Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #83906 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83894 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#2145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70658 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70652 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13334 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5830 | — | 2 | 1 | no | — |
| 11 | C2×#949 | — | 2 | 1 | no | — |
| 12 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#427 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5195 | — | 2 | 1 | no | — |
| 17 | #5194 | — | 2 | 2 | no | — |
| 18 | #5193 | — | 2 | 1 | no | — |
| 19 | #5191 | — | 2 | 1 | no | — |
| 20 | #5179 | — | 2 | 1 | no | — |
| 21 | #5176 | — | 2 | 2 | no | — |
| 22 | #5151 | — | 2 | 1 | no | — |
| 23 | #5147 | — | 2 | 1 | no | — |
| 24 | #5101 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#812 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5006 | — | 2 | 1 | no | — |
| 27 | #5005 | — | 2 | 1 | no | — |
| 28 | #4908 | — | 2 | 2 | no | — |
| 29 | #4908 | — | 2 | 2 | no | — |
| 30 | C2×#800 | — | 2 | 1 | no | — |
| 31 | C2×D48 | — | 2 | 1 | no | — |
| 32 | C3×#360 | — | 2 | 2 | no | — |
| 33 | #4491 | — | 2 | 2 | no | — |
| 34 | #3414 | — | 3 | 1 | no | — |
| 35 | C2×#509 | — | 3 | 1 | no | — |
| 36 | #3155 | — | 3 | 1 | no | — |
| 37 | #2145 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #2140 | — | 3 | 1 | no | — |
| 39 | #1976 | — | 3 | 1 | no | — |
| 40 | #1378 | — | 3 | 1 | no | — |
| 41 | C2×C3×#41 | — | 2 | 1 | no | — |
| 42 | C2×#235 | — | 2 | 1 | no | — |
| 43 | C22×D12 | — | 2 | 1 | no | — |
| 44 | C3×#135 | — | 2 | 1 | no | — |
| 45 | C3×#135 | — | 2 | 1 | no | — |
| 46 | C3×#135 | — | 2 | 1 | no | — |
| 47 | C3×#135 | — | 2 | 1 | no | — |
| 48 | C2×C3×Q16 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 50 | C2×C3×D8 | D4 | 1 | 1 | yes | characteristic |
| 51 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 52 | C3×#117 | — | 2 | 1 | no | — |
| 53 | #949 | — | 4 | 2 | no | — |
| 54 | #949 | — | 4 | 2 | no | — |
| 55 | #947 | — | 2 | 2 | no | — |
| 56 | C2×#215 | — | 2 | 2 | no | — |
| 57 | #940 | — | 2 | 2 | no | — |
| 58 | #937 | — | 4 | 2 | no | — |
| 59 | C2×#213 | — | 2 | 2 | no | — |
| 60 | #930 | — | 4 | 2 | no | — |
| 61 | #926 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | #904 | — | 2 | 1 | no | — |
| 65 | #904 | — | 2 | 1 | no | — |
| 66 | #904 | — | 2 | 1 | no | — |
| 67 | #904 | — | 2 | 1 | no | — |
| 68 | C2×D24 | — | 2 | 1 | no | — |
| 69 | C2×D24 | — | 2 | 1 | no | — |
| 70 | C2×D24 | — | 2 | 1 | no | — |
| 71 | C2×D24 | — | 2 | 1 | no | — |
| 72 | C2×D24 | — | 2 | 1 | no | — |
| 73 | C2×D24 | D4 | 1 | 2 | yes | — |
| 74 | C2×D24 | D4 | 1 | 1 | yes | characteristic, complemented |
| 75 | C2×#204 | — | 2 | 1 | no | — |
| 76 | C3×M32 | — | 2 | 1 | no | — |
