Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3107 conjugacy classes of subgroups.
The subgroup lattice has 409 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64316 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C4×#3832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×Q8×D12 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | Q8×#625 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10594530 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10594529 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10593972 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10593909 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10593869 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #86746 | — | 3 | 2 | no | maximal |
| 11 | C2×#3832 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×D3×Q8 | C22 | 1 | 4 | yes | — |
| 13 | #64316 | — | 2 | 16 | no | — |
| 14 | C2×#3799 | C22 | 1 | 12 | yes | — |
| 15 | C2×#3798 | C22 | 1 | 6 | yes | — |
| 16 | C2×#3797 | C22 | 1 | 6 | yes | — |
| 17 | C32×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64102 | C22 | 1 | 3 | yes | — |
| 20 | #64101 | C22 | 1 | 3 | yes | — |
| 21 | C4×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 22 | C42×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 23 | C3×#897 | C22 | 1 | 12 | yes | — |
| 24 | C3×C4×D12 | C22 | 1 | 6 | yes | — |
| 25 | C3×#869 | C22 | 1 | 6 | yes | — |
| 26 | #63919 | C22 | 1 | 3 | yes | — |
| 27 | #63919 | C22 | 1 | 6 | yes | — |
| 28 | #63916 | C22 | 1 | 6 | yes | — |
| 29 | #63915 | C22 | 1 | 6 | yes | — |
| 30 | #63914 | C22 | 1 | 1 | yes | characteristic |
| 31 | #63912 | C22 | 1 | 6 | yes | — |
| 32 | C4×#625 | C22 | 1 | 6 | yes | — |
| 33 | #63900 | C22 | 1 | 6 | yes | — |
| 34 | #63900 | C22 | 1 | 6 | yes | — |
| 35 | #63873 | C22 | 1 | 6 | yes | — |
| 36 | #63856 | C22 | 1 | 12 | yes | — |
| 37 | #63854 | C22 | 1 | 24 | yes | — |
| 38 | C2×#1007 | — | 3 | 4 | no | — |
| 39 | C3×D4×Q8 | — | 3 | 2 | no | — |
| 40 | Q8×#67 | — | 3 | 4 | no | — |
| 41 | #5726 | — | 3 | 6 | no | — |
| 42 | D3×C4⋊Q8 | — | 3 | 6 | no | — |
| 43 | #5631 | — | 3 | 12 | no | — |
| 44 | #5628 | — | 3 | 12 | no | — |
| 45 | Q8×D12 | D3 | 1 | 2 | yes | complemented |
| 46 | C4×#239 | — | 3 | 2 | no | — |
| 47 | C4×#239 | — | 6 | 1 | no | — |
| 48 | #5551 | — | 3 | 6 | no | — |
| 49 | #5548 | — | 3 | 6 | no | — |
| 50 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 51 | #3832 | D4 | 1 | 8 | yes | complemented |
| 52 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 53 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 54 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 55 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 56 | C3×D3×Q8 | — | 2 | 16 | no | — |
| 57 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 58 | C2×C3×C4×D3 | C23 | 1 | 12 | yes | — |
| 59 | C2×C3×Dic6 | C23 | 1 | 12 | yes | — |
| 60 | C2×#627 | C23 | 1 | 6 | yes | — |
| 61 | C2×#626 | C23 | 1 | 12 | yes | — |
| 62 | C2×#625 | C23 | 1 | 2 | yes | — |
