Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1129 conjugacy classes of subgroups.
The subgroup lattice has 559 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 | Q8×#624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#63940 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×#5185 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591604 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591577 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10591552 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10590940 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10590861 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10590658 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D3×#464 | — | 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×C32×Q16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#3756 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#3756 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | Q16×C3⋊D3 | — | 2 | 4 | no | — |
| 20 | C2×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#947 | C22 | 1 | 2 | yes | — |
| 23 | C3×Q8×Dic3 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×C3×#215 | C22 | 1 | 2 | yes | — |
| 25 | #63940 | — | 2 | 4 | no | — |
| 26 | #63921 | — | 2 | 1 | no | — |
| 27 | #63921 | — | 2 | 1 | no | — |
| 28 | #63913 | — | 2 | 2 | no | — |
| 29 | #63900 | — | 2 | 1 | no | — |
| 30 | #63900 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×#624 | — | 2 | 1 | no | — |
| 32 | C4×#624 | C22 | 1 | 1 | yes | characteristic |
| 33 | #63860 | C22 | 1 | 2 | yes | — |
| 34 | #63844 | — | 2 | 2 | no | — |
| 35 | #63844 | C22 | 1 | 2 | yes | complemented |
| 36 | C2×#3716 | C22 | 1 | 2 | yes | — |
| 37 | C2×#3710 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×#835 | C22 | 1 | 2 | yes | complemented |
| 39 | C3×#821 | C22 | 1 | 2 | yes | — |
| 40 | C3×Dic3⋊C8 | C22 | 1 | 2 | yes | complemented |
| 41 | Dic3⋊(C3⋊C8) | C22 | 1 | 2 | yes | complemented |
| 42 | #63567 | C22 | 1 | 2 | yes | complemented |
| 43 | #63562 | C22 | 1 | 2 | yes | — |
| 44 | C2×D3×Q16 | — | 3 | 2 | no | — |
| 45 | C2×D3×Q16 | — | 6 | 1 | no | — |
| 46 | C2×D3×SD16 | — | 3 | 2 | no | — |
| 47 | D3×#124 | — | 3 | 2 | no | — |
| 48 | C4×D3×Q8 | — | 3 | 2 | no | — |
| 49 | C3×#464 | — | 3 | 2 | no | — |
| 50 | #5185 | D3 | 1 | 2 | yes | complemented |
| 51 | #5166 | — | 3 | 2 | no | — |
| 52 | #5054 | — | 3 | 2 | no | — |
| 53 | #5028 | — | 3 | 2 | no | — |
| 54 | #4845 | — | 3 | 2 | no | — |
| 55 | D3×C4⋊C8 | — | 3 | 2 | no | — |
| 56 | D3×#103 | — | 3 | 2 | no | — |
| 57 | #4798 | — | 3 | 2 | no | — |
| 58 | D3×#102 | — | 3 | 2 | no | — |
| 59 | #4767 | — | 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 | D4 | 1 | 4 | yes | — |
| 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×#625 | — | 2 | 1 | no | — |
| 76 | C2×#624 | — | 2 | 1 | no | — |
