Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 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 | #78634 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #74016 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #69988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #69988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69968 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#1305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #9504 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C23×D12 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C4×#67 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#895 | — | 2 | 1 | no | — |
| 12 | C2×#882 | C4 | 1 | 2 | yes | — |
| 13 | C3×#407 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#407 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#380 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5207 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5207 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#823 | — | 2 | 2 | no | — |
| 19 | C2×#823 | — | 2 | 2 | no | — |
| 20 | #5128 | — | 2 | 2 | no | — |
| 21 | #4988 | — | 2 | 1 | no | — |
| 22 | #4955 | C4 | 1 | 2 | yes | — |
| 23 | #4729 | — | 2 | 2 | no | — |
| 24 | #4726 | — | 2 | 1 | no | — |
| 25 | #4718 | — | 2 | 1 | no | — |
| 26 | #4672 | — | 2 | 1 | no | — |
| 27 | #4671 | — | 2 | 1 | no | — |
| 28 | #4469 | — | 2 | 1 | no | — |
| 29 | #4468 | — | 2 | 1 | no | — |
| 30 | #2975 | — | 3 | 1 | no | — |
| 31 | #2408 | — | 3 | 1 | no | — |
| 32 | #1783 | — | 3 | 1 | no | — |
| 33 | #1783 | — | 3 | 1 | no | — |
| 34 | #1465 | — | 3 | 1 | no | — |
| 35 | #1305 | — | 3 | 1 | no | — |
| 36 | #1305 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C24×D3 | C2×C4 | 1 | 2 | yes | — |
| 38 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×#67 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C22×D12 | — | 2 | 1 | no | — |
| 41 | C22×D12 | — | 2 | 1 | no | — |
| 42 | C22×D12 | — | 2 | 1 | no | — |
| 43 | C22×D12 | — | 2 | 1 | no | — |
| 44 | C22×D12 | — | 2 | 1 | no | — |
| 45 | C22×D12 | — | 2 | 1 | no | — |
| 46 | C22×D12 | — | 2 | 2 | no | — |
| 47 | C22×D12 | — | 4 | 4 | no | — |
| 48 | C22×C4×D3 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×M16 | — | 2 | 1 | no | — |
| 50 | C2×C3×M16 | D4 | 1 | 2 | yes | complemented |
| 51 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 52 | C2×C3×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 53 | C2×#217 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C4×#67 | — | 2 | 1 | no | — |
| 55 | C4×#67 | — | 2 | 1 | no | — |
| 56 | C4×#67 | — | 2 | 1 | no | — |
| 57 | C4×#67 | — | 2 | 1 | no | — |
| 58 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 59 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 60 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 61 | C2×(C2×D3)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×Dic3⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×#208 | — | 2 | 1 | no | — |
