Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 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 | #82009 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #79256 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #71437 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#4488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#1383 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13318 | — | 3 | 1 | no | maximal, Sylow |
| 9 | #5748 | — | 2 | 1 | no | — |
| 10 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 13 | #5510 | — | 2 | 1 | no | — |
| 14 | C2×C3×M32 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#108 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×C3×#106 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5132 | — | 2 | 1 | no | — |
| 18 | C2×#812 | C22 | 1 | 1 | yes | characteristic |
| 19 | #4966 | — | 2 | 1 | no | — |
| 20 | #4909 | — | 2 | 1 | no | — |
| 21 | #4909 | — | 2 | 1 | no | — |
| 22 | #4908 | — | 2 | 1 | no | — |
| 23 | #4908 | — | 2 | 1 | no | — |
| 24 | #4904 | — | 2 | 2 | no | — |
| 25 | #4898 | — | 2 | 2 | no | — |
| 26 | #4897 | — | 2 | 1 | no | — |
| 27 | #4896 | — | 2 | 1 | no | — |
| 28 | #4867 | — | 2 | 1 | no | — |
| 29 | #4865 | — | 2 | 1 | no | — |
| 30 | #4864 | — | 2 | 2 | no | — |
| 31 | #4508 | — | 2 | 2 | no | — |
| 32 | #4497 | — | 2 | 2 | no | — |
| 33 | #4488 | — | 2 | 2 | no | — |
| 34 | #3414 | — | 3 | 1 | no | — |
| 35 | #3067 | — | 3 | 1 | no | — |
| 36 | #3060 | — | 3 | 1 | no | — |
| 37 | C2×#360 | — | 3 | 1 | no | — |
| 38 | #2143 | — | 3 | 1 | no | — |
| 39 | #2117 | — | 3 | 1 | no | — |
| 40 | #1383 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#235 | — | 2 | 1 | no | — |
| 42 | C2×#235 | — | 2 | 1 | no | — |
| 43 | C2×#235 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×C3×M16 | — | 2 | 1 | no | — |
| 45 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 47 | #930 | — | 4 | 2 | no | — |
| 48 | C2×#208 | D4 | 1 | 1 | yes | characteristic |
| 49 | #909 | — | 2 | 2 | no | — |
| 50 | #909 | — | 4 | 1 | no | — |
| 51 | #908 | — | 2 | 2 | no | — |
| 52 | #908 | — | 4 | 1 | no | — |
| 53 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 55 | #904 | — | 2 | 1 | no | — |
| 56 | #904 | — | 2 | 1 | no | — |
| 57 | #904 | — | 2 | 1 | no | — |
| 58 | #904 | — | 2 | 1 | no | — |
| 59 | #904 | — | 2 | 1 | no | — |
| 60 | #904 | — | 2 | 1 | no | — |
| 61 | #904 | — | 2 | 1 | no | — |
| 62 | #904 | — | 2 | 1 | no | — |
| 63 | #904 | — | 4 | 2 | no | — |
| 64 | C2×D24 | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×D24 | D4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×#204 | — | 2 | 1 | no | — |
| 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 | #897 | — | 2 | 2 | no | — |
| 75 | #897 | — | 4 | 1 | no | — |
| 76 | #895 | — | 2 | 2 | no | — |
| 77 | #895 | — | 4 | 1 | no | — |
| 78 | C3×M32 | — | 2 | 1 | no | — |
| 79 | C3×M32 | — | 2 | 1 | no | — |
| 80 | C2×C3×C16 | D4 | 1 | 2 | yes | complemented |
| 81 | C3×#108 | — | 2 | 1 | no | — |
| 82 | C3×#108 | D4 | 1 | 2 | yes | complemented |
