Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1190 conjugacy classes of subgroups.
The subgroup lattice has 572 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#5725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63949 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#63947 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10593969 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10592785 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#5086 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10591627 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591619 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590371 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10590354 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#803 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #83286 | — | 3 | 1 | no | maximal |
| 13 | #81869 | — | 3 | 1 | no | maximal |
| 14 | C2×C3×#239 | C22 | 1 | 2 | yes | — |
| 15 | C2×#3799 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#3795 | C22 | 1 | 1 | yes | characteristic |
| 17 | C32×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#3756 | C22 | 1 | 2 | yes | — |
| 19 | C2×#3755 | C22 | 1 | 2 | yes | — |
| 20 | #64084 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#947 | C22 | 1 | 2 | yes | — |
| 22 | C2×C3×#216 | C22 | 1 | 2 | yes | — |
| 23 | C2×C3×#215 | C22 | 1 | 2 | yes | — |
| 24 | C3×#895 | — | 2 | 2 | no | — |
| 25 | C3×#893 | — | 2 | 2 | no | — |
| 26 | C3×#875 | C22 | 1 | 1 | yes | characteristic |
| 27 | C3×#874 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 29 | #63949 | — | 2 | 8 | no | — |
| 30 | #63947 | — | 2 | 8 | no | — |
| 31 | #63911 | C22 | 1 | 1 | yes | characteristic |
| 32 | #63906 | — | 2 | 2 | no | — |
| 33 | #63880 | — | 2 | 2 | no | — |
| 34 | #63866 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#3716 | C22 | 1 | 2 | yes | — |
| 36 | C2×#3715 | C22 | 1 | 2 | yes | — |
| 37 | C2×#3714 | C22 | 1 | 2 | yes | — |
| 38 | C2×#3713 | C22 | 1 | 2 | yes | — |
| 39 | C2×D3×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 40 | #63630 | C22 | 1 | 1 | yes | characteristic |
| 41 | C3×#803 | C22 | 1 | 1 | yes | characteristic |
| 42 | #63554 | C22 | 1 | 2 | yes | — |
| 43 | C3×#532 | — | 3 | 1 | no | — |
| 44 | C2×#950 | — | 3 | 2 | no | — |
| 45 | C2×#950 | — | 3 | 2 | no | — |
| 46 | C2×#919 | — | 3 | 2 | no | — |
| 47 | C2×#916 | — | 3 | 2 | no | — |
| 48 | #5725 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5668 | — | 3 | 1 | no | — |
| 50 | #5477 | — | 3 | 1 | no | — |
| 51 | C3×#497 | — | 3 | 1 | no | — |
| 52 | #5190 | — | 3 | 2 | no | — |
| 53 | #5176 | — | 3 | 2 | no | — |
| 54 | #5086 | — | 3 | 1 | no | — |
| 55 | #5086 | — | 3 | 1 | no | — |
| 56 | #5086 | — | 6 | 1 | no | — |
| 57 | #5086 | D3 | 1 | 1 | yes | characteristic, complemented |
| 58 | #5074 | — | 3 | 1 | no | — |
| 59 | #5074 | — | 3 | 1 | no | — |
| 60 | #5060 | — | 3 | 2 | no | — |
| 61 | #5058 | — | 3 | 2 | no | — |
| 62 | #5058 | — | 3 | 1 | no | — |
| 63 | C2×#803 | — | 3 | 1 | no | — |
| 64 | #4712 | — | 3 | 1 | no | — |
