Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #83836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×C3×#361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71450 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71437 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #67735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13310 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×C3×D8 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5805 | — | 2 | 1 | no | — |
| 11 | #5748 | — | 2 | 1 | no | — |
| 12 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 16 | #5215 | — | 2 | 1 | no | — |
| 17 | #5159 | — | 2 | 2 | no | — |
| 18 | #5157 | — | 2 | 2 | no | — |
| 19 | C2×#827 | — | 2 | 1 | no | — |
| 20 | #5147 | — | 2 | 2 | no | — |
| 21 | #5147 | — | 2 | 2 | no | — |
| 22 | C2×#826 | — | 2 | 1 | no | — |
| 23 | #5132 | — | 2 | 1 | no | — |
| 24 | #5106 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#812 | C22 | 1 | 1 | yes | characteristic |
| 26 | #4898 | — | 2 | 2 | no | — |
| 27 | #4897 | — | 2 | 1 | no | — |
| 28 | #4896 | — | 2 | 1 | no | — |
| 29 | C3×#361 | — | 2 | 2 | no | — |
| 30 | #4518 | — | 2 | 2 | no | — |
| 31 | #4508 | — | 2 | 2 | no | — |
| 32 | C2×#509 | — | 3 | 1 | no | — |
| 33 | #3067 | — | 3 | 1 | no | — |
| 34 | #3058 | — | 3 | 1 | no | — |
| 35 | C2×#361 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #2145 | — | 3 | 1 | no | — |
| 37 | #2117 | — | 3 | 1 | no | — |
| 38 | #1389 | — | 3 | 1 | no | — |
| 39 | C22×C3×D4 | — | 2 | 1 | no | — |
| 40 | C2×#235 | — | 2 | 1 | no | — |
| 41 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×C3×D8 | — | 2 | 1 | no | — |
| 43 | C2×C3×D8 | — | 2 | 1 | no | — |
| 44 | C2×C3×D8 | — | 2 | 1 | no | — |
| 45 | C2×C3×D8 | — | 2 | 1 | no | — |
| 46 | C2×C3×D8 | — | 2 | 1 | no | — |
| 47 | C2×C3×D8 | D4 | 1 | 2 | yes | — |
| 48 | C2×C3×M16 | — | 2 | 1 | no | — |
| 49 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 50 | #953 | — | 4 | 2 | no | — |
| 51 | #940 | — | 4 | 1 | no | — |
| 52 | #938 | — | 2 | 4 | no | — |
| 53 | #936 | — | 4 | 1 | no | — |
| 54 | #926 | — | 2 | 1 | no | — |
| 55 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 56 | #909 | — | 2 | 2 | no | — |
| 57 | #909 | — | 4 | 1 | no | — |
| 58 | #908 | — | 2 | 2 | no | — |
| 59 | #908 | — | 4 | 1 | no | — |
| 60 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | #904 | — | 2 | 1 | no | — |
| 62 | #904 | — | 2 | 1 | no | — |
| 63 | #904 | — | 2 | 1 | no | — |
| 64 | #904 | — | 2 | 1 | no | — |
| 65 | #904 | — | 4 | 2 | no | — |
| 66 | C2×D24 | D4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C2×#204 | — | 2 | 1 | no | — |
| 68 | #901 | — | 2 | 1 | no | — |
| 69 | #901 | — | 2 | 1 | no | — |
| 70 | #901 | — | 2 | 1 | no | — |
| 71 | #901 | — | 2 | 1 | no | — |
| 72 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 73 | C2×D3×C8 | — | 2 | 1 | no | — |
