← C89×#62826 #36440674
Subgroups — C89×#62826 #36440674
Order 22784.
6670 conjugacy classes of subgroups.
The subgroup lattice has 460 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C89×#3564 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | C89×#3560 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C89×#3521 | C2 | 1 | 24 | yes | maximal, complemented |
| 4 | C89×#3492 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C89×#3490 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C89×#3444 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C22×#126×C89 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #563×C89 | C22 | 1 | 24 | yes | complemented |
| 9 | #560×C89 | C22 | 1 | 8 | yes | complemented |
| 10 | #556×C89 | C22 | 1 | 24 | yes | complemented |
| 11 | #554×C89 | C22 | 1 | 24 | yes | complemented |
| 12 | #553×C89 | C22 | 1 | 24 | yes | complemented |
| 13 | #553×C89 | C22 | 1 | 24 | yes | complemented |
| 14 | #552×C89 | C22 | 1 | 24 | yes | complemented |
| 15 | #552×C89 | C22 | 1 | 24 | yes | complemented |
| 16 | #551×C89 | C22 | 1 | 24 | yes | complemented |
| 17 | #551×C89 | C22 | 1 | 24 | yes | complemented |
| 18 | #551×C89 | C22 | 1 | 24 | yes | complemented |
| 19 | #547×C89 | C22 | 1 | 24 | yes | complemented |
| 20 | #546×C89 | C22 | 1 | 24 | yes | complemented |
| 21 | #546×C89 | C22 | 1 | 24 | yes | complemented |
| 22 | #544×C89 | C22 | 1 | 6 | yes | complemented |
| 23 | #543×C89 | C22 | 1 | 6 | yes | complemented |
| 24 | #542×C89 | C22 | 1 | 24 | yes | complemented |
| 25 | #541×C89 | C22 | 1 | 24 | yes | complemented |
| 26 | #539×C89 | C22 | 1 | 12 | yes | complemented |
| 27 | #539×C89 | C22 | 1 | 12 | yes | complemented |
| 28 | #539×C89 | C22 | 1 | 24 | yes | complemented |
| 29 | #538×C89 | C22 | 1 | 12 | yes | — |
| 30 | #538×C89 | C22 | 1 | 12 | yes | — |
| 31 | #538×C89 | C22 | 1 | 24 | yes | complemented |
| 32 | #537×C89 | C22 | 1 | 6 | yes | complemented |
| 33 | #534×C89 | C22 | 1 | 6 | yes | complemented |
| 34 | #533×C89 | C22 | 1 | 6 | yes | complemented |
| 35 | #532×C89 | C22 | 1 | 6 | yes | complemented |
| 36 | #529×C89 | C22 | 1 | 12 | yes | complemented |
| 37 | #529×C89 | C22 | 1 | 12 | yes | complemented |
| 38 | #529×C89 | C22 | 1 | 24 | yes | complemented |
| 39 | C2×#126×C89 | C22 | 1 | 12 | yes | complemented |
| 40 | C2×#126×C89 | C22 | 1 | 12 | yes | complemented |
| 41 | C2×#126×C89 | C22 | 1 | 8 | yes | complemented |
| 42 | #525×C89 | C22 | 1 | 12 | yes | complemented |
| 43 | #525×C89 | C22 | 1 | 12 | yes | complemented |
| 44 | C2×#120×C89 | C22 | 1 | 4 | yes | — |
| 45 | #520×C89 | C22 | 1 | 12 | yes | complemented |
| 46 | #518×C89 | C22 | 1 | 12 | yes | complemented |
| 47 | C4×#41×C89 | C22 | 1 | 12 | yes | complemented |
| 48 | C22×C4⋊C4×C89 | C22 | 1 | 3 | yes | complemented |
