Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
701 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 701 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #10596521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10594757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10594752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593784 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10593484 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10593482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10593473 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10593470 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #10593469 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10593467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10593304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #10593302 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10593298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #10593291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #64320 | C22 | 1 | 1 | yes | characteristic |
| 17 | #64316 | C22 | 1 | 1 | yes | characteristic |
| 18 | #64309 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64309 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #64289 | C22 | 1 | 1 | yes | characteristic |
| 21 | #64287 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#3776 | — | 2 | 1 | no | — |
| 23 | #64239 | — | 2 | 1 | no | — |
| 24 | #64239 | — | 2 | 1 | no | — |
| 25 | #64237 | — | 2 | 1 | no | — |
| 26 | #64228 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #64227 | — | 2 | 1 | no | — |
| 28 | #64227 | C22 | 1 | 1 | yes | characteristic |
| 29 | #64226 | — | 2 | 1 | no | — |
| 30 | #64226 | C22 | 1 | 1 | yes | characteristic |
| 31 | #64226 | C22 | 1 | 1 | yes | characteristic |
| 32 | #64226 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #64224 | — | 2 | 1 | no | — |
| 34 | #64224 | C22 | 1 | 1 | yes | characteristic |
| 35 | #64223 | — | 2 | 1 | no | — |
| 36 | #64223 | C22 | 1 | 1 | yes | characteristic |
| 37 | #64222 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #64221 | C22 | 1 | 1 | yes | characteristic |
| 39 | #64125 | C22 | 1 | 1 | yes | characteristic |
| 40 | C3×#916 | — | 2 | 1 | no | — |
| 41 | C3×#915 | — | 2 | 1 | no | — |
| 42 | #63945 | C22 | 1 | 1 | yes | characteristic |
| 43 | #63945 | C22 | 1 | 1 | yes | characteristic |
| 44 | #63943 | — | 2 | 1 | no | — |
| 45 | D3×#216 | — | 2 | 1 | no | — |
| 46 | #63935 | — | 2 | 1 | no | — |
| 47 | #63931 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #63927 | C22 | 1 | 1 | yes | characteristic |
| 49 | #63925 | — | 2 | 1 | no | — |
| 50 | #63805 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #63803 | C22 | 1 | 1 | yes | characteristic |
| 52 | #63802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #63801 | — | 2 | 1 | no | — |
