Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2238 conjugacy classes of subgroups.
The subgroup lattice has 426 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#63713 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | D4×Q8×C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10589919 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589829 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #10589827 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10589735 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10589731 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #10589679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C4×Q8×D9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10589655 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #10589650 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #86760 | — | 3 | 1 | no | maximal |
| 13 | C22×Q8×C9 | C22 | 1 | 2 | yes | — |
| 14 | #63713 | — | 2 | 16 | no | — |
| 15 | C2×#3701 | C22 | 1 | 6 | yes | — |
| 16 | C2×#3701 | C22 | 1 | 2 | yes | — |
| 17 | C2×Q8×D9 | C22 | 1 | 6 | yes | — |
| 18 | C2×Q8×D9 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#3697 | C22 | 1 | 6 | yes | — |
| 20 | C2×#3697 | C22 | 1 | 6 | yes | — |
| 21 | C9×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 22 | C9×C22⋊Q8 | C22 | 1 | 6 | yes | — |
| 23 | C4×Q8×C9 | C22 | 1 | 1 | yes | characteristic |
| 24 | C4×D4×C9 | C22 | 1 | 3 | yes | — |
| 25 | #63509 | C22 | 1 | 6 | yes | — |
| 26 | #63508 | C22 | 1 | 6 | yes | — |
| 27 | Q8×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 28 | #63502 | C22 | 1 | 3 | yes | — |
| 29 | #63500 | C22 | 1 | 1 | yes | characteristic |
| 30 | #63492 | C22 | 1 | 6 | yes | — |
| 31 | C4×#611 | C22 | 1 | 6 | yes | — |
| 32 | #63458 | C22 | 1 | 12 | yes | — |
| 33 | #63457 | C22 | 1 | 6 | yes | — |
| 34 | #63457 | C22 | 1 | 6 | yes | — |
| 35 | #63457 | C22 | 1 | 3 | yes | — |
| 36 | #63455 | C22 | 1 | 6 | yes | — |
| 37 | #63455 | C22 | 1 | 6 | yes | — |
| 38 | C4⋊C4×D9 | C22 | 1 | 3 | yes | — |
| 39 | #63450 | C22 | 1 | 3 | yes | — |
| 40 | #63449 | C22 | 1 | 3 | yes | — |
| 41 | #63447 | C22 | 1 | 6 | yes | — |
| 42 | #63446 | C22 | 1 | 6 | yes | — |
| 43 | #63446 | C22 | 1 | 12 | yes | — |
| 44 | #63436 | C22 | 1 | 3 | yes | — |
| 45 | C4×D36 | C22 | 1 | 3 | yes | — |
| 46 | C42×D9 | C22 | 1 | 3 | yes | — |
| 47 | C4×Dic18 | C22 | 1 | 3 | yes | — |
| 48 | C2×#1007 | — | 3 | 2 | no | — |
| 49 | C3×D4×Q8 | D3 | 1 | 1 | yes | characteristic |
| 50 | #5817 | — | 3 | 2 | no | — |
| 51 | #5727 | — | 3 | 3 | no | — |
| 52 | #5725 | — | 3 | 3 | no | — |
| 53 | #5633 | — | 3 | 6 | no | — |
| 54 | #5629 | — | 3 | 6 | no | — |