| 77 | C3×M32 | D4 | 1 | 2 | yes | complemented |
| 78 | C2×C3×C16 | — | 2 | 1 | no | — |
| 79 | C3×#107 | — | 2 | 1 | no | — |
| 80 | C3×#106 | — | 2 | 1 | no | — |
| 81 | #829 | — | 2 | 2 | no | — |
| 82 | #828 | — | 2 | 2 | no | — |
| 83 | #827 | — | 2 | 2 | no | — |
| 84 | #826 | — | 2 | 2 | no | — |
| 85 | #815 | — | 2 | 1 | no | — |
| 86 | C8×Dic3 | — | 2 | 1 | no | — |
| 87 | #812 | — | 2 | 1 | no | — |
| 88 | #812 | — | 2 | 1 | no | — |
| 89 | C2×C3⋊C16 | D4 | 1 | 2 | yes | complemented |
| 90 | #806 | — | 4 | 2 | no | — |
| 91 | #805 | — | 4 | 2 | no | — |
| 92 | #800 | — | 2 | 4 | no | — |
| 93 | D48 | — | 2 | 4 | no | — |
| 94 | C2×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 95 | C2×#135 | — | 3 | 1 | no | — |
| 96 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | C22×D8 | — | 3 | 1 | no | — |
| 98 | #535 | — | 6 | 1 | no | — |
| 99 | #510 | — | 6 | 1 | no | — |
| 100 | #510 | — | 6 | 1 | no | — |
| 101 | #509 | — | 6 | 2 | no | — |
| 102 | #509 | — | 6 | 1 | no | — |
| 103 | #509 | — | 6 | 1 | no | — |
| 104 | #509 | — | 6 | 2 | no | — |
| 105 | #508 | — | 6 | 2 | no | — |
| 106 | C2×SD32 | — | 6 | 1 | no | — |
| 107 | C2×D16 | — | 6 | 1 | no | — |
| 108 | C2×M32 | — | 3 | 1 | no | — |
| 109 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | #496 | — | 6 | 2 | no | — |
| 111 | #495 | — | 6 | 1 | no | — |
| 112 | #493 | — | 6 | 1 | no | — |
| 113 | #427 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | #421 | — | 6 | 1 | no | — |
| 115 | #410 | — | 6 | 1 | no | — |
| 116 | #405 | — | 3 | 1 | no | — |
| 117 | #360 | — | 2 | 2 | no | — |
| 118 | #357 | — | 6 | 2 | no | — |
| 119 | C23×D3 | — | 4 | 1 | no | — |
| 120 | C3×#41 | — | 4 | 1 | no | — |
| 121 | C3×#41 | — | 4 | 1 | no | — |
| 122 | C3×#41 | — | 4 | 1 | no | — |
| 123 | C3×#41 | — | 4 | 1 | no | — |
| 124 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 125 | C2×C3×D4 | — | 2 | 1 | no | — |
| 126 | C2×C3×D4 | — | 4 | 1 | no | — |
| 127 | C22×C3×C4 | — | 4 | 1 | no | — |
| 128 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×#67 | — | 4 | 4 | no | — |
| 130 | C2×#67 | — | 4 | 1 | no | — |
| 131 | #235 | — | 4 | 1 | no | — |
| 132 | #235 | — | 4 | 1 | no | — |
| 133 | #235 | — | 4 | 1 | no | — |
| 134 | #235 | — | 4 | 1 | no | — |
| 135 | C2×D12 | — | 2 | 2 | no | — |
| 136 | C2×D12 | — | 2 | 1 | no | — |
| 137 | C2×D12 | — | 4 | 1 | no | — |
| 138 | C2×D12 | — | 4 | 1 | no | — |
| 139 | C2×D12 | — | 4 | 1 | no | — |
| 140 | C2×D12 | — | 4 | 1 | no | — |
| 141 | C2×D12 | — | 4 | 1 | no | — |
| 142 | C2×C4×D3 | — | 4 | 1 | no | — |
| 143 | C2×Dic6 | — | 2 | 1 | no | — |
| 144 | C3×Q16 | — | 2 | 1 | no | — |
| 145 | C3×Q16 | — | 2 | 1 | no | — |
| 146 | C3×SD16 | — | 4 | 1 | no | — |
| 147 | C3×SD16 | — | 4 | 1 | no | — |
| 148 | C3×D8 | — | 2 | 1 | no | — |
| 149 | C3×D8 | — | 2 | 1 | no | — |
| 150 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C3×C8 | #41 | 1 | 1 | yes | characteristic |
