Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
996 conjugacy classes of subgroups.
The subgroup lattice has 590 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22626705 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22626562 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22626068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22626018 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22625968 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22625932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22625892 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #22625696 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #22619278 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #17989666 | C22 | 1 | 2 | yes | — |
| 11 | #17989665 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #41×#64408 | C22 | 1 | 2 | yes | — |
| 13 | #17989634 | — | 2 | 2 | no | — |
| 14 | #17989632 | — | 2 | 2 | no | — |
| 15 | #17989630 | — | 2 | 2 | no | — |
| 16 | #17989629 | — | 2 | 2 | no | — |
| 17 | #17989602 | C22 | 1 | 2 | yes | complemented |
| 18 | #17989591 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #17989586 | — | 2 | 2 | no | — |
| 20 | #17989586 | C22 | 1 | 2 | yes | — |
| 21 | #17989584 | — | 2 | 2 | no | — |
| 22 | #17989584 | C22 | 1 | 2 | yes | — |
| 23 | C2×#14556656 | — | 2 | 2 | no | — |
| 24 | C2×#14556656 | C22 | 1 | 2 | yes | — |
| 25 | D73⋊#104 | — | 2 | 2 | no | — |
| 26 | D73⋊#104 | C22 | 1 | 2 | yes | — |
| 27 | C2×#14556655 | C22 | 1 | 2 | yes | complemented |
| 28 | #17989567 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | M16×#64408 | C22 | 1 | 2 | yes | complemented |
| 30 | #17989523 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #17989470 | C22 | 1 | 2 | yes | complemented |
| 32 | #17989459 | C22 | 1 | 2 | yes | complemented |
| 33 | #17989458 | C22 | 1 | 2 | yes | complemented |
| 34 | #17989424 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17989383 | C22 | 1 | 2 | yes | — |
| 36 | #17989136 | C22 | 1 | 1 | yes | characteristic |
| 37 | #17988772 | C4 | 1 | 1 | yes | characteristic, complemented |
| 38 | #17988770 | C4 | 1 | 1 | yes | characteristic, complemented |
| 39 | #17988766 | C4 | 1 | 2 | yes | complemented |
| 40 | #17988759 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #17988753 | C4 | 1 | 2 | yes | complemented |
| 42 | #104×D73 | C22 | 1 | 2 | yes | — |
| 43 | #17988570 | C22 | 1 | 1 | yes | characteristic |
| 44 | #454×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | #14556679 | — | 2 | 2 | no | — |
| 46 | #14556678 | — | 2 | 2 | no | — |
| 47 | #14556678 | — | 2 | 2 | no | — |
| 48 | #14556678 | — | 2 | 2 | no | — |
| 49 | #14556678 | — | 4 | 2 | no | — |
| 50 | C2×#11924038 | — | 2 | 2 | no | — |
| 51 | C2×#11924038 | C23 | 1 | 2 | yes | — |
| 52 | D73⋊M16 | — | 2 | 2 | no | — |
| 53 | D73⋊M16 | C23 | 1 | 2 | yes | — |
| 54 | C2×#11924037 | — | 4 | 1 | no | — |
| 55 | Q8×#64408 | — | 2 | 2 | no | — |
| 56 | D4×#64408 | — | 2 | 2 | no | — |
| 57 | D4×#64408 | — | 4 | 2 | no | — |
| 58 | #14556670 | — | 2 | 2 | no | — |
| 59 | #14556670 | C23 | 1 | 2 | yes | — |
| 60 | C2×C4×#64408 | — | 2 | 2 | no | — |
| 61 | C2×C4×#64408 | C23 | 1 | 2 | yes | — |
| 62 | #14556662 | — | 2 | 2 | no | — |
| 63 | #14556661 | — | 2 | 2 | no | — |
| 64 | C4⋊#10596833 | — | 4 | 1 | no | — |
