← #30544134
Subgroups — #30544134
Order 15616.
2706 conjugacy classes of subgroups.
The subgroup lattice has 426 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16840562 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21459020 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #21454664 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #21454653 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #21454621 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C4×#14519799 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #21454409 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#16839759 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×C61×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×#11758222 | C22 | 1 | 2 | yes | — |
| 11 | #16840562 | C4 | 1 | 16 | yes | complemented |
| 12 | C2×#14519810 | C22 | 1 | 4 | yes | — |
| 13 | C2×#14519805 | C22 | 1 | 4 | yes | — |
| 14 | C2×#14519799 | C22 | 1 | 4 | yes | — |
| 15 | #16840243 | — | 2 | 4 | no | — |
| 16 | #16840242 | C22 | 1 | 8 | yes | — |
| 17 | #16840239 | C22 | 1 | 4 | yes | complemented |
| 18 | #16840236 | C22 | 1 | 4 | yes | complemented |
| 19 | #16840235 | — | 2 | 4 | no | — |
| 20 | C4×#11758222 | C22 | 1 | 8 | yes | complemented |
| 21 | #16840230 | — | 2 | 4 | no | — |
| 22 | C2×#14519736 | C22 | 1 | 2 | yes | — |
| 23 | #117×D61 | — | 2 | 4 | no | — |
| 24 | #16839875 | C22 | 1 | 8 | yes | complemented |
| 25 | #16839870 | C22 | 1 | 8 | yes | complemented |
| 26 | #16839864 | C22 | 1 | 16 | yes | complemented |
| 27 | C4×Dic244 | C22 | 1 | 8 | yes | complemented |
| 28 | C4×#11758190 | C22 | 1 | 16 | yes | complemented |
| 29 | C4×D488 | C22 | 1 | 8 | yes | complemented |
| 30 | #16839804 | C22 | 1 | 8 | yes | complemented |
| 31 | #16839800 | C22 | 1 | 4 | yes | complemented |
| 32 | #16839759 | C22 | 1 | 8 | yes | — |
| 33 | #16839759 | C22 | 1 | 4 | yes | complemented |
| 34 | #16839759 | C22 | 1 | 4 | yes | complemented |
| 35 | C2×#14519702 | C22 | 1 | 4 | yes | complemented |
| 36 | C2×#14519699 | C22 | 1 | 4 | yes | complemented |
| 37 | C22×M16×C61 | C22 | 1 | 1 | yes | characteristic |
| 38 | C23×C8×C61 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#117×C61 | C22 | 1 | 1 | yes | characteristic |
| 40 | C61×#405 | C22 | 1 | 8 | yes | complemented |
| 41 | C2×#97×C61 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×C4×C8×C61 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#11758222 | — | 2 | 2 | no | — |
| 44 | C2×#11758222 | — | 2 | 2 | no | — |
| 45 | C2×#11758222 | — | 2 | 8 | no | — |
| 46 | C2×#11758222 | C2×C4 | 1 | 16 | yes | complemented |
| 47 | C2×#11758222 | C23 | 1 | 4 | yes | — |
| 48 | C2×#11758222 | C23 | 1 | 4 | yes | — |
