← #72341472
Subgroups — #72341472
Order 2048.
Only the 1294 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 179 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72341465 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72341362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72311145 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #72306417 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #72260657 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72241337 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #72213504 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #72210025 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | H(9,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | #10586106 | C22 | 1 | 1 | yes | characteristic |
| 11 | #10574841 | C22 | 1 | 6 | yes | — |
| 12 | C2×#60389 | C22 | 1 | 6 | yes | — |
| 13 | #10574064 | C22 | 1 | 1 | yes | characteristic |
| 14 | #7742598 | C22 | 1 | 3 | yes | complemented |
| 15 | C22×#2199 | C22 | 1 | 4 | yes | complemented |
| 16 | #6628896 | C22 | 1 | 2 | yes | — |
| 17 | #6628896 | C22 | 1 | 12 | yes | complemented |
| 18 | #6470234 | C22 | 1 | 6 | yes | complemented |
| 19 | #6385981 | C22 | 1 | 3 | yes | complemented |
| 20 | #498927 | C22 | 1 | 24 | yes | complemented |
| 21 | #494682 | C22 | 1 | 12 | yes | complemented |
| 22 | #494597 | C22 | 1 | 12 | yes | complemented |
| 23 | #493433 | C22 | 1 | 6 | yes | complemented |
| 24 | #493397 | C22 | 1 | 6 | yes | complemented |
| 25 | #392135 | C22 | 1 | 2 | yes | — |
| 26 | #392135 | C22 | 1 | 12 | yes | complemented |
| 27 | #147767 | C22 | 1 | 24 | yes | complemented |
| 28 | #146577 | C22 | 1 | 12 | yes | complemented |
| 29 | C2×2−1+6 | D4 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×H(7,𝔽2) | C23 | 1 | 6 | yes | — |
| 31 | C2×H(7,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 32 | #62859 | D4 | 1 | 3 | yes | complemented |
| 33 | #62852 | C23 | 1 | 3 | yes | — |
| 34 | #62812 | D4 | 1 | 3 | yes | complemented |
| 35 | C2×#3500 | C23 | 1 | 3 | yes | — |
| 36 | C22×H(3,𝔽4) | C23 | 1 | 1 | yes | characteristic, complemented |
| 37 | C4×#585 | D4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C22×B(4,𝔽2) | D4 | 1 | 8 | yes | complemented |
| 39 | C22×B(4,𝔽2) | C23 | 1 | 8 | yes | — |
| 40 | C2×#3022 | D4 | 1 | 12 | yes | complemented |
| 41 | C2×#3019 | D4 | 1 | 12 | yes | complemented |
| 42 | C2×#3019 | C23 | 1 | 12 | yes | — |
| 43 | C2×#3018 | D4 | 1 | 12 | yes | complemented |
| 44 | C22×#455 | D4 | 1 | 12 | yes | complemented |
| 45 | C22×#455 | C23 | 1 | 4 | yes | — |
| 46 | C2×#2888 | C23 | 1 | 6 | yes | — |
| 47 | #36702 | C23 | 1 | 6 | yes | complemented |
| 48 | #35346 | C23 | 1 | 6 | yes | — |
| 49 | #34366 | C23 | 1 | 3 | yes | complemented |
| 50 | C2×#2127 | C23 | 1 | 12 | yes | complemented |
| 51 | C22×#354 | C23 | 1 | 4 | yes | complemented |
| 52 | C22×AΣL(1,𝔽16) | C23 | 1 | 8 | yes | complemented |
| 53 | #21750 | C23 | 1 | 6 | yes | complemented |