| 83 | C3×#106 | — | 2 | 1 | no | — |
| 84 | C3×#106 | D4 | 1 | 2 | yes | — |
| 85 | #824 | — | 2 | 2 | no | — |
| 86 | #823 | — | 2 | 2 | no | — |
| 87 | #812 | — | 2 | 1 | no | — |
| 88 | #812 | — | 2 | 1 | no | — |
| 89 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 90 | #810 | — | 2 | 2 | no | — |
| 91 | #809 | — | 2 | 2 | no | — |
| 92 | Dic24 | — | 2 | 2 | no | — |
| 93 | #800 | — | 2 | 2 | no | — |
| 94 | #800 | — | 2 | 2 | no | — |
| 95 | D48 | — | 2 | 2 | no | — |
| 96 | #575 | — | 6 | 1 | no | — |
| 97 | C2×#135 | — | 3 | 1 | no | — |
| 98 | C2×#135 | — | 3 | 1 | no | — |
| 99 | C2×#131 | — | 3 | 1 | no | — |
| 100 | #537 | — | 6 | 1 | no | — |
| 101 | #510 | — | 6 | 1 | no | — |
| 102 | #510 | — | 6 | 1 | no | — |
| 103 | #509 | — | 6 | 1 | no | — |
| 104 | #509 | — | 6 | 1 | no | — |
| 105 | #508 | — | 6 | 2 | no | — |
| 106 | C2×M32 | — | 3 | 1 | no | — |
| 107 | C2×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 108 | #473 | — | 6 | 1 | no | — |
| 109 | #472 | — | 6 | 1 | no | — |
| 110 | #471 | — | 6 | 2 | no | — |
| 111 | #470 | — | 6 | 1 | no | — |
| 112 | #469 | — | 6 | 1 | no | — |
| 113 | #465 | — | 6 | 2 | no | — |
| 114 | C2×#108 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | C2×#106 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | #417 | — | 6 | 1 | no | — |
| 117 | #413 | — | 6 | 1 | no | — |
| 118 | #360 | — | 6 | 2 | no | — |
| 119 | #359 | — | 6 | 2 | no | — |
| 120 | #350 | — | 6 | 2 | no | — |
| 121 | C22×C3×C4 | — | 4 | 1 | no | — |
| 122 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×#67 | — | 2 | 1 | no | — |
| 124 | C2×#67 | — | 4 | 1 | no | — |
| 125 | C2×#67 | — | 4 | 1 | no | — |
| 126 | #235 | — | 2 | 1 | no | — |
| 127 | #235 | — | 2 | 1 | no | — |
| 128 | #235 | — | 2 | 1 | no | — |
| 129 | #235 | — | 2 | 1 | no | — |
| 130 | #235 | — | 4 | 1 | no | — |
| 131 | #235 | — | 4 | 1 | no | — |
| 132 | #235 | — | 4 | 1 | no | — |
| 133 | #235 | — | 4 | 1 | no | — |
| 134 | #235 | — | 4 | 1 | no | — |
| 135 | #235 | — | 4 | 1 | no | — |
| 136 | #235 | — | 4 | 1 | no | — |
| 137 | #235 | — | 4 | 1 | no | — |
| 138 | C2×D12 | — | 2 | 1 | no | — |
| 139 | C2×D12 | — | 2 | 1 | no | — |
| 140 | C2×D12 | — | 4 | 2 | no | — |
| 141 | C2×D12 | D8 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×D3 | — | 2 | 1 | no | — |
| 143 | C2×C4×D3 | — | 4 | 1 | no | — |
| 144 | C2×C4×D3 | — | 4 | 1 | no | — |
| 145 | C2×Dic6 | — | 2 | 1 | no | — |
| 146 | C2×Dic6 | — | 2 | 1 | no | — |
| 147 | C2×Dic6 | D8 | 1 | 1 | yes | characteristic |
| 148 | C3×M16 | — | 2 | 2 | no | — |
| 149 | C3×M16 | — | 4 | 1 | no | — |
| 150 | C2×C3×C8 | — | 4 | 1 | no | — |
| 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 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×C3×C8 | #41 | 1 | 1 | yes | characteristic |
| 157 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 158 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 159 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 160 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 161 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 162 | #208 | — | 2 | 1 | no | — |