| 55 | #5577 | — | 3 | 1 | no | — |
| 56 | C4×D3×Q8 | — | 3 | 1 | no | — |
| 57 | #5553 | — | 3 | 3 | no | — |
| 58 | #5548 | — | 3 | 3 | no | — |
| 59 | C2×Q8×C9 | — | 2 | 8 | no | — |
| 60 | C2×Q8×C9 | C23 | 1 | 6 | yes | — |
| 61 | C2×Q8×C9 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×D4×C9 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C4×C9 | C23 | 1 | 6 | yes | — |
| 64 | C2×#611 | C23 | 1 | 2 | yes | — |
| 65 | C2×#611 | C23 | 1 | 6 | yes | — |
| 66 | C2×#611 | C23 | 1 | 6 | yes | — |
| 67 | #3701 | — | 2 | 8 | no | — |
| 68 | #3701 | — | 2 | 24 | no | — |
| 69 | Q8×D9 | — | 2 | 24 | no | — |
| 70 | Q8×D9 | D4 | 1 | 8 | yes | complemented |
| 71 | #3697 | — | 2 | 24 | no | — |
| 72 | #3697 | — | 2 | 24 | no | — |
| 73 | C2×D36 | C23 | 1 | 6 | yes | — |
| 74 | C2×D36 | C23 | 1 | 3 | yes | — |
| 75 | C2×D36 | C23 | 1 | 6 | yes | — |
| 76 | C2×D36 | C23 | 1 | 6 | yes | — |
| 77 | C2×C4×D9 | C23 | 1 | 6 | yes | — |
| 78 | C2×C4×D9 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×C4×D9 | C23 | 1 | 12 | yes | — |
| 80 | C2×C4×D9 | C23 | 1 | 3 | yes | — |
| 81 | C2×C4×D9 | C23 | 1 | 3 | yes | — |
| 82 | C2×Dic18 | C23 | 1 | 6 | yes | — |
| 83 | C2×Dic18 | C23 | 1 | 3 | yes | — |
| 84 | C9×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 85 | C9×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 86 | C9×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 87 | C9×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 88 | C42×C9 | C23 | 1 | 3 | yes | — |
| 89 | #3676 | C23 | 1 | 2 | yes | — |
| 90 | (C2×D9)⋊C4 | C23 | 1 | 6 | yes | — |
| 91 | (C2×D9)⋊C4 | C23 | 1 | 12 | yes | — |
| 92 | (C2×D9)⋊C4 | C23 | 1 | 6 | yes | — |
| 93 | C4⋊Dic9 | C23 | 1 | 3 | yes | — |
| 94 | C4⋊Dic9 | C23 | 1 | 1 | yes | characteristic |
| 95 | Dic9⋊C4 | C23 | 1 | 6 | yes | — |
| 96 | Dic9⋊C4 | C23 | 1 | 6 | yes | — |
| 97 | C4×Dic9 | C23 | 1 | 3 | yes | — |
| 98 | C4×Dic9 | C23 | 1 | 3 | yes | — |
| 99 | C4×Dic9 | C23 | 1 | 3 | yes | — |
| 100 | #3497 | — | 9 | 1 | no | Sylow |
| 101 | C22×C3×Q8 | C2×D3 | 1 | 2 | yes | — |
| 102 | #1007 | — | 6 | 16 | no | — |
| 103 | C2×#239 | — | 3 | 6 | no | — |
| 104 | C2×#239 | — | 3 | 2 | no | — |
| 105 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 106 | C2×D3×Q8 | — | 3 | 6 | no | — |
| 107 | C2×#235 | — | 3 | 6 | no | — |
| 108 | C2×#235 | — | 3 | 6 | no | — |
| 109 | C3×C4⋊Q8 | C2×D3 | 1 | 3 | yes | — |
| 110 | C3×C22⋊Q8 | C2×D3 | 1 | 6 | yes | — |
| 111 | C3×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 112 | C3×C4×D4 | C2×D3 | 1 | 3 | yes | — |
| 113 | #947 | — | 3 | 6 | no | — |
| 114 | #946 | — | 3 | 6 | no | — |
| 115 | Q8×Dic3 | — | 3 | 1 | no | — |
