Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1768 conjugacy classes of subgroups.
The subgroup lattice has 564 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22623843 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22621397 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22621071 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22621060 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22620884 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22620867 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22620838 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #22620669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22620491 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #22620206 | C2 | 1 | 8 | yes | maximal, complemented |
| 11 | #22618576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C73×#3185 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #17989309 | — | 2 | 2 | no | — |
| 14 | #17989300 | — | 2 | 2 | no | — |
| 15 | #17989293 | — | 2 | 2 | no | — |
| 16 | #17989290 | — | 2 | 2 | no | — |
| 17 | #17989281 | — | 2 | 2 | no | — |
| 18 | #17989249 | — | 2 | 2 | no | — |
| 19 | #17989247 | — | 2 | 2 | no | — |
| 20 | #17989239 | — | 2 | 2 | no | — |
| 21 | #17989210 | C22 | 1 | 4 | yes | — |
| 22 | #17989209 | C22 | 1 | 4 | yes | — |
| 23 | #17989167 | C22 | 1 | 4 | yes | — |
| 24 | #17989142 | C22 | 1 | 2 | yes | — |
| 25 | #17989138 | C22 | 1 | 2 | yes | — |
| 26 | #17989138 | C22 | 1 | 2 | yes | — |
| 27 | #17989137 | C22 | 1 | 2 | yes | — |
| 28 | C4⋊Q8×D73 | C22 | 1 | 2 | yes | — |
| 29 | #17989069 | C22 | 1 | 4 | yes | — |
| 30 | C4×#11924028 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17988985 | C22 | 1 | 1 | yes | characteristic |
| 32 | #17988983 | C22 | 1 | 2 | yes | — |
| 33 | #17988964 | C22 | 1 | 1 | yes | characteristic |
| 34 | #17988961 | C22 | 1 | 2 | yes | — |
| 35 | #17988937 | C22 | 1 | 2 | yes | — |
| 36 | #17988935 | C22 | 1 | 2 | yes | — |
| 37 | #17988934 | C22 | 1 | 2 | yes | — |
| 38 | #17988916 | C22 | 1 | 8 | yes | — |
| 39 | #17988907 | C22 | 1 | 8 | yes | — |
| 40 | #17988876 | C22 | 1 | 8 | yes | — |
| 41 | #17988870 | C22 | 1 | 8 | yes | — |
| 42 | #17988840 | C22 | 1 | 4 | yes | — |
| 43 | #17988818 | C22 | 1 | 8 | yes | — |
| 44 | #17988811 | C22 | 1 | 8 | yes | — |
| 45 | #17988805 | C22 | 1 | 8 | yes | — |
| 46 | #17988748 | C22 | 1 | 8 | yes | — |
| 47 | #17988735 | C22 | 1 | 8 | yes | — |
| 48 | #17988700 | C22 | 1 | 4 | yes | — |
| 49 | C4×#11924015 | C22 | 1 | 8 | yes | — |
| 50 | #17988649 | C22 | 1 | 4 | yes | — |
| 51 | #17988638 | C22 | 1 | 2 | yes | — |
| 52 | #17988638 | C22 | 1 | 2 | yes | — |
| 53 | #17988615 | C22 | 1 | 2 | yes | — |
| 54 | #17988555 | C22 | 1 | 2 | yes | — |
| 55 | C2×C4×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 56 | #533×C73 | C22 | 1 | 2 | yes | — |
| 57 | #498×C73 | C22 | 1 | 1 | yes | characteristic |
| 58 | #494×C73 | C22 | 1 | 1 | yes | characteristic |
| 59 | #487×C73 | C22 | 1 | 2 | yes | — |
| 60 | #470×C73 | C22 | 1 | 4 | yes | — |
| 61 | #441×C73 | C22 | 1 | 4 | yes | — |