| 54 | #63796 | C22 | 1 | 1 | yes | characteristic |
| 55 | D3×#204 | — | 2 | 1 | no | — |
| 56 | #63785 | C22 | 1 | 1 | yes | characteristic |
| 57 | #63783 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #63771 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #63767 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #63733 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #63731 | C22 | 1 | 1 | yes | characteristic |
| 62 | #63731 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #63728 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #63728 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #63728 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #63727 | C22 | 1 | 1 | yes | characteristic |
| 67 | #5779 | — | 6 | 1 | no | — |
| 68 | #5770 | — | 6 | 1 | no | — |
| 69 | #3832 | C23 | 1 | 1 | yes | characteristic |
| 70 | #3830 | C23 | 1 | 1 | yes | characteristic |
| 71 | C3×#239 | — | 2 | 1 | no | — |
| 72 | C3×D3×Q8 | — | 2 | 1 | no | — |
| 73 | C3×#237 | — | 2 | 1 | no | — |
| 74 | C3×#237 | — | 2 | 1 | no | — |
| 75 | C2×#627 | — | 2 | 1 | no | — |
| 76 | C2×#627 | — | 2 | 1 | no | — |
| 77 | #3805 | — | 2 | 1 | no | — |
| 78 | #3805 | — | 2 | 1 | no | — |
| 79 | #3804 | — | 4 | 1 | no | — |
| 80 | #3804 | — | 4 | 1 | no | — |
| 81 | #3802 | — | 2 | 1 | no | — |
| 82 | #3802 | C23 | 1 | 1 | yes | characteristic |
| 83 | D3×D12 | — | 2 | 1 | no | — |
| 84 | D3×D12 | — | 4 | 1 | no | — |
| 85 | #3799 | — | 2 | 1 | no | — |
| 86 | #3799 | — | 4 | 1 | no | — |
| 87 | #3798 | — | 2 | 1 | no | — |
| 88 | #3798 | — | 2 | 1 | no | — |
| 89 | #3798 | C23 | 1 | 1 | yes | characteristic |
| 90 | #3798 | C23 | 1 | 1 | yes | characteristic |
| 91 | #3797 | — | 2 | 1 | no | — |
| 92 | #3797 | C23 | 1 | 1 | yes | characteristic |
| 93 | #3797 | C23 | 1 | 1 | yes | characteristic |
| 94 | #3797 | C23 | 1 | 1 | yes | characteristic |
| 95 | D3×Dic6 | — | 2 | 1 | no | — |
| 96 | D3×Dic6 | — | 2 | 1 | no | — |
| 97 | #3792 | — | 2 | 1 | no | — |
| 98 | C2×#622 | — | 2 | 1 | no | — |
| 99 | C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 100 | #3788 | — | 2 | 1 | no | — |
| 101 | #3788 | C23 | 1 | 1 | yes | characteristic |
| 102 | #3788 | C23 | 1 | 1 | yes | characteristic |
| 103 | #3787 | — | 2 | 1 | no | — |
| 104 | #3787 | C23 | 1 | 1 | yes | characteristic |
| 105 | #3776 | — | 2 | 1 | no | — |
| 106 | #3776 | — | 2 | 1 | no | — |
| 107 | #3776 | — | 2 | 1 | no | — |
| 108 | #3776 | — | 2 | 1 | no | — |
| 109 | #3776 | — | 2 | 1 | no | — |
| 110 | #3776 | D4 | 1 | 1 | yes | characteristic |
| 111 | #3775 | — | 2 | 1 | no | — |
| 112 | #3775 | — | 2 | 1 | no | — |
| 113 | #3775 | — | 2 | 1 | no | — |
| 114 | #3775 | — | 2 | 1 | no | — |
| 115 | #3775 | — | 2 | 1 | no | — |
| 116 | #3775 | — | 2 | 1 | no | — |
| 117 | #3775 | D4 | 1 | 1 | yes | characteristic |
| 118 | #3775 | D4 | 1 | 1 | yes | characteristic |
| 119 | #3774 | — | 2 | 1 | no | — |