| 65 | D3×#97 | — | 3 | 1 | no | — |
| 66 | C2×C32×Q8 | C23 | 1 | 2 | yes | — |
| 67 | C2×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 69 | C3×#239 | — | 2 | 4 | no | — |
| 70 | C3×#239 | — | 2 | 4 | no | — |
| 71 | C2×C3×D12 | — | 2 | 2 | no | — |
| 72 | C2×C3×D12 | — | 2 | 2 | no | — |
| 73 | C2×C3×D12 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 75 | C2×C3×C4×D3 | — | 2 | 2 | no | — |
| 76 | C2×C3×C4×D3 | D4 | 1 | 2 | yes | — |
| 77 | C2×C3×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C3×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#626 | — | 2 | 1 | no | — |
| 80 | C2×#626 | — | 2 | 2 | no | — |
| 81 | C2×#625 | — | 2 | 1 | no | — |
| 82 | C2×#624 | — | 2 | 1 | no | — |
| 83 | C2×D3×Dic3 | — | 2 | 1 | no | — |
| 84 | #3799 | — | 2 | 4 | no | — |
| 85 | #3795 | — | 2 | 4 | no | — |
| 86 | C32×C4⋊C4 | — | 2 | 2 | no | — |
| 87 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 88 | #3756 | — | 2 | 4 | no | — |
| 89 | #3755 | — | 2 | 4 | no | — |
| 90 | #3752 | — | 2 | 2 | no | — |
| 91 | C2×C3⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 92 | C3×#216 | — | 2 | 4 | no | — |
| 93 | C3×#215 | — | 2 | 4 | no | — |
| 94 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 95 | C3×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 96 | C3×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 97 | C3×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 99 | Dic3⋊Dic3 | — | 2 | 2 | no | — |
| 100 | #3716 | — | 2 | 4 | no | — |
| 101 | #3715 | — | 2 | 4 | no | — |
| 102 | #3714 | — | 2 | 4 | no | — |
| 103 | #3713 | — | 2 | 4 | no | — |
| 104 | D3×C3⋊C8 | D4 | 1 | 8 | yes | complemented |
| 105 | #3150 | — | 9 | 1 | no | Sylow |
| 106 | C2×C3×#41 | — | 3 | 2 | no | — |
| 107 | C2×#239 | — | 3 | 1 | no | — |
| 108 | C2×#239 | C2×D3 | 1 | 2 | yes | — |
| 109 | C2×#237 | — | 3 | 1 | no | — |
| 110 | C2×#235 | — | 3 | 1 | no | — |
| 111 | C2×#235 | — | 3 | 1 | no | — |
| 112 | C2×C3×Q16 | — | 3 | 2 | no | — |
| 113 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 114 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 115 | C3×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | C3×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C3×#127 | — | 3 | 1 | no | — |
| 118 | C3×#124 | — | 3 | 2 | no | — |
| 119 | C3×#124 | — | 3 | 1 | no | — |
| 120 | C3×#121 | — | 6 | 2 | no | — |
| 121 | C3×C4×D4 | — | 6 | 2 | no | — |
| 122 | C2×C3×C42 | — | 3 | 1 | no | — |
| 123 | #950 | — | 6 | 8 | no | — |
| 124 | #950 | — | 6 | 8 | no | — |
| 125 | #947 | C2×D3 | 1 | 2 | yes | — |
| 126 | #944 | — | 3 | 1 | no | — |
| 127 | C2×#216 | — | 3 | 2 | no | — |
| 128 | C2×#216 | — | 3 | 2 | no | — |
| 129 | C2×#216 | — | 6 | 2 | no | — |
| 130 | C2×#216 | C2×D3 | 1 | 2 | yes | — |
| 131 | C2×#215 | — | 3 | 2 | no | — |
| 132 | C2×#215 | — | 3 | 2 | no | — |
| 133 | C2×#215 | — | 3 | 2 | no | — |
| 134 | C2×#215 | — | 6 | 2 | no | — |
| 135 | C2×#215 | C2×D3 | 1 | 2 | yes | — |
| 136 | #940 | — | 3 | 1 | no | — |
| 137 | C2×#214 | — | 3 | 2 | no | — |
| 138 | C2×#214 | — | 3 | 2 | no | — |
