Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
452 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 57 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 | A4×#235 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×A4×M16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C4×Dic3×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#825 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#104 | — | 3 | 1 | no | maximal |
| 6 | C2×C3×C4×A4 | C22 | 1 | 1 | yes | characteristic |
| 7 | A4×#67 | — | 2 | 1 | no | — |
| 8 | C2×Dic3×A4 | — | 2 | 1 | no | — |
| 9 | A4×D12 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C4×D3×A4 | — | 2 | 1 | no | — |
| 11 | A4×Dic6 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×C8×A4 | — | 2 | 1 | no | — |
| 13 | C3×#825 | — | 4 | 1 | no | maximal |
| 14 | C22×#235 | C2×C3 | 1 | 1 | yes | characteristic |
| 15 | A4×#41 | — | 3 | 1 | no | — |
| 16 | C22×C3×M16 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C22×C4×Dic3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | A4×M16 | — | 2 | 1 | no | — |
| 19 | A4×M16 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C42×A4 | — | 3 | 1 | no | — |
| 21 | C2×#825 | — | 3 | 1 | no | — |
| 22 | C2×#825 | — | 3 | 1 | no | — |
| 23 | C2×#825 | — | 3 | 1 | no | — |
| 24 | C2×#825 | — | 3 | 1 | no | — |
| 25 | C22×C3×A4 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×D3×A4 | — | 2 | 1 | no | — |
| 27 | C3×#235 | — | 4 | 1 | no | — |
| 28 | C3×C4×A4 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C3×C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 30 | Dic3×A4 | — | 2 | 2 | no | — |
| 31 | Dic3×A4 | — | 2 | 1 | no | — |
| 32 | C32×M16 | — | 4 | 1 | no | — |
| 33 | C3×C4×Dic3 | — | 4 | 1 | no | — |
| 34 | C22×#104 | — | 3 | 1 | no | Sylow |
| 35 | C23×C3×C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 36 | C22×#67 | — | 2 | 1 | no | — |
| 37 | C23×Dic3 | — | 2 | 1 | no | — |
| 38 | C2×#235 | — | 3 | 1 | no | — |
| 39 | C2×#235 | — | 3 | 1 | no | — |
| 40 | C2×#235 | — | 3 | 1 | no | — |
| 41 | C2×#235 | — | 3 | 1 | no | — |
| 42 | C2×#235 | — | 6 | 1 | no | — |
| 43 | C2×#235 | — | 6 | 1 | no | — |
| 44 | C22×D12 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C22×C4×D3 | — | 2 | 1 | no | — |
| 46 | C22×Dic6 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 47 | Q8×A4 | — | 3 | 1 | no | — |
| 48 | D4×A4 | — | 3 | 1 | no | — |
| 49 | D4×A4 | — | 6 | 1 | no | — |
| 50 | C2×C4×A4 | — | 2 | 1 | no | — |
| 51 | C2×C4×A4 | — | 6 | 1 | no | — |
| 52 | C2×C4×A4 | — | 6 | 1 | no | — |