| 120 | #3774 | D4 | 1 | 1 | yes | characteristic |
| 121 | #3773 | — | 4 | 1 | no | — |
| 122 | D32⋊C4 | — | 4 | 1 | no | — |
| 123 | C32×SD16 | D4 | 1 | 1 | yes | characteristic |
| 124 | #3756 | D4 | 1 | 1 | yes | characteristic |
| 125 | #3753 | D4 | 1 | 1 | yes | characteristic |
| 126 | #3744 | D4 | 1 | 1 | yes | characteristic |
| 127 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 128 | C3×#216 | — | 2 | 1 | no | — |
| 129 | C3×#216 | — | 2 | 1 | no | — |
| 130 | C3×#214 | — | 2 | 1 | no | — |
| 131 | C3×#213 | — | 2 | 1 | no | — |
| 132 | C3×Dic12 | — | 2 | 1 | no | — |
| 133 | C3×#204 | — | 2 | 1 | no | — |
| 134 | C3×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 135 | C3×D3×C8 | — | 2 | 1 | no | — |
| 136 | #3719 | — | 2 | 1 | no | — |
| 137 | #3718 | — | 2 | 1 | no | — |
| 138 | #3717 | — | 2 | 1 | no | — |
| 139 | #3717 | — | 2 | 1 | no | — |
| 140 | #3716 | — | 2 | 1 | no | — |
| 141 | #3715 | — | 2 | 1 | no | — |
| 142 | #3712 | C23 | 1 | 1 | yes | characteristic |
| 143 | #3712 | C23 | 1 | 1 | yes | characteristic |
| 144 | #3711 | — | 2 | 1 | no | — |
| 145 | D3×C3⋊C8 | — | 2 | 1 | no | — |
| 146 | #3289 | — | 9 | 1 | no | maximal, Sylow |
| 147 | #1010 | — | 6 | 1 | no | — |
| 148 | #1010 | — | 6 | 1 | no | — |
| 149 | #1009 | — | 6 | 1 | no | — |
| 150 | #1007 | — | 6 | 1 | no | — |
| 151 | C3×#137 | — | 6 | 1 | no | — |
| 152 | C3×#135 | — | 6 | 1 | no | — |
| 153 | #951 | — | 6 | 1 | no | — |
| 154 | #950 | — | 6 | 1 | no | — |
| 155 | #949 | — | 6 | 1 | no | — |
| 156 | C2×#216 | — | 6 | 1 | no | — |
| 157 | #918 | — | 6 | 1 | no | — |
| 158 | #918 | — | 6 | 1 | no | — |
| 159 | #918 | — | 6 | 1 | no | — |
| 160 | #918 | — | 6 | 1 | no | — |
| 161 | D3×Q16 | — | 6 | 1 | no | — |
| 162 | D3×Q16 | — | 6 | 1 | no | — |
| 163 | #916 | — | 2 | 1 | no | — |
| 164 | #916 | — | 6 | 1 | no | — |
| 165 | #916 | — | 6 | 1 | no | — |
| 166 | #916 | — | 6 | 1 | no | — |
| 167 | #915 | — | 2 | 1 | no | — |
| 168 | #915 | — | 6 | 1 | no | — |
| 169 | D3×SD16 | — | 6 | 1 | no | — |
| 170 | D3×SD16 | — | 6 | 1 | no | — |
| 171 | #911 | — | 6 | 1 | no | — |
| 172 | #911 | — | 6 | 1 | no | — |
| 173 | #909 | — | 6 | 1 | no | — |
| 174 | #907 | — | 6 | 1 | no | — |
| 175 | C2×#204 | — | 6 | 1 | no | — |
| 176 | #901 | — | 6 | 1 | no | — |
| 177 | C2×D32 | — | 2 | 1 | no | — |
| 178 | C2×D32 | — | 4 | 1 | no | — |
| 179 | C2×#157 | — | 2 | 1 | no | — |
| 180 | C32×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C32×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | #638 | — | 2 | 1 | no | — |
| 183 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 184 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 185 | C4⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 187 | C4×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 188 | #634 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C3×#67 | — | 4 | 1 | no | — |