| 74 | C3×M32 | — | 2 | 1 | no | — |
| 75 | C3×M32 | — | 2 | 1 | no | — |
| 76 | C2×C3×C16 | — | 2 | 1 | no | — |
| 77 | C3×#108 | — | 2 | 1 | no | — |
| 78 | C3×#108 | D4 | 1 | 2 | yes | complemented |
| 79 | #832 | — | 2 | 4 | no | — |
| 80 | #827 | — | 2 | 4 | no | — |
| 81 | #826 | — | 2 | 4 | no | — |
| 82 | #824 | — | 2 | 2 | no | — |
| 83 | #823 | — | 2 | 2 | no | — |
| 84 | #818 | — | 2 | 1 | no | — |
| 85 | #817 | D4 | 1 | 2 | yes | — |
| 86 | #812 | — | 2 | 1 | no | — |
| 87 | #812 | D4 | 1 | 2 | yes | complemented |
| 88 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 89 | #575 | — | 6 | 1 | no | — |
| 90 | C2×#135 | — | 3 | 1 | no | — |
| 91 | C22×D8 | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | C2×#131 | — | 3 | 1 | no | — |
| 93 | #535 | — | 6 | 1 | no | — |
| 94 | #509 | — | 6 | 2 | no | — |
| 95 | #509 | — | 6 | 2 | no | — |
| 96 | C2×SD32 | — | 6 | 1 | no | — |
| 97 | C2×D16 | — | 6 | 1 | no | — |
| 98 | C2×M32 | — | 3 | 1 | no | — |
| 99 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | #473 | — | 6 | 1 | no | — |
| 101 | #472 | — | 6 | 1 | no | — |
| 102 | #471 | — | 6 | 2 | no | — |
| 103 | #469 | — | 6 | 2 | no | — |
| 104 | #466 | — | 6 | 2 | no | — |
| 105 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 106 | #427 | — | 3 | 1 | no | — |
| 107 | #418 | — | 6 | 1 | no | — |
| 108 | #413 | — | 6 | 1 | no | — |
| 109 | #361 | — | 2 | 2 | no | — |
| 110 | #360 | — | 6 | 2 | no | — |
| 111 | #350 | — | 6 | 2 | no | — |
| 112 | C24×C3 | — | 4 | 1 | no | — |
| 113 | C2×C3×D4 | — | 2 | 2 | no | — |
| 114 | C2×C3×D4 | — | 4 | 1 | no | — |
| 115 | C2×C3×D4 | — | 4 | 1 | no | — |
| 116 | C2×C3×D4 | — | 4 | 1 | no | — |
| 117 | C2×C3×D4 | — | 4 | 1 | no | — |
| 118 | C2×C3×D4 | — | 4 | 1 | no | — |
| 119 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#67 | — | 2 | 1 | no | — |
| 121 | C2×#67 | — | 4 | 1 | no | — |
| 122 | C2×#67 | — | 4 | 4 | no | — |
| 123 | #235 | — | 2 | 1 | no | — |
| 124 | #235 | — | 2 | 1 | no | — |
| 125 | #235 | — | 2 | 1 | no | — |
| 126 | #235 | — | 2 | 1 | no | — |
| 127 | #235 | — | 4 | 1 | no | — |
| 128 | #235 | — | 4 | 1 | no | — |
| 129 | #235 | — | 4 | 1 | no | — |
| 130 | #235 | — | 4 | 1 | no | — |
| 131 | C2×D12 | — | 2 | 1 | no | — |
| 132 | C2×D12 | D8 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×D3 | — | 2 | 1 | no | — |
| 134 | C2×C4×D3 | — | 4 | 1 | no | — |
| 135 | C2×Dic6 | — | 2 | 1 | no | — |
| 136 | C2×Dic6 | D8 | 1 | 1 | yes | characteristic |
| 137 | C3×D8 | — | 2 | 2 | no | — |
| 138 | C3×D8 | — | 2 | 2 | no | — |
| 139 | C3×D8 | — | 4 | 1 | no | — |
| 140 | C3×D8 | — | 4 | 1 | no | — |
| 141 | C3×M16 | — | 2 | 2 | no | — |
| 142 | C3×M16 | — | 4 | 1 | no | — |
| 143 | C2×C3×C8 | — | 4 | 1 | no | — |
| 144 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C3×C8 | #41 | 1 | 1 | yes | characteristic |
| 150 | #217 | — | 4 | 4 | no | — |