| 139 | C2×#213 | — | 3 | 2 | no | — |
| 140 | C2×#213 | — | 3 | 2 | no | — |
| 141 | C2×#213 | — | 3 | 2 | no | — |
| 142 | #930 | — | 6 | 2 | no | — |
| 143 | C22×C3⋊C8 | — | 3 | 2 | no | — |
| 144 | #919 | — | 6 | 8 | no | — |
| 145 | #916 | — | 6 | 8 | no | — |
| 146 | C2×D24 | — | 3 | 2 | no | — |
| 147 | C2×#204 | — | 3 | 2 | no | — |
| 148 | C2×D3×C8 | — | 3 | 2 | no | — |
| 149 | #895 | — | 2 | 2 | no | — |
| 150 | #893 | — | 2 | 2 | no | — |
| 151 | #884 | — | 6 | 2 | no | — |
| 152 | #67⋊C4 | — | 6 | 2 | no | — |
| 153 | #875 | — | 3 | 1 | no | — |
| 154 | #875 | — | 3 | 1 | no | — |
| 155 | #875 | — | 6 | 1 | no | — |
| 156 | #875 | C2×D3 | 1 | 1 | yes | characteristic |
| 157 | #874 | — | 3 | 1 | no | — |
| 158 | #874 | C2×D3 | 1 | 1 | yes | characteristic |
| 159 | C4×D12 | — | 6 | 2 | no | — |
| 160 | C42×D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 161 | #869 | — | 3 | 1 | no | — |
| 162 | C3×#97 | — | 3 | 1 | no | — |
| 163 | #815 | — | 3 | 2 | no | — |
| 164 | #803 | — | 3 | 1 | no | — |
| 165 | #803 | — | 3 | 1 | no | — |
| 166 | #803 | — | 3 | 2 | no | — |
| 167 | #803 | — | 6 | 1 | no | — |
| 168 | #803 | C2×D3 | 1 | 1 | yes | characteristic |
| 169 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 170 | C22×C3×D3 | — | 2 | 1 | no | — |
| 171 | C22×C3×D3 | — | 2 | 2 | no | — |
| 172 | C22×C3×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C32×Q8 | — | 2 | 2 | no | — |
| 174 | C32×Q8 | — | 2 | 2 | no | — |
| 175 | C2×C32×C4 | — | 2 | 2 | no | — |
| 176 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 177 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 178 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 179 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 180 | #634 | — | 2 | 2 | no | — |
| 181 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 182 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 183 | C2×C3×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C3×D12 | — | 2 | 2 | no | — |
| 185 | C3×D12 | — | 2 | 2 | no | — |
| 186 | C3×D12 | — | 2 | 2 | no | — |
| 187 | C3×D12 | — | 4 | 4 | no | — |
| 188 | C3×D12 | — | 4 | 4 | no | — |
| 189 | C3×C4×D3 | — | 4 | 2 | no | — |
| 190 | C3×C4×D3 | — | 4 | 4 | no | — |
| 191 | C3×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 192 | C3×Dic6 | — | 2 | 2 | no | — |
| 193 | #626 | — | 4 | 4 | no | — |
| 194 | #626 | — | 4 | 2 | no | — |
| 195 | #625 | — | 4 | 2 | no | — |
| 196 | #624 | — | 4 | 2 | no | — |
| 197 | D3×Dic3 | — | 4 | 2 | no | — |
| 198 | C3⋊(C3⋊C8) | C2×D4 | 1 | 4 | yes | — |
| 199 | C3×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 200 | C2×#135 | — | 9 | 2 | no | — |
| 201 | C2×#135 | — | 9 | 2 | no | — |
| 202 | #532 | — | 3 | 1 | no | — |
| 203 | #532 | — | 9 | 1 | no | — |
| 204 | #497 | — | 3 | 1 | no | — |
| 205 | #497 | — | 9 | 2 | no | — |
| 206 | #497 | — | 9 | 1 | no | — |
| 207 | #496 | — | 9 | 1 | no | — |
| 208 | #496 | — | 9 | 1 | no | — |
| 209 | #496 | — | 9 | 2 | no | — |
| 210 | C2×#97 | — | 9 | 1 | no | — |
| 211 | C3×#41 | — | 6 | 4 | no | — |