| 65 | C2×#208 | D4 | 1 | 2 | yes | complemented |
| 66 | C2×ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 67 | #895 | — | 4 | 4 | no | — |
| 68 | #882 | — | 4 | 4 | no | — |
| 69 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 70 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 71 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 72 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 73 | C3×#95 | — | 2 | 1 | no | — |
| 74 | #830 | — | 2 | 1 | no | — |
| 75 | #830 | — | 2 | 1 | no | — |
| 76 | #830 | — | 2 | 1 | no | — |
| 77 | #830 | — | 2 | 1 | no | — |
| 78 | #823 | — | 4 | 4 | no | — |
| 79 | #823 | — | 4 | 4 | no | — |
| 80 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 81 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 82 | C8×Dic3 | — | 2 | 2 | no | — |
| 83 | C23×D4 | — | 3 | 1 | no | — |
| 84 | C2×#121 | — | 6 | 1 | no | — |
| 85 | C2×#120 | — | 3 | 2 | no | — |
| 86 | C2×C4×D4 | — | 3 | 1 | no | — |
| 87 | #436 | — | 6 | 2 | no | — |
| 88 | #436 | — | 6 | 2 | no | — |
| 89 | #431 | — | 6 | 1 | no | — |
| 90 | C2×#100 | — | 6 | 2 | no | — |
| 91 | C2×#100 | — | 6 | 2 | no | — |
| 92 | #407 | — | 3 | 1 | no | — |
| 93 | #407 | — | 3 | 1 | no | — |
| 94 | #407 | — | 6 | 1 | no | — |
| 95 | #407 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #407 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | #394 | — | 6 | 1 | no | — |
| 98 | #392 | — | 6 | 1 | no | — |
| 99 | #390 | — | 6 | 1 | no | — |
| 100 | #380 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | #379 | — | 3 | 2 | no | — |
| 102 | #324 | — | 6 | 1 | no | — |
| 103 | #323 | — | 6 | 1 | no | — |
| 104 | C24×C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C23×D3 | — | 2 | 2 | no | — |
| 106 | C23×D3 | — | 2 | 2 | no | — |
| 107 | C23×D3 | — | 2 | 2 | no | — |
| 108 | C23×D3 | — | 4 | 4 | no | — |
| 109 | C23×D3 | — | 4 | 2 | no | — |
| 110 | C23×D3 | — | 4 | 2 | no | — |
| 111 | C23×D3 | — | 8 | 2 | no | — |
| 112 | C23×D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C22×C3×C4 | — | 2 | 2 | no | — |
| 114 | C22×C3×C4 | — | 4 | 2 | no | — |
| 115 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 120 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 121 | C2×#67 | — | 2 | 1 | no | — |
| 122 | C2×#67 | — | 2 | 1 | no | — |
| 123 | C2×#67 | — | 2 | 2 | no | — |
| 124 | C2×#67 | — | 4 | 1 | no | — |
| 125 | C22×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C22×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 127 | C22×Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C2×D12 | — | 2 | 4 | no | — |
| 129 | C2×D12 | — | 2 | 4 | no | — |
| 130 | C2×D12 | — | 2 | 4 | no | — |
| 131 | C2×D12 | — | 4 | 2 | no | — |
| 132 | C2×D12 | — | 4 | 2 | no | — |
| 133 | C2×D12 | — | 4 | 2 | no | — |
| 134 | C2×D12 | — | 4 | 4 | no | — |
| 135 | C2×D12 | — | 4 | 4 | no | — |
| 136 | C2×D12 | — | 4 | 4 | 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 | 4 | no | — |