| 77 | C2×#624 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×#624 | D4 | 1 | 1 | yes | characteristic |
| 79 | #3802 | — | 2 | 2 | no | — |
| 80 | #3802 | — | 2 | 2 | no | — |
| 81 | C32×Q16 | — | 2 | 2 | no | — |
| 82 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 83 | #3756 | — | 2 | 2 | no | — |
| 84 | #3756 | — | 2 | 2 | no | — |
| 85 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 86 | #3746 | — | 2 | 2 | no | — |
| 87 | C8×C3⋊D3 | — | 2 | 2 | no | — |
| 88 | C3×#215 | — | 2 | 4 | no | — |
| 89 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 90 | C3×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 91 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 92 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 93 | C3×C4×Dic3 | — | 2 | 2 | no | — |
| 94 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 95 | C2×C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 96 | #3724 | — | 2 | 1 | no | — |
| 97 | #3724 | — | 2 | 2 | no | — |
| 98 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 99 | (C2×D3)⋊Dic3 | — | 2 | 2 | no | — |
| 100 | Dic32 | — | 2 | 2 | no | — |
| 101 | Dic32 | D4 | 1 | 2 | yes | — |
| 102 | #3716 | — | 2 | 4 | no | — |
| 103 | #3710 | — | 2 | 2 | no | — |
| 104 | C2×#464 | — | 9 | 1 | no | Sylow |
| 105 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 106 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 107 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 108 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 109 | C2×D3×D4 | — | 3 | 2 | no | — |
| 110 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 111 | C2×C3×Q16 | C2×D3 | 1 | 2 | yes | complemented |
| 112 | C2×C3×SD16 | — | 3 | 2 | no | — |
| 113 | C3×#124 | — | 3 | 2 | no | — |
| 114 | C3×C4×Q8 | — | 3 | 2 | no | — |
| 115 | #947 | C2×D3 | 1 | 2 | yes | — |
| 116 | Q8×Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 117 | C2×#216 | — | 3 | 2 | no | — |
| 118 | C2×#216 | — | 3 | 2 | no | — |
| 119 | C2×#216 | — | 6 | 1 | no | — |
| 120 | C2×#216 | — | 6 | 1 | no | — |
| 121 | C2×#215 | C2×D3 | 1 | 2 | yes | — |
| 122 | #936 | — | 3 | 2 | no | — |
| 123 | C2×#214 | — | 3 | 2 | no | — |
| 124 | D3×Q16 | — | 6 | 8 | no | — |
| 125 | D3×Q16 | — | 6 | 8 | no | — |
| 126 | D3×SD16 | — | 6 | 8 | no | — |
| 127 | C2×Dic12 | — | 3 | 2 | no | — |
| 128 | C2×Dic12 | — | 6 | 1 | no | — |
| 129 | C2×#204 | — | 3 | 2 | no | — |
| 130 | C2×D3×C8 | — | 3 | 2 | no | — |
| 131 | C2×D3×C8 | — | 3 | 2 | no | — |
| 132 | C2×D3×C8 | — | 6 | 1 | no | — |
| 133 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 134 | D3×C4⋊C4 | — | 6 | 2 | no | — |
| 135 | #887 | — | 3 | 2 | no | — |
| 136 | #887 | — | 6 | 2 | no | — |
| 137 | #885 | — | 6 | 2 | no | — |
| 138 | #885 | — | 6 | 2 | no | — |
| 139 | D3×C22⋊C4 | — | 6 | 2 | no | — |
| 140 | D3×C22⋊C4 | — | 6 | 2 | no | — |