| 65 | #14556656 | — | 2 | 2 | no | — |
| 66 | #14556656 | — | 2 | 2 | no | — |
| 67 | #14556656 | — | 2 | 2 | no | — |
| 68 | #14556656 | — | 2 | 2 | no | — |
| 69 | #14556656 | — | 2 | 2 | no | — |
| 70 | #14556656 | D4 | 1 | 2 | yes | complemented |
| 71 | #14556656 | D4 | 1 | 2 | yes | complemented |
| 72 | #14556655 | — | 2 | 2 | no | — |
| 73 | #14556655 | — | 2 | 2 | no | — |
| 74 | #14556655 | — | 2 | 2 | no | — |
| 75 | #14556655 | D4 | 1 | 2 | yes | complemented |
| 76 | #14556655 | D4 | 1 | 2 | yes | complemented |
| 77 | #14556649 | — | 4 | 1 | no | — |
| 78 | #14556645 | — | 2 | 2 | no | — |
| 79 | C8×#64408 | — | 2 | 2 | no | — |
| 80 | (C2×#64408)⋊C4 | — | 4 | 1 | no | — |
| 81 | #14556639 | — | 2 | 2 | no | — |
| 82 | #14556639 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | #14556637 | — | 2 | 2 | no | — |
| 84 | #14556637 | — | 4 | 1 | no | — |
| 85 | #14556637 | C2×C4 | 1 | 2 | yes | — |
| 86 | C2×#11924029 | — | 2 | 2 | no | — |
| 87 | C2×#11924029 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#11924027 | C23 | 1 | 1 | yes | characteristic |
| 89 | #41×D73 | — | 2 | 2 | no | — |
| 90 | #41×D73 | — | 4 | 1 | no | — |
| 91 | #41×D73 | C23 | 1 | 2 | yes | — |
| 92 | #14556624 | C2×C4 | 1 | 2 | yes | complemented |
| 93 | #14556621 | C2×C4 | 1 | 2 | yes | complemented |
| 94 | #14556620 | — | 2 | 2 | no | — |
| 95 | #14556617 | C2×C4 | 1 | 2 | yes | complemented |
| 96 | #14556615 | — | 2 | 2 | no | — |
| 97 | #14556612 | — | 2 | 2 | no | — |
| 98 | #14556610 | — | 2 | 2 | no | — |
| 99 | M16×D73 | C23 | 1 | 2 | yes | — |
| 100 | #14556589 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 101 | #14556587 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 102 | #14556579 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 103 | #14556564 | — | 4 | 1 | no | — |
| 104 | #14556551 | — | 4 | 1 | no | — |
| 105 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 106 | #14556519 | C2×C4 | 1 | 2 | yes | complemented |
| 107 | #14556518 | C2×C4 | 1 | 2 | yes | complemented |
| 108 | #14556517 | C2×C4 | 1 | 2 | yes | complemented |
| 109 | #14556510 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 110 | #14556507 | C2×C4 | 1 | 2 | yes | complemented |
| 111 | 2−1+4×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | AGL(1,ℤ/8)×C73 | C2×C4 | 1 | 2 | yes | complemented |
| 113 | #124×C73 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 114 | #104×C73 | C2×C4 | 1 | 2 | yes | complemented |
| 115 | #101×C73 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 116 | C22×#64408 | — | 2 | 2 | no | — |
| 117 | C22×#64408 | — | 4 | 2 | no | — |
| 118 | #11924038 | — | 2 | 2 | no | — |
| 119 | #11924038 | — | 2 | 2 | no | — |
| 120 | #11924038 | — | 4 | 2 | no | — |
| 121 | #11924038 | C2×D4 | 1 | 2 | yes | — |
| 122 | #11924038 | C2×D4 | 1 | 2 | yes | — |
| 123 | #11924037 | — | 2 | 2 | no | — |
| 124 | #11924037 | — | 4 | 2 | no | — |
| 125 | #11924037 | — | 4 | 2 | no | — |
| 126 | #11924036 | — | 2 | 2 | no | — |
| 127 | #11924036 | — | 4 | 2 | no | — |
| 128 | C2×#10596833 | — | 2 | 2 | no | — |
| 129 | C2×#10596833 | — | 4 | 1 | no | — |
| 130 | C2×#10596833 | — | 4 | 1 | no | — |
| 131 | C2×#10596833 | — | 4 | 2 | no | — |
| 132 | C4⋊#64408 | — | 2 | 2 | no | — |
| 133 | C4⋊#64408 | — | 4 | 2 | no | — |
| 134 | C22⋊#64408 | — | 2 | 2 | no | — |
| 135 | C22⋊#64408 | — | 4 | 2 | no | — |
