Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1942 conjugacy classes of subgroups.
The subgroup lattice has 642 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21437880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #21437716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×D472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q8×#11745669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21436734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21436683 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #21436682 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #21436404 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #21436400 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #21435480 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #21435243 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #21434154 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #21433906 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #21433227 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C59×#3359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#14273775 | — | 2 | 1 | no | — |
| 17 | #16838125 | C22 | 1 | 3 | yes | — |
| 18 | #16838090 | — | 2 | 3 | no | — |
| 19 | Q8×D236 | C22 | 1 | 1 | yes | characteristic |
| 20 | Q8×D236 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×C22⋊D59 | — | 2 | 1 | no | — |
| 22 | #16838064 | — | 2 | 1 | no | — |
| 23 | #16838057 | C22 | 1 | 3 | yes | — |
| 24 | #16838055 | C22 | 1 | 3 | yes | — |
| 25 | #16838055 | C22 | 1 | 3 | yes | — |
| 26 | #16838054 | — | 2 | 3 | no | — |
| 27 | #16837975 | — | 2 | 3 | no | — |
| 28 | #16837957 | C22 | 1 | 3 | yes | — |
| 29 | #16837949 | C22 | 1 | 3 | yes | — |
| 30 | C4⋊Q8×D59 | C22 | 1 | 3 | yes | — |
| 31 | #16837937 | — | 2 | 3 | no | — |
| 32 | C4×#11745689 | C22 | 1 | 3 | yes | — |
| 33 | C4×#11745689 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×Q8×D59 | — | 2 | 1 | no | — |
| 35 | #16837807 | C22 | 1 | 3 | yes | — |
| 36 | #16837805 | C22 | 1 | 3 | yes | — |
| 37 | #16837752 | C22 | 1 | 3 | yes | — |
| 38 | #16837736 | C22 | 1 | 6 | yes | — |
| 39 | #16837736 | C22 | 1 | 6 | yes | — |
| 40 | #16837728 | C22 | 1 | 3 | yes | — |
| 41 | #16837724 | C22 | 1 | 3 | yes | — |
| 42 | #16837695 | C22 | 1 | 3 | yes | — |
| 43 | #16837695 | C22 | 1 | 6 | yes | — |
| 44 | #16837691 | C22 | 1 | 3 | yes | — |
| 45 | #16837687 | C22 | 1 | 3 | yes | — |
| 46 | #16837683 | C22 | 1 | 3 | yes | — |
| 47 | #16837683 | C22 | 1 | 3 | yes | — |
| 48 | #16837682 | C22 | 1 | 3 | yes | — |
| 49 | #16837679 | C22 | 1 | 3 | yes | — |
| 50 | #16837651 | C22 | 1 | 6 | yes | — |
| 51 | #16837645 | C22 | 1 | 6 | yes | — |
| 52 | #16837604 | C22 | 1 | 3 | yes | — |
| 53 | #16837600 | C22 | 1 | 3 | yes | — |
| 54 | #16837596 | C22 | 1 | 1 | yes | characteristic |
| 55 | #16837550 | C22 | 1 | 3 | yes | — |
| 56 | #16837546 | C22 | 1 | 3 | yes | — |
| 57 | Q8×C59⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#11745671 | C22 | 1 | 3 | yes | — |
| 59 | C4×D472 | C22 | 1 | 3 | yes | — |
| 60 | C4×#11745669 | C22 | 1 | 3 | yes | — |
| 61 | #16837481 | C22 | 1 | 3 | yes | — |
| 62 | #16837479 | C22 | 1 | 3 | yes | — |
| 63 | #16837453 | C22 | 1 | 3 | yes | — |
| 64 | #16837441 | C22 | 1 | 6 | yes | — |
| 65 | #16837424 | C22 | 1 | 3 | yes | — |
| 66 | #16837402 | C22 | 1 | 6 | yes | — |
| 67 | C59×#557 | C22 | 1 | 1 | yes | characteristic |
| 68 | D4×Q8×C59 | C22 | 1 | 1 | yes | characteristic |
| 69 | C59×#487 | C22 | 1 | 3 | yes | — |