| 141 | #875 | — | 3 | 2 | no | — |
| 142 | C42×D3 | — | 3 | 2 | no | — |
| 143 | C42×D3 | — | 6 | 2 | no | — |
| 144 | C4×Dic6 | — | 3 | 2 | no | — |
| 145 | C4×Dic6 | — | 6 | 2 | no | — |
| 146 | C3×C4⋊C8 | — | 3 | 2 | no | — |
| 147 | C3×#103 | — | 3 | 2 | no | — |
| 148 | C3×#102 | — | 3 | 2 | no | — |
| 149 | #835 | C2×D3 | 1 | 2 | yes | complemented |
| 150 | #832 | — | 3 | 2 | no | — |
| 151 | #821 | C2×D3 | 1 | 2 | yes | — |
| 152 | #816 | — | 3 | 2 | no | — |
| 153 | Dic3⋊C8 | — | 3 | 2 | no | — |
| 154 | Dic3⋊C8 | C2×D3 | 1 | 2 | yes | complemented |
| 155 | #810 | — | 3 | 2 | no | — |
| 156 | #809 | — | 3 | 2 | no | — |
| 157 | C4⋊(C3⋊C8) | — | 3 | 2 | no | — |
| 158 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×C3×D3 | — | 2 | 2 | no | — |
| 160 | C2×D32 | — | 4 | 2 | no | — |
| 161 | C2×D32 | — | 4 | 2 | no | — |
| 162 | C2×D32 | — | 4 | 2 | no | — |
| 163 | C32×Q8 | — | 2 | 1 | no | — |
| 164 | C32×Q8 | — | 2 | 1 | no | — |
| 165 | C32×Q8 | — | 2 | 1 | no | — |
| 166 | C32×Q8 | C2×D4 | 1 | 2 | yes | — |
| 167 | C2×C32×C4 | — | 2 | 1 | no | — |
| 168 | C2×C32×C4 | — | 2 | 1 | no | — |
| 169 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 170 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 171 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 172 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 174 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 175 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 176 | C4×C3⋊D3 | #41 | 1 | 2 | yes | — |
| 177 | #634 | — | 2 | 1 | no | — |
| 178 | #634 | — | 2 | 1 | no | — |
| 179 | #634 | — | 2 | 4 | no | — |
| 180 | #634 | — | 2 | 1 | no | — |
| 181 | #634 | — | 4 | 2 | no | — |
| 182 | #634 | C2×D4 | 1 | 2 | yes | — |
| 183 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 184 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 185 | C2×C3×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 186 | C3×D12 | — | 2 | 2 | no | — |
| 187 | C3×D12 | — | 2 | 2 | no | — |
| 188 | #625 | — | 4 | 2 | no | — |
| 189 | #624 | — | 2 | 2 | no | — |
| 190 | #624 | — | 2 | 2 | no | — |
| 191 | #624 | — | 4 | 2 | no | — |
| 192 | C32×C8 | — | 2 | 1 | no | — |
| 193 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 194 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 195 | C22×Q16 | — | 9 | 1 | no | — |
| 196 | C22×SD16 | — | 9 | 1 | no | — |
| 197 | C2×#124 | — | 9 | 1 | no | — |
| 198 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 199 | #464 | — | 3 | 2 | no | — |
| 200 | #464 | — | 9 | 2 | no | — |
| 201 | #464 | — | 9 | 2 | no | — |
| 202 | #464 | — | 9 | 2 | no | — |
| 203 | C2×C4⋊C8 | — | 9 | 1 | no | — |
| 204 | C2×#103 | — | 9 | 1 | no | — |
| 205 | C2×#102 | — | 9 | 1 | no | — |
| 206 | C23×D3 | — | 6 | 2 | no | — |