| 136 | C4×#64408 | — | 2 | 2 | no | — |
| 137 | C4×#64408 | — | 2 | 2 | no | — |
| 138 | C4×#64408 | — | 4 | 2 | no | — |
| 139 | C4×#64408 | C2×D4 | 1 | 2 | yes | — |
| 140 | C4×#64408 | C2×D4 | 1 | 2 | yes | — |
| 141 | #11924029 | — | 2 | 2 | no | — |
| 142 | #11924029 | — | 2 | 2 | no | — |
| 143 | #11924029 | — | 2 | 2 | no | — |
| 144 | #11924029 | — | 2 | 2 | no | — |
| 145 | #11924029 | — | 4 | 1 | no | — |
| 146 | #11924029 | — | 4 | 2 | no | — |
| 147 | #11924029 | C2×D4 | 1 | 2 | yes | — |
| 148 | #11924028 | — | 2 | 2 | no | — |
| 149 | #11924028 | — | 2 | 2 | no | — |
| 150 | #11924028 | — | 4 | 2 | no | — |
| 151 | #11924028 | — | 4 | 2 | no | — |
| 152 | #11924028 | — | 4 | 1 | no | — |
| 153 | #11924028 | C22×C4 | 1 | 2 | yes | — |
| 154 | #11924027 | — | 2 | 2 | no | — |
| 155 | #11924027 | — | 2 | 2 | no | — |
| 156 | #11924027 | — | 2 | 2 | no | — |
| 157 | #11924027 | — | 4 | 1 | no | — |
| 158 | #11924027 | C2×D4 | 1 | 2 | yes | — |
| 159 | C2×Dic146 | C22×C4 | 1 | 1 | yes | characteristic |
| 160 | Q8×D73 | — | 2 | 2 | no | — |
| 161 | Q8×D73 | — | 4 | 1 | no | — |
| 162 | Q8×D73 | #41 | 1 | 2 | yes | — |
| 163 | C2×D292 | — | 2 | 2 | no | — |
| 164 | C2×D292 | — | 2 | 1 | no | — |
| 165 | C2×D292 | — | 4 | 2 | no | — |
| 166 | C2×D292 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 168 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 169 | D4×D73 | — | 2 | 2 | no | — |
| 170 | D4×D73 | — | 2 | 2 | no | — |
| 171 | D4×D73 | — | 4 | 1 | no | — |
| 172 | D4×D73 | — | 4 | 2 | no | — |
| 173 | D4×D73 | — | 4 | 2 | no | — |
| 174 | D4×D73 | #41 | 1 | 2 | yes | — |
| 175 | C22×Dic73 | — | 2 | 1 | no | — |
| 176 | C2×C4×D73 | — | 2 | 2 | no | — |
| 177 | C2×C4×D73 | — | 2 | 1 | no | — |
| 178 | C2×C4×D73 | — | 2 | 1 | no | — |
| 179 | C2×C4×D73 | — | 4 | 2 | no | — |
| 180 | C2×C4×D73 | C24 | 1 | 1 | yes | characteristic |
| 181 | Dic292 | — | 2 | 2 | no | — |
| 182 | #11924018 | — | 2 | 2 | no | — |
| 183 | #11924017 | — | 2 | 2 | no | — |
| 184 | #11924016 | — | 2 | 2 | no | — |
| 185 | #11924016 | — | 2 | 2 | no | — |
| 186 | #11924013 | — | 2 | 2 | no | — |
| 187 | #11924012 | C22×C4 | 1 | 2 | yes | — |
| 188 | #11924011 | — | 2 | 2 | no | — |
| 189 | C8×D73 | — | 2 | 2 | no | — |
| 190 | #11924007 | — | 4 | 1 | no | — |
| 191 | #11924005 | — | 4 | 1 | no | — |
| 192 | C4×Dic73 | — | 2 | 1 | no | — |
| 193 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 194 | #41×C73 | — | 2 | 2 | no | — |
| 195 | #41×C73 | — | 4 | 1 | no | — |
| 196 | #41×C73 | C22×C4 | 1 | 2 | yes | — |
| 197 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 198 | C2×Q8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 199 | C2×D4×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 200 | SD16×C73 | — | 2 | 2 | no | — |
| 201 | D8×C73 | — | 2 | 2 | no | — |
| 202 | M16×C73 | C22×C4 | 1 | 2 | yes | — |
| 203 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 204 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 205 | C23×C73 | — | 2 | 1 | no | — |
| 206 | C22×D73 | — | 2 | 2 | no | — |
| 207 | C22×D73 | — | 2 | 1 | no | — |
| 208 | C22×D73 | — | 4 | 2 | no | — |
| 209 | C22×D73 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 210 | C2×#64408 | — | 2 | 2 | no | — |
| 211 | C2×#64408 | — | 2 | 2 | no | — |
| 212 | C2×#64408 | — | 4 | 2 | no | — |
