← C22×#63040 #72301085
Subgroups — C22×#63040 #72301085
Order 1024.
539577 conjugacy classes of subgroups.
The subgroup lattice has 174 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#63040 | C2 | 1 | 192 | yes | maximal, direct product factor |
| 2 | C22×#3549 | C2 | 1 | 27 | yes | maximal, complemented |
| 3 | C22×#3498 | C2 | 1 | 27 | yes | maximal, complemented |
| 4 | C22×#3483 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C23×H(5,𝔽2) | C22 | 1 | 18 | yes | complemented |
| 6 | #63040 | C22 | 1 | 4096 | yes | direct product factor |
| 7 | C2×#3498 | C22 | 1 | 2592 | yes | complemented |
| 8 | C2×#3549 | C22 | 1 | 2592 | yes | complemented |
| 9 | C2×#3483 | C22 | 1 | 864 | yes | complemented |
| 10 | C22×Q82 | C22 | 1 | 3 | yes | complemented |
| 11 | C22×#555 | C22 | 1 | 81 | yes | complemented |
| 12 | C22×#550 | C22 | 1 | 54 | yes | complemented |
| 13 | C22×D42 | C22 | 1 | 162 | yes | complemented |
| 14 | C22×H(3,𝔽4) | C22 | 1 | 36 | yes | complemented |
| 15 | C22×#535 | C22 | 1 | 162 | yes | complemented |
| 16 | C22×#532 | C22 | 1 | 81 | yes | complemented |
| 17 | C23×#127 | C22 | 1 | 27 | yes | complemented |
| 18 | C22×C4×#41 | C22 | 1 | 27 | yes | complemented |
| 19 | C22×H(5,𝔽2) | — | 4 | 288 | no | — |
| 20 | C22×H(5,𝔽2) | C23 | 1 | 864 | yes | complemented |
| 21 | C23×#41 | C23 | 1 | 27 | yes | — |
| 22 | C23×#41 | C23 | 1 | 54 | yes | — |
| 23 | C24×D4 | C23 | 1 | 162 | yes | — |
| 24 | #3549 | C23 | 1 | 27648 | yes | complemented |
| 25 | C2×H(3,𝔽4) | C23 | 1 | 1728 | yes | complemented |
| 26 | #3498 | C23 | 1 | 27648 | yes | complemented |
| 27 | #3483 | C23 | 1 | 9216 | yes | complemented |
| 28 | C2×Q82 | C23 | 1 | 144 | yes | complemented |
| 29 | C2×#555 | C23 | 1 | 3888 | yes | complemented |
| 30 | C2×#550 | C23 | 1 | 2592 | yes | complemented |
| 31 | C2×D42 | C23 | 1 | 7776 | yes | complemented |
| 32 | C2×#535 | C23 | 1 | 7776 | yes | complemented |
| 33 | C2×#532 | C23 | 1 | 3888 | yes | complemented |
| 34 | C22×C4⋊Q8 | C23 | 1 | 27 | yes | — |
| 35 | C22×#127 | C23 | 1 | 81 | yes | — |
| 36 | C22×#127 | C23 | 1 | 54 | yes | — |
| 37 | C22×#127 | C23 | 1 | 1296 | yes | complemented |
| 38 | C22×#124 | C23 | 1 | 162 | yes | — |
| 39 | C22×#121 | C23 | 1 | 324 | yes | — |
| 40 | C22×#120 | C23 | 1 | 216 | yes | — |
| 41 | C2×C4×#41 | C23 | 1 | 1296 | yes | complemented |
| 42 | C22×C4×Q8 | C23 | 1 | 18 | yes | — |
| 43 | C22×C4×D4 | C23 | 1 | 162 | yes | — |
| 44 | C22×#117 | C23 | 1 | 81 | yes | — |
| 45 | C23×C42 | C23 | 1 | 27 | yes | — |
| 46 | C26 | C24 | 1 | 36 | yes | — |
| 47 | C2×H(5,𝔽2) | — | 4 | 6912 | no | — |
| 48 | C2×H(5,𝔽2) | C24 | 1 | 4608 | yes | complemented |
| 49 | C22×#41 | — | 2 | 432 | no | — |