| 163 | #208 | — | 2 | 1 | no | — |
| 164 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 165 | Dic12 | — | 2 | 1 | no | — |
| 166 | Dic12 | — | 2 | 1 | no | — |
| 167 | Dic12 | — | 2 | 1 | no | — |
| 168 | Dic12 | — | 2 | 1 | no | — |
| 169 | Dic12 | — | 4 | 2 | no | — |
| 170 | D24 | — | 2 | 1 | no | — |
| 171 | D24 | — | 2 | 1 | no | — |
| 172 | D24 | — | 2 | 1 | no | — |
| 173 | D24 | — | 2 | 1 | no | — |
| 174 | D24 | — | 4 | 2 | no | — |
| 175 | #204 | — | 4 | 2 | no | — |
| 176 | #204 | — | 4 | 2 | no | — |
| 177 | #204 | — | 4 | 1 | no | — |
| 178 | #204 | — | 4 | 1 | no | — |
| 179 | #204 | — | 4 | 1 | no | — |
| 180 | #204 | — | 4 | 1 | no | — |
| 181 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 182 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 183 | D3×C8 | — | 4 | 1 | no | — |
| 184 | D3×C8 | — | 4 | 1 | no | — |
| 185 | C3×C16 | — | 2 | 2 | no | — |
| 186 | C3⋊C16 | — | 4 | 1 | no | — |
| 187 | C2×#41 | — | 3 | 1 | no | — |
| 188 | C2×#41 | — | 6 | 1 | no | — |
| 189 | C2×#41 | — | 6 | 1 | no | — |
| 190 | #137 | — | 6 | 2 | no | — |
| 191 | #137 | — | 12 | 1 | no | — |
| 192 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 193 | AGL(1,ℤ/8) | — | 12 | 1 | no | — |
| 194 | #135 | — | 6 | 1 | no | — |
| 195 | #135 | — | 6 | 1 | no | — |
| 196 | #135 | — | 6 | 1 | no | — |
| 197 | #135 | — | 6 | 1 | no | — |
| 198 | #135 | — | 6 | 1 | no | — |
| 199 | #135 | — | 6 | 1 | no | — |
| 200 | #135 | — | 6 | 1 | no | — |
| 201 | #135 | — | 6 | 1 | no | — |
| 202 | #135 | — | 12 | 2 | no | — |
| 203 | C2×Q16 | — | 3 | 1 | no | — |
| 204 | C2×Q16 | — | 3 | 1 | no | — |
| 205 | C2×SD16 | — | 6 | 1 | no | — |
| 206 | C2×SD16 | — | 6 | 1 | no | — |
| 207 | C2×D8 | — | 3 | 1 | no | — |
| 208 | C2×D8 | — | 3 | 1 | no | — |
| 209 | #131 | — | 6 | 1 | no | — |
| 210 | #131 | — | 6 | 1 | no | — |
| 211 | #131 | — | 6 | 1 | no | — |
| 212 | #131 | — | 6 | 1 | no | — |
| 213 | C2×M16 | — | 2 | 1 | no | — |
| 214 | C2×M16 | — | 3 | 1 | no | — |
| 215 | C2×M16 | — | 6 | 1 | no | — |
| 216 | C22×C8 | — | 6 | 1 | no | — |
| 217 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | C22⋊Q8 | — | 6 | 2 | no | — |
| 219 | C22⋊Q8 | — | 12 | 1 | no | — |
| 220 | #121 | — | 6 | 2 | no | — |
| 221 | #121 | — | 12 | 1 | no | — |
| 222 | #121 | — | 12 | 2 | no | — |
| 223 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 224 | Q32 | — | 6 | 2 | no | — |
| 225 | SD32 | — | 6 | 2 | no | — |
| 226 | SD32 | — | 6 | 2 | no | — |
| 227 | D16 | — | 6 | 2 | no | — |
| 228 | M32 | — | 2 | 1 | no | — |
| 229 | M32 | — | 2 | 1 | no | — |
| 230 | M32 | — | 6 | 1 | no | — |
| 231 | M32 | — | 6 | 1 | no | — |
| 232 | C2×C16 | — | 6 | 1 | no | — |
| 233 | C2×C16 | D12 | 1 | 2 | yes | complemented |
| 234 | #108 | — | 2 | 1 | no | — |
| 235 | #108 | D12 | 1 | 2 | yes | complemented |
| 236 | #106 | — | 2 | 1 | no | — |
| 237 | #106 | D12 | 1 | 2 | yes | — |
| 238 | #103 | — | 6 | 2 | no | — |
| 239 | #102 | — | 6 | 2 | no | — |
| 240 | #101 | — | 6 | 2 | no | — |
