Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2014 conjugacy classes of subgroups.
The subgroup lattice has 586 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22623855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22623714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22621015 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22620993 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22620971 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22620959 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #22620388 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22620377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22620334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22619486 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #22619251 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #22618580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C2×#491×C73 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C2×#14556639 | C22 | 1 | 2 | yes | — |
| 15 | C2×#14556622 | C22 | 1 | 4 | yes | — |
| 16 | C2×#14556613 | C22 | 1 | 4 | yes | — |
| 17 | #17989290 | — | 2 | 2 | no | — |
| 18 | #17989285 | — | 2 | 4 | no | — |
| 19 | #17989275 | — | 2 | 2 | no | — |
| 20 | #17989252 | — | 2 | 2 | no | — |
| 21 | #17989240 | — | 2 | 2 | no | — |
| 22 | #17989238 | — | 2 | 4 | no | — |
| 23 | #17989200 | C22 | 1 | 2 | yes | — |
| 24 | #17989193 | C22 | 1 | 2 | yes | — |
| 25 | #17989168 | C22 | 1 | 2 | yes | — |
| 26 | #17989162 | C22 | 1 | 4 | yes | — |
| 27 | #17989161 | C22 | 1 | 2 | yes | — |
| 28 | #17989138 | C22 | 1 | 2 | yes | — |
| 29 | #17989137 | C22 | 1 | 1 | yes | characteristic |
| 30 | #17989137 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4⋊Q8×D73 | C22 | 1 | 2 | yes | — |
| 32 | #17989122 | C22 | 1 | 4 | yes | — |
| 33 | #17989068 | C22 | 1 | 2 | yes | — |
| 34 | C4×#11924028 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17988981 | C22 | 1 | 2 | yes | — |
| 36 | #17988981 | C22 | 1 | 2 | yes | — |
| 37 | #17988979 | C22 | 1 | 4 | yes | — |
| 38 | #17988976 | C22 | 1 | 2 | yes | — |
| 39 | #17988976 | C22 | 1 | 2 | yes | — |
| 40 | #17988966 | C22 | 1 | 2 | yes | — |
| 41 | #17988961 | C22 | 1 | 2 | yes | — |
| 42 | #17988957 | C22 | 1 | 2 | yes | — |
| 43 | #17988953 | C22 | 1 | 2 | yes | — |
| 44 | #17988944 | C22 | 1 | 4 | yes | — |
| 45 | #17988812 | C22 | 1 | 8 | yes | — |
| 46 | #17988805 | C22 | 1 | 8 | yes | — |
| 47 | #17988796 | C22 | 1 | 8 | yes | — |
| 48 | #17988791 | C22 | 1 | 8 | yes | — |
| 49 | #17988752 | C22 | 1 | 8 | yes | — |
| 50 | #17988744 | C22 | 1 | 8 | yes | — |
| 51 | #17988735 | C22 | 1 | 8 | yes | — |
| 52 | #17988727 | C22 | 1 | 8 | yes | — |
| 53 | #17988649 | C22 | 1 | 4 | yes | — |
| 54 | #17988642 | C22 | 1 | 4 | yes | — |
| 55 | #17988613 | C22 | 1 | 2 | yes | — |
| 56 | #17988586 | C22 | 1 | 4 | yes | — |
| 57 | #17988553 | C22 | 1 | 2 | yes | — |
| 58 | C4×#11924012 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×C4⋊Q8×C73 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×#125×C73 | C22 | 1 | 1 | yes | characteristic |
| 61 | #491×C73 | C22 | 1 | 4 | yes | — |
| 62 | #491×C73 | C22 | 1 | 4 | yes | — |
| 63 | C2×#103×C73 | C22 | 1 | 4 | yes | — |