| 53 | C2×C4×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | C2×C3×M16 | — | 3 | 1 | no | — |
| 55 | C2×C3×M16 | — | 3 | 1 | no | — |
| 56 | C2×C3×M16 | — | 6 | 1 | no | — |
| 57 | C22×C3×C8 | — | 2 | 1 | no | — |
| 58 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 59 | C2×C4×Dic3 | — | 3 | 1 | no | — |
| 60 | C2×C4×Dic3 | — | 6 | 1 | no | — |
| 61 | C8×A4 | — | 2 | 2 | no | — |
| 62 | C8×A4 | — | 2 | 1 | no | — |
| 63 | C3×#104 | — | 12 | 1 | no | — |
| 64 | #825 | — | 3 | 2 | no | — |
| 65 | #825 | — | 3 | 1 | no | — |
| 66 | #825 | — | 3 | 1 | no | — |
| 67 | #825 | — | 3 | 1 | no | — |
| 68 | #825 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 69 | C2×C3×A4 | — | 2 | 1 | no | — |
| 70 | C2×C3×A4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 71 | D3×A4 | — | 4 | 1 | no | — |
| 72 | C2×C32×C4 | — | 4 | 1 | no | — |
| 73 | C3×#67 | — | 8 | 1 | no | — |
| 74 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 75 | C3×D12 | — | 4 | 1 | no | — |
| 76 | C3×C4×D3 | — | 8 | 1 | no | — |
| 77 | C3×Dic6 | — | 4 | 1 | no | — |
| 78 | C32×C8 | — | 8 | 1 | no | — |
| 79 | C22×#41 | — | 3 | 1 | no | — |
| 80 | C22×M16 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | C22×C42 | — | 3 | 1 | no | — |
| 82 | C2×#104 | — | 9 | 1 | no | — |
| 83 | C2×#104 | — | 9 | 1 | no | — |
| 84 | C2×#104 | — | 9 | 1 | no | — |
| 85 | C2×#104 | — | 9 | 1 | no | — |
| 86 | C24×C3 | C3×D4 | 1 | 1 | yes | characteristic |
| 87 | C23×D3 | — | 2 | 1 | no | — |
| 88 | C22×A4 | — | 2 | 1 | no | — |
| 89 | C22×A4 | — | 6 | 1 | no | — |
| 90 | C22×A4 | D12 | 1 | 1 | yes | characteristic |
| 91 | C3×#41 | — | 12 | 1 | no | — |
| 92 | C22×C3×C4 | — | 3 | 1 | no | — |
| 93 | C22×C3×C4 | — | 3 | 1 | no | — |
| 94 | C22×C3×C4 | — | 3 | 1 | no | — |
| 95 | C22×C3×C4 | — | 3 | 1 | no | — |
| 96 | C22×C3×C4 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 97 | C22×C3×C4 | C3×D4 | 1 | 1 | yes | characteristic |
| 98 | C2×#67 | — | 6 | 1 | no | — |
| 99 | C2×#67 | — | 6 | 1 | no | — |
| 100 | C2×#67 | — | 6 | 1 | no | — |
| 101 | C2×#67 | — | 6 | 1 | no | — |
| 102 | C22×Dic3 | — | 2 | 2 | no | — |
| 103 | C22×Dic3 | — | 2 | 1 | no | — |
| 104 | C22×Dic3 | — | 6 | 1 | no | — |
| 105 | C22×Dic3 | — | 6 | 1 | no | — |
| 106 | C22×Dic3 | — | 6 | 2 | no | — |
| 107 | #235 | — | 3 | 2 | no | — |
| 108 | #235 | — | 3 | 1 | no | — |
| 109 | #235 | — | 3 | 1 | no | — |
| 110 | #235 | — | 3 | 1 | no | — |
| 111 | #235 | — | 6 | 1 | no | — |
| 112 | #235 | — | 6 | 1 | no | — |
| 113 | #235 | — | 6 | 2 | no | — |
| 114 | #235 | — | 6 | 2 | no | — |