| 142 | C2×D12 | — | 4 | 4 | no | — |
| 143 | C2×D12 | — | 8 | 2 | no | — |
| 144 | C2×C4×D3 | — | 2 | 1 | no | — |
| 145 | C2×C4×D3 | — | 2 | 1 | no | — |
| 146 | C2×C4×D3 | — | 4 | 2 | no | — |
| 147 | C3×M16 | — | 4 | 2 | no | — |
| 148 | C3×M16 | — | 4 | 2 | no | — |
| 149 | C2×C3×C8 | — | 2 | 2 | no | — |
| 150 | C2×C3×C8 | — | 4 | 1 | no | — |
| 151 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 152 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 153 | #217 | — | 2 | 1 | no | — |
| 154 | #217 | — | 2 | 1 | no | — |
| 155 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 156 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 157 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 158 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 159 | (C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 160 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 161 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 162 | C4×Dic3 | — | 2 | 1 | no | — |
| 163 | C4×Dic3 | — | 2 | 1 | no | — |
| 164 | #208 | — | 4 | 2 | no | — |
| 165 | #208 | — | 4 | 2 | no | — |
| 166 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 167 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 168 | ΓL(1,𝔽25) | — | 8 | 2 | no | — |
| 169 | C25 | — | 3 | 2 | no | — |
| 170 | C22×D4 | — | 3 | 1 | no | — |
| 171 | C22×D4 | — | 6 | 2 | no | — |
| 172 | C22×D4 | — | 6 | 1 | no | — |
| 173 | C22×D4 | — | 6 | 1 | no | — |
| 174 | C22×D4 | — | 6 | 1 | no | — |
| 175 | C22×D4 | — | 6 | 1 | no | — |
| 176 | C22×D4 | — | 6 | 1 | no | — |
| 177 | C22×D4 | — | 6 | 1 | no | — |
| 178 | C22×D4 | — | 12 | 4 | no | — |
| 179 | C23×C4 | — | 3 | 1 | no | — |
| 180 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C2×M16 | — | 2 | 1 | no | — |
| 182 | C2×M16 | — | 3 | 2 | no | — |
| 183 | C2×M16 | — | 6 | 2 | no | — |
| 184 | C2×M16 | — | 6 | 1 | no | — |
| 185 | C2×M16 | D12 | 1 | 2 | yes | complemented |
| 186 | #121 | — | 12 | 4 | no | — |
| 187 | #120 | — | 12 | 4 | no | — |
| 188 | C4×D4 | — | 6 | 1 | no | — |
| 189 | C4×D4 | — | 6 | 1 | no | — |
| 190 | C4×D4 | — | 6 | 1 | no | — |
| 191 | C4×D4 | — | 6 | 1 | no | — |
| 192 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 193 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 194 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 195 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 196 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 197 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 198 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 199 | C2×C22⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 200 | C2×C42 | — | 3 | 1 | no | — |
| 201 | C4⋊C8 | — | 6 | 2 | no | — |
| 202 | #100 | — | 12 | 4 | no | — |
| 203 | #100 | — | 12 | 4 | no | — |
| 204 | C22⋊C8 | — | 2 | 1 | no | — |
| 205 | C22⋊C8 | — | 2 | 1 | no | — |
| 206 | C22⋊C8 | — | 2 | 1 | no | — |
| 207 | C22⋊C8 | — | 2 | 1 | no | — |