| 49 | C22×Dic122 | C23 | 1 | 2 | yes | — |
| 50 | C22×D244 | C23 | 1 | 2 | yes | — |
| 51 | C22×C22⋊D61 | — | 2 | 2 | no | — |
| 52 | C22×C4×D61 | — | 2 | 2 | no | — |
| 53 | #14519810 | C2×C4 | 1 | 32 | yes | complemented |
| 54 | #14519805 | C2×C4 | 1 | 32 | yes | complemented |
| 55 | #14519799 | C2×C4 | 1 | 32 | yes | complemented |
| 56 | C2×Dic244 | C23 | 1 | 4 | yes | — |
| 57 | C2×#11758190 | C23 | 1 | 8 | yes | — |
| 58 | C2×D488 | C23 | 1 | 4 | yes | — |
| 59 | C4×Dic122 | C23 | 1 | 16 | yes | — |
| 60 | #14519742 | — | 2 | 8 | no | — |
| 61 | C4×D244 | C23 | 1 | 16 | yes | — |
| 62 | #14519739 | — | 2 | 8 | no | — |
| 63 | C4×C22⋊D61 | — | 2 | 16 | no | — |
| 64 | #14519737 | — | 2 | 16 | no | — |
| 65 | #14519736 | — | 2 | 2 | no | — |
| 66 | #14519736 | — | 2 | 2 | no | — |
| 67 | #14519736 | C23 | 1 | 4 | yes | — |
| 68 | #14519736 | C23 | 1 | 4 | yes | — |
| 69 | #14519735 | — | 2 | 8 | no | — |
| 70 | #14519734 | — | 2 | 8 | no | — |
| 71 | #14519733 | — | 2 | 8 | no | — |
| 72 | C2×C4⋊Dic61 | C23 | 1 | 4 | yes | — |
| 73 | C4⋊C4×D61 | — | 2 | 8 | no | — |
| 74 | C2×C22⋊Dic61 | — | 2 | 2 | no | — |
| 75 | C22⋊C4×D61 | — | 2 | 8 | no | — |
| 76 | C2×C4×Dic61 | — | 2 | 2 | no | — |
| 77 | C42×D61 | — | 2 | 8 | no | — |
| 78 | #14519711 | C23 | 1 | 8 | yes | — |
| 79 | #14519709 | C23 | 1 | 8 | yes | — |
| 80 | #14519702 | C23 | 1 | 8 | yes | — |
| 81 | #14519702 | C23 | 1 | 8 | yes | — |
| 82 | #14519699 | C23 | 1 | 8 | yes | — |
| 83 | #14519699 | C23 | 1 | 8 | yes | — |
| 84 | C23×C4×C61 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×M16×C61 | C2×C4 | 1 | 8 | yes | complemented |
| 86 | C2×M16×C61 | C23 | 1 | 4 | yes | — |
| 87 | C22×C8×C61 | — | 2 | 4 | no | — |
| 88 | C22×C8×C61 | C23 | 1 | 4 | yes | — |
| 89 | C22×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C8×C61 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C8×C61 | C23 | 1 | 2 | yes | — |
| 92 | #117×C61 | D4 | 1 | 4 | yes | — |
| 93 | #117×C61 | C23 | 1 | 4 | yes | — |
| 94 | C2×C4⋊C4×C61 | D4 | 1 | 2 | yes | — |
| 95 | C2×C22⋊C4×C61 | D4 | 1 | 2 | yes | — |
| 96 | C2×C42×C61 | C23 | 1 | 2 | yes | — |
| 97 | #97×C61 | C23 | 1 | 8 | yes | — |
| 98 | C4×C8×C61 | C23 | 1 | 8 | yes | — |
| 99 | C24×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C23×D61 | — | 2 | 2 | no | — |
| 101 | C22×C4×C61 | C22×C4 | 1 | 4 | yes | — |
| 102 | C22×C4×C61 | C2×D4 | 1 | 4 | yes | — |
| 103 | C22×C4×C61 | C2×D4 | 1 | 2 | yes | — |
| 104 | C22×C4×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C22×C4×C61 | #41 | 1 | 4 | yes | — |
| 106 | C22×C4×C61 | C24 | 1 | 2 | yes | — |
| 107 | C22×C4×C61 | C24 | 1 | 1 | yes | characteristic |
