Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1257 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Q16×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10595432 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10595365 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#63944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#63940 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#63796 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C3×#5190 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591627 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10591605 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10590897 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10590668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D3×#497 | — | 3 | 2 | no | maximal |
| 13 | C2×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#3802 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#3797 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C32×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#3756 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#3756 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q16×C3⋊D3 | — | 2 | 4 | no | — |
| 21 | C2×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×#947 | C22 | 1 | 2 | yes | — |
| 24 | C3×#944 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×C3×#216 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×C3×#215 | C22 | 1 | 2 | yes | — |
| 27 | C2×C3×#204 | C22 | 1 | 2 | yes | — |
| 28 | #63944 | — | 2 | 4 | no | — |
| 29 | #63940 | — | 2 | 4 | no | — |
| 30 | #63921 | — | 2 | 2 | no | — |
| 31 | #63913 | — | 2 | 2 | no | — |
| 32 | #63883 | — | 2 | 2 | no | — |
| 33 | C4×#624 | C22 | 1 | 1 | yes | characteristic |
| 34 | #63866 | C22 | 1 | 2 | yes | complemented |
| 35 | #63860 | C22 | 1 | 2 | yes | — |
| 36 | #63840 | — | 2 | 2 | no | — |
| 37 | C2×#3719 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#3716 | C22 | 1 | 2 | yes | — |
| 39 | C2×#3715 | C22 | 1 | 2 | yes | — |
| 40 | C2×#3710 | C22 | 1 | 1 | yes | characteristic |
| 41 | #63796 | — | 2 | 4 | no | — |
| 42 | C3×#815 | C22 | 1 | 2 | yes | complemented |
| 43 | #63554 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×D3×Q16 | — | 3 | 2 | no | — |
| 45 | C2×D3×Q16 | — | 3 | 2 | no | — |
| 46 | C2×D3×Q16 | — | 6 | 1 | no | — |
| 47 | C2×D3×SD16 | — | 3 | 2 | no | — |
| 48 | C2×D3×SD16 | — | 3 | 2 | no | — |
| 49 | D3×C4⋊Q8 | — | 3 | 2 | no | — |
| 50 | D3×#124 | — | 3 | 2 | no | — |
| 51 | C3×#497 | — | 3 | 2 | no | — |
| 52 | #5190 | — | 3 | 2 | no | — |
| 53 | #5190 | D3 | 1 | 2 | yes | complemented |
| 54 | #5167 | — | 3 | 2 | no | — |
| 55 | #5167 | — | 3 | 2 | no | — |
| 56 | #5086 | — | 3 | 2 | no | — |
| 57 | #5060 | — | 3 | 2 | no | — |
| 58 | #4715 | — | 3 | 2 | no | — |
| 59 | D3×#97 | — | 3 | 2 | no | — |
| 60 | C22×D32 | — | 2 | 1 | no | — |
