Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1056 conjugacy classes of subgroups.
The subgroup lattice has 579 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10593139 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#63511 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10589628 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C9×#421 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10588814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10588685 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10588506 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10588505 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #78995 | — | 3 | 1 | no | maximal |
| 11 | C2×C9×#41 | C22 | 1 | 1 | yes | characteristic |
| 12 | #63716 | — | 2 | 1 | no | — |
| 13 | #63716 | C22 | 1 | 2 | yes | — |
| 14 | #63715 | — | 2 | 1 | no | — |
| 15 | #63715 | C22 | 1 | 2 | yes | — |
| 16 | #41×D9 | — | 2 | 2 | no | — |
| 17 | #41×D9 | — | 2 | 2 | no | — |
| 18 | #63713 | — | 2 | 1 | no | — |
| 19 | #63710 | — | 2 | 1 | no | — |
| 20 | #63710 | — | 2 | 2 | no | — |
| 21 | C2×#3697 | — | 2 | 2 | no | — |
| 22 | C2×#3697 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#3697 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×Dic18 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×C9×M16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C9×#117 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #63511 | — | 2 | 2 | no | — |
| 28 | #63511 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×#3674 | — | 2 | 1 | no | — |
| 30 | C2×#3672 | — | 2 | 1 | no | — |
| 31 | C2×#3667 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #63471 | — | 2 | 2 | no | — |
| 33 | #63471 | C22 | 1 | 4 | yes | complemented |
| 34 | C2×#3664 | — | 2 | 1 | no | — |
| 35 | C2×Dic36 | — | 2 | 1 | no | — |
| 36 | #63459 | — | 2 | 2 | no | — |
| 37 | #63448 | — | 2 | 2 | no | — |
| 38 | #63437 | C22 | 1 | 2 | yes | complemented |
| 39 | #63431 | C22 | 1 | 2 | yes | complemented |
| 40 | C9×#104 | C22 | 1 | 4 | yes | complemented |
| 41 | #63383 | C22 | 1 | 2 | yes | complemented |
| 42 | #63382 | C22 | 1 | 2 | yes | complemented |
| 43 | #63364 | C22 | 1 | 4 | yes | complemented |
| 44 | #5964 | — | 3 | 1 | no | — |
| 45 | C2×#951 | — | 3 | 1 | no | — |
| 46 | C2×#909 | — | 3 | 1 | no | — |
| 47 | #5526 | — | 3 | 1 | no | — |
| 48 | C3×#421 | D3 | 1 | 1 | yes | characteristic |
| 49 | #5132 | — | 3 | 1 | no | — |
| 50 | #5005 | — | 3 | 1 | no | — |
| 51 | #4826 | — | 3 | 4 | no | — |
| 52 | #4825 | — | 3 | 4 | no | — |
| 53 | C9×#41 | — | 2 | 1 | no | — |
| 54 | C9×#41 | — | 2 | 1 | no | — |
| 55 | C9×#41 | D4 | 1 | 2 | yes | — |
| 56 | C9×#41 | C23 | 1 | 2 | yes | — |
| 57 | C2×Q8×C9 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×D4×C9 | — | 2 | 1 | no | — |
| 59 | C2×D4×C9 | D4 | 1 | 1 | yes | characteristic |
| 60 | C22×C4×C9 | — | 2 | 1 | no | — |
| 61 | C22×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#611 | — | 2 | 4 | no | — |
| 63 | C2×#611 | — | 2 | 1 | no | — |