| 54 | #20609 | D4 | 1 | 8 | yes | complemented |
| 55 | #20609 | C23 | 1 | 24 | yes | — |
| 56 | #20585 | C23 | 1 | 6 | yes | — |
| 57 | #20585 | C23 | 1 | 12 | yes | — |
| 58 | #12574 | C23 | 1 | 24 | yes | complemented |
| 59 | C2×#585 | C2×D4 | 1 | 3 | yes | — |
| 60 | C2×#585 | C2×D4 | 1 | 3 | yes | — |
| 61 | C2×#585 | C2×D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#585 | C2×D4 | 1 | 12 | yes | — |
| 63 | C22×2−1+4 | C2×D4 | 1 | 3 | yes | — |
| 64 | C22×H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 65 | C22×H(5,𝔽2) | C2×D4 | 1 | 12 | yes | — |
| 66 | C22×H(5,𝔽2) | C24 | 1 | 3 | yes | — |
| 67 | C22×H(5,𝔽2) | C24 | 1 | 4 | yes | — |
| 68 | #3449 | C2×D4 | 1 | 6 | yes | — |
| 69 | C2×#536 | C2×D4 | 1 | 6 | yes | — |
| 70 | C2×#536 | C2×D4 | 1 | 3 | yes | — |
| 71 | C2×#535 | C2×D4 | 1 | 6 | yes | — |
| 72 | C2×#535 | C24 | 1 | 3 | yes | — |
| 73 | C2×#532 | C2×D4 | 1 | 3 | yes | — |
| 74 | C2×#532 | C2×D4 | 1 | 6 | yes | — |
| 75 | C22×#124 | C2×D4 | 1 | 6 | yes | — |
| 76 | C22×#124 | C24 | 1 | 1 | yes | characteristic |
| 77 | C22×#120 | C2×D4 | 1 | 12 | yes | — |
| 78 | C22×#120 | C24 | 1 | 2 | yes | — |
| 79 | #3428 | C2×D4 | 1 | 3 | yes | — |
| 80 | C2×C4×#41 | C2×D4 | 1 | 3 | yes | — |
| 81 | C2×#455 | C2×D4 | 1 | 24 | yes | — |
| 82 | C2×#455 | C2×D4 | 1 | 24 | yes | — |
| 83 | C2×#455 | C2×D4 | 1 | 24 | yes | — |
| 84 | C2×#453 | C2×D4 | 1 | 24 | yes | — |
| 85 | C2×#413 | C2×D4 | 1 | 12 | yes | — |
| 86 | C22×#100 | C2×D4 | 1 | 12 | yes | — |
| 87 | C22×#100 | C24 | 1 | 4 | yes | — |
| 88 | C22×#99 | C2×D4 | 1 | 24 | yes | — |
| 89 | C22×#99 | C24 | 1 | 8 | yes | — |
| 90 | #2308 | C2×D4 | 1 | 12 | yes | — |
| 91 | #2308 | C24 | 1 | 6 | yes | — |
| 92 | C26 | C22×D4 | 1 | 2 | yes | — |
| 93 | C2×H(5,𝔽2) | #120 | 1 | 12 | yes | — |
| 94 | C2×H(5,𝔽2) | #120 | 1 | 4 | yes | — |
| 95 | C2×H(5,𝔽2) | C22×D4 | 1 | 24 | yes | — |
| 96 | C22×#41 | #120 | 1 | 6 | yes | complemented |
| 97 | C22×#41 | C22×D4 | 1 | 3 | yes | — |
| 98 | C22×#41 | C22×D4 | 1 | 6 | yes | — |
| 99 | C22×#41 | C22×D4 | 1 | 3 | yes | — |
| 100 | C22×#41 | C22×D4 | 1 | 3 | yes | — |
| 101 | C22×#41 | H(5,𝔽2) | 1 | 6 | yes | — |
| 102 | C23×Q8 | #120 | 1 | 6 | yes | complemented |
| 103 | C23×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 104 | C23×D4 | C22×D4 | 1 | 6 | yes | — |
| 105 | C23×D4 | C22×D4 | 1 | 12 | yes | — |
| 106 | C23×D4 | H(5,𝔽2) | 1 | 6 | yes | — |
| 107 | C23×D4 | C25 | 1 | 1 | yes | characteristic |
| 108 | C2×C4⋊Q8 | #120 | 1 | 3 | yes | complemented |
| 109 | C2×C4⋊Q8 | #120 | 1 | 6 | yes | complemented |
| 110 | C2×#127 | #120 | 1 | 3 | yes | complemented |
| 111 | C2×#127 | C22×D4 | 1 | 6 | yes | — |
| 112 | C2×#124 | #120 | 1 | 3 | yes | complemented |
| 113 | C2×#124 | #120 | 1 | 6 | yes | complemented |
| 114 | C2×#124 | #120 | 1 | 3 | yes | complemented |
| 115 | C2×#124 | C22×D4 | 1 | 6 | yes | — |
| 116 | C2×#124 | C22×D4 | 1 | 6 | yes | — |