| 207 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 208 | C2×C3×Q8 | — | 2 | 1 | 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 | — | 3 | 8 | 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 | — | 12 | 2 | no | — |
| 220 | D3×Q8 | — | 12 | 2 | no | — |
| 221 | D3×D4 | — | 6 | 4 | no | — |
| 222 | D3×D4 | — | 6 | 4 | no | — |
| 223 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 224 | C2×C4×D3 | — | 3 | 2 | no | — |
| 225 | C2×C4×D3 | — | 3 | 2 | no | — |
| 226 | C2×C4×D3 | — | 3 | 2 | no | — |
| 227 | C2×C4×D3 | — | 6 | 1 | no | — |
| 228 | C2×C4×D3 | — | 6 | 2 | no | — |
| 229 | C2×C4×D3 | — | 6 | 2 | no | — |
| 230 | C2×C4×D3 | — | 6 | 2 | no | — |
| 231 | C2×C4×D3 | — | 12 | 1 | no | — |
| 232 | C2×C4×D3 | — | 12 | 1 | no | — |
| 233 | C2×Dic6 | — | 3 | 2 | no | — |
| 234 | C2×Dic6 | — | 3 | 2 | no | — |
| 235 | C2×Dic6 | — | 6 | 1 | no | — |
| 236 | C2×Dic6 | — | 6 | 1 | no | — |
| 237 | C2×Dic6 | — | 6 | 2 | no | — |
| 238 | C2×Dic6 | — | 6 | 2 | no | — |
| 239 | C2×Dic6 | — | 12 | 1 | no | — |
| 240 | C2×Dic6 | — | 12 | 1 | no | — |
| 241 | C3×Q16 | — | 2 | 4 | no | — |
| 242 | C3×Q16 | — | 2 | 4 | no | — |
| 243 | C3×SD16 | — | 6 | 4 | no | — |
| 244 | C2×C3×C8 | — | 2 | 1 | no | — |
| 245 | C2×C3×C8 | — | 3 | 2 | no | — |
| 246 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 247 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 248 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 249 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 250 | C3×C22⋊C4 | — | 6 | 2 | no | — |
| 251 | C3×C42 | — | 3 | 2 | no | — |
| 252 | C3×C42 | — | 6 | 2 | no | — |
| 253 | #217 | — | 6 | 2 | no | — |
| 254 | #217 | — | 6 | 2 | no | — |
| 255 | #216 | — | 6 | 4 | no | — |
| 256 | #216 | — | 6 | 4 | no | — |
| 257 | #216 | — | 6 | 4 | no | — |
| 258 | #216 | — | 6 | 4 | no | — |
| 259 | #215 | — | 2 | 4 | no | — |
| 260 | #214 | — | 6 | 4 | no | — |
| 261 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 262 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 263 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 264 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 265 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 266 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 267 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 268 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 269 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 270 | C4×Dic3 | — | 2 | 2 | no | — |
| 271 | C4×Dic3 | — | 3 | 2 | no | — |
| 272 | C4×Dic3 | — | 3 | 2 | no | — |
| 273 | C4×Dic3 | — | 6 | 2 | no | — |
| 274 | C4×Dic3 | — | 6 | 2 | no | — |
| 275 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 276 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 277 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 278 | C2×C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 279 | Dic12 | — | 6 | 4 | no | — |
| 280 | Dic12 | — | 6 | 4 | no | — |