| 49 | C22×C22⋊C4×C89 | C22 | 1 | 3 | yes | — |
| 50 | C22×C42×C89 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C25×C89 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×#41×C89 | C23 | 1 | 12 | yes | — |
| 53 | C2×#41×C89 | C23 | 1 | 12 | yes | — |
| 54 | C22×D4×C89 | C23 | 1 | 12 | yes | — |
| 55 | C23×C4×C89 | C23 | 1 | 3 | yes | — |
| 56 | C23×C4×C89 | C23 | 1 | 3 | yes | — |
| 57 | C4⋊Q8×C89 | C23 | 1 | 6 | yes | complemented |
| 58 | C4⋊Q8×C89 | C23 | 1 | 24 | yes | complemented |
| 59 | #127×C89 | C23 | 1 | 2 | yes | complemented |
| 60 | #126×C89 | C23 | 1 | 8 | yes | — |
| 61 | #126×C89 | C23 | 1 | 24 | yes | — |
| 62 | #126×C89 | C23 | 1 | 24 | yes | — |
| 63 | #126×C89 | C23 | 1 | 8 | yes | — |
| 64 | #126×C89 | C23 | 1 | 24 | yes | — |
| 65 | #126×C89 | C23 | 1 | 24 | yes | — |
| 66 | #126×C89 | C23 | 1 | 8 | yes | complemented |
| 67 | #126×C89 | C23 | 1 | 24 | yes | complemented |
| 68 | #126×C89 | C23 | 1 | 8 | yes | complemented |
| 69 | #126×C89 | C23 | 1 | 24 | yes | complemented |
| 70 | #125×C89 | C23 | 1 | 12 | yes | complemented |
| 71 | #125×C89 | C23 | 1 | 24 | yes | complemented |
| 72 | #125×C89 | C23 | 1 | 24 | yes | complemented |
| 73 | #125×C89 | C23 | 1 | 24 | yes | complemented |
| 74 | #124×C89 | C23 | 1 | 24 | yes | — |
| 75 | #124×C89 | C23 | 1 | 24 | yes | — |
| 76 | #124×C89 | C23 | 1 | 12 | yes | complemented |
| 77 | #123×C89 | C23 | 1 | 24 | yes | — |
| 78 | #123×C89 | C23 | 1 | 24 | yes | — |
| 79 | #123×C89 | C23 | 1 | 24 | yes | — |
| 80 | #123×C89 | C23 | 1 | 24 | yes | — |
| 81 | #123×C89 | C23 | 1 | 24 | yes | — |
| 82 | #123×C89 | C23 | 1 | 24 | yes | complemented |
| 83 | #123×C89 | C23 | 1 | 24 | yes | complemented |
| 84 | C22⋊Q8×C89 | C23 | 1 | 12 | yes | — |
| 85 | C22⋊Q8×C89 | C23 | 1 | 12 | yes | — |
| 86 | C22⋊Q8×C89 | C23 | 1 | 12 | yes | — |
| 87 | C22⋊Q8×C89 | C23 | 1 | 12 | yes | — |
| 88 | C22⋊Q8×C89 | C23 | 1 | 24 | yes | — |
| 89 | C22⋊Q8×C89 | C23 | 1 | 24 | yes | — |
| 90 | C22⋊Q8×C89 | C23 | 1 | 24 | yes | complemented |
| 91 | C22⋊Q8×C89 | C23 | 1 | 24 | yes | complemented |
| 92 | C22⋊Q8×C89 | C23 | 1 | 24 | yes | complemented |
| 93 | #121×C89 | C23 | 1 | 12 | yes | — |
| 94 | #121×C89 | C23 | 1 | 12 | yes | — |
| 95 | #121×C89 | C23 | 1 | 12 | yes | — |
| 96 | #121×C89 | C23 | 1 | 12 | yes | — |
| 97 | #121×C89 | C23 | 1 | 24 | yes | — |
| 98 | #121×C89 | C23 | 1 | 24 | yes | — |
| 99 | #121×C89 | C23 | 1 | 24 | yes | complemented |
| 100 | #120×C89 | C23 | 1 | 8 | yes | — |
| 101 | #120×C89 | C23 | 1 | 24 | yes | — |
| 102 | #120×C89 | C23 | 1 | 24 | yes | — |
| 103 | C4×Q8×C89 | C23 | 1 | 12 | yes | complemented |
| 104 | C4×Q8×C89 | C23 | 1 | 12 | yes | complemented |
| 105 | C4×Q8×C89 | C23 | 1 | 24 | yes | complemented |
