← #72266186
Subgroups — #72266186
Order 4096.
At least 6320 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
The subgroup lattice has 128 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72266170 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #72266169 | C4 | 1 | 2 | yes | complemented |
| 3 | #72266168 | C4 | 1 | 2 | yes | complemented |
| 4 | #72266156 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72266136 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72266085 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72258946 | C2 | 1 | 2 | yes | maximal |
| 8 | #72258752 | C4 | 1 | 4 | yes | complemented |
| 9 | #72235054 | C4 | 1 | 4 | yes | complemented |
| 10 | C2×#188035 | C22 | 1 | 1 | yes | characteristic |
| 11 | #72225737 | C22 | 1 | 1 | yes | characteristic |
| 12 | #72225621 | C22 | 1 | 2 | yes | — |
| 13 | #72219377 | C22 | 1 | 1 | yes | characteristic |
| 14 | #72219307 | C22 | 1 | 2 | yes | — |
| 15 | C23×D42 | C23 | 1 | 1 | yes | characteristic |
| 16 | C2×#35527 | C2×C4 | 1 | 1 | yes | characteristic |
| 17 | C2×#35346 | C2×C4 | 1 | 2 | yes | — |
| 18 | C2×#21746 | D4 | 1 | 1 | yes | characteristic |
| 19 | C2×#21746 | D4 | 1 | 1 | yes | characteristic |
| 20 | #555905 | C2×C4 | 1 | 1 | yes | characteristic |
| 21 | #555894 | C2×C4 | 1 | 2 | yes | — |
| 22 | #517411 | D4 | 1 | 2 | yes | — |
| 23 | #517411 | D4 | 1 | 2 | yes | — |
| 24 | #392109 | D4 | 1 | 4 | yes | — |
| 25 | #382422 | C2×C4 | 1 | 4 | yes | — |
| 26 | C2×#10965 | C2×C4 | 1 | 4 | yes | — |
| 27 | C2×#8546 | C2×C4 | 1 | 2 | yes | — |
| 28 | C2×#8546 | C2×C4 | 1 | 2 | yes | — |
| 29 | C2×#8541 | D4 | 1 | 2 | yes | — |
| 30 | C23×H(5,𝔽2) | C42 | 1 | 1 | yes | characteristic, complemented |
| 31 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 32 | C25×D4 | C2×D4 | 1 | 2 | yes | — |
| 33 | C23×#127 | C22×C4 | 1 | 1 | yes | characteristic |
| 34 | C23×#121 | #41 | 1 | 2 | yes | — |
| 35 | C23×#121 | #41 | 1 | 2 | yes | — |
| 36 | C23×#120 | C22×C4 | 1 | 2 | yes | — |
| 37 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 38 | C23×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 39 | C23×C4×D4 | #41 | 1 | 2 | yes | — |
| 40 | C2×#2309 | C42 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#2308 | C42 | 1 | 2 | yes | complemented |
| 42 | C2×#1781 | C22⋊C4 | 1 | 2 | yes | — |
| 43 | C2×#1781 | C22⋊C4 | 1 | 2 | yes | — |
| 44 | #14679 | C22⋊C4 | 1 | 4 | yes | — |
| 45 | #14679 | C22⋊C4 | 1 | 4 | yes | — |
| 46 | C27 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 47 | C27 | #120 | 1 | 1 | yes | characteristic |
| 48 | C27 | #127 | 1 | 1 | yes | characteristic |
| 49 | C24×D4 | C2×C42 | 1 | 1 | yes | characteristic |
| 50 | C24×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 51 | C24×D4 | C4×D4 | 1 | 2 | yes | — |
| 52 | C24×D4 | C4×D4 | 1 | 2 | yes | — |
| 53 | C24×D4 | C4×D4 | 1 | 2 | yes | — |
| 54 | C24×D4 | C4×D4 | 1 | 2 | yes | — |
| 55 | C24×D4 | #121 | 1 | 2 | yes | — |
| 56 | C24×D4 | #121 | 1 | 2 | yes | — |
| 57 | C24×D4 | #121 | 1 | 2 | yes | — |
| 58 | C25×C4 | #123 | 1 | 2 | yes | — |
| 59 | C25×C4 | #124 | 1 | 2 | yes | — |
| 60 | C23×C4⋊C4 | #126 | 1 | 2 | yes | — |