| 281 | #204 | — | 6 | 4 | no | — |
| 282 | D3×C8 | — | 6 | 4 | no | — |
| 283 | D3×C8 | — | 6 | 4 | no | — |
| 284 | D3×C8 | — | 6 | 4 | no | — |
| 285 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 286 | C2×C3⋊D3 | #121 | 1 | 2 | yes | — |
| 287 | C2×C3⋊D3 | #135 | 1 | 2 | yes | — |
| 288 | C2×C3⋊D3 | #137 | 1 | 2 | yes | — |
| 289 | C2×C3×D3 | — | 4 | 2 | no | — |
| 290 | C2×C3×D3 | — | 4 | 2 | no | — |
| 291 | C2×C3×D3 | — | 4 | 2 | no | — |
| 292 | D32 | — | 8 | 4 | no | — |
| 293 | C32×C4 | — | 2 | 2 | no | — |
| 294 | C32×C4 | — | 4 | 1 | no | — |
| 295 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 296 | C32×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 297 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 298 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 299 | C3⋊Dic3 | #121 | 1 | 2 | yes | — |
| 300 | C3×Dic3 | — | 2 | 2 | no | — |
| 301 | C3×Dic3 | — | 2 | 2 | no | — |
| 302 | C3×Dic3 | — | 4 | 2 | no | — |
| 303 | C22×Q8 | — | 9 | 1 | no | — |
| 304 | C22×Q8 | — | 9 | 1 | no | — |
| 305 | C22×D4 | — | 9 | 1 | no | — |
| 306 | C2×Q16 | — | 9 | 1 | no | — |
| 307 | C2×Q16 | — | 9 | 1 | no | — |
| 308 | C2×Q16 | — | 9 | 1 | 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 | — | 9 | 2 | no | — |
| 313 | C2×SD16 | — | 18 | 4 | no | — |
| 314 | C22×C8 | — | 9 | 1 | no | — |
| 315 | C22×C8 | — | 9 | 1 | no | — |
| 316 | #124 | — | 3 | 2 | no | — |
| 317 | #124 | — | 9 | 2 | no | — |
| 318 | #124 | — | 18 | 2 | no | — |
| 319 | C4×Q8 | — | 3 | 2 | no | — |
| 320 | C4×Q8 | — | 9 | 2 | no | — |
| 321 | C4×Q8 | — | 18 | 2 | no | — |
| 322 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 323 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 324 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 325 | C2×C22⋊C4 | — | 18 | 1 | no | — |
| 326 | C2×C42 | — | 9 | 1 | no | — |
| 327 | C2×C42 | — | 18 | 1 | no | — |
| 328 | C4⋊C8 | — | 3 | 2 | no | — |
| 329 | C4⋊C8 | — | 9 | 2 | no | — |
| 330 | #103 | — | 3 | 2 | no | — |
| 331 | #103 | — | 9 | 2 | no | — |
| 332 | #102 | — | 3 | 2 | no | — |
| 333 | #102 | — | 9 | 2 | no | — |
| 334 | C23×C3 | — | 6 | 2 | no | — |
| 335 | C22×D3 | — | 2 | 2 | no | — |
| 336 | C22×D3 | — | 3 | 2 | no | — |
| 337 | C22×D3 | — | 6 | 1 | no | — |
| 338 | C22×D3 | — | 12 | 4 | no | — |
| 339 | C22×D3 | — | 12 | 4 | no | — |
| 340 | C22×D3 | — | 12 | 4 | no | — |
| 341 | C3×Q8 | — | 2 | 2 | no | — |
| 342 | C3×Q8 | — | 2 | 2 | no | — |
| 343 | C3×Q8 | — | 2 | 2 | no | — |
| 344 | C3×Q8 | — | 2 | 2 | no | — |
| 345 | C3×Q8 | — | 2 | 2 | no | — |
| 346 | C3×Q8 | — | 4 | 1 | no | — |
| 347 | C3×Q8 | — | 4 | 1 | no | — |
| 348 | C3×Q8 | D3×D4 | 1 | 4 | yes | — |
| 349 | C3×D4 | — | 6 | 2 | no | — |
| 350 | C3×D4 | — | 6 | 2 | no | — |
| 351 | C2×C3×C4 | — | 2 | 2 | no | — |
| 352 | C2×C3×C4 | — | 2 | 2 | no | — |
| 353 | C2×C3×C4 | — | 2 | 1 | no | — |