| 213 | C2×#64408 | — | 8 | 2 | no | — |
| 214 | C2×#64408 | — | 8 | 4 | no | — |
| 215 | Q8×C73 | — | 2 | 2 | no | — |
| 216 | Q8×C73 | — | 4 | 1 | no | — |
| 217 | Q8×C73 | C4×D4 | 1 | 2 | yes | — |
| 218 | D4×C73 | — | 2 | 2 | no | — |
| 219 | D4×C73 | — | 2 | 2 | no | — |
| 220 | D4×C73 | — | 4 | 1 | no | — |
| 221 | D4×C73 | C4×D4 | 1 | 2 | yes | — |
| 222 | C2×C4×C73 | — | 2 | 2 | no | — |
| 223 | C2×C4×C73 | — | 2 | 1 | no | — |
| 224 | C2×C4×C73 | — | 2 | 1 | no | — |
| 225 | C2×C4×C73 | — | 4 | 2 | no | — |
| 226 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 227 | C22⋊D73 | — | 2 | 2 | no | — |
| 228 | C22⋊D73 | — | 2 | 2 | no | — |
| 229 | C22⋊D73 | — | 2 | 2 | no | — |
| 230 | C22⋊D73 | — | 4 | 2 | no | — |
| 231 | C22⋊D73 | — | 4 | 2 | no | — |
| 232 | C22⋊D73 | — | 8 | 2 | no | — |
| 233 | C2×Dic73 | — | 2 | 2 | no | — |
| 234 | C2×Dic73 | — | 2 | 1 | no | — |
| 235 | C2×Dic73 | — | 2 | 1 | no | — |
| 236 | C2×Dic73 | — | 4 | 1 | no | — |
| 237 | C2×Dic73 | — | 4 | 1 | no | — |
| 238 | C2×Dic73 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 239 | D292 | — | 2 | 2 | no | — |
| 240 | D292 | — | 2 | 2 | no | — |
| 241 | D292 | — | 4 | 2 | no | — |
| 242 | D292 | — | 4 | 1 | no | — |
| 243 | D292 | — | 4 | 2 | no | — |
| 244 | D292 | C4×D4 | 1 | 2 | yes | — |
| 245 | C4×D73 | — | 2 | 2 | no | — |
| 246 | C4×D73 | — | 2 | 2 | no | — |
| 247 | C4×D73 | — | 2 | 2 | no | — |
| 248 | C4×D73 | — | 4 | 2 | no | — |
| 249 | C4×D73 | — | 4 | 2 | no | — |
| 250 | C4×D73 | — | 4 | 1 | no | — |
| 251 | C4×D73 | — | 4 | 1 | no | — |
| 252 | C4×D73 | — | 8 | 1 | no | — |
| 253 | C4×D73 | C22×D4 | 1 | 2 | yes | — |
| 254 | C4×D73 | C2×#41 | 1 | 2 | yes | — |
| 255 | Dic146 | — | 2 | 2 | no | — |
| 256 | Dic146 | — | 2 | 2 | no | — |
| 257 | Dic146 | — | 4 | 1 | no | — |
| 258 | Dic146 | C4×D4 | 1 | 2 | yes | — |
| 259 | #10596833 | — | 2 | 2 | no | — |
| 260 | #10596833 | — | 2 | 2 | no | — |
| 261 | #10596833 | — | 4 | 2 | no | — |
| 262 | C8×C73 | — | 2 | 2 | no | — |
| 263 | #10596831 | — | 2 | 2 | no | — |
| 264 | C22×C73 | — | 2 | 2 | no | — |
| 265 | C22×C73 | — | 4 | 1 | no | — |
| 266 | C22×C73 | — | 8 | 1 | no | — |
| 267 | C22×C73 | #518 | 1 | 1 | yes | characteristic |
| 268 | C2×D73 | — | 2 | 2 | no | — |
| 269 | C2×D73 | — | 4 | 1 | no | — |
| 270 | C2×D73 | — | 4 | 1 | no | — |
| 271 | C2×D73 | — | 8 | 2 | no | — |
| 272 | C2×D73 | — | 8 | 1 | no | — |
| 273 | C2×D73 | — | 16 | 2 | no | — |
| 274 | C2×D73 | #546 | 1 | 2 | yes | — |
| 275 | #64408 | — | 4 | 2 | no | — |
| 276 | #64408 | — | 4 | 2 | no | — |
| 277 | #64408 | — | 8 | 2 | no | — |
| 278 | C4×C73 | — | 2 | 2 | no | — |
| 279 | C4×C73 | — | 4 | 1 | no | — |
| 280 | C4×C73 | — | 4 | 1 | no | — |
| 281 | C4×C73 | C2×C4×D4 | 1 | 2 | yes | — |
| 282 | Dic73 | — | 2 | 2 | no | — |
| 283 | Dic73 | — | 4 | 1 | no | — |
| 284 | Dic73 | — | 4 | 1 | no | — |
| 285 | Dic73 | D42 | 1 | 1 | yes | characteristic |
| 286 | Dic73 | #551 | 1 | 1 | yes | characteristic |
| 287 | #22898 | — | 73 | 1 | no | maximal, Sylow |
| 288 | C2×C73 | — | 2 | 1 | no | — |
| 289 | C2×C73 | — | 4 | 2 | no | — |
| 290 | C2×C73 | — | 8 | 1 | no | — |
| 291 | C2×C73 | #2358 | 1 | 1 | yes | characteristic |
| 292 | D73 | — | 2 | 2 | no | — |
| 293 | D73 | — | 4 | 2 | no | — |
| 294 | D73 | — | 8 | 1 | no | — |
| 295 | #3018 | — | 73 | 1 | no | — |