| 115 | #235 | — | 6 | 1 | no | — |
| 116 | #235 | — | 6 | 1 | no | — |
| 117 | #235 | C2×A4 | 1 | 1 | yes | characteristic |
| 118 | C2×D12 | — | 3 | 1 | no | — |
| 119 | C2×D12 | — | 3 | 1 | no | — |
| 120 | C2×D12 | — | 6 | 1 | no | — |
| 121 | C2×C4×D3 | — | 6 | 1 | no | — |
| 122 | C2×C4×D3 | — | 6 | 1 | no | — |
| 123 | C2×C4×D3 | — | 6 | 1 | no | — |
| 124 | C2×C4×D3 | — | 6 | 1 | no | — |
| 125 | C2×Dic6 | — | 3 | 1 | no | — |
| 126 | C2×Dic6 | — | 3 | 1 | no | — |
| 127 | C2×Dic6 | — | 6 | 1 | no | — |
| 128 | C4×A4 | — | 2 | 1 | no | — |
| 129 | C4×A4 | — | 2 | 1 | no | — |
| 130 | C4×A4 | — | 6 | 2 | no | — |
| 131 | C4×A4 | — | 6 | 1 | no | — |
| 132 | C4×A4 | C4×D3 | 1 | 1 | yes | characteristic |
| 133 | C4×A4 | #67 | 1 | 1 | yes | characteristic |
| 134 | C3×M16 | — | 3 | 1 | no | — |
| 135 | C3×M16 | — | 4 | 1 | no | — |
| 136 | C3×M16 | — | 6 | 1 | no | — |
| 137 | C3×M16 | — | 6 | 1 | no | — |
| 138 | C3×M16 | — | 8 | 1 | no | — |
| 139 | C3×M16 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 140 | C2×C3×C8 | — | 6 | 1 | no | — |
| 141 | C2×C3×C8 | — | 6 | 1 | no | — |
| 142 | C3×C42 | — | 12 | 1 | no | — |
| 143 | C4×Dic3 | — | 3 | 1 | no | — |
| 144 | C4×Dic3 | — | 6 | 1 | no | — |
| 145 | C4×Dic3 | — | 6 | 1 | no | — |
| 146 | C4×Dic3 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 147 | C22×C32 | — | 4 | 1 | no | — |
| 148 | C2×C3×D3 | — | 8 | 1 | no | — |
| 149 | C3×A4 | #104 | 1 | 1 | yes | characteristic, complemented |
| 150 | C32×C4 | — | 4 | 1 | no | — |
| 151 | C32×C4 | — | 4 | 1 | no | — |
| 152 | C3×Dic3 | — | 8 | 1 | no | — |
| 153 | C3×Dic3 | — | 8 | 2 | no | — |
| 154 | C2×#41 | — | 9 | 1 | no | — |
| 155 | C2×#41 | — | 9 | 1 | no | — |
| 156 | C2×#41 | — | 9 | 1 | no | — |
| 157 | C2×#41 | — | 9 | 1 | no | — |
| 158 | C2×#41 | — | 18 | 1 | no | — |
| 159 | C2×#41 | — | 18 | 1 | no | — |
| 160 | C22×Q8 | — | 3 | 1 | no | — |
| 161 | C22×D4 | — | 3 | 1 | no | — |
| 162 | C22×D4 | — | 6 | 1 | no | — |
| 163 | C23×C4 | — | 6 | 1 | no | — |
| 164 | C23×C4 | — | 6 | 1 | no | — |
| 165 | C23×C4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 166 | C2×M16 | — | 3 | 1 | no | — |
| 167 | C2×M16 | — | 3 | 1 | no | — |
| 168 | C2×M16 | — | 6 | 1 | no | — |
| 169 | C22×C8 | — | 2 | 1 | no | — |
| 170 | C2×C42 | — | 9 | 1 | no | — |
| 171 | C2×C42 | — | 9 | 1 | no | — |
| 172 | C2×C42 | — | 18 | 1 | no | — |
| 173 | #104 | — | 3 | 1 | no | — |
| 174 | #104 | — | 9 | 1 | no | — |
| 175 | #104 | — | 9 | 1 | no | — |
| 176 | #104 | — | 9 | 2 | no | — |
| 177 | #104 | — | 9 | 1 | no | — |
