← #33955675
Subgroups — #33955675
Order 18688.
1834 conjugacy classes of subgroups.
The subgroup lattice has 470 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22623743 | C2 | 1 | 2 | yes | maximal |
| 2 | #22620478 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22620472 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22620471 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22620468 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #22620442 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#17988992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #500×D73 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22618528 | C2 | 1 | 4 | yes | maximal |
| 10 | C4×#14556597 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C73×#3160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14556597 | C22 | 1 | 2 | yes | — |
| 13 | Q8×Dic146 | — | 2 | 2 | no | — |
| 14 | #17989315 | — | 2 | 2 | no | — |
| 15 | #17989297 | — | 2 | 2 | no | — |
| 16 | #17989295 | — | 2 | 4 | no | — |
| 17 | Q8×D292 | — | 2 | 2 | no | — |
| 18 | #17989250 | — | 2 | 4 | no | — |
| 19 | #17989217 | C22 | 1 | 8 | yes | — |
| 20 | #17989215 | C22 | 1 | 4 | yes | — |
| 21 | #17989142 | C22 | 1 | 4 | yes | — |
| 22 | C2×#14556591 | C22 | 1 | 2 | yes | — |
| 23 | C4⋊Q8×D73 | C22 | 1 | 4 | yes | — |
| 24 | #17989067 | C22 | 1 | 4 | yes | — |
| 25 | C4×#11924028 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17988997 | C22 | 1 | 8 | yes | — |
| 27 | #17988994 | C22 | 1 | 16 | yes | — |
| 28 | #17988992 | C22 | 1 | 2 | yes | — |
| 29 | #17988992 | C22 | 1 | 4 | yes | — |
| 30 | #17988992 | C22 | 1 | 2 | yes | — |
| 31 | #17988991 | C22 | 1 | 8 | yes | — |
| 32 | #17988990 | C22 | 1 | 4 | yes | — |
| 33 | #17988988 | C22 | 1 | 8 | yes | — |
| 34 | #17988983 | C22 | 1 | 4 | yes | — |
| 35 | #17988630 | C22 | 1 | 8 | yes | — |
| 36 | #17988626 | C22 | 1 | 16 | yes | — |
| 37 | #17988624 | C22 | 1 | 8 | yes | — |
| 38 | C2×#14556525 | C22 | 1 | 4 | yes | — |
| 39 | #107×D73 | C22 | 1 | 8 | yes | — |
| 40 | #17988542 | C22 | 1 | 2 | yes | — |
| 41 | #17988541 | C22 | 1 | 4 | yes | — |
| 42 | C4×#11924012 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×#11924011 | C22 | 1 | 2 | yes | — |
| 44 | C4×C8×D73 | C22 | 1 | 2 | yes | — |
| 45 | #533×C73 | C22 | 1 | 2 | yes | — |
| 46 | #500×C73 | C22 | 1 | 1 | yes | characteristic |
| 47 | #500×C73 | C22 | 1 | 1 | yes | characteristic |
| 48 | #499×C73 | C22 | 1 | 4 | yes | — |
| 49 | #498×C73 | C22 | 1 | 2 | yes | — |
| 50 | #427×C73 | C22 | 1 | 4 | yes | — |
| 51 | C2×C4×C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#11924028 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×Dic146 | — | 2 | 2 | no | — |
| 54 | C2×Q8×D73 | — | 2 | 4 | no | — |
| 55 | #14556597 | Q8 | 1 | 16 | yes | complemented |
| 56 | C2×#11924012 | C23 | 1 | 2 | yes | — |
| 57 | C2×#11924011 | C23 | 1 | 4 | yes | — |