| 190 | C3×#67 | — | 4 | 1 | no | — |
| 191 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 192 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 193 | C3×D12 | — | 2 | 1 | no | — |
| 194 | C3×D12 | — | 4 | 1 | no | — |
| 195 | C3×C4×D3 | — | 2 | 1 | no | — |
| 196 | C3×C4×D3 | — | 2 | 1 | no | — |
| 197 | C3×C4×D3 | — | 4 | 1 | no | — |
| 198 | C3×C4×D3 | — | 4 | 1 | no | — |
| 199 | C3×Dic6 | — | 2 | 1 | no | — |
| 200 | C3×Dic6 | — | 2 | 1 | no | — |
| 201 | C3×Dic6 | — | 2 | 1 | no | — |
| 202 | C3×Dic6 | — | 4 | 1 | no | — |
| 203 | #627 | — | 2 | 1 | no | — |
| 204 | #627 | — | 2 | 1 | no | — |
| 205 | #627 | — | 2 | 1 | no | — |
| 206 | #627 | — | 4 | 1 | no | — |
| 207 | #627 | — | 4 | 1 | no | — |
| 208 | #627 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | #627 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | #626 | — | 2 | 1 | no | — |
| 211 | #626 | — | 2 | 1 | no | — |
| 212 | #626 | — | 4 | 1 | no | — |
| 213 | #626 | — | 4 | 1 | no | — |
| 214 | #625 | — | 2 | 1 | no | — |
| 215 | #625 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | #625 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | #624 | — | 2 | 1 | no | — |
| 218 | #624 | — | 2 | 1 | no | — |
| 219 | #624 | — | 2 | 1 | no | — |
| 220 | #624 | — | 4 | 1 | no | — |
| 221 | D3×Dic3 | — | 4 | 1 | no | — |
| 222 | D3×Dic3 | — | 4 | 1 | no | — |
| 223 | #622 | — | 2 | 1 | no | — |
| 224 | #622 | — | 2 | 1 | no | — |
| 225 | #622 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | #622 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C3⋊(C3⋊C8) | C2×D4 | 1 | 1 | yes | characteristic |
| 229 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 230 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 231 | #578 | — | 9 | 1 | no | — |
| 232 | #578 | — | 9 | 1 | no | — |
| 233 | #577 | — | 9 | 1 | no | — |
| 234 | #577 | — | 9 | 1 | no | — |
| 235 | #497 | — | 9 | 1 | no | — |
| 236 | #473 | — | 9 | 1 | no | — |
| 237 | #473 | — | 9 | 1 | no | — |
| 238 | #471 | — | 9 | 1 | no | — |
| 239 | #471 | — | 9 | 1 | no | — |
| 240 | #456 | — | 9 | 1 | no | — |
| 241 | #456 | — | 9 | 1 | no | — |
| 242 | #455 | — | 9 | 1 | no | — |
| 243 | #454 | — | 9 | 1 | no | — |
| 244 | #444 | — | 9 | 1 | no | — |
| 245 | #444 | — | 9 | 1 | no | — |
| 246 | C3×#41 | — | 6 | 1 | no | — |
| 247 | C3×#41 | — | 6 | 1 | no | — |
| 248 | C3×#41 | — | 6 | 1 | no | — |
| 249 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 250 | #239 | — | 2 | 1 | no | — |
| 251 | #239 | — | 6 | 1 | no | — |
| 252 | #239 | — | 6 | 1 | no | — |
| 253 | #239 | — | 6 | 1 | no | — |
| 254 | #239 | — | 12 | 1 | no | — |
| 255 | D3×Q8 | — | 2 | 1 | no | — |
| 256 | D3×Q8 | — | 6 | 1 | no | — |
| 257 | D3×Q8 | — | 6 | 1 | no | — |
| 258 | D3×Q8 | — | 6 | 1 | no | — |
| 259 | D3×Q8 | — | 6 | 1 | no | — |
| 260 | D3×Q8 | — | 6 | 1 | no | — |