| 64 | C2×#97×C73 | C22 | 1 | 1 | yes | characteristic |
| 65 | #14556639 | — | 4 | 8 | no | — |
| 66 | C2×#11924029 | — | 2 | 2 | no | — |
| 67 | C2×#11924029 | C23 | 1 | 4 | yes | — |
| 68 | C2×#11924028 | — | 2 | 4 | no | — |
| 69 | C2×#11924028 | C23 | 1 | 2 | yes | — |
| 70 | C2×#11924028 | C23 | 1 | 2 | yes | — |
| 71 | C2×#11924028 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×Q8×D73 | — | 2 | 2 | no | — |
| 73 | C2×Q8×D73 | C23 | 1 | 4 | yes | — |
| 74 | #14556622 | — | 4 | 8 | no | — |
| 75 | #14556613 | — | 4 | 8 | no | — |
| 76 | C2×Dic292 | C23 | 1 | 4 | yes | — |
| 77 | C2×#11924018 | C23 | 1 | 8 | yes | — |
| 78 | C2×#11924017 | C23 | 1 | 4 | yes | — |
| 79 | C2×#11924017 | C23 | 1 | 4 | yes | — |
| 80 | C2×#11924015 | C23 | 1 | 8 | yes | — |
| 81 | C2×D584 | C23 | 1 | 4 | yes | — |
| 82 | C2×#11924012 | C23 | 1 | 2 | yes | — |
| 83 | #14556591 | C23 | 1 | 1 | yes | characteristic |
| 84 | #14556591 | C23 | 1 | 1 | yes | characteristic |
| 85 | #14556590 | — | 2 | 4 | no | — |
| 86 | #14556589 | C23 | 1 | 4 | yes | — |
| 87 | #14556588 | C23 | 1 | 1 | yes | characteristic |
| 88 | #14556588 | C23 | 1 | 1 | yes | characteristic |
| 89 | #14556586 | — | 2 | 4 | no | — |
| 90 | #14556586 | — | 2 | 4 | no | — |
| 91 | #14556582 | — | 2 | 4 | no | — |
| 92 | #14556580 | C23 | 1 | 4 | yes | — |
| 93 | #14556579 | C23 | 1 | 2 | yes | — |
| 94 | #14556579 | C23 | 1 | 2 | yes | — |
| 95 | #14556576 | — | 2 | 4 | no | — |
| 96 | #14556576 | — | 2 | 4 | no | — |
| 97 | #14556576 | — | 2 | 8 | no | — |
| 98 | #14556574 | — | 2 | 4 | no | — |
| 99 | #14556571 | — | 2 | 2 | no | — |
| 100 | #14556571 | C23 | 1 | 4 | yes | — |
| 101 | #14556569 | — | 2 | 8 | no | — |
| 102 | #14556567 | — | 2 | 4 | no | — |
| 103 | #14556566 | — | 2 | 2 | no | — |
| 104 | #14556566 | — | 2 | 4 | no | — |
| 105 | #14556566 | — | 2 | 4 | no | — |
| 106 | #14556566 | C23 | 1 | 4 | yes | — |
| 107 | #14556565 | — | 2 | 4 | no | — |
| 108 | #14556565 | — | 2 | 2 | no | — |
| 109 | #14556565 | — | 2 | 2 | no | — |
| 110 | C4×Dic146 | D4 | 1 | 2 | yes | — |
| 111 | #14556556 | C23 | 1 | 4 | yes | — |
| 112 | C4×D292 | — | 2 | 2 | no | — |
| 113 | C4×D292 | — | 2 | 2 | no | — |
| 114 | C4×D292 | D4 | 1 | 2 | yes | — |
| 115 | #14556553 | — | 2 | 4 | no | — |
| 116 | #14556553 | — | 2 | 4 | no | — |
| 117 | #14556553 | C23 | 1 | 4 | yes | — |
| 118 | C4×C22⋊D73 | — | 2 | 4 | no | — |
| 119 | C4×C22⋊D73 | D4 | 1 | 4 | yes | — |
| 120 | #14556550 | C23 | 1 | 1 | yes | characteristic |
| 121 | #14556549 | — | 2 | 2 | no | — |
| 122 | #14556549 | — | 2 | 4 | no | — |
| 123 | #14556548 | C23 | 1 | 2 | yes | — |
| 124 | C4⋊C4×D73 | — | 2 | 4 | no | — |
| 125 | C4⋊C4×D73 | — | 2 | 2 | no | — |
| 126 | C42×D73 | C23 | 1 | 2 | yes | — |
| 127 | #14556520 | C23 | 1 | 8 | yes | — |
| 128 | #14556514 | C23 | 1 | 8 | yes | — |
| 129 | #14556511 | C23 | 1 | 8 | yes | — |
| 130 | #14556503 | C23 | 1 | 8 | yes | — |
| 131 | #14556502 | C23 | 1 | 2 | yes | — |
| 132 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 133 | C22×Q8×C73 | C23 | 1 | 2 | yes | — |
| 134 | C22×C8×C73 | C23 | 1 | 2 | yes | — |
| 135 | C4⋊Q8×C73 | — | 2 | 2 | no | — |