| 208 | C22⋊C8 | — | 6 | 2 | no | — |
| 209 | C22⋊C8 | — | 6 | 1 | no | — |
| 210 | C22⋊C8 | — | 6 | 1 | no | — |
| 211 | C22⋊C8 | — | 6 | 1 | no | — |
| 212 | C22⋊C8 | — | 6 | 1 | no | — |
| 213 | C4×C8 | — | 6 | 2 | no | — |
| 214 | #95 | — | 2 | 1 | no | — |
| 215 | C23×C3 | — | 2 | 1 | no | — |
| 216 | C23×C3 | — | 2 | 1 | no | — |
| 217 | C23×C3 | — | 4 | 1 | no | — |
| 218 | C23×C3 | — | 4 | 1 | no | — |
| 219 | C23×C3 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 220 | C23×C3 | C4×D4 | 1 | 1 | yes | characteristic |
| 221 | C23×C3 | C4×D4 | 1 | 1 | yes | characteristic |
| 222 | C22×D3 | — | 2 | 4 | no | — |
| 223 | C22×D3 | — | 2 | 1 | no | — |
| 224 | C22×D3 | — | 2 | 1 | no | — |
| 225 | C22×D3 | — | 2 | 4 | no | — |
| 226 | C22×D3 | — | 2 | 4 | no | — |
| 227 | C22×D3 | — | 2 | 1 | no | — |
| 228 | C22×D3 | — | 4 | 1 | no | — |
| 229 | C22×D3 | — | 4 | 1 | no | — |
| 230 | C22×D3 | — | 4 | 2 | no | — |
| 231 | C22×D3 | — | 4 | 2 | no | — |
| 232 | C22×D3 | — | 4 | 2 | no | — |
| 233 | C22×D3 | — | 4 | 2 | no | — |
| 234 | C22×D3 | — | 4 | 2 | no | — |
| 235 | C22×D3 | — | 4 | 2 | no | — |
| 236 | C22×D3 | — | 4 | 2 | no | — |
| 237 | C22×D3 | — | 4 | 2 | no | — |
| 238 | C22×D3 | — | 8 | 8 | no | — |
| 239 | C22×D3 | — | 8 | 8 | no | — |
| 240 | C22×D3 | — | 8 | 2 | no | — |
| 241 | C22×D3 | — | 8 | 2 | no | — |
| 242 | C22×D3 | — | 8 | 2 | no | — |
| 243 | C22×D3 | — | 8 | 2 | no | — |
| 244 | C2×C3×C4 | — | 2 | 2 | no | — |
| 245 | C2×C3×C4 | — | 2 | 2 | no | — |
| 246 | C2×C3×C4 | — | 2 | 2 | no | — |
| 247 | C2×C3×C4 | — | 4 | 1 | no | — |
| 248 | C2×C3×C4 | — | 4 | 1 | no | — |
| 249 | C2×C3×C4 | — | 4 | 1 | no | — |
| 250 | C2×C3×C4 | — | 4 | 2 | no | — |
| 251 | C2×C3×C4 | — | 4 | 2 | no | — |
| 252 | C2×C3×C4 | — | 4 | 2 | no | — |
| 253 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 254 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 256 | C2×C3×C4 | #123 | 1 | 1 | yes | characteristic |
| 257 | #67 | — | 4 | 2 | no | — |
| 258 | #67 | — | 4 | 2 | no | — |
| 259 | C2×Dic3 | — | 2 | 1 | no | — |
| 260 | C2×Dic3 | — | 2 | 1 | no | — |
| 261 | C2×Dic3 | — | 2 | 1 | no | — |
| 262 | C2×Dic3 | — | 2 | 1 | no | — |
| 263 | C2×Dic3 | — | 4 | 1 | no | — |
| 264 | C2×Dic3 | — | 4 | 1 | no | — |
| 265 | C2×Dic3 | #100 | 1 | 2 | yes | complemented |
| 266 | D12 | — | 4 | 4 | no | — |
| 267 | D12 | — | 4 | 4 | no | — |
| 268 | D12 | — | 4 | 4 | no | — |
| 269 | D12 | — | 4 | 4 | no | — |
| 270 | D12 | — | 8 | 8 | no | — |
| 271 | C4×D3 | — | 4 | 2 | no | — |
| 272 | C4×D3 | — | 8 | 1 | no | — |
| 273 | C3×C8 | — | 4 | 2 | no | — |
| 274 | C3×C8 | — | 8 | 1 | no | — |
| 275 | C3⋊C8 | — | 4 | 2 | no | — |
| 276 | C3⋊C8 | — | 8 | 1 | no | — |
| 277 | C24 | — | 3 | 1 | no | — |
| 278 | C24 | — | 6 | 2 | no | — |
| 279 | C24 | — | 6 | 2 | no | — |
| 280 | C24 | — | 6 | 2 | no | — |
| 281 | C24 | — | 12 | 2 | no | — |
| 282 | C24 | — | 12 | 2 | no | — |
| 283 | C24 | — | 12 | 4 | no | — |