| 50 | C22×#41 | — | 4 | 432 | no | — |
| 51 | C22×#41 | C24 | 1 | 648 | yes | — |
| 52 | C22×#41 | C24 | 1 | 1296 | yes | — |
| 53 | C23×Q8 | C24 | 1 | 18 | yes | — |
| 54 | C23×Q8 | C24 | 1 | 3 | yes | — |
| 55 | C23×D4 | — | 4 | 1296 | no | — |
| 56 | C23×D4 | C24 | 1 | 81 | yes | — |
| 57 | C23×D4 | C24 | 1 | 162 | yes | — |
| 58 | C23×D4 | C24 | 1 | 3888 | yes | — |
| 59 | C24×C4 | C24 | 1 | 81 | yes | — |
| 60 | H(3,𝔽4) | C24 | 1 | 9216 | yes | complemented |
| 61 | Q82 | C24 | 1 | 768 | yes | complemented |
| 62 | #555 | C24 | 1 | 20736 | yes | complemented |
| 63 | #550 | C24 | 1 | 13824 | yes | complemented |
| 64 | D42 | C24 | 1 | 41472 | yes | complemented |
| 65 | #535 | C24 | 1 | 41472 | yes | complemented |
| 66 | #532 | C24 | 1 | 20736 | yes | complemented |
| 67 | C2×C4⋊Q8 | C24 | 1 | 648 | yes | — |
| 68 | C2×#127 | C24 | 1 | 1944 | yes | — |
| 69 | C2×#127 | C24 | 1 | 1296 | yes | — |
| 70 | C2×#127 | C24 | 1 | 6912 | yes | complemented |
| 71 | C2×#124 | C24 | 1 | 3888 | yes | — |
| 72 | C2×#121 | C24 | 1 | 7776 | yes | — |
| 73 | C2×#120 | C24 | 1 | 5184 | yes | — |
| 74 | C4×#41 | C24 | 1 | 6912 | yes | complemented |
| 75 | C2×C4×Q8 | C24 | 1 | 432 | yes | — |
| 76 | C2×C4×D4 | C24 | 1 | 3888 | yes | — |
| 77 | C2×#117 | C24 | 1 | 1944 | yes | — |
| 78 | C22×C4⋊C4 | C24 | 1 | 54 | yes | — |
| 79 | C22×C22⋊C4 | C24 | 1 | 162 | yes | — |
| 80 | C22×C42 | C24 | 1 | 27 | yes | — |
| 81 | C22×C42 | C24 | 1 | 27 | yes | — |
| 82 | C22×C42 | C24 | 1 | 648 | yes | — |
| 83 | C25 | — | 4 | 432 | no | — |
| 84 | C25 | C25 | 1 | 27 | yes | — |
| 85 | C25 | C25 | 1 | 432 | yes | — |
| 86 | H(5,𝔽2) | — | 4 | 18432 | no | — |
| 87 | C2×#41 | — | 2 | 5184 | no | — |
| 88 | C2×#41 | — | 4 | 5184 | no | — |
| 89 | C2×#41 | C25 | 1 | 1728 | yes | — |
| 90 | C2×#41 | C25 | 1 | 3456 | yes | — |
| 91 | C22×Q8 | — | 4 | 72 | no | — |
| 92 | C22×Q8 | H(5,𝔽2) | 1 | 48 | yes | complemented |
| 93 | C22×Q8 | C25 | 1 | 216 | yes | — |
| 94 | C22×Q8 | C25 | 1 | 36 | yes | — |
| 95 | C22×D4 | — | 2 | 648 | no | — |
| 96 | C22×D4 | — | 4 | 15552 | no | — |
| 97 | C22×D4 | — | 4 | 648 | no | — |
| 98 | C22×D4 | C25 | 1 | 972 | yes | — |
| 99 | C22×D4 | C25 | 1 | 1944 | yes | — |
| 100 | C22×D4 | C25 | 1 | 10368 | yes | — |
| 101 | C23×C4 | — | 2 | 648 | no | — |
| 102 | C23×C4 | C25 | 1 | 972 | yes | — |
| 103 | C23×C4 | C25 | 1 | 27 | yes | — |
| 104 | C23×C4 | C25 | 1 | 9 | yes | — |
| 105 | C4⋊Q8 | C25 | 1 | 1728 | yes | — |
| 106 | #127 | C25 | 1 | 5184 | yes | — |
| 107 | #127 | C25 | 1 | 3456 | yes | — |
| 108 | #124 | C25 | 1 | 10368 | yes | — |
| 109 | #121 | C25 | 1 | 20736 | yes | — |
| 110 | #120 | C25 | 1 | 13824 | yes | — |