| 261 | D3×Q8 | — | 12 | 1 | no | — |
| 262 | #237 | — | 2 | 1 | no | — |
| 263 | #237 | — | 2 | 1 | no | — |
| 264 | #237 | — | 6 | 1 | no | — |
| 265 | #237 | — | 6 | 1 | no | — |
| 266 | #237 | — | 12 | 1 | no | — |
| 267 | #237 | — | 12 | 1 | no | — |
| 268 | #237 | — | 12 | 1 | no | — |
| 269 | #237 | — | 12 | 1 | no | — |
| 270 | D3×D4 | — | 6 | 1 | no | — |
| 271 | D3×D4 | — | 6 | 1 | no | — |
| 272 | D3×D4 | — | 12 | 1 | no | — |
| 273 | D3×D4 | — | 12 | 1 | no | — |
| 274 | #235 | — | 6 | 1 | no | — |
| 275 | #235 | — | 6 | 1 | no | — |
| 276 | #235 | — | 6 | 1 | no | — |
| 277 | #235 | — | 12 | 1 | no | — |
| 278 | #235 | — | 12 | 1 | no | — |
| 279 | #235 | — | 12 | 1 | no | — |
| 280 | #235 | — | 12 | 1 | no | — |
| 281 | #235 | — | 12 | 1 | no | — |
| 282 | C2×D12 | — | 6 | 1 | no | — |
| 283 | C2×D12 | — | 12 | 1 | no | — |
| 284 | C2×Dic6 | — | 6 | 1 | no | — |
| 285 | C2×Dic6 | — | 6 | 1 | no | — |
| 286 | C2×Dic6 | — | 12 | 1 | no | — |
| 287 | C2×Dic6 | — | 12 | 1 | no | — |
| 288 | C3×Q16 | — | 6 | 1 | no | — |
| 289 | C3×Q16 | — | 6 | 1 | no | — |
| 290 | C3×Q16 | — | 6 | 1 | no | — |
| 291 | C3×SD16 | — | 2 | 1 | no | — |
| 292 | C3×SD16 | — | 2 | 1 | no | — |
| 293 | C3×SD16 | — | 6 | 1 | no | — |
| 294 | C3×SD16 | — | 6 | 1 | no | — |
| 295 | C3×D8 | — | 6 | 1 | no | — |
| 296 | C3×M16 | — | 6 | 1 | no | — |
| 297 | C2×C3×C8 | — | 6 | 1 | no | — |
| 298 | #216 | — | 2 | 1 | no | — |
| 299 | #216 | — | 2 | 1 | no | — |
| 300 | #216 | — | 6 | 1 | no | — |
| 301 | #216 | — | 6 | 1 | no | — |
| 302 | #216 | — | 6 | 1 | no | — |
| 303 | #216 | — | 6 | 1 | no | — |
| 304 | #216 | — | 6 | 1 | no | — |
| 305 | #215 | — | 6 | 1 | no | — |
| 306 | #215 | — | 6 | 1 | no | — |
| 307 | #215 | — | 6 | 1 | no | — |
| 308 | #214 | — | 2 | 1 | no | — |
| 309 | #214 | — | 6 | 1 | no | — |
| 310 | #214 | — | 6 | 1 | no | — |
| 311 | #213 | — | 2 | 1 | no | — |
| 312 | #213 | — | 6 | 1 | no | — |
| 313 | #213 | — | 6 | 1 | no | — |
| 314 | #208 | — | 6 | 1 | no | — |
| 315 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 316 | Dic12 | — | 2 | 1 | no | — |
| 317 | Dic12 | — | 6 | 1 | no | — |
| 318 | #204 | — | 2 | 1 | no | — |
| 319 | #204 | — | 6 | 1 | no | — |
| 320 | #204 | — | 6 | 1 | no | — |
| 321 | #204 | — | 6 | 1 | no | — |
| 322 | #204 | — | 6 | 1 | no | — |
| 323 | #204 | — | 6 | 1 | no | — |
| 324 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 325 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 326 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 327 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 328 | D3×C8 | — | 2 | 1 | no | — |
| 329 | D3×C8 | — | 6 | 1 | no | — |
| 330 | D3×C8 | — | 6 | 1 | no | — |
| 331 | D3×C8 | — | 6 | 1 | no | — |
| 332 | C22×C32 | — | 2 | 1 | no | — |
| 333 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 334 | C2×C3⋊D3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 335 | C2×C3×D3 | — | 2 | 1 | no | — |