| 151 | #217 | — | 4 | 1 | no | — |
| 152 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 153 | C4×Dic3 | — | 4 | 1 | no | — |
| 154 | #208 | — | 2 | 1 | no | — |
| 155 | #208 | — | 2 | 1 | no | — |
| 156 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 157 | Dic12 | — | 2 | 1 | no | — |
| 158 | Dic12 | — | 2 | 1 | no | — |
| 159 | Dic12 | — | 4 | 2 | no | — |
| 160 | D24 | — | 2 | 1 | no | — |
| 161 | D24 | — | 2 | 1 | no | — |
| 162 | D24 | — | 4 | 2 | no | — |
| 163 | #204 | — | 4 | 2 | no | — |
| 164 | #204 | — | 4 | 2 | no | — |
| 165 | #204 | — | 4 | 1 | no | — |
| 166 | #204 | — | 4 | 1 | no | — |
| 167 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 168 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 169 | D3×C8 | — | 4 | 1 | no | — |
| 170 | D3×C8 | — | 4 | 1 | no | — |
| 171 | C3×C16 | — | 4 | 1 | no | — |
| 172 | C3⋊C16 | — | 2 | 2 | no | — |
| 173 | C2×#41 | — | 3 | 1 | no | — |
| 174 | C2×#41 | — | 6 | 1 | no | — |
| 175 | C22×D4 | — | 2 | 1 | no | — |
| 176 | #137 | — | 6 | 2 | no | — |
| 177 | #137 | — | 12 | 1 | no | — |
| 178 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 179 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 180 | #135 | — | 6 | 1 | no | — |
| 181 | #135 | — | 6 | 1 | no | — |
| 182 | #135 | — | 6 | 1 | no | — |
| 183 | #135 | — | 6 | 1 | no | — |
| 184 | #135 | — | 12 | 2 | no | — |
| 185 | C2×Q16 | — | 3 | 1 | no | — |
| 186 | C2×SD16 | — | 6 | 1 | no | — |
| 187 | C2×D8 | — | 2 | 1 | no | — |
| 188 | C2×D8 | — | 2 | 1 | no | — |
| 189 | C2×D8 | — | 2 | 1 | no | — |
| 190 | C2×D8 | — | 2 | 1 | no | — |
| 191 | C2×D8 | — | 2 | 1 | no | — |
| 192 | C2×D8 | — | 3 | 1 | no | — |
| 193 | C2×D8 | D12 | 1 | 2 | yes | — |
| 194 | #131 | — | 6 | 1 | no | — |
| 195 | #131 | — | 6 | 1 | no | — |
| 196 | #131 | — | 6 | 1 | no | — |
| 197 | #131 | — | 6 | 1 | no | — |
| 198 | C2×M16 | — | 2 | 1 | no | — |
| 199 | C2×M16 | — | 3 | 1 | no | — |
| 200 | C2×M16 | — | 6 | 1 | no | — |
| 201 | C22×C8 | — | 6 | 1 | no | — |
| 202 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 203 | #127 | — | 12 | 1 | no | — |
| 204 | #124 | — | 12 | 1 | no | — |
| 205 | #121 | — | 6 | 4 | no | — |
| 206 | #120 | — | 12 | 2 | no | — |
| 207 | #117 | — | 6 | 1 | no | — |
| 208 | SD32 | — | 6 | 4 | no | — |
| 209 | D16 | — | 6 | 4 | no | — |
| 210 | M32 | — | 2 | 1 | no | — |
| 211 | M32 | — | 2 | 1 | no | — |
| 212 | M32 | — | 3 | 2 | no | — |
| 213 | M32 | — | 6 | 1 | no | — |
| 214 | C2×C16 | — | 2 | 1 | no | — |
| 215 | C2×C16 | — | 6 | 1 | no | — |
| 216 | #108 | — | 2 | 1 | no | — |
| 217 | #108 | #67 | 1 | 2 | yes | complemented |
| 218 | #107 | — | 6 | 1 | no | — |
| 219 | #106 | — | 3 | 2 | no | — |
| 220 | #102 | — | 6 | 4 | no | — |
| 221 | #101 | — | 6 | 2 | no | — |
| 222 | #100 | — | 6 | 2 | no | — |
| 223 | C23×C3 | — | 4 | 2 | no | — |
| 224 | C23×C3 | — | 8 | 1 | no | — |
