Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
961 conjugacy classes of subgroups.
The subgroup lattice has 579 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10595464 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10595444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10594723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10592523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4825 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591683 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10590988 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10590979 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590400 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10590389 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10590353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #80296 | — | 3 | 2 | no | maximal |
| 13 | C3×#1009 | C22 | 1 | 2 | yes | — |
| 14 | #64297 | C22 | 1 | 2 | yes | complemented |
| 15 | #64159 | C22 | 1 | 1 | yes | characteristic |
| 16 | #64157 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64116 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×#951 | C22 | 1 | 2 | yes | — |
| 19 | C3×#909 | C22 | 1 | 2 | yes | complemented |
| 20 | C3×#875 | C22 | 1 | 2 | yes | complemented |
| 21 | #63949 | — | 2 | 2 | no | — |
| 22 | #63943 | — | 2 | 2 | no | — |
| 23 | #63934 | — | 2 | 2 | no | — |
| 24 | D3×#214 | — | 2 | 2 | no | — |
| 25 | C2×#3718 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #63830 | C22 | 1 | 2 | yes | complemented |
| 27 | C2×#3715 | C22 | 1 | 2 | yes | complemented |
| 28 | #63823 | — | 2 | 2 | no | — |
| 29 | #63823 | C22 | 1 | 2 | yes | — |
| 30 | #63822 | — | 2 | 1 | no | — |
| 31 | #63822 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#3713 | — | 2 | 1 | no | — |
| 33 | C2×#3713 | C22 | 1 | 1 | yes | characteristic |
| 34 | #63815 | C22 | 1 | 2 | yes | complemented |
| 35 | #63811 | — | 2 | 2 | no | — |
| 36 | #63809 | — | 2 | 1 | no | — |
| 37 | #63802 | — | 2 | 1 | no | — |
| 38 | C32×#104 | C22 | 1 | 1 | yes | characteristic |
| 39 | #63649 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #63632 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×#823 | C22 | 1 | 2 | yes | complemented |
| 43 | C3×#805 | C22 | 1 | 2 | yes | complemented |
| 44 | #63578 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #63560 | C22 | 1 | 2 | yes | complemented |
| 46 | #5836 | — | 3 | 2 | no | — |
| 47 | #5835 | — | 3 | 2 | no | — |
| 48 | #5779 | — | 3 | 2 | no | — |
| 49 | #5778 | — | 3 | 2 | no | — |
| 50 | C3×#455 | — | 3 | 2 | no | — |
| 51 | #5204 | — | 3 | 2 | no | — |
| 52 | #5203 | — | 3 | 2 | no | — |
| 53 | #5062 | — | 3 | 2 | no | — |
| 54 | #5059 | — | 3 | 2 | no | — |
| 55 | #4827 | — | 3 | 2 | no | — |
| 56 | #4825 | D3 | 1 | 2 | yes | complemented |
| 57 | #4824 | — | 3 | 2 | no | — |
| 58 | #4824 | — | 3 | 2 | no | — |
| 59 | #4824 | — | 6 | 1 | no | — |
| 60 | #4749 | — | 3 | 2 | no | — |
| 61 | #4748 | — | 3 | 2 | no | — |
| 62 | C32×#41 | C23 | 1 | 1 | yes | characteristic |