| 136 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 137 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 138 | #125×C73 | — | 2 | 2 | no | — |
| 139 | #125×C73 | C23 | 1 | 2 | yes | — |
| 140 | #125×C73 | C23 | 1 | 2 | yes | — |
| 141 | C2×C4⋊C4×C73 | — | 2 | 2 | no | — |
| 142 | C2×C4⋊C4×C73 | — | 2 | 2 | no | — |
| 143 | C2×C4⋊C4×C73 | C23 | 1 | 2 | yes | — |
| 144 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 145 | #103×C73 | C23 | 1 | 8 | yes | — |
| 146 | #103×C73 | C23 | 1 | 8 | yes | — |
| 147 | #97×C73 | C23 | 1 | 2 | yes | — |
| 148 | #97×C73 | C23 | 1 | 2 | yes | — |
| 149 | #11924029 | — | 4 | 8 | no | — |
| 150 | #11924029 | — | 4 | 8 | no | — |
| 151 | #11924028 | — | 2 | 4 | no | — |
| 152 | #11924028 | — | 2 | 8 | no | — |
| 153 | #11924028 | — | 2 | 8 | no | — |
| 154 | #11924028 | — | 4 | 16 | no | — |
| 155 | C2×Dic146 | — | 2 | 4 | no | — |
| 156 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×Dic146 | C24 | 1 | 2 | yes | — |
| 158 | C2×Dic146 | C24 | 1 | 2 | yes | — |
| 159 | Q8×D73 | — | 4 | 8 | no | — |
| 160 | Q8×D73 | — | 4 | 8 | no | — |
| 161 | C2×D292 | — | 2 | 4 | no | — |
| 162 | C2×D292 | — | 2 | 2 | no | — |
| 163 | C2×D292 | — | 2 | 4 | no | — |
| 164 | C2×D292 | — | 2 | 2 | no | — |
| 165 | C2×D292 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×D292 | C24 | 1 | 2 | yes | — |
| 167 | C2×D292 | C24 | 1 | 2 | yes | — |
| 168 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 169 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊D73 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×C4×D73 | — | 2 | 4 | no | — |
| 172 | C2×C4×D73 | — | 2 | 2 | no | — |
| 173 | C2×C4×D73 | — | 2 | 2 | no | — |
| 174 | C2×C4×D73 | — | 2 | 4 | no | — |
| 175 | C2×C4×D73 | — | 2 | 4 | no | — |
| 176 | C2×C4×D73 | C2×D4 | 1 | 4 | yes | — |
| 177 | C2×C4×D73 | C24 | 1 | 2 | yes | — |
| 178 | Dic292 | — | 4 | 4 | no | — |
| 179 | #11924018 | — | 4 | 8 | no | — |
| 180 | #11924017 | — | 4 | 4 | no | — |
| 181 | #11924017 | — | 4 | 4 | no | — |
| 182 | #11924015 | — | 4 | 8 | no | — |
| 183 | D584 | — | 4 | 4 | no | — |
| 184 | #11924012 | — | 2 | 4 | no | — |
| 185 | C2×#10596831 | C24 | 1 | 4 | yes | — |
| 186 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 187 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 188 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 189 | C4⋊Dic73 | C2×D4 | 1 | 2 | yes | — |
| 190 | #11924007 | — | 2 | 4 | no | — |
| 191 | #11924007 | — | 2 | 8 | no | — |
| 192 | #11924007 | C2×D4 | 1 | 4 | yes | — |
| 193 | C22⋊Dic73 | C2×D4 | 1 | 2 | yes | — |
| 194 | #11924005 | — | 2 | 4 | no | — |
| 195 | #11924005 | — | 2 | 2 | no | — |
| 196 | #11924005 | — | 2 | 2 | no | — |
| 197 | #11924005 | — | 2 | 4 | no | — |
| 198 | #11924005 | — | 2 | 4 | no | — |
| 199 | #11924005 | — | 2 | 4 | no | — |
| 200 | #11924005 | — | 2 | 8 | no | — |
| 201 | #11924005 | C2×D4 | 1 | 4 | yes | — |
| 202 | C4×Dic73 | — | 2 | 4 | no | — |
| 203 | C4×Dic73 | C2×D4 | 1 | 4 | yes | — |
| 204 | C4×Dic73 | C24 | 1 | 2 | yes | — |
| 205 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 206 | C2×Q8×C73 | — | 2 | 8 | no | — |
| 207 | C2×Q8×C73 | C24 | 1 | 4 | yes | — |
| 208 | C22×C4×C73 | — | 2 | 2 | no | — |