| 336 | C2×C3×D3 | — | 2 | 1 | no | — |
| 337 | C2×C3×D3 | — | 4 | 1 | no | — |
| 338 | D32 | — | 8 | 1 | no | — |
| 339 | D32 | — | 16 | 1 | no | — |
| 340 | #157 | — | 4 | 1 | no | — |
| 341 | C32×C4 | — | 2 | 1 | no | — |
| 342 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 344 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | C3×Dic3 | — | 2 | 1 | no | — |
| 346 | C3×Dic3 | — | 2 | 1 | no | — |
| 347 | C3×Dic3 | — | 4 | 1 | no | — |
| 348 | C3×Dic3 | — | 4 | 1 | no | — |
| 349 | C3×Dic3 | — | 4 | 1 | no | — |
| 350 | 2−1+4 | — | 9 | 1 | no | — |
| 351 | 2−1+4 | — | 9 | 1 | no | — |
| 352 | 2−1+4 | — | 9 | 1 | no | — |
| 353 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 354 | #137 | — | 6 | 1 | no | — |
| 355 | #137 | — | 9 | 1 | no | — |
| 356 | #137 | — | 9 | 1 | no | — |
| 357 | #137 | — | 9 | 1 | no | — |
| 358 | #137 | — | 9 | 1 | no | — |
| 359 | #137 | — | 9 | 1 | no | — |
| 360 | #137 | — | 9 | 1 | no | — |
| 361 | #137 | — | 18 | 1 | no | — |
| 362 | #137 | — | 18 | 1 | no | — |
| 363 | #137 | — | 18 | 1 | no | — |
| 364 | #137 | — | 18 | 1 | no | — |
| 365 | #137 | — | 18 | 1 | no | — |
| 366 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 367 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 368 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 369 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 370 | #135 | — | 6 | 1 | no | — |
| 371 | #135 | — | 9 | 1 | no | — |
| 372 | #135 | — | 9 | 1 | no | — |
| 373 | #135 | — | 18 | 1 | no | — |
| 374 | #135 | — | 18 | 1 | no | — |
| 375 | #135 | — | 18 | 1 | no | — |
| 376 | C2×Q16 | — | 9 | 1 | no | — |
| 377 | C2×Q16 | — | 9 | 1 | no | — |
| 378 | C2×Q16 | — | 18 | 1 | no | — |
| 379 | C2×Q16 | — | 18 | 1 | no | — |
| 380 | C2×SD16 | — | 9 | 1 | no | — |
| 381 | C2×SD16 | — | 9 | 1 | no | — |
| 382 | C2×SD16 | — | 18 | 1 | no | — |
| 383 | C2×SD16 | — | 18 | 1 | no | — |
| 384 | #131 | — | 9 | 1 | no | — |
| 385 | #131 | — | 9 | 1 | no | — |
| 386 | #131 | — | 9 | 1 | no | — |
| 387 | #131 | — | 9 | 1 | no | — |
| 388 | C4⋊Q8 | — | 9 | 1 | no | — |
| 389 | #124 | — | 9 | 1 | no | — |
| 390 | #108 | — | 9 | 1 | no | — |
| 391 | #108 | — | 9 | 1 | no | — |
| 392 | #104 | — | 9 | 1 | no | — |
| 393 | #104 | — | 9 | 1 | no | — |
| 394 | #104 | — | 9 | 1 | no | — |
| 395 | #104 | — | 9 | 1 | no | — |
| 396 | #101 | — | 9 | 1 | no | — |
| 397 | #101 | — | 9 | 1 | no | — |
| 398 | #101 | — | 9 | 1 | no | — |
| 399 | #100 | — | 9 | 1 | no | — |
| 400 | #97 | — | 9 | 1 | no | — |
| 401 | C22×D3 | — | 12 | 1 | no | — |
| 402 | C22×D3 | — | 12 | 1 | no | — |
| 403 | C22×D3 | — | 12 | 1 | no | — |
| 404 | C3×Q8 | — | 2 | 1 | no | — |
| 405 | C3×Q8 | — | 2 | 1 | no | — |
| 406 | C3×Q8 | — | 6 | 1 | no | — |
| 407 | C3×Q8 | — | 6 | 1 | no | — |
| 408 | C3×Q8 | — | 6 | 1 | no | — |
| 409 | C3×Q8 | — | 12 | 1 | no | — |