| 62 | C4×M16×C73 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×#11924029 | — | 2 | 2 | no | — |
| 64 | C2×#11924029 | C23 | 1 | 4 | yes | — |
| 65 | C2×#11924028 | — | 2 | 2 | no | — |
| 66 | C2×#11924028 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×Q8×D73 | — | 2 | 2 | no | — |
| 68 | C2×#11924015 | C23 | 1 | 8 | yes | — |
| 69 | C2×D584 | C23 | 1 | 4 | yes | — |
| 70 | C22×#10596831 | C23 | 1 | 2 | yes | — |
| 71 | #14556591 | C23 | 1 | 2 | yes | — |
| 72 | #14556590 | — | 2 | 2 | no | — |
| 73 | #14556590 | C23 | 1 | 4 | yes | — |
| 74 | #14556589 | — | 2 | 2 | no | — |
| 75 | #14556588 | C23 | 1 | 2 | yes | — |
| 76 | #14556586 | — | 2 | 4 | no | — |
| 77 | #14556585 | — | 2 | 4 | no | — |
| 78 | #14556582 | — | 2 | 2 | no | — |
| 79 | #14556580 | — | 2 | 2 | no | — |
| 80 | #14556580 | C23 | 1 | 4 | yes | — |
| 81 | #14556579 | — | 2 | 4 | no | — |
| 82 | #14556579 | — | 2 | 2 | no | — |
| 83 | #14556577 | — | 2 | 4 | no | — |
| 84 | #14556576 | — | 2 | 4 | no | — |
| 85 | #14556573 | — | 2 | 4 | no | — |
| 86 | #14556571 | — | 2 | 2 | no | — |
| 87 | #14556571 | — | 2 | 4 | no | — |
| 88 | #14556569 | — | 2 | 4 | no | — |
| 89 | #14556569 | — | 2 | 4 | no | — |
| 90 | #14556567 | C23 | 1 | 4 | yes | — |
| 91 | #14556566 | — | 2 | 4 | no | — |
| 92 | #14556566 | — | 2 | 2 | no | — |
| 93 | #14556566 | — | 2 | 2 | no | — |
| 94 | #14556566 | — | 2 | 2 | no | — |
| 95 | #14556566 | C23 | 1 | 4 | yes | — |
| 96 | #14556565 | — | 2 | 2 | no | — |
| 97 | #14556565 | C23 | 1 | 4 | yes | — |
| 98 | #14556564 | — | 2 | 4 | no | — |
| 99 | #14556564 | — | 2 | 4 | no | — |
| 100 | Q8×Dic73 | C23 | 1 | 4 | yes | — |
| 101 | C4×Dic146 | D4 | 1 | 2 | yes | — |
| 102 | #14556556 | — | 2 | 2 | no | — |
| 103 | C4×D292 | — | 2 | 4 | no | — |
| 104 | C4×D292 | — | 2 | 2 | no | — |
| 105 | C4×D292 | D4 | 1 | 2 | yes | — |
| 106 | C4×D292 | C23 | 1 | 4 | yes | — |
| 107 | #14556553 | — | 2 | 4 | no | — |
| 108 | #14556553 | — | 2 | 2 | no | — |
| 109 | #14556553 | — | 2 | 2 | no | — |
| 110 | #14556553 | — | 2 | 2 | no | — |
| 111 | #14556553 | C23 | 1 | 4 | yes | — |
| 112 | C4×C22⋊D73 | D4 | 1 | 2 | yes | — |
| 113 | C4×C22⋊D73 | D4 | 1 | 2 | yes | — |
| 114 | #14556550 | C23 | 1 | 1 | yes | characteristic |
| 115 | #14556549 | — | 2 | 2 | no | — |
| 116 | #14556548 | — | 2 | 4 | no | — |
| 117 | #14556548 | C23 | 1 | 2 | yes | — |
| 118 | C4⋊C4×D73 | — | 2 | 2 | no | — |
| 119 | C4⋊C4×D73 | — | 2 | 4 | no | — |
| 120 | C4⋊C4×D73 | C23 | 1 | 4 | yes | — |
| 121 | C42×D73 | C23 | 1 | 2 | yes | — |
| 122 | #14556523 | C23 | 1 | 4 | yes | — |
| 123 | #14556522 | C23 | 1 | 8 | yes | — |
| 124 | #14556520 | C23 | 1 | 4 | yes | — |
| 125 | #14556520 | C23 | 1 | 4 | yes | — |
| 126 | #14556515 | C23 | 1 | 8 | yes | — |
| 127 | #14556513 | C23 | 1 | 8 | yes | — |
| 128 | #14556511 | C23 | 1 | 8 | yes | — |
| 129 | #14556503 | C23 | 1 | 4 | yes | — |
| 130 | #14556503 | C23 | 1 | 4 | yes | — |
| 131 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 132 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 133 | C2×Q16×C73 | C23 | 1 | 4 | yes | — |