| 178 | C23×C3 | — | 2 | 1 | no | — |
| 179 | C23×C3 | — | 3 | 1 | no | — |
| 180 | C23×C3 | — | 3 | 1 | no | — |
| 181 | C23×C3 | — | 6 | 1 | no | — |
| 182 | C23×C3 | C3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 183 | C22×D3 | — | 4 | 1 | no | — |
| 184 | C22×D3 | — | 6 | 1 | no | — |
| 185 | C22×D3 | — | 6 | 1 | no | — |
| 186 | C22×D3 | — | 12 | 1 | no | — |
| 187 | C2×A4 | — | 2 | 1 | no | — |
| 188 | C2×A4 | — | 2 | 1 | no | — |
| 189 | C2×A4 | — | 4 | 1 | no | — |
| 190 | C2×A4 | — | 12 | 1 | no | — |
| 191 | C2×A4 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 192 | C3×Q8 | — | 12 | 1 | no | — |
| 193 | C3×D4 | — | 12 | 1 | no | — |
| 194 | C3×D4 | — | 24 | 1 | no | — |
| 195 | C2×C3×C4 | — | 3 | 2 | no | — |
| 196 | C2×C3×C4 | — | 3 | 1 | no | — |
| 197 | C2×C3×C4 | — | 3 | 1 | no | — |
| 198 | C2×C3×C4 | — | 3 | 1 | no | — |
| 199 | C2×C3×C4 | — | 3 | 1 | no | — |
| 200 | C2×C3×C4 | — | 3 | 1 | no | — |
| 201 | C2×C3×C4 | — | 3 | 1 | no | — |
| 202 | C2×C3×C4 | — | 3 | 1 | no | — |
| 203 | C2×C3×C4 | — | 4 | 1 | no | — |
| 204 | C2×C3×C4 | — | 8 | 1 | no | — |
| 205 | C2×C3×C4 | — | 24 | 1 | no | — |
| 206 | C2×C3×C4 | — | 24 | 1 | no | — |
| 207 | C2×C3×C4 | C22×A4 | 1 | 1 | yes | characteristic |
| 208 | #67 | — | 2 | 1 | no | — |
| 209 | #67 | — | 6 | 1 | no | — |
| 210 | #67 | — | 6 | 1 | no | — |
| 211 | #67 | — | 6 | 2 | no | — |
| 212 | #67 | — | 6 | 1 | no | — |
| 213 | C2×Dic3 | — | 2 | 1 | no | — |
| 214 | C2×Dic3 | — | 6 | 1 | no | — |
| 215 | C2×Dic3 | — | 6 | 2 | no | — |
| 216 | C2×Dic3 | — | 6 | 2 | no | — |
| 217 | C2×Dic3 | — | 6 | 2 | no | — |
| 218 | C2×Dic3 | — | 6 | 1 | no | — |
| 219 | C2×Dic3 | — | 6 | 1 | no | — |
| 220 | C2×Dic3 | — | 6 | 2 | no | — |
| 221 | D12 | — | 3 | 1 | no | — |
| 222 | D12 | — | 6 | 1 | no | — |
| 223 | D12 | — | 6 | 1 | no | — |
| 224 | D12 | C4×A4 | 1 | 1 | yes | characteristic, complemented |
| 225 | C4×D3 | — | 2 | 1 | no | — |
| 226 | C4×D3 | — | 6 | 1 | no | — |
| 227 | C4×D3 | — | 6 | 1 | no | — |
| 228 | C4×D3 | — | 6 | 2 | no | — |
| 229 | C4×D3 | — | 6 | 1 | no | — |
| 230 | Dic6 | — | 3 | 1 | no | — |
| 231 | Dic6 | — | 6 | 1 | no | — |
| 232 | Dic6 | — | 6 | 1 | no | — |
| 233 | Dic6 | C4×A4 | 1 | 1 | yes | characteristic, complemented |
| 234 | C3×C8 | — | 2 | 1 | no | — |
| 235 | C3×C8 | — | 6 | 1 | no | — |
| 236 | C3×C8 | — | 8 | 1 | no | — |
| 237 | C3×C8 | — | 8 | 2 | no | — |
| 238 | C2×C32 | — | 4 | 1 | no | — |
| 239 | C2×C32 | — | 8 | 1 | no | — |
| 240 | C3×D3 | — | 16 | 1 | no | — |
| 241 | C24 | — | 6 | 1 | no | — |
