Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
658 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×A4×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5912 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5417 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#5415 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#5414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C3×A4⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85514 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 9 | C3×#3002 | — | 3 | 1 | no | maximal |
| 10 | C3×Q8×A4 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×D4×A4 | — | 2 | 1 | no | — |
| 12 | C3×D4×A4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×C4×A4 | — | 2 | 1 | no | — |
| 14 | C2×C3×C4×A4 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×GL(2,ℤ/4) | — | 2 | 1 | no | — |
| 16 | C3×C4⋊S4 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×C4×S4 | — | 2 | 1 | no | — |
| 18 | C3×A4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#950 | — | 4 | 1 | no | maximal |
| 20 | C3×A4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×A4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×C3×#41 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | A4×#41 | — | 2 | 1 | no | — |
| 24 | A4×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #5912 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C3×#135 | — | 3 | 1 | no | — |
| 27 | C2×C3×#135 | — | 3 | 1 | no | — |
| 28 | C3×#525 | — | 3 | 1 | no | — |
| 29 | #5417 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5416 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5415 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5414 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×A4⋊C8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×#452 | — | 3 | 1 | no | — |
| 35 | C3×#452 | — | 3 | 1 | no | — |
| 36 | C3×#451 | — | 3 | 1 | no | — |
| 37 | C3×#450 | — | 3 | 1 | no | — |
| 38 | C3×#449 | — | 3 | 1 | no | — |
| 39 | C3×#449 | — | 3 | 1 | no | — |
| 40 | C3×#448 | — | 3 | 1 | no | — |
| 41 | C3×#447 | — | 3 | 1 | no | — |
| 42 | C3×#416 | — | 3 | 1 | no | — |
| 43 | C3×#416 | — | 3 | 1 | no | — |
| 44 | C2×C3×C22⋊C8 | — | 3 | 1 | no | — |
| 45 | C22×C3×A4 | — | 2 | 1 | no | — |
| 46 | C22×C3×A4 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C3×S4 | — | 2 | 1 | no | — |
| 48 | C32×#41 | — | 4 | 1 | no | — |
| 49 | C3×#235 | — | 4 | 1 | no | — |
| 50 | C3×C4×A4 | — | 2 | 1 | no | — |
| 51 | C3×C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 52 | C3×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 53 | C3×SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 54 | C3×#216 | — | 4 | 1 | no | — |
| 55 | C3×#215 | — | 4 | 1 | no | — |
| 56 | C3×#214 | — | 4 | 1 | no | — |
| 57 | C3×#213 | — | 4 | 1 | no | — |
| 58 | C2×C3×C3⋊C8 | — | 4 | 1 | no | — |
| 59 | #3002 | — | 3 | 1 | no | Sylow |
| 60 | C2×C3×#41 | — | 3 | 1 | no | — |
| 61 | C2×C3×#41 | — | 3 | 1 | no | — |
| 62 | C2×C3×#41 | — | 3 | 1 | no | — |
| 63 | C2×C3×#41 | — | 3 | 1 | no | — |
| 64 | C2×C3×#41 | — | 3 | 1 | no | — |
| 65 | C2×C3×#41 | — | 6 | 1 | no | — |
| 66 | C2×C3×#41 | — | 6 | 1 | no | — |
| 67 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | C22×C3×D4 | — | 2 | 1 | no | — |