| 58 | C2×C8×D73 | C23 | 1 | 4 | yes | — |
| 59 | #14556591 | — | 2 | 4 | no | — |
| 60 | #14556591 | — | 2 | 2 | no | — |
| 61 | #14556591 | — | 2 | 2 | no | — |
| 62 | #14556591 | C23 | 1 | 4 | yes | — |
| 63 | #14556591 | C23 | 1 | 4 | yes | — |
| 64 | #14556590 | — | 2 | 8 | no | — |
| 65 | #14556590 | — | 2 | 4 | no | — |
| 66 | #14556590 | C23 | 1 | 8 | yes | — |
| 67 | #14556589 | — | 2 | 4 | no | — |
| 68 | #14556583 | — | 2 | 4 | no | — |
| 69 | #14556582 | C23 | 1 | 8 | yes | — |
| 70 | #14556581 | — | 2 | 8 | no | — |
| 71 | #14556571 | — | 2 | 4 | no | — |
| 72 | #14556571 | — | 2 | 8 | no | — |
| 73 | #14556569 | — | 2 | 8 | no | — |
| 74 | #14556568 | — | 2 | 8 | no | — |
| 75 | #14556567 | — | 2 | 4 | no | — |
| 76 | Q8×Dic73 | — | 2 | 4 | no | — |
| 77 | C4×Dic146 | — | 2 | 4 | no | — |
| 78 | C4×Dic146 | D4 | 1 | 1 | yes | characteristic |
| 79 | C4×Dic146 | D4 | 1 | 1 | yes | characteristic |
| 80 | #14556556 | — | 2 | 4 | no | — |
| 81 | C4×D292 | — | 2 | 4 | no | — |
| 82 | C4×D292 | D4 | 1 | 1 | yes | characteristic |
| 83 | C4×D292 | D4 | 1 | 1 | yes | characteristic |
| 84 | C4×C22⋊D73 | D4 | 1 | 2 | yes | — |
| 85 | C4×C22⋊D73 | D4 | 1 | 2 | yes | — |
| 86 | #14556551 | — | 2 | 8 | no | — |
| 87 | #14556550 | C23 | 1 | 1 | yes | characteristic |
| 88 | #14556549 | C23 | 1 | 8 | yes | — |
| 89 | #14556548 | C23 | 1 | 2 | yes | — |
| 90 | C2×C4⋊Dic73 | — | 2 | 2 | no | — |
| 91 | C2×C4⋊Dic73 | C23 | 1 | 4 | yes | — |
| 92 | C4⋊C4×D73 | — | 2 | 4 | no | — |
| 93 | C4⋊C4×D73 | C23 | 1 | 8 | yes | — |
| 94 | C42×D73 | C23 | 1 | 2 | yes | — |
| 95 | #14556525 | C23 | 1 | 8 | yes | — |
| 96 | #14556525 | C23 | 1 | 8 | yes | — |
| 97 | #14556524 | C23 | 1 | 16 | yes | — |
| 98 | #14556522 | C23 | 1 | 16 | yes | — |
| 99 | #14556502 | C23 | 1 | 2 | yes | — |
| 100 | #14556501 | C23 | 1 | 4 | yes | — |
| 101 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 102 | C8×Dic73 | C23 | 1 | 4 | yes | — |
| 103 | C22×C8×C73 | C23 | 1 | 2 | yes | — |
| 104 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 105 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 106 | #125×C73 | C23 | 1 | 4 | yes | — |
| 107 | C22⋊Q8×C73 | — | 2 | 2 | no | — |
| 108 | C22⋊Q8×C73 | — | 2 | 2 | no | — |
| 109 | C4×Q8×C73 | — | 2 | 2 | no | — |
| 110 | C4×Q8×C73 | — | 2 | 2 | no | — |
| 111 | #117×C73 | C23 | 1 | 4 | yes | — |
| 112 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 113 | #107×C73 | C23 | 1 | 4 | yes | — |
| 114 | #107×C73 | C23 | 1 | 4 | yes | — |
| 115 | #106×C73 | C23 | 1 | 8 | yes | — |
| 116 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 117 | C4×C8×C73 | C23 | 1 | 2 | yes | — |
| 118 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 119 | #11924028 | C2×Q8 | 1 | 8 | yes | — |
| 120 | C2×Dic146 | — | 2 | 4 | no | — |
| 121 | C2×Dic146 | — | 2 | 4 | no | — |
| 122 | C2×Dic146 | — | 2 | 8 | no | — |