| 63 | #3828 | C23 | 1 | 1 | yes | characteristic |
| 64 | C3×#239 | — | 2 | 2 | no | — |
| 65 | C3×D3×D4 | — | 2 | 2 | no | — |
| 66 | C3×D3×D4 | — | 4 | 2 | no | — |
| 67 | C3×#235 | — | 2 | 2 | no | — |
| 68 | C3×#235 | C23 | 1 | 2 | yes | — |
| 69 | C2×C3×D12 | — | 2 | 2 | no | — |
| 70 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 71 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 72 | #3804 | — | 4 | 2 | no | — |
| 73 | #3799 | — | 2 | 2 | no | — |
| 74 | #3797 | — | 2 | 2 | no | — |
| 75 | #3796 | — | 2 | 2 | no | — |
| 76 | D3×Dic6 | — | 2 | 2 | no | — |
| 77 | C32×M16 | C23 | 1 | 1 | yes | characteristic |
| 78 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 79 | #3756 | D4 | 1 | 1 | yes | characteristic |
| 80 | #3755 | D4 | 1 | 1 | yes | characteristic |
| 81 | #3754 | D4 | 1 | 1 | yes | characteristic |
| 82 | #3753 | D4 | 1 | 1 | yes | characteristic |
| 83 | #3748 | — | 2 | 1 | no | — |
| 84 | #3748 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 86 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 88 | #3743 | — | 2 | 1 | no | — |
| 89 | C8×C3⋊D3 | — | 2 | 1 | no | — |
| 90 | C3×#216 | — | 2 | 2 | no | — |
| 91 | C3×#214 | — | 2 | 2 | no | — |
| 92 | C3×(C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 93 | C3×#208 | C23 | 1 | 2 | yes | — |
| 94 | C3×Dic12 | — | 2 | 2 | no | — |
| 95 | C3×#204 | — | 2 | 2 | no | — |
| 96 | #3718 | — | 2 | 1 | no | — |
| 97 | #3718 | — | 2 | 1 | no | — |
| 98 | #3718 | D4 | 1 | 1 | yes | characteristic |
| 99 | #3716 | — | 2 | 2 | no | — |
| 100 | #3715 | — | 2 | 2 | no | — |
| 101 | #3715 | — | 2 | 2 | no | — |
| 102 | #3715 | — | 2 | 2 | no | — |
| 103 | #3715 | D4 | 1 | 2 | yes | — |
| 104 | #3714 | — | 2 | 2 | no | — |
| 105 | #3713 | — | 2 | 2 | no | — |
| 106 | #3713 | — | 2 | 1 | no | — |
| 107 | #3713 | — | 2 | 1 | no | — |
| 108 | #3713 | D4 | 1 | 1 | yes | characteristic |
| 109 | #3711 | — | 2 | 2 | no | — |
| 110 | D3×C3⋊C8 | — | 2 | 2 | no | — |
| 111 | #3290 | — | 9 | 1 | no | Sylow |
| 112 | C3×H(5,𝔽2) | — | 3 | 2 | no | — |
| 113 | #1010 | — | 3 | 2 | no | — |
| 114 | #1009 | C2×D3 | 1 | 2 | yes | — |
| 115 | #1007 | — | 3 | 2 | no | — |
| 116 | C3×#137 | — | 3 | 2 | no | — |
| 117 | C3×#137 | — | 3 | 2 | no | — |
| 118 | C3×#124 | — | 3 | 2 | no | — |
| 119 | #951 | — | 6 | 2 | no | — |
| 120 | #951 | C2×D3 | 1 | 2 | yes | — |
| 121 | #950 | — | 3 | 2 | no | — |
| 122 | #950 | — | 3 | 2 | no | — |
| 123 | #950 | — | 6 | 1 | no | — |
| 124 | #950 | — | 6 | 2 | no | — |
| 125 | #950 | — | 6 | 2 | no | — |
| 126 | #949 | — | 3 | 2 | no | — |
| 127 | #949 | — | 6 | 2 | no | — |
| 128 | #948 | — | 3 | 2 | no | — |
| 129 | #948 | — | 3 | 2 | no | — |
| 130 | #948 | — | 6 | 1 | no | — |
| 131 | C2×#216 | — | 3 | 2 | no | — |
| 132 | C2×#215 | — | 3 | 2 | no | — |
| 133 | C2×#214 | — | 3 | 2 | no | — |
| 134 | C2×#214 | — | 6 | 2 | no | — |
| 135 | #932 | — | 3 | 2 | no | — |
| 136 | #932 | — | 3 | 2 | no | — |
| 137 | #932 | — | 6 | 2 | no | — |
| 138 | #932 | — | 6 | 2 | no | — |
| 139 | C2×#213 | — | 3 | 2 | no | — |
| 140 | C2×#213 | — | 6 | 2 | no | — |