| 69 | C22×C3×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 70 | C23×C3×C4 | — | 2 | 1 | no | — |
| 71 | C23×C3×C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | Q8×A4 | — | 2 | 1 | no | — |
| 73 | Q8×A4 | C22×C3 | 1 | 1 | yes | characteristic |
| 74 | D4×A4 | — | 2 | 2 | no | — |
| 75 | D4×A4 | — | 2 | 1 | no | — |
| 76 | D4×A4 | — | 2 | 1 | no | — |
| 77 | D4×A4 | C22×C3 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×A4 | — | 2 | 2 | no | — |
| 79 | C2×C4×A4 | — | 2 | 1 | no | — |
| 80 | C2×C4×A4 | — | 2 | 1 | no | — |
| 81 | C2×C4×A4 | C22×C3 | 1 | 1 | yes | characteristic |
| 82 | GL(2,ℤ/4) | — | 2 | 1 | no | — |
| 83 | C4⋊S4 | C22×C3 | 1 | 1 | yes | characteristic |
| 84 | C4×S4 | — | 2 | 1 | no | — |
| 85 | A4⋊Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 86 | C3×#135 | — | 6 | 2 | no | — |
| 87 | C3×#135 | — | 6 | 2 | no | — |
| 88 | C3×#135 | — | 6 | 1 | no | — |
| 89 | C3×#135 | — | 6 | 1 | no | — |
| 90 | C3×#135 | — | 6 | 1 | no | — |
| 91 | C3×#135 | — | 6 | 1 | no | — |
| 92 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 93 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 94 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 95 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 96 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 97 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 98 | C2×C3×D8 | — | 3 | 1 | no | — |
| 99 | C2×C3×D8 | — | 3 | 1 | no | — |
| 100 | C22×C3×C8 | — | 3 | 1 | no | — |
| 101 | C22×C3×C8 | — | 3 | 1 | no | — |
| 102 | C3×#123 | — | 6 | 1 | no | — |
| 103 | C3×C22⋊Q8 | — | 3 | 1 | no | — |
| 104 | C3×C22⋊Q8 | — | 3 | 1 | no | — |
| 105 | C3×#121 | — | 3 | 1 | no | — |
| 106 | C3×#121 | — | 3 | 1 | no | — |
| 107 | C3×#120 | — | 6 | 1 | no | — |
| 108 | C3×C4×D4 | — | 6 | 1 | no | — |
| 109 | C3×C4×D4 | — | 6 | 1 | no | — |
| 110 | C3×#117 | — | 3 | 1 | no | — |
| 111 | #950 | — | 4 | 1 | no | — |
| 112 | A4⋊C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 113 | A4⋊C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 114 | C3×#103 | — | 3 | 1 | no | — |
| 115 | C3×#103 | — | 3 | 1 | no | — |
| 116 | C3×#103 | — | 3 | 1 | no | — |
| 117 | C3×#103 | — | 3 | 1 | no | — |
| 118 | C3×#102 | — | 3 | 1 | no | — |
| 119 | C3×#102 | — | 3 | 1 | no | — |
| 120 | C3×#102 | — | 3 | 1 | no | — |
| 121 | C3×#102 | — | 3 | 1 | no | — |
| 122 | C3×C22⋊C8 | — | 3 | 1 | no | — |
| 123 | C3×C22⋊C8 | — | 3 | 1 | no | — |
| 124 | C3×C22⋊C8 | — | 3 | 1 | no | — |
| 125 | C3×C22⋊C8 | — | 3 | 1 | no | — |
| 126 | C2×C3×A4 | — | 2 | 1 | no | — |
| 127 | C2×C3×A4 | — | 4 | 1 | no | — |
| 128 | C2×C3×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C3×S4 | — | 4 | 1 | no | — |
| 130 | C32×Q8 | — | 4 | 1 | no | — |
| 131 | C32×D4 | — | 4 | 1 | no | — |
| 132 | C32×D4 | — | 8 | 1 | no | — |
| 133 | C2×C32×C4 | — | 4 | 1 | no | — |
| 134 | C2×C32×C4 | — | 8 | 1 | no | — |
| 135 | C3×#67 | — | 8 | 1 | no | — |
| 136 | C3×D12 | — | 4 | 1 | no | — |
| 137 | C3×C4×D3 | — | 8 | 1 | no | — |
| 138 | C3×Dic6 | — | 4 | 1 | no | — |
| 139 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 140 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 141 | C22×#41 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 142 | C2×#135 | — | 3 | 1 | no | — |
| 143 | C2×#135 | — | 3 | 1 | no | — |
| 144 | #525 | — | 3 | 1 | no | — |