| 134 | C2×M16×C73 | C23 | 1 | 2 | yes | — |
| 135 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 136 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 137 | #125×C73 | — | 2 | 2 | no | — |
| 138 | C22⋊Q8×C73 | — | 2 | 2 | no | — |
| 139 | C22⋊Q8×C73 | C23 | 1 | 4 | yes | — |
| 140 | C4×Q8×C73 | — | 2 | 2 | no | — |
| 141 | C4×Q8×C73 | C23 | 1 | 4 | yes | — |
| 142 | #117×C73 | — | 2 | 2 | no | — |
| 143 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 144 | #106×C73 | C23 | 1 | 4 | yes | — |
| 145 | #103×C73 | C23 | 1 | 8 | yes | — |
| 146 | #97×C73 | C23 | 1 | 2 | yes | — |
| 147 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 148 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 149 | #11924029 | — | 4 | 8 | no | — |
| 150 | #11924029 | — | 8 | 4 | no | — |
| 151 | #11924028 | — | 4 | 2 | no | — |
| 152 | #11924028 | — | 8 | 4 | no | — |
| 153 | C2×Dic146 | — | 2 | 2 | no | — |
| 154 | C2×Dic146 | — | 2 | 4 | no | — |
| 155 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | Q8×D73 | — | 8 | 4 | no | — |
| 157 | C2×D292 | — | 2 | 4 | no | — |
| 158 | C2×D292 | — | 2 | 2 | no | — |
| 159 | C2×D292 | — | 2 | 2 | no | — |
| 160 | C2×D292 | — | 2 | 4 | no | — |
| 161 | C2×D292 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×D292 | C24 | 1 | 4 | yes | — |
| 163 | C2×C22⋊D73 | — | 2 | 4 | no | — |
| 164 | C2×C22⋊D73 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×C4×D73 | — | 2 | 4 | no | — |
| 166 | C2×C4×D73 | — | 2 | 4 | no | — |
| 167 | C2×C4×D73 | — | 2 | 4 | no | — |
| 168 | C2×C4×D73 | — | 2 | 4 | no | — |
| 169 | C2×C4×D73 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C4×D73 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×C4×D73 | C24 | 1 | 2 | yes | — |
| 172 | #11924015 | — | 4 | 8 | no | — |
| 173 | D584 | — | 4 | 4 | no | — |
| 174 | C2×#10596831 | — | 4 | 2 | no | — |
| 175 | C2×#10596831 | C24 | 1 | 4 | yes | — |
| 176 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 177 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 178 | C4⋊Dic73 | C2×D4 | 1 | 2 | yes | — |
| 179 | C4⋊Dic73 | C24 | 1 | 4 | yes | — |
| 180 | #11924007 | — | 2 | 4 | no | — |
| 181 | #11924007 | — | 2 | 4 | no | — |
| 182 | #11924007 | — | 2 | 4 | no | — |
| 183 | #11924007 | C2×D4 | 1 | 2 | yes | — |
| 184 | #11924007 | C2×D4 | 1 | 2 | yes | — |
| 185 | C22⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C22⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | #11924005 | — | 2 | 4 | no | — |
| 188 | #11924005 | — | 2 | 4 | no | — |
| 189 | #11924005 | — | 2 | 4 | no | — |
| 190 | #11924005 | — | 2 | 4 | no | — |
| 191 | #11924005 | — | 2 | 4 | no | — |
| 192 | #11924005 | — | 2 | 4 | no | — |
| 193 | #11924005 | — | 2 | 4 | no | — |
| 194 | #11924005 | C2×D4 | 1 | 2 | yes | — |
| 195 | #11924005 | C2×D4 | 1 | 2 | yes | — |
| 196 | C4×Dic73 | — | 2 | 4 | no | — |
| 197 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 198 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 199 | C4×Dic73 | C24 | 1 | 2 | yes | — |
