Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
808 conjugacy classes of subgroups.
The subgroup lattice has 404 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #79199 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#4869 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79071 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#2090 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70676 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #70593 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #68986 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #68972 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #68942 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #68917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #23719 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×#908 | C22 | 1 | 2 | yes | — |
| 14 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 15 | #5522 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#893 | C22 | 1 | 2 | yes | — |
| 17 | C3×#428 | C22 | 1 | 2 | yes | — |
| 18 | C2×C3×#106 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#424 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#823 | C22 | 1 | 2 | yes | — |
| 21 | C2×#823 | C22 | 1 | 2 | yes | — |
| 22 | #5129 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#822 | C22 | 1 | 2 | yes | — |
| 24 | Dic3×M16 | C22 | 1 | 2 | yes | — |
| 25 | Dic3×M16 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5110 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#815 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5001 | C22 | 1 | 2 | yes | — |
| 29 | #4999 | C22 | 1 | 1 | yes | characteristic |
| 30 | #4966 | C22 | 1 | 2 | yes | — |
| 31 | C2×#809 | C22 | 1 | 2 | yes | — |
| 32 | #4889 | — | 2 | 2 | no | — |
| 33 | #4872 | — | 2 | 2 | no | — |
| 34 | #4869 | — | 2 | 2 | no | — |
| 35 | #4869 | — | 2 | 2 | no | — |
| 36 | #4869 | — | 2 | 2 | no | — |
| 37 | #4852 | — | 2 | 2 | no | — |
| 38 | #4840 | — | 2 | 2 | no | — |
| 39 | #4835 | — | 2 | 2 | no | — |
| 40 | C3×#343 | C22 | 1 | 2 | yes | — |
| 41 | C3×#341 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4552 | C22 | 1 | 1 | yes | characteristic |
| 43 | #4530 | C22 | 1 | 2 | yes | — |
| 44 | C4×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 45 | C2×#442 | — | 3 | 1 | no | — |
| 46 | #2923 | — | 3 | 1 | no | — |
| 47 | #2090 | D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | #2079 | — | 3 | 1 | no | — |
| 49 | #2063 | — | 3 | 2 | no | — |
| 50 | #2051 | — | 3 | 2 | no | — |
| 51 | #2045 | — | 3 | 1 | no | — |
| 52 | #2018 | — | 3 | 1 | no | — |
| 53 | #1778 | — | 3 | 1 | no | — |
| 54 | C4×#100 | — | 3 | 2 | no | — |
| 55 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×D12 | C23 | 1 | 2 | yes | — |
| 57 | C22×C4×D3 | — | 2 | 2 | no | — |
| 58 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 60 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 61 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 63 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 64 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×#208 | C23 | 1 | 2 | yes | — |
| 66 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 68 | #908 | — | 2 | 4 | no | — |
| 69 | #908 | — | 2 | 4 | no | — |
| 70 | C2×D24 | — | 2 | 2 | no | — |
| 71 | C2×D24 | — | 2 | 4 | no | — |
| 72 | C2×D24 | — | 2 | 2 | no | — |
| 73 | C2×#204 | — | 2 | 2 | no | — |