| 284 | C24 | — | 24 | 2 | no | — |
| 285 | C24 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 286 | C2×D4 | — | 6 | 4 | no | — |
| 287 | C2×D4 | — | 6 | 4 | no | — |
| 288 | C2×D4 | — | 6 | 4 | no | — |
| 289 | C2×D4 | — | 6 | 2 | no | — |
| 290 | C2×D4 | — | 6 | 1 | no | — |
| 291 | C2×D4 | — | 6 | 1 | no | — |
| 292 | C2×D4 | — | 12 | 2 | no | — |
| 293 | C2×D4 | — | 12 | 2 | no | — |
| 294 | C2×D4 | — | 12 | 2 | no | — |
| 295 | C2×D4 | — | 12 | 4 | no | — |
| 296 | C2×D4 | — | 12 | 4 | no | — |
| 297 | C2×D4 | — | 12 | 4 | no | — |
| 298 | C2×D4 | — | 12 | 4 | no | — |
| 299 | C2×D4 | — | 12 | 4 | no | — |
| 300 | C2×D4 | — | 12 | 1 | no | — |
| 301 | C2×D4 | — | 12 | 1 | no | — |
| 302 | C2×D4 | — | 12 | 1 | no | — |
| 303 | C2×D4 | — | 12 | 1 | no | — |
| 304 | C2×D4 | — | 12 | 1 | no | — |
| 305 | C2×D4 | — | 24 | 2 | no | — |
| 306 | C22×C4 | — | 2 | 2 | no | — |
| 307 | C22×C4 | — | 3 | 1 | no | — |
| 308 | C22×C4 | — | 3 | 1 | no | — |
| 309 | C22×C4 | — | 3 | 1 | no | — |
| 310 | C22×C4 | — | 4 | 2 | no | — |
| 311 | C22×C4 | — | 6 | 1 | no | — |
| 312 | C22×C4 | — | 6 | 1 | no | — |
| 313 | C22×C4 | — | 12 | 2 | no | — |
| 314 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 315 | C22×C4 | #235 | 1 | 1 | yes | characteristic |
| 316 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 317 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 318 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 319 | C22×C4 | #239 | 1 | 1 | yes | characteristic |
| 320 | M16 | — | 4 | 2 | no | — |
| 321 | M16 | — | 4 | 2 | no | — |
| 322 | M16 | — | 12 | 2 | no | — |
| 323 | M16 | — | 12 | 2 | no | — |
| 324 | M16 | — | 24 | 2 | no | — |
| 325 | C2×C8 | — | 2 | 2 | no | — |
| 326 | C2×C8 | — | 4 | 1 | no | — |
| 327 | C2×C8 | — | 6 | 2 | no | — |
| 328 | C2×C8 | — | 12 | 1 | no | — |
| 329 | C4⋊C4 | — | 4 | 2 | no | — |
| 330 | C4⋊C4 | — | 6 | 1 | no | — |
| 331 | C4⋊C4 | — | 6 | 1 | no | — |
| 332 | C22⋊C4 | — | 4 | 2 | no | — |
| 333 | C22⋊C4 | — | 6 | 1 | no | — |
| 334 | C22⋊C4 | — | 6 | 1 | no | — |
| 335 | C22⋊C4 | — | 6 | 1 | no | — |
| 336 | C22⋊C4 | — | 6 | 1 | no | — |
| 337 | C22⋊C4 | — | 12 | 4 | no | — |
| 338 | C22⋊C4 | — | 12 | 4 | no | — |
| 339 | C22⋊C4 | — | 24 | 2 | no | — |
| 340 | C42 | — | 6 | 1 | no | — |
| 341 | C42 | — | 6 | 1 | no | — |
| 342 | C22×C3 | — | 2 | 1 | no | — |
| 343 | C22×C3 | — | 2 | 1 | no | — |
| 344 | C22×C3 | — | 2 | 1 | no | — |
| 345 | C22×C3 | — | 2 | 1 | no | — |
| 346 | C22×C3 | — | 2 | 1 | no | — |
| 347 | C22×C3 | — | 2 | 1 | no | — |
| 348 | C22×C3 | — | 2 | 1 | no | — |
| 349 | C22×C3 | — | 2 | 1 | no | — |
| 350 | C22×C3 | — | 4 | 2 | no | — |
| 351 | C22×C3 | — | 4 | 2 | no | — |
| 352 | C22×C3 | #386 | 1 | 1 | yes | characteristic |
| 353 | C22×C3 | C2×#100 | 1 | 1 | yes | characteristic |
| 354 | C22×C3 | #413 | 1 | 1 | yes | characteristic |
| 355 | C2×D3 | — | 4 | 2 | no | — |
| 356 | C2×D3 | — | 4 | 4 | no | — |
| 357 | C2×D3 | — | 4 | 4 | no | — |