| 209 | C22×C4×C73 | — | 2 | 2 | no | — |
| 210 | C22×C4×C73 | C2×D4 | 1 | 2 | yes | — |
| 211 | C22×C4×C73 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×C8×C73 | — | 2 | 4 | no | — |
| 213 | C2×C8×C73 | C24 | 1 | 4 | yes | — |
| 214 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 215 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 216 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 217 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 218 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 219 | C4⋊C4×C73 | C24 | 1 | 4 | yes | — |
| 220 | C42×C73 | C2×D4 | 1 | 2 | yes | — |
| 221 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 222 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 223 | C23×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×D73 | — | 2 | 2 | no | — |
| 225 | C22×D73 | — | 2 | 2 | no | — |
| 226 | C22×D73 | C22×D4 | 1 | 2 | yes | — |
| 227 | Q8×C73 | — | 2 | 8 | no | — |
| 228 | Q8×C73 | — | 4 | 4 | no | — |
| 229 | C2×C4×C73 | — | 2 | 4 | no | — |
| 230 | C2×C4×C73 | — | 2 | 4 | no | — |
| 231 | C2×C4×C73 | — | 4 | 2 | no | — |
| 232 | C2×C4×C73 | — | 4 | 4 | no | — |
| 233 | C2×C4×C73 | — | 8 | 2 | no | — |
| 234 | C2×C4×C73 | C22×D4 | 1 | 2 | yes | — |
| 235 | C2×C4×C73 | C22×D4 | 1 | 2 | yes | — |
| 236 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C73 | H(5,𝔽2) | 1 | 4 | yes | — |
| 238 | C2×C4×C73 | C25 | 1 | 1 | yes | characteristic |
| 239 | C22⋊D73 | — | 2 | 4 | no | — |
| 240 | C22⋊D73 | — | 4 | 4 | no | — |
| 241 | C22⋊D73 | — | 4 | 4 | no | — |
| 242 | C2×Dic73 | — | 2 | 2 | no | — |
| 243 | C2×Dic73 | — | 2 | 2 | no | — |
| 244 | C2×Dic73 | C22×D4 | 1 | 4 | yes | — |
| 245 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 246 | D292 | — | 2 | 2 | no | — |
| 247 | D292 | — | 2 | 4 | no | — |
| 248 | D292 | — | 2 | 4 | no | — |
| 249 | D292 | — | 4 | 4 | no | — |
| 250 | D292 | — | 4 | 8 | no | — |
| 251 | D292 | — | 8 | 2 | no | — |
| 252 | D292 | — | 8 | 4 | no | — |
| 253 | C4×D73 | — | 2 | 4 | no | — |
| 254 | C4×D73 | — | 4 | 4 | no | — |
| 255 | C4×D73 | — | 4 | 8 | no | — |
| 256 | C4×D73 | — | 4 | 8 | no | — |
| 257 | C4×D73 | — | 4 | 4 | no | — |
| 258 | C4×D73 | — | 4 | 4 | no | — |
| 259 | C4×D73 | — | 8 | 4 | no | — |
| 260 | Dic146 | — | 2 | 2 | no | — |
| 261 | Dic146 | — | 2 | 4 | no | — |
| 262 | Dic146 | — | 2 | 4 | no | — |
| 263 | Dic146 | — | 4 | 8 | no | — |
| 264 | C8×C73 | — | 2 | 4 | no | — |
| 265 | #10596831 | — | 2 | 4 | no | — |
| 266 | C22×C73 | — | 2 | 2 | no | — |
| 267 | C22×C73 | #535 | 1 | 2 | yes | — |
| 268 | C22×C73 | C23×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×D73 | — | 2 | 4 | no | — |
| 270 | C2×D73 | — | 2 | 2 | no | — |
| 271 | C2×D73 | — | 4 | 2 | no | — |
| 272 | C2×D73 | — | 4 | 4 | no | — |
| 273 | C2×D73 | — | 4 | 2 | no | — |
| 274 | C2×D73 | — | 4 | 2 | no | — |
| 275 | C2×D73 | — | 4 | 2 | no | — |
| 276 | C4×C73 | — | 2 | 2 | no | — |
| 277 | C4×C73 | — | 2 | 2 | no | — |
| 278 | C4×C73 | — | 4 | 4 | no | — |
| 279 | C4×C73 | — | 4 | 4 | no | — |
| 280 | C4×C73 | #535 | 1 | 2 | yes | — |
| 281 | C4×C73 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 282 | Dic73 | — | 2 | 4 | no | — |