| 117 | C2×#124 | C22×D4 | 1 | 6 | yes | — |
| 118 | C2×#117 | #120 | 1 | 6 | yes | complemented |
| 119 | C2×#117 | C22×D4 | 1 | 3 | yes | — |
| 120 | C22×C22⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 121 | C22×C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 122 | C22×C42 | #120 | 1 | 6 | yes | complemented |
| 123 | C22×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 124 | #455 | #120 | 1 | 16 | yes | complemented |
| 125 | #455 | #120 | 1 | 48 | yes | complemented |
| 126 | C2×#100 | C22×D4 | 1 | 24 | yes | — |
| 127 | C25 | D42 | 1 | 12 | yes | — |
| 128 | C25 | C23×D4 | 1 | 2 | yes | — |
| 129 | H(5,𝔽2) | B(4,𝔽2) | 1 | 16 | yes | — |
| 130 | H(5,𝔽2) | C2×#120 | 1 | 16 | yes | — |
| 131 | C22×Q8 | C2×#120 | 1 | 3 | yes | — |
| 132 | C22×Q8 | C2×#120 | 1 | 3 | yes | — |
| 133 | C22×Q8 | C2×#120 | 1 | 6 | yes | — |
| 134 | C22×Q8 | #534 | 1 | 3 | yes | — |
| 135 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 136 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 137 | C22×D4 | C2×#120 | 1 | 3 | yes | — |
| 138 | C22×D4 | C2×#120 | 1 | 3 | yes | — |
| 139 | C22×D4 | #534 | 1 | 3 | yes | — |
| 140 | C22×D4 | D42 | 1 | 12 | yes | — |
| 141 | C22×D4 | D42 | 1 | 12 | yes | — |
| 142 | C22×D4 | C23×D4 | 1 | 6 | yes | — |
| 143 | C22×D4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 144 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 145 | C23×C4 | #534 | 1 | 6 | yes | — |
| 146 | C23×C4 | D42 | 1 | 12 | yes | — |
| 147 | C23×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 148 | #124 | C2×#120 | 1 | 4 | yes | — |
| 149 | #124 | C2×#120 | 1 | 12 | yes | — |
| 150 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 151 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 152 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 153 | #100 | C2×#120 | 1 | 16 | yes | — |
| 154 | C24 | #2403 | 1 | 6 | yes | — |
| 155 | C24 | #2403 | 1 | 6 | yes | — |
| 156 | C24 | C22×#120 | 1 | 1 | yes | characteristic |
| 157 | C24 | C2×D42 | 1 | 12 | yes | — |
| 158 | C2×Q8 | #2846 | 1 | 4 | yes | — |
| 159 | C2×D4 | C2×B(4,𝔽2) | 1 | 24 | yes | — |
| 160 | C2×D4 | C22×#120 | 1 | 4 | yes | — |
| 161 | C2×D4 | #3484 | 1 | 12 | yes | — |
| 162 | C22×C4 | #2403 | 1 | 6 | yes | — |
| 163 | C22×C4 | #2403 | 1 | 6 | yes | — |
| 164 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 165 | C22×C4 | C2×#534 | 1 | 3 | yes | — |
| 166 | C42 | #2846 | 1 | 3 | yes | — |
| 167 | C42 | #2846 | 1 | 1 | yes | characteristic |
| 168 | C23 | #23900 | 1 | 12 | yes | — |
| 169 | C23 | C2×#2403 | 1 | 3 | yes | — |
| 170 | C23 | D4×#120 | 1 | 8 | yes | — |
| 171 | C23 | C22×B(4,𝔽2) | 1 | 4 | yes | — |
| 172 | C2×C4 | #23900 | 1 | 12 | yes | — |
| 173 | C2×C4 | #34980 | 1 | 3 | yes | — |
| 174 | C2×C4 | C2×#2846 | 1 | 1 | yes | characteristic |
| 175 | C22 | #612424 | 1 | 1 | yes | characteristic |
| 176 | C22 | C2×#23900 | 1 | 6 | yes | — |
| 177 | C2 | #72215858 | 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