| 106 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 107 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 108 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 109 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 110 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 111 | C4×D4×C89 | C23 | 1 | 24 | yes | — |
| 112 | C4×D4×C89 | C23 | 1 | 12 | yes | complemented |
| 113 | C4×D4×C89 | C23 | 1 | 12 | yes | complemented |
| 114 | C4×D4×C89 | C23 | 1 | 24 | yes | complemented |
| 115 | #117×C89 | C23 | 1 | 12 | yes | — |
| 116 | #117×C89 | C23 | 1 | 24 | yes | — |
| 117 | #117×C89 | C23 | 1 | 12 | yes | — |
| 118 | #117×C89 | C23 | 1 | 24 | yes | complemented |
| 119 | #117×C89 | C23 | 1 | 24 | yes | complemented |
| 120 | C2×C4⋊C4×C89 | C23 | 1 | 6 | yes | — |
| 121 | C2×C4⋊C4×C89 | C23 | 1 | 6 | yes | — |
| 122 | C2×C4⋊C4×C89 | C23 | 1 | 12 | yes | — |
| 123 | C2×C4⋊C4×C89 | C23 | 1 | 12 | yes | — |
| 124 | C2×C4⋊C4×C89 | C23 | 1 | 24 | yes | complemented |
| 125 | C2×C22⋊C4×C89 | C23 | 1 | 6 | yes | — |
| 126 | C2×C22⋊C4×C89 | C23 | 1 | 6 | yes | — |
| 127 | C2×C22⋊C4×C89 | C23 | 1 | 12 | yes | — |
| 128 | C2×C22⋊C4×C89 | C23 | 1 | 12 | yes | — |
| 129 | C2×C22⋊C4×C89 | C23 | 1 | 12 | yes | — |
| 130 | C2×C22⋊C4×C89 | C23 | 1 | 24 | yes | — |
| 131 | C2×C42×C89 | C23 | 1 | 6 | yes | — |
| 132 | C2×C42×C89 | C23 | 1 | 6 | yes | — |
| 133 | C2×C42×C89 | C23 | 1 | 8 | yes | complemented |
| 134 | C24×C89 | — | 4 | 6 | no | — |
| 135 | C24×C89 | C24 | 1 | 1 | yes | characteristic |
| 136 | C24×C89 | C24 | 1 | 6 | yes | — |
| 137 | C24×C89 | C24 | 1 | 4 | yes | — |
| 138 | #41×C89 | — | 4 | 24 | no | — |
| 139 | #41×C89 | — | 4 | 24 | no | — |
| 140 | C2×Q8×C89 | C24 | 1 | 12 | yes | — |
| 141 | C2×Q8×C89 | C24 | 1 | 12 | yes | — |
| 142 | C2×D4×C89 | — | 4 | 24 | no | — |
| 143 | C2×D4×C89 | C24 | 1 | 24 | yes | — |
| 144 | C2×D4×C89 | C24 | 1 | 24 | yes | — |
| 145 | C2×D4×C89 | C24 | 1 | 12 | yes | — |
| 146 | C2×D4×C89 | C24 | 1 | 12 | yes | — |
| 147 | C22×C4×C89 | — | 4 | 6 | no | — |
| 148 | C22×C4×C89 | — | 4 | 6 | no | — |
| 149 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 150 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 151 | C22×C4×C89 | C24 | 1 | 3 | yes | — |
| 152 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 153 | C22×C4×C89 | C24 | 1 | 3 | yes | — |
| 154 | C22×C4×C89 | C24 | 1 | 24 | yes | — |
| 155 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 156 | C22×C4×C89 | C24 | 1 | 6 | yes | — |
| 157 | C22×C4×C89 | C24 | 1 | 12 | yes | — |
| 158 | C22×C4×C89 | C24 | 1 | 24 | yes | — |
| 159 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 160 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 161 | C4⋊C4×C89 | C24 | 1 | 12 | yes | — |
| 162 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 163 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 164 | C4⋊C4×C89 | C24 | 1 | 12 | yes | — |