| 74 | #893 | — | 2 | 2 | no | — |
| 75 | #893 | — | 2 | 2 | no | — |
| 76 | #893 | — | 2 | 2 | no | — |
| 77 | #893 | — | 2 | 2 | no | — |
| 78 | #893 | D4 | 1 | 2 | yes | — |
| 79 | #887 | D4 | 1 | 2 | yes | — |
| 80 | #67⋊C4 | — | 2 | 2 | no | — |
| 81 | #872 | — | 2 | 1 | no | — |
| 82 | C42×D3 | — | 2 | 1 | no | — |
| 83 | C3×#107 | — | 2 | 2 | no | — |
| 84 | C3×#106 | — | 2 | 2 | no | — |
| 85 | C3×#106 | — | 2 | 2 | no | — |
| 86 | C3×C4⋊C8 | — | 2 | 2 | no | — |
| 87 | #823 | — | 2 | 4 | no | — |
| 88 | #823 | — | 2 | 4 | no | — |
| 89 | #822 | — | 2 | 4 | no | — |
| 90 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 91 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 92 | #815 | — | 2 | 2 | no | — |
| 93 | #815 | — | 2 | 1 | no | — |
| 94 | #815 | D4 | 1 | 2 | yes | — |
| 95 | #815 | D4 | 1 | 2 | yes | — |
| 96 | C8×Dic3 | — | 2 | 2 | no | — |
| 97 | C8×Dic3 | — | 2 | 1 | no | — |
| 98 | #810 | — | 2 | 2 | no | — |
| 99 | #809 | — | 2 | 2 | no | — |
| 100 | #809 | — | 2 | 2 | no | — |
| 101 | #809 | — | 2 | 2 | no | — |
| 102 | #809 | — | 2 | 4 | no | — |
| 103 | C4⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 104 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 105 | C22×D8 | — | 3 | 1 | no | — |
| 106 | C4×#41 | — | 3 | 1 | no | — |
| 107 | C2×C4×D4 | — | 3 | 2 | no | — |
| 108 | #442 | — | 6 | 2 | no | — |
| 109 | #442 | — | 6 | 2 | no | — |
| 110 | #442 | — | 6 | 2 | no | — |
| 111 | #440 | — | 6 | 2 | no | — |
| 112 | C4×SD16 | — | 6 | 2 | no | — |
| 113 | C4×D8 | — | 6 | 2 | no | — |
| 114 | #433 | — | 6 | 2 | no | — |
| 115 | #432 | — | 6 | 2 | no | — |
| 116 | C2×#108 | — | 3 | 2 | no | — |
| 117 | #428 | C2×D3 | 1 | 2 | yes | — |
| 118 | C2×#106 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | #424 | — | 3 | 1 | no | — |
| 120 | #424 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | #418 | — | 3 | 2 | no | — |
| 122 | #417 | — | 3 | 2 | no | — |
| 123 | C2×#102 | — | 3 | 2 | no | — |
| 124 | C2×#100 | — | 3 | 2 | no | — |
| 125 | C2×#100 | — | 3 | 2 | no | — |
| 126 | #408 | — | 3 | 1 | no | — |
| 127 | #408 | — | 3 | 1 | no | — |
| 128 | C4×M16 | — | 3 | 1 | no | — |
| 129 | C4×M16 | — | 3 | 2 | no | — |
| 130 | C2×#97 | — | 3 | 1 | no | — |
| 131 | #343 | — | 3 | 2 | no | — |
| 132 | #343 | C2×D3 | 1 | 2 | yes | — |
| 133 | #341 | — | 3 | 1 | no | — |
| 134 | #341 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | C23×D3 | — | 2 | 2 | no | — |
| 136 | C22×C3×C4 | — | 2 | 2 | no | — |
| 137 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 138 | C2×#67 | — | 2 | 1 | no | — |
| 139 | C22×Dic3 | #41 | 1 | 2 | yes | — |
| 140 | #235 | — | 2 | 2 | no | — |
| 141 | #235 | — | 2 | 2 | no | — |
| 142 | C2×D12 | — | 2 | 2 | no | — |
| 143 | C2×D12 | — | 2 | 2 | no | — |
| 144 | C2×D12 | — | 2 | 2 | no | — |
| 145 | C2×D12 | — | 2 | 2 | no | — |
| 146 | C2×D12 | — | 2 | 2 | no | — |
| 147 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×D12 | #41 | 1 | 4 | yes | — |
| 149 | C2×C4×D3 | — | 2 | 1 | no | — |
| 150 | C2×C4×D3 | — | 2 | 2 | no | — |
| 151 | C2×C4×D3 | — | 4 | 2 | no | — |
| 152 | C2×C4×D3 | — | 4 | 2 | no | — |
| 153 | C2×C4×D3 | — | 8 | 4 | no | — |
| 154 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C3×M16 | — | 2 | 2 | no | — |
| 156 | C3×M16 | — | 2 | 2 | no | — |
| 157 | C3×M16 | #41 | 1 | 4 | yes | — |
| 158 | C2×C3×C8 | — | 2 | 2 | no | — |
| 159 | C2×C3×C8 | — | 2 | 2 | no | — |