| 145 | #452 | — | 3 | 1 | no | — |
| 146 | #452 | — | 3 | 1 | no | — |
| 147 | #451 | — | 3 | 1 | no | — |
| 148 | #450 | — | 3 | 1 | no | — |
| 149 | #449 | — | 3 | 1 | no | — |
| 150 | #449 | — | 3 | 1 | no | — |
| 151 | #448 | — | 3 | 1 | no | — |
| 152 | #447 | — | 3 | 1 | no | — |
| 153 | #416 | — | 3 | 1 | no | — |
| 154 | #416 | — | 3 | 1 | no | — |
| 155 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 156 | C24×C3 | — | 2 | 1 | no | — |
| 157 | C24×C3 | #67 | 1 | 1 | yes | characteristic |
| 158 | C22×A4 | — | 2 | 2 | no | — |
| 159 | C22×A4 | — | 2 | 1 | no | — |
| 160 | C22×A4 | — | 2 | 1 | no | — |
| 161 | C22×A4 | C3×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×S4 | — | 2 | 1 | no | — |
| 163 | C3×#41 | — | 3 | 2 | no | — |
| 164 | C3×#41 | — | 3 | 2 | no | — |
| 165 | C3×#41 | — | 3 | 1 | no | — |
| 166 | C3×#41 | — | 3 | 1 | no | — |
| 167 | C3×#41 | — | 3 | 1 | no | — |
| 168 | C3×#41 | — | 4 | 1 | no | — |
| 169 | C3×#41 | — | 6 | 1 | no | — |
| 170 | C3×#41 | — | 6 | 1 | no | — |
| 171 | C3×#41 | — | 6 | 1 | no | — |
| 172 | C3×#41 | — | 6 | 1 | no | — |
| 173 | C3×#41 | — | 6 | 1 | no | — |
| 174 | C3×#41 | — | 6 | 1 | no | — |
| 175 | C3×#41 | — | 6 | 2 | no | — |
| 176 | C3×#41 | — | 6 | 2 | no | — |
| 177 | C3×#41 | — | 6 | 1 | no | — |
| 178 | C3×#41 | — | 8 | 1 | no | — |
| 179 | C3×#41 | S4 | 1 | 1 | yes | characteristic, complemented |
| 180 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 181 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 182 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 183 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 184 | C2×C3×D4 | — | 3 | 1 | no | — |
| 185 | C2×C3×D4 | — | 3 | 1 | no | — |
| 186 | C2×C3×D4 | — | 3 | 1 | no | — |
| 187 | C2×C3×D4 | — | 6 | 1 | no | — |
| 188 | C2×C3×D4 | — | 6 | 1 | no | — |
| 189 | C2×C3×D4 | — | 6 | 1 | no | — |
| 190 | C2×C3×D4 | — | 6 | 1 | no | — |
| 191 | C2×C3×D4 | — | 6 | 1 | no | — |
| 192 | C2×C3×D4 | — | 6 | 1 | no | — |
| 193 | C2×C3×D4 | — | 6 | 1 | no | — |
| 194 | C2×C3×D4 | — | 6 | 1 | no | — |
| 195 | C22×C3×C4 | — | 2 | 1 | no | — |
| 196 | C22×C3×C4 | — | 3 | 1 | no | — |
| 197 | C22×C3×C4 | — | 3 | 1 | no | — |
| 198 | C22×C3×C4 | — | 3 | 1 | no | — |
| 199 | C22×C3×C4 | — | 3 | 1 | no | — |
| 200 | C22×C3×C4 | — | 6 | 1 | no | — |
| 201 | C22×C3×C4 | — | 6 | 1 | no | — |
| 202 | C22×C3×C4 | — | 6 | 1 | no | — |
| 203 | C22×C3×C4 | — | 6 | 1 | no | — |
| 204 | C22×C3×C4 | — | 6 | 1 | no | — |
| 205 | C22×C3×C4 | #67 | 1 | 1 | yes | characteristic |
| 206 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 207 | #235 | — | 4 | 1 | no | — |
| 208 | C4×A4 | — | 2 | 2 | no | — |
| 209 | C4×A4 | — | 2 | 1 | no | — |
| 210 | C4×A4 | — | 2 | 1 | no | — |
| 211 | C4×A4 | — | 2 | 1 | no | — |
| 212 | C4×A4 | C3×D4 | 1 | 1 | yes | characteristic |
| 213 | C4×A4 | C23×C3 | 1 | 1 | yes | characteristic |
| 214 | SL(2,ℤ/4) | — | 2 | 1 | no | — |
| 215 | C3×Q16 | — | 6 | 2 | no | — |
| 216 | C3×Q16 | — | 6 | 1 | no | — |
| 217 | C3×Q16 | — | 6 | 1 | no | — |
| 218 | C3×SD16 | — | 6 | 2 | no | — |
| 219 | C3×SD16 | — | 6 | 1 | no | — |
| 220 | C3×SD16 | — | 6 | 2 | no | — |
| 221 | C3×SD16 | — | 6 | 1 | no | — |
| 222 | C3×SD16 | — | 6 | 1 | no | — |
| 223 | C3×SD16 | — | 6 | 1 | no | — |