| 64 | C2×#611 | D4 | 1 | 2 | yes | — |
| 65 | C22×Dic9 | — | 2 | 1 | no | — |
| 66 | #3701 | — | 2 | 2 | no | — |
| 67 | #3701 | — | 2 | 2 | no | — |
| 68 | Q8×D9 | — | 2 | 2 | no | — |
| 69 | Q8×D9 | — | 2 | 2 | no | — |
| 70 | #3699 | — | 2 | 4 | no | — |
| 71 | #3699 | — | 2 | 2 | no | — |
| 72 | #3699 | — | 2 | 2 | no | — |
| 73 | #3699 | — | 2 | 4 | no | — |
| 74 | D4×D9 | — | 2 | 4 | no | — |
| 75 | D4×D9 | — | 2 | 2 | no | — |
| 76 | D4×D9 | — | 2 | 4 | no | — |
| 77 | D4×D9 | — | 2 | 2 | no | — |
| 78 | #3697 | — | 2 | 4 | no | — |
| 79 | #3697 | — | 2 | 4 | no | — |
| 80 | #3697 | — | 2 | 1 | no | — |
| 81 | #3697 | — | 2 | 1 | no | — |
| 82 | #3697 | — | 2 | 1 | no | — |
| 83 | #3697 | — | 2 | 1 | no | — |
| 84 | #3697 | — | 2 | 1 | no | — |
| 85 | #3697 | — | 2 | 1 | no | — |
| 86 | #3697 | — | 2 | 2 | no | — |
| 87 | #3697 | — | 2 | 2 | no | — |
| 88 | #3697 | D4 | 1 | 2 | yes | — |
| 89 | #3697 | C23 | 1 | 2 | yes | — |
| 90 | C2×D36 | — | 2 | 2 | no | — |
| 91 | C2×D36 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×D36 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×D9 | — | 2 | 4 | no | — |
| 94 | C2×C4×D9 | — | 2 | 1 | no | — |
| 95 | C2×C4×D9 | D4 | 1 | 2 | yes | — |
| 96 | C2×Dic18 | — | 2 | 2 | no | — |
| 97 | C2×Dic18 | — | 2 | 1 | no | — |
| 98 | C2×Dic18 | — | 2 | 1 | no | — |
| 99 | C2×Dic18 | — | 2 | 1 | no | — |
| 100 | C2×Dic18 | — | 2 | 1 | no | — |
| 101 | C2×Dic18 | — | 2 | 1 | no | — |
| 102 | C2×Dic18 | D4 | 1 | 1 | yes | characteristic |
| 103 | C2×Dic18 | C23 | 1 | 2 | yes | — |
| 104 | C2×Dic18 | C23 | 1 | 1 | yes | characteristic |
| 105 | C9×M16 | — | 2 | 1 | no | — |
| 106 | C9×M16 | C23 | 1 | 2 | yes | — |
| 107 | C2×C8×C9 | — | 2 | 1 | no | — |
| 108 | C9×C4⋊C4 | — | 2 | 1 | no | — |
| 109 | C9×C22⋊C4 | — | 2 | 1 | no | — |
| 110 | C42×C9 | C23 | 1 | 2 | yes | — |
| 111 | #3674 | — | 2 | 4 | no | — |
| 112 | #3672 | — | 2 | 4 | no | — |
| 113 | (C2×D9)⋊C4 | — | 2 | 4 | no | — |
| 114 | C4⋊Dic9 | — | 2 | 4 | no | — |
| 115 | #3667 | — | 2 | 1 | no | — |
| 116 | #3667 | C23 | 1 | 2 | yes | — |
| 117 | C2×C9⋊C8 | — | 2 | 1 | no | — |
| 118 | #3664 | — | 2 | 4 | no | — |
| 119 | Dic36 | — | 2 | 4 | no | — |
| 120 | #3022 | — | 9 | 1 | no | Sylow |
| 121 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 122 | #1010 | — | 3 | 2 | no | — |
| 123 | #1010 | — | 6 | 1 | no | — |
| 124 | #1009 | — | 3 | 2 | no | — |
| 125 | #1009 | — | 6 | 1 | no | — |
| 126 | D3×#41 | — | 6 | 2 | no | — |
| 127 | D3×#41 | — | 6 | 2 | no | — |
| 128 | #1007 | — | 6 | 1 | no | — |
| 129 | #1004 | — | 6 | 2 | no | — |
| 130 | #1004 | — | 6 | 1 | no | — |
| 131 | C2×#235 | — | 3 | 1 | no | — |
| 132 | C2×#235 | — | 3 | 1 | no | — |
| 133 | C2×#235 | — | 6 | 2 | no | — |
| 134 | C22×Dic6 | — | 3 | 1 | no | — |
| 135 | C2×C3×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 136 | C3×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 137 | #951 | — | 3 | 4 | no | — |
| 138 | #951 | — | 6 | 2 | no | — |
| 139 | C2×#216 | — | 6 | 1 | no | — |