| 160 | C2×C3×C8 | — | 2 | 1 | no | — |
| 161 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 162 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 163 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 164 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 165 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 166 | C3×C42 | — | 2 | 1 | no | — |
| 167 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 168 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 169 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 170 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 171 | C4×Dic3 | — | 2 | 2 | no | — |
| 172 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 173 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | #208 | — | 2 | 2 | no | — |
| 176 | #208 | — | 2 | 2 | no | — |
| 177 | #208 | — | 2 | 2 | no | — |
| 178 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 179 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 180 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 181 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 182 | D24 | — | 2 | 8 | no | — |
| 183 | D24 | — | 2 | 8 | no | — |
| 184 | #204 | — | 2 | 8 | no | — |
| 185 | C2×#41 | — | 3 | 1 | no | — |
| 186 | C22×D4 | — | 3 | 2 | no | — |
| 187 | C23×C4 | — | 6 | 2 | no | — |
| 188 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 189 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 190 | C2×SD16 | — | 6 | 2 | no | — |
| 191 | C2×D8 | — | 6 | 4 | no | — |
| 192 | C2×D8 | — | 6 | 2 | no | — |
| 193 | C2×D8 | — | 6 | 2 | no | — |
| 194 | C2×M16 | — | 3 | 2 | no | — |
| 195 | C2×M16 | — | 3 | 1 | no | — |
| 196 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 198 | C22×C8 | — | 3 | 1 | no | — |
| 199 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 200 | C4×Q8 | — | 3 | 2 | no | — |
| 201 | C4×D4 | — | 3 | 2 | no | — |
| 202 | C4×D4 | — | 6 | 2 | no | — |
| 203 | C4×D4 | — | 6 | 2 | no | — |
| 204 | C4×D4 | — | 6 | 2 | no | — |
| 205 | C4×D4 | — | 6 | 2 | no | — |
| 206 | C4×D4 | — | 6 | 2 | no | — |
| 207 | #117 | — | 6 | 1 | no | — |
| 208 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 209 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 210 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 211 | C2×C42 | — | 3 | 1 | no | — |
| 212 | C2×C42 | — | 6 | 1 | no | — |
| 213 | #108 | — | 6 | 4 | no | — |
| 214 | #107 | — | 2 | 2 | no | — |
| 215 | #106 | — | 2 | 2 | no | — |
| 216 | #106 | — | 2 | 2 | no | — |
| 217 | C4⋊C8 | — | 2 | 2 | no | — |
| 218 | C4⋊C8 | — | 6 | 2 | no | — |
| 219 | #103 | — | 6 | 2 | no | — |
| 220 | #102 | — | 6 | 4 | no | — |
| 221 | #102 | — | 6 | 2 | no | — |
| 222 | #102 | — | 6 | 2 | no | — |
| 223 | #102 | — | 6 | 2 | no | — |
| 224 | #100 | — | 6 | 4 | no | — |
| 225 | #100 | — | 6 | 4 | no | — |
| 226 | C22⋊C8 | — | 6 | 2 | no | — |
| 227 | C22⋊C8 | — | 6 | 2 | no | — |
| 228 | #97 | — | 3 | 2 | no | — |
| 229 | #97 | — | 3 | 2 | no | — |
| 230 | #97 | — | 6 | 1 | no | — |
| 231 | #97 | — | 6 | 2 | no | — |
| 232 | C4×C8 | — | 6 | 1 | no | — |
| 233 | C4×C8 | — | 6 | 2 | no | — |
| 234 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 235 | C22×D3 | — | 2 | 1 | no | — |
| 236 | C22×D3 | — | 2 | 4 | no | — |
| 237 | C22×D3 | — | 4 | 2 | no | — |
| 238 | C22×D3 | — | 4 | 2 | no | — |
| 239 | C22×D3 | — | 8 | 2 | no | — |
| 240 | C22×D3 | — | 8 | 2 | no | — |