| 200 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 201 | C2×Q8×C73 | C24 | 1 | 4 | yes | — |
| 202 | C22×C4×C73 | C2×D4 | 1 | 2 | yes | — |
| 203 | C22×C4×C73 | C24 | 1 | 1 | yes | characteristic |
| 204 | Q16×C73 | — | 4 | 4 | no | — |
| 205 | M16×C73 | — | 4 | 2 | no | — |
| 206 | C2×C8×C73 | C24 | 1 | 2 | yes | — |
| 207 | C2×C8×C73 | C24 | 1 | 2 | yes | — |
| 208 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 209 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 210 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 211 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 212 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 213 | C4⋊C4×C73 | C24 | 1 | 4 | yes | — |
| 214 | C22⋊C4×C73 | — | 2 | 4 | no | — |
| 215 | C42×C73 | — | 2 | 4 | no | — |
| 216 | C42×C73 | C2×D4 | 1 | 2 | yes | — |
| 217 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 218 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 219 | C23×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 220 | C22×D73 | — | 2 | 4 | no | — |
| 221 | C22×D73 | C22×D4 | 1 | 2 | yes | — |
| 222 | Q8×C73 | — | 2 | 8 | no | — |
| 223 | Q8×C73 | — | 4 | 4 | no | — |
| 224 | C2×C4×C73 | — | 2 | 4 | no | — |
| 225 | C2×C4×C73 | — | 2 | 2 | no | — |
| 226 | C2×C4×C73 | — | 2 | 4 | no | — |
| 227 | C2×C4×C73 | — | 2 | 4 | no | — |
| 228 | C2×C4×C73 | C22×D4 | 1 | 2 | yes | — |
| 229 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C73 | C22×D4 | 1 | 2 | yes | — |
| 231 | C2×C4×C73 | C25 | 1 | 1 | yes | characteristic |
| 232 | C22⋊D73 | — | 4 | 2 | no | — |
| 233 | C22⋊D73 | — | 8 | 4 | no | — |
| 234 | C2×Dic73 | — | 2 | 4 | no | — |
| 235 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 236 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 237 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 238 | D292 | — | 2 | 8 | no | — |
| 239 | D292 | — | 4 | 1 | no | — |
| 240 | D292 | — | 4 | 8 | no | — |
| 241 | D292 | — | 4 | 4 | no | — |
| 242 | D292 | — | 4 | 4 | no | — |
| 243 | D292 | — | 8 | 4 | no | — |
| 244 | C4×D73 | — | 2 | 4 | no | — |
| 245 | C4×D73 | — | 2 | 4 | no | — |
| 246 | C4×D73 | — | 2 | 4 | no | — |
| 247 | C4×D73 | — | 4 | 8 | no | — |
| 248 | C4×D73 | — | 8 | 4 | no | — |
| 249 | C4×D73 | — | 8 | 4 | no | — |
| 250 | C4×D73 | — | 8 | 4 | no | — |
| 251 | Dic146 | — | 4 | 1 | no | — |
| 252 | Dic146 | — | 4 | 4 | no | — |
| 253 | Dic146 | — | 8 | 4 | no | — |
| 254 | C8×C73 | — | 2 | 2 | no | — |
| 255 | C8×C73 | — | 2 | 2 | no | — |
| 256 | #10596831 | — | 2 | 4 | no | — |
| 257 | C22×C73 | — | 2 | 1 | no | — |
| 258 | C22×C73 | — | 2 | 2 | no | — |
| 259 | C22×C73 | C23×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×D73 | — | 2 | 2 | no | — |
| 261 | C2×D73 | — | 2 | 2 | no | — |
| 262 | C2×D73 | — | 2 | 2 | no | — |
| 263 | C2×D73 | — | 4 | 4 | no | — |
| 264 | C2×D73 | — | 4 | 4 | no | — |
| 265 | C2×D73 | — | 4 | 4 | no | — |
| 266 | C4×C73 | — | 2 | 1 | no | — |
| 267 | C4×C73 | — | 2 | 2 | no | — |
| 268 | C4×C73 | — | 4 | 4 | no | — |
| 269 | C4×C73 | — | 4 | 4 | no | — |
| 270 | C4×C73 | #577 | 1 | 4 | yes | — |
| 271 | C4×C73 | #585 | 1 | 2 | yes | — |