| 242 | C24 | C3×D12 | 1 | 1 | yes | characteristic |
| 243 | #41 | — | 3 | 1 | no | — |
| 244 | #41 | — | 9 | 1 | no | — |
| 245 | #41 | — | 9 | 1 | no | — |
| 246 | #41 | — | 9 | 2 | no | — |
| 247 | #41 | — | 9 | 1 | no | — |
| 248 | #41 | — | 18 | 1 | no | — |
| 249 | #41 | — | 18 | 1 | no | — |
| 250 | #41 | — | 18 | 2 | no | — |
| 251 | #41 | — | 18 | 2 | no | — |
| 252 | #41 | — | 18 | 1 | no | — |
| 253 | #41 | — | 18 | 1 | no | — |
| 254 | C2×Q8 | — | 9 | 1 | no | — |
| 255 | C2×Q8 | — | 9 | 1 | no | — |
| 256 | C2×Q8 | — | 18 | 1 | no | — |
| 257 | C2×D4 | — | 9 | 1 | no | — |
| 258 | C2×D4 | — | 9 | 1 | no | — |
| 259 | C2×D4 | — | 18 | 1 | no | — |
| 260 | C2×D4 | — | 18 | 1 | no | — |
| 261 | C2×D4 | — | 18 | 1 | no | — |
| 262 | C2×D4 | — | 18 | 1 | no | — |
| 263 | C2×D4 | — | 18 | 1 | no | — |
| 264 | C22×C4 | — | 3 | 1 | no | — |
| 265 | C22×C4 | — | 3 | 1 | no | — |
| 266 | C22×C4 | — | 3 | 1 | no | — |
| 267 | C22×C4 | — | 3 | 1 | no | — |
| 268 | C22×C4 | — | 6 | 2 | no | — |
| 269 | C22×C4 | — | 6 | 1 | no | — |
| 270 | C22×C4 | — | 18 | 1 | no | — |
| 271 | C22×C4 | — | 18 | 1 | no | — |
| 272 | C22×C4 | — | 18 | 1 | no | — |
| 273 | C22×C4 | — | 18 | 1 | no | — |
| 274 | C22×C4 | — | 18 | 1 | no | — |
| 275 | C22×C4 | — | 18 | 1 | no | — |
| 276 | C22×C4 | — | 18 | 2 | no | — |
| 277 | C22×C4 | C3×C4×D3 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | C3×#67 | 1 | 1 | yes | characteristic |
| 279 | M16 | — | 3 | 1 | no | — |
| 280 | M16 | — | 6 | 1 | no | — |
| 281 | M16 | — | 6 | 1 | no | — |
| 282 | M16 | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 283 | C2×C8 | — | 6 | 1 | no | — |
| 284 | C2×C8 | — | 6 | 1 | no | — |
| 285 | C42 | — | 3 | 1 | no | — |
| 286 | C42 | — | 9 | 1 | no | — |
| 287 | C42 | — | 18 | 1 | no | — |
| 288 | C42 | — | 18 | 1 | no | — |
| 289 | C22×C3 | — | 3 | 1 | no | — |
| 290 | C22×C3 | — | 3 | 1 | no | — |
| 291 | C22×C3 | — | 3 | 1 | no | — |
| 292 | C22×C3 | — | 4 | 1 | no | — |
| 293 | C22×C3 | — | 6 | 1 | no | — |
| 294 | C22×C3 | — | 6 | 1 | no | — |
| 295 | C22×C3 | — | 6 | 1 | no | — |
| 296 | C22×C3 | — | 6 | 1 | no | — |
| 297 | C22×C3 | — | 8 | 1 | no | — |
| 298 | C22×C3 | — | 24 | 1 | no | — |
| 299 | C22×C3 | C3×#104 | 1 | 1 | yes | characteristic, complemented |
| 300 | C22×C3 | D4×A4 | 1 | 1 | yes | characteristic |
| 301 | C2×D3 | — | 2 | 1 | no | — |
| 302 | C2×D3 | — | 6 | 1 | no | — |
| 303 | C2×D3 | — | 12 | 1 | no | — |
| 304 | C2×D3 | — | 12 | 1 | no | — |
| 305 | C2×D3 | — | 12 | 1 | no | — |
| 306 | C2×D3 | — | 12 | 1 | no | — |