| 283 | Dic73 | — | 2 | 2 | no | — |
| 284 | Dic73 | — | 4 | 2 | no | — |
| 285 | Dic73 | — | 4 | 2 | no | — |
| 286 | #60831 | — | 73 | 1 | no | maximal, Sylow |
| 287 | C2×C73 | — | 2 | 2 | no | — |
| 288 | C2×C73 | C2×#535 | 1 | 1 | yes | characteristic |
| 289 | C2×C73 | #3586 | 1 | 2 | yes | — |
| 290 | D73 | — | 4 | 2 | no | — |
| 291 | D73 | — | 8 | 2 | no | — |
| 292 | D73 | — | 8 | 2 | no | — |
| 293 | #3512 | — | 73 | 1 | no | — |
| 294 | #3499 | — | 73 | 1 | no | — |
| 295 | #3223 | — | 73 | 4 | no | — |
| 296 | #3221 | — | 73 | 4 | no | — |
| 297 | #3219 | — | 73 | 4 | no | — |
| 298 | #3218 | — | 73 | 4 | no | — |
| 299 | #3152 | — | 73 | 1 | no | — |
| 300 | #3150 | — | 73 | 1 | no | — |
| 301 | #3142 | — | 73 | 1 | no | — |
| 302 | C2×#491 | D73 | 1 | 1 | yes | characteristic, complemented |
| 303 | #3046 | — | 73 | 4 | no | — |
| 304 | #3013 | — | 73 | 4 | no | — |
| 305 | #2923 | — | 73 | 1 | no | — |
| 306 | C73 | #60831 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 307 | C2×2−1+4 | — | 73 | 2 | no | — |
| 308 | C2×#137 | — | 73 | 4 | no | — |
| 309 | C2×#135 | — | 73 | 4 | no | — |
| 310 | #553 | — | 146 | 4 | no | — |
| 311 | #553 | — | 146 | 2 | no | — |
| 312 | #552 | — | 146 | 2 | no | — |
| 313 | D4×Q8 | — | 146 | 2 | no | — |
| 314 | #547 | — | 146 | 4 | no | — |
| 315 | #547 | — | 146 | 2 | no | — |
| 316 | #541 | — | 73 | 2 | no | — |
| 317 | #540 | — | 73 | 2 | no | — |
| 318 | #537 | — | 73 | 2 | no | — |
| 319 | #536 | — | 73 | 2 | no | — |
| 320 | #536 | — | 73 | 4 | no | — |
| 321 | #532 | — | 73 | 2 | no | — |
| 322 | #532 | — | 73 | 1 | no | — |
| 323 | #532 | — | 73 | 1 | no | — |
| 324 | C2×C4⋊Q8 | — | 73 | 2 | no | — |
| 325 | C2×C4⋊Q8 | C2×D73 | 1 | 1 | yes | characteristic |
| 326 | #529 | — | 73 | 4 | no | — |
| 327 | C2×#125 | C2×D73 | 1 | 1 | yes | characteristic |
| 328 | #520 | — | 73 | 2 | no | — |
| 329 | C4×#41 | — | 73 | 1 | no | — |
| 330 | #497 | — | 73 | 4 | no | — |
| 331 | #497 | — | 73 | 2 | no | — |
| 332 | #497 | — | 73 | 2 | no | — |
| 333 | #496 | — | 73 | 2 | no | — |
| 334 | #496 | — | 73 | 2 | no | — |
| 335 | #494 | — | 73 | 2 | no | — |
| 336 | #492 | — | 73 | 2 | no | — |
| 337 | #491 | — | 73 | 2 | no | — |
| 338 | #491 | C2×D73 | 1 | 4 | yes | — |
| 339 | #491 | C2×D73 | 1 | 4 | yes | — |
| 340 | #490 | — | 73 | 2 | no | — |
| 341 | #488 | — | 73 | 4 | no | — |
| 342 | #464 | — | 73 | 8 | no | — |
| 343 | #463 | — | 73 | 8 | no | — |
| 344 | #462 | — | 73 | 8 | no | — |
| 345 | #461 | — | 73 | 8 | no | — |
| 346 | #452 | — | 73 | 8 | no | — |
| 347 | #451 | — | 73 | 8 | no | — |
| 348 | #449 | — | 73 | 8 | no | — |
| 349 | #448 | — | 73 | 8 | no | — |
| 350 | #433 | — | 73 | 4 | no | — |
| 351 | #432 | — | 73 | 4 | no | — |
| 352 | #424 | — | 73 | 2 | no | — |
| 353 | #417 | — | 73 | 4 | no | — |
| 354 | C2×#103 | C2×D73 | 1 | 4 | yes | — |
| 355 | #408 | — | 73 | 2 | no | — |
| 356 | C4×M16 | — | 73 | 1 | no | — |
| 357 | C2×#97 | C2×D73 | 1 | 1 | yes | characteristic |
| 358 | 2−1+4 | — | 292 | 8 | no | — |
| 359 | C2×#41 | — | 73 | 1 | no | — |
| 360 | C2×#41 | — | 73 | 4 | no | — |
| 361 | C2×#41 | — | 73 | 2 | no | — |
| 362 | C2×#41 | — | 73 | 2 | no | — |