| 410 | C3×D4 | — | 2 | 1 | no | — |
| 411 | C3×D4 | — | 2 | 1 | no | — |
| 412 | C3×D4 | — | 6 | 1 | no | — |
| 413 | C3×D4 | — | 12 | 1 | no | — |
| 414 | C3×D4 | — | 12 | 1 | no | — |
| 415 | C3×D4 | — | 12 | 1 | no | — |
| 416 | C2×C3×C4 | — | 6 | 1 | no | — |
| 417 | C2×C3×C4 | — | 6 | 1 | no | — |
| 418 | C2×C3×C4 | — | 12 | 1 | no | — |
| 419 | C2×C3×C4 | — | 12 | 1 | no | — |
| 420 | C2×C3×C4 | — | 12 | 1 | no | — |
| 421 | C2×C3×C4 | — | 12 | 1 | no | — |
| 422 | #67 | — | 4 | 1 | no | — |
| 423 | #67 | — | 4 | 1 | no | — |
| 424 | #67 | — | 6 | 1 | no | — |
| 425 | #67 | — | 6 | 1 | no | — |
| 426 | #67 | — | 6 | 1 | no | — |
| 427 | #67 | — | 6 | 1 | no | — |
| 428 | #67 | — | 12 | 1 | no | — |
| 429 | #67 | — | 12 | 1 | no | — |
| 430 | #67 | — | 12 | 1 | no | — |
| 431 | #67 | — | 12 | 1 | no | — |
| 432 | #67 | — | 12 | 1 | no | — |
| 433 | C2×Dic3 | — | 4 | 1 | no | — |
| 434 | C2×Dic3 | — | 4 | 1 | no | — |
| 435 | C2×Dic3 | — | 12 | 1 | no | — |
| 436 | C2×Dic3 | — | 12 | 1 | no | — |
| 437 | C2×Dic3 | — | 12 | 1 | no | — |
| 438 | C2×Dic3 | — | 12 | 1 | no | — |
| 439 | D12 | — | 2 | 1 | no | — |
| 440 | D12 | — | 4 | 1 | no | — |
| 441 | D12 | — | 6 | 1 | no | — |
| 442 | D12 | — | 6 | 1 | no | — |
| 443 | D12 | — | 6 | 1 | no | — |
| 444 | D12 | — | 6 | 1 | no | — |
| 445 | D12 | — | 12 | 1 | no | — |
| 446 | D12 | — | 12 | 1 | no | — |
| 447 | D12 | — | 12 | 1 | no | — |
| 448 | D12 | — | 12 | 1 | no | — |
| 449 | C4×D3 | — | 2 | 1 | no | — |
| 450 | C4×D3 | — | 2 | 1 | no | — |
| 451 | C4×D3 | — | 4 | 1 | no | — |
| 452 | C4×D3 | — | 4 | 1 | no | — |
| 453 | C4×D3 | — | 6 | 1 | no | — |
| 454 | C4×D3 | — | 6 | 1 | no | — |
| 455 | C4×D3 | — | 12 | 1 | no | — |
| 456 | C4×D3 | — | 12 | 1 | no | — |
| 457 | C4×D3 | — | 12 | 1 | no | — |
| 458 | C4×D3 | — | 12 | 1 | no | — |
| 459 | C4×D3 | — | 12 | 1 | no | — |
| 460 | C4×D3 | — | 12 | 1 | no | — |
| 461 | C4×D3 | — | 12 | 1 | no | — |
| 462 | C4×D3 | — | 12 | 1 | no | — |
| 463 | C4×D3 | — | 12 | 1 | no | — |
| 464 | Dic6 | — | 2 | 1 | no | — |
| 465 | Dic6 | — | 2 | 1 | no | — |
| 466 | Dic6 | — | 2 | 1 | no | — |
| 467 | Dic6 | — | 4 | 1 | no | — |
| 468 | Dic6 | — | 6 | 1 | no | — |
| 469 | Dic6 | — | 6 | 1 | no | — |
| 470 | Dic6 | — | 6 | 1 | no | — |
| 471 | Dic6 | — | 6 | 1 | no | — |
| 472 | Dic6 | — | 12 | 1 | no | — |
| 473 | Dic6 | — | 12 | 1 | no | — |
| 474 | Dic6 | — | 12 | 1 | no | — |
| 475 | Dic6 | — | 12 | 1 | no | — |
| 476 | Dic6 | — | 12 | 1 | no | — |
| 477 | Dic6 | — | 12 | 1 | no | — |
| 478 | Dic6 | — | 12 | 1 | no | — |
| 479 | C3×C8 | — | 2 | 1 | no | — |
| 480 | C3×C8 | — | 2 | 1 | no | — |
| 481 | C3×C8 | — | 6 | 1 | no | — |
| 482 | C3×C8 | — | 6 | 1 | no | — |
| 483 | C3⋊C8 | — | 2 | 1 | no | — |
| 484 | C3⋊C8 | — | 2 | 1 | no | — |
| 485 | C3⋊C8 | — | 6 | 1 | no | — |
| 486 | C3⋊C8 | — | 6 | 1 | no | — |