| 61 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 63 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 64 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 65 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 66 | Q8×C3⋊D3 | — | 2 | 2 | no | — |
| 67 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 68 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 69 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#634 | — | 2 | 1 | no | — |
| 71 | C2×#634 | — | 2 | 1 | no | — |
| 72 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 75 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 76 | C2×#627 | — | 2 | 1 | no | — |
| 77 | C2×#625 | — | 2 | 1 | no | — |
| 78 | C2×#624 | — | 2 | 1 | no | — |
| 79 | C2×#624 | D4 | 1 | 2 | yes | — |
| 80 | #3802 | — | 2 | 2 | no | — |
| 81 | #3802 | — | 2 | 2 | no | — |
| 82 | #3797 | — | 2 | 2 | no | — |
| 83 | #3797 | — | 2 | 2 | no | — |
| 84 | C32×Q16 | — | 2 | 2 | no | — |
| 85 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 86 | #3756 | — | 2 | 2 | no | — |
| 87 | #3756 | — | 2 | 2 | no | — |
| 88 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 89 | #3746 | — | 2 | 2 | no | — |
| 90 | C8×C3⋊D3 | D4 | 1 | 4 | yes | — |
| 91 | C3×#216 | — | 2 | 4 | no | — |
| 92 | C3×#215 | — | 2 | 4 | no | — |
| 93 | C3×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 94 | C3×Dic3⋊C4 | — | 2 | 4 | no | — |
| 95 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 96 | C2×C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 97 | C3×#204 | — | 2 | 4 | no | — |
| 98 | Dic3⋊Dic3 | — | 2 | 4 | no | — |
| 99 | (C2×D3)⋊Dic3 | — | 2 | 4 | no | — |
| 100 | Dic32 | D4 | 1 | 2 | yes | — |
| 101 | #3719 | — | 2 | 4 | no | — |
| 102 | #3716 | — | 2 | 4 | no | — |
| 103 | #3715 | — | 2 | 4 | no | — |
| 104 | #3710 | D4 | 1 | 4 | yes | — |
| 105 | C2×#497 | — | 9 | 1 | no | Sylow |
| 106 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 107 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 108 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 109 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 110 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 111 | C2×D3×D4 | — | 3 | 2 | no | — |
| 112 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 113 | C2×C3×Q16 | — | 3 | 2 | no | — |
| 114 | C2×C3×Q16 | C2×D3 | 1 | 2 | yes | complemented |
| 115 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 116 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 117 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 118 | C3×#124 | — | 3 | 2 | no | — |
| 119 | #947 | C2×D3 | 1 | 2 | yes | — |
| 120 | #944 | — | 3 | 2 | no | — |
| 121 | #944 | C2×D3 | 1 | 2 | yes | complemented |
| 122 | C2×#216 | — | 3 | 2 | no | — |
| 123 | C2×#216 | — | 3 | 2 | no | — |
| 124 | C2×#216 | — | 3 | 2 | no | — |
| 125 | C2×#216 | — | 6 | 1 | no | — |
| 126 | C2×#216 | — | 6 | 1 | no | — |
| 127 | C2×#216 | C2×D3 | 1 | 2 | yes | complemented |
| 128 | C2×#215 | — | 3 | 2 | no | — |
| 129 | C2×#215 | C2×D3 | 1 | 2 | yes | — |