| 141 | #919 | — | 6 | 2 | no | — |
| 142 | #918 | — | 6 | 2 | no | — |
| 143 | #918 | — | 6 | 2 | no | — |
| 144 | D3×Q16 | — | 6 | 2 | no | — |
| 145 | #916 | — | 6 | 2 | no | — |
| 146 | #915 | — | 6 | 2 | no | — |
| 147 | #914 | — | 6 | 2 | no | — |
| 148 | D3×SD16 | — | 6 | 2 | no | — |
| 149 | #909 | C2×D3 | 1 | 2 | yes | complemented |
| 150 | #908 | — | 3 | 2 | no | — |
| 151 | #907 | — | 3 | 2 | no | — |
| 152 | #907 | — | 3 | 2 | no | — |
| 153 | #907 | — | 6 | 1 | no | — |
| 154 | #875 | C2×D3 | 1 | 2 | yes | complemented |
| 155 | C3×#104 | — | 2 | 1 | no | — |
| 156 | C3×#104 | — | 3 | 2 | no | — |
| 157 | C3×#104 | C2×D3 | 1 | 2 | yes | — |
| 158 | C3×#100 | — | 3 | 2 | no | — |
| 159 | #836 | — | 3 | 2 | no | — |
| 160 | #824 | — | 3 | 2 | no | — |
| 161 | #823 | C2×D3 | 1 | 2 | yes | complemented |
| 162 | #822 | — | 3 | 2 | no | — |
| 163 | #822 | — | 3 | 2 | no | — |
| 164 | #822 | — | 6 | 1 | no | — |
| 165 | #805 | — | 3 | 2 | no | — |
| 166 | #805 | — | 6 | 1 | no | — |
| 167 | #805 | C2×D3 | 1 | 2 | yes | complemented |
| 168 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 169 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 170 | C22×C3×D3 | — | 2 | 2 | no | — |
| 171 | C22×C3×D3 | — | 4 | 2 | no | — |
| 172 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C32×D4 | — | 2 | 1 | no | — |
| 174 | C32×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C32×C4 | — | 2 | 1 | no | — |
| 176 | C2×C32×C4 | — | 2 | 1 | no | — |
| 177 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 178 | #638 | — | 2 | 1 | no | — |
| 179 | C4⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 181 | #634 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C3×#67 | — | 2 | 2 | no | — |
| 183 | C3×#67 | — | 4 | 2 | no | — |
| 184 | C2×C3×Dic3 | — | 2 | 2 | no | — |
| 185 | C3×D12 | — | 2 | 2 | no | — |
| 186 | C3×D12 | — | 2 | 2 | no | — |
| 187 | C3×D12 | — | 4 | 2 | no | — |
| 188 | C3×D12 | C2×D4 | 1 | 2 | yes | — |
| 189 | C3×C4×D3 | — | 2 | 2 | no | — |
| 190 | C3×C4×D3 | — | 4 | 2 | no | — |
| 191 | C3×Dic6 | — | 2 | 2 | no | — |
| 192 | C3×Dic6 | — | 2 | 2 | no | — |
| 193 | C3×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 194 | #627 | — | 4 | 2 | no | — |
| 195 | #626 | — | 4 | 2 | no | — |
| 196 | #624 | — | 4 | 2 | no | — |
| 197 | D3×Dic3 | — | 4 | 2 | no | — |
| 198 | C32×C8 | — | 2 | 1 | no | — |
| 199 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 200 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 205 | #578 | — | 9 | 1 | no | — |
| 206 | #577 | — | 9 | 2 | no | — |
| 207 | #576 | — | 9 | 1 | no | — |
| 208 | #495 | — | 9 | 1 | no | — |
| 209 | #473 | — | 9 | 1 | no | — |
| 210 | #472 | — | 9 | 1 | no | — |
| 211 | #471 | — | 9 | 2 | no | — |
| 212 | #455 | — | 3 | 2 | no | — |
| 213 | #454 | — | 9 | 2 | no | — |
| 214 | #443 | — | 9 | 1 | no | — |
| 215 | #443 | — | 9 | 1 | no | — |
| 216 | C3×#41 | — | 2 | 1 | no | — |
| 217 | C3×#41 | — | 3 | 2 | no | — |
| 218 | C3×#41 | — | 6 | 2 | no | — |
| 219 | C3×#41 | — | 6 | 2 | no | — |