| 224 | C3×D8 | — | 6 | 2 | no | — |
| 225 | C3×D8 | — | 6 | 1 | no | — |
| 226 | C3×D8 | — | 6 | 1 | no | — |
| 227 | C2×C3×C8 | — | 3 | 1 | no | — |
| 228 | C2×C3×C8 | — | 3 | 1 | no | — |
| 229 | C2×C3×C8 | — | 3 | 1 | no | — |
| 230 | C2×C3×C8 | — | 3 | 1 | no | — |
| 231 | C2×C3×C8 | — | 6 | 1 | no | — |
| 232 | C2×C3×C8 | — | 6 | 1 | no | — |
| 233 | C2×C3×C8 | — | 6 | 1 | no | — |
| 234 | C2×C3×C8 | — | 6 | 1 | no | — |
| 235 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 236 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 237 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 238 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 239 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 240 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 241 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 242 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 243 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 244 | C3×C42 | — | 6 | 1 | no | — |
| 245 | #216 | — | 4 | 1 | no | — |
| 246 | #215 | — | 4 | 1 | no | — |
| 247 | #214 | — | 4 | 1 | no | — |
| 248 | #213 | — | 4 | 1 | no | — |
| 249 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 250 | C22×C32 | — | 4 | 1 | no | — |
| 251 | C22×C32 | — | 8 | 1 | no | — |
| 252 | C2×C3×D3 | — | 8 | 1 | no | — |
| 253 | C3×A4 | #135 | 1 | 1 | yes | characteristic, complemented |
| 254 | C32×C4 | — | 4 | 1 | no | — |
| 255 | C32×C4 | — | 4 | 1 | no | — |
| 256 | C32×C4 | — | 8 | 1 | no | — |
| 257 | C3×Dic3 | — | 8 | 1 | no | — |
| 258 | C2×#41 | — | 3 | 1 | no | — |
| 259 | C2×#41 | — | 3 | 1 | no | — |
| 260 | C2×#41 | — | 3 | 1 | no | — |
| 261 | C2×#41 | — | 3 | 1 | no | — |
| 262 | C2×#41 | — | 3 | 1 | no | — |
| 263 | C2×#41 | — | 6 | 1 | no | — |
| 264 | C2×#41 | — | 6 | 1 | no | — |
| 265 | C22×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 266 | C22×D4 | — | 2 | 1 | no | — |
| 267 | C22×D4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 268 | C23×C4 | — | 2 | 1 | no | — |
| 269 | C23×C4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 270 | #135 | — | 6 | 2 | no | — |
| 271 | #135 | — | 6 | 2 | no | — |
| 272 | #135 | — | 6 | 1 | no | — |
| 273 | #135 | — | 6 | 1 | no | — |
| 274 | #135 | — | 6 | 1 | no | — |
| 275 | #135 | — | 6 | 1 | no | — |
| 276 | C2×Q16 | — | 3 | 1 | no | — |
| 277 | C2×Q16 | — | 3 | 1 | no | — |
| 278 | C2×SD16 | — | 3 | 1 | no | — |
| 279 | C2×SD16 | — | 3 | 1 | no | — |
| 280 | C2×SD16 | — | 3 | 1 | no | — |
| 281 | C2×SD16 | — | 3 | 1 | no | — |
| 282 | C2×D8 | — | 3 | 1 | no | — |
| 283 | C2×D8 | — | 3 | 1 | no | — |
| 284 | C22×C8 | — | 3 | 1 | no | — |
| 285 | C22×C8 | — | 3 | 1 | no | — |
| 286 | #123 | — | 6 | 1 | no | — |
| 287 | C22⋊Q8 | — | 3 | 1 | no | — |
| 288 | C22⋊Q8 | — | 3 | 1 | no | — |
| 289 | #121 | — | 3 | 1 | no | — |
| 290 | #121 | — | 3 | 1 | no | — |
| 291 | #120 | — | 6 | 1 | no | — |
| 292 | C4×D4 | — | 6 | 1 | no | — |
| 293 | C4×D4 | — | 6 | 1 | no | — |
| 294 | #117 | — | 3 | 1 | no | — |
| 295 | #103 | — | 3 | 1 | no | — |
| 296 | #103 | — | 3 | 1 | no | — |
| 297 | #103 | — | 3 | 1 | no | — |
| 298 | #103 | — | 3 | 1 | no | — |
| 299 | #102 | — | 3 | 1 | no | — |
| 300 | #102 | — | 3 | 1 | no | — |
| 301 | #102 | — | 3 | 1 | no | — |
| 302 | #102 | — | 3 | 1 | no | — |
| 303 | C22⋊C8 | — | 3 | 1 | no | — |