| 156 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 157 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 158 | C3×C42 | — | 4 | 1 | no | — |
| 159 | #217 | D8 | 1 | 2 | yes | — |
| 160 | #215 | — | 4 | 4 | no | — |
| 161 | #213 | — | 4 | 4 | no | — |
| 162 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 163 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 164 | C4×Dic3 | — | 2 | 1 | no | — |
| 165 | #208 | — | 2 | 1 | no | — |
| 166 | #208 | D8 | 1 | 2 | yes | — |
| 167 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 168 | Dic12 | — | 2 | 1 | no | — |
| 169 | Dic12 | — | 2 | 1 | no | — |
| 170 | D24 | — | 2 | 1 | no | — |
| 171 | D24 | — | 2 | 2 | no | — |
| 172 | D24 | — | 2 | 1 | no | — |
| 173 | D24 | — | 2 | 2 | no | — |
| 174 | D24 | — | 4 | 1 | no | — |
| 175 | D24 | — | 4 | 1 | no | — |
| 176 | #204 | — | 4 | 1 | no | — |
| 177 | #204 | — | 4 | 1 | no | — |
| 178 | C3×C16 | — | 2 | 2 | no | — |
| 179 | C3⋊C16 | — | 2 | 2 | no | — |
| 180 | C2×#41 | — | 2 | 1 | no | — |
| 181 | C2×#41 | — | 6 | 1 | no | — |
| 182 | C22×D4 | — | 6 | 1 | no | — |
| 183 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 184 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 185 | #135 | — | 2 | 1 | no | — |
| 186 | #135 | — | 2 | 1 | no | — |
| 187 | #135 | — | 2 | 1 | no | — |
| 188 | #135 | — | 2 | 1 | no | — |
| 189 | #135 | — | 6 | 1 | no | — |
| 190 | #135 | — | 6 | 1 | no | — |
| 191 | #135 | — | 6 | 1 | no | — |
| 192 | #135 | — | 6 | 1 | no | — |
| 193 | C2×Q16 | — | 3 | 1 | no | — |
| 194 | C2×Q16 | D12 | 1 | 1 | yes | characteristic |
| 195 | C2×SD16 | — | 2 | 1 | no | — |
| 196 | C2×SD16 | — | 6 | 2 | no | — |
| 197 | C2×SD16 | — | 6 | 1 | no | — |
| 198 | C2×D8 | — | 3 | 2 | no | — |
| 199 | C2×D8 | — | 3 | 1 | no | — |
| 200 | C2×D8 | — | 6 | 2 | no | — |
| 201 | C2×D8 | — | 6 | 1 | no | — |
| 202 | C2×D8 | — | 6 | 1 | no | — |
| 203 | C2×D8 | — | 6 | 1 | no | — |
| 204 | C2×D8 | — | 6 | 1 | no | — |
| 205 | C2×D8 | — | 6 | 1 | no | — |
| 206 | C2×D8 | D12 | 1 | 1 | yes | characteristic |
| 207 | C2×M16 | — | 3 | 1 | no | — |
| 208 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 209 | #127 | — | 6 | 2 | no | — |
| 210 | #124 | — | 6 | 2 | no | — |
| 211 | #121 | — | 12 | 2 | no | — |
| 212 | #120 | — | 12 | 2 | no | — |
| 213 | #117 | — | 2 | 1 | no | — |
| 214 | #117 | — | 3 | 1 | no | — |
| 215 | Q32 | — | 6 | 2 | no | — |
| 216 | SD32 | — | 6 | 4 | no | — |
| 217 | SD32 | — | 6 | 2 | no | — |
| 218 | SD32 | — | 6 | 2 | no | — |
| 219 | D16 | — | 6 | 4 | no | — |
| 220 | D16 | — | 6 | 2 | no | — |
| 221 | M32 | — | 2 | 1 | no | — |
| 222 | M32 | — | 6 | 1 | no | — |
| 223 | M32 | — | 6 | 1 | no | — |
| 224 | M32 | #67 | 1 | 2 | yes | complemented |
| 225 | C2×C16 | — | 2 | 1 | no | — |
| 226 | C2×C16 | — | 3 | 2 | no | — |
| 227 | #107 | — | 2 | 1 | no | — |
| 228 | #106 | — | 2 | 1 | no | — |
