Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
730 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22626229 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22626227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D73⋊#356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22625979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22625978 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22625937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22624270 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989655 | C22 | 1 | 1 | yes | characteristic |
| 9 | #17989586 | — | 2 | 1 | no | — |
| 10 | #17989585 | — | 2 | 1 | no | — |
| 11 | #17989580 | — | 2 | 1 | no | — |
| 12 | D73⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 13 | D73⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 14 | D73⋊#101 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17989498 | — | 2 | 1 | no | — |
| 16 | #17989498 | — | 2 | 1 | no | — |
| 17 | #17989497 | — | 2 | 1 | no | — |
| 18 | #17989497 | — | 2 | 1 | no | — |
| 19 | #17989496 | — | 2 | 1 | no | — |
| 20 | #17989495 | — | 2 | 1 | no | — |
| 21 | #17989458 | — | 2 | 1 | no | — |
| 22 | #17989454 | — | 2 | 1 | no | — |
| 23 | #17989454 | — | 2 | 1 | no | — |
| 24 | #17989339 | — | 2 | 1 | no | — |
| 25 | #17989336 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #17989317 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #17989299 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #17989291 | — | 2 | 1 | no | — |
| 29 | #17989273 | — | 2 | 1 | no | — |
| 30 | #17989269 | — | 2 | 1 | no | — |
| 31 | #17989239 | — | 2 | 1 | no | — |
| 32 | #17989235 | — | 2 | 1 | no | — |
| 33 | #17989217 | — | 2 | 1 | no | — |
| 34 | #17989216 | — | 2 | 1 | no | — |
| 35 | #17989205 | — | 2 | 1 | no | — |
| 36 | #17989203 | — | 2 | 1 | no | — |
| 37 | #17989162 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17989160 | — | 2 | 1 | no | — |
| 39 | #17989157 | C22 | 1 | 1 | yes | characteristic |
| 40 | C4⋊Q8×D73 | C22 | 1 | 1 | yes | characteristic |
| 41 | #17989120 | — | 2 | 1 | no | — |
| 42 | #563×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | D73⋊M16 | — | 2 | 1 | no | — |
| 44 | D73⋊M16 | — | 2 | 1 | no | — |
| 45 | D73⋊M16 | — | 2 | 1 | no | — |
| 46 | Q8×#64408 | — | 4 | 2 | no | — |
| 47 | #14556670 | — | 2 | 1 | no | — |
| 48 | #14556670 | — | 2 | 1 | no | — |
| 49 | #14556670 | — | 2 | 1 | no | — |
| 50 | #14556656 | — | 4 | 2 | no | — |
| 51 | #14556655 | — | 4 | 2 | no | — |
| 52 | #14556654 | — | 4 | 2 | no | — |
| 53 | #14556652 | — | 2 | 1 | no | — |
| 54 | #14556652 | — | 2 | 1 | no | — |
| 55 | #14556652 | — | 2 | 1 | no | — |
| 56 | #14556652 | — | 2 | 1 | no | — |
| 57 | #14556652 | — | 2 | 1 | no | — |
| 58 | #14556652 | — | 2 | 1 | no | — |
| 59 | C2×#11924029 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×#11924028 | — | 2 | 1 | no | — |
| 61 | C2×#11924027 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×Q8×D73 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×Q8×D73 | C23 | 1 | 1 | yes | characteristic |
| 64 | #14556591 | D4 | 1 | 1 | yes | characteristic |
| 65 | #14556591 | D4 | 1 | 1 | yes | characteristic |
| 66 | #14556590 | — | 2 | 1 | no | — |
| 67 | #14556590 | — | 2 | 1 | no | — |
| 68 | #14556590 | — | 2 | 1 | no | — |
| 69 | #14556590 | — | 2 | 1 | no | — |
| 70 | #14556590 | — | 2 | 1 | no | — |
| 71 | #14556589 | — | 2 | 1 | no | — |
| 72 | #14556589 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #14556589 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #14556589 | D4 | 1 | 1 | yes | characteristic |
| 75 | #14556589 | D4 | 1 | 1 | yes | characteristic |
| 76 | #14556586 | — | 2 | 1 | no | — |