| 123 | C2×Dic146 | — | 8 | 4 | no | — |
| 124 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | Q8×D73 | — | 8 | 8 | no | — |
| 126 | C2×D292 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×C22⋊D73 | C2×D4 | 1 | 2 | yes | — |
| 128 | C22×Dic73 | — | 2 | 4 | no | — |
| 129 | C2×C4×D73 | — | 2 | 8 | no | — |
| 130 | C2×C4×D73 | C2×D4 | 1 | 2 | yes | — |
| 131 | C2×C4×D73 | C2×D4 | 1 | 2 | yes | — |
| 132 | C2×C4×D73 | C24 | 1 | 2 | yes | — |
| 133 | #11924012 | C2×Q8 | 1 | 8 | yes | complemented |
| 134 | #11924011 | C2×Q8 | 1 | 16 | yes | complemented |
| 135 | C2×#10596831 | C24 | 1 | 4 | yes | — |
| 136 | C8×D73 | C2×Q8 | 1 | 16 | yes | complemented |
| 137 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 138 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 139 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 140 | C4⋊Dic73 | — | 2 | 8 | no | — |
| 141 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C4⋊Dic73 | C24 | 1 | 8 | yes | — |
| 144 | #11924007 | — | 2 | 8 | no | — |
| 145 | #11924007 | — | 2 | 8 | no | — |
| 146 | #11924007 | — | 2 | 8 | no | — |
| 147 | #11924007 | C2×D4 | 1 | 2 | yes | — |
| 148 | #11924007 | C2×D4 | 1 | 2 | yes | — |
| 149 | C22⋊Dic73 | C2×D4 | 1 | 2 | yes | — |
| 150 | #11924005 | — | 2 | 8 | no | — |
| 151 | #11924005 | C2×D4 | 1 | 2 | yes | — |
| 152 | #11924005 | C2×D4 | 1 | 2 | yes | — |
| 153 | C4×Dic73 | — | 2 | 8 | no | — |
| 154 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 155 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 156 | C4×Dic73 | C24 | 1 | 2 | yes | — |
| 157 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 158 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 159 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C22×C4×C73 | C24 | 1 | 1 | yes | characteristic |
| 162 | C2×C8×C73 | C2×Q8 | 1 | 8 | yes | complemented |
| 163 | C2×C8×C73 | C24 | 1 | 2 | yes | — |
| 164 | C2×C8×C73 | C24 | 1 | 2 | yes | — |
| 165 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 166 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 167 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 168 | C4⋊C4×C73 | — | 2 | 2 | no | — |
| 169 | C4⋊C4×C73 | C24 | 1 | 4 | yes | — |
| 170 | C4⋊C4×C73 | C24 | 1 | 4 | yes | — |
| 171 | C22⋊C4×C73 | — | 2 | 4 | no | — |
| 172 | C42×C73 | — | 2 | 4 | no | — |
| 173 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 176 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 177 | C23×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C22×D73 | C22×D4 | 1 | 2 | yes | — |
| 179 | Q8×C73 | — | 4 | 4 | no | — |
| 180 | Q8×C73 | — | 4 | 4 | no | — |
| 181 | C2×C4×C73 | — | 2 | 2 | no | — |
| 182 | C2×C4×C73 | — | 2 | 2 | no | — |
| 183 | C2×C4×C73 | — | 2 | 4 | no | — |
| 184 | C2×C4×C73 | — | 2 | 4 | no | — |
| 185 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C4×C73 | C22×Q8 | 1 | 4 | yes | — |