| 229 | #104 | — | 12 | 2 | no | — |
| 230 | #99 | — | 12 | 2 | no | — |
| 231 | #97 | — | 6 | 1 | no | — |
| 232 | C4×C8 | — | 6 | 1 | no | — |
| 233 | C23×C3 | — | 4 | 1 | no | — |
| 234 | C23×C3 | C2×D8 | 1 | 1 | yes | characteristic |
| 235 | C22×D3 | — | 4 | 2 | no | — |
| 236 | C22×D3 | — | 4 | 1 | no | — |
| 237 | C22×D3 | — | 8 | 1 | no | — |
| 238 | C22×D3 | — | 8 | 1 | no | — |
| 239 | C22×D3 | — | 16 | 2 | no | — |
| 240 | C3×Q8 | — | 4 | 1 | no | — |
| 241 | C3×Q8 | — | 4 | 1 | no | — |
| 242 | C3×D4 | — | 4 | 1 | no | — |
| 243 | C3×D4 | — | 4 | 1 | no | — |
| 244 | C3×D4 | — | 8 | 1 | no | — |
| 245 | C3×D4 | — | 8 | 1 | no | — |
| 246 | C2×C3×C4 | — | 4 | 1 | no | — |
| 247 | C2×C3×C4 | — | 8 | 1 | no | — |
| 248 | C2×C3×C4 | — | 8 | 1 | no | — |
| 249 | C2×C3×C4 | — | 8 | 1 | no | — |
| 250 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 251 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 252 | C2×C3×C4 | #127 | 1 | 1 | yes | characteristic |
| 253 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 254 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 256 | #67 | — | 8 | 1 | no | — |
| 257 | #67 | — | 8 | 1 | no | — |
| 258 | #67 | — | 16 | 4 | no | — |
| 259 | C2×Dic3 | — | 2 | 2 | no | — |
| 260 | C2×Dic3 | — | 4 | 1 | no | — |
| 261 | D12 | — | 4 | 1 | no | — |
| 262 | D12 | — | 4 | 2 | no | — |
| 263 | D12 | — | 4 | 2 | no | — |
| 264 | D12 | — | 4 | 1 | no | — |
| 265 | D12 | — | 8 | 1 | no | — |
| 266 | D12 | — | 8 | 1 | no | — |
| 267 | C4×D3 | — | 8 | 1 | no | — |
| 268 | C4×D3 | — | 8 | 1 | no | — |
| 269 | Dic6 | — | 4 | 1 | no | — |
| 270 | Dic6 | — | 4 | 1 | no | — |
| 271 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 272 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 273 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 274 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 275 | C3⋊C8 | — | 2 | 2 | no | — |
| 276 | C24 | — | 12 | 1 | no | — |
| 277 | #41 | — | 4 | 1 | no | — |
| 278 | #41 | — | 4 | 1 | no | — |
| 279 | #41 | — | 4 | 1 | no | — |
| 280 | #41 | — | 4 | 1 | no | — |
| 281 | #41 | — | 12 | 1 | no | — |
| 282 | #41 | — | 12 | 1 | no | — |
| 283 | #41 | — | 12 | 1 | no | — |
| 284 | #41 | — | 12 | 1 | no | — |
| 285 | C2×Q8 | — | 2 | 1 | no | — |
| 286 | C2×Q8 | — | 6 | 1 | no | — |
| 287 | C2×D4 | — | 2 | 1 | no | — |
| 288 | C2×D4 | — | 4 | 1 | no | — |
| 289 | C2×D4 | — | 6 | 2 | no | — |
| 290 | C2×D4 | — | 6 | 1 | no | — |
| 291 | C2×D4 | — | 12 | 4 | no | — |
| 292 | C2×D4 | — | 12 | 1 | no | — |
| 293 | C2×D4 | — | 12 | 1 | no | — |
| 294 | C2×D4 | — | 12 | 1 | no | — |
| 295 | C2×D4 | — | 12 | 1 | no | — |
| 296 | C2×D4 | — | 12 | 1 | no | — |
| 297 | C2×D4 | — | 12 | 1 | no | — |
| 298 | C22×C4 | — | 4 | 1 | no | — |
| 299 | C22×C4 | — | 12 | 1 | no | — |
| 300 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 301 | Q16 | — | 2 | 1 | no | — |
| 302 | Q16 | — | 2 | 1 | no | — |