| 165 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 166 | C4⋊C4×C89 | C24 | 1 | 12 | yes | — |
| 167 | C4⋊C4×C89 | C24 | 1 | 12 | yes | — |
| 168 | C4⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 169 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 170 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 171 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 172 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 173 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 174 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 175 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 176 | C22⋊C4×C89 | C24 | 1 | 24 | yes | — |
| 177 | C42×C89 | C24 | 1 | 2 | yes | — |
| 178 | C42×C89 | C24 | 1 | 6 | yes | — |
| 179 | C42×C89 | C24 | 1 | 6 | yes | — |
| 180 | C42×C89 | C24 | 1 | 2 | yes | — |
| 181 | C42×C89 | C24 | 1 | 24 | yes | — |
| 182 | C42×C89 | C24 | 1 | 24 | yes | — |
| 183 | C23×C89 | — | 2 | 6 | no | — |
| 184 | C23×C89 | — | 2 | 12 | no | — |
| 185 | C23×C89 | — | 4 | 6 | no | — |
| 186 | C23×C89 | — | 4 | 6 | no | — |
| 187 | C23×C89 | — | 4 | 12 | no | — |
| 188 | C23×C89 | — | 8 | 8 | no | — |
| 189 | C23×C89 | C25 | 1 | 4 | yes | — |
| 190 | C23×C89 | C25 | 1 | 8 | yes | — |
| 191 | C23×C89 | C25 | 1 | 3 | yes | — |
| 192 | Q8×C89 | — | 4 | 12 | no | — |
| 193 | Q8×C89 | — | 4 | 12 | no | — |
| 194 | D4×C89 | — | 2 | 48 | no | — |
| 195 | D4×C89 | — | 4 | 24 | no | — |
| 196 | D4×C89 | — | 4 | 12 | no | — |
| 197 | D4×C89 | — | 4 | 12 | no | — |
| 198 | C2×C4×C89 | — | 2 | 12 | no | — |
| 199 | C2×C4×C89 | — | 2 | 12 | no | — |
| 200 | C2×C4×C89 | — | 4 | 3 | no | — |
| 201 | C2×C4×C89 | — | 4 | 6 | no | — |
| 202 | C2×C4×C89 | — | 4 | 6 | no | — |
| 203 | C2×C4×C89 | — | 4 | 6 | no | — |
| 204 | C2×C4×C89 | — | 4 | 3 | no | — |
| 205 | C2×C4×C89 | — | 4 | 12 | no | — |
| 206 | C2×C4×C89 | — | 4 | 24 | no | — |
| 207 | C2×C4×C89 | — | 4 | 24 | no | — |
| 208 | C2×C4×C89 | C25 | 1 | 6 | yes | — |
| 209 | C2×C4×C89 | C25 | 1 | 6 | yes | — |
| 210 | C2×C4×C89 | C25 | 1 | 24 | yes | — |
| 211 | C2×C4×C89 | C25 | 1 | 12 | yes | — |
| 212 | C22×C89 | — | 2 | 8 | no | — |
| 213 | C22×C89 | — | 2 | 3 | no | — |
| 214 | C22×C89 | — | 2 | 3 | no | — |
| 215 | C22×C89 | — | 2 | 24 | no | — |
| 216 | C22×C89 | — | 2 | 12 | no | — |
| 217 | C22×C89 | — | 8 | 12 | no | — |
| 218 | C22×C89 | — | 16 | 4 | no | — |
| 219 | C22×C89 | #585 | 1 | 6 | yes | — |
| 220 | C22×C89 | C26 | 1 | 1 | yes | characteristic |
| 221 | C4×C89 | — | 2 | 6 | no | — |
| 222 | C4×C89 | — | 2 | 12 | no | — |
| 223 | C4×C89 | — | 2 | 6 | no | — |
| 224 | C4×C89 | — | 2 | 24 | no | — |
| 225 | #62826 | C89 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 226 | C2×C89 | — | 2 | 6 | no | — |