| 307 | A4 | — | 2 | 1 | no | — |
| 308 | A4 | #825 | 1 | 1 | yes | characteristic, direct product factor |
| 309 | C3×C4 | — | 3 | 1 | no | — |
| 310 | C3×C4 | — | 3 | 1 | no | — |
| 311 | C3×C4 | — | 4 | 1 | no | — |
| 312 | C3×C4 | — | 4 | 1 | no | — |
| 313 | C3×C4 | — | 8 | 1 | no | — |
| 314 | C3×C4 | — | 8 | 1 | no | — |
| 315 | C3×C4 | — | 24 | 1 | no | — |
| 316 | C3×C4 | — | 24 | 2 | no | — |
| 317 | C3×C4 | C2×C4×A4 | 1 | 1 | yes | characteristic |
| 318 | C3×C4 | D4×A4 | 1 | 1 | yes | characteristic |
| 319 | Dic3 | — | 2 | 2 | no | — |
| 320 | Dic3 | — | 2 | 1 | no | — |
| 321 | Dic3 | — | 6 | 2 | no | — |
| 322 | Dic3 | — | 6 | 1 | no | — |
| 323 | C32 | — | 4 | 1 | no | Sylow |
| 324 | C23 | — | 2 | 1 | no | — |
| 325 | C23 | — | 3 | 1 | no | — |
| 326 | C23 | — | 3 | 1 | no | — |
| 327 | C23 | — | 6 | 1 | no | — |
| 328 | C23 | — | 12 | 1 | no | — |
| 329 | C23 | — | 18 | 1 | no | — |
| 330 | C23 | — | 18 | 1 | no | — |
| 331 | C23 | — | 36 | 1 | no | — |
| 332 | C23 | C3×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 333 | Q8 | — | 3 | 1 | no | — |
| 334 | Q8 | — | 9 | 1 | no | — |
| 335 | Q8 | — | 18 | 1 | no | — |
| 336 | Q8 | — | 18 | 1 | no | — |
| 337 | D4 | — | 3 | 1 | no | — |
| 338 | D4 | — | 6 | 1 | no | — |
| 339 | D4 | — | 9 | 1 | no | — |
| 340 | D4 | — | 18 | 1 | no | — |
| 341 | D4 | — | 18 | 1 | no | — |
| 342 | D4 | — | 18 | 1 | no | — |
| 343 | D4 | — | 18 | 1 | no | — |
| 344 | D4 | — | 18 | 2 | no | — |
| 345 | D4 | — | 18 | 1 | no | — |
| 346 | C2×C4 | — | 3 | 2 | no | — |
| 347 | C2×C4 | — | 3 | 1 | no | — |
| 348 | C2×C4 | — | 3 | 1 | no | — |
| 349 | C2×C4 | — | 3 | 1 | no | — |
| 350 | C2×C4 | — | 3 | 1 | no | — |
| 351 | C2×C4 | — | 3 | 1 | no | — |
| 352 | C2×C4 | — | 3 | 1 | no | — |
| 353 | C2×C4 | — | 3 | 1 | no | — |
| 354 | C2×C4 | — | 6 | 1 | no | — |
| 355 | C2×C4 | — | 6 | 1 | no | — |
| 356 | C2×C4 | — | 18 | 1 | no | — |
| 357 | C2×C4 | — | 18 | 1 | no | — |
| 358 | C2×C4 | — | 18 | 2 | no | — |
| 359 | C2×C4 | — | 18 | 1 | no | — |
| 360 | C2×C4 | — | 18 | 2 | no | — |
| 361 | C2×C4 | — | 18 | 2 | no | — |
| 362 | C2×C4 | — | 18 | 2 | no | — |
| 363 | C2×C4 | — | 18 | 1 | no | — |
| 364 | C2×C4 | — | 18 | 1 | no | — |
| 365 | C2×C4 | — | 18 | 1 | no | — |
| 366 | C2×C4 | — | 18 | 2 | no | — |
| 367 | C2×C4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 368 | C8 | — | 2 | 1 | no | — |
| 369 | C8 | — | 6 | 1 | no | — |
| 370 | C2×C3 | — | 2 | 1 | no | — |
| 371 | C2×C3 | — | 3 | 1 | no | — |
| 372 | C2×C3 | — | 3 | 1 | no | — |
| 373 | C2×C3 | — | 4 | 1 | no | — |