| 220 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 221 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 222 | C2×C3×D4 | — | 3 | 2 | no | — |
| 223 | C2×C3×D4 | — | 6 | 2 | no | — |
| 224 | C2×C3×D4 | — | 6 | 2 | no | — |
| 225 | C2×C3×D4 | — | 12 | 2 | no | — |
| 226 | #239 | — | 2 | 2 | no | — |
| 227 | #239 | — | 6 | 2 | no | — |
| 228 | #239 | — | 6 | 2 | no | — |
| 229 | D3×Q8 | — | 6 | 2 | no | — |
| 230 | D3×Q8 | — | 6 | 2 | no | — |
| 231 | D3×Q8 | — | 6 | 2 | no | — |
| 232 | #237 | — | 6 | 2 | no | — |
| 233 | #237 | — | 12 | 2 | no | — |
| 234 | D3×D4 | — | 2 | 2 | no | — |
| 235 | D3×D4 | — | 4 | 2 | no | — |
| 236 | #235 | — | 2 | 2 | no | — |
| 237 | #235 | — | 3 | 2 | no | — |
| 238 | #235 | — | 6 | 1 | no | — |
| 239 | #235 | — | 6 | 2 | no | — |
| 240 | #235 | — | 12 | 2 | no | — |
| 241 | #235 | C22×D3 | 1 | 2 | yes | — |
| 242 | C2×D12 | — | 2 | 2 | no | — |
| 243 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 244 | C2×Dic6 | — | 6 | 2 | no | — |
| 245 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 246 | C3×Q16 | — | 6 | 2 | no | — |
| 247 | C3×Q16 | — | 6 | 2 | no | — |
| 248 | C3×SD16 | — | 6 | 2 | no | — |
| 249 | C3×SD16 | — | 6 | 2 | no | — |
| 250 | C3×M16 | — | 2 | 1 | no | — |
| 251 | C3×M16 | — | 3 | 2 | no | — |
| 252 | C3×M16 | C22×D3 | 1 | 2 | yes | — |
| 253 | C3×C22⋊C4 | — | 12 | 2 | no | — |
| 254 | C3×C42 | — | 2 | 1 | no | — |
| 255 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 256 | #216 | — | 2 | 2 | no | — |
| 257 | #216 | — | 3 | 2 | no | — |
| 258 | #216 | — | 3 | 2 | no | — |
| 259 | #216 | — | 6 | 1 | no | — |
| 260 | #216 | — | 6 | 2 | no | — |
| 261 | #216 | — | 6 | 2 | no | — |
| 262 | #215 | — | 3 | 2 | no | — |
| 263 | #215 | — | 3 | 2 | no | — |
| 264 | #215 | — | 6 | 1 | no | — |
| 265 | #215 | — | 6 | 2 | no | — |
| 266 | #215 | — | 6 | 2 | no | — |
| 267 | #215 | — | 6 | 2 | no | — |
| 268 | #214 | — | 2 | 2 | no | — |
| 269 | #214 | — | 3 | 2 | no | — |
| 270 | #214 | — | 3 | 2 | no | — |
| 271 | #214 | — | 6 | 1 | no | — |
| 272 | #214 | — | 6 | 2 | no | — |
| 273 | #214 | — | 6 | 2 | no | — |
| 274 | #214 | — | 6 | 2 | no | — |
| 275 | #214 | — | 6 | 2 | no | — |
| 276 | #213 | — | 3 | 2 | no | — |
| 277 | #213 | — | 3 | 2 | no | — |
| 278 | #213 | — | 6 | 1 | no | — |
| 279 | #213 | — | 6 | 2 | no | — |
| 280 | #213 | — | 6 | 2 | no | — |
| 281 | #213 | — | 6 | 2 | no | — |
| 282 | #213 | — | 6 | 2 | no | — |
| 283 | #213 | — | 6 | 2 | no | — |
| 284 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 285 | #208 | — | 3 | 2 | no | — |
| 286 | #208 | — | 6 | 1 | no | — |
| 287 | #208 | — | 6 | 2 | no | — |
| 288 | #208 | — | 6 | 2 | no | — |
| 289 | #208 | — | 12 | 1 | no | — |
| 290 | #208 | C22×D3 | 1 | 2 | yes | — |
| 291 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 292 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 293 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 294 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 295 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 296 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 297 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 298 | Dic12 | — | 2 | 2 | no | — |