| 70 | C59×#475 | C22 | 1 | 3 | yes | — |
| 71 | C59×#461 | C22 | 1 | 3 | yes | — |
| 72 | C8×Q8×C59 | C22 | 1 | 1 | yes | characteristic |
| 73 | C4×SD16×C59 | C22 | 1 | 3 | yes | — |
| 74 | #14273775 | — | 4 | 8 | no | — |
| 75 | C2×#11745689 | — | 2 | 3 | no | — |
| 76 | C2×#11745689 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#11745689 | C23 | 1 | 3 | yes | — |
| 78 | C2×#11745685 | — | 2 | 3 | no | — |
| 79 | C2×#11745685 | — | 2 | 3 | no | — |
| 80 | C2×Q8×D59 | — | 2 | 1 | no | — |
| 81 | C2×Q8×D59 | — | 2 | 1 | no | — |
| 82 | C2×Q8×D59 | — | 2 | 3 | no | — |
| 83 | C2×#11745671 | C23 | 1 | 3 | yes | — |
| 84 | C2×D472 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×#11745669 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#11745659 | C23 | 1 | 6 | yes | — |
| 87 | #14273727 | C23 | 1 | 3 | yes | — |
| 88 | #14273727 | C23 | 1 | 3 | yes | — |
| 89 | #14273726 | — | 2 | 3 | no | — |
| 90 | #14273726 | C23 | 1 | 3 | yes | — |
| 91 | #14273725 | — | 2 | 3 | no | — |
| 92 | #14273723 | C23 | 1 | 1 | yes | characteristic |
| 93 | #14273722 | — | 2 | 6 | no | — |
| 94 | #14273718 | — | 2 | 3 | no | — |
| 95 | #14273715 | — | 2 | 3 | no | — |
| 96 | #14273713 | — | 2 | 3 | no | — |
| 97 | #14273712 | — | 2 | 6 | no | — |
| 98 | #14273712 | — | 2 | 6 | no | — |
| 99 | #14273709 | — | 2 | 6 | no | — |
| 100 | #14273707 | — | 2 | 3 | no | — |
| 101 | #14273707 | — | 2 | 3 | no | — |
| 102 | #14273707 | — | 2 | 3 | no | — |
| 103 | #14273706 | — | 2 | 3 | no | — |
| 104 | #14273703 | — | 2 | 3 | no | — |
| 105 | #14273703 | C23 | 1 | 6 | yes | — |
| 106 | #14273702 | — | 2 | 3 | no | — |
| 107 | #14273702 | C23 | 1 | 3 | yes | — |
| 108 | #14273700 | — | 2 | 3 | no | — |
| 109 | #14273698 | C23 | 1 | 3 | yes | — |
| 110 | Q8×Dic59 | D4 | 1 | 1 | yes | characteristic |
| 111 | Q8×Dic59 | C23 | 1 | 3 | yes | — |
| 112 | C4×Dic118 | — | 2 | 3 | no | — |
| 113 | #14273692 | — | 2 | 3 | no | — |
| 114 | C4×D236 | — | 2 | 3 | no | — |
| 115 | C4×D236 | C23 | 1 | 3 | yes | — |
| 116 | C4×D236 | C23 | 1 | 3 | yes | — |
| 117 | C4×D236 | C23 | 1 | 3 | yes | — |
| 118 | #14273689 | — | 2 | 3 | no | — |
| 119 | #14273689 | D4 | 1 | 3 | yes | — |
| 120 | #14273689 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4×C22⋊D59 | — | 2 | 3 | no | — |
| 122 | #14273685 | — | 2 | 3 | no | — |
| 123 | #14273685 | — | 2 | 3 | no | — |
| 124 | #14273685 | D4 | 1 | 3 | yes | — |
| 125 | #14273685 | C23 | 1 | 3 | yes | — |
| 126 | C4⋊C4×D59 | — | 2 | 3 | no | — |
| 127 | C4⋊C4×D59 | — | 2 | 3 | no | — |
| 128 | C4⋊C4×D59 | C23 | 1 | 6 | yes | — |
| 129 | C42×D59 | — | 2 | 3 | no | — |
| 130 | C42×D59 | C23 | 1 | 3 | yes | — |
| 131 | #14273661 | C23 | 1 | 6 | yes | — |
| 132 | #14273661 | C23 | 1 | 3 | yes | — |
| 133 | #14273660 | C23 | 1 | 6 | yes | — |
| 134 | #14273660 | C23 | 1 | 3 | yes | — |
| 135 | #14273658 | C23 | 1 | 3 | yes | — |
| 136 | C4⋊(C59⋊C8) | C23 | 1 | 3 | yes | — |
| 137 | Dic59⋊C8 | C23 | 1 | 3 | yes | — |
| 138 | Dic59⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 139 | #14273651 | C23 | 1 | 6 | yes | — |
| 140 | #14273651 | C23 | 1 | 3 | yes | — |
| 141 | #14273649 | C23 | 1 | 3 | yes | — |
| 142 | #14273649 | C23 | 1 | 3 | yes | — |
| 143 | #14273648 | C23 | 1 | 3 | yes | — |
| 144 | #14273647 | C23 | 1 | 3 | yes | — |
| 145 | #14273647 | C23 | 1 | 1 | yes | characteristic |
| 146 | (C2×D59)⋊C8 | C23 | 1 | 3 | yes | — |
| 147 | (C2×D59)⋊C8 | C23 | 1 | 3 | yes | — |
| 148 | C4×C59⋊C8 | C23 | 1 | 3 | yes | — |