| 212 | C3×#41 | — | 6 | 4 | no | — |
| 213 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 214 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 215 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 216 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 217 | C2×C3×D4 | — | 3 | 2 | no | — |
| 218 | C2×C3×D4 | — | 3 | 1 | no | — |
| 219 | C2×C3×D4 | — | 6 | 2 | no | — |
| 220 | C2×C3×D4 | — | 6 | 2 | no | — |
| 221 | C22×C3×C4 | — | 3 | 1 | no | — |
| 222 | C22×C3×C4 | — | 3 | 2 | no | — |
| 223 | C22×C3×C4 | — | 6 | 2 | no | — |
| 224 | C2×#67 | — | 6 | 1 | no | — |
| 225 | C2×#67 | — | 6 | 1 | no | — |
| 226 | C2×#67 | — | 6 | 1 | no | — |
| 227 | C2×#67 | — | 6 | 2 | no | — |
| 228 | C22×Dic3 | — | 6 | 1 | no | — |
| 229 | #239 | — | 2 | 4 | no | — |
| 230 | #239 | — | 2 | 4 | no | — |
| 231 | #239 | — | 6 | 4 | no | — |
| 232 | #237 | — | 6 | 4 | no | — |
| 233 | #235 | — | 6 | 4 | no | — |
| 234 | #235 | — | 6 | 4 | no | — |
| 235 | C2×D12 | — | 2 | 2 | no | — |
| 236 | C2×D12 | — | 2 | 2 | no | — |
| 237 | C2×D12 | — | 3 | 1 | no | — |
| 238 | C2×D12 | — | 3 | 1 | no | — |
| 239 | C2×D12 | — | 6 | 1 | no | — |
| 240 | C2×D12 | — | 6 | 2 | no | — |
| 241 | C2×D12 | — | 6 | 1 | no | — |
| 242 | C2×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 243 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 244 | C2×C4×D3 | — | 2 | 2 | no | — |
| 245 | C2×C4×D3 | — | 6 | 1 | no | — |
| 246 | C2×C4×D3 | — | 6 | 1 | no | — |
| 247 | C2×C4×D3 | — | 6 | 1 | no | — |
| 248 | C2×C4×D3 | #67 | 1 | 2 | yes | — |
| 249 | C2×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 250 | C2×Dic6 | — | 3 | 1 | no | — |
| 251 | C2×Dic6 | — | 3 | 1 | no | — |
| 252 | C2×Dic6 | — | 6 | 1 | no | — |
| 253 | C2×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 254 | C3×Q16 | — | 6 | 4 | no | — |
| 255 | C3×SD16 | — | 6 | 4 | no | — |
| 256 | C2×C3×C8 | — | 3 | 2 | no | — |
| 257 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 258 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 259 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 260 | C3×C22⋊C4 | — | 6 | 4 | no | — |
| 261 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 262 | C3×C42 | — | 2 | 1 | no | — |
| 263 | C3×C42 | — | 3 | 2 | no | — |
| 264 | C3×C42 | — | 3 | 1 | no | — |
| 265 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 266 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 267 | #216 | — | 2 | 4 | no | — |
| 268 | #216 | — | 6 | 4 | no | — |
| 269 | #216 | — | 6 | 4 | no | — |
| 270 | #216 | — | 12 | 4 | no | — |
| 271 | #215 | — | 2 | 4 | no | — |
| 272 | #215 | — | 6 | 4 | no | — |
| 273 | #215 | — | 6 | 4 | no | — |
| 274 | #215 | — | 6 | 4 | no | — |
| 275 | #215 | — | 12 | 4 | no | — |
| 276 | #214 | — | 6 | 4 | no | — |
| 277 | #214 | — | 6 | 4 | no | — |
| 278 | #213 | — | 6 | 4 | no | — |
| 279 | #213 | — | 6 | 4 | no | — |
| 280 | #213 | — | 6 | 4 | no | — |