| 130 | #936 | — | 3 | 2 | no | — |
| 131 | C2×#214 | — | 3 | 2 | no | — |
| 132 | C2×#214 | — | 3 | 2 | no | — |
| 133 | D3×Q16 | — | 6 | 8 | no | — |
| 134 | D3×Q16 | — | 6 | 8 | no | — |
| 135 | D3×Q16 | — | 6 | 8 | no | — |
| 136 | D3×SD16 | — | 6 | 8 | no | — |
| 137 | D3×SD16 | — | 6 | 8 | no | — |
| 138 | C2×Dic12 | — | 3 | 2 | no | — |
| 139 | C2×Dic12 | — | 3 | 2 | no | — |
| 140 | C2×Dic12 | — | 6 | 1 | no | — |
| 141 | C2×#204 | — | 3 | 2 | no | — |
| 142 | C2×#204 | C2×D3 | 1 | 2 | yes | — |
| 143 | C2×D3×C8 | — | 3 | 2 | no | — |
| 144 | C2×D3×C8 | — | 3 | 2 | no | — |
| 145 | C2×D3×C8 | — | 6 | 1 | no | — |
| 146 | D3×C4⋊C4 | — | 6 | 4 | no | — |
| 147 | #888 | — | 6 | 4 | no | — |
| 148 | #885 | — | 6 | 4 | no | — |
| 149 | D3×C22⋊C4 | — | 6 | 4 | no | — |
| 150 | #875 | — | 3 | 2 | no | — |
| 151 | C42×D3 | — | 3 | 2 | no | — |
| 152 | #869 | — | 3 | 2 | no | — |
| 153 | C3×#97 | — | 3 | 2 | no | — |
| 154 | #815 | — | 3 | 2 | no | — |
| 155 | #815 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | #803 | — | 3 | 2 | no | — |
| 157 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C22×C3×D3 | — | 2 | 2 | no | — |
| 159 | C2×D32 | — | 4 | 2 | no | — |
| 160 | C2×D32 | — | 4 | 4 | no | — |
| 161 | C32×Q8 | — | 2 | 1 | no | — |
| 162 | C32×Q8 | — | 2 | 1 | no | — |
| 163 | C32×Q8 | — | 2 | 1 | no | — |
| 164 | C32×Q8 | — | 2 | 1 | no | — |
| 165 | C2×C32×C4 | — | 2 | 1 | no | — |
| 166 | C2×C32×C4 | — | 2 | 1 | no | — |
| 167 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 168 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 169 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 170 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 172 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 173 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 174 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 175 | #634 | — | 2 | 1 | no | — |
| 176 | #634 | — | 2 | 1 | no | — |
| 177 | #634 | — | 2 | 1 | no | — |
| 178 | #634 | — | 2 | 1 | no | — |
| 179 | #634 | — | 4 | 2 | no | — |
| 180 | #634 | — | 4 | 2 | no | — |
| 181 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 182 | C2×C3×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 183 | C3×D12 | — | 2 | 2 | no | — |
| 184 | C3×D12 | — | 2 | 2 | no | — |
| 185 | C3×Dic6 | — | 2 | 2 | no | — |
| 186 | C3×Dic6 | — | 2 | 2 | no | — |
| 187 | #627 | — | 4 | 2 | no | — |
| 188 | #625 | — | 4 | 2 | no | — |
| 189 | #624 | — | 2 | 4 | no | — |
| 190 | #624 | — | 4 | 2 | no | — |
| 191 | C32×C8 | C2×D4 | 1 | 2 | yes | — |
| 192 | C3⋊(C3⋊C8) | C2×D4 | 1 | 2 | yes | — |
| 193 | C3×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 194 | C22×Q16 | — | 9 | 1 | no | — |
| 195 | C22×Q16 | — | 9 | 1 | no | — |
| 196 | C22×SD16 | — | 9 | 1 | no | — |
| 197 | C22×SD16 | — | 9 | 1 | no | — |
| 198 | C2×C4⋊Q8 | — | 9 | 1 | no | — |
| 199 | C2×#124 | — | 9 | 1 | no | — |
| 200 | #497 | — | 3 | 2 | no | — |