| 149 | C22×Q8×C59 | — | 2 | 1 | no | — |
| 150 | C2×SD16×C59 | C23 | 1 | 3 | yes | — |
| 151 | C4⋊Q8×C59 | C23 | 1 | 3 | yes | — |
| 152 | C4⋊Q8×C59 | C23 | 1 | 3 | yes | — |
| 153 | #125×C59 | — | 2 | 3 | no | — |
| 154 | C22⋊Q8×C59 | — | 2 | 3 | no | — |
| 155 | C4×Q8×C59 | — | 2 | 1 | no | — |
| 156 | C4×Q8×C59 | C23 | 1 | 3 | yes | — |
| 157 | C4×Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 158 | C4×D4×C59 | C23 | 1 | 3 | yes | — |
| 159 | #106×C59 | C23 | 1 | 3 | yes | — |
| 160 | C4⋊C8×C59 | C23 | 1 | 3 | yes | — |
| 161 | #103×C59 | C23 | 1 | 6 | yes | — |
| 162 | #103×C59 | C23 | 1 | 3 | yes | — |
| 163 | #102×C59 | C23 | 1 | 1 | yes | characteristic |
| 164 | C4×C8×C59 | C23 | 1 | 3 | yes | — |
| 165 | C2×Q8×C59 | — | 2 | 3 | no | — |
| 166 | C2×Q8×C59 | — | 4 | 4 | no | — |
| 167 | C2×Q8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×Q8×C59 | C24 | 1 | 3 | yes | — |
| 169 | C2×D4×C59 | C24 | 1 | 1 | yes | characteristic |
| 170 | C22×C4×C59 | — | 2 | 3 | no | — |
| 171 | C2×C22⋊D59 | — | 2 | 3 | no | — |
| 172 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 173 | C2×C22⋊D59 | — | 2 | 1 | no | — |
| 174 | #11745689 | — | 2 | 4 | no | — |
| 175 | #11745689 | — | 2 | 6 | no | — |
| 176 | #11745689 | — | 4 | 3 | no | — |
| 177 | #11745689 | — | 4 | 12 | no | — |
| 178 | Q8×D59 | — | 4 | 12 | no | — |
| 179 | Q8×D59 | — | 4 | 4 | no | — |
| 180 | Q8×D59 | — | 4 | 4 | no | — |
| 181 | #11745685 | — | 4 | 12 | no | — |
| 182 | #11745685 | — | 4 | 12 | no | — |
| 183 | C2×D236 | — | 2 | 3 | no | — |
| 184 | C2×D236 | — | 2 | 3 | no | — |
| 185 | C2×D236 | C2×D4 | 1 | 3 | yes | — |
| 186 | C2×D236 | C24 | 1 | 1 | yes | characteristic |
| 187 | C2×D236 | C24 | 1 | 1 | yes | characteristic |
| 188 | C2×C4×D59 | — | 2 | 6 | no | — |
| 189 | C2×C4×D59 | — | 2 | 3 | no | — |
| 190 | C2×C4×D59 | — | 2 | 3 | no | — |
| 191 | C2×C4×D59 | — | 2 | 1 | no | — |
| 192 | C2×C4×D59 | — | 2 | 3 | no | — |
| 193 | C2×C4×D59 | C2×D4 | 1 | 3 | yes | — |
| 194 | C2×C4×D59 | C2×D4 | 1 | 3 | yes | — |
| 195 | C2×C4×D59 | C24 | 1 | 3 | yes | — |
| 196 | C2×Dic118 | — | 2 | 3 | no | — |
| 197 | C2×Dic118 | — | 2 | 3 | no | — |
| 198 | C2×Dic118 | — | 2 | 3 | no | — |
| 199 | SD16×C59 | — | 4 | 3 | no | — |
| 200 | C2×C8×C59 | C24 | 1 | 1 | yes | characteristic |
| 201 | C2×C8×C59 | C24 | 1 | 3 | yes | — |
| 202 | C4⋊C4×C59 | — | 2 | 3 | no | — |
| 203 | C4⋊C4×C59 | — | 2 | 3 | no | — |
| 204 | C4⋊C4×C59 | — | 2 | 3 | no | — |
| 205 | C4⋊C4×C59 | — | 2 | 3 | no | — |
| 206 | C4⋊C4×C59 | C2×D4 | 1 | 3 | yes | — |
| 207 | C4⋊C4×C59 | C24 | 1 | 1 | yes | characteristic |
| 208 | C4⋊C4×C59 | C24 | 1 | 3 | yes | — |
| 209 | C22⋊C4×C59 | — | 2 | 3 | no | — |
| 210 | C42×C59 | — | 2 | 3 | no | — |
| 211 | C42×C59 | C24 | 1 | 3 | yes | — |
| 212 | C22⋊Dic59 | — | 2 | 3 | no | — |
| 213 | #11745671 | — | 4 | 3 | no | — |
| 214 | #11745669 | — | 2 | 2 | no | — |
| 215 | (C2×D59)⋊C4 | — | 2 | 6 | no | — |
| 216 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 217 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 218 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 219 | (C2×D59)⋊C4 | — | 2 | 1 | no | — |
| 220 | (C2×D59)⋊C4 | — | 2 | 3 | no | — |
| 221 | (C2×D59)⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 222 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 223 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 224 | C4⋊Dic59 | — | 2 | 3 | no | — |
| 225 | C4⋊Dic59 | C2×D4 | 1 | 3 | yes | — |
| 226 | C4⋊Dic59 | C24 | 1 | 3 | yes | — |