| 108 | C2×C22⋊D61 | — | 2 | 16 | no | — |
| 109 | C2×C22⋊D61 | — | 2 | 4 | no | — |
| 110 | C2×C22⋊D61 | — | 2 | 4 | no | — |
| 111 | C22×Dic61 | — | 2 | 2 | no | — |
| 112 | C22×Dic61 | — | 2 | 4 | no | — |
| 113 | #11758222 | — | 2 | 16 | no | — |
| 114 | #11758222 | — | 2 | 16 | no | — |
| 115 | #11758222 | — | 2 | 8 | no | — |
| 116 | #11758222 | — | 2 | 8 | no | — |
| 117 | #11758222 | C22×C4 | 1 | 16 | yes | — |
| 118 | #11758222 | C22×C4 | 1 | 16 | yes | — |
| 119 | C2×D244 | — | 2 | 2 | no | — |
| 120 | C2×D244 | — | 2 | 4 | no | — |
| 121 | C2×D244 | C22×C4 | 1 | 8 | yes | — |
| 122 | C2×D244 | C24 | 1 | 4 | yes | — |
| 123 | C2×C4×D61 | — | 2 | 16 | no | — |
| 124 | C2×C4×D61 | — | 2 | 4 | no | — |
| 125 | C2×C4×D61 | — | 2 | 4 | no | — |
| 126 | C2×C4×D61 | — | 2 | 16 | no | — |
| 127 | C2×Dic122 | — | 2 | 2 | no | — |
| 128 | C2×Dic122 | — | 2 | 4 | no | — |
| 129 | C2×Dic122 | C22×C4 | 1 | 8 | yes | — |
| 130 | C2×Dic122 | C24 | 1 | 4 | yes | — |
| 131 | M16×C61 | C22×C4 | 1 | 16 | yes | — |
| 132 | C2×C8×C61 | — | 2 | 8 | no | — |
| 133 | C2×C8×C61 | — | 2 | 2 | no | — |
| 134 | C2×C8×C61 | — | 2 | 2 | no | — |
| 135 | C2×C8×C61 | C22×C4 | 1 | 8 | yes | — |
| 136 | C2×C8×C61 | C24 | 1 | 2 | yes | — |
| 137 | C2×C8×C61 | C24 | 1 | 2 | yes | — |
| 138 | C2×C8×C61 | C24 | 1 | 4 | yes | — |
| 139 | C4⋊C4×C61 | C2×D4 | 1 | 8 | yes | — |
| 140 | C22⋊C4×C61 | C2×D4 | 1 | 8 | yes | — |
| 141 | C42×C61 | C2×D4 | 1 | 4 | yes | — |
| 142 | C42×C61 | C24 | 1 | 4 | yes | — |
| 143 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 144 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 145 | #11758198 | — | 2 | 16 | no | — |
| 146 | C4⋊Dic61 | — | 2 | 4 | no | — |
| 147 | C4⋊Dic61 | C24 | 1 | 8 | yes | — |
| 148 | #11758196 | — | 2 | 16 | no | — |
| 149 | C4×Dic61 | — | 2 | 4 | no | — |
| 150 | C4×Dic61 | — | 2 | 16 | no | — |
| 151 | C4×Dic61 | — | 2 | 4 | no | — |
| 152 | Dic244 | C22×C4 | 1 | 16 | yes | — |
| 153 | D488 | C22×C4 | 1 | 16 | yes | — |
| 154 | #11758190 | C22×C4 | 1 | 32 | yes | — |
| 155 | C23×C61 | — | 4 | 2 | no | — |
| 156 | C23×C61 | C4×D4 | 1 | 4 | yes | — |
| 157 | C23×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 158 | C23×C61 | C22×D4 | 1 | 2 | yes | — |
| 159 | C22×D61 | — | 2 | 4 | no | — |
| 160 | C22×D61 | — | 2 | 8 | no | — |
| 161 | C22×D61 | — | 8 | 4 | no | — |
| 162 | C2×C4×C61 | — | 4 | 4 | no | — |
| 163 | C2×C4×C61 | C4×D4 | 1 | 8 | yes | — |
| 164 | C2×C4×C61 | C4×D4 | 1 | 4 | yes | — |
| 165 | C2×C4×C61 | C23×C4 | 1 | 2 | yes | — |
| 166 | C2×C4×C61 | C23×C4 | 1 | 4 | yes | — |
| 167 | C2×C4×C61 | C22×D4 | 1 | 8 | yes | — |
| 168 | C2×C4×C61 | C22×D4 | 1 | 2 | yes | — |