| 241 | C2×C3×C4 | — | 2 | 2 | no | — |
| 242 | C2×C3×C4 | — | 4 | 2 | no | — |
| 243 | C2×C3×C4 | — | 8 | 2 | no | — |
| 244 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 247 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 248 | #67 | — | 4 | 2 | no | — |
| 249 | C2×Dic3 | — | 2 | 1 | no | — |
| 250 | C2×Dic3 | — | 4 | 2 | no | — |
| 251 | C2×Dic3 | #121 | 1 | 2 | yes | — |
| 252 | C2×Dic3 | #121 | 1 | 2 | yes | — |
| 253 | D12 | — | 2 | 4 | no | — |
| 254 | D12 | — | 2 | 4 | no | — |
| 255 | D12 | — | 2 | 2 | no | — |
| 256 | D12 | — | 4 | 2 | no | — |
| 257 | D12 | — | 4 | 2 | no | — |
| 258 | C4×D3 | — | 4 | 1 | no | — |
| 259 | C4×D3 | — | 4 | 1 | no | — |
| 260 | C4×D3 | — | 8 | 2 | no | — |
| 261 | C4×D3 | — | 8 | 4 | no | — |
| 262 | C4×D3 | — | 8 | 4 | no | — |
| 263 | Dic6 | — | 2 | 2 | no | — |
| 264 | C3×C8 | — | 2 | 4 | no | — |
| 265 | C3×C8 | — | 2 | 2 | no | — |
| 266 | C3×C8 | — | 4 | 1 | no | — |
| 267 | C3⋊C8 | — | 2 | 2 | no | — |
| 268 | C3⋊C8 | — | 4 | 2 | no | — |
| 269 | C3⋊C8 | — | 4 | 1 | no | — |
| 270 | C24 | — | 6 | 2 | no | — |
| 271 | #41 | — | 6 | 2 | no | — |
| 272 | #41 | — | 6 | 2 | no | — |
| 273 | C2×Q8 | — | 3 | 1 | no | — |
| 274 | C2×D4 | — | 3 | 1 | no | — |
| 275 | C2×D4 | — | 3 | 4 | no | — |
| 276 | C2×D4 | — | 6 | 1 | no | — |
| 277 | C2×D4 | — | 6 | 2 | no | — |
| 278 | C2×D4 | — | 6 | 2 | no | — |
| 279 | C2×D4 | — | 6 | 2 | no | — |
| 280 | C2×D4 | — | 6 | 2 | no | — |
| 281 | C2×D4 | — | 6 | 2 | no | — |
| 282 | C22×C4 | — | 2 | 2 | no | — |
| 283 | C22×C4 | — | 3 | 2 | no | — |
| 284 | C22×C4 | — | 6 | 2 | no | — |
| 285 | C22×C4 | — | 6 | 1 | no | — |
| 286 | C22×C4 | — | 12 | 2 | no | — |
| 287 | C22×C4 | — | 12 | 2 | no | — |
| 288 | C22×C4 | — | 24 | 4 | no | — |
| 289 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 290 | SD16 | — | 6 | 8 | no | — |
| 291 | D8 | — | 6 | 8 | no | — |
| 292 | D8 | — | 6 | 8 | no | — |
| 293 | M16 | — | 2 | 2 | no | — |
| 294 | M16 | — | 2 | 2 | no | — |
| 295 | M16 | — | 6 | 2 | no | — |
| 296 | M16 | — | 6 | 2 | no | — |
| 297 | M16 | — | 6 | 2 | no | — |
| 298 | M16 | #239 | 1 | 4 | yes | — |
| 299 | C2×C8 | — | 2 | 2 | no | — |
| 300 | C2×C8 | — | 2 | 2 | no | — |
| 301 | C2×C8 | — | 2 | 1 | no | — |
| 302 | C2×C8 | — | 3 | 2 | no | — |
| 303 | C2×C8 | — | 6 | 2 | no | — |
| 304 | C2×C8 | — | 6 | 1 | no | — |
| 305 | C2×C8 | — | 6 | 2 | no | — |
| 306 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 307 | C4⋊C4 | — | 2 | 2 | no | — |
| 308 | C4⋊C4 | — | 2 | 2 | no | — |
| 309 | C4⋊C4 | — | 6 | 2 | no | — |
| 310 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 311 | C22⋊C4 | — | 2 | 1 | no | — |
| 312 | C22⋊C4 | — | 6 | 2 | no | — |
| 313 | C22⋊C4 | — | 12 | 2 | no | — |
| 314 | C22⋊C4 | — | 12 | 2 | no | — |
| 315 | C42 | — | 2 | 1 | no | — |
| 316 | C42 | — | 3 | 1 | no | — |
| 317 | C42 | — | 3 | 2 | no | — |
| 318 | C42 | — | 3 | 1 | no | — |
| 319 | C42 | — | 6 | 2 | no | — |
| 320 | C22×C3 | — | 2 | 2 | no | — |
| 321 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 322 | C22×C3 | #529 | 1 | 2 | yes | — |
| 323 | C2×D3 | — | 4 | 1 | no | — |
| 324 | C2×D3 | — | 4 | 4 | no | — |
| 325 | C2×D3 | — | 4 | 2 | no | — |
| 326 | C2×D3 | — | 8 | 4 | no | — |
| 327 | C2×D3 | — | 8 | 2 | no | — |
| 328 | C2×D3 | — | 8 | 2 | no | — |
| 329 | C2×D3 | — | 8 | 4 | no | — |
| 330 | C3×C4 | — | 4 | 2 | no | — |