| 304 | C22⋊C8 | — | 3 | 1 | no | — |
| 305 | C22⋊C8 | — | 3 | 1 | no | — |
| 306 | C22⋊C8 | — | 3 | 1 | no | — |
| 307 | C23×C3 | — | 2 | 1 | no | — |
| 308 | C23×C3 | — | 3 | 1 | no | — |
| 309 | C23×C3 | — | 3 | 1 | no | — |
| 310 | C23×C3 | — | 4 | 1 | no | — |
| 311 | C23×C3 | — | 6 | 1 | no | — |
| 312 | C23×C3 | — | 6 | 1 | no | — |
| 313 | C23×C3 | — | 6 | 1 | no | — |
| 314 | C23×C3 | — | 6 | 1 | no | — |
| 315 | C23×C3 | — | 12 | 1 | no | — |
| 316 | C23×C3 | C2×#67 | 1 | 1 | yes | characteristic |
| 317 | C2×A4 | — | 2 | 1 | no | — |
| 318 | C2×A4 | — | 2 | 1 | no | — |
| 319 | C2×A4 | — | 4 | 1 | no | — |
| 320 | C2×A4 | — | 4 | 2 | no | — |
| 321 | C2×A4 | — | 4 | 1 | no | — |
| 322 | C2×A4 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 323 | S4 | — | 4 | 1 | no | — |
| 324 | C3×Q8 | — | 3 | 2 | no | — |
| 325 | C3×Q8 | — | 3 | 1 | no | — |
| 326 | C3×Q8 | — | 4 | 1 | no | — |
| 327 | C3×Q8 | — | 6 | 1 | no | — |
| 328 | C3×Q8 | — | 6 | 1 | no | — |
| 329 | C3×Q8 | — | 6 | 1 | no | — |
| 330 | C3×Q8 | — | 8 | 1 | no | — |
| 331 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 332 | C3×D4 | — | 2 | 1 | no | — |
| 333 | C3×D4 | — | 3 | 2 | no | — |
| 334 | C3×D4 | — | 3 | 1 | no | — |
| 335 | C3×D4 | — | 4 | 1 | no | — |
| 336 | C3×D4 | — | 6 | 1 | no | — |
| 337 | C3×D4 | — | 6 | 1 | no | — |
| 338 | C3×D4 | — | 6 | 1 | no | — |
| 339 | C3×D4 | — | 6 | 1 | no | — |
| 340 | C3×D4 | — | 6 | 2 | no | — |
| 341 | C3×D4 | — | 6 | 1 | no | — |
| 342 | C3×D4 | — | 6 | 1 | no | — |
| 343 | C3×D4 | — | 8 | 1 | no | — |
| 344 | C3×D4 | — | 8 | 2 | no | — |
| 345 | C3×D4 | — | 8 | 1 | no | — |
| 346 | C3×D4 | — | 12 | 1 | no | — |
| 347 | C3×D4 | — | 12 | 1 | no | — |
| 348 | C3×D4 | — | 12 | 2 | no | — |
| 349 | C3×D4 | — | 12 | 1 | no | — |
| 350 | C3×D4 | — | 12 | 1 | no | — |
| 351 | C3×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 352 | C2×C3×C4 | — | 2 | 1 | no | — |
| 353 | C2×C3×C4 | — | 3 | 1 | no | — |
| 354 | C2×C3×C4 | — | 3 | 1 | no | — |
| 355 | C2×C3×C4 | — | 3 | 1 | no | — |
| 356 | C2×C3×C4 | — | 3 | 1 | no | — |
| 357 | C2×C3×C4 | — | 3 | 1 | no | — |
| 358 | C2×C3×C4 | — | 3 | 1 | no | — |
| 359 | C2×C3×C4 | — | 3 | 1 | no | — |
| 360 | C2×C3×C4 | — | 4 | 1 | no | — |
| 361 | C2×C3×C4 | — | 6 | 1 | no | — |
| 362 | C2×C3×C4 | — | 6 | 1 | no | — |
| 363 | C2×C3×C4 | — | 6 | 1 | no | — |
| 364 | C2×C3×C4 | — | 6 | 1 | no | — |
| 365 | C2×C3×C4 | — | 6 | 2 | no | — |
| 366 | C2×C3×C4 | — | 6 | 1 | no | — |
| 367 | C2×C3×C4 | — | 6 | 1 | no | — |
| 368 | C2×C3×C4 | — | 6 | 1 | no | — |
| 369 | C2×C3×C4 | — | 6 | 1 | no | — |
| 370 | C2×C3×C4 | — | 6 | 1 | no | — |
| 371 | C2×C3×C4 | — | 8 | 1 | no | — |
| 372 | C2×C3×C4 | — | 8 | 2 | no | — |
| 373 | C2×C3×C4 | — | 8 | 1 | no | — |
| 374 | C2×C3×C4 | — | 12 | 1 | no | — |
| 375 | C2×C3×C4 | — | 12 | 1 | no | — |
| 376 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 377 | #67 | — | 8 | 1 | no | — |
| 378 | D12 | — | 4 | 1 | no | — |
| 379 | C4×D3 | — | 8 | 1 | no | — |
| 380 | Dic6 | — | 4 | 1 | no | — |
| 381 | C3×C8 | — | 6 | 1 | no | — |
| 382 | C3×C8 | — | 6 | 1 | no | — |
| 383 | C3×C8 | — | 6 | 1 | no | — |
| 384 | C3×C8 | — | 6 | 1 | no | — |
| 385 | C3⋊C8 | — | 4 | 1 | no | — |
| 386 | C3⋊C8 | — | 4 | 1 | no | — |
| 387 | C2×C32 | — | 4 | 1 | no | — |