| 191 | C2×C4×C73 | C25 | 1 | 1 | yes | characteristic |
| 192 | C22⋊D73 | C4⋊Q8 | 1 | 8 | yes | — |
| 193 | C2×Dic73 | — | 2 | 8 | no | — |
| 194 | C2×Dic73 | — | 8 | 4 | no | — |
| 195 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 196 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 197 | C2×Dic73 | C22×D4 | 1 | 2 | yes | — |
| 198 | D292 | C4⋊Q8 | 1 | 4 | yes | — |
| 199 | C4×D73 | — | 2 | 4 | no | — |
| 200 | C4×D73 | — | 2 | 4 | no | — |
| 201 | C4×D73 | — | 8 | 8 | no | — |
| 202 | C4×D73 | C22×Q8 | 1 | 8 | yes | — |
| 203 | Dic146 | — | 4 | 8 | no | — |
| 204 | Dic146 | — | 8 | 8 | no | — |
| 205 | Dic146 | — | 8 | 4 | no | — |
| 206 | Dic146 | C4⋊Q8 | 1 | 4 | yes | — |
| 207 | C8×C73 | C22×Q8 | 1 | 4 | yes | — |
| 208 | C8×C73 | C22×Q8 | 1 | 4 | yes | — |
| 209 | #10596831 | C22×Q8 | 1 | 8 | yes | — |
| 210 | C22×C73 | — | 2 | 1 | no | — |
| 211 | C22×C73 | — | 2 | 1 | no | — |
| 212 | C22×C73 | C2×C4⋊Q8 | 1 | 2 | yes | — |
| 213 | C22×C73 | C23×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×D73 | — | 2 | 2 | no | — |
| 215 | C2×D73 | — | 2 | 2 | no | — |
| 216 | C2×D73 | C2×C4⋊Q8 | 1 | 4 | yes | — |
| 217 | C4×C73 | — | 2 | 1 | no | — |
| 218 | C4×C73 | — | 2 | 1 | no | — |
| 219 | C4×C73 | — | 4 | 4 | no | — |
| 220 | C4×C73 | — | 4 | 4 | no | — |
| 221 | C4×C73 | C2×C4⋊Q8 | 1 | 2 | yes | — |
| 222 | C4×C73 | #576 | 1 | 2 | yes | — |
| 223 | C4×C73 | #578 | 1 | 2 | yes | — |
| 224 | C4×C73 | C23×Q8 | 1 | 2 | yes | — |
| 225 | Dic73 | — | 2 | 2 | no | — |
| 226 | Dic73 | — | 2 | 2 | no | — |
| 227 | Dic73 | — | 4 | 8 | no | — |
| 228 | Dic73 | C2×C4⋊Q8 | 1 | 4 | yes | — |
| 229 | #60667 | — | 73 | 1 | no | maximal, Sylow |
| 230 | C2×C73 | — | 2 | 2 | no | — |
| 231 | C2×C73 | C22×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 232 | C2×C73 | C2×#576 | 1 | 1 | yes | characteristic |
| 233 | C2×C73 | C2×#578 | 1 | 1 | yes | characteristic |
| 234 | D73 | — | 2 | 4 | no | — |
| 235 | #3503 | — | 73 | 2 | no | — |
| 236 | #3165 | — | 73 | 4 | no | — |
| 237 | #3165 | — | 73 | 2 | no | — |
| 238 | #3164 | — | 73 | 8 | no | — |
| 239 | #3164 | — | 73 | 4 | no | — |
| 240 | #3160 | — | 73 | 2 | no | — |
| 241 | #3160 | D73 | 1 | 1 | yes | characteristic, complemented |
| 242 | C2×#500 | — | 73 | 2 | no | — |
| 243 | C2×#500 | — | 73 | 1 | no | — |
| 244 | #2913 | — | 73 | 4 | no | — |
| 245 | C4×#131 | — | 73 | 1 | no | — |
| 246 | C73 | #60667 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 247 | C2×#131 | — | 73 | 2 | no | — |
| 248 | Q82 | — | 146 | 2 | no | — |
| 249 | #557 | — | 146 | 2 | no | — |
| 250 | #554 | — | 146 | 2 | no | — |
| 251 | #554 | — | 146 | 4 | no | — |
| 252 | D4×Q8 | — | 146 | 2 | no | — |
| 253 | D4×Q8 | — | 146 | 4 | no | — |
| 254 | #544 | — | 73 | 8 | no | — |
| 255 | #544 | — | 73 | 4 | no | — |
| 256 | #533 | — | 73 | 4 | no | — |