| 63 | C2×#625 | C23 | 1 | 2 | yes | — |
| 64 | C2×#624 | C23 | 1 | 12 | yes | — |
| 65 | #3799 | — | 2 | 48 | no | — |
| 66 | #3798 | — | 2 | 24 | no | — |
| 67 | #3797 | — | 2 | 24 | no | — |
| 68 | C32×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 69 | C32×C42 | C23 | 1 | 3 | yes | — |
| 70 | #3752 | C23 | 1 | 6 | yes | — |
| 71 | C4⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 72 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 73 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 74 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 75 | C3×(C2×D3)⋊C4 | C23 | 1 | 12 | yes | — |
| 76 | C3×C4⋊Dic3 | C23 | 1 | 12 | yes | — |
| 77 | C3×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 78 | #3724 | C23 | 1 | 12 | yes | — |
| 79 | #3724 | C23 | 1 | 6 | yes | — |
| 80 | (C2×D3)⋊Dic3 | C23 | 1 | 12 | yes | — |
| 81 | #3499 | — | 9 | 1 | no | Sylow |
| 82 | C22×C3×Q8 | — | 3 | 4 | no | — |
| 83 | #1007 | — | 6 | 32 | no | — |
| 84 | C2×#239 | — | 3 | 2 | no | — |
| 85 | C2×#239 | — | 3 | 12 | no | — |
| 86 | C2×#239 | — | 6 | 1 | no | — |
| 87 | C2×D3×Q8 | — | 3 | 12 | no | — |
| 88 | C2×D3×Q8 | C2×D3 | 1 | 4 | yes | — |
| 89 | C2×#235 | — | 3 | 12 | no | — |
| 90 | C2×#235 | — | 3 | 12 | no | — |
| 91 | C3×C4⋊Q8 | — | 3 | 6 | no | — |
| 92 | C3×C22⋊Q8 | — | 3 | 12 | no | — |
| 93 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 94 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 95 | C3×C4×D4 | — | 3 | 6 | no | — |
| 96 | #946 | — | 3 | 12 | no | — |
| 97 | Q8×Dic3 | — | 3 | 2 | no | — |
| 98 | Q8×Dic3 | — | 6 | 1 | no | — |
| 99 | #944 | — | 3 | 12 | no | — |
| 100 | #940 | — | 3 | 2 | no | — |
| 101 | #938 | — | 3 | 6 | no | — |
| 102 | C4×#67 | — | 3 | 12 | no | — |
| 103 | #924 | — | 3 | 12 | no | — |
| 104 | #897 | C2×D3 | 1 | 12 | yes | — |
| 105 | #895 | — | 3 | 6 | no | — |
| 106 | #894 | — | 3 | 24 | no | — |
| 107 | #893 | — | 3 | 6 | no | — |
| 108 | #893 | — | 6 | 3 | no | — |
| 109 | #892 | — | 3 | 6 | no | — |
| 110 | #892 | — | 6 | 3 | no | — |
| 111 | D3×C4⋊C4 | — | 3 | 12 | no | — |
| 112 | D3×C4⋊C4 | — | 3 | 12 | no | — |
| 113 | #888 | — | 3 | 6 | no | — |
| 114 | #888 | — | 3 | 12 | no | — |
| 115 | #885 | — | 3 | 12 | no | — |
| 116 | #884 | — | 3 | 12 | no | — |
| 117 | #883 | — | 3 | 24 | no | — |
| 118 | C4×D12 | — | 3 | 6 | no | — |
| 119 | C4×D12 | — | 6 | 3 | no | — |
| 120 | C4×D12 | C2×D3 | 1 | 6 | yes | — |
| 121 | C42×D3 | — | 3 | 6 | no | — |
| 122 | C42×D3 | — | 6 | 3 | no | — |
| 123 | #869 | C2×D3 | 1 | 6 | yes | — |
| 124 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 125 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 126 | C32×Q8 | C2×D4 | 1 | 4 | yes | — |
| 127 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 128 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 129 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 130 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 131 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 132 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 133 | C4⋊(C3⋊D3) | C2×D4 | 1 | 12 | yes | — |