| 388 | C2×C32 | — | 8 | 1 | no | — |
| 389 | C2×C32 | — | 16 | 1 | no | — |
| 390 | C3×D3 | — | 16 | 1 | no | — |
| 391 | C24 | — | 2 | 1 | no | — |
| 392 | C24 | C3×#67 | 1 | 1 | yes | characteristic |
| 393 | #41 | — | 3 | 2 | no | — |
| 394 | #41 | — | 3 | 2 | no | — |
| 395 | #41 | — | 3 | 1 | no | — |
| 396 | #41 | — | 3 | 1 | no | — |
| 397 | #41 | — | 3 | 1 | no | — |
| 398 | #41 | — | 6 | 1 | no | — |
| 399 | #41 | — | 6 | 1 | no | — |
| 400 | #41 | — | 6 | 1 | no | — |
| 401 | #41 | — | 6 | 1 | no | — |
| 402 | #41 | — | 6 | 1 | no | — |
| 403 | #41 | — | 6 | 1 | no | — |
| 404 | #41 | — | 6 | 2 | no | — |
| 405 | #41 | — | 6 | 2 | no | — |
| 406 | #41 | — | 6 | 1 | no | — |
| 407 | #41 | C3×S4 | 1 | 1 | yes | characteristic, complemented |
| 408 | C2×Q8 | — | 3 | 1 | no | — |
| 409 | C2×Q8 | — | 3 | 1 | no | — |
| 410 | C2×Q8 | — | 3 | 1 | no | — |
| 411 | C2×Q8 | — | 6 | 1 | no | — |
| 412 | C2×D4 | — | 3 | 1 | no | — |
| 413 | C2×D4 | — | 3 | 1 | no | — |
| 414 | C2×D4 | — | 3 | 1 | no | — |
| 415 | C2×D4 | — | 6 | 1 | no | — |
| 416 | C2×D4 | — | 6 | 1 | no | — |
| 417 | C2×D4 | — | 6 | 1 | no | — |
| 418 | C2×D4 | — | 6 | 1 | no | — |
| 419 | C2×D4 | — | 6 | 1 | no | — |
| 420 | C2×D4 | — | 6 | 1 | no | — |
| 421 | C2×D4 | — | 6 | 1 | no | — |
| 422 | C2×D4 | — | 6 | 1 | no | — |
| 423 | C22×C4 | — | 2 | 1 | no | — |
| 424 | C22×C4 | — | 3 | 1 | no | — |
| 425 | C22×C4 | — | 3 | 1 | no | — |
| 426 | C22×C4 | — | 3 | 1 | no | — |
| 427 | C22×C4 | — | 3 | 1 | no | — |
| 428 | C22×C4 | — | 6 | 1 | no | — |
| 429 | C22×C4 | — | 6 | 1 | no | — |
| 430 | C22×C4 | — | 6 | 1 | no | — |
| 431 | C22×C4 | — | 6 | 1 | no | — |
| 432 | C22×C4 | — | 6 | 1 | no | — |
| 433 | C22×C4 | C3×#67 | 1 | 1 | yes | characteristic |
| 434 | C22×C4 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 435 | Q16 | — | 6 | 2 | no | — |
| 436 | Q16 | — | 6 | 1 | no | — |
| 437 | Q16 | — | 6 | 1 | no | — |
| 438 | SD16 | — | 6 | 2 | no | — |
| 439 | SD16 | — | 6 | 1 | no | — |
| 440 | SD16 | — | 6 | 2 | no | — |
| 441 | SD16 | — | 6 | 1 | no | — |
| 442 | SD16 | — | 6 | 1 | no | — |
| 443 | SD16 | — | 6 | 1 | no | — |
| 444 | D8 | — | 6 | 2 | no | — |
| 445 | D8 | — | 6 | 1 | no | — |
| 446 | D8 | — | 6 | 1 | no | — |
| 447 | C2×C8 | — | 3 | 1 | no | — |
| 448 | C2×C8 | — | 3 | 1 | no | — |
| 449 | C2×C8 | — | 3 | 1 | no | — |
| 450 | C2×C8 | — | 3 | 1 | no | — |
| 451 | C2×C8 | — | 6 | 1 | no | — |
| 452 | C2×C8 | — | 6 | 1 | no | — |
| 453 | C2×C8 | — | 6 | 1 | no | — |
| 454 | C2×C8 | — | 6 | 1 | no | — |
| 455 | C4⋊C4 | — | 3 | 1 | no | — |
| 456 | C4⋊C4 | — | 3 | 1 | no | — |
| 457 | C4⋊C4 | — | 6 | 1 | no | — |
| 458 | C4⋊C4 | — | 6 | 1 | no | — |
| 459 | C22⋊C4 | — | 6 | 1 | no | — |
| 460 | C22⋊C4 | — | 6 | 1 | no | — |
| 461 | C22⋊C4 | — | 6 | 1 | no | — |
| 462 | C22⋊C4 | — | 6 | 1 | no | — |
| 463 | C22⋊C4 | — | 6 | 1 | no | — |
| 464 | C42 | — | 6 | 1 | no | — |
| 465 | C22×C3 | — | 2 | 1 | no | — |
| 466 | C22×C3 | — | 3 | 1 | no | — |
| 467 | C22×C3 | — | 3 | 1 | no | — |
| 468 | C22×C3 | — | 3 | 1 | no | — |
| 469 | C22×C3 | — | 4 | 1 | no | — |
| 470 | C22×C3 | — | 6 | 1 | no | — |
| 471 | C22×C3 | — | 6 | 1 | no | — |
| 472 | C22×C3 | — | 6 | 1 | no | — |
| 473 | C22×C3 | — | 6 | 1 | no | — |
| 474 | C22×C3 | — | 6 | 1 | no | — |