| 169 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C61 | C2×#41 | 1 | 4 | yes | — |
| 171 | C2×C4×C61 | C2×#41 | 1 | 2 | yes | — |
| 172 | C2×C4×C61 | C25 | 1 | 1 | yes | characteristic |
| 173 | C22⋊D61 | — | 2 | 16 | no | — |
| 174 | C22⋊D61 | — | 2 | 16 | no | — |
| 175 | C2×Dic61 | — | 2 | 8 | no | — |
| 176 | C2×Dic61 | — | 2 | 4 | no | — |
| 177 | C2×Dic61 | — | 2 | 8 | no | — |
| 178 | C2×Dic61 | — | 8 | 4 | no | — |
| 179 | D244 | — | 2 | 8 | no | — |
| 180 | D244 | — | 2 | 4 | no | — |
| 181 | D244 | C23×C4 | 1 | 8 | yes | — |
| 182 | C4×D61 | — | 2 | 16 | no | — |
| 183 | C4×D61 | — | 2 | 16 | no | — |
| 184 | C4×D61 | — | 8 | 16 | no | — |
| 185 | Dic122 | — | 2 | 8 | no | — |
| 186 | Dic122 | — | 2 | 4 | no | — |
| 187 | Dic122 | C23×C4 | 1 | 8 | yes | — |
| 188 | C8×C61 | — | 2 | 2 | no | — |
| 189 | C8×C61 | — | 2 | 2 | no | — |
| 190 | C8×C61 | C23×C4 | 1 | 8 | yes | — |
| 191 | #60161 | — | 61 | 1 | no | maximal, Sylow |
| 192 | C22×C61 | — | 2 | 4 | no | — |
| 193 | C22×C61 | — | 2 | 2 | no | — |
| 194 | C22×C61 | — | 4 | 4 | no | — |
| 195 | C22×C61 | C2×C4×D4 | 1 | 4 | yes | — |
| 196 | C22×C61 | C2×C4×D4 | 1 | 2 | yes | — |
| 197 | C22×C61 | C23×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×D61 | — | 2 | 8 | no | — |
| 199 | C2×D61 | — | 4 | 8 | no | — |
| 200 | C2×D61 | — | 8 | 8 | no | — |
| 201 | C4×C61 | — | 2 | 8 | no | — |
| 202 | C4×C61 | C2×C4×D4 | 1 | 4 | yes | — |
| 203 | C4×C61 | C2×C4×D4 | 1 | 2 | yes | — |
| 204 | C4×C61 | C24×C4 | 1 | 1 | yes | characteristic |
| 205 | C4×C61 | C22×#41 | 1 | 1 | yes | characteristic |
| 206 | Dic61 | — | 2 | 8 | no | — |
| 207 | Dic61 | — | 4 | 8 | no | — |
| 208 | C2×#575 | — | 61 | 1 | no | — |
| 209 | #3428 | — | 61 | 2 | no | — |
| 210 | #2947 | — | 61 | 8 | no | — |
| 211 | #2946 | — | 61 | 8 | no | — |
| 212 | #2943 | — | 61 | 4 | no | — |
| 213 | C4×#135 | — | 61 | 4 | no | — |
| 214 | #2911 | — | 61 | 1 | no | — |
| 215 | C2×#416 | — | 61 | 2 | no | — |
| 216 | C2×#405 | D61 | 1 | 1 | yes | characteristic, complemented |
| 217 | C2×C61 | — | 2 | 4 | no | — |
| 218 | C2×C61 | — | 2 | 2 | no | — |
| 219 | C2×C61 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C61 | #3584 | 1 | 2 | yes | — |
| 221 | D61 | — | 4 | 8 | no | — |
| 222 | C22×#41 | — | 61 | 2 | no | — |
| 223 | #575 | — | 61 | 16 | no | — |
| 224 | C2×#137 | — | 61 | 4 | no | — |
| 225 | C2×AGL(1,ℤ/8) | — | 61 | 4 | no | — |
| 226 | C2×#135 | — | 61 | 4 | no | — |
| 227 | C22×M16 | C2×D61 | 1 | 1 | yes | characteristic |
| 228 | C23×C8 | C2×D61 | 1 | 1 | yes | characteristic |
| 229 | #520 | — | 61 | 8 | no | — |
| 230 | #520 | — | 122 | 4 | no | — |
| 231 | #519 | — | 61 | 4 | no | — |