| 227 | C4⋊Dic59 | C24 | 1 | 3 | yes | — |
| 228 | Dic59⋊C4 | — | 2 | 3 | no | — |
| 229 | Dic59⋊C4 | — | 2 | 6 | no | — |
| 230 | Dic59⋊C4 | — | 2 | 6 | no | — |
| 231 | C4×Dic59 | — | 2 | 3 | no | — |
| 232 | C4×Dic59 | — | 2 | 3 | no | — |
| 233 | C4×Dic59 | C2×D4 | 1 | 3 | yes | — |
| 234 | C4×Dic59 | C2×D4 | 1 | 3 | yes | — |
| 235 | C4×Dic59 | C24 | 1 | 1 | yes | characteristic |
| 236 | C2×C59⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 237 | C2×C59⋊C8 | C24 | 1 | 3 | yes | — |
| 238 | D472 | — | 2 | 2 | no | — |
| 239 | #11745659 | — | 4 | 6 | no | — |
| 240 | C23×C59 | — | 2 | 1 | no | — |
| 241 | C22×D59 | — | 2 | 1 | no | — |
| 242 | C22×D59 | — | 2 | 1 | no | — |
| 243 | C22×D59 | C22×D4 | 1 | 3 | yes | — |
| 244 | Q8×C59 | — | 2 | 3 | no | — |
| 245 | Q8×C59 | — | 2 | 3 | no | — |
| 246 | Q8×C59 | — | 4 | 6 | no | — |
| 247 | Q8×C59 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 248 | D4×C59 | — | 2 | 1 | no | — |
| 249 | D4×C59 | — | 2 | 1 | no | — |
| 250 | C2×C4×C59 | — | 2 | 1 | no | — |
| 251 | C2×C4×C59 | — | 2 | 3 | no | — |
| 252 | C2×C4×C59 | — | 2 | 3 | no | — |
| 253 | C2×C4×C59 | — | 4 | 6 | no | — |
| 254 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 255 | C2×C4×C59 | C22×D4 | 1 | 3 | yes | — |
| 256 | C2×C4×C59 | C25 | 1 | 1 | yes | characteristic |
| 257 | C22⋊D59 | — | 4 | 2 | no | — |
| 258 | C22⋊D59 | — | 4 | 6 | no | — |
| 259 | C22⋊D59 | — | 4 | 2 | no | — |
| 260 | C2×Dic59 | — | 2 | 3 | no | — |
| 261 | C2×Dic59 | — | 2 | 3 | no | — |
| 262 | C2×Dic59 | C22×D4 | 1 | 3 | yes | — |
| 263 | C2×Dic59 | C22×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×Dic59 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | D236 | — | 2 | 6 | no | — |
| 266 | D236 | — | 2 | 1 | no | — |
| 267 | D236 | — | 2 | 1 | no | — |
| 268 | D236 | — | 2 | 1 | no | — |
| 269 | D236 | — | 4 | 6 | no | — |
| 270 | D236 | — | 4 | 6 | no | — |
| 271 | D236 | 2−1+4 | 1 | 2 | yes | complemented |
| 272 | C4×D59 | — | 2 | 6 | no | — |
| 273 | C4×D59 | — | 2 | 3 | no | — |
| 274 | C4×D59 | — | 2 | 3 | no | — |
| 275 | C4×D59 | — | 2 | 6 | no | — |
| 276 | C4×D59 | — | 4 | 6 | no | — |
| 277 | C4×D59 | — | 4 | 12 | no | — |
| 278 | C4×D59 | — | 4 | 6 | no | — |
| 279 | C4×D59 | — | 4 | 6 | no | — |
| 280 | C4×D59 | — | 4 | 2 | no | — |
| 281 | Dic118 | — | 4 | 6 | no | — |
| 282 | Dic118 | — | 4 | 6 | no | — |
| 283 | Dic118 | — | 4 | 6 | no | — |
| 284 | C8×C59 | — | 2 | 1 | no | — |
| 285 | C8×C59 | — | 2 | 3 | no | — |
| 286 | C59⋊C8 | — | 2 | 1 | no | — |
| 287 | C59⋊C8 | — | 2 | 3 | no | — |
| 288 | #62148 | — | 59 | 1 | no | maximal, Sylow |
| 289 | C22×C59 | — | 4 | 1 | no | — |
| 290 | C22×C59 | — | 4 | 1 | no | — |
| 291 | C22×C59 | — | 4 | 1 | no | — |
| 292 | C22×C59 | C23×D4 | 1 | 1 | yes | characteristic |
| 293 | C2×D59 | — | 2 | 3 | no | — |
| 294 | C2×D59 | — | 2 | 2 | no | — |
| 295 | C2×D59 | — | 2 | 3 | no | — |
| 296 | C2×D59 | — | 2 | 3 | no | — |
| 297 | C2×D59 | — | 4 | 1 | no | — |
| 298 | C2×D59 | — | 4 | 1 | no | — |
| 299 | C2×D59 | — | 4 | 1 | no | — |
| 300 | C2×D59 | — | 4 | 1 | no | — |
| 301 | C2×D59 | — | 4 | 1 | no | — |
| 302 | C4×C59 | — | 2 | 3 | no | — |
| 303 | C4×C59 | — | 4 | 3 | no | — |
| 304 | C4×C59 | — | 4 | 3 | no | — |
| 305 | C4×C59 | — | 4 | 1 | no | — |
| 306 | C4×C59 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 307 | C4×C59 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 308 | C4×C59 | #585 | 1 | 1 | yes | characteristic |
| 309 | Dic59 | — | 2 | 3 | no | — |