| 363 | C2×#41 | — | 146 | 4 | no | — |
| 364 | C2×#41 | — | 146 | 2 | no | — |
| 365 | C22×Q8 | — | 73 | 4 | no | — |
| 366 | C22×Q8 | — | 146 | 2 | no | — |
| 367 | C22×Q8 | C22×D73 | 1 | 2 | yes | — |
| 368 | #137 | — | 292 | 8 | no | — |
| 369 | #135 | — | 292 | 8 | no | — |
| 370 | C2×Q16 | — | 73 | 8 | no | — |
| 371 | C2×Q16 | — | 73 | 4 | no | — |
| 372 | C2×SD16 | — | 73 | 8 | no | — |
| 373 | C2×SD16 | — | 73 | 4 | no | — |
| 374 | C2×SD16 | — | 73 | 4 | no | — |
| 375 | C2×D8 | — | 73 | 4 | no | — |
| 376 | C2×M16 | — | 73 | 2 | no | — |
| 377 | C22×C8 | C22×D73 | 1 | 2 | yes | — |
| 378 | C4⋊Q8 | — | 2 | 2 | no | — |
| 379 | C4⋊Q8 | — | 73 | 4 | no | — |
| 380 | C4⋊Q8 | — | 73 | 1 | no | — |
| 381 | C4⋊Q8 | — | 73 | 1 | no | — |
| 382 | C4⋊Q8 | — | 146 | 4 | no | — |
| 383 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 384 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 385 | #127 | — | 73 | 1 | no | — |
| 386 | #127 | — | 73 | 1 | no | — |
| 387 | #126 | — | 146 | 4 | no | — |
| 388 | #126 | — | 146 | 4 | no | — |
| 389 | #125 | — | 2 | 2 | no | — |
| 390 | #125 | — | 146 | 4 | no | — |
| 391 | #125 | C22×D73 | 1 | 2 | yes | — |
| 392 | #125 | C22×D73 | 1 | 2 | yes | — |
| 393 | #124 | — | 73 | 4 | no | — |
| 394 | #124 | — | 73 | 2 | no | — |
| 395 | #124 | — | 73 | 2 | no | — |
| 396 | #123 | — | 146 | 8 | no | — |
| 397 | #123 | — | 146 | 4 | no | — |
| 398 | #123 | — | 146 | 4 | no | — |
| 399 | #123 | — | 146 | 4 | no | — |
| 400 | C22⋊Q8 | — | 73 | 4 | no | — |
| 401 | C22⋊Q8 | — | 146 | 8 | no | — |
| 402 | C22⋊Q8 | — | 146 | 2 | no | — |
| 403 | C22⋊Q8 | — | 146 | 4 | no | — |
| 404 | #121 | — | 73 | 4 | no | — |
| 405 | #121 | — | 146 | 4 | no | — |
| 406 | #121 | — | 146 | 4 | no | — |
| 407 | #121 | — | 146 | 2 | no | — |
| 408 | #121 | — | 146 | 4 | no | — |
| 409 | #121 | — | 146 | 2 | no | — |
| 410 | #121 | — | 146 | 2 | no | — |
| 411 | C4×Q8 | — | 73 | 2 | no | — |
| 412 | C4×Q8 | — | 73 | 4 | no | — |
| 413 | C4×D4 | — | 73 | 4 | no | — |
| 414 | C4×D4 | — | 73 | 4 | no | — |
| 415 | C4×D4 | — | 73 | 2 | no | — |
| 416 | C4×D4 | — | 146 | 4 | no | — |
| 417 | C4×D4 | — | 146 | 4 | no | — |
| 418 | C4×D4 | — | 146 | 4 | no | — |
| 419 | C4×D4 | — | 146 | 2 | no | — |
| 420 | C4×D4 | — | 146 | 2 | no | — |
| 421 | #117 | — | 73 | 1 | no | — |
| 422 | #117 | — | 73 | 2 | no | — |
| 423 | #117 | — | 146 | 4 | no | — |
| 424 | #117 | — | 146 | 2 | no | — |
| 425 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 426 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 427 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 428 | C2×C4⋊C4 | — | 146 | 4 | no | — |
| 429 | C2×C4⋊C4 | C22×D73 | 1 | 2 | yes | — |
| 430 | C2×C42 | — | 73 | 2 | no | — |
| 431 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 432 | C4⋊C8 | — | 73 | 8 | no | — |
| 433 | #103 | — | 73 | 8 | no | — |
| 434 | #103 | C22×D73 | 1 | 8 | yes | — |
| 435 | #103 | C22×D73 | 1 | 8 | yes | — |
| 436 | #102 | — | 73 | 8 | no | — |
| 437 | C22⋊C8 | — | 73 | 8 | no | — |
| 438 | #97 | — | 73 | 2 | no | — |
| 439 | #97 | C22×D73 | 1 | 2 | yes | — |
| 440 | #97 | C22×D73 | 1 | 2 | yes | — |
| 441 | C4×C8 | — | 73 | 2 | no | — |
| 442 | #41 | — | 292 | 16 | no | — |