| 225 | C23×C3 | — | 8 | 1 | no | — |
| 226 | C23×C3 | — | 16 | 2 | no | — |
| 227 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 228 | C22×D3 | — | 2 | 1 | no | — |
| 229 | C22×D3 | — | 4 | 1 | no | — |
| 230 | C3×D4 | — | 4 | 2 | no | — |
| 231 | C3×D4 | — | 4 | 2 | no | — |
| 232 | C3×D4 | — | 8 | 1 | no | — |
| 233 | C3×D4 | — | 8 | 1 | no | — |
| 234 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 235 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 236 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 237 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 238 | C2×C3×C4 | #135 | 1 | 1 | yes | characteristic |
| 239 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 240 | #67 | — | 4 | 1 | no | — |
| 241 | #67 | — | 4 | 1 | no | — |
| 242 | #67 | — | 8 | 1 | no | — |
| 243 | #67 | — | 8 | 1 | no | — |
| 244 | #67 | — | 16 | 4 | no | — |
| 245 | C2×Dic3 | — | 2 | 1 | no | — |
| 246 | C2×Dic3 | — | 4 | 2 | no | — |
| 247 | C2×Dic3 | — | 4 | 1 | no | — |
| 248 | D12 | — | 2 | 1 | no | — |
| 249 | D12 | — | 2 | 1 | no | — |
| 250 | D12 | — | 4 | 1 | no | — |
| 251 | D12 | — | 4 | 1 | no | — |
| 252 | C4×D3 | — | 4 | 1 | no | — |
| 253 | C4×D3 | — | 4 | 1 | no | — |
| 254 | C4×D3 | — | 8 | 1 | no | — |
| 255 | C4×D3 | — | 8 | 1 | no | — |
| 256 | Dic6 | — | 2 | 1 | no | — |
| 257 | Dic6 | — | 2 | 1 | no | — |
| 258 | Dic6 | — | 4 | 1 | no | — |
| 259 | Dic6 | — | 4 | 1 | no | — |
| 260 | C3×C8 | — | 4 | 2 | no | — |
| 261 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 262 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 263 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 264 | C3×C8 | #127 | 1 | 1 | yes | characteristic |
| 265 | C3⋊C8 | — | 4 | 1 | no | — |
| 266 | C24 | — | 4 | 1 | no | — |
| 267 | #41 | — | 6 | 1 | no | — |
| 268 | #41 | — | 6 | 1 | no | — |
| 269 | #41 | — | 6 | 1 | no | — |
| 270 | #41 | — | 6 | 1 | no | — |
| 271 | #41 | — | 12 | 1 | no | — |
| 272 | #41 | — | 12 | 1 | no | — |
| 273 | #41 | — | 12 | 1 | no | — |
| 274 | #41 | — | 12 | 1 | no | — |
| 275 | C2×Q8 | — | 3 | 1 | no | — |
| 276 | C2×Q8 | — | 6 | 1 | no | — |
| 277 | C2×D4 | — | 2 | 2 | no | — |
| 278 | C2×D4 | — | 3 | 1 | no | — |
| 279 | C2×D4 | — | 4 | 1 | no | — |
| 280 | C2×D4 | — | 4 | 1 | no | — |
| 281 | C2×D4 | — | 4 | 1 | no | — |
| 282 | C2×D4 | — | 4 | 1 | no | — |
| 283 | C2×D4 | — | 4 | 1 | no | — |
| 284 | C2×D4 | — | 6 | 1 | no | — |
| 285 | C2×D4 | — | 6 | 1 | no | — |
| 286 | C2×D4 | — | 12 | 1 | no | — |
| 287 | C2×D4 | — | 12 | 4 | no | — |
| 288 | C22×C4 | — | 6 | 1 | no | — |
| 289 | C22×C4 | — | 12 | 1 | no | — |
| 290 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 291 | Q16 | — | 6 | 1 | no | — |
| 292 | Q16 | — | 6 | 1 | no | — |
| 293 | Q16 | — | 12 | 2 | no | — |
| 294 | SD16 | — | 12 | 2 | no | — |
| 295 | SD16 | — | 12 | 2 | no | — |
| 296 | SD16 | — | 12 | 1 | no | — |