| 310 | Dic59 | — | 2 | 1 | no | — |
| 311 | Dic59 | — | 4 | 3 | no | — |
| 312 | Dic59 | — | 4 | 3 | no | — |
| 313 | Dic59 | #578 | 1 | 2 | yes | — |
| 314 | #3499 | — | 59 | 1 | no | — |
| 315 | #3482 | — | 59 | 1 | no | — |
| 316 | Q8×D8 | — | 59 | 1 | no | — |
| 317 | Q8×D8 | — | 59 | 1 | no | — |
| 318 | #3359 | — | 59 | 1 | no | — |
| 319 | #3359 | D59 | 1 | 1 | yes | characteristic, complemented |
| 320 | #3353 | — | 59 | 3 | no | — |
| 321 | #3353 | — | 59 | 3 | no | — |
| 322 | #3330 | — | 59 | 3 | no | — |
| 323 | #3330 | — | 59 | 3 | no | — |
| 324 | #3254 | — | 59 | 3 | no | — |
| 325 | #3230 | — | 59 | 3 | no | — |
| 326 | #3106 | — | 59 | 3 | no | — |
| 327 | #3079 | — | 59 | 3 | no | — |
| 328 | #2991 | — | 59 | 1 | no | — |
| 329 | C2×C59 | — | 8 | 1 | no | — |
| 330 | C2×C59 | #3489 | 1 | 1 | yes | characteristic |
| 331 | C2×C59 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 332 | C2×C59 | C2×#578 | 1 | 1 | yes | characteristic |
| 333 | D59 | — | 4 | 3 | no | — |
| 334 | D59 | — | 4 | 2 | no | — |
| 335 | D59 | — | 8 | 1 | no | — |
| 336 | C2×2−1+4 | — | 118 | 1 | no | — |
| 337 | #557 | C2×D59 | 1 | 1 | yes | characteristic |
| 338 | #556 | — | 59 | 3 | no | — |
| 339 | #552 | — | 118 | 3 | no | — |
| 340 | D4×Q8 | — | 59 | 1 | no | — |
| 341 | D4×Q8 | — | 59 | 1 | no | — |
| 342 | D4×Q8 | — | 118 | 1 | no | — |
| 343 | D4×Q8 | C2×D59 | 1 | 1 | yes | characteristic |
| 344 | #548 | — | 118 | 1 | no | — |
| 345 | #547 | — | 59 | 3 | no | — |
| 346 | #547 | — | 59 | 3 | no | — |
| 347 | #547 | — | 59 | 3 | no | — |
| 348 | #547 | — | 118 | 3 | no | — |
| 349 | #536 | — | 118 | 3 | no | — |
| 350 | #533 | — | 59 | 3 | no | — |
| 351 | #532 | — | 59 | 3 | no | — |
| 352 | C2×C4⋊Q8 | — | 59 | 3 | no | — |
| 353 | #529 | — | 118 | 3 | no | — |
| 354 | C4×#41 | — | 59 | 1 | no | — |
| 355 | C4×#41 | — | 59 | 3 | no | — |
| 356 | C2×C4×Q8 | — | 118 | 1 | no | — |
| 357 | #500 | — | 59 | 3 | no | — |
| 358 | #500 | — | 59 | 3 | no | — |
| 359 | #487 | — | 59 | 3 | no | — |
| 360 | #487 | C2×D59 | 1 | 3 | yes | — |
| 361 | #484 | — | 59 | 6 | no | — |
| 362 | #484 | — | 59 | 6 | no | — |
| 363 | #482 | — | 59 | 3 | no | — |
| 364 | #482 | — | 59 | 3 | no | — |
| 365 | #477 | — | 59 | 6 | no | — |
| 366 | #477 | — | 59 | 3 | no | — |
| 367 | #476 | — | 59 | 3 | no | — |
| 368 | #475 | — | 59 | 3 | no | — |
| 369 | #475 | C2×D59 | 1 | 3 | yes | — |
| 370 | #474 | — | 59 | 3 | no | — |
| 371 | #474 | — | 59 | 3 | no | — |
| 372 | #474 | — | 59 | 3 | no | — |
| 373 | #474 | — | 59 | 3 | no | — |
| 374 | #468 | — | 59 | 6 | no | — |
| 375 | #468 | — | 59 | 6 | no | — |
| 376 | #461 | — | 59 | 3 | no | — |
| 377 | #461 | C2×D59 | 1 | 3 | yes | — |
| 378 | #460 | — | 59 | 3 | no | — |
| 379 | #459 | — | 59 | 1 | no | — |
| 380 | #449 | — | 59 | 3 | no | — |
| 381 | #449 | — | 59 | 3 | no | — |
| 382 | C8×Q8 | — | 59 | 1 | no | — |
| 383 | C8×Q8 | C2×D59 | 1 | 1 | yes | characteristic |
| 384 | C4×SD16 | — | 59 | 3 | no | — |
| 385 | C4×SD16 | C2×D59 | 1 | 3 | yes | — |
| 386 | C4×D8 | — | 59 | 3 | no | — |
| 387 | C4×D8 | — | 59 | 3 | no | — |
| 388 | #436 | — | 59 | 3 | no | — |
| 389 | #436 | — | 59 | 3 | no | — |
| 390 | #431 | — | 59 | 3 | no | — |
| 391 | #428 | — | 59 | 6 | no | — |
| 392 | #423 | — | 59 | 3 | no | — |
| 393 | #417 | — | 59 | 6 | no | — |
| 394 | C59 | #62148 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 395 | 2−1+4 | — | 236 | 8 | no | — |
| 396 | C2×#41 | — | 59 | 1 | no | — |