| 296 | #2956 | — | 73 | 2 | no | — |
| 297 | #2901 | — | 73 | 2 | no | — |
| 298 | #1963 | — | 73 | 1 | no | — |
| 299 | #1932 | — | 73 | 2 | no | — |
| 300 | #1906 | — | 73 | 2 | no | — |
| 301 | #1884 | — | 73 | 1 | no | — |
| 302 | #1861 | — | 73 | 2 | no | — |
| 303 | #1759 | — | 73 | 2 | no | — |
| 304 | C73 | #22898 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 305 | #585 | — | 73 | 1 | no | — |
| 306 | #575 | — | 73 | 2 | no | — |
| 307 | #568 | — | 73 | 1 | no | — |
| 308 | #568 | — | 73 | 2 | no | — |
| 309 | #532 | — | 73 | 1 | no | — |
| 310 | C4×#41 | — | 73 | 2 | no | — |
| 311 | #456 | — | 73 | 1 | no | — |
| 312 | #456 | — | 73 | 1 | no | — |
| 313 | #455 | — | 73 | 2 | no | — |
| 314 | #454 | — | 73 | 1 | no | — |
| 315 | #454 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 316 | #453 | — | 73 | 2 | no | — |
| 317 | #444 | — | 146 | 2 | no | — |
| 318 | #444 | — | 146 | 2 | no | — |
| 319 | #443 | — | 146 | 2 | no | — |
| 320 | #443 | — | 146 | 2 | no | — |
| 321 | #430 | — | 73 | 2 | no | — |
| 322 | #423 | — | 73 | 1 | no | — |
| 323 | #421 | — | 73 | 2 | no | — |
| 324 | #421 | — | 73 | 2 | no | — |
| 325 | #421 | — | 146 | 2 | no | — |
| 326 | #421 | — | 146 | 2 | no | — |
| 327 | C2×#104 | — | 73 | 2 | no | — |
| 328 | C2×#104 | — | 73 | 2 | no | — |
| 329 | C2×#104 | — | 73 | 2 | no | — |
| 330 | C2×#104 | — | 73 | 2 | no | — |
| 331 | C2×#104 | — | 146 | 2 | no | — |
| 332 | C2×#104 | — | 146 | 2 | no | — |
| 333 | #413 | — | 73 | 1 | no | — |
| 334 | #410 | — | 73 | 1 | no | — |
| 335 | C4×M16 | — | 73 | 2 | no | — |
| 336 | #376 | — | 73 | 1 | no | — |
| 337 | #344 | — | 73 | 2 | no | — |
| 338 | #339 | — | 73 | 2 | no | — |
| 339 | #339 | — | 73 | 2 | no | — |
| 340 | 2−1+4 | — | 73 | 1 | no | — |
| 341 | 2−1+4 | — | 146 | 2 | no | — |
| 342 | 2−1+4 | C2×#64408 | 1 | 1 | yes | characteristic |
| 343 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 344 | H(5,𝔽2) | — | 73 | 2 | no | — |
| 345 | H(5,𝔽2) | — | 146 | 2 | no | — |
| 346 | C2×#41 | — | 292 | 1 | no | — |
| 347 | C2×#41 | — | 73 | 2 | no | — |
| 348 | C2×#41 | — | 73 | 1 | no | — |
| 349 | C2×#41 | — | 73 | 1 | no | — |
| 350 | C2×#41 | — | 146 | 2 | no | — |
| 351 | C2×#41 | — | 146 | 2 | no | — |
| 352 | #137 | — | 73 | 2 | no | — |
| 353 | #137 | — | 73 | 2 | no | — |
| 354 | #137 | — | 146 | 2 | no | — |
| 355 | AGL(1,ℤ/8) | — | 73 | 2 | no | — |
| 356 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 357 | AGL(1,ℤ/8) | C2×#64408 | 1 | 2 | yes | complemented |
| 358 | #135 | — | 146 | 2 | no | — |
| 359 | #135 | — | 146 | 2 | no | — |
| 360 | #131 | — | 292 | 2 | no | — |
| 361 | #131 | — | 146 | 2 | no | — |
| 362 | #131 | — | 146 | 2 | no | — |
| 363 | #131 | — | 146 | 2 | no | — |
| 364 | #131 | — | 146 | 2 | no | — |
| 365 | C2×M16 | — | 292 | 1 | no | — |
| 366 | C2×M16 | — | 73 | 2 | no | — |
| 367 | C2×M16 | — | 73 | 2 | no | — |
| 368 | C2×M16 | — | 73 | 2 | no | — |
| 369 | C2×M16 | — | 146 | 2 | no | — |
| 370 | C2×M16 | — | 146 | 2 | no | — |
| 371 | C4⋊Q8 | — | 73 | 1 | no | — |
| 372 | #127 | — | 73 | 1 | no | — |
| 373 | #124 | — | 73 | 1 | no | — |
| 374 | #124 | C2×#64408 | 1 | 1 | yes | characteristic, complemented |
| 375 | #121 | — | 292 | 1 | no | — |
| 376 | C4×Q8 | — | 146 | 2 | no | — |
| 377 | C4×D4 | — | 292 | 2 | no | — |
| 378 | C4×D4 | — | 292 | 1 | no | — |