| 281 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 282 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 283 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 284 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 285 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 286 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 287 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 288 | C4×Dic3 | #67 | 1 | 2 | yes | — |
| 289 | C4×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 290 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 291 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 292 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 293 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 294 | C2×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 295 | D24 | — | 6 | 4 | no | — |
| 296 | #204 | — | 6 | 4 | no | — |
| 297 | D3×C8 | — | 3 | 8 | no | — |
| 298 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 300 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 301 | C2×C3×D3 | — | 2 | 2 | no | — |
| 302 | C2×C3×D3 | — | 4 | 1 | no | — |
| 303 | C2×C3×D3 | — | 4 | 2 | no | — |
| 304 | C2×C3×D3 | — | 4 | 2 | no | — |
| 305 | C2×C3×D3 | — | 4 | 4 | no | — |
| 306 | C2×C3×D3 | #127 | 1 | 2 | yes | — |
| 307 | C32×C4 | — | 2 | 2 | no | — |
| 308 | C32×C4 | — | 4 | 2 | no | — |
| 309 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 310 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 311 | C3×Dic3 | — | 2 | 2 | no | — |
| 312 | C3×Dic3 | — | 4 | 1 | no | — |
| 313 | C3×Dic3 | #127 | 1 | 2 | yes | — |
| 314 | C2×#41 | — | 3 | 2 | no | — |
| 315 | C2×#41 | — | 9 | 1 | no | — |
| 316 | C2×#41 | — | 9 | 1 | no | — |
| 317 | #135 | — | 18 | 8 | no | — |
| 318 | #135 | — | 18 | 8 | no | — |
| 319 | C2×Q16 | — | 3 | 2 | no | — |
| 320 | C2×Q16 | — | 9 | 2 | no | — |
| 321 | C2×SD16 | — | 3 | 2 | no | — |
| 322 | C2×SD16 | — | 9 | 2 | no | — |
| 323 | C2×SD16 | — | 9 | 2 | no | — |
| 324 | C2×SD16 | — | 9 | 2 | no | — |
| 325 | C2×D8 | — | 9 | 2 | no | — |
| 326 | C2×D8 | — | 9 | 2 | no | — |
| 327 | C22×C8 | — | 9 | 2 | no | — |
| 328 | C4⋊Q8 | — | 9 | 1 | no | — |
| 329 | C4⋊Q8 | D32 | 1 | 1 | yes | characteristic |
| 330 | #127 | — | 3 | 1 | no | — |
| 331 | #127 | — | 9 | 1 | no | — |
| 332 | #124 | — | 3 | 2 | no | — |
| 333 | #124 | — | 3 | 1 | no | — |
| 334 | #124 | — | 9 | 1 | no | — |
| 335 | #121 | — | 6 | 2 | no | — |
| 336 | #121 | — | 18 | 2 | no | — |
| 337 | C4×D4 | — | 6 | 2 | no | — |
| 338 | C4×D4 | — | 18 | 2 | no | — |
| 339 | C2×C42 | — | 3 | 1 | no | — |
| 340 | #97 | — | 3 | 1 | no | — |
| 341 | #97 | — | 9 | 2 | no | — |
| 342 | #97 | — | 9 | 1 | no | — |
| 343 | C23×C3 | — | 3 | 1 | no | — |
| 344 | C23×C3 | — | 6 | 2 | no | — |
| 345 | C23×C3 | — | 6 | 1 | no | — |
| 346 | C22×D3 | — | 2 | 1 | no | — |
| 347 | C22×D3 | — | 2 | 2 | no | — |
| 348 | C22×D3 | — | 6 | 1 | no | — |
| 349 | C22×D3 | — | 6 | 1 | no | — |
| 350 | C22×D3 | — | 12 | 1 | no | — |
| 351 | C22×D3 | C2×#67 | 1 | 1 | yes | characteristic |
| 352 | C3×Q8 | — | 2 | 2 | no | — |
| 353 | C3×Q8 | — | 2 | 2 | no | — |
| 354 | C3×Q8 | — | 2 | 2 | no | — |
| 355 | C3×Q8 | — | 2 | 2 | no | — |
| 356 | C3×Q8 | — | 4 | 2 | no | — |