| 77 | #14556586 | — | 2 | 1 | no | — |
| 78 | #14556585 | — | 2 | 1 | no | — |
| 79 | #14556584 | — | 2 | 1 | no | — |
| 80 | #14556582 | — | 2 | 1 | no | — |
| 81 | #14556581 | — | 2 | 1 | no | — |
| 82 | #14556581 | — | 2 | 1 | no | — |
| 83 | #14556581 | — | 2 | 1 | no | — |
| 84 | #14556581 | — | 2 | 1 | no | — |
| 85 | #14556581 | — | 2 | 1 | no | — |
| 86 | #14556580 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #14556579 | D4 | 1 | 1 | yes | characteristic |
| 88 | #14556578 | D4 | 1 | 1 | yes | characteristic |
| 89 | #14556577 | — | 2 | 1 | no | — |
| 90 | #14556577 | — | 2 | 1 | no | — |
| 91 | #14556577 | — | 2 | 1 | no | — |
| 92 | #14556576 | — | 2 | 1 | no | — |
| 93 | #14556576 | — | 2 | 1 | no | — |
| 94 | #14556576 | — | 2 | 1 | no | — |
| 95 | #14556576 | — | 2 | 1 | no | — |
| 96 | #14556575 | — | 2 | 1 | no | — |
| 97 | #14556573 | — | 2 | 1 | no | — |
| 98 | #14556573 | — | 2 | 1 | no | — |
| 99 | #14556573 | — | 2 | 1 | no | — |
| 100 | #14556573 | — | 2 | 1 | no | — |
| 101 | #14556571 | — | 2 | 1 | no | — |
| 102 | #14556571 | — | 2 | 1 | no | — |
| 103 | #14556570 | — | 2 | 1 | no | — |
| 104 | #14556569 | — | 2 | 1 | no | — |
| 105 | #14556569 | — | 2 | 1 | no | — |
| 106 | #14556569 | — | 2 | 1 | no | — |
| 107 | #14556569 | — | 2 | 1 | no | — |
| 108 | #14556569 | — | 2 | 1 | no | — |
| 109 | #14556568 | — | 2 | 1 | no | — |
| 110 | #14556568 | — | 2 | 1 | no | — |
| 111 | #14556568 | — | 2 | 1 | no | — |
| 112 | #14556568 | — | 2 | 1 | no | — |
| 113 | #14556567 | — | 2 | 1 | no | — |
| 114 | #14556564 | — | 2 | 1 | no | — |
| 115 | #14556564 | — | 2 | 1 | no | — |
| 116 | #14556563 | — | 2 | 1 | no | — |
| 117 | C4×Dic146 | — | 2 | 1 | no | — |
| 118 | #14556556 | — | 2 | 1 | no | — |
| 119 | #14556556 | — | 2 | 1 | no | — |
| 120 | #14556553 | — | 2 | 1 | no | — |
| 121 | C4×C22⋊D73 | — | 2 | 1 | no | — |
| 122 | #14556551 | — | 2 | 1 | no | — |
| 123 | #14556551 | — | 2 | 1 | no | — |
| 124 | #14556551 | — | 2 | 1 | no | — |
| 125 | #14556549 | — | 2 | 1 | no | — |
| 126 | #14556549 | — | 2 | 1 | no | — |
| 127 | #14556548 | — | 2 | 1 | no | — |
| 128 | #14556548 | D4 | 1 | 1 | yes | characteristic |
| 129 | #14556548 | D4 | 1 | 1 | yes | characteristic |
| 130 | #14556547 | — | 2 | 1 | no | — |
| 131 | #14556547 | — | 2 | 1 | no | — |
| 132 | C2×#11924007 | — | 2 | 1 | no | — |
| 133 | C4⋊C4×D73 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×D73 | — | 2 | 1 | no | — |
| 135 | C4⋊C4×D73 | — | 2 | 1 | no | — |
| 136 | C42×D73 | D4 | 1 | 1 | yes | characteristic |
| 137 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 138 | C4⋊Q8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 139 | #126×C73 | — | 2 | 1 | no | — |
| 140 | #126×C73 | — | 2 | 1 | no | — |
| 141 | #125×C73 | — | 2 | 1 | no | — |
| 142 | #124×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 143 | #123×C73 | — | 2 | 1 | no | — |
| 144 | C22⋊Q8×C73 | — | 2 | 1 | no | — |
| 145 | C22⋊Q8×C73 | — | 2 | 1 | no | — |
| 146 | #11924038 | — | 4 | 1 | no | — |
| 147 | #11924038 | — | 4 | 1 | no | — |
| 148 | #11924038 | — | 4 | 1 | no | — |
| 149 | #11924037 | — | 4 | 1 | no | — |
| 150 | #11924037 | — | 4 | 1 | no | — |
| 151 | #11924037 | — | 4 | 1 | no | — |
| 152 | #11924036 | — | 4 | 1 | no | — |
| 153 | #11924036 | — | 4 | 1 | no | — |
| 154 | #11924036 | — | 4 | 1 | no | — |
| 155 | C4⋊#64408 | — | 2 | 2 | no | — |
| 156 | C4⋊#64408 | — | 4 | 1 | no | — |
| 157 | C4⋊#64408 | — | 4 | 1 | no | — |
| 158 | C22⋊#64408 | — | 4 | 1 | no | — |
| 159 | C4×#64408 | — | 2 | 2 | no | — |
| 160 | C4×#64408 | — | 2 | 2 | no | — |
| 161 | C4×#64408 | — | 4 | 1 | no | — |
| 162 | #11924029 | — | 4 | 1 | no | — |
| 163 | #11924029 | — | 4 | 1 | no | — |