| 140 | C2×#214 | — | 6 | 1 | no | — |
| 141 | C2×#208 | — | 3 | 1 | no | — |
| 142 | #909 | — | 3 | 4 | no | — |
| 143 | #909 | — | 6 | 2 | no | — |
| 144 | C2×Dic12 | — | 6 | 1 | no | — |
| 145 | C2×#204 | — | 6 | 1 | no | — |
| 146 | #897 | — | 6 | 2 | no | — |
| 147 | #886 | — | 6 | 2 | no | — |
| 148 | #875 | — | 3 | 2 | no | — |
| 149 | #869 | — | 3 | 2 | no | — |
| 150 | C3×#104 | C2×D3 | 1 | 4 | yes | — |
| 151 | #824 | — | 3 | 2 | no | — |
| 152 | #823 | — | 3 | 2 | no | — |
| 153 | #805 | — | 3 | 4 | no | — |
| 154 | C23×C9 | — | 2 | 1 | no | — |
| 155 | C23×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×D9 | — | 2 | 4 | no | — |
| 157 | C22×D9 | — | 2 | 1 | no | — |
| 158 | C22×D9 | C2×D4 | 1 | 2 | yes | — |
| 159 | Q8×C9 | — | 2 | 1 | no | — |
| 160 | Q8×C9 | C2×D4 | 1 | 2 | yes | — |
| 161 | D4×C9 | — | 2 | 2 | no | — |
| 162 | D4×C9 | — | 2 | 2 | no | — |
| 163 | D4×C9 | — | 2 | 1 | no | — |
| 164 | D4×C9 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×C4×C9 | — | 2 | 1 | no | — |
| 166 | C2×C4×C9 | — | 2 | 2 | no | — |
| 167 | C2×C4×C9 | — | 2 | 2 | no | — |
| 168 | C2×C4×C9 | — | 2 | 2 | no | — |
| 169 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 175 | #611 | — | 2 | 4 | no | — |
| 176 | #611 | — | 2 | 4 | no | — |
| 177 | #611 | — | 2 | 2 | no | — |
| 178 | #611 | — | 2 | 2 | no | — |
| 179 | #611 | — | 2 | 2 | no | — |
| 180 | #611 | — | 2 | 2 | no | — |
| 181 | C2×Dic9 | — | 2 | 4 | no | — |
| 182 | C2×Dic9 | — | 2 | 1 | no | — |
| 183 | C2×Dic9 | — | 2 | 2 | no | — |
| 184 | C2×Dic9 | — | 4 | 1 | no | — |
| 185 | C2×Dic9 | — | 4 | 1 | no | — |
| 186 | C2×Dic9 | C2×D4 | 1 | 2 | yes | — |
| 187 | D36 | — | 2 | 4 | no | — |
| 188 | D36 | — | 2 | 1 | no | — |
| 189 | D36 | — | 2 | 1 | no | — |
| 190 | D36 | — | 2 | 1 | no | — |
| 191 | D36 | C2×D4 | 1 | 2 | yes | — |
| 192 | C4×D9 | — | 2 | 4 | no | — |
| 193 | C4×D9 | — | 2 | 4 | no | — |
| 194 | C4×D9 | — | 2 | 2 | no | — |
| 195 | C4×D9 | — | 2 | 2 | no | — |
| 196 | C4×D9 | — | 2 | 2 | no | — |
| 197 | C4×D9 | — | 2 | 2 | no | — |
| 198 | Dic18 | — | 2 | 4 | no | — |
| 199 | Dic18 | — | 2 | 1 | no | — |
| 200 | Dic18 | — | 2 | 1 | no | — |
| 201 | Dic18 | — | 2 | 1 | no | — |
| 202 | Dic18 | — | 2 | 2 | no | — |
| 203 | Dic18 | — | 2 | 2 | no | — |
| 204 | Dic18 | — | 4 | 1 | no | — |
| 205 | Dic18 | — | 4 | 1 | no | — |
| 206 | Dic18 | C2×D4 | 1 | 2 | yes | — |
| 207 | C8×C9 | — | 2 | 2 | no | — |
| 208 | C9⋊C8 | — | 2 | 2 | no | — |
| 209 | #585 | — | 9 | 1 | no | — |
| 210 | C2×#137 | — | 9 | 1 | no | — |
| 211 | C2×#137 | — | 9 | 1 | no | — |
| 212 | #536 | — | 9 | 1 | no | — |
| 213 | #456 | — | 9 | 4 | no | — |
| 214 | #455 | — | 9 | 4 | no | — |
| 215 | #421 | — | 9 | 1 | no | — |
| 216 | #421 | D9 | 1 | 1 | yes | characteristic, complemented |
| 217 | #413 | — | 9 | 1 | no | — |
| 218 | C3×#41 | — | 2 | 1 | no | — |
| 219 | C3×#41 | — | 2 | 1 | no | — |
| 220 | C3×#41 | D12 | 1 | 2 | yes | — |
| 221 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 222 | C2×C3×Q8 | D12 | 1 | 1 | yes | characteristic |