| 201 | #497 | — | 9 | 2 | no | — |
| 202 | #497 | — | 9 | 2 | no | — |
| 203 | #497 | — | 9 | 2 | no | — |
| 204 | C2×#97 | — | 9 | 1 | no | — |
| 205 | C23×D3 | — | 6 | 2 | no | — |
| 206 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 207 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 208 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 209 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 210 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 211 | C2×C3×D4 | — | 3 | 2 | no | — |
| 212 | C2×#67 | — | 6 | 2 | no | — |
| 213 | D3×Q8 | — | 6 | 4 | no | — |
| 214 | D3×Q8 | — | 6 | 4 | no | — |
| 215 | D3×Q8 | — | 6 | 4 | no | — |
| 216 | D3×Q8 | — | 6 | 4 | no | — |
| 217 | D3×Q8 | — | 6 | 4 | no | — |
| 218 | D3×Q8 | — | 6 | 4 | no | — |
| 219 | D3×Q8 | — | 6 | 4 | no | — |
| 220 | D3×Q8 | — | 6 | 4 | no | — |
| 221 | D3×Q8 | — | 12 | 2 | no | — |
| 222 | D3×Q8 | — | 12 | 2 | no | — |
| 223 | D3×D4 | — | 6 | 4 | no | — |
| 224 | D3×D4 | — | 6 | 4 | no | — |
| 225 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 226 | C2×C4×D3 | — | 3 | 2 | no | — |
| 227 | C2×C4×D3 | — | 3 | 4 | no | — |
| 228 | C2×C4×D3 | — | 6 | 1 | no | — |
| 229 | C2×C4×D3 | — | 6 | 2 | no | — |
| 230 | C2×C4×D3 | — | 6 | 2 | no | — |
| 231 | C2×C4×D3 | — | 6 | 2 | no | — |
| 232 | C2×C4×D3 | — | 12 | 1 | no | — |
| 233 | C2×C4×D3 | — | 12 | 1 | no | — |
| 234 | C2×Dic6 | — | 3 | 2 | no | — |
| 235 | C2×Dic6 | — | 3 | 2 | no | — |
| 236 | C2×Dic6 | — | 6 | 1 | no | — |
| 237 | C2×Dic6 | — | 6 | 1 | no | — |
| 238 | C2×Dic6 | — | 6 | 2 | no | — |
| 239 | C2×Dic6 | — | 6 | 2 | no | — |
| 240 | C2×Dic6 | — | 6 | 2 | no | — |
| 241 | C2×Dic6 | — | 12 | 1 | no | — |
| 242 | C2×Dic6 | — | 12 | 1 | no | — |
| 243 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 244 | C3×Q16 | — | 2 | 4 | no | — |
| 245 | C3×Q16 | — | 2 | 4 | no | — |
| 246 | C3×Q16 | — | 6 | 4 | no | — |
| 247 | C3×SD16 | — | 6 | 4 | no | — |
| 248 | C3×SD16 | — | 6 | 4 | no | — |
| 249 | C2×C3×C8 | — | 2 | 1 | no | — |
| 250 | C2×C3×C8 | — | 3 | 2 | no | — |
| 251 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 252 | C3×C4⋊C4 | — | 6 | 4 | no | — |
| 253 | C3×C22⋊C4 | — | 6 | 4 | no | — |
| 254 | C3×C42 | — | 3 | 2 | no | — |
| 255 | #217 | — | 6 | 4 | no | — |
| 256 | #216 | — | 2 | 4 | no | — |
| 257 | #216 | — | 6 | 4 | no | — |
| 258 | #216 | — | 6 | 4 | no | — |
| 259 | #216 | — | 6 | 4 | no | — |
| 260 | #216 | — | 6 | 4 | no | — |
| 261 | #216 | — | 6 | 4 | no | — |
| 262 | #215 | — | 2 | 4 | no | — |
| 263 | #215 | — | 6 | 4 | no | — |
| 264 | #214 | — | 6 | 4 | no | — |
| 265 | #214 | — | 6 | 4 | no | — |
| 266 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 267 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 268 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 269 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 270 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 271 | C4×Dic3 | — | 3 | 4 | no | — |