| 379 | C4×D4 | — | 146 | 2 | no | — |
| 380 | #117 | — | 73 | 2 | no | — |
| 381 | #117 | — | 146 | 2 | no | — |
| 382 | C2×C42 | — | 73 | 2 | no | — |
| 383 | C2×C42 | — | 73 | 1 | no | — |
| 384 | C2×C42 | — | 146 | 2 | no | — |
| 385 | #108 | — | 146 | 2 | no | — |
| 386 | #108 | — | 146 | 2 | no | — |
| 387 | C4⋊C8 | — | 292 | 1 | no | — |
| 388 | #104 | — | 73 | 2 | no | — |
| 389 | #104 | — | 73 | 2 | no | — |
| 390 | #104 | — | 73 | 2 | no | — |
| 391 | #104 | — | 73 | 2 | no | — |
| 392 | #104 | — | 73 | 2 | no | — |
| 393 | #104 | — | 73 | 2 | no | — |
| 394 | #104 | — | 73 | 2 | no | — |
| 395 | #104 | — | 146 | 2 | no | — |
| 396 | #104 | — | 146 | 2 | no | — |
| 397 | #104 | — | 146 | 2 | no | — |
| 398 | #104 | — | 146 | 2 | no | — |
| 399 | #104 | — | 146 | 2 | no | — |
| 400 | #104 | — | 146 | 2 | no | — |
| 401 | #104 | — | 146 | 2 | no | — |
| 402 | #104 | — | 146 | 2 | no | — |
| 403 | #104 | C2×#64408 | 1 | 2 | yes | complemented |
| 404 | #101 | — | 73 | 1 | no | — |
| 405 | #101 | C2×#64408 | 1 | 1 | yes | characteristic, complemented |
| 406 | #100 | — | 73 | 2 | no | — |
| 407 | #99 | — | 292 | 1 | no | — |
| 408 | #97 | — | 146 | 2 | no | — |
| 409 | C4×C8 | — | 146 | 2 | no | — |
| 410 | #95 | — | 292 | 1 | no | — |
| 411 | #41 | — | 2 | 2 | no | — |
| 412 | #41 | — | 4 | 1 | no | — |
| 413 | #41 | — | 292 | 1 | no | — |
| 414 | #41 | — | 292 | 2 | no | — |
| 415 | #41 | — | 292 | 2 | no | — |
| 416 | #41 | — | 292 | 2 | no | — |
| 417 | #41 | — | 292 | 1 | no | — |
| 418 | #41 | — | 292 | 1 | no | — |
| 419 | #41 | — | 73 | 2 | no | — |
| 420 | #41 | — | 73 | 2 | no | — |
| 421 | #41 | — | 73 | 2 | no | — |
| 422 | #41 | — | 146 | 2 | no | — |
| 423 | #41 | — | 146 | 2 | no | — |
| 424 | #41 | — | 146 | 2 | no | — |
| 425 | #41 | — | 146 | 2 | no | — |
| 426 | #41 | — | 146 | 2 | no | — |
| 427 | #41 | — | 146 | 2 | no | — |
| 428 | #41 | — | 146 | 2 | no | — |
| 429 | #41 | — | 146 | 2 | no | — |
| 430 | #41 | — | 146 | 2 | no | — |
| 431 | #41 | C22×#64408 | 1 | 2 | yes | — |
| 432 | C2×Q8 | — | 2 | 2 | no | — |
| 433 | C2×Q8 | — | 292 | 1 | no | — |
| 434 | C2×Q8 | — | 73 | 2 | no | — |
| 435 | C2×Q8 | — | 73 | 1 | no | — |
| 436 | C2×Q8 | — | 146 | 2 | no | — |
| 437 | C2×Q8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 438 | C2×D4 | — | 292 | 2 | no | — |
| 439 | C2×D4 | — | 292 | 2 | no | — |
| 440 | C2×D4 | — | 292 | 2 | no | — |
| 441 | C2×D4 | — | 292 | 1 | no | — |
| 442 | C2×D4 | — | 292 | 1 | no | — |
| 443 | C2×D4 | — | 73 | 2 | no | — |
| 444 | C2×D4 | — | 73 | 1 | no | — |
| 445 | C2×D4 | — | 146 | 1 | no | — |
| 446 | C2×D4 | — | 146 | 2 | no | — |
| 447 | C2×D4 | — | 146 | 2 | no | — |
| 448 | C2×D4 | — | 146 | 1 | no | — |
| 449 | C2×D4 | — | 146 | 2 | no | — |
| 450 | C2×D4 | C22×#64408 | 1 | 1 | yes | characteristic |
| 451 | C22×C4 | — | 292 | 2 | no | — |
| 452 | C22×C4 | — | 292 | 2 | no | — |
| 453 | C22×C4 | — | 73 | 1 | no | — |
| 454 | C22×C4 | — | 146 | 1 | no | — |
| 455 | C22×C4 | — | 146 | 1 | no | — |
| 456 | C22×C4 | — | 146 | 2 | no | — |
| 457 | C22×C4 | — | 146 | 1 | no | — |
| 458 | C22×C4 | — | 146 | 2 | no | — |
| 459 | Q16 | — | 146 | 2 | no | — |
| 460 | Q16 | — | 146 | 2 | no | — |
| 461 | SD16 | — | 2 | 2 | no | — |
| 462 | SD16 | — | 146 | 2 | no | — |
| 463 | SD16 | — | 146 | 2 | no | — |
| 464 | SD16 | — | 146 | 2 | no | — |