| 116 | #940 | — | 3 | 3 | no | — |
| 117 | #938 | — | 3 | 1 | no | — |
| 118 | #930 | — | 3 | 6 | no | — |
| 119 | C4×#67 | — | 3 | 6 | no | — |
| 120 | #896 | — | 3 | 12 | no | — |
| 121 | #895 | — | 3 | 6 | no | — |
| 122 | #895 | — | 3 | 3 | no | — |
| 123 | #895 | — | 3 | 6 | no | — |
| 124 | #893 | — | 3 | 6 | no | — |
| 125 | #893 | — | 3 | 6 | no | — |
| 126 | D3×C4⋊C4 | — | 3 | 3 | no | — |
| 127 | #888 | — | 3 | 3 | no | — |
| 128 | #887 | — | 3 | 3 | no | — |
| 129 | #885 | — | 3 | 6 | no | — |
| 130 | #884 | — | 3 | 12 | no | — |
| 131 | #884 | — | 3 | 6 | no | — |
| 132 | #874 | — | 3 | 3 | no | — |
| 133 | C4×D12 | — | 3 | 3 | no | — |
| 134 | C42×D3 | — | 3 | 3 | no | — |
| 135 | C4×Dic6 | — | 3 | 3 | no | — |
| 136 | C23×C9 | C24 | 1 | 2 | yes | — |
| 137 | C22×D9 | C24 | 1 | 6 | yes | — |
| 138 | C22×D9 | C24 | 1 | 1 | yes | characteristic |
| 139 | Q8×C9 | — | 2 | 12 | no | — |
| 140 | Q8×C9 | C2×D4 | 1 | 4 | yes | — |
| 141 | D4×C9 | — | 2 | 2 | no | — |
| 142 | C2×C4×C9 | — | 2 | 12 | no | — |
| 143 | C2×C4×C9 | C24 | 1 | 3 | yes | — |
| 144 | C2×C4×C9 | C24 | 1 | 6 | yes | — |
| 145 | C2×C4×C9 | C24 | 1 | 3 | yes | — |
| 146 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 147 | #611 | — | 2 | 4 | no | — |
| 148 | #611 | — | 2 | 12 | no | — |
| 149 | #611 | — | 4 | 6 | no | — |
| 150 | C2×Dic9 | C24 | 1 | 1 | yes | characteristic |
| 151 | C2×Dic9 | C24 | 1 | 3 | yes | — |
| 152 | C2×Dic9 | C24 | 1 | 2 | yes | — |
| 153 | C2×Dic9 | C24 | 1 | 3 | yes | — |
| 154 | D36 | — | 2 | 12 | no | — |
| 155 | D36 | — | 2 | 12 | no | — |
| 156 | D36 | — | 2 | 6 | no | — |
| 157 | D36 | — | 4 | 6 | no | — |
| 158 | C4×D9 | — | 2 | 12 | no | — |
| 159 | C4×D9 | — | 2 | 2 | no | — |
| 160 | C4×D9 | — | 2 | 24 | no | — |
| 161 | C4×D9 | — | 4 | 3 | no | — |
| 162 | C4×D9 | C2×D4 | 1 | 12 | yes | — |
| 163 | Dic18 | — | 2 | 12 | no | — |
| 164 | Dic18 | C2×D4 | 1 | 12 | yes | — |
| 165 | C2×2−1+4 | — | 9 | 2 | no | — |
| 166 | #550 | — | 9 | 1 | no | — |
| 167 | #550 | — | 9 | 3 | no | — |
| 168 | D4×Q8 | — | 9 | 3 | no | — |
| 169 | D4×Q8 | D9 | 1 | 1 | yes | characteristic, complemented |
| 170 | #548 | — | 9 | 2 | no | — |
| 171 | #548 | — | 9 | 6 | no | — |
| 172 | #537 | — | 9 | 6 | no | — |
| 173 | #532 | — | 9 | 3 | no | — |
| 174 | #532 | — | 9 | 3 | no | — |
| 175 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 176 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 177 | C2×C3×Q8 | C22×D3 | 1 | 6 | yes | — |
| 178 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 179 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 180 | C22×C3×C4 | C22×D3 | 1 | 6 | yes | — |
| 181 | C2×#67 | — | 3 | 2 | no | — |