| 272 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 273 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 274 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 275 | C2×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 276 | Dic12 | — | 6 | 4 | no | — |
| 277 | Dic12 | — | 6 | 4 | no | — |
| 278 | Dic12 | — | 6 | 4 | no | — |
| 279 | #204 | — | 2 | 4 | no | — |
| 280 | #204 | — | 6 | 4 | no | — |
| 281 | D3×C8 | — | 3 | 8 | no | — |
| 282 | D3×C8 | — | 3 | 8 | no | — |
| 283 | D3×C8 | — | 6 | 4 | no | — |
| 284 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C3⋊D3 | #127 | 1 | 2 | yes | — |
| 286 | C2×C3⋊D3 | #137 | 1 | 4 | yes | — |
| 287 | C2×C3×D3 | — | 4 | 2 | no | — |
| 288 | C2×C3×D3 | — | 4 | 4 | no | — |
| 289 | D32 | — | 8 | 4 | no | — |
| 290 | C32×C4 | — | 4 | 1 | no | — |
| 291 | C32×C4 | — | 4 | 1 | no | — |
| 292 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 293 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 295 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 296 | C3⋊Dic3 | #127 | 1 | 2 | yes | — |
| 297 | C3×Dic3 | — | 2 | 4 | no | — |
| 298 | C3×Dic3 | — | 4 | 2 | no | — |
| 299 | C22×Q8 | — | 9 | 1 | no | — |
| 300 | C22×Q8 | — | 9 | 1 | no | — |
| 301 | C22×Q8 | — | 9 | 1 | no | — |
| 302 | C22×D4 | — | 9 | 1 | no | — |
| 303 | C2×Q16 | — | 3 | 2 | no | — |
| 304 | C2×Q16 | — | 9 | 2 | no | — |
| 305 | C2×Q16 | — | 9 | 1 | no | — |
| 306 | C2×Q16 | — | 9 | 1 | no | — |
| 307 | C2×Q16 | — | 9 | 1 | no | — |
| 308 | C2×Q16 | — | 18 | 4 | no | — |
| 309 | C2×Q16 | — | 18 | 4 | no | — |
| 310 | C2×Q16 | D32 | 1 | 1 | yes | characteristic, complemented |
| 311 | C2×SD16 | — | 3 | 2 | no | — |
| 312 | C2×SD16 | — | 3 | 2 | no | — |
| 313 | C2×SD16 | — | 9 | 2 | no | — |
| 314 | C2×SD16 | — | 9 | 2 | no | — |
| 315 | C2×SD16 | — | 18 | 4 | no | — |
| 316 | C2×SD16 | — | 18 | 4 | no | — |
| 317 | C22×C8 | — | 9 | 1 | no | — |
| 318 | C22×C8 | — | 9 | 1 | no | — |
| 319 | C4⋊Q8 | — | 3 | 2 | no | — |
| 320 | C4⋊Q8 | — | 9 | 2 | no | — |
| 321 | C4⋊Q8 | — | 18 | 2 | no | — |
| 322 | #124 | — | 3 | 2 | no | — |
| 323 | #124 | — | 9 | 2 | no | — |
| 324 | #124 | — | 18 | 2 | no | — |
| 325 | C2×C4⋊C4 | — | 18 | 2 | no | — |
| 326 | C2×C22⋊C4 | — | 18 | 2 | no | — |
| 327 | C2×C42 | — | 9 | 1 | no | — |
| 328 | #97 | — | 3 | 2 | no | — |
| 329 | #97 | — | 9 | 2 | no | — |
| 330 | C23×C3 | — | 6 | 2 | no | — |
| 331 | C22×D3 | — | 2 | 2 | no | — |
| 332 | C22×D3 | — | 3 | 2 | no | — |
| 333 | C22×D3 | — | 6 | 1 | no | — |
| 334 | C22×D3 | — | 12 | 4 | no | — |
| 335 | C22×D3 | — | 12 | 8 | no | — |
| 336 | C3×Q8 | — | 2 | 2 | no | — |
| 337 | C3×Q8 | — | 2 | 2 | no | — |
| 338 | C3×Q8 | — | 2 | 2 | no | — |
| 339 | C3×Q8 | — | 2 | 2 | no | — |
| 340 | C3×Q8 | — | 2 | 2 | no | — |
| 341 | C3×Q8 | — | 2 | 2 | no | — |
| 342 | C3×Q8 | — | 4 | 1 | no | — |
| 343 | C3×Q8 | — | 4 | 1 | no | — |
| 344 | C3×Q8 | — | 6 | 2 | no | — |