| 223 | C2×C3×D4 | — | 2 | 1 | no | — |
| 224 | C2×C3×D4 | D12 | 1 | 1 | yes | characteristic |
| 225 | C22×C3×C4 | — | 2 | 1 | no | — |
| 226 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 227 | C2×#67 | — | 3 | 2 | no | — |
| 228 | C2×#67 | — | 6 | 4 | no | — |
| 229 | C2×#67 | — | 6 | 1 | no | — |
| 230 | C22×Dic3 | — | 6 | 1 | no | — |
| 231 | #239 | — | 6 | 2 | no | — |
| 232 | #239 | — | 6 | 2 | no | — |
| 233 | D3×Q8 | — | 6 | 2 | no | — |
| 234 | D3×Q8 | — | 6 | 2 | no | — |
| 235 | #237 | — | 6 | 4 | no | — |
| 236 | #237 | — | 6 | 4 | no | — |
| 237 | #237 | — | 6 | 2 | no | — |
| 238 | #237 | — | 6 | 2 | no | — |
| 239 | D3×D4 | — | 6 | 4 | no | — |
| 240 | D3×D4 | — | 6 | 4 | no | — |
| 241 | D3×D4 | — | 6 | 2 | no | — |
| 242 | D3×D4 | — | 6 | 2 | no | — |
| 243 | #235 | — | 3 | 2 | no | — |
| 244 | #235 | — | 3 | 2 | no | — |
| 245 | #235 | — | 6 | 2 | no | — |
| 246 | #235 | — | 6 | 2 | no | — |
| 247 | #235 | — | 6 | 4 | no | — |
| 248 | #235 | — | 6 | 4 | no | — |
| 249 | #235 | — | 6 | 1 | no | — |
| 250 | #235 | — | 6 | 1 | no | — |
| 251 | #235 | — | 6 | 1 | no | — |
| 252 | #235 | — | 6 | 1 | no | — |
| 253 | #235 | — | 6 | 1 | no | — |
| 254 | #235 | — | 6 | 1 | no | — |
| 255 | C2×D12 | — | 3 | 1 | no | — |
| 256 | C2×D12 | — | 3 | 1 | no | — |
| 257 | C2×D12 | — | 6 | 2 | no | — |
| 258 | C2×C4×D3 | — | 3 | 2 | no | — |
| 259 | C2×C4×D3 | — | 6 | 4 | no | — |
| 260 | C2×C4×D3 | — | 6 | 1 | no | — |
| 261 | C2×Dic6 | — | 3 | 1 | no | — |
| 262 | C2×Dic6 | — | 3 | 1 | no | — |
| 263 | C2×Dic6 | — | 3 | 2 | no | — |
| 264 | C2×Dic6 | — | 6 | 2 | no | — |
| 265 | C2×Dic6 | — | 6 | 1 | no | — |
| 266 | C2×Dic6 | — | 6 | 1 | no | — |
| 267 | C2×Dic6 | — | 6 | 1 | no | — |
| 268 | C2×Dic6 | — | 6 | 1 | no | — |
| 269 | C2×Dic6 | — | 6 | 1 | no | — |
| 270 | C3×M16 | — | 2 | 1 | no | — |
| 271 | C3×M16 | C22×D3 | 1 | 2 | yes | — |
| 272 | C2×C3×C8 | — | 2 | 1 | no | — |
| 273 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 274 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 275 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 276 | #216 | — | 6 | 4 | no | — |
| 277 | #214 | — | 6 | 4 | no | — |
| 278 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 279 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 280 | #208 | — | 3 | 2 | no | — |
| 281 | #208 | — | 6 | 1 | no | — |
| 282 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 283 | Dic12 | — | 6 | 4 | no | — |
| 284 | #204 | — | 6 | 4 | no | — |
| 285 | C22×C9 | — | 2 | 2 | no | — |
| 286 | C22×C9 | — | 4 | 1 | no | — |
| 287 | C22×C9 | — | 8 | 1 | no | — |
| 288 | C22×C9 | #120 | 1 | 1 | yes | characteristic |
| 289 | C22×C9 | #120 | 1 | 1 | yes | characteristic |
| 290 | C22×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×D9 | — | 2 | 2 | no | — |
| 292 | C2×D9 | — | 2 | 2 | no | — |
| 293 | C2×D9 | — | 4 | 2 | no | — |
| 294 | C2×D9 | — | 8 | 1 | no | — |
| 295 | C2×D9 | — | 8 | 4 | no | — |
| 296 | C4×C9 | — | 2 | 2 | no | — |
| 297 | C4×C9 | — | 4 | 2 | no | — |