| 303 | Q16 | — | 6 | 1 | no | — |
| 304 | Q16 | — | 6 | 1 | no | — |
| 305 | SD16 | — | 4 | 1 | no | — |
| 306 | SD16 | — | 4 | 1 | no | — |
| 307 | SD16 | — | 12 | 4 | no | — |
| 308 | SD16 | — | 12 | 1 | no | — |
| 309 | SD16 | — | 12 | 1 | no | — |
| 310 | D8 | — | 2 | 1 | no | — |
| 311 | D8 | — | 2 | 1 | no | — |
| 312 | D8 | — | 6 | 1 | no | — |
| 313 | D8 | — | 6 | 2 | no | — |
| 314 | D8 | — | 6 | 1 | no | — |
| 315 | D8 | — | 6 | 2 | no | — |
| 316 | D8 | — | 12 | 4 | no | — |
| 317 | D8 | — | 12 | 1 | no | — |
| 318 | D8 | — | 12 | 1 | no | — |
| 319 | M16 | — | 3 | 2 | no | — |
| 320 | M16 | — | 6 | 1 | no | — |
| 321 | C2×C8 | — | 6 | 1 | no | — |
| 322 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 323 | C2×C8 | #235 | 1 | 1 | yes | characteristic |
| 324 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 325 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 326 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 328 | C4⋊C4 | — | 4 | 1 | no | — |
| 329 | C4⋊C4 | — | 6 | 1 | no | — |
| 330 | C22⋊C4 | — | 3 | 2 | no | — |
| 331 | C22⋊C4 | — | 4 | 1 | no | — |
| 332 | C22⋊C4 | — | 12 | 4 | no | — |
| 333 | C42 | — | 4 | 1 | no | — |
| 334 | C42 | — | 6 | 1 | no | — |
| 335 | C16 | — | 2 | 2 | no | — |
| 336 | C16 | — | 6 | 2 | no | — |
| 337 | C22×C3 | — | 4 | 1 | no | — |
| 338 | C22×C3 | — | 8 | 2 | no | — |
| 339 | C22×C3 | — | 8 | 1 | no | — |
| 340 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 341 | C22×C3 | #459 | 1 | 1 | yes | characteristic |
| 342 | C22×C3 | #493 | 1 | 1 | yes | characteristic |
| 343 | C2×D3 | — | 8 | 4 | no | — |
| 344 | C2×D3 | — | 8 | 1 | no | — |
| 345 | C2×D3 | — | 8 | 2 | no | — |
| 346 | C2×D3 | — | 16 | 2 | no | — |
| 347 | C2×D3 | — | 16 | 2 | no | — |
| 348 | C2×D3 | — | 16 | 1 | no | — |
| 349 | C3×C4 | — | 8 | 1 | no | — |
| 350 | C3×C4 | — | 16 | 1 | no | — |
| 351 | C3×C4 | #392 | 1 | 1 | yes | characteristic |
| 352 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 353 | C3×C4 | #459 | 1 | 1 | yes | characteristic |
| 354 | C3×C4 | #496 | 1 | 1 | yes | characteristic |
| 355 | Dic3 | — | 4 | 2 | no | — |
| 356 | Dic3 | — | 8 | 1 | no | — |
| 357 | C23 | — | 4 | 1 | no | — |
| 358 | C23 | — | 12 | 2 | no | — |
| 359 | C23 | — | 12 | 1 | no | — |
| 360 | C23 | — | 24 | 1 | no | — |
| 361 | C23 | — | 24 | 1 | no | — |
| 362 | C23 | — | 48 | 2 | no | — |
| 363 | C23 | D3×D8 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 4 | 1 | no | — |
| 365 | Q8 | — | 4 | 1 | no | — |
| 366 | Q8 | — | 12 | 1 | no | — |
| 367 | Q8 | — | 12 | 1 | no | — |
| 368 | D4 | — | 4 | 1 | no | — |
| 369 | D4 | — | 4 | 1 | no | — |
| 370 | D4 | — | 8 | 1 | no | — |
| 371 | D4 | — | 8 | 1 | no | — |
| 372 | D4 | — | 12 | 2 | no | — |
| 373 | D4 | — | 12 | 1 | no | — |
| 374 | D4 | — | 12 | 2 | no | — |
| 375 | D4 | — | 12 | 1 | no | — |
| 376 | D4 | — | 24 | 1 | no | — |
| 377 | D4 | — | 24 | 1 | no | — |