| 272 | Dic73 | — | 2 | 2 | no | — |
| 273 | Dic73 | — | 2 | 2 | no | — |
| 274 | Dic73 | — | 2 | 2 | no | — |
| 275 | Dic73 | — | 4 | 4 | no | — |
| 276 | #61015 | — | 73 | 1 | no | maximal, Sylow |
| 277 | C2×C73 | — | 4 | 1 | no | — |
| 278 | C2×C73 | #3449 | 1 | 1 | yes | characteristic |
| 279 | C2×C73 | C2×#577 | 1 | 2 | yes | — |
| 280 | D73 | — | 4 | 2 | no | — |
| 281 | D73 | — | 8 | 4 | no | — |
| 282 | #3511 | — | 73 | 2 | no | — |
| 283 | #3263 | — | 73 | 4 | no | — |
| 284 | #3229 | — | 73 | 2 | no | — |
| 285 | #3227 | — | 73 | 2 | no | — |
| 286 | #3210 | — | 73 | 2 | no | — |
| 287 | #3207 | — | 73 | 2 | no | — |
| 288 | #3204 | — | 73 | 4 | no | — |
| 289 | #3185 | D73 | 1 | 1 | yes | characteristic, complemented |
| 290 | #3184 | — | 73 | 1 | no | — |
| 291 | #3167 | — | 73 | 2 | no | — |
| 292 | #3125 | — | 73 | 8 | no | — |
| 293 | #2922 | — | 73 | 1 | no | — |
| 294 | C73 | #61015 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 295 | #556 | — | 146 | 2 | no | — |
| 296 | #555 | — | 146 | 2 | no | — |
| 297 | #554 | — | 146 | 2 | no | — |
| 298 | #553 | — | 146 | 2 | no | — |
| 299 | #553 | — | 146 | 2 | no | — |
| 300 | #548 | — | 146 | 2 | no | — |
| 301 | #548 | — | 146 | 2 | no | — |
| 302 | #547 | — | 146 | 2 | no | — |
| 303 | #542 | — | 73 | 4 | no | — |
| 304 | #542 | — | 73 | 4 | no | — |
| 305 | #537 | — | 73 | 4 | no | — |
| 306 | #533 | — | 73 | 2 | no | — |
| 307 | #533 | C2×D73 | 1 | 2 | yes | — |
| 308 | #532 | — | 73 | 2 | no | — |
| 309 | #532 | — | 73 | 2 | no | — |
| 310 | #532 | — | 73 | 2 | no | — |
| 311 | C2×C4⋊Q8 | — | 73 | 2 | no | — |
| 312 | #520 | — | 73 | 4 | no | — |
| 313 | C4×#41 | — | 73 | 1 | no | — |
| 314 | #498 | — | 73 | 2 | no | — |
| 315 | #498 | — | 73 | 1 | no | — |
| 316 | #498 | C2×D73 | 1 | 1 | yes | characteristic |
| 317 | #494 | C2×D73 | 1 | 1 | yes | characteristic |
| 318 | #493 | — | 73 | 1 | no | — |
| 319 | #492 | — | 73 | 2 | no | — |
| 320 | #487 | — | 73 | 2 | no | — |
| 321 | #487 | C2×D73 | 1 | 2 | yes | — |
| 322 | #486 | — | 73 | 2 | no | — |
| 323 | #486 | — | 73 | 2 | no | — |
| 324 | #483 | — | 73 | 8 | no | — |
| 325 | #481 | — | 73 | 8 | no | — |
| 326 | #476 | — | 73 | 8 | no | — |
| 327 | #475 | — | 73 | 8 | no | — |
| 328 | #470 | C2×D73 | 1 | 4 | yes | — |
| 329 | #469 | — | 73 | 4 | no | — |
| 330 | #465 | — | 73 | 8 | no | — |
| 331 | #464 | — | 73 | 8 | no | — |
| 332 | #463 | — | 73 | 8 | no | — |
| 333 | #452 | — | 73 | 8 | no | — |
| 334 | #449 | — | 73 | 8 | no | — |
| 335 | #442 | — | 73 | 4 | no | — |
| 336 | #441 | C2×D73 | 1 | 4 | yes | — |
| 337 | C4×SD16 | — | 73 | 8 | no | — |
| 338 | #433 | — | 73 | 4 | no | — |
| 339 | #431 | — | 73 | 2 | no | — |
| 340 | #431 | — | 73 | 2 | no | — |
| 341 | #424 | — | 73 | 2 | no | — |
| 342 | #408 | — | 73 | 2 | no | — |
| 343 | C4×M16 | C2×D73 | 1 | 1 | yes | characteristic |
| 344 | C2×C4×C8 | — | 73 | 1 | no | — |
| 345 | C2×#41 | — | 73 | 1 | no | — |
| 346 | C2×#41 | — | 73 | 4 | no | — |
| 347 | C2×#41 | — | 146 | 2 | no | — |
| 348 | C2×#41 | — | 146 | 2 | no | — |