| 164 | #11924028 | — | 8 | 1 | no | — |
| 165 | #11924028 | — | 8 | 1 | no | — |
| 166 | #11924027 | — | 4 | 1 | no | — |
| 167 | #11924027 | — | 4 | 1 | no | — |
| 168 | C2×Dic146 | — | 2 | 1 | no | — |
| 169 | C2×Dic146 | — | 2 | 1 | no | — |
| 170 | C2×Dic146 | — | 2 | 1 | no | — |
| 171 | C2×Dic146 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C2×Dic146 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | Q8×D73 | — | 4 | 1 | no | — |
| 177 | Q8×D73 | — | 4 | 1 | no | — |
| 178 | Q8×D73 | — | 4 | 1 | no | — |
| 179 | Q8×D73 | — | 4 | 1 | no | — |
| 180 | C2×D292 | — | 2 | 1 | no | — |
| 181 | C2×D292 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 183 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 184 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 185 | C22×Dic73 | — | 2 | 1 | no | — |
| 186 | C22×Dic73 | — | 2 | 1 | no | — |
| 187 | C2×C4×D73 | — | 2 | 1 | no | — |
| 188 | C2×C4×D73 | — | 2 | 1 | no | — |
| 189 | C2×C4×D73 | — | 2 | 1 | no | — |
| 190 | C2×C4×D73 | — | 2 | 1 | no | — |
| 191 | C2×C4×D73 | — | 2 | 1 | no | — |
| 192 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 196 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 197 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 198 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 199 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 200 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 201 | #11924007 | — | 2 | 1 | no | — |
| 202 | #11924007 | — | 2 | 1 | no | — |
| 203 | #11924007 | — | 2 | 1 | no | — |
| 204 | #11924007 | — | 2 | 1 | no | — |
| 205 | #11924007 | — | 2 | 1 | no | — |
| 206 | #11924007 | — | 2 | 1 | no | — |
| 207 | #11924007 | — | 2 | 1 | no | — |
| 208 | #11924007 | — | 2 | 1 | no | — |
| 209 | #11924007 | — | 2 | 1 | no | — |
| 210 | #11924007 | — | 2 | 1 | no | — |
| 211 | #11924007 | — | 2 | 1 | no | — |
| 212 | #11924007 | — | 2 | 1 | no | — |
| 213 | #11924007 | — | 2 | 1 | no | — |
| 214 | #11924007 | — | 2 | 1 | no | — |
| 215 | #11924007 | — | 2 | 1 | no | — |
| 216 | #11924007 | — | 2 | 1 | no | — |
| 217 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 218 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 219 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 220 | #11924005 | — | 2 | 1 | no | — |
| 221 | #11924005 | — | 2 | 1 | no | — |
| 222 | #11924005 | — | 2 | 1 | no | — |
| 223 | #11924005 | — | 2 | 1 | no | — |
| 224 | #11924005 | — | 2 | 1 | no | — |
| 225 | #11924005 | — | 2 | 1 | no | — |
| 226 | #11924005 | — | 2 | 1 | no | — |
| 227 | #11924005 | — | 2 | 1 | no | — |
| 228 | #11924005 | — | 2 | 1 | no | — |
| 229 | #11924005 | — | 2 | 1 | no | — |
| 230 | C4×Dic73 | — | 2 | 1 | no | — |
| 231 | C4×Dic73 | — | 2 | 1 | no | — |
| 232 | C4×Dic73 | — | 2 | 1 | no | — |
| 233 | C4×Dic73 | — | 2 | 1 | no | — |
| 234 | C4×Dic73 | — | 2 | 1 | no | — |
| 235 | C4×Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 236 | C4×Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 237 | C4×Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 238 | C2×Q8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 239 | C2×Q8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 240 | C2×Q8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 241 | C2×D4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 242 | C22×C4×C73 | — | 2 | 1 | no | — |