| 227 | C2×C89 | — | 4 | 4 | no | — |
| 228 | C2×C89 | — | 4 | 8 | no | — |
| 229 | C2×C89 | C2×#585 | 1 | 3 | yes | — |
| 230 | #3564 | C2×C89 | 1 | 12 | yes | complemented |
| 231 | #3560 | C2×C89 | 1 | 12 | yes | complemented |
| 232 | #3521 | C2×C89 | 1 | 24 | yes | complemented |
| 233 | #3492 | C2×C89 | 1 | 6 | yes | complemented |
| 234 | #3490 | C2×C89 | 1 | 6 | yes | complemented |
| 235 | #3444 | C2×C89 | 1 | 2 | yes | complemented |
| 236 | C22×#126 | C2×C89 | 1 | 1 | yes | characteristic, complemented |
| 237 | C89 | #62826 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 238 | #563 | C22×C89 | 1 | 24 | yes | complemented |
| 239 | #560 | C22×C89 | 1 | 8 | yes | complemented |
| 240 | #556 | C22×C89 | 1 | 24 | yes | complemented |
| 241 | #554 | C22×C89 | 1 | 24 | yes | complemented |
| 242 | #553 | C22×C89 | 1 | 24 | yes | complemented |
| 243 | #553 | C22×C89 | 1 | 24 | yes | complemented |
| 244 | #552 | C22×C89 | 1 | 24 | yes | complemented |
| 245 | #552 | C22×C89 | 1 | 24 | yes | complemented |
| 246 | #551 | C22×C89 | 1 | 24 | yes | complemented |
| 247 | #551 | C22×C89 | 1 | 24 | yes | complemented |
| 248 | #551 | C22×C89 | 1 | 24 | yes | complemented |
| 249 | #547 | C22×C89 | 1 | 24 | yes | complemented |
| 250 | #546 | C22×C89 | 1 | 24 | yes | complemented |
| 251 | #546 | C22×C89 | 1 | 24 | yes | complemented |
| 252 | #544 | C22×C89 | 1 | 6 | yes | complemented |
| 253 | #543 | C22×C89 | 1 | 6 | yes | complemented |
| 254 | #542 | C22×C89 | 1 | 24 | yes | complemented |
| 255 | #541 | C22×C89 | 1 | 24 | yes | complemented |
| 256 | #539 | C22×C89 | 1 | 12 | yes | complemented |
| 257 | #539 | C22×C89 | 1 | 12 | yes | complemented |
| 258 | #539 | C22×C89 | 1 | 24 | yes | complemented |
| 259 | #538 | C22×C89 | 1 | 12 | yes | — |
| 260 | #538 | C22×C89 | 1 | 12 | yes | — |
| 261 | #538 | C22×C89 | 1 | 24 | yes | complemented |
| 262 | #537 | C22×C89 | 1 | 6 | yes | complemented |
| 263 | #534 | C22×C89 | 1 | 6 | yes | complemented |
| 264 | #533 | C22×C89 | 1 | 6 | yes | complemented |
| 265 | #532 | C22×C89 | 1 | 6 | yes | complemented |
| 266 | #529 | C22×C89 | 1 | 12 | yes | complemented |
| 267 | #529 | C22×C89 | 1 | 12 | yes | complemented |
| 268 | #529 | C22×C89 | 1 | 24 | yes | complemented |
| 269 | C2×#126 | C22×C89 | 1 | 12 | yes | complemented |
| 270 | C2×#126 | C22×C89 | 1 | 12 | yes | complemented |
| 271 | C2×#126 | C22×C89 | 1 | 8 | yes | complemented |
| 272 | #525 | C22×C89 | 1 | 12 | yes | complemented |
| 273 | #525 | C22×C89 | 1 | 12 | yes | complemented |
| 274 | C2×#120 | C22×C89 | 1 | 4 | yes | — |
| 275 | #520 | C22×C89 | 1 | 12 | yes | complemented |
| 276 | #518 | C22×C89 | 1 | 12 | yes | complemented |
| 277 | C4×#41 | C22×C89 | 1 | 12 | yes | complemented |