| 298 | C4×C9 | #120 | 1 | 1 | yes | characteristic |
| 299 | C4×C9 | #120 | 1 | 1 | yes | characteristic |
| 300 | C4×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C4×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | Dic9 | — | 2 | 2 | no | — |
| 303 | Dic9 | — | 2 | 2 | no | — |
| 304 | Dic9 | — | 4 | 2 | no | — |
| 305 | 2−1+4 | — | 9 | 2 | no | — |
| 306 | 2−1+4 | — | 18 | 1 | no | — |
| 307 | 2−1+4 | — | 18 | 1 | no | — |
| 308 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 309 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 310 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 311 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 312 | C2×#41 | — | 9 | 1 | no | — |
| 313 | C2×#41 | — | 9 | 1 | no | — |
| 314 | C2×#41 | — | 18 | 2 | no | — |
| 315 | C2×#41 | — | 18 | 2 | no | — |
| 316 | C2×#41 | — | 18 | 2 | no | — |
| 317 | C2×#41 | C2×D9 | 1 | 1 | yes | characteristic |
| 318 | C22×Q8 | — | 9 | 1 | no | — |
| 319 | #137 | — | 9 | 4 | no | — |
| 320 | #137 | — | 9 | 4 | no | — |
| 321 | #137 | — | 18 | 2 | no | — |
| 322 | #137 | — | 18 | 2 | no | — |
| 323 | C2×Q16 | — | 18 | 1 | no | — |
| 324 | C2×Q16 | — | 18 | 1 | no | — |
| 325 | C2×SD16 | — | 18 | 1 | no | — |
| 326 | C2×SD16 | — | 18 | 1 | no | — |
| 327 | C2×M16 | — | 9 | 1 | no | — |
| 328 | C2×M16 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 329 | C4⋊Q8 | — | 9 | 2 | no | — |
| 330 | #124 | — | 9 | 2 | no | — |
| 331 | #123 | — | 18 | 2 | no | — |
| 332 | C22⋊Q8 | — | 18 | 2 | no | — |
| 333 | #117 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 334 | #104 | — | 9 | 4 | no | — |
| 335 | #104 | C2×D9 | 1 | 4 | yes | complemented |
| 336 | #101 | — | 9 | 2 | no | — |
| 337 | #100 | — | 9 | 2 | no | — |
| 338 | C23×C3 | — | 2 | 1 | no | — |
| 339 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 340 | C22×D3 | — | 3 | 2 | no | — |
| 341 | C22×D3 | — | 6 | 4 | no | — |
| 342 | C22×D3 | — | 6 | 1 | no | — |
| 343 | C3×Q8 | — | 2 | 1 | no | — |
| 344 | C3×Q8 | C2×D12 | 1 | 2 | yes | — |
| 345 | C3×D4 | — | 2 | 2 | no | — |
| 346 | C3×D4 | — | 2 | 2 | no | — |
| 347 | C3×D4 | — | 2 | 1 | no | — |
| 348 | C3×D4 | C2×D12 | 1 | 2 | yes | — |
| 349 | C2×C3×C4 | — | 2 | 1 | no | — |
| 350 | C2×C3×C4 | — | 2 | 2 | no | — |
| 351 | C2×C3×C4 | — | 2 | 2 | no | — |
| 352 | C2×C3×C4 | — | 2 | 2 | no | — |
| 353 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 354 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 355 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 356 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 359 | #67 | — | 6 | 4 | no | — |
| 360 | #67 | — | 6 | 4 | no | — |
| 361 | #67 | — | 6 | 2 | no | — |
| 362 | #67 | — | 6 | 2 | no | — |
| 363 | #67 | — | 6 | 2 | no | — |
| 364 | #67 | — | 6 | 2 | no | — |
| 365 | C2×Dic3 | — | 3 | 2 | no | — |
| 366 | C2×Dic3 | — | 6 | 4 | no | — |
| 367 | C2×Dic3 | — | 6 | 1 | no | — |
| 368 | C2×Dic3 | — | 6 | 2 | no | — |
| 369 | C2×Dic3 | — | 12 | 1 | no | — |
| 370 | C2×Dic3 | — | 12 | 1 | no | — |