| 243 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 244 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 245 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 246 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 247 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 248 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 249 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 250 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 251 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 252 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 253 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 254 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 255 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 256 | C42×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 257 | C42×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 258 | C42×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C23×C73 | — | 2 | 1 | no | — |
| 260 | C22×D73 | — | 2 | 1 | no | — |
| 261 | C22×D73 | #120 | 1 | 1 | yes | characteristic |
| 262 | C2×#64408 | — | 4 | 2 | no | — |
| 263 | Q8×C73 | — | 4 | 1 | no | — |
| 264 | Q8×C73 | — | 4 | 1 | no | — |
| 265 | Q8×C73 | — | 4 | 1 | no | — |
| 266 | D4×C73 | — | 4 | 1 | no | — |
| 267 | C2×C4×C73 | — | 2 | 1 | no | — |
| 268 | C2×C4×C73 | — | 2 | 1 | no | — |
| 269 | C2×C4×C73 | — | 2 | 1 | no | — |
| 270 | C2×C4×C73 | — | 2 | 1 | no | — |
| 271 | C2×C4×C73 | — | 2 | 1 | no | — |
| 272 | C2×C4×C73 | — | 8 | 1 | no | — |
| 273 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 275 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 276 | C22⋊D73 | — | 4 | 2 | no | — |
| 277 | C22⋊D73 | — | 4 | 1 | no | — |
| 278 | C22⋊D73 | — | 4 | 1 | no | — |
| 279 | C22⋊D73 | — | 8 | 1 | no | — |
| 280 | C2×Dic73 | — | 2 | 1 | no | — |
| 281 | C2×Dic73 | — | 2 | 1 | no | — |
| 282 | C2×Dic73 | — | 2 | 1 | no | — |
| 283 | C2×Dic73 | — | 2 | 1 | no | — |
| 284 | C2×Dic73 | — | 2 | 1 | no | — |
| 285 | C2×Dic73 | — | 4 | 2 | no | — |
| 286 | C2×Dic73 | — | 8 | 1 | no | — |
| 287 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 288 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 289 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 290 | D292 | — | 4 | 1 | no | — |
| 291 | D292 | — | 4 | 1 | no | — |
| 292 | D292 | — | 4 | 1 | no | — |
| 293 | C4×D73 | — | 2 | 1 | no | — |
| 294 | C4×D73 | — | 2 | 1 | no | — |
| 295 | C4×D73 | — | 2 | 1 | no | — |
| 296 | C4×D73 | — | 2 | 1 | no | — |
| 297 | C4×D73 | — | 2 | 1 | no | — |
| 298 | C4×D73 | — | 2 | 1 | no | — |
| 299 | C4×D73 | — | 4 | 2 | no | — |
| 300 | C4×D73 | — | 4 | 2 | no | — |
| 301 | C4×D73 | — | 4 | 1 | no | — |
| 302 | C4×D73 | — | 4 | 1 | no | — |
| 303 | C4×D73 | — | 8 | 1 | no | — |
| 304 | C4×D73 | — | 8 | 1 | no | — |
| 305 | Dic146 | — | 4 | 1 | no | — |
| 306 | Dic146 | — | 4 | 1 | no | — |
| 307 | Dic146 | — | 4 | 1 | no | — |
| 308 | Dic146 | — | 4 | 2 | no | — |
| 309 | Dic146 | — | 4 | 1 | no | — |
| 310 | Dic146 | — | 4 | 1 | no | — |
| 311 | Dic146 | — | 8 | 1 | no | — |
| 312 | Dic146 | — | 8 | 1 | no | — |
| 313 | #10596833 | — | 8 | 1 | no | — |
| 314 | #10596833 | — | 8 | 1 | no | — |
| 315 | #10596833 | — | 8 | 1 | no | — |
| 316 | C22×C73 | — | 4 | 1 | no | — |
| 317 | C22×C73 | — | 4 | 1 | no | — |
| 318 | C22×C73 | — | 4 | 1 | no | — |
| 319 | C22×C73 | #379 | 1 | 1 | yes | characteristic |
| 320 | C2×D73 | — | 4 | 1 | no | — |
| 321 | C2×D73 | — | 4 | 1 | no | — |
| 322 | C2×D73 | — | 4 | 1 | no | — |
| 323 | C2×D73 | — | 4 | 1 | no | — |
| 324 | C2×D73 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 325 | C2×D73 | #458 | 1 | 1 | yes | characteristic |
| 326 | #64408 | — | 8 | 2 | no | — |
| 327 | C4×C73 | — | 2 | 1 | no | — |
| 328 | C4×C73 | — | 2 | 1 | no | — |
| 329 | C4×C73 | — | 2 | 1 | no | — |
| 330 | C4×C73 | — | 4 | 1 | no | — |
| 331 | C4×C73 | — | 4 | 1 | no | — |
| 332 | C4×C73 | — | 4 | 1 | no | — |
| 333 | C4×C73 | — | 4 | 1 | no | — |
| 334 | C4×C73 | — | 4 | 1 | no | — |
| 335 | Dic73 | — | 2 | 2 | no | — |