| 443 | #41 | — | 292 | 8 | no | — |
| 444 | #41 | — | 292 | 8 | no | — |
| 445 | #41 | — | 146 | 8 | no | — |
| 446 | #41 | — | 146 | 8 | no | — |
| 447 | #41 | — | 146 | 4 | no | — |
| 448 | C2×Q8 | — | 2 | 2 | no | — |
| 449 | C2×Q8 | — | 2 | 8 | no | — |
| 450 | C2×Q8 | — | 292 | 8 | no | — |
| 451 | C2×Q8 | — | 292 | 8 | no | — |
| 452 | C2×Q8 | — | 73 | 1 | no | — |
| 453 | C2×Q8 | — | 73 | 2 | no | — |
| 454 | C2×Q8 | — | 73 | 2 | no | — |
| 455 | C2×Q8 | — | 146 | 4 | no | — |
| 456 | C2×Q8 | C23×D73 | 1 | 4 | yes | — |
| 457 | C2×D4 | — | 73 | 2 | no | — |
| 458 | C2×D4 | — | 73 | 1 | no | — |
| 459 | C2×D4 | — | 73 | 2 | no | — |
| 460 | C2×D4 | — | 73 | 2 | no | — |
| 461 | C2×D4 | — | 146 | 4 | no | — |
| 462 | C2×D4 | — | 146 | 4 | no | — |
| 463 | C2×D4 | — | 146 | 2 | no | — |
| 464 | C2×D4 | — | 146 | 2 | no | — |
| 465 | C2×D4 | — | 146 | 2 | no | — |
| 466 | C2×D4 | — | 146 | 2 | no | — |
| 467 | C22×C4 | — | 2 | 2 | no | — |
| 468 | C22×C4 | — | 2 | 2 | no | — |
| 469 | C22×C4 | — | 73 | 4 | no | — |
| 470 | C22×C4 | — | 73 | 2 | no | — |
| 471 | C22×C4 | — | 146 | 4 | no | — |
| 472 | C22×C4 | — | 146 | 4 | no | — |
| 473 | C22×C4 | — | 146 | 4 | no | — |
| 474 | C22×C4 | — | 146 | 2 | no | — |
| 475 | C22×C4 | — | 146 | 2 | no | — |
| 476 | C22×C4 | D4×D73 | 1 | 2 | yes | — |
| 477 | C22×C4 | C23×D73 | 1 | 1 | yes | characteristic |
| 478 | Q16 | — | 292 | 4 | no | — |
| 479 | Q16 | — | 292 | 8 | no | — |
| 480 | SD16 | — | 292 | 4 | no | — |
| 481 | SD16 | — | 292 | 4 | no | — |
| 482 | SD16 | — | 292 | 8 | no | — |
| 483 | D8 | — | 292 | 4 | no | — |
| 484 | M16 | — | 146 | 4 | no | — |
| 485 | C2×C8 | — | 2 | 4 | no | — |
| 486 | C2×C8 | — | 73 | 4 | no | — |
| 487 | C2×C8 | C23×D73 | 1 | 4 | yes | — |
| 488 | C4⋊C4 | — | 2 | 4 | no | — |
| 489 | C4⋊C4 | — | 2 | 4 | no | — |
| 490 | C4⋊C4 | — | 2 | 4 | no | — |
| 491 | C4⋊C4 | — | 2 | 4 | no | — |
| 492 | C4⋊C4 | — | 2 | 2 | no | — |
| 493 | C4⋊C4 | — | 73 | 4 | no | — |
| 494 | C4⋊C4 | — | 73 | 2 | no | — |
| 495 | C4⋊C4 | — | 146 | 4 | no | — |
| 496 | C4⋊C4 | — | 146 | 8 | no | — |
| 497 | C4⋊C4 | — | 146 | 4 | no | — |
| 498 | C4⋊C4 | — | 146 | 2 | no | — |
| 499 | C4⋊C4 | — | 146 | 2 | no | — |
| 500 | C4⋊C4 | C23×D73 | 1 | 4 | yes | — |
| 501 | C22⋊C4 | — | 73 | 2 | no | — |
| 502 | C22⋊C4 | — | 73 | 4 | no | — |
| 503 | C22⋊C4 | — | 146 | 4 | no | — |
| 504 | C22⋊C4 | — | 146 | 4 | no | — |
| 505 | C22⋊C4 | — | 146 | 8 | no | — |
| 506 | C22⋊C4 | — | 146 | 4 | no | — |
| 507 | C22⋊C4 | — | 146 | 2 | no | — |
| 508 | C22⋊C4 | — | 146 | 2 | no | — |
| 509 | C22⋊C4 | — | 146 | 4 | no | — |
| 510 | C42 | — | 73 | 4 | no | — |
| 511 | C42 | — | 73 | 2 | no | — |
| 512 | C42 | — | 146 | 4 | no | — |
| 513 | C42 | D4×D73 | 1 | 2 | yes | — |
| 514 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 515 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 516 | C23 | — | 73 | 2 | no | — |
| 517 | C23 | — | 146 | 2 | no | — |
| 518 | C23 | — | 146 | 2 | no | — |
| 519 | C23 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 520 | Q8 | — | 2 | 8 | no | — |
| 521 | Q8 | — | 4 | 4 | no | — |
| 522 | Q8 | — | 292 | 8 | no | — |
| 523 | Q8 | — | 146 | 4 | no | — |