| 354 | C2×C3×C4 | — | 3 | 2 | no | — |
| 355 | C2×C3×C4 | — | 3 | 2 | no | — |
| 356 | C2×C3×C4 | — | 4 | 1 | no | — |
| 357 | C2×C3×C4 | — | 4 | 1 | no | — |
| 358 | C2×C3×C4 | — | 6 | 2 | no | — |
| 359 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 360 | #67 | — | 12 | 4 | no | — |
| 361 | C2×Dic3 | — | 2 | 2 | no | — |
| 362 | C2×Dic3 | — | 3 | 2 | no | — |
| 363 | C2×Dic3 | — | 6 | 1 | no | — |
| 364 | C2×Dic3 | — | 6 | 2 | no | — |
| 365 | C2×Dic3 | — | 6 | 2 | no | — |
| 366 | C2×Dic3 | — | 12 | 1 | no | — |
| 367 | C2×Dic3 | — | 12 | 1 | no | — |
| 368 | C2×Dic3 | D3×D4 | 1 | 2 | yes | — |
| 369 | C2×Dic3 | D3×D4 | 1 | 2 | yes | — |
| 370 | D12 | — | 2 | 2 | no | — |
| 371 | D12 | — | 2 | 2 | no | — |
| 372 | C4×D3 | — | 3 | 4 | no | — |
| 373 | C4×D3 | — | 3 | 4 | no | — |
| 374 | C4×D3 | — | 6 | 2 | no | — |
| 375 | C4×D3 | — | 6 | 2 | no | — |
| 376 | C4×D3 | — | 6 | 4 | no | — |
| 377 | C4×D3 | — | 6 | 4 | no | — |
| 378 | C4×D3 | — | 6 | 8 | no | — |
| 379 | C4×D3 | — | 12 | 4 | no | — |
| 380 | C4×D3 | — | 12 | 4 | no | — |
| 381 | C4×D3 | — | 12 | 4 | no | — |
| 382 | C4×D3 | — | 12 | 4 | no | — |
| 383 | Dic6 | — | 3 | 4 | no | — |
| 384 | Dic6 | — | 6 | 2 | no | — |
| 385 | Dic6 | — | 6 | 8 | no | — |
| 386 | Dic6 | — | 6 | 2 | no | — |
| 387 | Dic6 | — | 6 | 2 | no | — |
| 388 | Dic6 | — | 6 | 2 | no | — |
| 389 | Dic6 | — | 6 | 2 | no | — |
| 390 | Dic6 | — | 12 | 4 | no | — |
| 391 | Dic6 | — | 12 | 1 | no | — |
| 392 | Dic6 | — | 12 | 1 | no | — |
| 393 | Dic6 | — | 12 | 4 | no | — |
| 394 | Dic6 | — | 12 | 4 | no | — |
| 395 | C3×C8 | — | 2 | 2 | no | — |
| 396 | C3×C8 | — | 2 | 2 | no | — |
| 397 | C3×C8 | — | 6 | 2 | no | — |
| 398 | C3⋊C8 | — | 2 | 2 | no | — |
| 399 | C3⋊C8 | — | 6 | 2 | no | — |
| 400 | C3⋊C8 | — | 6 | 2 | no | — |
| 401 | C2×C32 | C2×#121 | 1 | 1 | yes | characteristic |
| 402 | C2×C32 | C2×#135 | 1 | 1 | yes | characteristic |
| 403 | C2×C32 | C2×#137 | 1 | 1 | yes | characteristic |
| 404 | C3⋊D3 | #464 | 1 | 4 | yes | complemented |
| 405 | C3×D3 | — | 8 | 2 | no | — |
| 406 | C24 | — | 18 | 1 | no | — |
| 407 | C2×Q8 | — | 9 | 4 | no | — |
| 408 | C2×Q8 | — | 9 | 1 | no | — |
| 409 | C2×Q8 | — | 9 | 1 | no | — |
| 410 | C2×Q8 | — | 18 | 1 | no | — |
| 411 | C2×Q8 | — | 18 | 1 | 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 | 1 | no | — |
| 422 | C22×C4 | — | 9 | 1 | no | — |
| 423 | C22×C4 | — | 9 | 1 | no | — |
| 424 | C22×C4 | — | 18 | 1 | no | — |
| 425 | C22×C4 | — | 18 | 1 | no | — |
| 426 | C22×C4 | — | 18 | 1 | no | — |
| 427 | Q16 | — | 2 | 2 | no | — |
| 428 | Q16 | — | 18 | 2 | no | — |
| 429 | Q16 | — | 18 | 2 | no | — |
| 430 | Q16 | — | 18 | 2 | no | — |
| 431 | SD16 | — | 6 | 4 | no | — |
| 432 | SD16 | — | 18 | 4 | no | — |
| 433 | C2×C8 | — | 3 | 2 | no | — |
| 434 | C2×C8 | — | 9 | 1 | no | — |
| 435 | C2×C8 | — | 18 | 2 | no | — |