| 475 | C22×C3 | — | 8 | 1 | no | — |
| 476 | C22×C3 | — | 8 | 2 | no | — |
| 477 | C22×C3 | — | 8 | 1 | no | — |
| 478 | C22×C3 | — | 12 | 1 | no | — |
| 479 | C22×C3 | — | 12 | 1 | no | — |
| 480 | C22×C3 | — | 12 | 1 | no | — |
| 481 | C22×C3 | — | 12 | 1 | no | — |
| 482 | C22×C3 | — | 12 | 1 | no | — |
| 483 | C22×C3 | — | 12 | 1 | no | — |
| 484 | C22×C3 | — | 12 | 1 | no | — |
| 485 | C22×C3 | #950 | 1 | 1 | yes | characteristic, complemented |
| 486 | C22×C3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 487 | C2×D3 | — | 8 | 1 | no | — |
| 488 | A4 | — | 2 | 1 | no | — |
| 489 | A4 | C3×#135 | 1 | 1 | yes | characteristic, complemented |
| 490 | C3×C4 | — | 2 | 1 | no | — |
| 491 | C3×C4 | — | 3 | 1 | no | — |
| 492 | C3×C4 | — | 3 | 1 | no | — |
| 493 | C3×C4 | — | 4 | 1 | no | — |
| 494 | C3×C4 | — | 4 | 1 | no | — |
| 495 | C3×C4 | — | 6 | 1 | no | — |
| 496 | C3×C4 | — | 8 | 1 | no | — |
| 497 | C3×C4 | — | 8 | 2 | no | — |
| 498 | C3×C4 | — | 8 | 1 | no | — |
| 499 | C3×C4 | — | 8 | 1 | no | — |
| 500 | C3×C4 | — | 12 | 1 | no | — |
| 501 | C3×C4 | — | 12 | 1 | no | — |
| 502 | C3×C4 | — | 12 | 1 | no | — |
| 503 | C3×C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 504 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 505 | Dic3 | — | 8 | 1 | no | — |
| 506 | C32 | — | 4 | 1 | no | Sylow |
| 507 | C23 | — | 2 | 1 | no | — |
| 508 | C23 | — | 3 | 1 | no | — |
| 509 | C23 | — | 3 | 1 | no | — |
| 510 | C23 | — | 4 | 1 | no | — |
| 511 | C23 | — | 6 | 1 | no | — |
| 512 | C23 | — | 6 | 1 | no | — |
| 513 | C23 | — | 6 | 1 | no | — |
| 514 | C23 | — | 6 | 1 | no | — |
| 515 | C23 | — | 12 | 1 | no | — |
| 516 | C23 | C2×C3×#67 | 1 | 1 | yes | characteristic |
| 517 | Q8 | — | 3 | 2 | no | — |
| 518 | Q8 | — | 3 | 1 | no | — |
| 519 | Q8 | — | 6 | 1 | no | — |
| 520 | Q8 | — | 6 | 1 | no | — |
| 521 | Q8 | — | 6 | 1 | no | — |
| 522 | Q8 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 523 | D4 | — | 2 | 1 | no | — |
| 524 | D4 | — | 3 | 2 | no | — |
| 525 | D4 | — | 3 | 1 | no | — |
| 526 | D4 | — | 6 | 1 | no | — |
| 527 | D4 | — | 6 | 1 | no | — |
| 528 | D4 | — | 6 | 1 | no | — |
| 529 | D4 | — | 6 | 1 | no | — |
| 530 | D4 | — | 6 | 2 | no | — |
| 531 | D4 | — | 6 | 1 | no | — |
| 532 | D4 | — | 6 | 1 | no | — |
| 533 | D4 | — | 12 | 1 | no | — |
| 534 | D4 | — | 12 | 1 | no | — |
| 535 | D4 | — | 12 | 2 | no | — |
| 536 | D4 | — | 12 | 1 | no | — |
| 537 | D4 | — | 12 | 1 | no | — |
| 538 | D4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 539 | C2×C4 | — | 2 | 1 | no | — |
| 540 | C2×C4 | — | 3 | 1 | no | — |
| 541 | C2×C4 | — | 3 | 1 | no | — |
| 542 | C2×C4 | — | 3 | 1 | no | — |
| 543 | C2×C4 | — | 3 | 1 | no | — |
| 544 | C2×C4 | — | 3 | 1 | no | — |
| 545 | C2×C4 | — | 3 | 1 | no | — |
| 546 | C2×C4 | — | 3 | 1 | no | — |
| 547 | C2×C4 | — | 6 | 1 | no | — |
| 548 | C2×C4 | — | 6 | 1 | no | — |
| 549 | C2×C4 | — | 6 | 1 | no | — |
| 550 | C2×C4 | — | 6 | 1 | no | — |
| 551 | C2×C4 | — | 6 | 2 | no | — |
| 552 | C2×C4 | — | 6 | 1 | no | — |
| 553 | C2×C4 | — | 6 | 1 | no | — |
| 554 | C2×C4 | — | 6 | 1 | no | — |
| 555 | C2×C4 | — | 6 | 1 | no | — |
| 556 | C2×C4 | — | 6 | 1 | no | — |
| 557 | C2×C4 | — | 12 | 1 | no | — |
| 558 | C2×C4 | — | 12 | 1 | no | — |