| 278 | C22×C4⋊C4 | C22×C89 | 1 | 3 | yes | complemented |
| 279 | C22×C22⋊C4 | C22×C89 | 1 | 3 | yes | — |
| 280 | C22×C42 | C22×C89 | 1 | 1 | yes | characteristic, complemented |
| 281 | C25 | C23×C89 | 1 | 1 | yes | characteristic |
| 282 | C2×#41 | C23×C89 | 1 | 12 | yes | — |
| 283 | C2×#41 | C23×C89 | 1 | 12 | yes | — |
| 284 | C22×D4 | C23×C89 | 1 | 12 | yes | — |
| 285 | C23×C4 | C23×C89 | 1 | 3 | yes | — |
| 286 | C23×C4 | C23×C89 | 1 | 3 | yes | — |
| 287 | C4⋊Q8 | C23×C89 | 1 | 6 | yes | complemented |
| 288 | C4⋊Q8 | C23×C89 | 1 | 24 | yes | complemented |
| 289 | #127 | C23×C89 | 1 | 2 | yes | complemented |
| 290 | #126 | C23×C89 | 1 | 8 | yes | — |
| 291 | #126 | C23×C89 | 1 | 24 | yes | — |
| 292 | #126 | C23×C89 | 1 | 24 | yes | — |
| 293 | #126 | C23×C89 | 1 | 8 | yes | — |
| 294 | #126 | C23×C89 | 1 | 24 | yes | — |
| 295 | #126 | C23×C89 | 1 | 24 | yes | — |
| 296 | #126 | C23×C89 | 1 | 8 | yes | complemented |
| 297 | #126 | C23×C89 | 1 | 24 | yes | complemented |
| 298 | #126 | C23×C89 | 1 | 8 | yes | complemented |
| 299 | #126 | C23×C89 | 1 | 24 | yes | complemented |
| 300 | #125 | C23×C89 | 1 | 12 | yes | complemented |
| 301 | #125 | C23×C89 | 1 | 24 | yes | complemented |
| 302 | #125 | C23×C89 | 1 | 24 | yes | complemented |
| 303 | #125 | C23×C89 | 1 | 24 | yes | complemented |
| 304 | #124 | C23×C89 | 1 | 24 | yes | — |
| 305 | #124 | C23×C89 | 1 | 24 | yes | — |
| 306 | #124 | C23×C89 | 1 | 12 | yes | complemented |
| 307 | #123 | C23×C89 | 1 | 24 | yes | — |
| 308 | #123 | C23×C89 | 1 | 24 | yes | — |
| 309 | #123 | C23×C89 | 1 | 24 | yes | — |
| 310 | #123 | C23×C89 | 1 | 24 | yes | — |
| 311 | #123 | C23×C89 | 1 | 24 | yes | — |
| 312 | #123 | C23×C89 | 1 | 24 | yes | complemented |
| 313 | #123 | C23×C89 | 1 | 24 | yes | complemented |
| 314 | C22⋊Q8 | C23×C89 | 1 | 12 | yes | — |
| 315 | C22⋊Q8 | C23×C89 | 1 | 12 | yes | — |
| 316 | C22⋊Q8 | C23×C89 | 1 | 12 | yes | — |
| 317 | C22⋊Q8 | C23×C89 | 1 | 12 | yes | — |
| 318 | C22⋊Q8 | C23×C89 | 1 | 24 | yes | — |
| 319 | C22⋊Q8 | C23×C89 | 1 | 24 | yes | — |
| 320 | C22⋊Q8 | C23×C89 | 1 | 24 | yes | complemented |
| 321 | C22⋊Q8 | C23×C89 | 1 | 24 | yes | complemented |
| 322 | C22⋊Q8 | C23×C89 | 1 | 24 | yes | complemented |
| 323 | #121 | C23×C89 | 1 | 12 | yes | — |
| 324 | #121 | C23×C89 | 1 | 12 | yes | — |
| 325 | #121 | C23×C89 | 1 | 12 | yes | — |
| 326 | #121 | C23×C89 | 1 | 12 | yes | — |
| 327 | #121 | C23×C89 | 1 | 24 | yes | — |
| 328 | #121 | C23×C89 | 1 | 24 | yes | — |
| 329 | #121 | C23×C89 | 1 | 24 | yes | complemented |
| 330 | #120 | C23×C89 | 1 | 8 | yes | — |
| 331 | #120 | C23×C89 | 1 | 24 | yes | — |
| 332 | #120 | C23×C89 | 1 | 24 | yes | — |
| 333 | C4×Q8 | C23×C89 | 1 | 12 | yes | complemented |
| 334 | C4×Q8 | C23×C89 | 1 | 12 | yes | complemented |