| 299 | D24 | — | 6 | 2 | no | — |
| 300 | #204 | — | 2 | 2 | no | — |
| 301 | #204 | — | 6 | 2 | no | — |
| 302 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 303 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 304 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 305 | D3×C8 | — | 6 | 2 | no | — |
| 306 | D3×C8 | — | 6 | 2 | no | — |
| 307 | D3×C8 | — | 12 | 1 | no | — |
| 308 | C22×C32 | — | 2 | 1 | no | — |
| 309 | C22×C32 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 310 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 311 | C2×C3×D3 | — | 2 | 2 | no | — |
| 312 | C2×C3×D3 | — | 4 | 2 | no | — |
| 313 | C2×C3×D3 | — | 8 | 2 | no | — |
| 314 | C2×C3×D3 | — | 16 | 2 | no | — |
| 315 | C32×C4 | — | 2 | 1 | no | — |
| 316 | C32×C4 | — | 4 | 1 | no | — |
| 317 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 318 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 319 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 320 | C3×Dic3 | — | 2 | 2 | no | — |
| 321 | C3×Dic3 | — | 4 | 2 | no | — |
| 322 | 2−1+4 | — | 9 | 2 | no | — |
| 323 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 324 | #137 | — | 3 | 2 | no | — |
| 325 | #137 | — | 3 | 2 | no | — |
| 326 | #137 | — | 18 | 2 | no | — |
| 327 | #137 | — | 18 | 2 | no | — |
| 328 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 329 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 330 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 331 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 332 | #135 | — | 9 | 1 | no | — |
| 333 | #135 | — | 9 | 1 | no | — |
| 334 | #135 | — | 18 | 1 | no | — |
| 335 | #135 | — | 18 | 2 | no | — |
| 336 | #135 | — | 18 | 1 | no | — |
| 337 | C2×Q16 | — | 9 | 1 | no | — |
| 338 | C2×Q16 | — | 18 | 1 | no | — |
| 339 | C2×SD16 | — | 9 | 2 | no | — |
| 340 | C2×SD16 | — | 18 | 2 | no | — |
| 341 | C2×D8 | — | 9 | 1 | no | — |
| 342 | C2×D8 | — | 18 | 1 | no | — |
| 343 | #131 | — | 9 | 2 | no | — |
| 344 | #131 | — | 9 | 1 | no | — |
| 345 | #131 | — | 9 | 1 | no | — |
| 346 | #124 | — | 3 | 2 | no | — |
| 347 | #108 | — | 9 | 1 | no | — |
| 348 | #108 | — | 9 | 1 | no | — |
| 349 | #104 | — | 3 | 2 | no | — |
| 350 | #104 | — | 9 | 1 | no | — |
| 351 | #104 | D32 | 1 | 1 | yes | characteristic |
| 352 | #101 | — | 9 | 2 | no | — |
| 353 | #100 | — | 3 | 2 | no | — |
| 354 | C4×C8 | — | 9 | 1 | no | — |
| 355 | C23×C3 | — | 6 | 2 | no | — |
| 356 | C23×C3 | — | 12 | 2 | no | — |
| 357 | C22×D3 | — | 2 | 2 | no | — |
| 358 | C22×D3 | — | 4 | 2 | no | — |
| 359 | C3×Q8 | — | 2 | 1 | no | — |
| 360 | C3×Q8 | — | 3 | 2 | no | — |
| 361 | C3×Q8 | — | 6 | 2 | no | — |
| 362 | C3×Q8 | — | 6 | 2 | no | — |
| 363 | C3×Q8 | D3×D4 | 1 | 2 | yes | — |
| 364 | C3×D4 | — | 2 | 2 | no | — |
| 365 | C3×D4 | — | 2 | 1 | no | — |
| 366 | C3×D4 | — | 3 | 2 | no | — |
| 367 | C3×D4 | — | 4 | 1 | no | — |
| 368 | C3×D4 | — | 6 | 2 | no | — |
| 369 | C3×D4 | — | 6 | 2 | no | — |
| 370 | C3×D4 | — | 6 | 2 | no | — |
| 371 | C3×D4 | — | 12 | 2 | no | — |