| 232 | #518 | — | 61 | 4 | no | — |
| 233 | #518 | — | 122 | 4 | no | — |
| 234 | C4×#41 | — | 61 | 8 | no | — |
| 235 | C4×#41 | — | 122 | 4 | no | — |
| 236 | C2×#117 | — | 61 | 2 | no | — |
| 237 | C2×#117 | — | 122 | 4 | no | — |
| 238 | C2×#117 | C2×D61 | 1 | 1 | yes | characteristic |
| 239 | #442 | — | 61 | 8 | no | — |
| 240 | #441 | — | 61 | 8 | no | — |
| 241 | #440 | — | 61 | 16 | no | — |
| 242 | C4×Q16 | — | 61 | 8 | no | — |
| 243 | C4×SD16 | — | 61 | 16 | no | — |
| 244 | C4×D8 | — | 61 | 8 | no | — |
| 245 | #428 | — | 61 | 8 | no | — |
| 246 | #427 | — | 61 | 4 | no | — |
| 247 | #416 | — | 61 | 8 | no | — |
| 248 | #416 | — | 61 | 4 | no | — |
| 249 | #416 | — | 61 | 4 | no | — |
| 250 | C2×#103 | — | 61 | 4 | no | — |
| 251 | C2×#102 | — | 61 | 4 | no | — |
| 252 | #405 | C2×D61 | 1 | 8 | yes | complemented |
| 253 | C2×#97 | C2×D61 | 1 | 2 | yes | complemented |
| 254 | C2×C4×C8 | C2×D61 | 1 | 2 | yes | complemented |
| 255 | C61 | #60161 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 256 | C2×#41 | — | 61 | 16 | no | — |
| 257 | C2×#41 | — | 61 | 4 | no | — |
| 258 | C2×#41 | — | 61 | 4 | no | — |
| 259 | C2×#41 | — | 122 | 2 | no | — |
| 260 | C2×#41 | — | 122 | 2 | no | — |
| 261 | C2×#41 | — | 122 | 8 | no | — |
| 262 | C22×Q8 | — | 61 | 2 | no | — |
| 263 | C22×D4 | — | 61 | 2 | no | — |
| 264 | C22×D4 | — | 122 | 2 | no | — |
| 265 | C23×C4 | — | 122 | 2 | no | — |
| 266 | C23×C4 | C22×D61 | 1 | 1 | yes | characteristic |
| 267 | #137 | — | 61 | 32 | no | — |
| 268 | AGL(1,ℤ/8) | — | 61 | 32 | no | — |
| 269 | #135 | — | 61 | 32 | no | — |
| 270 | C2×Q16 | — | 61 | 4 | no | — |
| 271 | C2×SD16 | — | 61 | 8 | no | — |
| 272 | C2×D8 | — | 61 | 4 | no | — |
| 273 | C2×M16 | C4×D61 | 1 | 8 | yes | complemented |
| 274 | C2×M16 | C22×D61 | 1 | 4 | yes | — |
| 275 | C22×C8 | — | 2 | 4 | no | — |
| 276 | C22×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 277 | C22×C8 | C22×D61 | 1 | 1 | yes | characteristic |
| 278 | C22×C8 | C22×D61 | 1 | 4 | yes | — |
| 279 | C22×C8 | C22×D61 | 1 | 2 | yes | — |
| 280 | C4×Q8 | — | 61 | 16 | no | — |
| 281 | C4×Q8 | — | 122 | 8 | no | — |
| 282 | C4×D4 | — | 61 | 16 | no | — |
| 283 | C4×D4 | — | 122 | 16 | no | — |
| 284 | C4×D4 | — | 122 | 8 | no | — |
| 285 | C4×D4 | — | 122 | 16 | no | — |
| 286 | #117 | — | 61 | 4 | no | — |
| 287 | #117 | — | 61 | 4 | no | — |
| 288 | #117 | — | 122 | 2 | no | — |
| 289 | #117 | — | 122 | 2 | no | — |
| 290 | #117 | — | 122 | 8 | no | — |
| 291 | #117 | — | 122 | 8 | no | — |
| 292 | #117 | — | 122 | 8 | no | — |
| 293 | #117 | D244 | 1 | 4 | yes | — |
| 294 | #117 | C22×D61 | 1 | 4 | yes | — |
| 295 | C2×C4⋊C4 | — | 61 | 4 | no | — |