| 335 | C4×Q8 | C23×C89 | 1 | 24 | yes | complemented |
| 336 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 337 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 338 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 339 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 340 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 341 | C4×D4 | C23×C89 | 1 | 24 | yes | — |
| 342 | C4×D4 | C23×C89 | 1 | 12 | yes | complemented |
| 343 | C4×D4 | C23×C89 | 1 | 12 | yes | complemented |
| 344 | C4×D4 | C23×C89 | 1 | 24 | yes | complemented |
| 345 | #117 | C23×C89 | 1 | 12 | yes | — |
| 346 | #117 | C23×C89 | 1 | 24 | yes | — |
| 347 | #117 | C23×C89 | 1 | 12 | yes | — |
| 348 | #117 | C23×C89 | 1 | 24 | yes | complemented |
| 349 | #117 | C23×C89 | 1 | 24 | yes | complemented |
| 350 | C2×C4⋊C4 | C23×C89 | 1 | 6 | yes | — |
| 351 | C2×C4⋊C4 | C23×C89 | 1 | 6 | yes | — |
| 352 | C2×C4⋊C4 | C23×C89 | 1 | 12 | yes | — |
| 353 | C2×C4⋊C4 | C23×C89 | 1 | 12 | yes | — |
| 354 | C2×C4⋊C4 | C23×C89 | 1 | 24 | yes | complemented |
| 355 | C2×C22⋊C4 | C23×C89 | 1 | 6 | yes | — |
| 356 | C2×C22⋊C4 | C23×C89 | 1 | 6 | yes | — |
| 357 | C2×C22⋊C4 | C23×C89 | 1 | 12 | yes | — |
| 358 | C2×C22⋊C4 | C23×C89 | 1 | 12 | yes | — |
| 359 | C2×C22⋊C4 | C23×C89 | 1 | 12 | yes | — |
| 360 | C2×C22⋊C4 | C23×C89 | 1 | 24 | yes | — |
| 361 | C2×C42 | C23×C89 | 1 | 6 | yes | — |
| 362 | C2×C42 | C23×C89 | 1 | 6 | yes | — |
| 363 | C2×C42 | C23×C89 | 1 | 8 | yes | complemented |
| 364 | C24 | — | 4 | 6 | no | — |
| 365 | C24 | C24×C89 | 1 | 1 | yes | characteristic |
| 366 | C24 | C24×C89 | 1 | 6 | yes | — |
| 367 | C24 | C24×C89 | 1 | 4 | yes | — |
| 368 | #41 | — | 4 | 24 | no | — |
| 369 | #41 | — | 4 | 24 | no | — |
| 370 | C2×Q8 | C24×C89 | 1 | 12 | yes | — |
| 371 | C2×Q8 | C24×C89 | 1 | 12 | yes | — |
| 372 | C2×D4 | — | 4 | 24 | no | — |
| 373 | C2×D4 | C24×C89 | 1 | 24 | yes | — |
| 374 | C2×D4 | C24×C89 | 1 | 24 | yes | — |
| 375 | C2×D4 | C24×C89 | 1 | 12 | yes | — |
| 376 | C2×D4 | C24×C89 | 1 | 12 | yes | — |
| 377 | C22×C4 | — | 4 | 6 | no | — |
| 378 | C22×C4 | — | 4 | 6 | no | — |
| 379 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 380 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 381 | C22×C4 | C24×C89 | 1 | 3 | yes | — |
| 382 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 383 | C22×C4 | C24×C89 | 1 | 3 | yes | — |
| 384 | C22×C4 | C24×C89 | 1 | 24 | yes | — |
| 385 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 386 | C22×C4 | C24×C89 | 1 | 6 | yes | — |
| 387 | C22×C4 | C24×C89 | 1 | 12 | yes | — |
| 388 | C22×C4 | C24×C89 | 1 | 24 | yes | — |
| 389 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 390 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 391 | C4⋊C4 | C24×C89 | 1 | 12 | yes | — |