| 134 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 135 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 136 | C4×C3⋊D3 | C2×D4 | 1 | 12 | yes | — |
| 137 | C2×C3×Dic3 | C24 | 1 | 12 | yes | — |
| 138 | C3×D12 | — | 2 | 4 | no | — |
| 139 | C3×C4×D3 | — | 2 | 24 | no | — |
| 140 | C3×Dic6 | — | 2 | 24 | no | — |
| 141 | #627 | — | 2 | 12 | no | — |
| 142 | #626 | — | 2 | 24 | no | — |
| 143 | #625 | — | 2 | 4 | no | — |
| 144 | #625 | — | 2 | 4 | no | — |
| 145 | #624 | — | 2 | 24 | no | — |
| 146 | C2×2−1+4 | — | 9 | 2 | no | — |
| 147 | D4×Q8 | — | 3 | 2 | no | — |
| 148 | D4×Q8 | — | 9 | 2 | no | — |
| 149 | #547 | — | 9 | 6 | no | — |
| 150 | #547 | — | 9 | 6 | no | — |
| 151 | #536 | — | 9 | 6 | no | — |
| 152 | #532 | — | 9 | 3 | no | — |
| 153 | C2×C4⋊Q8 | — | 9 | 3 | no | — |
| 154 | C4×#41 | — | 9 | 1 | no | — |
| 155 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 156 | C2×C3×Q8 | — | 3 | 12 | no | — |
| 157 | C2×C3×Q8 | — | 6 | 16 | no | — |
| 158 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 159 | C2×C3×D4 | — | 3 | 2 | no | — |
| 160 | C22×C3×C4 | — | 3 | 12 | no | — |
| 161 | C2×#67 | — | 3 | 4 | no | — |
| 162 | C2×#67 | — | 3 | 4 | no | — |
| 163 | C2×#67 | — | 3 | 12 | no | — |
| 164 | #239 | — | 3 | 16 | no | — |
| 165 | #239 | — | 6 | 8 | no | — |
| 166 | #239 | — | 6 | 48 | no | — |
| 167 | D3×Q8 | — | 2 | 16 | no | — |
| 168 | D3×Q8 | — | 6 | 48 | no | — |
| 169 | #235 | — | 6 | 48 | no | — |
| 170 | #235 | — | 6 | 48 | no | — |
| 171 | C2×D12 | — | 3 | 6 | no | — |
| 172 | C2×D12 | — | 3 | 12 | no | — |
| 173 | C2×D12 | — | 6 | 3 | no | — |
| 174 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 175 | C2×C4×D3 | — | 3 | 6 | no | — |
| 176 | C2×C4×D3 | — | 3 | 6 | no | — |
| 177 | C2×C4×D3 | — | 3 | 6 | no | — |
| 178 | C2×C4×D3 | — | 3 | 24 | no | — |
| 179 | C2×C4×D3 | — | 6 | 3 | no | — |
| 180 | C2×C4×D3 | — | 6 | 3 | no | — |
| 181 | C2×C4×D3 | — | 6 | 3 | no | — |
| 182 | C2×C4×D3 | C22×D3 | 1 | 12 | yes | — |
| 183 | C2×Dic6 | — | 3 | 12 | no | — |
| 184 | C2×Dic6 | C22×D3 | 1 | 12 | yes | — |
| 185 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 186 | C3×C4⋊C4 | — | 3 | 6 | no | — |
| 187 | C3×C4⋊C4 | — | 3 | 12 | no | — |
| 188 | C3×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 189 | C3×C22⋊C4 | — | 3 | 12 | no | — |
| 190 | C3×C42 | — | 2 | 3 | no | — |
| 191 | C3×C42 | C22×D3 | 1 | 6 | yes | — |
| 192 | #217 | — | 3 | 12 | no | — |
| 193 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 194 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 195 | (C2×D3)⋊C4 | — | 6 | 6 | no | — |
| 196 | (C2×D3)⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 197 | C4⋊Dic3 | — | 3 | 6 | no | — |
| 198 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 199 | C4⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 200 | C4⋊Dic3 | C22×D3 | 1 | 12 | yes | — |
| 201 | Dic3⋊C4 | — | 3 | 24 | no | — |
| 202 | Dic3⋊C4 | — | 3 | 12 | no | — |
| 203 | C4×Dic3 | — | 3 | 2 | no | — |