| 349 | C22×Q8 | — | 146 | 2 | no | — |
| 350 | C2×Q16 | C22×D73 | 1 | 4 | yes | — |
| 351 | C2×SD16 | — | 73 | 8 | no | — |
| 352 | C2×D8 | — | 73 | 4 | no | — |
| 353 | C2×M16 | C22×D73 | 1 | 2 | yes | — |
| 354 | C22×C8 | — | 73 | 2 | no | — |
| 355 | C4⋊Q8 | — | 73 | 4 | no | — |
| 356 | C4⋊Q8 | — | 73 | 2 | no | — |
| 357 | C4⋊Q8 | — | 146 | 2 | no | — |
| 358 | C4⋊Q8 | — | 146 | 2 | no | — |
| 359 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 360 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 361 | #127 | — | 73 | 2 | no | — |
| 362 | #126 | — | 146 | 4 | no | — |
| 363 | #126 | — | 146 | 4 | no | — |
| 364 | #125 | — | 2 | 2 | no | — |
| 365 | #125 | — | 146 | 2 | no | — |
| 366 | #124 | — | 73 | 4 | no | — |
| 367 | #124 | — | 146 | 4 | no | — |
| 368 | #124 | — | 146 | 2 | no | — |
| 369 | #124 | — | 146 | 4 | no | — |
| 370 | #124 | — | 146 | 2 | no | — |
| 371 | #123 | — | 146 | 4 | no | — |
| 372 | #123 | — | 146 | 4 | no | — |
| 373 | C22⋊Q8 | — | 2 | 2 | no | — |
| 374 | C22⋊Q8 | — | 73 | 4 | no | — |
| 375 | C22⋊Q8 | — | 146 | 4 | no | — |
| 376 | C22⋊Q8 | — | 146 | 4 | no | — |
| 377 | C22⋊Q8 | — | 146 | 2 | no | — |
| 378 | C22⋊Q8 | — | 146 | 4 | no | — |
| 379 | C22⋊Q8 | C22×D73 | 1 | 4 | yes | — |
| 380 | #121 | — | 73 | 4 | no | — |
| 381 | #121 | — | 73 | 4 | no | — |
| 382 | #121 | — | 146 | 4 | no | — |
| 383 | #121 | — | 146 | 4 | no | — |
| 384 | #121 | — | 146 | 2 | no | — |
| 385 | #121 | — | 146 | 2 | no | — |
| 386 | #121 | — | 146 | 2 | no | — |
| 387 | #121 | — | 146 | 4 | no | — |
| 388 | #121 | — | 146 | 2 | no | — |
| 389 | C4×Q8 | — | 2 | 2 | no | — |
| 390 | C4×Q8 | — | 73 | 2 | no | — |
| 391 | C4×Q8 | — | 73 | 4 | no | — |
| 392 | C4×Q8 | — | 146 | 2 | no | — |
| 393 | C4×Q8 | C22×D73 | 1 | 4 | yes | — |
| 394 | C4×D4 | — | 73 | 2 | no | — |
| 395 | C4×D4 | — | 73 | 2 | no | — |
| 396 | C4×D4 | — | 73 | 4 | no | — |
| 397 | C4×D4 | — | 73 | 2 | no | — |
| 398 | C4×D4 | — | 73 | 4 | no | — |
| 399 | C4×D4 | — | 146 | 4 | no | — |
| 400 | C4×D4 | — | 146 | 2 | no | — |
| 401 | C4×D4 | — | 146 | 2 | no | — |
| 402 | C4×D4 | — | 146 | 2 | no | — |
| 403 | C4×D4 | — | 146 | 4 | no | — |
| 404 | C4×D4 | — | 146 | 2 | no | — |
| 405 | #117 | — | 2 | 2 | no | — |
| 406 | #117 | — | 73 | 1 | no | — |
| 407 | #117 | — | 73 | 2 | no | — |
| 408 | #117 | — | 146 | 4 | no | — |
| 409 | #117 | — | 146 | 2 | no | — |
| 410 | C2×C4⋊C4 | — | 73 | 4 | no | — |
| 411 | C2×C4⋊C4 | — | 146 | 4 | no | — |
| 412 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 413 | C2×C42 | — | 73 | 2 | no | — |
| 414 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 415 | #106 | — | 73 | 4 | no | — |
| 416 | #106 | — | 73 | 8 | no | — |
| 417 | #106 | C22×D73 | 1 | 4 | yes | — |
| 418 | C4⋊C8 | — | 73 | 4 | no | — |
| 419 | C4⋊C8 | — | 73 | 4 | no | — |
| 420 | #103 | — | 73 | 8 | no | — |
| 421 | #103 | C22×D73 | 1 | 8 | yes | — |
| 422 | #102 | — | 73 | 8 | no | — |
| 423 | #102 | — | 73 | 8 | no | — |
| 424 | C22⋊C8 | — | 73 | 4 | no | — |
| 425 | C22⋊C8 | — | 73 | 4 | no | — |
| 426 | #97 | C22×D73 | 1 | 2 | yes | — |