| 336 | Dic73 | — | 2 | 1 | no | — |
| 337 | Dic73 | — | 2 | 1 | no | — |
| 338 | Dic73 | — | 2 | 1 | no | — |
| 339 | Dic73 | — | 4 | 1 | no | — |
| 340 | Dic73 | — | 4 | 1 | no | — |
| 341 | Dic73 | — | 4 | 1 | no | — |
| 342 | Dic73 | — | 4 | 1 | no | — |
| 343 | #12782 | — | 73 | 1 | no | maximal, Sylow |
| 344 | C2×C73 | — | 2 | 1 | no | — |
| 345 | C2×C73 | — | 8 | 1 | no | — |
| 346 | C2×C73 | #1790 | 1 | 1 | yes | characteristic |
| 347 | D73 | — | 2 | 1 | no | — |
| 348 | D73 | — | 2 | 1 | no | — |
| 349 | D73 | — | 8 | 1 | no | — |
| 350 | #3544 | — | 73 | 1 | no | — |
| 351 | #2133 | — | 73 | 1 | no | — |
| 352 | #2133 | — | 73 | 1 | no | — |
| 353 | C2×#356 | — | 73 | 1 | no | — |
| 354 | #1912 | — | 73 | 1 | no | — |
| 355 | #1912 | — | 73 | 1 | no | — |
| 356 | #1886 | — | 73 | 1 | no | — |
| 357 | C73 | #12782 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | #563 | — | 73 | 1 | no | — |
| 359 | #563 | — | 146 | 1 | no | — |
| 360 | #563 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 361 | Q82 | — | 73 | 1 | no | — |
| 362 | #555 | — | 73 | 1 | no | — |
| 363 | #554 | — | 146 | 1 | no | — |
| 364 | #552 | — | 146 | 1 | no | — |
| 365 | #552 | — | 146 | 1 | no | — |
| 366 | #547 | — | 146 | 1 | no | — |
| 367 | #547 | — | 146 | 1 | no | — |
| 368 | #544 | — | 146 | 1 | no | — |
| 369 | #544 | — | 146 | 1 | no | — |
| 370 | #542 | — | 146 | 1 | no | — |
| 371 | #542 | — | 146 | 1 | no | — |
| 372 | #536 | — | 73 | 1 | no | — |
| 373 | #536 | — | 73 | 1 | no | — |
| 374 | #536 | — | 146 | 1 | no | — |
| 375 | C2×C4⋊Q8 | — | 73 | 1 | no | — |
| 376 | #529 | — | 146 | 1 | no | — |
| 377 | #519 | — | 73 | 1 | no | — |
| 378 | #421 | — | 146 | 1 | no | — |
| 379 | #421 | — | 146 | 1 | no | — |
| 380 | #419 | — | 146 | 1 | no | — |
| 381 | C2×#101 | — | 73 | 1 | no | — |
| 382 | C2×#101 | — | 73 | 1 | no | — |
| 383 | C2×#101 | — | 73 | 1 | no | — |
| 384 | #356 | — | 146 | 1 | no | — |
| 385 | #356 | — | 146 | 1 | no | — |
| 386 | #356 | — | 146 | 1 | no | — |
| 387 | #356 | — | 146 | 1 | no | — |
| 388 | #355 | — | 146 | 1 | no | — |
| 389 | #355 | — | 146 | 1 | no | — |
| 390 | #339 | — | 146 | 1 | no | — |
| 391 | H(3,ℤ/4) | — | 146 | 1 | no | — |
| 392 | H(3,ℤ/4) | — | 146 | 1 | no | — |
| 393 | C2×#41 | — | 73 | 1 | no | — |
| 394 | C2×#41 | — | 73 | 1 | no | — |
| 395 | C2×#41 | — | 146 | 1 | no | — |
| 396 | C22×Q8 | — | 73 | 1 | no | — |
| 397 | C22×Q8 | — | 73 | 1 | no | — |
| 398 | C2×M16 | — | 146 | 1 | no | — |
| 399 | C2×M16 | — | 146 | 1 | no | — |
| 400 | C2×M16 | — | 146 | 1 | no | — |
| 401 | C4⋊Q8 | — | 73 | 1 | no | — |
| 402 | C4⋊Q8 | — | 73 | 1 | no | — |
| 403 | C4⋊Q8 | — | 73 | 1 | no | — |
| 404 | C4⋊Q8 | — | 73 | 1 | no | — |
| 405 | C4⋊Q8 | — | 73 | 1 | no | — |
| 406 | C4⋊Q8 | — | 73 | 1 | no | — |
| 407 | C4⋊Q8 | — | 146 | 1 | no | — |
| 408 | C4⋊Q8 | — | 146 | 1 | no | — |
| 409 | C4⋊Q8 | — | 146 | 1 | no | — |
| 410 | C4⋊Q8 | — | 146 | 1 | no | — |
| 411 | C4⋊Q8 | — | 146 | 1 | no | — |
| 412 | C4⋊Q8 | — | 146 | 1 | no | — |
| 413 | C4⋊Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 414 | C4⋊Q8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 415 | #126 | — | 2 | 1 | no | — |
| 416 | #126 | — | 2 | 1 | no | — |
| 417 | #126 | — | 146 | 1 | no | — |
| 418 | #126 | — | 146 | 1 | no | — |
| 419 | #126 | — | 146 | 1 | no | — |
| 420 | #126 | — | 146 | 1 | no | — |
| 421 | #125 | — | 2 | 1 | no | — |
| 422 | #125 | — | 146 | 1 | no | — |
| 423 | #125 | — | 146 | 1 | no | — |
| 424 | #125 | — | 146 | 1 | no | — |
| 425 | #125 | — | 146 | 1 | no | — |
| 426 | #125 | — | 146 | 1 | no | — |
| 427 | #125 | — | 146 | 1 | no | — |
| 428 | #124 | — | 73 | 1 | no | — |
| 429 | #124 | — | 73 | 1 | no | — |