| 182 | C2×#67 | — | 3 | 6 | no | — |
| 183 | C2×#67 | — | 3 | 6 | no | — |
| 184 | #239 | — | 6 | 24 | no | — |
| 185 | #239 | — | 6 | 8 | no | — |
| 186 | D3×Q8 | — | 3 | 8 | no | — |
| 187 | D3×Q8 | — | 6 | 24 | no | — |
| 188 | #235 | — | 6 | 24 | no | — |
| 189 | #235 | — | 6 | 24 | no | — |
| 190 | C2×D12 | — | 3 | 3 | no | — |
| 191 | C2×D12 | — | 3 | 6 | no | — |
| 192 | C2×D12 | — | 3 | 6 | no | — |
| 193 | C2×D12 | — | 3 | 6 | no | — |
| 194 | C2×C4×D3 | — | 3 | 3 | no | — |
| 195 | C2×C4×D3 | — | 3 | 1 | no | — |
| 196 | C2×C4×D3 | — | 3 | 6 | no | — |
| 197 | C2×C4×D3 | — | 3 | 12 | no | — |
| 198 | C2×C4×D3 | — | 3 | 3 | no | — |
| 199 | C2×Dic6 | — | 3 | 3 | no | — |
| 200 | C2×Dic6 | — | 3 | 6 | no | — |
| 201 | C3×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 202 | C3×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 203 | C3×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 204 | C3×C22⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 205 | C3×C42 | C22×D3 | 1 | 3 | yes | — |
| 206 | #217 | — | 3 | 2 | no | — |
| 207 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 208 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 209 | (C2×D3)⋊C4 | — | 3 | 6 | no | — |
| 210 | C4⋊Dic3 | — | 3 | 3 | no | — |
| 211 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 212 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 213 | Dic3⋊C4 | — | 3 | 6 | no | — |
| 214 | C4×Dic3 | — | 3 | 3 | no | — |
| 215 | C4×Dic3 | — | 3 | 3 | no | — |
| 216 | C4×Dic3 | — | 3 | 3 | no | — |
| 217 | C22×C9 | — | 2 | 2 | no | — |
| 218 | C22×C9 | — | 2 | 2 | no | — |
| 219 | C22×C9 | — | 2 | 2 | no | — |
| 220 | C22×C9 | C25 | 1 | 1 | yes | characteristic |
| 221 | C2×D9 | — | 2 | 1 | no | — |
| 222 | C2×D9 | — | 2 | 1 | no | — |
| 223 | C2×D9 | — | 2 | 6 | no | — |
| 224 | C2×D9 | — | 2 | 6 | no | — |
| 225 | C2×D9 | — | 2 | 6 | no | — |
| 226 | C2×D9 | C22×D4 | 1 | 2 | yes | — |
| 227 | C4×C9 | — | 2 | 6 | no | — |
| 228 | C4×C9 | — | 2 | 3 | no | — |
| 229 | C4×C9 | C22×D4 | 1 | 6 | yes | — |
| 230 | C4×C9 | 2−1+4 | 1 | 2 | yes | complemented |
| 231 | Dic9 | — | 2 | 2 | no | — |
| 232 | Dic9 | — | 2 | 1 | no | — |
| 233 | Dic9 | — | 2 | 3 | no | — |
| 234 | Dic9 | C22×D4 | 1 | 6 | yes | — |
| 235 | 2−1+4 | — | 18 | 16 | no | — |
| 236 | C2×#41 | — | 9 | 6 | no | — |
| 237 | C2×#41 | — | 9 | 2 | no | — |
| 238 | C2×#41 | — | 9 | 6 | no | — |
| 239 | C2×#41 | — | 9 | 6 | no | — |
| 240 | C22×Q8 | — | 9 | 1 | no | — |
| 241 | C22×Q8 | — | 9 | 6 | no | — |
| 242 | C22×Q8 | C2×D9 | 1 | 2 | yes | — |
| 243 | C4⋊Q8 | — | 9 | 3 | no | — |
| 244 | C4⋊Q8 | C2×D9 | 1 | 3 | yes | — |
| 245 | #127 | — | 9 | 3 | no | — |