| 427 | C4×C8 | — | 73 | 2 | no | — |
| 428 | C4×C8 | — | 73 | 2 | no | — |
| 429 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 430 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 431 | #41 | — | 292 | 2 | no | — |
| 432 | #41 | — | 292 | 8 | no | — |
| 433 | #41 | — | 584 | 4 | no | — |
| 434 | #41 | — | 584 | 4 | no | — |
| 435 | C2×Q8 | — | 2 | 2 | no | — |
| 436 | C2×Q8 | — | 584 | 4 | no | — |
| 437 | C2×Q8 | — | 73 | 1 | no | — |
| 438 | C2×Q8 | — | 146 | 4 | no | — |
| 439 | C2×Q8 | — | 146 | 2 | no | — |
| 440 | C2×Q8 | C23×D73 | 1 | 4 | yes | — |
| 441 | C2×D4 | — | 73 | 2 | no | — |
| 442 | C2×D4 | — | 73 | 1 | no | — |
| 443 | C2×D4 | — | 73 | 4 | no | — |
| 444 | C2×D4 | — | 146 | 4 | no | — |
| 445 | C2×D4 | — | 146 | 4 | no | — |
| 446 | C2×D4 | — | 146 | 4 | no | — |
| 447 | C2×D4 | — | 146 | 2 | no | — |
| 448 | C2×D4 | — | 146 | 2 | no | — |
| 449 | C22×C4 | — | 73 | 2 | no | — |
| 450 | C22×C4 | — | 73 | 2 | no | — |
| 451 | C22×C4 | — | 73 | 2 | no | — |
| 452 | C22×C4 | — | 146 | 4 | no | — |
| 453 | C22×C4 | — | 146 | 4 | no | — |
| 454 | C22×C4 | — | 146 | 4 | no | — |
| 455 | C22×C4 | — | 146 | 4 | no | — |
| 456 | C22×C4 | D4×D73 | 1 | 2 | yes | — |
| 457 | C22×C4 | C23×D73 | 1 | 1 | yes | characteristic |
| 458 | Q16 | — | 4 | 4 | no | — |
| 459 | SD16 | — | 292 | 8 | no | — |
| 460 | D8 | — | 292 | 4 | no | — |
| 461 | M16 | — | 4 | 2 | no | — |
| 462 | C2×C8 | — | 292 | 2 | no | — |
| 463 | C2×C8 | — | 73 | 4 | no | — |
| 464 | C2×C8 | C23×D73 | 1 | 2 | yes | — |
| 465 | C2×C8 | C23×D73 | 1 | 2 | yes | — |
| 466 | C4⋊C4 | — | 2 | 2 | no | — |
| 467 | C4⋊C4 | — | 2 | 4 | no | — |
| 468 | C4⋊C4 | — | 2 | 2 | no | — |
| 469 | C4⋊C4 | — | 2 | 2 | no | — |
| 470 | C4⋊C4 | — | 2 | 4 | no | — |
| 471 | C4⋊C4 | — | 73 | 2 | no | — |
| 472 | C4⋊C4 | — | 73 | 2 | no | — |
| 473 | C4⋊C4 | — | 73 | 2 | no | — |
| 474 | C4⋊C4 | — | 73 | 4 | no | — |
| 475 | C4⋊C4 | — | 146 | 4 | no | — |
| 476 | C4⋊C4 | — | 146 | 4 | no | — |
| 477 | C4⋊C4 | — | 146 | 4 | no | — |
| 478 | C4⋊C4 | — | 146 | 4 | no | — |
| 479 | C4⋊C4 | — | 146 | 2 | no | — |
| 480 | C4⋊C4 | C23×D73 | 1 | 4 | yes | — |
| 481 | C22⋊C4 | — | 2 | 4 | no | — |
| 482 | C22⋊C4 | — | 73 | 1 | no | — |
| 483 | C22⋊C4 | — | 73 | 1 | no | — |
| 484 | C22⋊C4 | — | 73 | 2 | no | — |
| 485 | C22⋊C4 | — | 73 | 2 | no | — |
| 486 | C22⋊C4 | — | 146 | 4 | no | — |
| 487 | C22⋊C4 | — | 146 | 4 | no | — |
| 488 | C22⋊C4 | — | 146 | 4 | no | — |
| 489 | C22⋊C4 | — | 146 | 4 | no | — |
| 490 | C22⋊C4 | — | 146 | 4 | no | — |
| 491 | C22⋊C4 | — | 146 | 4 | no | — |
| 492 | C22⋊C4 | — | 146 | 4 | no | — |
| 493 | C42 | — | 2 | 4 | no | — |
| 494 | C42 | — | 73 | 2 | no | — |
| 495 | C42 | — | 73 | 2 | no | — |
| 496 | C42 | — | 73 | 2 | no | — |
| 497 | C42 | — | 146 | 4 | no | — |
| 498 | C42 | D4×D73 | 1 | 2 | yes | — |
| 499 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 500 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 501 | C23 | — | 73 | 2 | no | — |
| 502 | C23 | — | 146 | 4 | no | — |