| 430 | #124 | — | 73 | 1 | no | — |
| 431 | #124 | — | 146 | 1 | no | — |
| 432 | #124 | — | 146 | 1 | no | — |
| 433 | #124 | — | 146 | 1 | no | — |
| 434 | #124 | C2×#64408 | 1 | 1 | yes | characteristic |
| 435 | #123 | — | 2 | 1 | no | — |
| 436 | #123 | — | 146 | 1 | no | — |
| 437 | #123 | — | 146 | 1 | no | — |
| 438 | #123 | — | 146 | 1 | no | — |
| 439 | #123 | — | 146 | 1 | no | — |
| 440 | #123 | — | 146 | 1 | no | — |
| 441 | #123 | — | 146 | 1 | no | — |
| 442 | #123 | — | 146 | 1 | no | — |
| 443 | #123 | — | 146 | 1 | no | — |
| 444 | #123 | — | 146 | 1 | no | — |
| 445 | C22⋊Q8 | — | 2 | 1 | no | — |
| 446 | C22⋊Q8 | — | 2 | 1 | no | — |
| 447 | C22⋊Q8 | — | 146 | 1 | no | — |
| 448 | C22⋊Q8 | — | 146 | 1 | no | — |
| 449 | C22⋊Q8 | — | 146 | 1 | no | — |
| 450 | C22⋊Q8 | — | 146 | 1 | no | — |
| 451 | C22⋊Q8 | — | 146 | 1 | no | — |
| 452 | C22⋊Q8 | — | 146 | 1 | no | — |
| 453 | C22⋊Q8 | — | 146 | 1 | no | — |
| 454 | C22⋊Q8 | — | 146 | 1 | no | — |
| 455 | C22⋊Q8 | — | 146 | 1 | no | — |
| 456 | C22⋊Q8 | — | 146 | 1 | no | — |
| 457 | C22⋊Q8 | — | 146 | 1 | no | — |
| 458 | C22⋊Q8 | — | 146 | 1 | no | — |
| 459 | C22⋊Q8 | — | 146 | 1 | no | — |
| 460 | #121 | — | 146 | 1 | no | — |
| 461 | #121 | — | 146 | 1 | no | — |
| 462 | #121 | — | 146 | 1 | no | — |
| 463 | C4×Q8 | — | 292 | 2 | no | — |
| 464 | C4×Q8 | — | 146 | 1 | no | — |
| 465 | C4×Q8 | — | 146 | 1 | no | — |
| 466 | C4×Q8 | — | 146 | 1 | no | — |
| 467 | C4×D4 | — | 146 | 1 | no | — |
| 468 | C4×D4 | — | 146 | 1 | no | — |
| 469 | C4×D4 | — | 146 | 1 | no | — |
| 470 | C4×D4 | — | 146 | 1 | no | — |
| 471 | C4×D4 | — | 146 | 1 | no | — |
| 472 | #117 | — | 73 | 1 | no | — |
| 473 | #117 | — | 73 | 1 | no | — |
| 474 | #117 | — | 146 | 1 | no | — |
| 475 | #117 | — | 146 | 1 | no | — |
| 476 | #117 | — | 146 | 1 | no | — |
| 477 | #117 | — | 146 | 1 | no | — |
| 478 | #117 | — | 146 | 1 | no | — |
| 479 | #117 | — | 146 | 1 | no | — |
| 480 | #117 | — | 146 | 1 | no | — |
| 481 | #117 | — | 146 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 483 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 484 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 485 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 486 | C2×C42 | — | 73 | 1 | no | — |
| 487 | #104 | — | 292 | 2 | no | — |
| 488 | #104 | — | 292 | 2 | no | — |
| 489 | #103 | — | 292 | 2 | no | — |
| 490 | #101 | — | 146 | 1 | no | — |
| 491 | #101 | — | 146 | 1 | no | — |
| 492 | #101 | — | 146 | 1 | no | — |
| 493 | #101 | — | 146 | 1 | no | — |
| 494 | #101 | — | 146 | 1 | no | — |
| 495 | #101 | — | 146 | 1 | no | — |
| 496 | #41 | — | 292 | 1 | no | — |
| 497 | #41 | — | 292 | 1 | no | — |
| 498 | #41 | — | 292 | 1 | no | — |
| 499 | #41 | — | 292 | 1 | no | — |
| 500 | #41 | — | 584 | 1 | no | — |
| 501 | #41 | — | 584 | 1 | no | — |
| 502 | C2×Q8 | — | 292 | 1 | no | — |
| 503 | C2×Q8 | — | 292 | 1 | no | — |
| 504 | C2×Q8 | — | 292 | 1 | no | — |
| 505 | C2×Q8 | — | 292 | 1 | no | — |
| 506 | C2×Q8 | — | 73 | 1 | no | — |
| 507 | C2×Q8 | — | 73 | 1 | no | — |
| 508 | C2×Q8 | — | 73 | 1 | no | — |
| 509 | C2×Q8 | — | 73 | 1 | no | — |
| 510 | C2×Q8 | — | 73 | 1 | no | — |
| 511 | C2×Q8 | — | 146 | 1 | no | — |
| 512 | C2×Q8 | — | 146 | 1 | no | — |
| 513 | C2×Q8 | — | 146 | 1 | no | — |
| 514 | C2×Q8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 515 | C2×Q8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 516 | C2×Q8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 517 | C2×D4 | — | 73 | 1 | no | — |
| 518 | C2×D4 | — | 146 | 1 | no | — |
| 519 | C2×D4 | — | 146 | 1 | no | — |
| 520 | C2×D4 | — | 146 | 1 | no | — |
| 521 | C2×D4 | — | 146 | 1 | no | — |