| 241 | #100 | — | 6 | 2 | no | — |
| 242 | C23×C3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 243 | C22×D3 | — | 2 | 1 | no | — |
| 244 | C22×D3 | — | 4 | 1 | no | — |
| 245 | C22×D3 | — | 4 | 1 | no | — |
| 246 | C2×C3×C4 | — | 4 | 2 | no | — |
| 247 | C2×C3×C4 | — | 16 | 1 | no | — |
| 248 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 249 | C2×C3×C4 | #120 | 1 | 1 | yes | characteristic |
| 250 | C2×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 251 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 252 | C2×C3×C4 | #135 | 1 | 1 | yes | characteristic |
| 253 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 254 | #67 | — | 4 | 1 | no | — |
| 255 | #67 | — | 4 | 1 | no | — |
| 256 | #67 | — | 8 | 1 | no | — |
| 257 | #67 | — | 8 | 1 | no | — |
| 258 | #67 | — | 8 | 1 | no | — |
| 259 | #67 | — | 8 | 1 | no | — |
| 260 | C2×Dic3 | — | 2 | 1 | no | — |
| 261 | C2×Dic3 | — | 4 | 1 | no | — |
| 262 | C2×Dic3 | — | 4 | 1 | no | — |
| 263 | D12 | — | 2 | 1 | no | — |
| 264 | D12 | — | 2 | 1 | no | — |
| 265 | D12 | — | 4 | 1 | no | — |
| 266 | D12 | — | 4 | 1 | no | — |
| 267 | D12 | — | 4 | 1 | no | — |
| 268 | D12 | — | 4 | 1 | no | — |
| 269 | D12 | — | 16 | 2 | no | — |
| 270 | C4×D3 | — | 4 | 1 | no | — |
| 271 | C4×D3 | — | 4 | 1 | no | — |
| 272 | C4×D3 | — | 8 | 1 | no | — |
| 273 | C4×D3 | — | 8 | 1 | no | — |
| 274 | C4×D3 | — | 8 | 1 | no | — |
| 275 | C4×D3 | — | 8 | 1 | no | — |
| 276 | Dic6 | — | 2 | 1 | no | — |
| 277 | Dic6 | — | 2 | 1 | no | — |
| 278 | Dic6 | — | 4 | 1 | no | — |
| 279 | Dic6 | — | 4 | 1 | no | — |
| 280 | Dic6 | — | 4 | 1 | no | — |
| 281 | Dic6 | — | 4 | 1 | no | — |
| 282 | C3×C8 | — | 4 | 2 | no | — |
| 283 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 284 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 285 | C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 286 | C3×C8 | #127 | 1 | 1 | yes | characteristic |
| 287 | C3⋊C8 | — | 4 | 1 | no | — |
| 288 | #41 | — | 6 | 1 | no | — |
| 289 | #41 | — | 6 | 1 | no | — |
| 290 | #41 | — | 6 | 1 | no | — |
| 291 | #41 | — | 6 | 1 | no | — |
| 292 | #41 | — | 12 | 1 | no | — |
| 293 | #41 | — | 12 | 1 | no | — |
| 294 | #41 | — | 12 | 1 | no | — |
| 295 | #41 | — | 12 | 1 | no | — |
| 296 | #41 | — | 12 | 1 | no | — |
| 297 | #41 | — | 12 | 1 | no | — |
| 298 | #41 | — | 12 | 1 | no | — |
| 299 | #41 | — | 12 | 1 | no | — |
| 300 | C2×Q8 | — | 3 | 1 | no | — |
| 301 | C2×Q8 | — | 6 | 1 | no | — |
| 302 | C2×Q8 | — | 6 | 1 | no | — |
| 303 | C2×D4 | — | 3 | 1 | no | — |
| 304 | C2×D4 | — | 6 | 1 | no | — |
| 305 | C2×D4 | — | 6 | 1 | no | — |
| 306 | C2×D4 | — | 6 | 1 | no | — |
| 307 | C2×D4 | — | 12 | 2 | no | — |
| 308 | C2×D4 | — | 12 | 1 | no | — |
| 309 | C2×D4 | — | 12 | 1 | no | — |
| 310 | C22×C4 | — | 4 | 1 | no | — |
| 311 | C22×C4 | — | 6 | 1 | no | — |
| 312 | C22×C4 | — | 12 | 1 | no | — |
| 313 | C22×C4 | — | 12 | 1 | no | — |
| 314 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 315 | Q16 | — | 6 | 1 | no | — |
| 316 | Q16 | — | 6 | 1 | no | — |
| 317 | Q16 | — | 6 | 1 | no | — |