| 297 | SD16 | — | 12 | 1 | no | — |
| 298 | D8 | — | 2 | 2 | no | — |
| 299 | D8 | — | 2 | 2 | no | — |
| 300 | D8 | — | 4 | 1 | no | — |
| 301 | D8 | — | 4 | 1 | no | — |
| 302 | D8 | — | 6 | 1 | no | — |
| 303 | D8 | — | 6 | 1 | no | — |
| 304 | D8 | — | 12 | 2 | no | — |
| 305 | M16 | — | 2 | 2 | no | — |
| 306 | M16 | — | 4 | 1 | no | — |
| 307 | M16 | — | 6 | 1 | no | — |
| 308 | M16 | — | 6 | 1 | no | — |
| 309 | M16 | — | 12 | 1 | no | — |
| 310 | M16 | — | 12 | 1 | no | — |
| 311 | C2×C8 | — | 4 | 1 | no | — |
| 312 | C2×C8 | — | 6 | 1 | no | — |
| 313 | C2×C8 | — | 12 | 1 | no | — |
| 314 | C2×C8 | — | 12 | 1 | no | — |
| 315 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 316 | C2×C8 | #235 | 1 | 1 | yes | characteristic |
| 317 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 318 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 319 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 320 | C2×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 321 | C4⋊C4 | — | 6 | 2 | no | — |
| 322 | C22⋊C4 | — | 12 | 4 | no | — |
| 323 | C22⋊C4 | — | 12 | 1 | no | — |
| 324 | C42 | — | 12 | 1 | no | — |
| 325 | C16 | — | 4 | 1 | no | — |
| 326 | C16 | — | 6 | 2 | no | — |
| 327 | C22×C3 | — | 4 | 1 | no | — |
| 328 | C22×C3 | — | 8 | 4 | no | — |
| 329 | C22×C3 | — | 8 | 2 | no | — |
| 330 | C22×C3 | — | 16 | 2 | no | — |
| 331 | C22×C3 | — | 16 | 2 | no | — |
| 332 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 333 | C22×C3 | #449 | 1 | 1 | yes | characteristic |
| 334 | C22×C3 | #469 | 1 | 1 | yes | characteristic |
| 335 | C2×D3 | — | 4 | 2 | no | — |
| 336 | C2×D3 | — | 4 | 1 | no | — |
| 337 | C2×D3 | — | 8 | 1 | no | — |
| 338 | C2×D3 | — | 16 | 1 | no | — |
| 339 | C3×C4 | #392 | 1 | 1 | yes | characteristic |
| 340 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 341 | C3×C4 | #449 | 1 | 1 | yes | characteristic |
| 342 | C3×C4 | #466 | 1 | 1 | yes | characteristic |
| 343 | Dic3 | — | 4 | 1 | no | — |
| 344 | Dic3 | — | 8 | 2 | no | — |
| 345 | Dic3 | — | 8 | 1 | no | — |
| 346 | C23 | — | 4 | 2 | no | — |
| 347 | C23 | — | 6 | 1 | no | — |
| 348 | C23 | — | 8 | 1 | no | — |
| 349 | C23 | — | 8 | 1 | no | — |
| 350 | C23 | — | 12 | 1 | no | — |
| 351 | C23 | — | 16 | 2 | no | — |
| 352 | C23 | #914 | 1 | 1 | yes | characteristic |
| 353 | Q8 | — | 6 | 1 | no | — |
| 354 | Q8 | — | 6 | 1 | no | — |
| 355 | Q8 | — | 12 | 1 | no | — |
| 356 | Q8 | — | 12 | 1 | no | — |
| 357 | D4 | — | 4 | 2 | no | — |
| 358 | D4 | — | 4 | 2 | no | — |
| 359 | D4 | — | 6 | 1 | no | — |
| 360 | D4 | — | 6 | 1 | no | — |
| 361 | D4 | — | 8 | 1 | no | — |
| 362 | D4 | — | 8 | 1 | no | — |
| 363 | D4 | — | 12 | 1 | no | — |
| 364 | D4 | — | 12 | 1 | no | — |
| 365 | D4 | — | 12 | 1 | no | — |
| 366 | D4 | — | 12 | 1 | no | — |
| 367 | D4 | — | 24 | 1 | no | — |
| 368 | D4 | — | 24 | 1 | no | — |