| 522 | C2×D4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 523 | C22×C4 | — | 2 | 1 | no | — |
| 524 | C22×C4 | — | 73 | 1 | no | — |
| 525 | C22×C4 | — | 73 | 1 | no | — |
| 526 | C22×C4 | — | 73 | 1 | no | — |
| 527 | C22×C4 | — | 146 | 1 | no | — |
| 528 | C22×C4 | — | 146 | 1 | no | — |
| 529 | C22×C4 | — | 146 | 1 | no | — |
| 530 | C22×C4 | — | 146 | 1 | no | — |
| 531 | C22×C4 | — | 146 | 1 | no | — |
| 532 | C22×C4 | — | 146 | 1 | no | — |
| 533 | C22×C4 | — | 146 | 1 | no | — |
| 534 | M16 | — | 292 | 1 | no | — |
| 535 | M16 | — | 292 | 1 | no | — |
| 536 | M16 | — | 292 | 1 | no | — |
| 537 | M16 | — | 292 | 1 | no | — |
| 538 | M16 | — | 292 | 1 | no | — |
| 539 | M16 | — | 292 | 1 | no | — |
| 540 | C2×C8 | — | 292 | 1 | no | — |
| 541 | C2×C8 | — | 292 | 1 | no | — |
| 542 | C2×C8 | — | 292 | 1 | no | — |
| 543 | C4⋊C4 | — | 2 | 1 | no | — |
| 544 | C4⋊C4 | — | 2 | 1 | no | — |
| 545 | C4⋊C4 | — | 2 | 1 | no | — |
| 546 | C4⋊C4 | — | 2 | 1 | no | — |
| 547 | C4⋊C4 | — | 2 | 1 | no | — |
| 548 | C4⋊C4 | — | 2 | 1 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 2 | 1 | no | — |
| 551 | C4⋊C4 | — | 292 | 1 | no | — |
| 552 | C4⋊C4 | — | 292 | 1 | no | — |
| 553 | C4⋊C4 | — | 146 | 1 | no | — |
| 554 | C4⋊C4 | — | 146 | 1 | no | — |
| 555 | C4⋊C4 | — | 146 | 1 | no | — |
| 556 | C4⋊C4 | — | 146 | 1 | no | — |
| 557 | C4⋊C4 | — | 146 | 1 | no | — |
| 558 | C4⋊C4 | — | 146 | 1 | no | — |
| 559 | C4⋊C4 | — | 146 | 1 | no | — |
| 560 | C4⋊C4 | — | 146 | 1 | no | — |
| 561 | C4⋊C4 | — | 146 | 1 | no | — |
| 562 | C4⋊C4 | — | 146 | 1 | no | — |
| 563 | C4⋊C4 | — | 146 | 1 | no | — |
| 564 | C4⋊C4 | — | 146 | 1 | no | — |
| 565 | C4⋊C4 | — | 146 | 1 | no | — |
| 566 | C4⋊C4 | — | 146 | 1 | no | — |
| 567 | C4⋊C4 | — | 146 | 1 | no | — |
| 568 | C4⋊C4 | — | 146 | 1 | no | — |
| 569 | C4⋊C4 | — | 146 | 1 | no | — |
| 570 | C4⋊C4 | — | 146 | 1 | no | — |
| 571 | C4⋊C4 | — | 146 | 2 | no | — |
| 572 | C4⋊C4 | — | 146 | 1 | no | — |
| 573 | C4⋊C4 | — | 146 | 1 | no | — |
| 574 | C4⋊C4 | — | 146 | 1 | no | — |
| 575 | C4⋊C4 | — | 146 | 1 | no | — |
| 576 | C22⋊C4 | — | 2 | 1 | no | — |
| 577 | C22⋊C4 | — | 2 | 1 | no | — |
| 578 | C22⋊C4 | — | 2 | 1 | no | — |
| 579 | C22⋊C4 | — | 2 | 1 | no | — |
| 580 | C22⋊C4 | — | 2 | 1 | no | — |
| 581 | C22⋊C4 | — | 292 | 1 | no | — |
| 582 | C22⋊C4 | — | 146 | 1 | no | — |
| 583 | C22⋊C4 | — | 146 | 1 | no | — |
| 584 | C22⋊C4 | — | 146 | 1 | no | — |
| 585 | C22⋊C4 | — | 146 | 1 | no | — |
| 586 | C22⋊C4 | — | 146 | 1 | no | — |
| 587 | C22⋊C4 | — | 146 | 1 | no | — |
| 588 | C22⋊C4 | — | 146 | 1 | no | — |
| 589 | C22⋊C4 | — | 146 | 1 | no | — |
| 590 | C22⋊C4 | — | 146 | 1 | no | — |
| 591 | C22⋊C4 | — | 146 | 1 | no | — |
| 592 | C22⋊C4 | — | 146 | 1 | no | — |
| 593 | C22⋊C4 | — | 146 | 1 | no | — |
| 594 | C22⋊C4 | — | 146 | 1 | no | — |
| 595 | C42 | — | 292 | 1 | no | — |
| 596 | C42 | — | 73 | 1 | no | — |
| 597 | C42 | — | 73 | 1 | no | — |
| 598 | C42 | — | 73 | 1 | no | — |
| 599 | C42 | — | 146 | 1 | no | — |
| 600 | C42 | — | 146 | 1 | no | — |
| 601 | C42 | — | 146 | 1 | no | — |
| 602 | C42 | — | 146 | 1 | no | — |
| 603 | C42 | — | 146 | 1 | no | — |
| 604 | C42 | — | 146 | 2 | no | — |
| 605 | C42 | — | 146 | 2 | no | — |
| 606 | C42 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 607 | C42 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 608 | C42 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 609 | C23 | — | 2 | 1 | no | — |
| 610 | C23 | — | 73 | 1 | no | — |
| 611 | C23 | — | 146 | 1 | no | — |
| 612 | Q8 | — | 4 | 1 | no | — |
| 613 | Q8 | — | 4 | 1 | no | — |
| 614 | Q8 | — | 4 | 1 | no | — |
| 615 | Q8 | — | 292 | 1 | no | — |
| 616 | Q8 | — | 292 | 1 | no | — |