| 296 | C2×C4⋊C4 | — | 122 | 8 | no | — |
| 297 | C2×C4⋊C4 | D244 | 1 | 2 | yes | — |
| 298 | C2×C22⋊C4 | — | 122 | 2 | no | — |
| 299 | C2×C22⋊C4 | — | 122 | 8 | no | — |
| 300 | C2×C22⋊C4 | D244 | 1 | 2 | yes | — |
| 301 | C2×C42 | — | 122 | 2 | no | — |
| 302 | C2×C42 | — | 122 | 8 | no | — |
| 303 | C2×C42 | C22×D61 | 1 | 2 | yes | — |
| 304 | #107 | — | 61 | 8 | no | — |
| 305 | #106 | — | 61 | 8 | no | — |
| 306 | #103 | — | 61 | 8 | no | — |
| 307 | #103 | — | 61 | 8 | no | — |
| 308 | #102 | — | 61 | 8 | no | — |
| 309 | #102 | — | 61 | 8 | no | — |
| 310 | #97 | C22×D61 | 1 | 8 | yes | — |
| 311 | C4×C8 | C22×D61 | 1 | 8 | yes | — |
| 312 | C24 | — | 122 | 2 | no | — |
| 313 | C24 | C2×D244 | 1 | 1 | yes | characteristic |
| 314 | #41 | — | 61 | 16 | no | — |
| 315 | #41 | — | 61 | 16 | no | — |
| 316 | #41 | — | 122 | 8 | no | — |
| 317 | #41 | — | 122 | 8 | no | — |
| 318 | #41 | — | 122 | 16 | no | — |
| 319 | #41 | — | 122 | 16 | no | — |
| 320 | C2×Q8 | — | 61 | 8 | no | — |
| 321 | C2×Q8 | — | 61 | 4 | no | — |
| 322 | C2×Q8 | — | 122 | 2 | no | — |
| 323 | C2×Q8 | — | 122 | 4 | no | — |
| 324 | C2×D4 | — | 61 | 8 | no | — |
| 325 | C2×D4 | — | 61 | 4 | no | — |
| 326 | C2×D4 | — | 122 | 4 | no | — |
| 327 | C2×D4 | — | 122 | 4 | no | — |
| 328 | C2×D4 | — | 122 | 16 | no | — |
| 329 | C2×D4 | — | 122 | 2 | no | — |
| 330 | C2×D4 | — | 122 | 4 | no | — |
| 331 | C22×C4 | — | 122 | 2 | no | — |
| 332 | C22×C4 | — | 122 | 4 | no | — |
| 333 | C22×C4 | — | 122 | 4 | no | — |
| 334 | C22×C4 | — | 122 | 16 | no | — |
| 335 | C22×C4 | — | 122 | 4 | no | — |
| 336 | C22×C4 | — | 122 | 16 | no | — |
| 337 | C22×C4 | C2×C4×D61 | 1 | 4 | yes | — |
| 338 | C22×C4 | C2×D244 | 1 | 4 | yes | — |
| 339 | C22×C4 | C2×D244 | 1 | 1 | yes | characteristic |
| 340 | C22×C4 | C2×D244 | 1 | 2 | yes | — |
| 341 | C22×C4 | #11758222 | 1 | 4 | yes | — |
| 342 | C22×C4 | C23×D61 | 1 | 2 | yes | — |
| 343 | C22×C4 | C23×D61 | 1 | 1 | yes | characteristic |
| 344 | Q16 | — | 61 | 16 | no | — |
| 345 | SD16 | — | 61 | 32 | no | — |
| 346 | D8 | — | 61 | 16 | no | — |
| 347 | M16 | C2×C4×D61 | 1 | 16 | yes | — |
| 348 | C2×C8 | — | 2 | 8 | no | — |
| 349 | C2×C8 | — | 2 | 2 | no | — |
| 350 | C2×C8 | — | 2 | 2 | no | — |
| 351 | C2×C8 | C2×C4×D61 | 1 | 8 | yes | — |
| 352 | C2×C8 | C23×D61 | 1 | 2 | yes | — |
| 353 | C2×C8 | C23×D61 | 1 | 2 | yes | — |
| 354 | C2×C8 | C23×D61 | 1 | 4 | yes | — |
| 355 | C4⋊C4 | — | 61 | 8 | no | — |
| 356 | C4⋊C4 | — | 122 | 4 | no | — |
| 357 | C4⋊C4 | — | 122 | 16 | no | — |
| 358 | C4⋊C4 | C2×D244 | 1 | 8 | yes | — |
| 359 | C22⋊C4 | — | 122 | 4 | no | — |
| 360 | C22⋊C4 | — | 122 | 4 | no | — |