| 345 | C3×Q8 | — | 6 | 2 | no | — |
| 346 | C3×D4 | — | 6 | 2 | no | — |
| 347 | C3×D4 | — | 6 | 2 | no | — |
| 348 | C2×C3×C4 | — | 2 | 2 | no | — |
| 349 | C2×C3×C4 | — | 2 | 2 | no | — |
| 350 | C2×C3×C4 | — | 2 | 1 | no | — |
| 351 | C2×C3×C4 | — | 3 | 4 | no | — |
| 352 | C2×C3×C4 | — | 4 | 1 | no | — |
| 353 | C2×C3×C4 | — | 4 | 1 | no | — |
| 354 | C2×C3×C4 | — | 6 | 2 | no | — |
| 355 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 356 | #67 | — | 12 | 4 | no | — |
| 357 | C2×Dic3 | — | 2 | 2 | no | — |
| 358 | C2×Dic3 | — | 3 | 2 | no | — |
| 359 | C2×Dic3 | — | 6 | 1 | no | — |
| 360 | C2×Dic3 | — | 6 | 2 | no | — |
| 361 | C2×Dic3 | — | 6 | 2 | no | — |
| 362 | C2×Dic3 | — | 12 | 1 | no | — |
| 363 | C2×Dic3 | — | 12 | 1 | no | — |
| 364 | C2×Dic3 | D3×D4 | 1 | 4 | yes | — |
| 365 | D12 | — | 2 | 2 | no | — |
| 366 | D12 | — | 2 | 2 | no | — |
| 367 | C4×D3 | — | 3 | 4 | no | — |
| 368 | C4×D3 | — | 3 | 4 | no | — |
| 369 | C4×D3 | — | 6 | 2 | no | — |
| 370 | C4×D3 | — | 6 | 2 | no | — |
| 371 | C4×D3 | — | 6 | 8 | no | — |
| 372 | C4×D3 | — | 12 | 4 | no | — |
| 373 | C4×D3 | — | 12 | 4 | no | — |
| 374 | C4×D3 | — | 12 | 4 | no | — |
| 375 | C4×D3 | — | 12 | 4 | no | — |
| 376 | C4×D3 | — | 12 | 4 | no | — |
| 377 | Dic6 | — | 2 | 2 | no | — |
| 378 | Dic6 | — | 2 | 2 | no | — |
| 379 | Dic6 | — | 6 | 2 | no | — |
| 380 | Dic6 | — | 6 | 2 | no | — |
| 381 | Dic6 | — | 6 | 2 | no | — |
| 382 | Dic6 | — | 6 | 2 | no | — |
| 383 | Dic6 | — | 6 | 2 | no | — |
| 384 | Dic6 | — | 6 | 2 | no | — |
| 385 | Dic6 | — | 12 | 1 | no | — |
| 386 | Dic6 | — | 12 | 1 | no | — |
| 387 | Dic6 | — | 12 | 4 | no | — |
| 388 | Dic6 | — | 12 | 4 | no | — |
| 389 | Dic6 | — | 12 | 4 | no | — |
| 390 | Dic6 | — | 12 | 4 | no | — |
| 391 | Dic6 | — | 12 | 4 | no | — |
| 392 | C3×C8 | — | 2 | 2 | no | — |
| 393 | C3×C8 | — | 3 | 4 | no | — |
| 394 | C3×C8 | D3×D4 | 1 | 4 | yes | — |
| 395 | C3⋊C8 | — | 3 | 4 | no | — |
| 396 | C3⋊C8 | — | 6 | 2 | no | — |
| 397 | C3⋊C8 | D3×D4 | 1 | 4 | yes | — |
| 398 | C2×C32 | C2×#127 | 1 | 1 | yes | characteristic |
| 399 | C2×C32 | C2×#137 | 1 | 2 | yes | — |
| 400 | C3⋊D3 | #497 | 1 | 4 | yes | complemented |
| 401 | C3×D3 | — | 8 | 2 | no | — |
| 402 | C24 | — | 18 | 1 | no | — |
| 403 | C2×Q8 | — | 3 | 2 | no | — |
| 404 | C2×Q8 | — | 9 | 1 | no | — |
| 405 | C2×Q8 | — | 9 | 1 | no | — |
| 406 | C2×Q8 | — | 18 | 1 | no | — |
| 407 | C2×Q8 | — | 18 | 1 | no | — |
| 408 | C2×Q8 | — | 18 | 1 | no | — |
| 409 | C2×Q8 | — | 18 | 2 | no | — |
| 410 | C2×Q8 | — | 18 | 2 | no | — |
| 411 | C2×Q8 | — | 18 | 2 | no | — |
| 412 | C2×Q8 | — | 18 | 2 | no | — |
| 413 | C2×Q8 | — | 18 | 2 | no | — |
| 414 | C2×Q8 | — | 18 | 2 | no | — |
| 415 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 416 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 417 | C2×D4 | — | 3 | 2 | no | — |
| 418 | C2×D4 | — | 18 | 2 | no | — |
| 419 | C2×D4 | — | 18 | 2 | no | — |