| 617 | Q8 | — | 292 | 1 | no | — |
| 618 | Q8 | — | 292 | 1 | no | — |
| 619 | Q8 | — | 292 | 1 | no | — |
| 620 | Q8 | — | 292 | 2 | no | — |
| 621 | Q8 | — | 584 | 1 | no | — |
| 622 | Q8 | — | 584 | 1 | no | — |
| 623 | D4 | — | 4 | 1 | no | — |
| 624 | D4 | — | 292 | 1 | no | — |
| 625 | D4 | — | 292 | 1 | no | — |
| 626 | D4 | — | 292 | 1 | no | — |
| 627 | D4 | — | 292 | 1 | no | — |
| 628 | D4 | — | 292 | 1 | no | — |
| 629 | D4 | — | 292 | 2 | no | — |
| 630 | D4 | — | 584 | 1 | no | — |
| 631 | C2×C4 | — | 2 | 1 | no | — |
| 632 | C2×C4 | — | 2 | 1 | no | — |
| 633 | C2×C4 | — | 2 | 1 | no | — |
| 634 | C2×C4 | — | 2 | 1 | no | — |
| 635 | C2×C4 | — | 2 | 1 | no | — |
| 636 | C2×C4 | — | 8 | 1 | no | — |
| 637 | C2×C4 | — | 292 | 1 | no | — |
| 638 | C2×C4 | — | 292 | 1 | no | — |
| 639 | C2×C4 | — | 292 | 2 | no | — |
| 640 | C2×C4 | — | 292 | 2 | no | — |
| 641 | C2×C4 | — | 292 | 2 | no | — |
| 642 | C2×C4 | — | 292 | 2 | no | — |
| 643 | C2×C4 | — | 584 | 1 | no | — |
| 644 | C2×C4 | — | 584 | 1 | no | — |
| 645 | C2×C4 | — | 584 | 1 | no | — |
| 646 | C2×C4 | — | 73 | 1 | no | — |
| 647 | C2×C4 | — | 73 | 1 | no | — |
| 648 | C2×C4 | — | 73 | 1 | no | — |
| 649 | C2×C4 | — | 146 | 1 | no | — |
| 650 | C2×C4 | — | 146 | 1 | no | — |
| 651 | C2×C4 | — | 146 | 1 | no | — |
| 652 | C2×C4 | — | 146 | 1 | no | — |
| 653 | C2×C4 | — | 146 | 1 | no | — |
| 654 | C2×C4 | — | 146 | 1 | no | — |
| 655 | C2×C4 | — | 146 | 1 | no | — |
| 656 | C2×C4 | — | 146 | 1 | no | — |
| 657 | C2×C4 | — | 146 | 1 | no | — |
| 658 | C2×C4 | — | 146 | 1 | no | — |
| 659 | C2×C4 | — | 146 | 1 | no | — |
| 660 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 661 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 662 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 663 | C8 | — | 584 | 1 | no | — |
| 664 | C8 | — | 584 | 1 | no | — |
| 665 | C8 | — | 584 | 1 | no | — |
| 666 | C22 | — | 4 | 1 | no | — |
| 667 | C22 | — | 4 | 1 | no | — |
| 668 | C22 | — | 4 | 1 | no | — |
| 669 | C22 | — | 292 | 1 | no | — |
| 670 | C22 | — | 292 | 1 | no | — |
| 671 | C22 | — | 292 | 1 | no | — |
| 672 | C22 | — | 292 | 1 | no | — |
| 673 | C22 | — | 73 | 1 | no | — |
| 674 | C22 | — | 73 | 1 | no | — |
| 675 | C22 | #17989528 | 1 | 1 | yes | characteristic |
| 676 | C4 | — | 2 | 1 | no | — |
| 677 | C4 | — | 2 | 1 | no | — |
| 678 | C4 | — | 2 | 1 | no | — |
| 679 | C4 | — | 4 | 1 | no | — |
| 680 | C4 | — | 4 | 1 | no | — |
| 681 | C4 | — | 4 | 1 | no | — |
| 682 | C4 | — | 4 | 1 | no | — |
| 683 | C4 | — | 4 | 1 | no | — |
| 684 | C4 | — | 292 | 1 | no | — |
| 685 | C4 | — | 292 | 1 | no | — |
| 686 | C4 | — | 292 | 1 | no | — |
| 687 | C4 | — | 292 | 1 | no | — |
| 688 | C4 | — | 584 | 2 | no | — |
| 689 | C4 | — | 146 | 2 | no | — |
| 690 | C4 | — | 146 | 1 | no | — |
| 691 | C4 | — | 146 | 1 | no | — |
| 692 | C4 | — | 146 | 1 | no | — |
| 693 | C2 | — | 2 | 1 | no | — |
| 694 | C2 | — | 8 | 1 | no | — |
| 695 | C2 | — | 584 | 1 | no | — |
| 696 | C2 | — | 146 | 1 | no | — |
| 697 | C2 | — | 146 | 1 | no | — |
| 698 | C2 | #22625775 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626229 | C2 | semidirect |
| 2. #22626227 | C2 | semidirect |
| 3. D73⋊#356 | C2 | semidirect |
| 4. #22625979 | C2 | semidirect |
| 5. #22625978 | C2 | semidirect |
| 6. #22625937 | C2 | semidirect |
| 25. #17989336 | C4 | semidirect |
| 26. #17989317 | C4 | semidirect |
| 27. #17989299 | C4 | semidirect |
| 42. #563×C73 | C4 | semidirect |
| 357. C73 | #12782 | semidirect |
| 360. #563 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626229 | 2 |
| #22626227 | 2 |
| D73⋊#356 | 2 |
| #22625979 | 2 |
| #22625978 | 2 |
| #22625937 | 2 |
| #22624270 | 2 |
| #12782 | 73 |