| 559 | C2×C4 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 560 | C8 | — | 6 | 1 | no | — |
| 561 | C8 | — | 6 | 1 | no | — |
| 562 | C8 | — | 6 | 1 | no | — |
| 563 | C8 | — | 6 | 1 | no | — |
| 564 | C2×C3 | — | 2 | 1 | no | — |
| 565 | C2×C3 | — | 3 | 1 | no | — |
| 566 | C2×C3 | — | 3 | 1 | no | — |
| 567 | C2×C3 | — | 4 | 1 | no | — |
| 568 | C2×C3 | — | 4 | 1 | no | — |
| 569 | C2×C3 | — | 6 | 1 | no | — |
| 570 | C2×C3 | — | 8 | 1 | no | — |
| 571 | C2×C3 | — | 8 | 1 | no | — |
| 572 | C2×C3 | — | 12 | 1 | no | — |
| 573 | C2×C3 | — | 16 | 1 | no | — |
| 574 | C2×C3 | — | 16 | 1 | no | — |
| 575 | C2×C3 | — | 16 | 2 | no | — |
| 576 | C2×C3 | — | 24 | 1 | no | — |
| 577 | C2×C3 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 578 | D3 | — | 16 | 1 | no | — |
| 579 | C22 | — | 2 | 1 | no | — |
| 580 | C22 | — | 3 | 1 | no | — |
| 581 | C22 | — | 3 | 1 | no | — |
| 582 | C22 | — | 3 | 1 | no | — |
| 583 | C22 | — | 6 | 1 | no | — |
| 584 | C22 | — | 6 | 1 | no | — |
| 585 | C22 | — | 6 | 1 | no | — |
| 586 | C22 | — | 6 | 1 | no | — |
| 587 | C22 | — | 6 | 1 | no | — |
| 588 | C22 | — | 12 | 1 | no | — |
| 589 | C22 | — | 12 | 1 | no | — |
| 590 | C22 | — | 12 | 1 | no | — |
| 591 | C22 | — | 12 | 1 | no | — |
| 592 | C22 | — | 12 | 1 | no | — |
| 593 | C22 | — | 12 | 1 | no | — |
| 594 | C22 | — | 12 | 1 | no | — |
| 595 | C22 | C3×#950 | 1 | 1 | yes | characteristic, complemented |
| 596 | C22 | C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 597 | C4 | — | 2 | 1 | no | — |
| 598 | C4 | — | 3 | 1 | no | — |
| 599 | C4 | — | 3 | 1 | no | — |
| 600 | C4 | — | 6 | 1 | no | — |
| 601 | C4 | — | 12 | 1 | no | — |
| 602 | C4 | — | 12 | 1 | no | — |
| 603 | C4 | — | 12 | 1 | no | — |
| 604 | C4 | C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 605 | C4 | C22×C3×S4 | 1 | 1 | yes | characteristic |
| 606 | C3 | — | 4 | 1 | no | — |
| 607 | C3 | — | 8 | 1 | no | — |
| 608 | C3 | #85514 | 1 | 1 | yes | characteristic, direct product factor |
| 609 | C2 | — | 2 | 1 | no | — |
| 610 | C2 | — | 3 | 1 | no | — |
| 611 | C2 | — | 3 | 1 | no | — |
| 612 | C2 | — | 4 | 1 | no | — |
| 613 | C2 | — | 6 | 1 | no | — |
| 614 | C2 | — | 12 | 1 | no | — |
| 615 | C2 | — | 24 | 1 | no | — |
| 616 | C2 | C2×C3×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×#41 | C2 | semidirect |
| 2. C3×#5912 | C2 | semidirect |
| 3. C3×#5417 | C2 | semidirect |
| 4. C3×#5416 | C2 | semidirect |
| 5. C3×#5415 | C2 | semidirect |
| 6. C3×#5414 | C2 | semidirect |
| 7. C2×C3×A4⋊C8 | C2 | semidirect |
| 8. #85514 | C3 | direct (N × H) |
| 22. C22×C3×#41 | D3 | semidirect |
| 24. A4×#41 | C2×C3 | semidirect |
| 25. #5912 | C2×C3 | semidirect |
| 29. #5417 | C2×C3 | semidirect |
| 30. #5416 | C2×C3 | semidirect |
| 31. #5415 | C2×C3 | semidirect |
| 32. #5414 | C2×C3 | semidirect |
| 33. C2×A4⋊C8 | C2×C3 | semidirect |
| 141. C22×#41 | C3×D3 | semidirect |
| 179. C3×#41 | S4 | semidirect |
| 253. C3×A4 | #135 | semidirect |
| 407. #41 | C3×S4 | semidirect |
| 485. C22×C3 | #950 | semidirect |
| 489. A4 | C3×#135 | semidirect |
| 595. C22 | C3×#950 | semidirect |
| 608. C3 | #85514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×#41 | 2 |
| C3×#5912 | 2 |
| C3×#5417 | 2 |
| C3×#5416 | 2 |
| C3×#5415 | 2 |
| C3×#5414 | 2 |
| C2×C3×A4⋊C8 | 2 |
| #85514 | 3 |
| C3×#3002 | 3 |
| C3×#950 | 4 |