| 361 | C22⋊C4 | — | 122 | 16 | no | — |
| 362 | C22⋊C4 | C2×D244 | 1 | 8 | yes | — |
| 363 | C42 | — | 122 | 4 | no | — |
| 364 | C42 | — | 122 | 16 | no | — |
| 365 | C42 | — | 122 | 4 | no | — |
| 366 | C42 | C2×D244 | 1 | 4 | yes | — |
| 367 | C42 | C23×D61 | 1 | 4 | yes | — |
| 368 | C23 | — | 4 | 2 | no | — |
| 369 | C23 | — | 122 | 8 | no | — |
| 370 | C23 | — | 122 | 4 | no | — |
| 371 | C23 | — | 488 | 4 | no | — |
| 372 | C23 | C4×D244 | 1 | 4 | yes | — |
| 373 | C23 | C22×D244 | 1 | 1 | yes | characteristic |
| 374 | C23 | C22×D244 | 1 | 2 | yes | — |
| 375 | Q8 | — | 61 | 8 | no | — |
| 376 | Q8 | — | 122 | 8 | no | — |
| 377 | Q8 | — | 122 | 4 | no | — |
| 378 | D4 | — | 61 | 8 | no | — |
| 379 | D4 | — | 122 | 16 | no | — |
| 380 | D4 | — | 122 | 16 | no | — |
| 381 | D4 | — | 122 | 8 | no | — |
| 382 | D4 | — | 122 | 4 | no | — |
| 383 | C2×C4 | — | 4 | 4 | no | — |
| 384 | C2×C4 | — | 122 | 8 | no | — |
| 385 | C2×C4 | — | 122 | 4 | no | — |
| 386 | C2×C4 | — | 122 | 16 | no | — |
| 387 | C2×C4 | — | 122 | 16 | no | — |
| 388 | C2×C4 | — | 122 | 8 | no | — |
| 389 | C2×C4 | — | 488 | 16 | no | — |
| 390 | C2×C4 | — | 488 | 4 | no | — |
| 391 | C2×C4 | C4×D244 | 1 | 8 | yes | — |
| 392 | C2×C4 | C4×D244 | 1 | 4 | yes | — |
| 393 | C2×C4 | C22×C4×D61 | 1 | 2 | yes | — |
| 394 | C2×C4 | C22×C4×D61 | 1 | 4 | yes | — |
| 395 | C2×C4 | C22×D244 | 1 | 8 | yes | — |
| 396 | C2×C4 | C22×D244 | 1 | 2 | yes | — |
| 397 | C2×C4 | C22×D244 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | C2×#11758222 | 1 | 4 | yes | — |
| 399 | C2×C4 | C2×#11758222 | 1 | 2 | yes | — |
| 400 | C2×C4 | C24×D61 | 1 | 1 | yes | characteristic |
| 401 | C8 | — | 2 | 2 | no | — |
| 402 | C8 | — | 2 | 2 | no | — |
| 403 | C8 | C22×C4×D61 | 1 | 8 | yes | — |
| 404 | C22 | — | 2 | 2 | no | — |
| 405 | C22 | — | 2 | 4 | no | — |
| 406 | C22 | — | 4 | 4 | no | — |
| 407 | C22 | — | 122 | 8 | no | — |
| 408 | C22 | — | 488 | 8 | no | — |
| 409 | C22 | — | 244 | 8 | no | — |
| 410 | C22 | C2×C4×D244 | 1 | 4 | yes | — |
| 411 | C22 | C2×C4×D244 | 1 | 2 | yes | — |
| 412 | C22 | C23×D244 | 1 | 1 | yes | characteristic |
| 413 | C4 | — | 2 | 8 | no | — |
| 414 | C4 | — | 122 | 8 | no | — |
| 415 | C4 | — | 244 | 8 | no | — |
| 416 | C4 | C2×C4×D244 | 1 | 2 | yes | — |
| 417 | C4 | C2×C4×D244 | 1 | 4 | yes | — |
| 418 | C4 | C23×C4×D61 | 1 | 1 | yes | characteristic |
| 419 | C4 | C22×#11758222 | 1 | 1 | yes | characteristic |
| 420 | C2 | — | 2 | 4 | no | — |
| 421 | C2 | — | 2 | 2 | no | — |
| 422 | C2 | — | 244 | 8 | no | — |
| 423 | C2 | C22×C4×D244 | 1 | 1 | yes | characteristic |
| 424 | C2 | #21460593 | 1 | 2 | yes | — |
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