| 397 | C2×#41 | — | 59 | 3 | no | — |
| 398 | C2×#41 | — | 118 | 3 | no | — |
| 399 | C2×#41 | — | 118 | 3 | no | — |
| 400 | C2×#41 | — | 118 | 3 | no | — |
| 401 | C22×Q8 | — | 2 | 1 | no | — |
| 402 | C22×Q8 | — | 118 | 3 | no | — |
| 403 | C22×Q8 | — | 118 | 1 | no | — |
| 404 | C22×Q8 | — | 118 | 1 | no | — |
| 405 | C2×SD16 | — | 59 | 3 | no | — |
| 406 | C2×SD16 | C22×D59 | 1 | 3 | yes | — |
| 407 | C2×D8 | — | 59 | 1 | no | — |
| 408 | C2×D8 | — | 59 | 1 | no | — |
| 409 | C2×M16 | — | 59 | 6 | no | — |
| 410 | C4⋊Q8 | — | 59 | 3 | no | — |
| 411 | C4⋊Q8 | — | 59 | 3 | no | — |
| 412 | C4⋊Q8 | — | 59 | 3 | no | — |
| 413 | C4⋊Q8 | — | 118 | 3 | no | — |
| 414 | C4⋊Q8 | — | 118 | 3 | no | — |
| 415 | C4⋊Q8 | C22×D59 | 1 | 3 | yes | — |
| 416 | C4⋊Q8 | C22×D59 | 1 | 3 | yes | — |
| 417 | #127 | — | 59 | 1 | no | — |
| 418 | #126 | — | 118 | 6 | no | — |
| 419 | #125 | — | 2 | 3 | no | — |
| 420 | #125 | — | 118 | 3 | no | — |
| 421 | #124 | — | 118 | 3 | no | — |
| 422 | #124 | — | 118 | 3 | no | — |
| 423 | #123 | — | 118 | 6 | no | — |
| 424 | #123 | — | 118 | 6 | no | — |
| 425 | #123 | — | 118 | 6 | no | — |
| 426 | C22⋊Q8 | — | 2 | 3 | no | — |
| 427 | C22⋊Q8 | — | 59 | 6 | no | — |
| 428 | C22⋊Q8 | — | 118 | 3 | no | — |
| 429 | C22⋊Q8 | — | 118 | 3 | no | — |
| 430 | C22⋊Q8 | — | 118 | 3 | no | — |
| 431 | C22⋊Q8 | — | 118 | 3 | no | — |
| 432 | C22⋊Q8 | — | 118 | 3 | no | — |
| 433 | #121 | — | 59 | 3 | no | — |
| 434 | #121 | — | 59 | 3 | no | — |
| 435 | #121 | — | 118 | 3 | no | — |
| 436 | #121 | — | 118 | 3 | no | — |
| 437 | C4×Q8 | — | 2 | 1 | no | — |
| 438 | C4×Q8 | — | 59 | 1 | no | — |
| 439 | C4×Q8 | — | 59 | 3 | no | — |
| 440 | C4×Q8 | — | 118 | 3 | no | — |
| 441 | C4×Q8 | — | 118 | 3 | no | — |
| 442 | C4×Q8 | C22×D59 | 1 | 3 | yes | — |
| 443 | C4×Q8 | C22×D59 | 1 | 1 | yes | characteristic |
| 444 | C4×D4 | — | 59 | 3 | no | — |
| 445 | C4×D4 | — | 59 | 1 | no | — |
| 446 | C4×D4 | — | 59 | 3 | no | — |
| 447 | C4×D4 | — | 59 | 3 | no | — |
| 448 | C4×D4 | — | 59 | 3 | no | — |
| 449 | C4×D4 | — | 118 | 3 | no | — |
| 450 | C4×D4 | — | 118 | 3 | no | — |
| 451 | C4×D4 | — | 118 | 3 | no | — |
| 452 | C4×D4 | C22×D59 | 1 | 3 | yes | — |
| 453 | #117 | — | 59 | 3 | no | — |
| 454 | #117 | — | 59 | 3 | no | — |
| 455 | #117 | — | 118 | 3 | no | — |
| 456 | #117 | — | 118 | 3 | no | — |
| 457 | C2×C4⋊C4 | — | 59 | 6 | no | — |
| 458 | C2×C4⋊C4 | — | 118 | 3 | no | — |
| 459 | C2×C4⋊C4 | — | 118 | 3 | no | — |
| 460 | C2×C42 | — | 59 | 3 | no | — |
| 461 | C2×C42 | — | 118 | 3 | no | — |
| 462 | #107 | — | 59 | 6 | no | — |
| 463 | #107 | — | 59 | 3 | no | — |
| 464 | #107 | — | 59 | 6 | no | — |
| 465 | #107 | — | 59 | 3 | no | — |
| 466 | #106 | — | 59 | 3 | no | — |
| 467 | #106 | C22×D59 | 1 | 3 | yes | — |
| 468 | C4⋊C8 | — | 59 | 3 | no | — |
| 469 | C4⋊C8 | — | 59 | 1 | no | — |
| 470 | C4⋊C8 | — | 59 | 3 | no | — |
| 471 | C4⋊C8 | C22×D59 | 1 | 3 | yes | — |
| 472 | #103 | — | 59 | 6 | no | — |
| 473 | #103 | — | 59 | 3 | no | — |
| 474 | #103 | C22×D59 | 1 | 6 | yes | — |
| 475 | #103 | C22×D59 | 1 | 3 | yes | — |
| 476 | #102 | — | 59 | 3 | no | — |
| 477 | #102 | — | 59 | 3 | no | — |
| 478 | #102 | — | 59 | 3 | no | — |
| 479 | #102 | — | 59 | 3 | no | — |
| 480 | #102 | — | 59 | 1 | no | — |
| 481 | #102 | C22×D59 | 1 | 1 | yes | characteristic |
| 482 | C22⋊C8 | — | 59 | 3 | no | — |
| 483 | C22⋊C8 | — | 59 | 3 | no | — |
| 484 | C4×C8 | — | 59 | 3 | no | — |
| 485 | C4×C8 | C22×D59 | 1 | 3 | yes | — |