| 372 | C3×D4 | — | 12 | 2 | no | — |
| 373 | C3×D4 | D3×D4 | 1 | 2 | yes | — |
| 374 | C2×C3×C4 | — | 2 | 2 | no | — |
| 375 | C2×C3×C4 | — | 2 | 2 | no | — |
| 376 | C2×C3×C4 | — | 2 | 1 | no | — |
| 377 | C2×C3×C4 | — | 4 | 1 | no | — |
| 378 | C2×C3×C4 | — | 4 | 1 | no | — |
| 379 | C2×C3×C4 | — | 6 | 2 | no | — |
| 380 | C2×C3×C4 | — | 6 | 2 | no | — |
| 381 | C2×C3×C4 | — | 12 | 2 | no | — |
| 382 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 383 | #67 | — | 2 | 2 | no | — |
| 384 | #67 | — | 4 | 2 | no | — |
| 385 | #67 | — | 6 | 2 | no | — |
| 386 | #67 | — | 12 | 1 | no | — |
| 387 | #67 | — | 12 | 2 | no | — |
| 388 | C2×Dic3 | — | 2 | 2 | no | — |
| 389 | C2×Dic3 | — | 12 | 2 | no | — |
| 390 | D12 | — | 2 | 2 | no | — |
| 391 | D12 | — | 2 | 2 | no | — |
| 392 | D12 | — | 3 | 2 | no | — |
| 393 | D12 | — | 4 | 2 | no | — |
| 394 | D12 | — | 6 | 1 | no | — |
| 395 | D12 | — | 12 | 2 | no | — |
| 396 | D12 | D3×D4 | 1 | 2 | yes | — |
| 397 | C4×D3 | — | 2 | 2 | no | — |
| 398 | C4×D3 | — | 4 | 2 | no | — |
| 399 | C4×D3 | — | 6 | 2 | no | — |
| 400 | C4×D3 | — | 12 | 1 | no | — |
| 401 | C4×D3 | — | 12 | 2 | no | — |
| 402 | C4×D3 | — | 12 | 2 | no | — |
| 403 | C4×D3 | — | 12 | 2 | no | — |
| 404 | Dic6 | — | 2 | 2 | no | — |
| 405 | Dic6 | — | 2 | 2 | no | — |
| 406 | Dic6 | — | 3 | 2 | no | — |
| 407 | Dic6 | — | 6 | 1 | no | — |
| 408 | Dic6 | — | 12 | 2 | no | — |
| 409 | Dic6 | — | 12 | 2 | no | — |
| 410 | Dic6 | D3×D4 | 1 | 2 | yes | — |
| 411 | C3×C8 | — | 2 | 2 | no | — |
| 412 | C3×C8 | — | 4 | 1 | no | — |
| 413 | C3×C8 | — | 6 | 2 | no | — |
| 414 | C3⋊C8 | — | 2 | 2 | no | — |
| 415 | C3⋊C8 | — | 3 | 2 | no | — |
| 416 | C3⋊C8 | — | 3 | 2 | no | — |
| 417 | C3⋊C8 | — | 3 | 2 | no | — |
| 418 | C3⋊C8 | — | 3 | 2 | no | — |
| 419 | C3⋊C8 | — | 6 | 1 | no | — |
| 420 | C3⋊C8 | — | 6 | 1 | no | — |
| 421 | C3⋊C8 | — | 6 | 1 | no | — |
| 422 | C3⋊C8 | — | 6 | 1 | no | — |
| 423 | C3⋊C8 | — | 6 | 2 | no | — |
| 424 | C3⋊C8 | — | 12 | 1 | no | — |
| 425 | C2×C32 | — | 2 | 1 | no | — |
| 426 | C2×C32 | — | 4 | 1 | no | — |
| 427 | C2×C32 | D42 | 1 | 1 | yes | characteristic |
| 428 | C3⋊D3 | — | 4 | 1 | no | — |
| 429 | C3×D3 | — | 4 | 2 | no | — |
| 430 | C3×D3 | — | 8 | 2 | no | — |
| 431 | #41 | — | 3 | 2 | no | — |
| 432 | #41 | — | 6 | 2 | no | — |
| 433 | #41 | — | 6 | 2 | no | — |
| 434 | #41 | — | 9 | 1 | no | — |
| 435 | #41 | — | 18 | 2 | no | — |
| 436 | #41 | — | 18 | 2 | no | — |
| 437 | #41 | — | 36 | 2 | no | — |
| 438 | #41 | C2×D32 | 1 | 1 | yes | characteristic |
| 439 | C2×Q8 | — | 3 | 2 | no | — |
| 440 | C2×Q8 | — | 18 | 2 | no | — |
| 441 | C2×Q8 | — | 18 | 2 | no | — |
| 442 | C2×D4 | — | 3 | 2 | no | — |
| 443 | C2×D4 | — | 6 | 2 | no | — |
| 444 | C2×D4 | — | 6 | 2 | no | — |
| 445 | C2×D4 | — | 12 | 2 | no | — |
| 446 | Q16 | — | 6 | 2 | no | — |
| 447 | Q16 | — | 6 | 2 | no | — |
| 448 | Q16 | — | 9 | 1 | no | — |
| 449 | Q16 | — | 9 | 1 | no | — |
| 450 | Q16 | — | 18 | 1 | no | — |
| 451 | Q16 | — | 18 | 1 | no | — |
| 452 | SD16 | — | 6 | 2 | no | — |
| 453 | SD16 | — | 6 | 2 | no | — |