| 371 | D12 | — | 3 | 2 | no | — |
| 372 | D12 | — | 6 | 4 | no | — |
| 373 | D12 | — | 6 | 1 | no | — |
| 374 | D12 | — | 6 | 1 | no | — |
| 375 | D12 | — | 6 | 1 | no | — |
| 376 | C4×D3 | — | 6 | 4 | no | — |
| 377 | C4×D3 | — | 6 | 4 | no | — |
| 378 | C4×D3 | — | 6 | 2 | no | — |
| 379 | C4×D3 | — | 6 | 2 | no | — |
| 380 | C4×D3 | — | 6 | 2 | no | — |
| 381 | C4×D3 | — | 6 | 2 | no | — |
| 382 | Dic6 | — | 3 | 2 | no | — |
| 383 | Dic6 | — | 6 | 4 | no | — |
| 384 | Dic6 | — | 6 | 1 | no | — |
| 385 | Dic6 | — | 6 | 1 | no | — |
| 386 | Dic6 | — | 6 | 1 | no | — |
| 387 | Dic6 | — | 6 | 2 | no | — |
| 388 | Dic6 | — | 6 | 2 | no | — |
| 389 | Dic6 | — | 12 | 1 | no | — |
| 390 | Dic6 | — | 12 | 1 | no | — |
| 391 | C3×C8 | — | 2 | 2 | no | — |
| 392 | C3⋊C8 | — | 6 | 2 | no | — |
| 393 | C2×C9 | — | 2 | 1 | no | — |
| 394 | C2×C9 | — | 2 | 1 | no | — |
| 395 | C2×C9 | — | 2 | 1 | no | — |
| 396 | C2×C9 | — | 4 | 2 | no | — |
| 397 | C2×C9 | C2×#120 | 1 | 1 | yes | characteristic |
| 398 | D9 | — | 4 | 2 | no | — |
| 399 | D9 | — | 4 | 2 | no | — |
| 400 | #41 | — | 2 | 1 | no | — |
| 401 | #41 | — | 2 | 1 | no | — |
| 402 | #41 | — | 9 | 2 | no | — |
| 403 | #41 | — | 9 | 2 | no | — |
| 404 | #41 | — | 18 | 2 | no | — |
| 405 | #41 | — | 18 | 2 | no | — |
| 406 | #41 | — | 18 | 4 | no | — |
| 407 | #41 | — | 18 | 4 | no | — |
| 408 | #41 | — | 18 | 4 | no | — |
| 409 | #41 | — | 18 | 4 | no | — |
| 410 | #41 | — | 18 | 2 | no | — |
| 411 | #41 | — | 18 | 2 | no | — |
| 412 | #41 | — | 18 | 2 | no | — |
| 413 | #41 | — | 18 | 2 | no | — |
| 414 | #41 | — | 18 | 1 | no | — |
| 415 | #41 | — | 18 | 1 | no | — |
| 416 | #41 | — | 18 | 1 | no | — |
| 417 | #41 | — | 18 | 1 | no | — |
| 418 | #41 | — | 18 | 1 | no | — |
| 419 | #41 | — | 18 | 1 | no | — |
| 420 | #41 | D36 | 1 | 2 | yes | — |
| 421 | #41 | C22×D9 | 1 | 2 | yes | — |
| 422 | C2×Q8 | — | 9 | 1 | no | — |
| 423 | C2×Q8 | — | 9 | 1 | no | — |
| 424 | C2×Q8 | — | 9 | 2 | no | — |
| 425 | C2×Q8 | — | 18 | 2 | no | — |
| 426 | C2×Q8 | — | 18 | 2 | no | — |
| 427 | C2×Q8 | — | 18 | 2 | no | — |
| 428 | C2×Q8 | — | 18 | 1 | no | — |
| 429 | C2×Q8 | — | 18 | 1 | no | — |
| 430 | C2×Q8 | — | 18 | 1 | no | — |
| 431 | C2×Q8 | — | 18 | 1 | no | — |
| 432 | C2×Q8 | — | 18 | 1 | no | — |
| 433 | C2×Q8 | D36 | 1 | 1 | yes | characteristic |
| 434 | C2×D4 | — | 2 | 1 | no | — |
| 435 | C2×D4 | — | 9 | 2 | no | — |
| 436 | C2×D4 | — | 9 | 1 | no | — |
| 437 | C2×D4 | — | 9 | 1 | no | — |
| 438 | C2×D4 | — | 18 | 2 | no | — |
| 439 | C2×D4 | — | 18 | 4 | no | — |
| 440 | C2×D4 | — | 18 | 4 | no | — |
| 441 | C2×D4 | — | 18 | 2 | no | — |
| 442 | C2×D4 | — | 18 | 4 | no | — |
| 443 | C2×D4 | — | 18 | 1 | no | — |
| 444 | C2×D4 | — | 18 | 2 | no | — |
| 445 | C2×D4 | D36 | 1 | 1 | yes | characteristic |
| 446 | C22×C4 | — | 2 | 1 | no | — |
| 447 | C22×C4 | — | 9 | 2 | no | — |
| 448 | C22×C4 | — | 18 | 4 | no | — |
| 449 | C22×C4 | — | 18 | 1 | no | — |
| 450 | C22×C4 | — | 18 | 1 | no | — |
| 451 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 452 | Q16 | — | 18 | 4 | no | — |