| 524 | Q8 | — | 146 | 4 | no | — |
| 525 | Q8 | — | 146 | 2 | no | — |
| 526 | D4 | — | 292 | 4 | no | — |
| 527 | D4 | — | 292 | 8 | no | — |
| 528 | D4 | — | 292 | 4 | no | — |
| 529 | D4 | — | 292 | 4 | no | — |
| 530 | D4 | — | 584 | 2 | no | — |
| 531 | D4 | — | 584 | 4 | no | — |
| 532 | D4 | — | 146 | 4 | no | — |
| 533 | D4 | — | 146 | 2 | no | — |
| 534 | D4 | — | 146 | 4 | no | — |
| 535 | D4 | — | 146 | 4 | no | — |
| 536 | C2×C4 | — | 2 | 4 | no | — |
| 537 | C2×C4 | — | 2 | 4 | no | — |
| 538 | C2×C4 | — | 4 | 2 | no | — |
| 539 | C2×C4 | — | 4 | 4 | no | — |
| 540 | C2×C4 | — | 8 | 2 | no | — |
| 541 | C2×C4 | — | 292 | 4 | no | — |
| 542 | C2×C4 | — | 292 | 8 | no | — |
| 543 | C2×C4 | — | 292 | 8 | no | — |
| 544 | C2×C4 | — | 292 | 4 | no | — |
| 545 | C2×C4 | — | 292 | 4 | no | — |
| 546 | C2×C4 | — | 584 | 4 | no | — |
| 547 | C2×C4 | — | 73 | 4 | no | — |
| 548 | C2×C4 | — | 73 | 2 | no | — |
| 549 | C2×C4 | — | 146 | 2 | no | — |
| 550 | C2×C4 | — | 146 | 2 | no | — |
| 551 | C2×C4 | — | 146 | 4 | no | — |
| 552 | C2×C4 | C2×D4×D73 | 1 | 2 | yes | — |
| 553 | C2×C4 | C2×D4×D73 | 1 | 2 | yes | — |
| 554 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | #14556637 | 1 | 4 | yes | — |
| 556 | C2×C4 | C24×D73 | 1 | 1 | yes | characteristic |
| 557 | C8 | — | 2 | 4 | no | — |
| 558 | C8 | — | 146 | 4 | no | — |
| 559 | C22 | — | 2 | 2 | no | — |
| 560 | C22 | — | 292 | 2 | no | — |
| 561 | C22 | — | 292 | 2 | no | — |
| 562 | C22 | — | 292 | 2 | no | — |
| 563 | C22 | — | 292 | 4 | no | — |
| 564 | C22 | — | 292 | 2 | no | — |
| 565 | C22 | — | 146 | 2 | no | — |
| 566 | C22 | — | 146 | 4 | no | — |
| 567 | C22 | #17989155 | 1 | 2 | yes | — |
| 568 | C22 | C22×D4×D73 | 1 | 1 | yes | characteristic |
| 569 | C4 | — | 2 | 2 | no | — |
| 570 | C4 | — | 2 | 2 | no | — |
| 571 | C4 | — | 4 | 4 | no | — |
| 572 | C4 | — | 4 | 4 | no | — |
| 573 | C4 | — | 292 | 2 | no | — |
| 574 | C4 | — | 292 | 2 | no | — |
| 575 | C4 | — | 146 | 2 | no | — |
| 576 | C4 | — | 146 | 4 | no | — |
| 577 | C4 | #17989155 | 1 | 2 | yes | — |
| 578 | C4 | C2×#14556637 | 1 | 2 | yes | — |
| 579 | C2 | — | 2 | 2 | no | — |
| 580 | C2 | — | 292 | 2 | no | — |
| 581 | C2 | — | 584 | 2 | no | — |
| 582 | C2 | — | 584 | 2 | no | — |
| 583 | C2 | C2×#17989155 | 1 | 1 | yes | characteristic |
| 584 | C2 | #22624714 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22623855 | C2 | semidirect |
| 2. #22623714 | C2 | semidirect |
| 3. #22621015 | C2 | semidirect |
| 4. #22620993 | C2 | semidirect |
| 5. #22620971 | C2 | semidirect |
| 6. #22620959 | C2 | semidirect |
| 7. #22620388 | C2 | semidirect |
| 8. #22620377 | C2 | semidirect |
| 9. #22620334 | C2 | semidirect |
| 10. #22619486 | C2 | semidirect |
| 11. #22619251 | C2 | semidirect |
| 12. #22618580 | C2 | semidirect |
| 13. C2×#491×C73 | C2 | semidirect |
| 302. C2×#491 | D73 | semidirect |
| 306. C73 | #60831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623855 | 2 |
| #22623714 | 2 |
| #22621015 | 2 |
| #22620993 | 2 |
| #22620971 | 2 |
| #22620959 | 2 |
| #22620388 | 2 |
| #22620377 | 2 |
| #22620334 | 2 |
| #22619486 | 2 |
| #22619251 | 2 |
| #22618580 | 2 |
| C2×#491×C73 | 2 |
| #60831 | 73 |