| 61 | C23×C22⋊C4 | #117 | 1 | 2 | yes | — |
| 62 | C23×C22⋊C4 | C4×D4 | 1 | 2 | yes | — |
| 63 | C23×C22⋊C4 | C4×D4 | 1 | 2 | yes | — |
| 64 | C23×C22⋊C4 | #123 | 1 | 1 | yes | characteristic |
| 65 | C23×C22⋊C4 | #124 | 1 | 1 | yes | characteristic |
| 66 | C23×C42 | #117 | 1 | 1 | yes | characteristic |
| 67 | C2×#379 | #99 | 1 | 8 | yes | complemented |
| 68 | #1781 | #99 | 1 | 4 | yes | complemented |
| 69 | C26 | C4×C22⋊C4 | 1 | 2 | yes | — |
| 70 | C26 | #386 | 1 | 2 | yes | — |
| 71 | C26 | #386 | 1 | 1 | yes | characteristic |
| 72 | C26 | #390 | 1 | 2 | yes | — |
| 73 | C26 | #390 | 1 | 1 | yes | characteristic |
| 74 | C26 | C2×#99 | 1 | 4 | yes | — |
| 75 | C26 | #410 | 1 | 4 | yes | — |
| 76 | C26 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 77 | C26 | B(4,𝔽2) | 1 | 2 | yes | — |
| 78 | C26 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 79 | C23×D4 | C2×#99 | 1 | 2 | yes | — |
| 80 | C23×D4 | #410 | 1 | 2 | yes | — |
| 81 | C24×C4 | C4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C24×C4 | #388 | 1 | 2 | yes | — |
| 83 | C24×C4 | #388 | 1 | 2 | yes | — |
| 84 | C24×C4 | #388 | 1 | 2 | yes | — |
| 85 | C25 | #1437 | 1 | 1 | yes | characteristic |
| 86 | C25 | C4×#99 | 1 | 4 | yes | — |
| 87 | C25 | #1889 | 1 | 2 | yes | — |
| 88 | C25 | #1889 | 1 | 1 | yes | characteristic |
| 89 | C25 | #1889 | 1 | 2 | yes | — |
| 90 | C25 | #1889 | 1 | 1 | yes | characteristic |
| 91 | C25 | #1898 | 1 | 2 | yes | — |
| 92 | C25 | #1898 | 1 | 1 | yes | characteristic |
| 93 | C25 | #1899 | 1 | 2 | yes | — |
| 94 | C25 | #1899 | 1 | 1 | yes | characteristic |
| 95 | C25 | #1913 | 1 | 2 | yes | — |
| 96 | C25 | #1913 | 1 | 2 | yes | — |
| 97 | C25 | #1913 | 1 | 1 | yes | characteristic |
| 98 | C25 | #1913 | 1 | 1 | yes | characteristic |
| 99 | C25 | #1964 | 1 | 4 | yes | — |
| 100 | C25 | #1964 | 1 | 2 | yes | — |
| 101 | C23×C4 | C4×#99 | 1 | 2 | yes | — |
| 102 | C24 | #9495 | 1 | 2 | yes | — |
| 103 | C24 | #9495 | 1 | 1 | yes | characteristic |
| 104 | C24 | #9496 | 1 | 2 | yes | — |
| 105 | C24 | #9496 | 1 | 1 | yes | characteristic |
| 106 | C24 | #9497 | 1 | 2 | yes | — |
| 107 | C24 | #9497 | 1 | 1 | yes | characteristic |
| 108 | C24 | #9498 | 1 | 2 | yes | — |
| 109 | C24 | #9498 | 1 | 1 | yes | characteristic |
| 110 | C24 | #10935 | 1 | 1 | yes | characteristic |
| 111 | C24 | #10938 | 1 | 2 | yes | — |
| 112 | C24 | #10938 | 1 | 1 | yes | characteristic |
| 113 | C24 | #10960 | 1 | 2 | yes | — |
| 114 | C24 | #10960 | 1 | 1 | yes | characteristic |
| 115 | C23 | #110086 | 1 | 2 | yes | — |
| 116 | C23 | #110086 | 1 | 1 | yes | characteristic |
| 117 | C23 | #110180 | 1 | 1 | yes | characteristic |
| 118 | C23 | #110401 | 1 | 1 | yes | characteristic |
| 119 | C23 | #110401 | 1 | 2 | yes | — |
| 120 | C23 | #139743 | 1 | 4 | yes | — |
| 121 | C22 | #72246286 | 1 | 2 | yes | — |
| 122 | C22 | #72255986 | 1 | 2 | yes | — |
| 123 | C22 | #72264951 | 1 | 1 | yes | characteristic |
| 124 | C22 | #72265908 | 1 | 2 | yes | — |
| 125 | C2 | #72265612 | 1 | 2 | yes | — |
| 126 | C2 | #72265909 | 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