| 486 | #41 | — | 118 | 4 | no | — |
| 487 | #41 | — | 118 | 6 | no | — |
| 488 | #41 | — | 236 | 12 | no | — |
| 489 | #41 | — | 236 | 12 | no | — |
| 490 | #41 | — | 236 | 3 | no | — |
| 491 | #41 | — | 236 | 12 | no | — |
| 492 | C2×Q8 | — | 2 | 3 | no | — |
| 493 | C2×Q8 | — | 4 | 4 | no | — |
| 494 | C2×Q8 | — | 118 | 3 | no | — |
| 495 | C2×Q8 | — | 118 | 3 | no | — |
| 496 | C2×Q8 | — | 118 | 3 | no | — |
| 497 | C2×Q8 | — | 236 | 12 | no | — |
| 498 | C2×Q8 | — | 236 | 4 | no | — |
| 499 | C2×Q8 | — | 236 | 4 | no | — |
| 500 | C2×Q8 | D4×D59 | 1 | 1 | yes | characteristic |
| 501 | C2×Q8 | C23×D59 | 1 | 3 | yes | — |
| 502 | C2×D4 | — | 59 | 3 | no | — |
| 503 | C2×D4 | — | 59 | 1 | no | — |
| 504 | C2×D4 | — | 59 | 1 | no | — |
| 505 | C2×D4 | — | 118 | 3 | no | — |
| 506 | C2×D4 | — | 118 | 3 | no | — |
| 507 | C2×D4 | — | 118 | 1 | no | — |
| 508 | C2×D4 | — | 118 | 1 | no | — |
| 509 | C2×D4 | — | 118 | 3 | no | — |
| 510 | C2×D4 | C23×D59 | 1 | 1 | yes | characteristic |
| 511 | C22×C4 | — | 2 | 3 | no | — |
| 512 | C22×C4 | — | 59 | 3 | no | — |
| 513 | C22×C4 | — | 59 | 3 | no | — |
| 514 | C22×C4 | — | 59 | 3 | no | — |
| 515 | C22×C4 | — | 118 | 1 | no | — |
| 516 | C22×C4 | — | 118 | 3 | no | — |
| 517 | C22×C4 | — | 118 | 6 | no | — |
| 518 | C22×C4 | — | 118 | 3 | no | — |
| 519 | C22×C4 | — | 118 | 3 | no | — |
| 520 | SD16 | — | 4 | 3 | no | — |
| 521 | SD16 | — | 236 | 3 | no | — |
| 522 | D8 | — | 118 | 2 | no | — |
| 523 | D8 | — | 118 | 2 | no | — |
| 524 | M16 | — | 236 | 6 | no | — |
| 525 | C2×C8 | — | 59 | 1 | no | — |
| 526 | C2×C8 | — | 59 | 3 | no | — |
| 527 | C2×C8 | C23×D59 | 1 | 1 | yes | characteristic |
| 528 | C2×C8 | C23×D59 | 1 | 3 | yes | — |
| 529 | C4⋊C4 | — | 2 | 3 | no | — |
| 530 | C4⋊C4 | — | 2 | 3 | no | — |
| 531 | C4⋊C4 | — | 2 | 3 | no | — |
| 532 | C4⋊C4 | — | 2 | 3 | no | — |
| 533 | C4⋊C4 | — | 59 | 3 | no | — |
| 534 | C4⋊C4 | — | 59 | 3 | no | — |
| 535 | C4⋊C4 | — | 59 | 3 | no | — |
| 536 | C4⋊C4 | — | 118 | 6 | no | — |
| 537 | C4⋊C4 | — | 118 | 3 | no | — |
| 538 | C4⋊C4 | — | 118 | 6 | no | — |
| 539 | C4⋊C4 | — | 118 | 3 | no | — |
| 540 | C4⋊C4 | — | 118 | 3 | no | — |
| 541 | C4⋊C4 | — | 118 | 3 | no | — |
| 542 | C4⋊C4 | D4×D59 | 1 | 3 | yes | — |
| 543 | C4⋊C4 | C23×D59 | 1 | 1 | yes | characteristic |
| 544 | C4⋊C4 | C23×D59 | 1 | 3 | yes | — |
| 545 | C22⋊C4 | — | 2 | 3 | no | — |
| 546 | C22⋊C4 | — | 59 | 6 | no | — |
| 547 | C22⋊C4 | — | 118 | 1 | no | — |
| 548 | C22⋊C4 | — | 118 | 3 | no | — |
| 549 | C22⋊C4 | — | 118 | 3 | no | — |
| 550 | C22⋊C4 | — | 118 | 6 | no | — |
| 551 | C22⋊C4 | — | 118 | 3 | no | — |
| 552 | C22⋊C4 | — | 118 | 3 | no | — |
| 553 | C22⋊C4 | — | 118 | 3 | no | — |
| 554 | C42 | — | 2 | 3 | no | — |
| 555 | C42 | — | 59 | 3 | no | — |
| 556 | C42 | — | 59 | 3 | no | — |
| 557 | C42 | — | 59 | 1 | no | — |
| 558 | C42 | — | 118 | 3 | no | — |
| 559 | C42 | — | 118 | 3 | no | — |
| 560 | C42 | C23×D59 | 1 | 3 | yes | — |
| 561 | C23 | — | 2 | 1 | no | — |
| 562 | C23 | — | 59 | 3 | no | — |
| 563 | C23 | — | 118 | 1 | no | — |
| 564 | C23 | — | 118 | 1 | no | — |
| 565 | Q8 | — | 2 | 3 | no | — |
| 566 | Q8 | — | 2 | 3 | no | — |
| 567 | Q8 | — | 4 | 6 | no | — |
| 568 | Q8 | — | 236 | 6 | no | — |
| 569 | Q8 | — | 236 | 6 | no | — |
| 570 | Q8 | — | 236 | 6 | no | — |
| 571 | Q8 | #14273754 | 1 | 4 | yes | — |
| 572 | D4 | — | 2 | 1 | no | — |
| 573 | D4 | — | 2 | 1 | no | — |
| 574 | D4 | — | 59 | 2 | no | — |
| 575 | D4 | — | 118 | 6 | no | — |