| 436 | C2×C8 | — | 18 | 2 | no | — |
| 437 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 438 | C4⋊C4 | — | 3 | 2 | no | — |
| 439 | C4⋊C4 | — | 6 | 2 | no | — |
| 440 | C4⋊C4 | — | 18 | 2 | no | — |
| 441 | C4⋊C4 | — | 18 | 1 | no | — |
| 442 | C22⋊C4 | — | 6 | 2 | no | — |
| 443 | C22⋊C4 | — | 6 | 2 | no | — |
| 444 | C22⋊C4 | — | 18 | 2 | no | — |
| 445 | C22⋊C4 | — | 18 | 2 | no | — |
| 446 | C42 | — | 3 | 2 | no | — |
| 447 | C42 | — | 6 | 2 | no | — |
| 448 | C42 | — | 9 | 2 | no | — |
| 449 | C42 | — | 18 | 2 | no | — |
| 450 | C22×C3 | — | 2 | 1 | no | — |
| 451 | C22×C3 | — | 12 | 2 | no | — |
| 452 | C22×C3 | — | 12 | 2 | no | — |
| 453 | C22×C3 | — | 12 | 2 | no | — |
| 454 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 455 | C2×D3 | — | 3 | 4 | no | — |
| 456 | C2×D3 | — | 3 | 4 | no | — |
| 457 | C2×D3 | — | 3 | 4 | no | — |
| 458 | C2×D3 | — | 4 | 2 | no | — |
| 459 | C2×D3 | — | 4 | 2 | no | — |
| 460 | C2×D3 | — | 4 | 2 | no | — |
| 461 | C2×D3 | — | 6 | 2 | no | — |
| 462 | C2×D3 | — | 6 | 2 | no | — |
| 463 | C2×D3 | — | 6 | 2 | no | — |
| 464 | C2×D3 | — | 24 | 8 | no | — |
| 465 | C3×C4 | — | 2 | 4 | no | — |
| 466 | C3×C4 | — | 2 | 1 | no | — |
| 467 | C3×C4 | — | 2 | 1 | no | — |
| 468 | C3×C4 | — | 4 | 2 | no | — |
| 469 | C3×C4 | — | 4 | 2 | no | — |
| 470 | C3×C4 | — | 4 | 2 | no | — |
| 471 | C3×C4 | — | 6 | 2 | no | — |
| 472 | C3×C4 | — | 6 | 2 | no | — |
| 473 | C3×C4 | — | 12 | 2 | no | — |
| 474 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 475 | C3×C4 | D3×#41 | 1 | 2 | yes | — |
| 476 | Dic3 | — | 2 | 2 | no | — |
| 477 | Dic3 | — | 2 | 2 | no | — |
| 478 | Dic3 | — | 3 | 4 | no | — |
| 479 | Dic3 | — | 4 | 2 | no | — |
| 480 | Dic3 | — | 6 | 2 | no | — |
| 481 | Dic3 | — | 6 | 4 | no | — |
| 482 | Dic3 | — | 12 | 2 | no | — |
| 483 | Dic3 | — | 12 | 2 | no | — |
| 484 | Dic3 | — | 12 | 2 | no | — |
| 485 | C32 | C2×#464 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 486 | C23 | — | 6 | 2 | no | — |
| 487 | C23 | — | 9 | 1 | no | — |
| 488 | C23 | — | 36 | 2 | no | — |
| 489 | C23 | — | 36 | 2 | no | — |
| 490 | C23 | — | 36 | 2 | no | — |
| 491 | Q8 | — | 2 | 1 | no | — |
| 492 | Q8 | — | 2 | 1 | no | — |
| 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 | — | 36 | 2 | no | — |
| 500 | Q8 | #3811 | 1 | 2 | yes | — |
| 501 | D4 | — | 6 | 2 | no | — |
| 502 | D4 | — | 6 | 2 | no | — |
| 503 | D4 | — | 36 | 2 | no | — |
| 504 | C2×C4 | — | 2 | 1 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 3 | 2 | no | — |
| 507 | C2×C4 | — | 3 | 2 | no | — |
| 508 | C2×C4 | — | 6 | 2 | no | — |
| 509 | C2×C4 | — | 9 | 1 | no | — |
| 510 | C2×C4 | — | 9 | 2 | no | — |
| 511 | C2×C4 | — | 9 | 2 | no | — |
| 512 | C2×C4 | — | 18 | 4 | no | — |
| 513 | C2×C4 | — | 18 | 2 | no | — |
| 514 | C2×C4 | — | 18 | 2 | no | — |