| 246 | #127 | — | 9 | 3 | no | — |
| 247 | #124 | — | 9 | 6 | no | — |
| 248 | #124 | — | 9 | 6 | no | — |
| 249 | C22⋊Q8 | — | 9 | 6 | no | — |
| 250 | C22⋊Q8 | — | 9 | 12 | no | — |
| 251 | C22⋊Q8 | C2×D9 | 1 | 6 | yes | — |
| 252 | #121 | — | 9 | 1 | no | — |
| 253 | #121 | — | 9 | 6 | no | — |
| 254 | #121 | — | 9 | 3 | no | — |
| 255 | #121 | — | 9 | 6 | no | — |
| 256 | #121 | — | 9 | 6 | no | — |
| 257 | #121 | — | 9 | 6 | no | — |
| 258 | #121 | — | 9 | 12 | no | — |
| 259 | C4×Q8 | — | 9 | 1 | no | — |
| 260 | C4×Q8 | — | 9 | 3 | no | — |
| 261 | C4×Q8 | — | 9 | 3 | no | — |
| 262 | C4×Q8 | C2×D9 | 1 | 1 | yes | characteristic |
| 263 | C4×D4 | — | 9 | 6 | no | — |
| 264 | C4×D4 | — | 9 | 6 | no | — |
| 265 | C4×D4 | — | 9 | 6 | no | — |
| 266 | C4×D4 | — | 9 | 3 | no | — |
| 267 | C4×D4 | C2×D9 | 1 | 3 | yes | — |
| 268 | C2×C4⋊C4 | — | 9 | 3 | no | — |
| 269 | C2×C42 | — | 9 | 3 | no | — |
| 270 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 271 | C22×D3 | — | 3 | 1 | no | — |
| 272 | C22×D3 | — | 3 | 6 | no | — |
| 273 | C3×Q8 | — | 2 | 12 | no | — |
| 274 | C3×Q8 | D3×D4 | 1 | 4 | yes | — |
| 275 | C3×D4 | — | 2 | 2 | no | — |
| 276 | C2×C3×C4 | — | 2 | 12 | no | — |
| 277 | C2×C3×C4 | C23×D3 | 1 | 3 | yes | — |
| 278 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 279 | C2×C3×C4 | C23×D3 | 1 | 3 | yes | — |
| 280 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 281 | #67 | — | 6 | 12 | no | — |
| 282 | #67 | — | 6 | 4 | no | — |
| 283 | #67 | — | 12 | 6 | no | — |
| 284 | C2×Dic3 | — | 3 | 3 | no | — |
| 285 | C2×Dic3 | — | 3 | 1 | no | — |
| 286 | C2×Dic3 | — | 3 | 3 | no | — |
| 287 | C2×Dic3 | — | 3 | 2 | no | — |
| 288 | D12 | — | 6 | 12 | no | — |
| 289 | D12 | — | 6 | 12 | no | — |
| 290 | D12 | — | 6 | 6 | no | — |
| 291 | D12 | — | 12 | 6 | no | — |
| 292 | C4×D3 | — | 3 | 12 | no | — |
| 293 | C4×D3 | — | 6 | 24 | no | — |
| 294 | C4×D3 | — | 6 | 12 | no | — |
| 295 | C4×D3 | — | 6 | 2 | no | — |
| 296 | C4×D3 | — | 12 | 3 | no | — |
| 297 | Dic6 | — | 3 | 12 | no | — |
| 298 | Dic6 | — | 6 | 12 | no | — |
| 299 | C2×C9 | — | 4 | 2 | no | — |
| 300 | C2×C9 | C23×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C9 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 302 | C2×C9 | #585 | 1 | 1 | yes | characteristic |
| 303 | D9 | — | 2 | 2 | no | — |
| 304 | D9 | — | 4 | 6 | no | — |
| 305 | #41 | — | 18 | 24 | no | — |
| 306 | #41 | — | 18 | 24 | no | — |
| 307 | #41 | — | 18 | 24 | no | — |
| 308 | #41 | — | 18 | 8 | no | — |
| 309 | C2×Q8 | — | 2 | 8 | no | — |
| 310 | C2×Q8 | — | 9 | 8 | no | — |
| 311 | C2×Q8 | — | 9 | 3 | no | — |
| 312 | C2×Q8 | — | 9 | 6 | no | — |
| 313 | C2×Q8 | — | 18 | 24 | no | — |