| 576 | D4 | — | 118 | 1 | no | — |
| 577 | D4 | — | 118 | 1 | no | — |
| 578 | D4 | — | 118 | 1 | no | — |
| 579 | D4 | — | 236 | 6 | no | — |
| 580 | D4 | — | 236 | 6 | no | — |
| 581 | D4 | — | 236 | 2 | no | — |
| 582 | D4 | — | 236 | 2 | no | — |
| 583 | D4 | — | 236 | 6 | no | — |
| 584 | C2×C4 | — | 2 | 1 | no | — |
| 585 | C2×C4 | — | 2 | 3 | no | — |
| 586 | C2×C4 | — | 2 | 3 | no | — |
| 587 | C2×C4 | — | 4 | 6 | no | — |
| 588 | C2×C4 | — | 59 | 1 | no | — |
| 589 | C2×C4 | — | 59 | 1 | no | — |
| 590 | C2×C4 | — | 59 | 3 | no | — |
| 591 | C2×C4 | — | 118 | 6 | no | — |
| 592 | C2×C4 | — | 118 | 6 | no | — |
| 593 | C2×C4 | — | 118 | 3 | no | — |
| 594 | C2×C4 | — | 118 | 3 | no | — |
| 595 | C2×C4 | — | 118 | 3 | no | — |
| 596 | C2×C4 | — | 118 | 3 | no | — |
| 597 | C2×C4 | — | 236 | 2 | no | — |
| 598 | C2×C4 | — | 236 | 6 | no | — |
| 599 | C2×C4 | — | 236 | 12 | no | — |
| 600 | C2×C4 | — | 236 | 6 | no | — |
| 601 | C2×C4 | — | 236 | 6 | no | — |
| 602 | C2×C4 | C2×D4×D59 | 1 | 3 | yes | — |
| 603 | C2×C4 | C2×D4×D59 | 1 | 3 | yes | — |
| 604 | C2×C4 | C24×D59 | 1 | 1 | yes | characteristic |
| 605 | C8 | — | 2 | 1 | no | — |
| 606 | C8 | — | 2 | 3 | no | — |
| 607 | C8 | — | 118 | 1 | no | — |
| 608 | C8 | — | 118 | 3 | no | — |
| 609 | C22 | — | 4 | 1 | no | — |
| 610 | C22 | — | 4 | 1 | no | — |
| 611 | C22 | — | 4 | 1 | no | — |
| 612 | C22 | — | 118 | 3 | no | — |
| 613 | C22 | — | 118 | 2 | no | — |
| 614 | C22 | — | 118 | 3 | no | — |
| 615 | C22 | — | 118 | 3 | no | — |
| 616 | C22 | — | 236 | 1 | no | — |
| 617 | C22 | — | 236 | 1 | no | — |
| 618 | C22 | — | 236 | 1 | no | — |
| 619 | C22 | — | 236 | 1 | no | — |
| 620 | C22 | — | 236 | 1 | no | — |
| 621 | C22 | C22×D4×D59 | 1 | 1 | yes | characteristic |
| 622 | C4 | — | 2 | 3 | no | — |
| 623 | C4 | — | 4 | 3 | no | — |
| 624 | C4 | — | 4 | 3 | no | — |
| 625 | C4 | — | 4 | 1 | no | — |
| 626 | C4 | — | 59 | 2 | no | — |
| 627 | C4 | — | 118 | 3 | no | — |
| 628 | C4 | — | 118 | 1 | no | — |
| 629 | C4 | — | 236 | 3 | no | — |
| 630 | C4 | — | 236 | 3 | no | — |
| 631 | C4 | C2×#14273754 | 1 | 6 | yes | — |
| 632 | C4 | 2−1+4×D59 | 1 | 1 | yes | characteristic |
| 633 | C4 | #16838238 | 1 | 1 | yes | characteristic |
| 634 | C2 | — | 8 | 1 | no | — |
| 635 | C2 | — | 472 | 1 | no | — |
| 636 | C2 | — | 236 | 3 | no | — |
| 637 | C2 | — | 236 | 2 | no | — |
| 638 | C2 | #21437775 | 1 | 1 | yes | characteristic |
| 639 | C2 | C22×#14273754 | 1 | 1 | yes | characteristic |
| 640 | C2 | #578×D59 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21437880 | C2 | semidirect |
| 2. #21437716 | C2 | semidirect |
| 3. Q8×D472 | C2 | semidirect |
| 4. Q8×#11745669 | C2 | semidirect |
| 5. #21436734 | C2 | semidirect |
| 6. #21436683 | C2 | semidirect |
| 7. #21436682 | C2 | semidirect |
| 8. #21436404 | C2 | semidirect |
| 9. #21436400 | C2 | semidirect |
| 10. #21435480 | C2 | semidirect |
| 11. #21435243 | C2 | semidirect |
| 12. #21434154 | C2 | semidirect |
| 13. #21433906 | C2 | semidirect |
| 14. #21433227 | C2 | semidirect |
| 15. C59×#3359 | C2 | semidirect |
| 271. D236 | 2−1+4 | semidirect |
| 319. #3359 | D59 | semidirect |
| 394. C59 | #62148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437880 | 2 |
| #21437716 | 2 |
| Q8×D472 | 2 |
| Q8×#11745669 | 2 |
| #21436734 | 2 |
| #21436683 | 2 |
| #21436682 | 2 |
| #21436404 | 2 |
| #21436400 | 2 |
| #21435480 | 2 |
| #21435243 | 2 |
| #21434154 | 2 |
| #21433906 | 2 |
| #21433227 | 2 |
| C59×#3359 | 2 |
| #62148 | 59 |