| 420 | C2×D4 | — | 18 | 1 | no | — |
| 421 | C22×C4 | — | 9 | 2 | no | — |
| 422 | C22×C4 | — | 9 | 1 | no | — |
| 423 | C22×C4 | — | 18 | 1 | no | — |
| 424 | C22×C4 | — | 18 | 1 | no | — |
| 425 | C22×C4 | — | 18 | 1 | no | — |
| 426 | Q16 | — | 2 | 2 | no | — |
| 427 | Q16 | — | 6 | 4 | no | — |
| 428 | Q16 | — | 18 | 4 | no | — |
| 429 | Q16 | — | 18 | 2 | no | — |
| 430 | Q16 | — | 18 | 2 | no | — |
| 431 | Q16 | — | 18 | 2 | no | — |
| 432 | SD16 | — | 6 | 4 | no | — |
| 433 | SD16 | — | 6 | 4 | no | — |
| 434 | SD16 | — | 18 | 4 | no | — |
| 435 | SD16 | — | 18 | 4 | no | — |
| 436 | C2×C8 | — | 3 | 2 | no | — |
| 437 | C2×C8 | — | 9 | 4 | no | — |
| 438 | C2×C8 | — | 9 | 1 | no | — |
| 439 | C2×C8 | — | 9 | 4 | no | — |
| 440 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 441 | C4⋊C4 | — | 6 | 4 | no | — |
| 442 | C4⋊C4 | — | 18 | 4 | no | — |
| 443 | C22⋊C4 | — | 6 | 4 | no | — |
| 444 | C22⋊C4 | — | 18 | 4 | no | — |
| 445 | C42 | — | 3 | 2 | no | — |
| 446 | C42 | — | 9 | 2 | no | — |
| 447 | C22×C3 | — | 2 | 1 | no | — |
| 448 | C22×C3 | — | 12 | 2 | no | — |
| 449 | C22×C3 | — | 12 | 4 | no | — |
| 450 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 451 | C2×D3 | — | 3 | 4 | no | — |
| 452 | C2×D3 | — | 3 | 8 | no | — |
| 453 | C2×D3 | — | 4 | 2 | no | — |
| 454 | C2×D3 | — | 4 | 4 | no | — |
| 455 | C2×D3 | — | 6 | 2 | no | — |
| 456 | C2×D3 | — | 6 | 4 | no | — |
| 457 | C2×D3 | — | 24 | 8 | no | — |
| 458 | C3×C4 | — | 2 | 1 | no | — |
| 459 | C3×C4 | — | 2 | 1 | no | — |
| 460 | C3×C4 | — | 4 | 2 | no | — |
| 461 | C3×C4 | — | 4 | 2 | no | — |
| 462 | C3×C4 | — | 4 | 2 | no | — |
| 463 | C3×C4 | — | 4 | 2 | no | — |
| 464 | C3×C4 | — | 6 | 4 | no | — |
| 465 | C3×C4 | — | 12 | 2 | no | — |
| 466 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 467 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 468 | Dic3 | — | 2 | 4 | no | — |
| 469 | Dic3 | — | 3 | 4 | no | — |
| 470 | Dic3 | — | 4 | 2 | no | — |
| 471 | Dic3 | — | 6 | 2 | no | — |
| 472 | Dic3 | — | 12 | 2 | no | — |
| 473 | Dic3 | — | 12 | 2 | no | — |
| 474 | Dic3 | — | 12 | 2 | no | — |
| 475 | Dic3 | — | 12 | 2 | no | — |
| 476 | C32 | C2×#497 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 477 | C23 | — | 6 | 2 | no | — |
| 478 | C23 | — | 9 | 1 | no | — |
| 479 | C23 | — | 36 | 2 | no | — |
| 480 | C23 | — | 36 | 4 | no | — |
| 481 | Q8 | — | 2 | 1 | no | — |
| 482 | Q8 | — | 2 | 1 | no | — |
| 483 | Q8 | — | 2 | 1 | no | — |
| 484 | Q8 | — | 2 | 1 | no | — |
| 485 | Q8 | — | 6 | 2 | no | — |
| 486 | Q8 | — | 6 | 2 | no | — |
| 487 | Q8 | — | 18 | 1 | no | — |
| 488 | Q8 | — | 18 | 1 | no | — |
| 489 | Q8 | — | 18 | 1 | no | — |
| 490 | Q8 | — | 18 | 1 | no | — |
| 491 | Q8 | — | 36 | 2 | no | — |
| 492 | Q8 | — | 36 | 2 | no | — |
| 493 | Q8 | — | 36 | 2 | no | — |
| 494 | D4 | — | 6 | 2 | no | — |
| 495 | D4 | — | 6 | 2 | no | — |
| 496 | D4 | — | 36 | 2 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 2 | 1 | no | — |