| 369 | D4 | — | 48 | 4 | no | — |
| 370 | C2×C4 | — | 6 | 1 | no | — |
| 371 | C2×C4 | — | 12 | 1 | no | — |
| 372 | C2×C4 | — | 12 | 1 | no | — |
| 373 | C2×C4 | — | 12 | 1 | no | — |
| 374 | C2×C4 | — | 12 | 2 | no | — |
| 375 | C2×C4 | — | 24 | 1 | no | — |
| 376 | C2×C4 | — | 24 | 1 | no | — |
| 377 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | #884 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | #911 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #916 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | #937 | 1 | 1 | yes | characteristic |
| 383 | C8 | — | 4 | 2 | no | — |
| 384 | C8 | — | 12 | 1 | no | — |
| 385 | C8 | #882 | 1 | 1 | yes | characteristic |
| 386 | C8 | #884 | 1 | 1 | yes | characteristic |
| 387 | C8 | #930 | 1 | 1 | yes | characteristic |
| 388 | C8 | #940 | 1 | 1 | yes | characteristic |
| 389 | C2×C3 | — | 2 | 1 | no | — |
| 390 | C2×C3 | — | 2 | 1 | no | — |
| 391 | C2×C3 | — | 2 | 1 | no | — |
| 392 | C2×C3 | — | 16 | 2 | no | — |
| 393 | C2×C3 | #1999 | 1 | 1 | yes | characteristic |
| 394 | D3 | — | 8 | 1 | no | — |
| 395 | D3 | — | 16 | 1 | no | — |
| 396 | C22 | — | 4 | 1 | no | — |
| 397 | C22 | — | 8 | 4 | no | — |
| 398 | C22 | — | 8 | 2 | no | — |
| 399 | C22 | — | 12 | 2 | no | — |
| 400 | C22 | — | 12 | 1 | no | — |
| 401 | C22 | — | 16 | 2 | no | — |
| 402 | C22 | — | 16 | 2 | no | — |
| 403 | C22 | — | 24 | 1 | no | — |
| 404 | C22 | — | 48 | 1 | no | — |
| 405 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 406 | C22 | #4782 | 1 | 1 | yes | characteristic |
| 407 | C22 | #5172 | 1 | 1 | yes | characteristic |
| 408 | C4 | — | 12 | 1 | no | — |
| 409 | C4 | — | 24 | 2 | no | — |
| 410 | C4 | — | 24 | 1 | no | — |
| 411 | C4 | #4775 | 1 | 1 | yes | characteristic |
| 412 | C4 | #4781 | 1 | 1 | yes | characteristic |
| 413 | C4 | #4960 | 1 | 1 | yes | characteristic |
| 414 | C4 | #5156 | 1 | 1 | yes | characteristic |
| 415 | C3 | #13310 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 416 | C2 | — | 2 | 1 | no | — |
| 417 | C2 | — | 2 | 1 | no | — |
| 418 | C2 | — | 2 | 1 | no | — |
| 419 | C2 | — | 16 | 2 | no | — |
| 420 | C2 | — | 24 | 1 | no | — |
| 421 | C2 | — | 48 | 1 | no | — |
| 422 | C2 | #70204 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #83836 | C2 | semidirect |
| 2. C2×#5147 | C2 | semidirect |
| 3. #79256 | C2 | semidirect |
| 4. C2×C3×#361 | C2 | semidirect |
| 5. #71450 | C2 | semidirect |
| 6. #71437 | C2 | semidirect |
| 7. #67735 | C2 | semidirect |
| 35. C2×#361 | D3 | semidirect |
| 60. C2×Dic12 | D4 | semidirect |
| 66. C2×D24 | D4 | semidirect |
| 78. C3×#108 | D4 | semidirect |
| 87. #812 | D4 | semidirect |
| 217. #108 | #67 | semidirect |
| 415. C3 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83836 | 2 |
| C2×#5147 | 2 |
| #79256 | 2 |
| C2×C3×#361 | 2 |
| #71450 | 2 |
| #71437 | 2 |
| #67735 | 2 |
| #13310 | 3 |