| 257 | #533 | C2×D73 | 1 | 2 | yes | — |
| 258 | C2×C4⋊Q8 | — | 73 | 4 | no | — |
| 259 | C2×C4⋊Q8 | — | 73 | 2 | no | — |
| 260 | #520 | — | 73 | 4 | no | — |
| 261 | C4×#41 | — | 73 | 1 | no | — |
| 262 | #501 | — | 73 | 8 | no | — |
| 263 | #501 | — | 73 | 16 | no | — |
| 264 | #500 | — | 73 | 4 | no | — |
| 265 | #500 | — | 73 | 8 | no | — |
| 266 | #500 | — | 73 | 2 | no | — |
| 267 | #500 | — | 73 | 4 | no | — |
| 268 | #500 | — | 73 | 2 | no | — |
| 269 | #500 | C2×D73 | 1 | 1 | yes | characteristic |
| 270 | #500 | C2×D73 | 1 | 1 | yes | characteristic |
| 271 | #499 | — | 73 | 8 | no | — |
| 272 | #499 | C2×D73 | 1 | 4 | yes | — |
| 273 | #498 | — | 73 | 4 | no | — |
| 274 | #498 | C2×D73 | 1 | 2 | yes | — |
| 275 | #428 | — | 73 | 8 | no | — |
| 276 | #428 | — | 73 | 16 | no | — |
| 277 | #427 | — | 73 | 8 | no | — |
| 278 | #427 | C2×D73 | 1 | 4 | yes | — |
| 279 | C2×#107 | — | 73 | 4 | no | — |
| 280 | C2×#107 | — | 73 | 8 | no | — |
| 281 | #405 | — | 73 | 2 | no | — |
| 282 | #405 | — | 73 | 4 | no | — |
| 283 | C4×M16 | — | 73 | 1 | no | — |
| 284 | C4×M16 | — | 73 | 2 | no | — |
| 285 | C2×C4×C8 | — | 73 | 2 | no | — |
| 286 | C2×C4×C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 287 | C2×#41 | — | 73 | 1 | no | — |
| 288 | C22×Q8 | — | 146 | 4 | no | — |
| 289 | C22×Q8 | — | 146 | 2 | no | — |
| 290 | #131 | — | 73 | 16 | no | — |
| 291 | C2×M16 | — | 73 | 2 | no | — |
| 292 | C2×M16 | — | 73 | 4 | no | — |
| 293 | C22×C8 | — | 73 | 4 | no | — |
| 294 | C22×C8 | C22×D73 | 1 | 2 | yes | — |
| 295 | C4⋊Q8 | — | 73 | 8 | no | — |
| 296 | C4⋊Q8 | — | 73 | 4 | no | — |
| 297 | C4⋊Q8 | — | 73 | 4 | no | — |
| 298 | C4⋊Q8 | — | 146 | 4 | no | — |
| 299 | C4⋊Q8 | — | 146 | 4 | no | — |
| 300 | C4⋊Q8 | — | 146 | 4 | no | — |
| 301 | C4⋊Q8 | — | 146 | 8 | no | — |
| 302 | C4⋊Q8 | — | 146 | 2 | no | — |
| 303 | C4⋊Q8 | — | 146 | 2 | no | — |
| 304 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 305 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 306 | #125 | — | 73 | 8 | no | — |
| 307 | #125 | — | 146 | 4 | no | — |
| 308 | #125 | — | 146 | 8 | no | — |
| 309 | #125 | C22×D73 | 1 | 4 | yes | — |
| 310 | C22⋊Q8 | — | 2 | 2 | no | — |
| 311 | C22⋊Q8 | — | 2 | 2 | no | — |
| 312 | C22⋊Q8 | — | 146 | 8 | no | — |
| 313 | C22⋊Q8 | — | 146 | 8 | no | — |
| 314 | C22⋊Q8 | — | 146 | 8 | no | — |
| 315 | C22⋊Q8 | — | 146 | 4 | no | — |
| 316 | C22⋊Q8 | — | 146 | 4 | no | — |
| 317 | C4×Q8 | — | 2 | 2 | no | — |
| 318 | C4×Q8 | — | 2 | 2 | no | — |
| 319 | C4×Q8 | — | 73 | 1 | no | — |
| 320 | C4×Q8 | — | 73 | 1 | no | — |
| 321 | C4×Q8 | — | 146 | 4 | no | — |
| 322 | C4×Q8 | — | 146 | 4 | no | — |
| 323 | C4×Q8 | — | 146 | 4 | no | — |
| 324 | C4×D4 | — | 73 | 2 | no | — |
| 325 | C4×D4 | — | 73 | 2 | no | — |
| 326 | C4×D4 | — | 73 | 1 | no | — |
| 327 | C4×D4 | — | 73 | 1 | no | — |
| 328 | C4×D4 | — | 146 | 4 | no | — |