| 453 | Q16 | — | 18 | 4 | no | — |
| 454 | SD16 | — | 18 | 4 | no | — |
| 455 | SD16 | — | 18 | 4 | no | — |
| 456 | M16 | — | 2 | 1 | no | — |
| 457 | M16 | — | 9 | 2 | no | — |
| 458 | M16 | — | 18 | 1 | no | — |
| 459 | M16 | C22×D9 | 1 | 2 | yes | — |
| 460 | C2×C8 | — | 2 | 1 | no | — |
| 461 | C2×C8 | — | 18 | 1 | no | — |
| 462 | C4⋊C4 | — | 2 | 1 | no | — |
| 463 | C4⋊C4 | — | 18 | 4 | no | — |
| 464 | C22⋊C4 | — | 2 | 1 | no | — |
| 465 | C22⋊C4 | — | 18 | 4 | no | — |
| 466 | C42 | C22×D9 | 1 | 2 | yes | — |
| 467 | C22×C3 | — | 2 | 2 | no | — |
| 468 | C22×C3 | — | 4 | 1 | no | — |
| 469 | C22×C3 | — | 8 | 1 | no | — |
| 470 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 471 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 472 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 473 | C2×D3 | — | 6 | 2 | no | — |
| 474 | C2×D3 | — | 6 | 2 | no | — |
| 475 | C2×D3 | — | 12 | 2 | no | — |
| 476 | C2×D3 | — | 24 | 1 | no | — |
| 477 | C2×D3 | — | 24 | 4 | no | — |
| 478 | C3×C4 | — | 2 | 2 | no | — |
| 479 | C3×C4 | — | 4 | 2 | no | — |
| 480 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 481 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 482 | C3×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 483 | C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 484 | Dic3 | — | 6 | 2 | no | — |
| 485 | Dic3 | — | 6 | 2 | no | — |
| 486 | Dic3 | — | 12 | 2 | no | — |
| 487 | C9 | #3022 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 488 | C23 | — | 2 | 1 | no | — |
| 489 | C23 | — | 9 | 2 | no | — |
| 490 | C23 | — | 18 | 4 | no | — |
| 491 | C23 | — | 18 | 1 | no | — |
| 492 | C23 | D4×D9 | 1 | 1 | yes | characteristic |
| 493 | Q8 | — | 2 | 1 | no | — |
| 494 | Q8 | — | 9 | 2 | no | — |
| 495 | Q8 | — | 18 | 4 | no | — |
| 496 | Q8 | — | 18 | 1 | no | — |
| 497 | Q8 | — | 18 | 1 | no | — |
| 498 | Q8 | — | 18 | 1 | no | — |
| 499 | Q8 | — | 18 | 2 | no | — |
| 500 | Q8 | — | 18 | 2 | no | — |
| 501 | Q8 | — | 36 | 1 | no | — |
| 502 | Q8 | — | 36 | 1 | no | — |
| 503 | Q8 | C2×D36 | 1 | 2 | yes | — |
| 504 | D4 | — | 2 | 2 | no | — |
| 505 | D4 | — | 2 | 2 | no | — |
| 506 | D4 | — | 2 | 1 | no | — |
| 507 | D4 | — | 9 | 2 | no | — |
| 508 | D4 | — | 18 | 4 | no | — |
| 509 | D4 | — | 18 | 4 | no | — |
| 510 | D4 | — | 18 | 4 | no | — |
| 511 | D4 | — | 18 | 2 | no | — |
| 512 | D4 | — | 18 | 2 | no | — |
| 513 | D4 | — | 18 | 2 | no | — |
| 514 | D4 | — | 18 | 2 | no | — |
| 515 | D4 | — | 18 | 1 | no | — |
| 516 | D4 | — | 18 | 1 | no | — |
| 517 | D4 | — | 18 | 1 | no | — |
| 518 | D4 | C2×D36 | 1 | 2 | yes | — |
| 519 | C2×C4 | — | 2 | 1 | no | — |
| 520 | C2×C4 | — | 2 | 2 | no | — |
| 521 | C2×C4 | — | 2 | 2 | no | — |
| 522 | C2×C4 | — | 2 | 2 | no | — |
| 523 | C2×C4 | — | 9 | 2 | no | — |
| 524 | C2×C4 | — | 18 | 4 | no | — |
| 525 | C2×C4 | — | 18 | 4 | no | — |
| 526 | C2×C4 | — | 18 | 4 | no | — |
| 527 | C2×C4 | — | 18 | 1 | no | — |
| 528 | C2×C4 | — | 18 | 2 | no | — |
| 529 | C2×C4 | — | 18 | 2 | no | — |