| 515 | C2×C4 | — | 18 | 1 | no | — |
| 516 | C2×C4 | — | 18 | 1 | no | — |
| 517 | C2×C4 | — | 36 | 2 | no | — |
| 518 | C2×C4 | — | 36 | 2 | no | — |
| 519 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 520 | C8 | — | 2 | 1 | no | — |
| 521 | C8 | — | 6 | 2 | no | — |
| 522 | C8 | — | 18 | 1 | no | — |
| 523 | C2×C3 | — | 2 | 1 | no | — |
| 524 | C2×C3 | — | 2 | 1 | no | — |
| 525 | C2×C3 | — | 2 | 1 | no | — |
| 526 | C2×C3 | — | 24 | 2 | no | — |
| 527 | C2×C3 | D3×#121 | 1 | 2 | yes | — |
| 528 | C2×C3 | D3×#135 | 1 | 2 | yes | — |
| 529 | C2×C3 | D3×#137 | 1 | 2 | yes | — |
| 530 | D3 | — | 3 | 8 | no | — |
| 531 | D3 | — | 6 | 4 | no | — |
| 532 | D3 | — | 8 | 2 | no | — |
| 533 | C22 | — | 9 | 2 | no | — |
| 534 | C22 | — | 9 | 2 | no | — |
| 535 | C22 | — | 9 | 2 | no | — |
| 536 | C22 | — | 12 | 2 | no | — |
| 537 | C22 | — | 12 | 2 | no | — |
| 538 | C22 | — | 12 | 2 | no | — |
| 539 | C22 | — | 72 | 4 | no | — |
| 540 | C22 | D32×D4 | 1 | 1 | yes | characteristic |
| 541 | C4 | — | 2 | 2 | no | — |
| 542 | C4 | — | 4 | 1 | no | — |
| 543 | C4 | — | 6 | 2 | no | — |
| 544 | C4 | — | 6 | 2 | no | — |
| 545 | C4 | — | 9 | 2 | no | — |
| 546 | C4 | — | 12 | 2 | no | — |
| 547 | C4 | — | 18 | 2 | no | — |
| 548 | C4 | — | 36 | 1 | no | — |
| 549 | C4 | #64312 | 1 | 1 | yes | characteristic |
| 550 | C4 | C2×#3811 | 1 | 1 | yes | characteristic |
| 551 | C3 | — | 2 | 1 | no | — |
| 552 | C3 | D3×#464 | 1 | 2 | yes | complemented |
| 553 | C2 | — | 9 | 4 | no | — |
| 554 | C2 | — | 24 | 2 | no | — |
| 555 | C2 | #10594760 | 1 | 1 | yes | characteristic |
| 556 | C2 | #10594764 | 1 | 1 | yes | characteristic |
| 557 | C2 | #10595298 | 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. Q8×#624 | C2 | semidirect |
| 5. C3×#5185 | C2 | semidirect |
| 6. #10591604 | C2 | semidirect |
| 7. #10591577 | C2 | semidirect |
| 8. #10591552 | C2 | semidirect |
| 10. #10590861 | C2 | semidirect |
| 11. #10590658 | C2 | semidirect |
| 16. C2×C32×Q16 | C22 | semidirect |
| 17. C2×#3756 | C22 | semidirect |
| 18. C2×#3756 | C22 | semidirect |
| 20. C2×#3746 | C22 | semidirect |
| 23. C3×Q8×Dic3 | C22 | semidirect |
| 35. #63844 | C22 | semidirect |
| 38. C3×#835 | C22 | semidirect |
| 40. C3×Dic3⋊C8 | C22 | semidirect |
| 41. Dic3⋊(C3⋊C8) | C22 | semidirect |
| 42. #63567 | C22 | semidirect |
| 50. #5185 | D3 | semidirect |
| 111. C2×C3×Q16 | C2×D3 | semidirect |
| 116. Q8×Dic3 | C2×D3 | semidirect |
| 149. #835 | C2×D3 | semidirect |
| 154. Dic3⋊C8 | C2×D3 | semidirect |
| 310. C2×Q16 | D32 | semidirect |
| 404. C3⋊D3 | #464 | semidirect |
| 485. C32 | C2×#464 | semidirect |
| 552. C3 | D3×#464 | 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 |
| Q8×#624 | 2 |
| C2×#63940 | 2 |
| C3×#5185 | 2 |
| #10591604 | 2 |
| #10591577 | 2 |
| #10591552 | 2 |
| #10590940 | 2 |
| #10590861 | 2 |
| #10590658 | 2 |
| D3×#464 | 3 |