | 1 | 4 | yes | complemented |
| 16 | #496205 | C22 | 1 | 2 | yes | complemented |
| 17 | #392138 | C22 | 1 | 2 | yes | — |
| 18 | #392136 | C22 | 1 | 1 | yes | characteristic |
| 19 | #392135 | C22 | 1 | 2 | yes | — |
| 20 | #392135 | C22 | 1 | 4 | yes | — |
| 21 | #213862 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #213854 | C22 | 1 | 2 | yes | complemented |
| 23 | #128079 | C22 | 1 | 4 | yes | complemented |
| 24 | #128062 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×H(7,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 26 | C2×H(7,𝔽2) | C23 | 1 | 2 | yes | — |
| 27 | C22×B(4,𝔽2) | D4 | 1 | 8 | yes | complemented |
| 28 | C2×#3022 | D4 | 1 | 4 | yes | complemented |
| 29 | #35616 | D4 | 1 | 2 | yes | complemented |
| 30 | #35616 | C23 | 1 | 1 | yes | characteristic |
| 31 | #35346 | D4 | 1 | 4 | yes | complemented |
| 32 | #35346 | C23 | 1 | 2 | yes | — |
| 33 | #20615 | D4 | 1 | 4 | yes | complemented |
| 34 | #20609 | D4 | 1 | 8 | yes | complemented |
| 35 | #20592 | C23 | 1 | 2 | yes | — |
| 36 | #20586 | D4 | 1 | 2 | yes | complemented |
| 37 | #20586 | C23 | 1 | 1 | yes | characteristic |
| 38 | #20585 | D4 | 1 | 4 | yes | complemented |
| 39 | #20585 | C23 | 1 | 2 | yes | — |
| 40 | #20585 | C23 | 1 | 4 | yes | — |
| 41 | C2×#585 | C2×D4 | 1 | 4 | yes | — |
| 42 | C22×H(5,𝔽2) | C2×D4 | 1 | 4 | yes | — |
| 43 | C22×H(5,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 44 | C22×H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 45 | C22×H(5,𝔽2) | C24 | 1 | 1 | yes | characteristic |
| 46 | C2×#536 | C2×D4 | 1 | 2 | yes | — |
| 47 | C22×#124 | C2×D4 | 1 | 1 | yes | characteristic |
| 48 | C22×#120 | C2×D4 | 1 | 2 | yes | — |
| 49 | C22×#120 | C2×D4 | 1 | 4 | yes | — |
| 50 | C2×#413 | C2×D4 | 1 | 4 | yes | — |
| 51 | C22×#99 | C2×D4 | 1 | 8 | yes | — |
| 52 | #2309 | C2×D4 | 1 | 1 | yes | characteristic |
| 53 | #2309 | C2×D4 | 1 | 2 | yes | — |
| 54 | #2308 | C2×D4 | 1 | 2 | yes | — |
| 55 | #2308 | C2×D4 | 1 | 4 | yes | — |
| 56 | #2308 | C2×D4 | 1 | 4 | yes | — |
| 57 | #2297 | C2×D4 | 1 | 2 | yes | — |
| 58 | C26 | #120 | 1 | 2 | yes | complemented |
| 59 | C2×H(5,𝔽2) | #120 | 1 | 8 | yes | — |
| 60 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 61 | C22×#41 | H(5,𝔽2) | 1 | 4 | yes | — |
| 62 | C23×Q8 | #120 | 1 | 1 | yes | characteristic, complemented |
| 63 | C23×D4 | #120 | 1 | 4 | yes | — |
| 64 | C23×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 65 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 66 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 67 | C23×D4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 68 | C2×#117 | #120 | 1 | 2 | yes | complemented |
| 69 | C22×C22⋊C4 | #120 | 1 | 4 | yes | complemented |
| 70 | C22×C22⋊C4 | #120 | 1 | 2 | yes | complemented |
| 71 | C22×C42 | #120 | 1 | 1 | yes | characteristic, complemented |
| 72 | C25 | B(4,𝔽2) | 1 | 4 | yes | — |
| 73 | C25 | C2×#120 | 1 | 2 | yes | — |
| 74 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 75 | C25 | #534 | 1 | 1 | yes | characteristic |
| 76 | C25 | D42 | 1 | 2 | yes | — |
| 77 | H(5,𝔽2) | B(4,𝔽2) | 1 | 16 | yes | — |
| 78 | C22×Q8 | #534 | 1 | 2 | yes | — |
| 79 | C22×D4 | C2×#120 | 1 | 2 | yes | — |
| 80 | C22×D4 | #534 | 1 | 4 | yes | — |
| 81 | C22×D4 | D42 | 1 | 4 | yes | — |
| 82 | C22×D4 | D42 | 1 | 4 | yes | — |
| 83 | C22×D4 | D42 | 1 | 4 | yes | — |
| 84 | C23×C4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 85 | C23×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 86 | C23×C4 | #534 | 1 | 2 | yes | — |
| 87 | C23×C4 | D42 | 1 | 4 | yes | — |
| 88 | C23×C4 | H(3,𝔽4) | 1 | 2 | yes | — |
| 89 | C24 | #2403 | 1 | 1 | yes | characteristic |
| 90 | C24 | #2403 | 1 | 2 | yes | — |
| 91 | C24 | #2403 | 1 | 4 | yes | — |
| 92 | C24 | #2679 | 1 | 2 | yes | — |
| 93 | C24 | C2×B(4,𝔽2) | 1 | 4 | yes | — |
| 94 | C2×D4 | C2×B(4,𝔽2) | 1 | 8 | yes | — |
| 95 | C22×C4 | #2403 | 1 | 2 | yes | — |
| 96 | C22×C4 | #2679 | 1 | 4 | yes | — |
| 97 | C23 | #15947 | 1 | 1 | yes | characteristic |
| 98 | C23 | #23900 | 1 | 8 | yes | — |
| 99 | C23 | #23900 | 1 | 2 | yes | — |
| 100 | C23 | #23900 | 1 | 4 | yes | — |
| 101 | C2×C4 | #23900 | 1 | 4 | yes | — |
| 102 | C22 | #449475 | 1 | 2 | yes | — |
| 103 | C22 | #449475 | 1 | 1 | yes | characteristic |
| 104 | C2 | #72209716 | 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