| 318 | Q16 | — | 6 | 1 | no | — |
| 319 | Q16 | — | 12 | 2 | no | — |
| 320 | SD16 | — | 12 | 2 | no | — |
| 321 | SD16 | — | 12 | 2 | no | — |
| 322 | SD16 | — | 12 | 1 | no | — |
| 323 | SD16 | — | 12 | 1 | no | — |
| 324 | SD16 | — | 12 | 1 | no | — |
| 325 | SD16 | — | 12 | 1 | no | — |
| 326 | D8 | — | 6 | 1 | no | — |
| 327 | D8 | — | 6 | 1 | no | — |
| 328 | D8 | — | 6 | 1 | no | — |
| 329 | D8 | — | 6 | 1 | no | — |
| 330 | D8 | — | 12 | 2 | no | — |
| 331 | M16 | — | 2 | 2 | no | — |
| 332 | M16 | — | 4 | 1 | no | — |
| 333 | M16 | — | 6 | 1 | no | — |
| 334 | M16 | — | 6 | 1 | no | — |
| 335 | M16 | — | 12 | 1 | no | — |
| 336 | M16 | — | 12 | 1 | no | — |
| 337 | C2×C8 | — | 4 | 1 | no | — |
| 338 | C2×C8 | — | 6 | 1 | no | — |
| 339 | C2×C8 | — | 12 | 1 | no | — |
| 340 | C2×C8 | — | 12 | 1 | no | — |
| 341 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 342 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 343 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 344 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 345 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×C8 | #239 | 1 | 1 | yes | characteristic |
| 347 | C4⋊C4 | — | 2 | 2 | no | — |
| 348 | C4⋊C4 | — | 4 | 1 | no | — |
| 349 | C4⋊C4 | — | 12 | 2 | no | — |
| 350 | C22⋊C4 | — | 12 | 2 | no | — |
| 351 | C22⋊C4 | — | 12 | 2 | no | — |
| 352 | C16 | — | 2 | 2 | no | — |
| 353 | C16 | — | 12 | 1 | no | — |
| 354 | C22×C3 | — | 4 | 1 | no | — |
| 355 | C22×C3 | #447 | 1 | 1 | yes | characteristic |
| 356 | C22×C3 | #449 | 1 | 1 | yes | characteristic |
| 357 | C22×C3 | #469 | 1 | 1 | yes | characteristic |
| 358 | C2×D3 | — | 4 | 2 | no | — |
| 359 | C2×D3 | — | 4 | 1 | no | — |
| 360 | C2×D3 | — | 8 | 1 | no | — |
| 361 | C2×D3 | — | 8 | 1 | no | — |
| 362 | C2×D3 | — | 8 | 1 | no | — |
| 363 | C2×D3 | — | 8 | 1 | no | — |
| 364 | C2×D3 | — | 16 | 1 | no | — |
| 365 | C3×C4 | — | 8 | 2 | no | — |
| 366 | C3×C4 | #392 | 1 | 1 | yes | characteristic |
| 367 | C3×C4 | #447 | 1 | 1 | yes | characteristic |
| 368 | C3×C4 | #449 | 1 | 1 | yes | characteristic |
| 369 | C3×C4 | #466 | 1 | 1 | yes | characteristic |
| 370 | Dic3 | — | 4 | 1 | no | — |
| 371 | Dic3 | — | 8 | 1 | no | — |
| 372 | Dic3 | — | 8 | 1 | no | — |
| 373 | C23 | — | 6 | 1 | no | — |
| 374 | C23 | — | 12 | 1 | no | — |
| 375 | C23 | — | 12 | 1 | no | — |
| 376 | C23 | #914 | 1 | 1 | yes | characteristic |
| 377 | Q8 | — | 6 | 1 | no | — |
| 378 | Q8 | — | 6 | 1 | no | — |
| 379 | Q8 | — | 12 | 1 | no | — |
| 380 | Q8 | — | 12 | 1 | no | — |
| 381 | Q8 | — | 12 | 1 | no | — |
| 382 | Q8 | — | 12 | 1 | no | — |
| 383 | D4 | — | 6 | 1 | no | — |
| 384 | D4 | — | 6 | 1 | no | — |
| 385 | D4 | — | 12 | 1 | no | — |
| 386 | D4 | — | 12 | 1 | no | — |
| 387 | D4 | — | 12 | 1 | no | — |
| 388 | D4 | — | 12 | 1 | no | — |
| 389 | D4 | — | 12 | 1 | no | — |
| 390 | D4 | — | 12 | 1 | no | — |
| 391 | D4 | — | 24 | 1 | no | — |
| 392 | D4 | — | 24 | 1 | no | — |
| 393 | D4 | — | 24 | 1 | no | — |
| 394 | D4 | — | 24 | 1 | no | — |
| 395 | D4 | — | 48 | 2 | no | — |