| 111 | C4×Q8 | C25 | 1 | 1152 | yes | — |
| 112 | C4×D4 | C25 | 1 | 10368 | yes | — |
| 113 | #117 | C25 | 1 | 5184 | yes | — |
| 114 | C2×C4⋊C4 | C25 | 1 | 648 | yes | — |
| 115 | C2×C22⋊C4 | C25 | 1 | 1944 | yes | — |
| 116 | C2×C42 | C25 | 1 | 324 | yes | — |
| 117 | C2×C42 | C25 | 1 | 324 | yes | — |
| 118 | C2×C42 | C25 | 1 | 1728 | yes | — |
| 119 | C24 | — | 2 | 324 | no | — |
| 120 | C24 | — | 4 | 2592 | no | — |
| 121 | C24 | — | 16 | 576 | no | — |
| 122 | C24 | C26 | 1 | 162 | yes | — |
| 123 | C24 | C26 | 1 | 576 | yes | — |
| 124 | C24 | C26 | 1 | 1 | yes | characteristic |
| 125 | #41 | — | 2 | 6912 | no | — |
| 126 | #41 | — | 4 | 6912 | no | — |
| 127 | C2×Q8 | — | 4 | 432 | no | — |
| 128 | C2×Q8 | C2×H(5,𝔽2) | 1 | 288 | yes | complemented |
| 129 | C2×Q8 | C26 | 1 | 288 | yes | — |
| 130 | C2×Q8 | C26 | 1 | 48 | yes | — |
| 131 | C2×D4 | — | 2 | 3888 | no | — |
| 132 | C2×D4 | — | 4 | 20736 | no | — |
| 133 | C2×D4 | — | 4 | 3888 | no | — |
| 134 | C2×D4 | C26 | 1 | 1296 | yes | — |
| 135 | C2×D4 | C26 | 1 | 2592 | yes | — |
| 136 | C22×C4 | — | 2 | 108 | no | — |
| 137 | C22×C4 | — | 2 | 3888 | no | — |
| 138 | C22×C4 | C2×H(5,𝔽2) | 1 | 72 | yes | — |
| 139 | C22×C4 | C26 | 1 | 162 | yes | — |
| 140 | C22×C4 | C26 | 1 | 1296 | yes | — |
| 141 | C22×C4 | C26 | 1 | 54 | yes | — |
| 142 | C4⋊C4 | C26 | 1 | 864 | yes | — |
| 143 | C22⋊C4 | C26 | 1 | 2592 | yes | — |
| 144 | C42 | C26 | 1 | 432 | yes | — |
| 145 | C42 | C26 | 1 | 432 | yes | — |
| 146 | C23 | — | 2 | 972 | no | — |
| 147 | C23 | — | 4 | 1728 | no | — |
| 148 | C23 | — | 4 | 432 | no | — |
| 149 | C23 | — | 16 | 1728 | no | — |
| 150 | C23 | C22×H(5,𝔽2) | 1 | 12 | yes | — |
| 151 | C23 | C27 | 1 | 108 | yes | — |
| 152 | C23 | C27 | 1 | 3 | yes | — |
| 153 | Q8 | — | 4 | 288 | no | — |
| 154 | Q8 | C22×H(5,𝔽2) | 1 | 192 | yes | complemented |
| 155 | D4 | — | 2 | 2592 | no | — |
| 156 | D4 | — | 4 | 2592 | no | — |
| 157 | C2×C4 | — | 2 | 324 | no | — |
| 158 | C2×C4 | — | 2 | 2592 | no | — |
| 159 | C2×C4 | C22×H(5,𝔽2) | 1 | 216 | yes | — |
| 160 | C2×C4 | C27 | 1 | 108 | yes | — |
| 161 | C2×C4 | C27 | 1 | 36 | yes | — |
| 162 | C22 | — | 2 | 324 | no | — |
| 163 | C22 | — | 4 | 648 | no | — |
| 164 | C22 | — | 16 | 576 | no | — |
| 165 | C22 | #63040 | 1 | 16 | yes | direct product factor |
| 166 | C22 | C23×H(5,𝔽2) | 1 | 18 | yes | — |
| 167 | C22 | C28 | 1 | 1 | yes | characteristic |
| 168 | C4 | — | 2 | 108 | no | — |
| 169 | C4 | C23×H(5,𝔽2) | 1 | 72 | yes | — |
| 170 | C2 | — | 4 | 108 | no | — |
| 171 | C2 | C2×#63040 | 1 | 12 | yes | direct product factor |
| 172 | C2 | C24×H(5,𝔽2) | 1 | 3 | yes | — |
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