| 204 | C4×Dic3 | — | 3 | 6 | no | — |
| 205 | C4×Dic3 | — | 3 | 6 | no | — |
| 206 | C4×Dic3 | — | 6 | 1 | no | — |
| 207 | C4×Dic3 | — | 6 | 3 | no | — |
| 208 | C4×Dic3 | — | 6 | 3 | no | — |
| 209 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 210 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 211 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 212 | C2×C3⋊D3 | C22×D4 | 1 | 6 | yes | — |
| 213 | C2×C3×D3 | — | 2 | 4 | no | — |
| 214 | C2×C3×D3 | — | 2 | 4 | no | — |
| 215 | C2×C3×D3 | — | 2 | 4 | no | — |
| 216 | C32×C4 | — | 2 | 3 | no | — |
| 217 | C32×C4 | C22×D4 | 1 | 6 | yes | — |
| 218 | C32×C4 | 2−1+4 | 1 | 2 | yes | complemented |
| 219 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 220 | C3⋊Dic3 | C22×D4 | 1 | 2 | yes | — |
| 221 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | complemented |
| 222 | C3×Dic3 | — | 2 | 12 | no | — |
| 223 | 2−1+4 | — | 18 | 16 | no | — |
| 224 | C2×#41 | — | 9 | 6 | no | — |
| 225 | C2×#41 | — | 9 | 12 | no | — |
| 226 | C2×#41 | — | 9 | 1 | no | — |
| 227 | C22×Q8 | — | 3 | 4 | no | — |
| 228 | C22×Q8 | — | 9 | 6 | no | — |
| 229 | C4⋊Q8 | — | 3 | 6 | no | — |
| 230 | C4⋊Q8 | — | 9 | 3 | no | — |
| 231 | C4⋊Q8 | — | 9 | 6 | no | — |
| 232 | C4⋊Q8 | — | 9 | 6 | no | — |
| 233 | #127 | — | 9 | 1 | no | — |
| 234 | #124 | — | 9 | 6 | no | — |
| 235 | #123 | — | 9 | 24 | no | — |
| 236 | C22⋊Q8 | — | 3 | 12 | no | — |
| 237 | C22⋊Q8 | — | 9 | 12 | no | — |
| 238 | #121 | — | 9 | 6 | no | — |
| 239 | #121 | — | 9 | 6 | no | — |
| 240 | C4×Q8 | — | 9 | 1 | no | — |
| 241 | C4×Q8 | D32 | 1 | 1 | yes | characteristic |
| 242 | C4×D4 | — | 3 | 6 | no | — |
| 243 | C4×D4 | — | 9 | 6 | no | — |
| 244 | C4×D4 | — | 9 | 3 | no | — |
| 245 | C4×D4 | — | 9 | 3 | no | — |
| 246 | #117 | — | 9 | 3 | no | — |
| 247 | C2×C4⋊C4 | — | 9 | 6 | no | — |
| 248 | C2×C4⋊C4 | — | 9 | 6 | no | — |
| 249 | C2×C42 | — | 9 | 3 | no | — |
| 250 | C23×C3 | — | 3 | 4 | no | — |
| 251 | C22×D3 | — | 3 | 6 | no | — |
| 252 | C22×D3 | — | 6 | 3 | no | — |
| 253 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 254 | C3×Q8 | — | 2 | 4 | no | — |
| 255 | C3×Q8 | — | 6 | 24 | no | — |
| 256 | C3×Q8 | D3×D4 | 1 | 8 | yes | — |
| 257 | C3×D4 | — | 6 | 4 | no | — |
| 258 | C2×C3×C4 | — | 2 | 3 | no | — |
| 259 | C2×C3×C4 | — | 2 | 1 | no | — |
| 260 | C2×C3×C4 | — | 2 | 3 | no | — |
| 261 | C2×C3×C4 | — | 3 | 12 | no | — |
| 262 | C2×C3×C4 | — | 6 | 24 | no | — |
| 263 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 264 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 265 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 266 | #67 | — | 6 | 24 | no | — |
| 267 | #67 | — | 6 | 8 | no | — |
| 268 | #67 | — | 6 | 8 | no | — |
| 269 | C2×Dic3 | — | 3 | 2 | no | — |
| 270 | C2×Dic3 | — | 3 | 2 | no | — |
| 271 | C2×Dic3 | — | 3 | 6 | no | — |
| 272 | C2×Dic3 | — | 6 | 1 | no | — |
| 273 | C2×Dic3 | — | 6 | 1 | no | — |
| 274 | C2×Dic3 | — | 6 | 3 | no | — |
| 275 | C2×Dic3 | C23×D3 | 1 | 12 | yes | — |
| 276 | D12 | — | 2 | 4 | no | — |