| 357 | C3×Q8 | — | 4 | 2 | no | — |
| 358 | C3×Q8 | — | 6 | 2 | no | — |
| 359 | C3×D4 | — | 6 | 2 | no | — |
| 360 | C3×D4 | — | 6 | 2 | no | — |
| 361 | C3×D4 | — | 6 | 2 | no | — |
| 362 | C3×D4 | — | 12 | 4 | no | — |
| 363 | C3×D4 | — | 12 | 4 | no | — |
| 364 | C2×C3×C4 | — | 2 | 2 | no | — |
| 365 | C2×C3×C4 | — | 2 | 2 | no | — |
| 366 | C2×C3×C4 | — | 2 | 1 | no | — |
| 367 | C2×C3×C4 | — | 2 | 2 | no | — |
| 368 | C2×C3×C4 | — | 3 | 1 | no | — |
| 369 | C2×C3×C4 | — | 3 | 4 | no | — |
| 370 | C2×C3×C4 | — | 3 | 2 | no | — |
| 371 | C2×C3×C4 | — | 4 | 2 | no | — |
| 372 | C2×C3×C4 | — | 6 | 1 | no | — |
| 373 | C2×C3×C4 | — | 12 | 2 | no | — |
| 374 | C2×C3×C4 | — | 12 | 4 | no | — |
| 375 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 376 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 377 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 378 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 379 | #67 | — | 12 | 4 | no | — |
| 380 | #67 | — | 12 | 2 | no | — |
| 381 | #67 | — | 12 | 2 | no | — |
| 382 | #67 | — | 12 | 2 | no | — |
| 383 | C2×Dic3 | — | 2 | 1 | no | — |
| 384 | C2×Dic3 | — | 6 | 1 | no | — |
| 385 | C2×Dic3 | — | 6 | 1 | no | — |
| 386 | C2×Dic3 | — | 12 | 1 | no | — |
| 387 | C2×Dic3 | — | 12 | 2 | no | — |
| 388 | C2×Dic3 | C2×#67 | 1 | 2 | yes | — |
| 389 | C2×Dic3 | C2×#67 | 1 | 1 | yes | characteristic |
| 390 | D12 | — | 2 | 2 | no | — |
| 391 | D12 | — | 2 | 2 | no | — |
| 392 | D12 | — | 2 | 2 | no | — |
| 393 | D12 | — | 4 | 4 | no | — |
| 394 | D12 | — | 4 | 4 | no | — |
| 395 | D12 | — | 6 | 2 | no | — |
| 396 | D12 | — | 6 | 2 | no | — |
| 397 | D12 | — | 12 | 2 | no | — |
| 398 | D12 | — | 12 | 4 | no | — |
| 399 | D12 | — | 12 | 2 | no | — |
| 400 | C4×D3 | — | 4 | 2 | no | — |
| 401 | C4×D3 | — | 4 | 4 | no | — |
| 402 | C4×D3 | — | 12 | 2 | no | — |
| 403 | C4×D3 | — | 12 | 2 | no | — |
| 404 | C4×D3 | — | 12 | 2 | no | — |
| 405 | C4×D3 | D3×D4 | 1 | 4 | yes | — |
| 406 | Dic6 | — | 2 | 2 | no | — |
| 407 | Dic6 | — | 6 | 2 | no | — |
| 408 | Dic6 | — | 6 | 2 | no | — |
| 409 | Dic6 | — | 12 | 2 | no | — |
| 410 | C3×C8 | — | 3 | 4 | no | — |
| 411 | C3⋊C8 | — | 3 | 4 | no | — |
| 412 | C3⋊C8 | — | 3 | 4 | no | — |
| 413 | C3⋊C8 | — | 6 | 4 | no | — |
| 414 | C3⋊C8 | D3×D4 | 1 | 4 | yes | — |
| 415 | C2×C32 | C2×#127 | 1 | 1 | yes | characteristic |
| 416 | C2×C32 | #575 | 1 | 2 | yes | — |
| 417 | C3⋊D3 | — | 8 | 1 | no | — |
| 418 | C3×D3 | — | 2 | 2 | no | — |
| 419 | C3×D3 | — | 8 | 2 | no | — |
| 420 | C3×D3 | — | 8 | 1 | no | — |
| 421 | #41 | — | 6 | 4 | no | — |
| 422 | #41 | — | 6 | 4 | no | — |
| 423 | #41 | — | 18 | 4 | no | — |
| 424 | #41 | — | 18 | 4 | no | — |
| 425 | C2×Q8 | — | 3 | 1 | no | — |
| 426 | C2×Q8 | — | 9 | 1 | no | — |
| 427 | C2×Q8 | C2×D32 | 1 | 2 | yes | — |
| 428 | C2×D4 | — | 3 | 2 | no | — |
| 429 | C2×D4 | — | 3 | 1 | no | — |
| 430 | C2×D4 | — | 6 | 2 | no | — |
| 431 | C2×D4 | — | 6 | 2 | no | — |
| 432 | C2×D4 | — | 9 | 1 | no | — |
| 433 | C2×D4 | — | 18 | 2 | no | — |
| 434 | C2×D4 | — | 18 | 1 | no | — |