| 378 | D4 | — | 24 | 1 | no | — |
| 379 | D4 | — | 24 | 1 | no | — |
| 380 | D4 | — | 48 | 4 | no | — |
| 381 | C2×C4 | — | 4 | 1 | no | — |
| 382 | C2×C4 | — | 6 | 2 | no | — |
| 383 | C2×C4 | — | 8 | 1 | no | — |
| 384 | C2×C4 | — | 8 | 1 | no | — |
| 385 | C2×C4 | — | 8 | 1 | no | — |
| 386 | C2×C4 | — | 12 | 1 | no | — |
| 387 | C2×C4 | — | 24 | 1 | no | — |
| 388 | C2×C4 | — | 24 | 1 | no | — |
| 389 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 390 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 391 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | #940 | 1 | 1 | yes | characteristic |
| 395 | C8 | — | 6 | 2 | no | — |
| 396 | C8 | #882 | 1 | 1 | yes | characteristic |
| 397 | C8 | #884 | 1 | 1 | yes | characteristic |
| 398 | C8 | #930 | 1 | 1 | yes | characteristic |
| 399 | C8 | #937 | 1 | 1 | yes | characteristic |
| 400 | C2×C3 | — | 2 | 1 | no | — |
| 401 | C2×C3 | — | 2 | 1 | no | — |
| 402 | C2×C3 | — | 2 | 1 | no | — |
| 403 | C2×C3 | — | 16 | 1 | no | — |
| 404 | C2×C3 | #2011 | 1 | 1 | yes | characteristic |
| 405 | D3 | — | 16 | 2 | no | — |
| 406 | D3 | — | 16 | 1 | no | — |
| 407 | C22 | — | 4 | 1 | no | — |
| 408 | C22 | — | 8 | 2 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 24 | 4 | no | — |
| 411 | C22 | — | 24 | 1 | no | — |
| 412 | C22 | — | 24 | 2 | no | — |
| 413 | C22 | — | 48 | 1 | no | — |
| 414 | C22 | — | 48 | 2 | no | — |
| 415 | C22 | — | 48 | 2 | no | — |
| 416 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 417 | C22 | #4786 | 1 | 1 | yes | characteristic |
| 418 | C22 | #5151 | 1 | 1 | yes | characteristic |
| 419 | C4 | — | 8 | 1 | no | — |
| 420 | C4 | — | 12 | 2 | no | — |
| 421 | C4 | — | 16 | 1 | no | — |
| 422 | C4 | — | 24 | 1 | no | — |
| 423 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 424 | C4 | #4786 | 1 | 1 | yes | characteristic |
| 425 | C4 | #4960 | 1 | 1 | yes | characteristic |
| 426 | C4 | #5176 | 1 | 1 | yes | characteristic |
| 427 | C3 | #13334 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 428 | C2 | — | 2 | 1 | no | — |
| 429 | C2 | — | 2 | 1 | no | — |
| 430 | C2 | — | 2 | 1 | no | — |
| 431 | C2 | — | 16 | 1 | no | — |
| 432 | C2 | — | 48 | 2 | no | — |
| 433 | C2 | — | 48 | 1 | no | — |
| 434 | C2 | #70209 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #83906 | C2 | semidirect |
| 2. #83894 | C2 | semidirect |
| 3. C2×#4908 | C2 | semidirect |
| 4. C3×#2145 | C2 | semidirect |
| 5. #70658 | C2 | semidirect |
| 6. #70652 | C2 | semidirect |
| 7. #67814 | C2 | semidirect |
| 37. #2145 | D3 | semidirect |
| 63. C2×Dic12 | D4 | semidirect |
| 74. C2×D24 | D4 | semidirect |
| 77. C3×M32 | D4 | semidirect |
| 89. C2×C3⋊C16 | D4 | semidirect |
| 224. M32 | #67 | semidirect |
| 427. C3 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83906 | 2 |
| #83894 | 2 |
| C2×#4908 | 2 |
| C3×#2145 | 2 |
| #70658 | 2 |
| #70652 | 2 |
| #67814 | 2 |
| #13334 | 3 |