| 396 | C2×C4 | — | 4 | 2 | no | — |
| 397 | C2×C4 | — | 6 | 1 | no | — |
| 398 | C2×C4 | — | 12 | 1 | no | — |
| 399 | C2×C4 | — | 12 | 1 | no | — |
| 400 | C2×C4 | — | 12 | 1 | no | — |
| 401 | C2×C4 | — | 12 | 1 | no | — |
| 402 | C2×C4 | — | 16 | 1 | no | — |
| 403 | C2×C4 | — | 24 | 1 | no | — |
| 404 | C2×C4 | — | 24 | 1 | no | — |
| 405 | C2×C4 | — | 24 | 1 | no | — |
| 406 | C2×C4 | — | 24 | 1 | no | — |
| 407 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 408 | C2×C4 | #882 | 1 | 1 | yes | characteristic |
| 409 | C2×C4 | #895 | 1 | 1 | yes | characteristic |
| 410 | C2×C4 | D3×D8 | 1 | 1 | yes | characteristic |
| 411 | C2×C4 | #914 | 1 | 1 | yes | characteristic |
| 412 | C2×C4 | #919 | 1 | 1 | yes | characteristic |
| 413 | C8 | — | 4 | 2 | no | — |
| 414 | C8 | — | 12 | 1 | no | — |
| 415 | C8 | #874 | 1 | 1 | yes | characteristic |
| 416 | C8 | #882 | 1 | 1 | yes | characteristic |
| 417 | C8 | #895 | 1 | 1 | yes | characteristic |
| 418 | C8 | #895 | 1 | 1 | yes | characteristic |
| 419 | C2×C3 | — | 2 | 1 | no | — |
| 420 | C2×C3 | — | 2 | 1 | no | — |
| 421 | C2×C3 | — | 2 | 1 | no | — |
| 422 | C2×C3 | #1999 | 1 | 1 | yes | characteristic |
| 423 | D3 | — | 8 | 1 | no | — |
| 424 | D3 | — | 16 | 1 | no | — |
| 425 | D3 | — | 16 | 1 | no | — |
| 426 | C22 | — | 4 | 1 | no | — |
| 427 | C22 | — | 12 | 2 | no | — |
| 428 | C22 | — | 12 | 1 | no | — |
| 429 | C22 | — | 24 | 1 | no | — |
| 430 | C22 | — | 24 | 1 | no | — |
| 431 | C22 | — | 24 | 1 | no | — |
| 432 | C22 | — | 24 | 1 | no | — |
| 433 | C22 | — | 48 | 1 | no | — |
| 434 | C22 | #4773 | 1 | 1 | yes | characteristic |
| 435 | C22 | #4810 | 1 | 1 | yes | characteristic |
| 436 | C22 | #4865 | 1 | 1 | yes | characteristic |
| 437 | C4 | — | 8 | 2 | no | — |
| 438 | C4 | — | 12 | 1 | no | — |
| 439 | C4 | — | 24 | 1 | no | — |
| 440 | C4 | — | 24 | 1 | no | — |
| 441 | C4 | #4671 | 1 | 1 | yes | characteristic |
| 442 | C4 | #4773 | 1 | 1 | yes | characteristic |
| 443 | C4 | #4810 | 1 | 1 | yes | characteristic |
| 444 | C4 | #4883 | 1 | 1 | yes | characteristic |
| 445 | C3 | #13318 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 446 | C2 | — | 2 | 1 | no | — |
| 447 | C2 | — | 2 | 1 | no | — |
| 448 | C2 | — | 2 | 1 | no | — |
| 449 | C2 | — | 24 | 1 | no | — |
| 450 | C2 | — | 48 | 1 | no | — |
| 451 | C2 | — | 48 | 1 | no | — |
| 452 | C2 | #68886 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #82009 | C2 | semidirect |
| 2. #79256 | C2 | semidirect |
| 3. #79120 | C2 | semidirect |
| 4. #71437 | C2 | semidirect |
| 5. #70690 | C2 | semidirect |
| 6. C2×#4488 | C2 | semidirect |
| 7. C3×#1383 | C2 | semidirect |
| 40. #1383 | D3 | semidirect |
| 54. C2×Dic12 | D4 | semidirect |
| 65. C2×D24 | D4 | semidirect |
| 80. C2×C3×C16 | D4 | semidirect |
| 82. C3×#108 | D4 | semidirect |
| 233. C2×C16 | D12 | semidirect |
| 235. #108 | D12 | semidirect |
| 445. C3 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #82009 | 2 |
| #79256 | 2 |
| #79120 | 2 |
| #71437 | 2 |
| #70690 | 2 |
| C2×#4488 | 2 |
| C3×#1383 | 2 |
| #13318 | 3 |