| 314 | C2×Q8 | C22×D9 | 1 | 6 | yes | — |
| 315 | C2×Q8 | C22×D9 | 1 | 1 | yes | characteristic |
| 316 | C2×D4 | — | 9 | 2 | no | — |
| 317 | C2×D4 | — | 9 | 6 | no | — |
| 318 | C2×D4 | — | 9 | 6 | no | — |
| 319 | C2×D4 | — | 9 | 3 | no | — |
| 320 | C2×D4 | — | 9 | 6 | no | — |
| 321 | C2×D4 | — | 9 | 6 | no | — |
| 322 | C2×D4 | — | 9 | 6 | no | — |
| 323 | C2×D4 | C22×D9 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 9 | 3 | no | — |
| 325 | C22×C4 | — | 9 | 1 | no | — |
| 326 | C22×C4 | — | 9 | 12 | no | — |
| 327 | C22×C4 | — | 9 | 6 | no | — |
| 328 | C22×C4 | — | 9 | 3 | no | — |
| 329 | C22×C4 | C22×D9 | 1 | 6 | yes | — |
| 330 | C4⋊C4 | — | 9 | 6 | no | — |
| 331 | C4⋊C4 | — | 9 | 3 | no | — |
| 332 | C4⋊C4 | — | 9 | 1 | no | — |
| 333 | C4⋊C4 | — | 9 | 6 | no | — |
| 334 | C4⋊C4 | C22×D9 | 1 | 3 | yes | — |
| 335 | C4⋊C4 | C22×D9 | 1 | 3 | yes | — |
| 336 | C4⋊C4 | C22×D9 | 1 | 6 | yes | — |
| 337 | C22⋊C4 | — | 9 | 2 | no | — |
| 338 | C22⋊C4 | — | 9 | 6 | no | — |
| 339 | C22⋊C4 | — | 9 | 12 | no | — |
| 340 | C22⋊C4 | — | 9 | 6 | no | — |
| 341 | C22⋊C4 | C22×D9 | 1 | 6 | yes | — |
| 342 | C42 | — | 9 | 3 | no | — |
| 343 | C42 | — | 9 | 3 | no | — |
| 344 | C42 | — | 9 | 3 | no | — |
| 345 | C42 | C22×D9 | 1 | 3 | yes | — |
| 346 | C22×C3 | — | 2 | 2 | no | — |
| 347 | C22×C3 | — | 2 | 2 | no | — |
| 348 | C22×C3 | — | 2 | 2 | no | — |
| 349 | C22×C3 | C24×D3 | 1 | 1 | yes | characteristic |
| 350 | C2×D3 | — | 3 | 2 | no | — |
| 351 | C2×D3 | — | 6 | 1 | no | — |
| 352 | C2×D3 | — | 6 | 1 | no | — |
| 353 | C2×D3 | — | 6 | 6 | no | — |
| 354 | C2×D3 | — | 6 | 6 | no | — |
| 355 | C2×D3 | — | 6 | 6 | no | — |
| 356 | C3×C4 | — | 2 | 6 | no | — |
| 357 | C3×C4 | — | 2 | 3 | no | — |
| 358 | C3×C4 | C2×D3×D4 | 1 | 6 | yes | — |
| 359 | C3×C4 | #1007 | 1 | 2 | yes | — |
| 360 | Dic3 | — | 3 | 6 | no | — |
| 361 | Dic3 | — | 6 | 2 | no | — |
| 362 | Dic3 | — | 6 | 1 | no | — |
| 363 | Dic3 | — | 6 | 3 | no | — |
| 364 | C9 | #3497 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 365 | C23 | — | 9 | 1 | no | — |
| 366 | C23 | — | 9 | 6 | no | — |
| 367 | C23 | C23×D9 | 1 | 2 | yes | — |
| 368 | Q8 | — | 2 | 12 | no | — |
| 369 | Q8 | — | 9 | 12 | no | — |
| 370 | Q8 | — | 18 | 12 | no | — |
| 371 | Q8 | D4×D9 | 1 | 4 | yes | — |
| 372 | D4 | — | 2 | 2 | no | — |
| 373 | D4 | — | 18 | 12 | no | — |
| 374 | D4 | — | 18 | 12 | no | — |
| 375 | D4 | — | 18 | 4 | no | — |
| 376 | D4 | — | 18 | 12 | no | — |
| 377 | D4 | — | 18 | 6 | no | — |
| 378 | D4 | — | 36 | 6 | no | — |
| 379 | D4 | — | 36 | 6 | no | — |
| 380 | C2×C4 | — | 2 | 12 | no | — |
| 381 | C2×C4 | — | 9 | 3 | no | — |