| 358 | C2×D3 | — | 4 | 1 | no | — |
| 359 | C2×D3 | — | 4 | 4 | no | — |
| 360 | C2×D3 | — | 4 | 1 | no | — |
| 361 | C2×D3 | — | 4 | 1 | no | — |
| 362 | C2×D3 | — | 8 | 2 | no | — |
| 363 | C2×D3 | — | 8 | 2 | no | — |
| 364 | C2×D3 | — | 8 | 4 | no | — |
| 365 | C2×D3 | — | 8 | 4 | no | — |
| 366 | C2×D3 | — | 8 | 2 | no | — |
| 367 | C2×D3 | — | 8 | 2 | no | — |
| 368 | C2×D3 | — | 8 | 1 | no | — |
| 369 | C2×D3 | — | 8 | 4 | no | — |
| 370 | C2×D3 | — | 8 | 4 | no | — |
| 371 | C3×C4 | — | 2 | 1 | no | — |
| 372 | C3×C4 | — | 2 | 1 | no | — |
| 373 | C3×C4 | — | 2 | 1 | no | — |
| 374 | C3×C4 | — | 8 | 2 | no | — |
| 375 | C3×C4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 376 | Dic3 | — | 2 | 2 | no | — |
| 377 | Dic3 | — | 4 | 1 | no | — |
| 378 | Dic3 | — | 4 | 1 | no | — |
| 379 | C23 | — | 2 | 1 | no | — |
| 380 | C23 | — | 2 | 1 | no | — |
| 381 | C23 | — | 4 | 1 | no | — |
| 382 | C23 | — | 4 | 1 | no | — |
| 383 | C23 | — | 6 | 4 | no | — |
| 384 | C23 | — | 6 | 4 | no | — |
| 385 | C23 | — | 6 | 4 | no | — |
| 386 | C23 | — | 6 | 1 | no | — |
| 387 | C23 | — | 6 | 1 | no | — |
| 388 | C23 | — | 6 | 1 | no | — |
| 389 | C23 | — | 12 | 1 | no | — |
| 390 | C23 | — | 12 | 1 | no | — |
| 391 | C23 | — | 12 | 2 | no | — |
| 392 | C23 | — | 12 | 2 | no | — |
| 393 | C23 | — | 12 | 2 | no | — |
| 394 | C23 | — | 12 | 2 | no | — |
| 395 | C23 | — | 12 | 2 | no | — |
| 396 | C23 | — | 12 | 2 | no | — |
| 397 | C23 | — | 12 | 2 | no | — |
| 398 | C23 | — | 12 | 2 | no | — |
| 399 | C23 | — | 24 | 2 | no | — |
| 400 | C23 | — | 24 | 2 | no | — |
| 401 | C23 | — | 24 | 2 | no | — |
| 402 | C23 | — | 24 | 2 | no | — |
| 403 | C23 | — | 24 | 8 | no | — |
| 404 | C23 | — | 24 | 8 | no | — |
| 405 | C23 | C4×D12 | 1 | 1 | yes | characteristic |
| 406 | C23 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 407 | C23 | #893 | 1 | 1 | yes | characteristic |
| 408 | D4 | — | 12 | 4 | no | — |
| 409 | D4 | — | 12 | 4 | no | — |
| 410 | D4 | — | 12 | 4 | no | — |
| 411 | D4 | — | 12 | 2 | no | — |
| 412 | D4 | — | 12 | 2 | no | — |
| 413 | D4 | — | 12 | 4 | no | — |
| 414 | D4 | — | 24 | 8 | no | — |
| 415 | C2×C4 | — | 2 | 2 | no | — |
| 416 | C2×C4 | — | 2 | 2 | no | — |
| 417 | C2×C4 | — | 2 | 2 | no | — |
| 418 | C2×C4 | — | 3 | 2 | no | — |
| 419 | C2×C4 | — | 4 | 1 | no | — |
| 420 | C2×C4 | — | 4 | 1 | no | — |
| 421 | C2×C4 | — | 4 | 1 | no | — |
| 422 | C2×C4 | — | 4 | 2 | no | — |
| 423 | C2×C4 | — | 4 | 2 | no | — |
| 424 | C2×C4 | — | 4 | 2 | no | — |
| 425 | C2×C4 | — | 6 | 1 | no | — |
| 426 | C2×C4 | — | 6 | 1 | no | — |
| 427 | C2×C4 | — | 6 | 1 | no | — |
| 428 | C2×C4 | — | 6 | 1 | no | — |
| 429 | C2×C4 | — | 12 | 2 | no | — |
| 430 | C2×C4 | — | 12 | 1 | no | — |
| 431 | C2×C4 | — | 12 | 1 | no | — |
| 432 | C2×C4 | — | 24 | 1 | no | — |
| 433 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 434 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 435 | C2×C4 | #894 | 1 | 1 | yes | characteristic |