| 392 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 393 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 394 | C4⋊C4 | C24×C89 | 1 | 12 | yes | — |
| 395 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 396 | C4⋊C4 | C24×C89 | 1 | 12 | yes | — |
| 397 | C4⋊C4 | C24×C89 | 1 | 12 | yes | — |
| 398 | C4⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 399 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 400 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 401 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 402 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 403 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 404 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 405 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 406 | C22⋊C4 | C24×C89 | 1 | 24 | yes | — |
| 407 | C42 | C24×C89 | 1 | 2 | yes | — |
| 408 | C42 | C24×C89 | 1 | 6 | yes | — |
| 409 | C42 | C24×C89 | 1 | 6 | yes | — |
| 410 | C42 | C24×C89 | 1 | 2 | yes | — |
| 411 | C42 | C24×C89 | 1 | 24 | yes | — |
| 412 | C42 | C24×C89 | 1 | 24 | yes | — |
| 413 | C23 | — | 2 | 6 | no | — |
| 414 | C23 | — | 2 | 12 | no | — |
| 415 | C23 | — | 4 | 6 | no | — |
| 416 | C23 | — | 4 | 6 | no | — |
| 417 | C23 | — | 4 | 12 | no | — |
| 418 | C23 | — | 8 | 8 | no | — |
| 419 | C23 | C25×C89 | 1 | 4 | yes | — |
| 420 | C23 | C25×C89 | 1 | 8 | yes | — |
| 421 | C23 | C25×C89 | 1 | 3 | yes | — |
| 422 | Q8 | — | 4 | 12 | no | — |
| 423 | Q8 | — | 4 | 12 | no | — |
| 424 | D4 | — | 2 | 48 | no | — |
| 425 | D4 | — | 4 | 24 | no | — |
| 426 | D4 | — | 4 | 12 | no | — |
| 427 | D4 | — | 4 | 12 | no | — |
| 428 | C2×C4 | — | 2 | 12 | no | — |
| 429 | C2×C4 | — | 2 | 12 | no | — |
| 430 | C2×C4 | — | 4 | 3 | no | — |
| 431 | C2×C4 | — | 4 | 6 | no | — |
| 432 | C2×C4 | — | 4 | 6 | no | — |
| 433 | C2×C4 | — | 4 | 6 | no | — |
| 434 | C2×C4 | — | 4 | 3 | no | — |
| 435 | C2×C4 | — | 4 | 12 | no | — |
| 436 | C2×C4 | — | 4 | 24 | no | — |
| 437 | C2×C4 | — | 4 | 24 | no | — |
| 438 | C2×C4 | C25×C89 | 1 | 6 | yes | — |
| 439 | C2×C4 | C25×C89 | 1 | 6 | yes | — |
| 440 | C2×C4 | C25×C89 | 1 | 24 | yes | — |
| 441 | C2×C4 | C25×C89 | 1 | 12 | yes | — |
| 442 | C22 | — | 2 | 8 | no | — |
| 443 | C22 | — | 2 | 3 | no | — |
| 444 | C22 | — | 2 | 3 | no | — |
| 445 | C22 | — | 2 | 24 | no | — |
| 446 | C22 | — | 2 | 12 | no | — |
| 447 | C22 | — | 8 | 12 | no | — |
| 448 | C22 | — | 16 | 4 | no | — |
| 449 | C22 | #585×C89 | 1 | 6 | yes | — |
| 450 | C22 | C26×C89 | 1 | 1 | yes | characteristic |
| 451 | C4 | — | 2 | 6 | no | — |
| 452 | C4 | — | 2 | 12 | no | — |
| 453 | C4 | — | 2 | 6 | no | — |
| 454 | C4 | — | 2 | 24 | no | — |
| 455 | C2 | — | 2 | 6 | no | — |
| 456 | C2 | — | 4 | 4 | no | — |
| 457 | C2 | — | 4 | 8 | no | — |
| 458 | C2 | C2×#585×C89 | 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