| 465 | D8 | — | 2 | 2 | no | — |
| 466 | D8 | — | 146 | 2 | no | — |
| 467 | M16 | — | 292 | 2 | no | — |
| 468 | M16 | — | 292 | 2 | no | — |
| 469 | M16 | — | 292 | 2 | no | — |
| 470 | M16 | — | 73 | 2 | no | — |
| 471 | M16 | — | 73 | 2 | no | — |
| 472 | M16 | — | 73 | 2 | no | — |
| 473 | M16 | — | 146 | 2 | no | — |
| 474 | M16 | — | 146 | 2 | no | — |
| 475 | M16 | — | 146 | 2 | no | — |
| 476 | M16 | — | 146 | 2 | no | — |
| 477 | M16 | C22×#64408 | 1 | 2 | yes | — |
| 478 | C2×C8 | — | 292 | 2 | no | — |
| 479 | C2×C8 | — | 292 | 2 | no | — |
| 480 | C2×C8 | — | 292 | 1 | no | — |
| 481 | C2×C8 | — | 292 | 1 | no | — |
| 482 | C2×C8 | — | 146 | 2 | no | — |
| 483 | C2×C8 | — | 146 | 2 | no | — |
| 484 | C2×C8 | — | 146 | 2 | no | — |
| 485 | C4⋊C4 | — | 292 | 1 | no | — |
| 486 | C4⋊C4 | — | 292 | 2 | no | — |
| 487 | C4⋊C4 | — | 146 | 2 | no | — |
| 488 | C22⋊C4 | — | 4 | 1 | no | — |
| 489 | C22⋊C4 | — | 292 | 1 | no | — |
| 490 | C22⋊C4 | — | 292 | 2 | no | — |
| 491 | C22⋊C4 | — | 146 | 2 | no | — |
| 492 | C42 | — | 292 | 2 | no | — |
| 493 | C42 | — | 73 | 2 | no | — |
| 494 | C42 | — | 73 | 2 | no | — |
| 495 | C42 | — | 73 | 1 | no | — |
| 496 | C42 | — | 146 | 1 | no | — |
| 497 | C42 | — | 146 | 2 | no | — |
| 498 | C42 | — | 146 | 2 | no | — |
| 499 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 500 | C23 | — | 2 | 1 | no | — |
| 501 | C23 | — | 292 | 2 | no | — |
| 502 | C23 | — | 73 | 1 | no | — |
| 503 | C23 | — | 146 | 2 | no | — |
| 504 | C23 | — | 146 | 1 | no | — |
| 505 | Q8 | — | 2 | 2 | no | — |
| 506 | Q8 | — | 4 | 1 | no | — |
| 507 | Q8 | — | 292 | 1 | no | — |
| 508 | Q8 | — | 73 | 2 | no | — |
| 509 | Q8 | — | 146 | 2 | no | — |
| 510 | Q8 | — | 146 | 2 | no | — |
| 511 | Q8 | D4×#64408 | 1 | 2 | yes | — |
| 512 | D4 | — | 2 | 2 | no | — |
| 513 | D4 | — | 2 | 2 | no | — |
| 514 | D4 | — | 4 | 1 | no | — |
| 515 | D4 | — | 292 | 2 | no | — |
| 516 | D4 | — | 292 | 2 | no | — |
| 517 | D4 | — | 292 | 1 | no | — |
| 518 | D4 | — | 292 | 2 | no | — |
| 519 | D4 | — | 292 | 2 | no | — |
| 520 | D4 | — | 584 | 2 | no | — |
| 521 | D4 | — | 73 | 2 | no | — |
| 522 | D4 | — | 146 | 2 | no | — |
| 523 | D4 | — | 146 | 2 | no | — |
| 524 | D4 | — | 146 | 2 | no | — |
| 525 | D4 | — | 146 | 2 | no | — |
| 526 | D4 | — | 146 | 2 | no | — |
| 527 | D4 | D4×#64408 | 1 | 2 | yes | — |
| 528 | C2×C4 | — | 2 | 2 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 2 | 1 | no | — |
| 531 | C2×C4 | — | 4 | 2 | no | — |
| 532 | C2×C4 | — | 292 | 2 | no | — |
| 533 | C2×C4 | — | 292 | 1 | no | — |
| 534 | C2×C4 | — | 292 | 1 | no | — |
| 535 | C2×C4 | — | 292 | 2 | no | — |
| 536 | C2×C4 | — | 292 | 1 | no | — |
| 537 | C2×C4 | — | 292 | 1 | no | — |
| 538 | C2×C4 | — | 292 | 2 | no | — |
| 539 | C2×C4 | — | 584 | 1 | no | — |
| 540 | C2×C4 | — | 584 | 2 | no | — |
| 541 | C2×C4 | — | 584 | 4 | no | — |
| 542 | C2×C4 | — | 73 | 1 | no | — |
| 543 | C2×C4 | — | 73 | 2 | no | — |
| 544 | C2×C4 | — | 73 | 2 | no | — |
| 545 | C2×C4 | — | 146 | 2 | no | — |
| 546 | C2×C4 | — | 146 | 2 | no | — |
| 547 | C2×C4 | — | 146 | 2 | no | — |
| 548 | C2×C4 | — | 146 | 2 | no | — |
| 549 | C2×C4 | — | 146 | 1 | no | — |
| 550 | C2×C4 | — | 146 | 1 | no | — |
| 551 | C2×C4 | — | 146 | 2 | no | — |
| 552 | C2×C4 | — | 146 | 2 | no | — |
| 553 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 554 | C8 | — | 2 | 2 | no | — |