| 454 | SD16 | — | 9 | 2 | no | — |
| 455 | SD16 | — | 9 | 1 | no | — |
| 456 | SD16 | — | 9 | 1 | no | — |
| 457 | SD16 | — | 18 | 2 | no | — |
| 458 | SD16 | — | 18 | 2 | no | — |
| 459 | SD16 | — | 18 | 2 | no | — |
| 460 | SD16 | — | 18 | 2 | no | — |
| 461 | D8 | — | 9 | 1 | no | — |
| 462 | D8 | — | 9 | 1 | no | — |
| 463 | D8 | — | 18 | 2 | no | — |
| 464 | D8 | — | 18 | 1 | no | — |
| 465 | D8 | — | 18 | 1 | no | — |
| 466 | D8 | — | 18 | 2 | no | — |
| 467 | M16 | — | 3 | 2 | no | — |
| 468 | M16 | — | 9 | 1 | no | — |
| 469 | M16 | — | 18 | 1 | no | — |
| 470 | M16 | — | 18 | 2 | no | — |
| 471 | M16 | — | 18 | 1 | no | — |
| 472 | M16 | C2×D32 | 1 | 1 | yes | characteristic |
| 473 | C2×C8 | — | 9 | 1 | no | — |
| 474 | C2×C8 | — | 9 | 1 | no | — |
| 475 | C2×C8 | — | 18 | 1 | no | — |
| 476 | C2×C8 | — | 18 | 2 | no | — |
| 477 | C2×C8 | — | 18 | 1 | no | — |
| 478 | C22⋊C4 | — | 12 | 2 | no | — |
| 479 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 480 | C22×C3 | — | 2 | 2 | no | — |
| 481 | C22×C3 | — | 2 | 1 | no | — |
| 482 | C22×C3 | — | 4 | 1 | no | — |
| 483 | C22×C3 | — | 6 | 2 | no | — |
| 484 | C22×C3 | — | 12 | 2 | no | — |
| 485 | C22×C3 | — | 24 | 2 | no | — |
| 486 | C22×C3 | — | 48 | 2 | no | — |
| 487 | C22×C3 | #1004 | 1 | 2 | yes | — |
| 488 | C2×D3 | — | 2 | 2 | no | — |
| 489 | C2×D3 | — | 4 | 2 | no | — |
| 490 | C2×D3 | — | 6 | 2 | no | — |
| 491 | C2×D3 | — | 8 | 2 | no | — |
| 492 | C2×D3 | — | 12 | 1 | no | — |
| 493 | C2×D3 | — | 16 | 2 | no | — |
| 494 | C3×C4 | — | 2 | 2 | no | — |
| 495 | C3×C4 | — | 2 | 1 | no | — |
| 496 | C3×C4 | — | 2 | 1 | no | — |
| 497 | C3×C4 | — | 4 | 1 | no | — |
| 498 | C3×C4 | — | 4 | 2 | no | — |
| 499 | C3×C4 | — | 4 | 2 | no | — |
| 500 | C3×C4 | — | 6 | 2 | no | — |
| 501 | C3×C4 | — | 12 | 2 | no | — |
| 502 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 503 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 504 | Dic3 | — | 2 | 2 | no | — |
| 505 | Dic3 | — | 4 | 2 | no | — |
| 506 | Dic3 | — | 6 | 2 | no | — |
| 507 | Dic3 | — | 12 | 1 | no | — |
| 508 | C32 | #3290 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 509 | C23 | — | 6 | 2 | no | — |
| 510 | C23 | — | 12 | 2 | no | — |
| 511 | Q8 | — | 3 | 2 | no | — |
| 512 | Q8 | — | 6 | 2 | no | — |
| 513 | Q8 | — | 6 | 2 | no | — |
| 514 | Q8 | — | 9 | 1 | no | — |
| 515 | Q8 | — | 36 | 2 | no | — |
| 516 | Q8 | #3802 | 1 | 1 | yes | characteristic |
| 517 | D4 | — | 2 | 1 | no | — |
| 518 | D4 | — | 3 | 2 | no | — |
| 519 | D4 | — | 6 | 2 | no | — |
| 520 | D4 | — | 6 | 2 | no | — |
| 521 | D4 | — | 6 | 2 | no | — |
| 522 | D4 | — | 9 | 1 | no | — |
| 523 | D4 | — | 12 | 2 | no | — |
| 524 | D4 | — | 12 | 2 | no | — |
| 525 | D4 | — | 18 | 1 | no | — |
| 526 | D4 | — | 36 | 2 | no | — |
| 527 | D4 | #3802 | 1 | 1 | yes | characteristic |
| 528 | C2×C4 | — | 2 | 1 | no | — |
| 529 | C2×C4 | — | 2 | 1 | no | — |
| 530 | C2×C4 | — | 6 | 2 | no | — |
| 531 | C2×C4 | — | 6 | 2 | no | — |
| 532 | C2×C4 | — | 12 | 2 | no | — |
| 533 | C2×C4 | — | 18 | 1 | no | — |