| 277 | D12 | — | 3 | 24 | no | — |
| 278 | D12 | — | 6 | 12 | no | — |
| 279 | D12 | — | 6 | 24 | no | — |
| 280 | C4×D3 | — | 2 | 24 | no | — |
| 281 | C4×D3 | — | 3 | 24 | no | — |
| 282 | C4×D3 | — | 6 | 12 | no | — |
| 283 | C4×D3 | — | 6 | 48 | no | — |
| 284 | C4×D3 | — | 6 | 12 | no | — |
| 285 | C4×D3 | — | 6 | 12 | no | — |
| 286 | C4×D3 | — | 12 | 6 | no | — |
| 287 | C4×D3 | — | 12 | 6 | no | — |
| 288 | Dic6 | — | 2 | 24 | no | — |
| 289 | Dic6 | — | 6 | 24 | no | — |
| 290 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 292 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 293 | C3⋊D3 | — | 2 | 6 | no | — |
| 294 | C3×D3 | — | 4 | 4 | no | — |
| 295 | #41 | — | 9 | 8 | no | — |
| 296 | #41 | — | 18 | 24 | no | — |
| 297 | #41 | — | 18 | 48 | no | — |
| 298 | C2×Q8 | — | 3 | 12 | no | — |
| 299 | C2×Q8 | — | 6 | 16 | no | — |
| 300 | C2×Q8 | — | 9 | 6 | no | — |
| 301 | C2×Q8 | — | 18 | 24 | no | — |
| 302 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 303 | C2×D4 | — | 3 | 2 | no | — |
| 304 | C2×D4 | — | 9 | 12 | no | — |
| 305 | C2×D4 | — | 9 | 2 | no | — |
| 306 | C2×D4 | — | 9 | 2 | no | — |
| 307 | C2×D4 | — | 9 | 3 | no | — |
| 308 | C22×C4 | — | 3 | 12 | no | — |
| 309 | C22×C4 | — | 9 | 12 | no | — |
| 310 | C22×C4 | — | 9 | 3 | no | — |
| 311 | C22×C4 | — | 9 | 3 | no | — |
| 312 | C22×C4 | — | 9 | 3 | no | — |
| 313 | C4⋊C4 | — | 3 | 6 | no | — |
| 314 | C4⋊C4 | — | 3 | 12 | no | — |
| 315 | C4⋊C4 | — | 9 | 6 | no | — |
| 316 | C4⋊C4 | — | 9 | 12 | no | — |
| 317 | C4⋊C4 | — | 9 | 3 | no | — |
| 318 | C4⋊C4 | C2×D32 | 1 | 3 | yes | — |
| 319 | C22⋊C4 | — | 3 | 12 | no | — |
| 320 | C22⋊C4 | — | 9 | 12 | no | — |
| 321 | C22⋊C4 | — | 9 | 6 | no | — |
| 322 | C42 | — | 9 | 1 | no | — |
| 323 | C42 | — | 9 | 3 | no | — |
| 324 | C42 | — | 9 | 3 | no | — |
| 325 | C42 | C2×D32 | 1 | 3 | yes | — |
| 326 | C22×C3 | — | 2 | 1 | no | — |
| 327 | C22×C3 | — | 6 | 4 | no | — |
| 328 | C22×C3 | — | 6 | 4 | no | — |
| 329 | C22×C3 | — | 6 | 4 | no | — |
| 330 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 331 | C2×D3 | — | 2 | 4 | no | — |
| 332 | C2×D3 | — | 2 | 4 | no | — |
| 333 | C2×D3 | — | 2 | 4 | no | — |
| 334 | C2×D3 | — | 3 | 12 | no | — |
| 335 | C2×D3 | — | 6 | 6 | no | — |
| 336 | C2×D3 | — | 6 | 6 | no | — |
| 337 | C2×D3 | — | 6 | 6 | no | — |
| 338 | C2×D3 | — | 12 | 3 | no | — |
| 339 | C2×D3 | — | 12 | 3 | no | — |
| 340 | C3×C4 | — | 2 | 6 | no | — |
| 341 | C3×C4 | — | 2 | 6 | no | — |
| 342 | C3×C4 | — | 2 | 2 | no | — |
| 343 | C3×C4 | — | 4 | 3 | no | — |
| 344 | C3×C4 | — | 6 | 12 | no | — |
| 345 | C3×C4 | C2×D3×D4 | 1 | 12 | yes | — |
| 346 | C3×C4 | #1007 | 1 | 4 | yes | complemented |
| 347 | Dic3 | — | 2 | 12 | no | — |
| 348 | Dic3 | — | 3 | 4 | no | — |
| 349 | Dic3 | — | 3 | 4 | no | — |
| 350 | Dic3 | — | 6 | 2 | no | — |
| 351 | Dic3 | — | 6 | 2 | no | — |
| 352 | Dic3 | — | 6 | 6 | no | — |
| 353 | Dic3 | — | 12 | 3 | no | — |
| 354 | C32 | #3499 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | C23 | — | 3 | 4 | no | — |