| 435 | C2×D4 | — | 18 | 1 | no | — |
| 436 | C22×C4 | — | 3 | 1 | no | — |
| 437 | C22×C4 | — | 3 | 2 | no | — |
| 438 | C22×C4 | — | 6 | 2 | no | — |
| 439 | C22×C4 | — | 18 | 1 | no | — |
| 440 | C22×C4 | — | 18 | 1 | no | — |
| 441 | Q16 | — | 6 | 4 | no | — |
| 442 | Q16 | — | 18 | 4 | no | — |
| 443 | SD16 | — | 6 | 4 | no | — |
| 444 | SD16 | — | 18 | 4 | no | — |
| 445 | SD16 | — | 18 | 4 | no | — |
| 446 | SD16 | — | 18 | 4 | no | — |
| 447 | D8 | — | 18 | 4 | no | — |
| 448 | D8 | — | 18 | 4 | no | — |
| 449 | C2×C8 | — | 3 | 2 | no | — |
| 450 | C2×C8 | — | 9 | 8 | no | — |
| 451 | C2×C8 | — | 9 | 2 | no | — |
| 452 | C4⋊C4 | — | 2 | 2 | no | — |
| 453 | C4⋊C4 | — | 18 | 2 | no | — |
| 454 | C22⋊C4 | — | 6 | 4 | no | — |
| 455 | C22⋊C4 | — | 6 | 2 | no | — |
| 456 | C22⋊C4 | — | 18 | 2 | no | — |
| 457 | C42 | — | 3 | 1 | no | — |
| 458 | C42 | — | 3 | 2 | no | — |
| 459 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 460 | C22×C3 | — | 2 | 1 | no | — |
| 461 | C22×C3 | — | 3 | 2 | no | — |
| 462 | C22×C3 | — | 6 | 2 | no | — |
| 463 | C22×C3 | — | 12 | 2 | no | — |
| 464 | C22×C3 | — | 12 | 4 | no | — |
| 465 | C22×C3 | — | 12 | 1 | no | — |
| 466 | C22×C3 | — | 12 | 2 | no | — |
| 467 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 468 | C22×C3 | C22×#67 | 1 | 1 | yes | characteristic |
| 469 | C2×D3 | — | 2 | 2 | no | — |
| 470 | C2×D3 | — | 4 | 1 | no | — |
| 471 | C2×D3 | — | 4 | 2 | no | — |
| 472 | C2×D3 | — | 4 | 2 | no | — |
| 473 | C2×D3 | — | 4 | 4 | no | — |
| 474 | C2×D3 | — | 12 | 1 | no | — |
| 475 | C2×D3 | — | 12 | 2 | no | — |
| 476 | C2×D3 | — | 12 | 1 | no | — |
| 477 | C2×D3 | — | 12 | 2 | no | — |
| 478 | C2×D3 | — | 24 | 1 | no | — |
| 479 | C2×D3 | — | 24 | 2 | no | — |
| 480 | C2×D3 | #940 | 1 | 2 | yes | — |
| 481 | C3×C4 | — | 2 | 2 | no | — |
| 482 | C3×C4 | — | 2 | 2 | no | — |
| 483 | C3×C4 | — | 2 | 2 | no | — |
| 484 | C3×C4 | — | 3 | 2 | no | — |
| 485 | C3×C4 | — | 4 | 2 | no | — |
| 486 | C3×C4 | — | 4 | 2 | no | — |
| 487 | C3×C4 | — | 4 | 2 | no | — |
| 488 | C3×C4 | — | 6 | 2 | no | — |
| 489 | C3×C4 | — | 8 | 2 | no | — |
| 490 | C3×C4 | — | 12 | 1 | no | — |
| 491 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 492 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 493 | Dic3 | — | 2 | 2 | no | — |
| 494 | Dic3 | — | 4 | 1 | no | — |
| 495 | Dic3 | — | 12 | 1 | no | — |
| 496 | Dic3 | — | 12 | 1 | no | — |
| 497 | Dic3 | — | 24 | 1 | no | — |
| 498 | Dic3 | #940 | 1 | 2 | yes | — |
| 499 | C32 | #3150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 500 | C23 | — | 3 | 1 | no | — |
| 501 | C23 | — | 6 | 2 | no | — |
| 502 | C23 | — | 6 | 1 | no | — |
| 503 | C23 | — | 18 | 1 | no | — |
| 504 | Q8 | — | 2 | 2 | no | — |
| 505 | Q8 | — | 2 | 2 | no | — |
| 506 | Q8 | — | 6 | 2 | no | — |
| 507 | Q8 | — | 18 | 2 | no | — |
| 508 | D4 | — | 6 | 2 | no | — |
| 509 | D4 | — | 6 | 2 | no | — |
| 510 | D4 | — | 6 | 2 | no | — |
| 511 | D4 | — | 12 | 4 | no | — |
| 512 | D4 | — | 12 | 4 | no | — |
| 513 | D4 | — | 18 | 2 | no | — |
| 514 | D4 | — | 36 | 4 | no | — |