| 534 | C2×C4 | — | 36 | 2 | no | — |
| 535 | C2×C4 | — | 36 | 2 | no | — |
| 536 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 537 | C8 | — | 2 | 1 | no | — |
| 538 | C8 | — | 6 | 2 | no | — |
| 539 | C8 | — | 9 | 1 | no | — |
| 540 | C8 | — | 9 | 1 | no | — |
| 541 | C8 | — | 9 | 1 | no | — |
| 542 | C8 | — | 9 | 1 | no | — |
| 543 | C8 | — | 18 | 1 | no | — |
| 544 | C2×C3 | — | 2 | 2 | no | — |
| 545 | C2×C3 | — | 2 | 1 | no | — |
| 546 | C2×C3 | — | 4 | 1 | no | — |
| 547 | C2×C3 | — | 4 | 2 | no | — |
| 548 | C2×C3 | — | 8 | 1 | no | — |
| 549 | C2×C3 | — | 12 | 2 | no | — |
| 550 | C2×C3 | — | 24 | 2 | no | — |
| 551 | C2×C3 | #5590 | 1 | 2 | yes | — |
| 552 | D3 | — | 4 | 2 | no | — |
| 553 | D3 | — | 8 | 2 | no | — |
| 554 | D3 | — | 12 | 2 | no | — |
| 555 | D3 | — | 24 | 1 | no | — |
| 556 | C22 | — | 2 | 1 | no | — |
| 557 | C22 | — | 6 | 2 | no | — |
| 558 | C22 | — | 12 | 2 | no | — |
| 559 | C22 | — | 18 | 1 | no | — |
| 560 | C22 | — | 24 | 2 | no | — |
| 561 | C22 | — | 48 | 2 | no | — |
| 562 | C22 | #64313 | 1 | 1 | yes | characteristic |
| 563 | C4 | — | 2 | 1 | no | — |
| 564 | C4 | — | 4 | 1 | no | — |
| 565 | C4 | — | 6 | 2 | no | — |
| 566 | C4 | — | 12 | 2 | no | — |
| 567 | C4 | — | 18 | 1 | no | — |
| 568 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 569 | C4 | D32×D4 | 1 | 1 | yes | characteristic |
| 570 | C3 | — | 2 | 1 | no | — |
| 571 | C3 | #80296 | 1 | 2 | yes | complemented |
| 572 | C2 | — | 2 | 1 | no | — |
| 573 | C2 | — | 4 | 1 | no | — |
| 574 | C2 | — | 12 | 2 | no | — |
| 575 | C2 | — | 24 | 2 | no | — |
| 576 | C2 | — | 36 | 1 | no | — |
| 577 | C2 | #10594271 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10595464 | C2 | semidirect |
| 2. #10595444 | C2 | semidirect |
| 3. #10594723 | C2 | semidirect |
| 4. #10592523 | C2 | semidirect |
| 5. C3×#4825 | C2 | semidirect |
| 6. #10591683 | C2 | semidirect |
| 7. #10590988 | C2 | semidirect |
| 8. #10590979 | C2 | semidirect |
| 9. #10590400 | C2 | semidirect |
| 10. #10590389 | C2 | semidirect |
| 11. #10590353 | C2 | semidirect |
| 14. #64297 | C22 | semidirect |
| 17. #64116 | C22 | semidirect |
| 19. C3×#909 | C22 | semidirect |
| 20. C3×#875 | C22 | semidirect |
| 25. C2×#3718 | C22 | semidirect |
| 26. #63830 | C22 | semidirect |
| 27. C2×#3715 | C22 | semidirect |
| 34. #63815 | C22 | semidirect |
| 39. #63649 | C22 | semidirect |
| 40. #63632 | C22 | semidirect |
| 41. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 42. C3×#823 | C22 | semidirect |
| 43. C3×#805 | C22 | semidirect |
| 44. #63578 | C22 | semidirect |
| 45. #63560 | C22 | semidirect |
| 56. #4825 | D3 | semidirect |
| 149. #909 | C2×D3 | semidirect |
| 154. #875 | C2×D3 | semidirect |
| 161. #823 | C2×D3 | semidirect |
| 167. #805 | C2×D3 | semidirect |
| 508. C32 | #3290 | semidirect |
| 571. C3 | #80296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595464 | 2 |
| #10595444 | 2 |
| #10594723 | 2 |
| #10592523 | 2 |
| C3×#4825 | 2 |
| #10591683 | 2 |
| #10590988 | 2 |
| #10590979 | 2 |
| #10590400 | 2 |
| #10590389 | 2 |
| #10590353 | 2 |
| #80296 | 3 |