| 356 | C23 | — | 9 | 3 | no | — |
| 357 | Q8 | — | 6 | 24 | no | — |
| 358 | Q8 | — | 18 | 12 | no | — |
| 359 | Q8 | #3802 | 1 | 4 | yes | — |
| 360 | D4 | — | 6 | 4 | no | — |
| 361 | D4 | — | 9 | 12 | no | — |
| 362 | D4 | — | 18 | 24 | no | — |
| 363 | D4 | — | 18 | 4 | no | — |
| 364 | D4 | — | 18 | 4 | no | — |
| 365 | C2×C4 | — | 3 | 12 | no | — |
| 366 | C2×C4 | — | 6 | 24 | no | — |
| 367 | C2×C4 | — | 9 | 1 | no | — |
| 368 | C2×C4 | — | 9 | 1 | no | — |
| 369 | C2×C4 | — | 9 | 12 | no | — |
| 370 | C2×C4 | — | 9 | 3 | no | — |
| 371 | C2×C4 | — | 18 | 6 | no | — |
| 372 | C2×C4 | — | 18 | 24 | no | — |
| 373 | C2×C4 | — | 18 | 6 | no | — |
| 374 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 375 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 376 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 377 | C2×C3 | — | 2 | 1 | no | — |
| 378 | C2×C3 | — | 2 | 1 | no | — |
| 379 | C2×C3 | — | 2 | 1 | no | — |
| 380 | C2×C3 | — | 12 | 4 | no | — |
| 381 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 382 | C2×C3 | C2×#1007 | 1 | 2 | yes | — |
| 383 | C2×C3 | D3×2−1+4 | 1 | 2 | yes | — |
| 384 | D3 | — | 4 | 4 | no | — |
| 385 | D3 | — | 6 | 12 | no | — |
| 386 | D3 | — | 12 | 6 | no | — |
| 387 | C22 | — | 6 | 4 | no | — |
| 388 | C22 | — | 6 | 4 | no | — |
| 389 | C22 | — | 6 | 4 | no | — |
| 390 | C22 | — | 9 | 6 | no | — |
| 391 | C22 | — | 18 | 3 | no | — |
| 392 | C22 | — | 18 | 3 | no | — |
| 393 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 394 | C4 | — | 2 | 3 | no | — |
| 395 | C4 | — | 6 | 12 | no | — |
| 396 | C4 | — | 9 | 2 | no | — |
| 397 | C4 | — | 9 | 2 | no | — |
| 398 | C4 | — | 18 | 3 | no | — |
| 399 | C4 | C2×#3802 | 1 | 6 | yes | — |
| 400 | C4 | #64316 | 1 | 2 | yes | complemented |
| 401 | C3 | — | 2 | 1 | no | — |
| 402 | C3 | #86746 | 1 | 2 | yes | complemented |
| 403 | C2 | — | 12 | 4 | no | — |
| 404 | C2 | — | 18 | 6 | no | — |
| 405 | C2 | C22×#3802 | 1 | 1 | yes | characteristic |
| 406 | C2 | C2×#64316 | 1 | 1 | yes | characteristic |
| 407 | C2 | #10596694 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C4×Q8 | C22 |
| hypercenter | C4×Q8 | D32 |
| hypocenter | C32 | #3499 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64316 | C2 | semidirect |
| 2. C4×#3832 | C2 | semidirect |
| 3. C3×Q8×D12 | C2 | semidirect |
| 4. Q8×#625 | C2 | semidirect |
| 5. #10594530 | C2 | semidirect |
| 6. #10594529 | C2 | semidirect |
| 7. #10593972 | C2 | semidirect |
| 8. #10593909 | C2 | semidirect |
| 9. #10593869 | C2 | semidirect |
| 45. Q8×D12 | D3 | semidirect |
| 51. #3832 | D4 | semidirect |
| 218. C32×C4 | 2−1+4 | semidirect |
| 221. C3⋊Dic3 | 2−1+4 | semidirect |
| 346. C3×C4 | #1007 | semidirect |
| 354. C32 | #3499 | semidirect |
| 400. C4 | #64316 | semidirect |
| 402. C3 | #86746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64316 | 2 |
| C4×#3832 | 2 |
| C3×Q8×D12 | 2 |
| Q8×#625 | 2 |
| #10594530 | 2 |
| #10594529 | 2 |
| #10593972 | 2 |
| #10593909 | 2 |
| #10593869 | 2 |
| #86746 | 3 |