| 499 | C2×C4 | — | 3 | 4 | no | — |
| 500 | C2×C4 | — | 6 | 2 | no | — |
| 501 | C2×C4 | — | 9 | 1 | no | — |
| 502 | C2×C4 | — | 9 | 2 | no | — |
| 503 | C2×C4 | — | 9 | 2 | no | — |
| 504 | C2×C4 | — | 18 | 4 | no | — |
| 505 | C2×C4 | — | 18 | 1 | no | — |
| 506 | C2×C4 | — | 18 | 1 | no | — |
| 507 | C2×C4 | — | 36 | 2 | no | — |
| 508 | C2×C4 | — | 36 | 2 | no | — |
| 509 | C2×C4 | — | 36 | 2 | no | — |
| 510 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 511 | C8 | — | 3 | 4 | no | — |
| 512 | C8 | — | 9 | 2 | no | — |
| 513 | C8 | #3811 | 1 | 2 | yes | — |
| 514 | C2×C3 | — | 2 | 2 | no | — |
| 515 | C2×C3 | — | 2 | 1 | no | — |
| 516 | C2×C3 | — | 24 | 2 | no | — |
| 517 | C2×C3 | D3×#127 | 1 | 2 | yes | — |
| 518 | C2×C3 | D3×#137 | 1 | 4 | yes | — |
| 519 | D3 | — | 3 | 8 | no | — |
| 520 | D3 | — | 6 | 4 | no | — |
| 521 | D3 | — | 8 | 2 | no | — |
| 522 | C22 | — | 9 | 4 | no | — |
| 523 | C22 | — | 9 | 2 | no | — |
| 524 | C22 | — | 12 | 4 | no | — |
| 525 | C22 | — | 12 | 2 | no | — |
| 526 | C22 | — | 72 | 4 | no | — |
| 527 | C22 | D32×D4 | 1 | 1 | yes | characteristic |
| 528 | C4 | — | 4 | 1 | no | — |
| 529 | C4 | — | 4 | 1 | no | — |
| 530 | C4 | — | 6 | 4 | no | — |
| 531 | C4 | — | 9 | 2 | no | — |
| 532 | C4 | — | 12 | 2 | no | — |
| 533 | C4 | — | 36 | 1 | no | — |
| 534 | C4 | — | 36 | 1 | no | — |
| 535 | C4 | D32×D4 | 1 | 1 | yes | characteristic |
| 536 | C4 | C2×#3811 | 1 | 1 | yes | characteristic |
| 537 | C3 | — | 2 | 1 | no | — |
| 538 | C3 | D3×#497 | 1 | 2 | yes | complemented |
| 539 | C2 | — | 9 | 4 | no | — |
| 540 | C2 | — | 24 | 2 | no | — |
| 541 | C2 | #10594760 | 1 | 2 | yes | — |
| 542 | C2 | #10595300 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×C3⋊D3 | C2 | semidirect |
| 3. #10595365 | C2 | semidirect |
| 4. C2×#63944 | C2 | semidirect |
| 7. C3×#5190 | C2 | semidirect |
| 8. #10591627 | C2 | semidirect |
| 9. #10591605 | C2 | semidirect |
| 10. #10590897 | C2 | semidirect |
| 11. #10590668 | C2 | semidirect |
| 17. C2×C32×Q16 | C22 | semidirect |
| 18. C2×#3756 | C22 | semidirect |
| 19. C2×#3756 | C22 | semidirect |
| 21. C2×#3746 | C22 | semidirect |
| 24. C3×#944 | C22 | semidirect |
| 25. C2×C3×#216 | C22 | semidirect |
| 34. #63866 | C22 | semidirect |
| 37. C2×#3719 | C22 | semidirect |
| 42. C3×#815 | C22 | semidirect |
| 43. #63554 | C22 | semidirect |
| 53. #5190 | D3 | semidirect |
| 114. C2×C3×Q16 | C2×D3 | semidirect |
| 121. #944 | C2×D3 | semidirect |
| 127. C2×#216 | C2×D3 | semidirect |
| 155. #815 | C2×D3 | semidirect |
| 310. C2×Q16 | D32 | semidirect |
| 400. C3⋊D3 | #497 | semidirect |
| 476. C32 | C2×#497 | semidirect |
| 538. C3 | D3×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| #10595432 | 2 |
| #10595365 | 2 |
| C2×#63944 | 2 |
| C2×#63940 | 2 |
| C2×#63796 | 2 |
| C3×#5190 | 2 |
| #10591627 | 2 |
| #10591605 | 2 |
| #10590897 | 2 |
| #10590668 | 2 |
| D3×#497 | 3 |