| 382 | C2×C4 | — | 9 | 12 | no | — |
| 383 | C2×C4 | — | 9 | 1 | no | — |
| 384 | C2×C4 | — | 9 | 3 | no | — |
| 385 | C2×C4 | — | 9 | 2 | no | — |
| 386 | C2×C4 | — | 18 | 24 | no | — |
| 387 | C2×C4 | — | 18 | 12 | no | — |
| 388 | C2×C4 | — | 18 | 2 | no | — |
| 389 | C2×C4 | — | 36 | 3 | no | — |
| 390 | C2×C4 | C23×D9 | 1 | 3 | yes | — |
| 391 | C2×C4 | C23×D9 | 1 | 6 | yes | — |
| 392 | C2×C4 | C23×D9 | 1 | 3 | yes | — |
| 393 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 394 | C2×C3 | — | 4 | 2 | no | — |
| 395 | C2×C3 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C3 | C2×#1007 | 1 | 1 | yes | characteristic |
| 397 | C2×C3 | #5968 | 1 | 1 | yes | characteristic |
| 398 | D3 | — | 6 | 2 | no | — |
| 399 | D3 | — | 12 | 6 | no | — |
| 400 | C22 | — | 2 | 2 | no | — |
| 401 | C22 | — | 2 | 2 | no | — |
| 402 | C22 | — | 2 | 2 | no | — |
| 403 | C22 | — | 9 | 2 | no | — |
| 404 | C22 | — | 18 | 1 | no | — |
| 405 | C22 | — | 18 | 1 | no | — |
| 406 | C22 | — | 18 | 6 | no | — |
| 407 | C22 | — | 18 | 6 | no | — |
| 408 | C22 | — | 18 | 6 | no | — |
| 409 | C22 | C24×D9 | 1 | 1 | yes | characteristic |
| 410 | C4 | — | 2 | 6 | no | — |
| 411 | C4 | — | 2 | 3 | no | — |
| 412 | C4 | — | 9 | 6 | no | — |
| 413 | C4 | — | 18 | 2 | no | — |
| 414 | C4 | — | 18 | 1 | no | — |
| 415 | C4 | — | 18 | 3 | no | — |
| 416 | C4 | C2×D4×D9 | 1 | 6 | yes | — |
| 417 | C4 | #63713 | 1 | 2 | yes | complemented |
| 418 | C3 | #86760 | 1 | 1 | yes | characteristic |
| 419 | C2 | — | 4 | 2 | no | — |
| 420 | C2 | — | 18 | 2 | no | — |
| 421 | C2 | — | 36 | 6 | no | — |
| 422 | C2 | C22×D4×D9 | 1 | 1 | yes | characteristic |
| 423 | C2 | C2×#63713 | 1 | 1 | yes | characteristic |
| 424 | C2 | #10593143 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | D4×Q8×C9 | C2 |
| hypercenter | D4×Q8 | D9 |
| hypocenter | C9 | #3497 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#63713 | C2 | semidirect |
| 2. D4×Q8×C9 | C2 | semidirect |
| 3. #10589919 | C2 | semidirect |
| 4. #10589829 | C2 | semidirect |
| 5. #10589827 | C2 | semidirect |
| 6. #10589735 | C2 | semidirect |
| 7. #10589731 | C2 | semidirect |
| 8. #10589679 | C2 | semidirect |
| 9. C4×Q8×D9 | C2 | semidirect |
| 10. #10589655 | C2 | semidirect |
| 11. #10589650 | C2 | semidirect |
| 70. Q8×D9 | D4 | semidirect |
| 169. D4×Q8 | D9 | semidirect |
| 230. C4×C9 | 2−1+4 | semidirect |
| 364. C9 | #3497 | semidirect |
| 417. C4 | #63713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63713 | 2 |
| D4×Q8×C9 | 2 |
| #10589919 | 2 |
| #10589829 | 2 |
| #10589827 | 2 |
| #10589735 | 2 |
| #10589731 | 2 |
| #10589679 | 2 |
| C4×Q8×D9 | 2 |
| #10589655 | 2 |
| #10589650 | 2 |
| #86760 | 3 |