| 374 | C2×C3 | — | 6 | 1 | no | — |
| 375 | C2×C3 | — | 8 | 1 | no | — |
| 376 | C2×C3 | — | 8 | 1 | no | — |
| 377 | C2×C3 | — | 16 | 1 | no | — |
| 378 | C2×C3 | — | 48 | 1 | no | — |
| 379 | C2×C3 | A4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 380 | D3 | — | 4 | 1 | no | — |
| 381 | D3 | — | 12 | 1 | no | — |
| 382 | C22 | — | 3 | 1 | no | — |
| 383 | C22 | — | 3 | 1 | no | — |
| 384 | C22 | — | 3 | 1 | no | — |
| 385 | C22 | — | 6 | 1 | no | — |
| 386 | C22 | — | 6 | 1 | no | — |
| 387 | C22 | — | 6 | 1 | no | — |
| 388 | C22 | — | 6 | 1 | no | — |
| 389 | C22 | — | 6 | 1 | no | — |
| 390 | C22 | — | 18 | 1 | no | — |
| 391 | C22 | — | 36 | 1 | no | — |
| 392 | C22 | — | 36 | 1 | no | — |
| 393 | C22 | — | 36 | 1 | no | — |
| 394 | C22 | — | 36 | 1 | no | — |
| 395 | C22 | C3×#825 | 1 | 1 | yes | characteristic, complemented |
| 396 | C22 | A4×D12 | 1 | 1 | yes | characteristic |
| 397 | C4 | — | 3 | 1 | no | — |
| 398 | C4 | — | 3 | 1 | no | — |
| 399 | C4 | — | 6 | 2 | no | — |
| 400 | C4 | — | 6 | 1 | no | — |
| 401 | C4 | — | 18 | 2 | no | — |
| 402 | C4 | — | 18 | 1 | no | — |
| 403 | C4 | C4×D3×A4 | 1 | 1 | yes | characteristic |
| 404 | C4 | A4×#67 | 1 | 1 | yes | characteristic |
| 405 | C3 | — | 4 | 1 | no | — |
| 406 | C3 | — | 8 | 1 | no | — |
| 407 | C3 | A4×#104 | 1 | 1 | yes | characteristic, complemented |
| 408 | C2 | — | 2 | 1 | no | — |
| 409 | C2 | — | 3 | 1 | no | — |
| 410 | C2 | — | 3 | 1 | no | — |
| 411 | C2 | — | 6 | 1 | no | — |
| 412 | C2 | — | 12 | 1 | no | — |
| 413 | C2 | — | 36 | 1 | no | — |
| 414 | C2 | A4×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×A4×M16 | C2 | semidirect |
| 3. C4×Dic3×A4 | C2 | semidirect |
| 4. C22×#825 | C3 | semidirect |
| 9. A4×D12 | C4 | semidirect |
| 11. A4×Dic6 | C4 | semidirect |
| 16. C22×C3×M16 | C2×C3 | semidirect |
| 17. C22×C4×Dic3 | C2×C3 | semidirect |
| 19. A4×M16 | D3 | semidirect |
| 44. C22×D12 | C3×C4 | semidirect |
| 46. C22×Dic6 | C3×C4 | semidirect |
| 68. #825 | A4 | direct (N × H) |
| 80. C22×M16 | C3×D3 | semidirect |
| 139. C3×M16 | C2×A4 | semidirect |
| 146. C4×Dic3 | C2×A4 | semidirect |
| 149. C3×A4 | #104 | semidirect |
| 224. D12 | C4×A4 | semidirect |
| 233. Dic6 | C4×A4 | semidirect |
| 282. M16 | D3×A4 | semidirect |
| 299. C22×C3 | C3×#104 | semidirect |
| 308. A4 | #825 | direct (N × H) |
| 395. C22 | C3×#825 | semidirect |
| 407. C3 | A4×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#235 | 2 |
| C3×A4×M16 | 2 |
| C4×Dic3×A4 | 2 |
| C22×#825 | 3 |
| A4×#104 | 3 |
| C3×#825 | 4 |