| 329 | C4×D4 | — | 146 | 8 | no | — |
| 330 | #117 | — | 73 | 1 | no | — |
| 331 | #117 | — | 73 | 2 | no | — |
| 332 | #117 | — | 73 | 8 | no | — |
| 333 | #117 | C22×D73 | 1 | 4 | yes | — |
| 334 | C2×C4⋊C4 | — | 73 | 4 | no | — |
| 335 | C2×C4⋊C4 | — | 73 | 8 | no | — |
| 336 | C2×C4⋊C4 | — | 146 | 4 | no | — |
| 337 | C2×C4⋊C4 | — | 146 | 2 | no | — |
| 338 | C2×C42 | — | 73 | 2 | no | — |
| 339 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 340 | #107 | — | 73 | 8 | no | — |
| 341 | #107 | — | 73 | 8 | no | — |
| 342 | #107 | — | 73 | 16 | no | — |
| 343 | #107 | C22×D73 | 1 | 4 | yes | — |
| 344 | #107 | C22×D73 | 1 | 4 | yes | — |
| 345 | #106 | — | 73 | 16 | no | — |
| 346 | #106 | C22×D73 | 1 | 8 | yes | — |
| 347 | #97 | — | 73 | 4 | no | — |
| 348 | #97 | — | 73 | 2 | no | — |
| 349 | C4×C8 | — | 73 | 4 | no | — |
| 350 | C4×C8 | — | 73 | 2 | no | — |
| 351 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 352 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 353 | C4×C8 | C22×D73 | 1 | 2 | yes | — |
| 354 | #41 | — | 73 | 8 | no | — |
| 355 | C2×Q8 | — | 2 | 2 | no | — |
| 356 | C2×Q8 | — | 2 | 2 | no | — |
| 357 | C2×Q8 | — | 584 | 4 | no | — |
| 358 | C2×Q8 | — | 584 | 8 | no | — |
| 359 | C2×Q8 | — | 73 | 1 | no | — |
| 360 | C2×Q8 | — | 146 | 8 | no | — |
| 361 | C2×Q8 | — | 146 | 4 | no | — |
| 362 | C2×Q8 | — | 146 | 4 | no | — |
| 363 | C2×D4 | — | 73 | 2 | no | — |
| 364 | C2×D4 | — | 73 | 1 | no | — |
| 365 | C22×C4 | — | 73 | 2 | no | — |
| 366 | C22×C4 | — | 73 | 2 | no | — |
| 367 | C22×C4 | — | 73 | 2 | no | — |
| 368 | C22×C4 | — | 146 | 8 | no | — |
| 369 | C22×C4 | — | 146 | 4 | no | — |
| 370 | C22×C4 | D4×D73 | 1 | 1 | yes | characteristic |
| 371 | C22×C4 | D4×D73 | 1 | 1 | yes | characteristic |
| 372 | C22×C4 | C23×D73 | 1 | 1 | yes | characteristic |
| 373 | M16 | — | 73 | 8 | no | — |
| 374 | M16 | — | 73 | 16 | no | — |
| 375 | C2×C8 | — | 73 | 4 | no | — |
| 376 | C2×C8 | — | 73 | 16 | no | — |
| 377 | C2×C8 | Q8×D73 | 1 | 8 | yes | complemented |
| 378 | C2×C8 | C23×D73 | 1 | 2 | yes | — |
| 379 | C2×C8 | C23×D73 | 1 | 2 | yes | — |
| 380 | C4⋊C4 | — | 2 | 2 | no | — |
| 381 | C4⋊C4 | — | 2 | 2 | no | — |
| 382 | C4⋊C4 | — | 2 | 4 | no | — |
| 383 | C4⋊C4 | — | 2 | 4 | no | — |
| 384 | C4⋊C4 | — | 73 | 2 | no | — |
| 385 | C4⋊C4 | — | 73 | 2 | no | — |
| 386 | C4⋊C4 | — | 73 | 1 | no | — |
| 387 | C4⋊C4 | — | 73 | 1 | no | — |
| 388 | C4⋊C4 | — | 73 | 8 | no | — |
| 389 | C4⋊C4 | — | 146 | 8 | no | — |
| 390 | C4⋊C4 | — | 146 | 8 | no | — |
| 391 | C4⋊C4 | — | 146 | 8 | no | — |
| 392 | C4⋊C4 | — | 146 | 8 | no | — |
| 393 | C4⋊C4 | — | 146 | 4 | no | — |
| 394 | C4⋊C4 | — | 146 | 4 | no | — |
| 395 | C4⋊C4 | — | 146 | 4 | no | — |
| 396 | C4⋊C4 | C23×D73 | 1 | 4 | yes | — |
| 397 | C4⋊C4 | C23×D73 | 1 | 4 | yes | — |
| 398 | C22⋊C4 | — | 2 | 4 | no | — |