| 555 | C8 | — | 292 | 2 | no | — |
| 556 | C8 | — | 146 | 2 | no | — |
| 557 | C8 | — | 146 | 2 | no | — |
| 558 | C8 | — | 146 | 2 | no | — |
| 559 | C22 | — | 2 | 2 | no | — |
| 560 | C22 | — | 4 | 1 | no | — |
| 561 | C22 | — | 8 | 1 | no | — |
| 562 | C22 | — | 292 | 1 | no | — |
| 563 | C22 | — | 292 | 1 | no | — |
| 564 | C22 | — | 584 | 1 | no | — |
| 565 | C22 | — | 584 | 2 | no | — |
| 566 | C22 | — | 73 | 2 | no | — |
| 567 | C22 | — | 1168 | 2 | no | — |
| 568 | C22 | — | 146 | 2 | no | — |
| 569 | C22 | #17989654 | 1 | 1 | yes | characteristic |
| 570 | C4 | — | 2 | 2 | no | — |
| 571 | C4 | — | 4 | 1 | no | — |
| 572 | C4 | — | 4 | 1 | no | — |
| 573 | C4 | — | 292 | 1 | no | — |
| 574 | C4 | — | 292 | 2 | no | — |
| 575 | C4 | — | 292 | 2 | no | — |
| 576 | C4 | — | 292 | 1 | no | — |
| 577 | C4 | — | 584 | 2 | no | — |
| 578 | C4 | — | 73 | 1 | no | — |
| 579 | C4 | — | 73 | 1 | no | — |
| 580 | C4 | — | 146 | 2 | no | — |
| 581 | C4 | C2×D4×#64408 | 1 | 2 | yes | — |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 4 | 2 | no | — |
| 584 | C2 | — | 8 | 1 | no | — |
| 585 | C2 | — | 292 | 2 | no | — |
| 586 | C2 | — | 584 | 1 | no | — |
| 587 | C2 | — | 146 | 2 | no | — |
| 588 | C2 | #22626453 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626705 | C2 | semidirect |
| 2. #22626562 | C2 | semidirect |
| 3. #22626068 | C2 | semidirect |
| 4. #22626018 | C2 | semidirect |
| 5. #22625968 | C2 | semidirect |
| 6. #22625932 | C2 | semidirect |
| 7. #22625892 | C2 | semidirect |
| 8. #22625696 | C2 | semidirect |
| 11. #17989665 | C22 | semidirect |
| 17. #17989602 | C22 | semidirect |
| 18. #17989591 | C22 | semidirect |
| 27. C2×#14556655 | C22 | semidirect |
| 28. #17989567 | C22 | semidirect |
| 29. M16×#64408 | C22 | semidirect |
| 30. #17989523 | C22 | semidirect |
| 31. #17989470 | C22 | semidirect |
| 32. #17989459 | C22 | semidirect |
| 33. #17989458 | C22 | semidirect |
| 37. #17988772 | C4 | semidirect |
| 38. #17988770 | C4 | semidirect |
| 39. #17988766 | C4 | semidirect |
| 40. #17988759 | C4 | semidirect |
| 41. #17988753 | C4 | semidirect |
| 44. #454×C73 | C4 | semidirect |
| 70. #14556656 | D4 | semidirect |
| 71. #14556656 | D4 | semidirect |
| 75. #14556655 | D4 | semidirect |
| 76. #14556655 | D4 | semidirect |
| 92. #14556624 | C2×C4 | semidirect |
| 93. #14556621 | C2×C4 | semidirect |
| 95. #14556617 | C2×C4 | semidirect |
| 100. #14556589 | C2×C4 | semidirect |
| 101. #14556587 | C2×C4 | semidirect |
| 102. #14556579 | C2×C4 | semidirect |
| 106. #14556519 | C2×C4 | semidirect |
| 107. #14556518 | C2×C4 | semidirect |
| 108. #14556517 | C2×C4 | semidirect |
| 109. #14556510 | C2×C4 | semidirect |
| 110. #14556507 | C2×C4 | semidirect |
| 112. AGL(1,ℤ/8)×C73 | C2×C4 | semidirect |
| 113. #124×C73 | C2×C4 | semidirect |
| 114. #104×C73 | C2×C4 | semidirect |
| 115. #101×C73 | C2×C4 | semidirect |
| 304. C73 | #22898 | semidirect |
| 315. #454 | #64408 | semidirect |
| 357. AGL(1,ℤ/8) | C2×#64408 | semidirect |
| 374. #124 | C2×#64408 | semidirect |
| 403. #104 | C2×#64408 | semidirect |
| 405. #101 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626705 | 2 |
| #22626562 | 2 |
| #22626068 | 2 |
| #22626018 | 2 |
| #22625968 | 2 |
| #22625932 | 2 |
| #22625892 | 2 |
| #22625696 | 2 |
| #22619278 | 2 |
| #22898 | 73 |