| 530 | C2×C4 | — | 18 | 2 | no | — |
| 531 | C2×C4 | — | 18 | 2 | no | — |
| 532 | C2×C4 | — | 18 | 2 | no | — |
| 533 | C2×C4 | — | 36 | 1 | no | — |
| 534 | C2×C4 | — | 36 | 1 | no | — |
| 535 | C2×C4 | C2×D36 | 1 | 1 | yes | characteristic |
| 536 | C2×C4 | C2×D36 | 1 | 1 | yes | characteristic |
| 537 | C2×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 538 | C2×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 541 | C8 | — | 2 | 2 | no | — |
| 542 | C8 | — | 18 | 2 | no | — |
| 543 | C2×C3 | — | 2 | 1 | no | — |
| 544 | C2×C3 | — | 2 | 1 | no | — |
| 545 | C2×C3 | — | 2 | 1 | no | — |
| 546 | C2×C3 | — | 4 | 2 | no | — |
| 547 | C2×C3 | C2×#882 | 1 | 1 | yes | characteristic |
| 548 | D3 | — | 12 | 2 | no | — |
| 549 | D3 | — | 12 | 2 | no | — |
| 550 | C22 | — | 2 | 2 | no | — |
| 551 | C22 | — | 4 | 1 | no | — |
| 552 | C22 | — | 8 | 1 | no | — |
| 553 | C22 | — | 18 | 2 | no | — |
| 554 | C22 | — | 18 | 2 | no | — |
| 555 | C22 | — | 36 | 2 | no | — |
| 556 | C22 | — | 72 | 1 | no | — |
| 557 | C22 | — | 72 | 4 | no | — |
| 558 | C22 | #63444 | 1 | 1 | yes | characteristic |
| 559 | C22 | #63444 | 1 | 1 | yes | characteristic |
| 560 | C22 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 561 | C4 | — | 2 | 2 | no | — |
| 562 | C4 | — | 4 | 2 | no | — |
| 563 | C4 | — | 18 | 2 | no | — |
| 564 | C4 | — | 18 | 2 | no | — |
| 565 | C4 | — | 36 | 2 | no | — |
| 566 | C4 | #63444 | 1 | 1 | yes | characteristic |
| 567 | C4 | #63444 | 1 | 1 | yes | characteristic |
| 568 | C4 | C22×D36 | 1 | 1 | yes | characteristic |
| 569 | C4 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 570 | C3 | #78995 | 1 | 1 | yes | characteristic |
| 571 | C2 | — | 2 | 1 | no | — |
| 572 | C2 | — | 2 | 1 | no | — |
| 573 | C2 | — | 2 | 1 | no | — |
| 574 | C2 | — | 4 | 2 | no | — |
| 575 | C2 | — | 36 | 2 | no | — |
| 576 | C2 | — | 36 | 2 | no | — |
| 577 | C2 | C2×#63444 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#63511 | C2 | semidirect |
| 3. C2×#63471 | C2 | semidirect |
| 4. #10589628 | C2 | semidirect |
| 5. C9×#421 | C2 | semidirect |
| 6. #10588814 | C2 | semidirect |
| 7. #10588685 | C2 | semidirect |
| 8. #10588506 | C2 | semidirect |
| 9. #10588505 | C2 | semidirect |
| 24. C22×Dic18 | C22 | semidirect |
| 25. C2×C9×M16 | C22 | semidirect |
| 26. C9×#117 | C22 | semidirect |
| 28. #63511 | C22 | semidirect |
| 31. C2×#3667 | C22 | semidirect |
| 33. #63471 | C22 | semidirect |
| 38. #63437 | C22 | semidirect |
| 39. #63431 | C22 | semidirect |
| 40. C9×#104 | C22 | semidirect |
| 41. #63383 | C22 | semidirect |
| 42. #63382 | C22 | semidirect |
| 43. #63364 | C22 | semidirect |
| 216. #421 | D9 | semidirect |
| 328. C2×M16 | C2×D9 | semidirect |
| 333. #117 | C2×D9 | semidirect |
| 335. #104 | C2×D9 | semidirect |
| 487. C9 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593139 | 2 |
| C2×#63511 | 2 |
| C2×#63471 | 2 |
| #10589628 | 2 |
| C9×#421 | 2 |
| #10588814 | 2 |
| #10588685 | 2 |
| #10588506 | 2 |
| #10588505 | 2 |
| #78995 | 3 |