| 399 | C22⋊C4 | — | 73 | 2 | no | — |
| 400 | C22⋊C4 | — | 73 | 2 | no | — |
| 401 | C22⋊C4 | — | 73 | 2 | no | — |
| 402 | C22⋊C4 | — | 146 | 8 | no | — |
| 403 | C42 | — | 2 | 4 | no | — |
| 404 | C42 | — | 73 | 2 | no | — |
| 405 | C42 | — | 73 | 2 | no | — |
| 406 | C42 | — | 73 | 2 | no | — |
| 407 | C42 | — | 146 | 8 | no | — |
| 408 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 409 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 410 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 411 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 412 | C23 | — | 73 | 2 | no | — |
| 413 | C23 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 414 | Q8 | — | 4 | 4 | no | — |
| 415 | Q8 | — | 4 | 4 | no | — |
| 416 | Q8 | — | 292 | 8 | no | — |
| 417 | Q8 | — | 584 | 4 | no | — |
| 418 | Q8 | — | 584 | 8 | no | — |
| 419 | Q8 | — | 73 | 4 | no | — |
| 420 | D4 | — | 73 | 8 | no | — |
| 421 | D4 | — | 73 | 4 | no | — |
| 422 | C2×C4 | — | 2 | 2 | no | — |
| 423 | C2×C4 | — | 2 | 2 | no | — |
| 424 | C2×C4 | — | 2 | 4 | no | — |
| 425 | C2×C4 | — | 2 | 4 | no | — |
| 426 | C2×C4 | — | 584 | 8 | no | — |
| 427 | C2×C4 | — | 584 | 4 | no | — |
| 428 | C2×C4 | — | 73 | 2 | no | — |
| 429 | C2×C4 | — | 73 | 8 | no | — |
| 430 | C2×C4 | — | 73 | 2 | no | — |
| 431 | C2×C4 | — | 73 | 2 | no | — |
| 432 | C2×C4 | — | 146 | 8 | no | — |
| 433 | C2×C4 | — | 146 | 4 | no | — |
| 434 | C2×C4 | — | 146 | 4 | no | — |
| 435 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 437 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 439 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 440 | C2×C4 | C2×Q8×D73 | 1 | 4 | yes | — |
| 441 | C2×C4 | C24×D73 | 1 | 1 | yes | characteristic |
| 442 | C8 | — | 73 | 8 | no | — |
| 443 | C8 | C2×Q8×D73 | 1 | 4 | yes | — |
| 444 | C8 | C2×Q8×D73 | 1 | 4 | yes | — |
| 445 | C22 | — | 2 | 1 | no | — |
| 446 | C22 | — | 2 | 1 | no | — |
| 447 | C22 | — | 73 | 4 | no | — |
| 448 | C22 | — | 146 | 2 | no | — |
| 449 | C22 | — | 146 | 2 | no | — |
| 450 | C22 | C4⋊Q8×D73 | 1 | 2 | yes | — |
| 451 | C22 | C22×D4×D73 | 1 | 1 | yes | characteristic |
| 452 | C4 | — | 2 | 1 | no | — |
| 453 | C4 | — | 2 | 1 | no | — |
| 454 | C4 | — | 4 | 4 | no | — |
| 455 | C4 | — | 4 | 4 | no | — |
| 456 | C4 | — | 292 | 8 | no | — |
| 457 | C4 | — | 73 | 4 | no | — |
| 458 | C4 | — | 146 | 2 | no | — |
| 459 | C4 | — | 146 | 2 | no | — |
| 460 | C4 | C4⋊Q8×D73 | 1 | 2 | yes | — |
| 461 | C4 | #17989389 | 1 | 2 | yes | — |
| 462 | C4 | #17989401 | 1 | 2 | yes | — |
| 463 | C4 | C22×Q8×D73 | 1 | 2 | yes | — |
| 464 | C2 | — | 2 | 2 | no | — |
| 465 | C2 | — | 146 | 4 | no | — |
| 466 | C2 | C2×C4⋊Q8×D73 | 1 | 1 | yes | characteristic |
| 467 | C2 | C2×#17989389 | 1 | 1 | yes | characteristic |
| 468 | C2 | C2×#17989401 | 1 | 1 | yes | characteristic |
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