| 515 | D4 | — | 36 | 2 | no | — |
| 516 | D4 | — | 36 | 2 | no | — |
| 517 | C2×C4 | — | 2 | 2 | no | — |
| 518 | C2×C4 | — | 3 | 1 | no | — |
| 519 | C2×C4 | — | 3 | 4 | no | — |
| 520 | C2×C4 | — | 3 | 2 | no | — |
| 521 | C2×C4 | — | 6 | 1 | no | — |
| 522 | C2×C4 | — | 12 | 2 | no | — |
| 523 | C2×C4 | — | 12 | 4 | no | — |
| 524 | C2×C4 | — | 18 | 1 | no | — |
| 525 | C2×C4 | — | 36 | 2 | no | — |
| 526 | C2×C4 | — | 36 | 2 | no | — |
| 527 | C2×C4 | D3×#67 | 1 | 2 | yes | — |
| 528 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 529 | C8 | — | 3 | 4 | no | — |
| 530 | C8 | — | 9 | 4 | no | — |
| 531 | C2×C3 | — | 2 | 1 | no | — |
| 532 | C2×C3 | — | 2 | 2 | no | — |
| 533 | C2×C3 | — | 6 | 2 | no | — |
| 534 | C2×C3 | — | 24 | 1 | no | — |
| 535 | C2×C3 | — | 24 | 2 | no | — |
| 536 | C2×C3 | D3×#127 | 1 | 1 | yes | characteristic |
| 537 | C2×C3 | #5777 | 1 | 2 | yes | — |
| 538 | C2×C3 | C2×#940 | 1 | 1 | yes | characteristic |
| 539 | C2×C3 | #5822 | 1 | 2 | yes | — |
| 540 | D3 | — | 2 | 2 | no | — |
| 541 | D3 | — | 8 | 2 | no | — |
| 542 | D3 | — | 8 | 1 | no | — |
| 543 | D3 | — | 24 | 1 | no | — |
| 544 | D3 | — | 24 | 1 | no | — |
| 545 | D3 | — | 48 | 1 | no | — |
| 546 | C22 | — | 3 | 2 | no | — |
| 547 | C22 | — | 6 | 2 | no | — |
| 548 | C22 | — | 12 | 2 | no | — |
| 549 | C22 | — | 12 | 1 | no | — |
| 550 | C22 | — | 12 | 4 | no | — |
| 551 | C22 | — | 12 | 2 | no | — |
| 552 | C22 | — | 36 | 1 | no | — |
| 553 | C22 | — | 36 | 2 | no | — |
| 554 | C22 | C2×D3×#67 | 1 | 1 | yes | characteristic |
| 555 | C4 | — | 2 | 2 | no | — |
| 556 | C4 | — | 3 | 2 | no | — |
| 557 | C4 | — | 4 | 2 | no | — |
| 558 | C4 | — | 6 | 2 | no | — |
| 559 | C4 | — | 12 | 1 | no | — |
| 560 | C4 | — | 36 | 1 | no | — |
| 561 | C4 | D32×D4 | 1 | 2 | yes | — |
| 562 | C3 | — | 2 | 1 | no | — |
| 563 | C3 | #81869 | 1 | 1 | yes | characteristic, complemented |
| 564 | C3 | #83286 | 1 | 1 | yes | characteristic, complemented |
| 565 | C2 | — | 6 | 2 | no | — |
| 566 | C2 | — | 24 | 2 | no | — |
| 567 | C2 | — | 24 | 1 | no | — |
| 568 | C2 | — | 72 | 1 | no | — |
| 569 | C2 | D3×#940 | 1 | 1 | yes | characteristic |
| 570 | C2 | #10595317 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5725 | C2 | semidirect |
| 2. C2×#63949 | C2 | semidirect |
| 3. C2×#63947 | C2 | semidirect |
| 4. #10593969 | C2 | semidirect |
| 5. #10592785 | C2 | semidirect |
| 6. C3×#5086 | C2 | semidirect |
| 7. #10591627 | C2 | semidirect |
| 8. #10591619 | C2 | semidirect |
| 9. #10590371 | C2 | semidirect |
| 10. #10590354 | C2 | semidirect |
| 11. D3×#803 | C2 | semidirect |
| 48. #5725 | D3 | semidirect |
| 57. #5086 | D3 | semidirect |
| 104. D3×C3⋊C8 | D4 | semidirect |
| 499. C32 | #3150 | semidirect |
| 563. C3 | #81869 | semidirect |
| 564. C3 | #83286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5725 | 2 |
| C2×#63949 | 2 |
| C2×#63947 | 2 |
| #10593969 | 2 |
| #10592785 | 2 |
| C3×#5086 | 2 |
| #10591627 | 2 |
| #10591619 | 2 |
| #10590371 | 2 |
| #10590354 | 2 |
| D3×#803 | 2 |
| #83286 | 3 |
| #81869 | 3 |