| 436 | C2×C4 | #895 | 1 | 1 | yes | characteristic |
| 437 | C8 | — | 4 | 2 | no | — |
| 438 | C8 | — | 8 | 1 | no | — |
| 439 | C8 | — | 12 | 2 | no | — |
| 440 | C8 | — | 24 | 1 | no | — |
| 441 | C2×C3 | — | 2 | 1 | no | — |
| 442 | C2×C3 | — | 2 | 1 | no | — |
| 443 | C2×C3 | — | 4 | 1 | no | — |
| 444 | C2×C3 | — | 4 | 1 | no | — |
| 445 | C2×C3 | #1889 | 1 | 1 | yes | characteristic |
| 446 | C2×C3 | #1900 | 1 | 1 | yes | characteristic |
| 447 | C2×C3 | #1914 | 1 | 1 | yes | characteristic |
| 448 | D3 | — | 8 | 1 | no | — |
| 449 | D3 | — | 8 | 4 | no | — |
| 450 | C22 | — | 2 | 1 | no | — |
| 451 | C22 | — | 2 | 1 | no | — |
| 452 | C22 | — | 2 | 1 | no | — |
| 453 | C22 | — | 2 | 1 | no | — |
| 454 | C22 | — | 2 | 1 | no | — |
| 455 | C22 | — | 2 | 1 | no | — |
| 456 | C22 | — | 2 | 1 | no | — |
| 457 | C22 | — | 2 | 1 | no | — |
| 458 | C22 | — | 4 | 2 | no | — |
| 459 | C22 | — | 4 | 2 | no | — |
| 460 | C22 | — | 12 | 2 | no | — |
| 461 | C22 | — | 12 | 4 | no | — |
| 462 | C22 | — | 12 | 4 | no | — |
| 463 | C22 | — | 12 | 1 | no | — |
| 464 | C22 | — | 12 | 4 | no | — |
| 465 | C22 | — | 12 | 1 | no | — |
| 466 | C22 | — | 12 | 1 | no | — |
| 467 | C22 | — | 24 | 1 | no | — |
| 468 | C22 | — | 24 | 2 | no | — |
| 469 | C22 | — | 24 | 2 | no | — |
| 470 | C22 | — | 24 | 4 | no | — |
| 471 | C22 | — | 24 | 4 | no | — |
| 472 | C22 | — | 24 | 4 | no | — |
| 473 | C22 | — | 24 | 4 | no | — |
| 474 | C22 | — | 24 | 2 | no | — |
| 475 | C22 | — | 24 | 2 | no | — |
| 476 | C22 | #4665 | 1 | 1 | yes | characteristic |
| 477 | C22 | D3×#100 | 1 | 1 | yes | characteristic |
| 478 | C22 | #4751 | 1 | 1 | yes | characteristic |
| 479 | C4 | — | 2 | 1 | no | — |
| 480 | C4 | — | 2 | 1 | no | — |
| 481 | C4 | — | 2 | 1 | no | — |
| 482 | C4 | — | 6 | 2 | no | — |
| 483 | C4 | — | 8 | 2 | no | — |
| 484 | C4 | — | 12 | 1 | no | — |
| 485 | C4 | — | 12 | 1 | no | — |
| 486 | C4 | #4741 | 1 | 2 | yes | — |
| 487 | C3 | #9504 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 488 | C2 | — | 2 | 1 | no | — |
| 489 | C2 | — | 2 | 1 | no | — |
| 490 | C2 | — | 4 | 1 | no | — |
| 491 | C2 | — | 4 | 1 | no | — |
| 492 | C2 | — | 24 | 1 | no | — |
| 493 | C2 | — | 24 | 4 | no | — |
| 494 | C2 | #68962 | 1 | 1 | yes | characteristic |
| 495 | C2 | #68992 | 1 | 1 | yes | characteristic |
| 496 | C2 | #69040 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #78634 | C2 | semidirect |
| 3. #69988 | C2 | semidirect |
| 4. #69988 | C2 | semidirect |
| 5. #69968 | C2 | semidirect |
| 6. C3×#1305 | C2 | semidirect |
| 7. #67626 | C2 | semidirect |
| 36. #1305 | D3 | semidirect |
| 50. C2×C3×M16 | D4 | semidirect |
| 65. C2×#208 | D4 | semidirect |
| 185. C2×M16 | D12 | semidirect |
| 265. C2×Dic3 | #100 | semidirect |
| 487. C3 | #9504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78634 | 2 |
| #74016 | 2 |
| #69988 | 2 |
| #69968 | 2 |
| C3×#1305 | 2 |
| #67626 | 2 |
| #9504 | 3 |