| 331 | C3×C4 | — | 8 | 2 | no | — |
| 332 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 333 | C3×C4 | #525 | 1 | 2 | yes | — |
| 334 | C3×C4 | #532 | 1 | 1 | yes | characteristic |
| 335 | Dic3 | — | 2 | 2 | no | — |
| 336 | Dic3 | — | 2 | 2 | no | — |
| 337 | Dic3 | — | 4 | 1 | no | — |
| 338 | C23 | — | 6 | 1 | no | — |
| 339 | C23 | — | 6 | 4 | no | — |
| 340 | C23 | — | 12 | 2 | no | — |
| 341 | C23 | — | 12 | 2 | no | — |
| 342 | C23 | — | 24 | 2 | no | — |
| 343 | C23 | — | 24 | 2 | no | — |
| 344 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 345 | Q8 | — | 6 | 2 | no | — |
| 346 | D4 | — | 6 | 4 | no | — |
| 347 | D4 | — | 6 | 2 | no | — |
| 348 | D4 | — | 6 | 4 | no | — |
| 349 | D4 | — | 12 | 2 | no | — |
| 350 | D4 | — | 12 | 2 | no | — |
| 351 | D4 | — | 12 | 2 | no | — |
| 352 | C2×C4 | — | 2 | 2 | no | — |
| 353 | C2×C4 | — | 3 | 2 | no | — |
| 354 | C2×C4 | — | 3 | 2 | no | — |
| 355 | C2×C4 | — | 4 | 2 | no | — |
| 356 | C2×C4 | — | 6 | 1 | no | — |
| 357 | C2×C4 | — | 8 | 2 | no | — |
| 358 | C2×C4 | — | 12 | 2 | no | — |
| 359 | C2×C4 | — | 12 | 1 | no | — |
| 360 | C2×C4 | — | 12 | 1 | no | — |
| 361 | C2×C4 | — | 24 | 2 | no | — |
| 362 | C2×C4 | — | 24 | 4 | no | — |
| 363 | C2×C4 | — | 24 | 4 | no | — |
| 364 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 366 | C2×C4 | C2×#239 | 1 | 2 | yes | — |
| 367 | C2×C4 | D3×#41 | 1 | 2 | yes | — |
| 368 | C8 | — | 2 | 2 | no | — |
| 369 | C8 | — | 2 | 4 | no | — |
| 370 | C8 | — | 4 | 1 | no | — |
| 371 | C8 | — | 6 | 2 | no | — |
| 372 | C8 | — | 12 | 1 | no | — |
| 373 | C8 | — | 12 | 2 | no | — |
| 374 | C2×C3 | — | 2 | 2 | no | — |
| 375 | C2×C3 | #2392 | 1 | 1 | yes | characteristic |
| 376 | C2×C3 | #3068 | 1 | 2 | yes | — |
| 377 | D3 | — | 8 | 1 | no | — |
| 378 | D3 | — | 8 | 4 | no | — |
| 379 | C22 | — | 2 | 2 | no | — |
| 380 | C22 | — | 12 | 2 | no | — |
| 381 | C22 | — | 12 | 1 | no | — |
| 382 | C22 | — | 12 | 4 | no | — |
| 383 | C22 | — | 24 | 4 | no | — |
| 384 | C22 | — | 24 | 4 | no | — |
| 385 | C22 | — | 24 | 2 | no | — |
| 386 | C22 | — | 24 | 2 | no | — |
| 387 | C22 | D3×#121 | 1 | 1 | yes | characteristic |
| 388 | C22 | #5691 | 1 | 2 | yes | — |
| 389 | C4 | — | 4 | 2 | no | — |
| 390 | C4 | — | 6 | 2 | no | — |
| 391 | C4 | — | 6 | 2 | no | — |
| 392 | C4 | — | 8 | 2 | no | — |
| 393 | C4 | — | 12 | 1 | no | — |
| 394 | C4 | #5627 | 1 | 2 | yes | — |
| 395 | C4 | #5656 | 1 | 1 | yes | characteristic |
| 396 | C4 | #5725 | 1 | 1 | yes | characteristic |
| 397 | C3 | #23719 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 398 | C2 | — | 2 | 2 | no | — |
| 399 | C2 | — | 24 | 1 | no | — |
| 400 | C2 | — | 24 | 4 | no | — |
| 401 | C2 | #77737 | 1 | 1 | yes | characteristic |
| 402 | C2 | #80930 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #79199 | C2 | semidirect |
| 2. C2×#4869 | C2 | semidirect |
| 3. #79071 | C2 | semidirect |
| 4. C3×#2090 | C2 | semidirect |
| 5. #70676 | C2 | semidirect |
| 6. #70593 | C2 | semidirect |
| 7. #70540 | C2 | semidirect |
| 8. #68986 | C2 | semidirect |
| 9. #68972 | C2 | semidirect |
| 11. #68917 | C2 | semidirect |
| 47. #2090 | D3 | semidirect |
| 397. C3 | #23719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79199 | 2 |
| C2×#4869 | 2 |
| #79071 | 2 |
| C3×#2090 | 2 |
| #70676 | 2 |
| #70593 | 2 |
| #70540 | 2 |
| #68986 | 2 |
| #68972 | 2 |
| #68942 | 2 |
| #68917 | 2 |
| #23719 | 3 |