| 503 | C23 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 504 | Q8 | — | 2 | 8 | no | — |
| 505 | Q8 | — | 4 | 4 | no | — |
| 506 | Q8 | — | 292 | 1 | no | — |
| 507 | Q8 | — | 292 | 4 | no | — |
| 508 | Q8 | — | 584 | 4 | no | — |
| 509 | D4 | — | 292 | 1 | no | — |
| 510 | D4 | — | 292 | 8 | no | — |
| 511 | D4 | — | 292 | 2 | no | — |
| 512 | D4 | — | 292 | 4 | no | — |
| 513 | D4 | — | 292 | 4 | no | — |
| 514 | D4 | — | 584 | 4 | no | — |
| 515 | D4 | — | 584 | 4 | no | — |
| 516 | D4 | — | 146 | 8 | no | — |
| 517 | C2×C4 | — | 2 | 4 | no | — |
| 518 | C2×C4 | — | 2 | 2 | no | — |
| 519 | C2×C4 | — | 2 | 4 | no | — |
| 520 | C2×C4 | — | 2 | 4 | no | — |
| 521 | C2×C4 | — | 292 | 8 | no | — |
| 522 | C2×C4 | — | 584 | 4 | no | — |
| 523 | C2×C4 | — | 584 | 4 | no | — |
| 524 | C2×C4 | — | 584 | 4 | no | — |
| 525 | C2×C4 | — | 73 | 2 | no | — |
| 526 | C2×C4 | — | 73 | 2 | no | — |
| 527 | C2×C4 | — | 73 | 2 | no | — |
| 528 | C2×C4 | — | 146 | 4 | no | — |
| 529 | C2×C4 | — | 146 | 4 | no | — |
| 530 | C2×C4 | — | 146 | 4 | no | — |
| 531 | C2×C4 | — | 146 | 4 | no | — |
| 532 | C2×C4 | C2×D4×D73 | 1 | 2 | yes | — |
| 533 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 534 | C2×C4 | C2×D4×D73 | 1 | 2 | yes | — |
| 535 | C2×C4 | C24×D73 | 1 | 1 | yes | characteristic |
| 536 | C8 | — | 2 | 2 | no | — |
| 537 | C8 | — | 2 | 2 | no | — |
| 538 | C8 | — | 146 | 4 | no | — |
| 539 | C22 | — | 2 | 1 | no | — |
| 540 | C22 | — | 2 | 2 | no | — |
| 541 | C22 | — | 292 | 4 | no | — |
| 542 | C22 | — | 292 | 4 | no | — |
| 543 | C22 | — | 292 | 4 | no | — |
| 544 | C22 | — | 146 | 2 | no | — |
| 545 | C22 | — | 146 | 2 | no | — |
| 546 | C22 | — | 146 | 2 | no | — |
| 547 | C22 | C22×D4×D73 | 1 | 1 | yes | characteristic |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 2 | 2 | no | — |
| 550 | C4 | — | 4 | 4 | no | — |
| 551 | C4 | — | 4 | 4 | no | — |
| 552 | C4 | — | 292 | 4 | no | — |
| 553 | C4 | — | 146 | 2 | no | — |
| 554 | C4 | — | 146 | 2 | no | — |
| 555 | C4 | — | 146 | 2 | no | — |
| 556 | C4 | #17989396 | 1 | 4 | yes | — |
| 557 | C4 | #17989423 | 1 | 2 | yes | — |
| 558 | C2 | — | 4 | 1 | no | — |
| 559 | C2 | — | 292 | 2 | no | — |
| 560 | C2 | — | 584 | 4 | no | — |
| 561 | C2 | #22623258 | 1 | 1 | yes | characteristic |
| 562 | C2 | C2×#17989396 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22623843 | C2 | semidirect |
| 2. #22621397 | C2 | semidirect |
| 3. #22621071 | C2 | semidirect |
| 4. #22621060 | C2 | semidirect |
| 5. #22620884 | C2 | semidirect |
| 6. #22620867 | C2 | semidirect |
| 7. #22620838 | C2 | semidirect |
| 8. #22620669 | C2 | semidirect |
| 9. #22620491 | C2 | semidirect |
| 10. #22620206 | C2 | semidirect |
| 11. #22618576 | C2 | semidirect |
| 12. C73×#3185 | C2 | semidirect |
| 289. #3185 | D73 | semidirect |
| 294. C73 | #61015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623843 | 2 |
| #22621397 | 2 |
| #22621071 | 2 |
| #22621060 | 2 |
| #22620884 | 2 |
| #22620867 | 2 |
| #22620838 | 2 |
| #22620669 | 2 |
| #22620491 | 2 |
| #22620206 | 2 |
| #22618576 | 2 |
| C73×#3185 | 2 |
| #61015 | 73 |