| 487 | C2×C32 | — | 4 | 1 | no | — |
| 488 | C2×C32 | D42 | 1 | 1 | yes | characteristic |
| 489 | C3⋊D3 | — | 2 | 1 | no | — |
| 490 | C3⋊D3 | — | 4 | 1 | no | — |
| 491 | C3×D3 | — | 4 | 1 | no | — |
| 492 | C3×D3 | — | 4 | 1 | no | — |
| 493 | C3×D3 | — | 8 | 1 | no | — |
| 494 | #41 | — | 6 | 1 | no | — |
| 495 | #41 | — | 6 | 1 | no | — |
| 496 | #41 | — | 6 | 1 | no | — |
| 497 | #41 | — | 9 | 1 | no | — |
| 498 | #41 | — | 9 | 1 | no | — |
| 499 | #41 | — | 9 | 1 | no | — |
| 500 | #41 | — | 9 | 1 | no | — |
| 501 | #41 | — | 18 | 1 | no | — |
| 502 | #41 | — | 18 | 1 | no | — |
| 503 | #41 | — | 18 | 1 | no | — |
| 504 | #41 | — | 18 | 1 | no | — |
| 505 | #41 | — | 18 | 1 | no | — |
| 506 | #41 | — | 36 | 1 | no | — |
| 507 | #41 | — | 36 | 1 | no | — |
| 508 | #41 | — | 36 | 1 | no | — |
| 509 | C2×Q8 | — | 6 | 1 | no | — |
| 510 | C2×Q8 | — | 9 | 1 | no | — |
| 511 | C2×Q8 | — | 9 | 1 | no | — |
| 512 | C2×Q8 | — | 9 | 1 | no | — |
| 513 | C2×Q8 | — | 18 | 1 | no | — |
| 514 | C2×Q8 | — | 18 | 1 | no | — |
| 515 | C2×Q8 | — | 18 | 1 | no | — |
| 516 | C2×Q8 | — | 18 | 1 | no | — |
| 517 | C2×Q8 | — | 18 | 1 | no | — |
| 518 | C2×D4 | — | 9 | 1 | no | — |
| 519 | C2×D4 | — | 18 | 1 | no | — |
| 520 | C2×D4 | — | 18 | 1 | no | — |
| 521 | C2×D4 | — | 36 | 1 | no | — |
| 522 | Q16 | — | 6 | 1 | no | — |
| 523 | Q16 | — | 6 | 1 | no | — |
| 524 | Q16 | — | 6 | 1 | no | — |
| 525 | Q16 | — | 9 | 1 | no | — |
| 526 | Q16 | — | 9 | 1 | no | — |
| 527 | Q16 | — | 18 | 1 | no | — |
| 528 | Q16 | — | 18 | 1 | no | — |
| 529 | Q16 | — | 18 | 1 | no | — |
| 530 | Q16 | — | 18 | 1 | no | — |
| 531 | Q16 | — | 18 | 1 | no | — |
| 532 | Q16 | — | 18 | 1 | no | — |
| 533 | Q16 | — | 18 | 1 | no | — |
| 534 | SD16 | — | 6 | 1 | no | — |
| 535 | SD16 | — | 6 | 1 | no | — |
| 536 | SD16 | — | 9 | 1 | no | — |
| 537 | SD16 | — | 9 | 1 | no | — |
| 538 | SD16 | — | 9 | 1 | no | — |
| 539 | SD16 | — | 18 | 1 | no | — |
| 540 | SD16 | — | 18 | 1 | no | — |
| 541 | SD16 | — | 18 | 1 | no | — |
| 542 | SD16 | — | 18 | 1 | no | — |
| 543 | SD16 | — | 18 | 1 | no | — |
| 544 | SD16 | — | 18 | 1 | no | — |
| 545 | SD16 | — | 18 | 1 | no | — |
| 546 | SD16 | — | 18 | 1 | no | — |
| 547 | SD16 | — | 18 | 1 | no | — |
| 548 | SD16 | — | 18 | 1 | no | — |
| 549 | SD16 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 550 | D8 | — | 6 | 1 | no | — |
| 551 | D8 | — | 9 | 1 | no | — |
| 552 | D8 | — | 9 | 1 | no | — |
| 553 | D8 | — | 18 | 1 | no | — |
| 554 | M16 | — | 6 | 1 | no | — |
| 555 | M16 | — | 9 | 1 | no | — |
| 556 | M16 | — | 9 | 1 | no | — |
| 557 | M16 | — | 9 | 1 | no | — |
| 558 | M16 | — | 9 | 1 | no | — |
| 559 | M16 | — | 18 | 1 | no | — |
| 560 | M16 | — | 18 | 1 | no | — |
| 561 | M16 | — | 18 | 1 | no | — |
| 562 | C2×C8 | — | 6 | 1 | no | — |
| 563 | C2×C8 | — | 9 | 1 | no | — |
| 564 | C2×C8 | — | 9 | 1 | no | — |
| 565 | C2×C8 | — | 18 | 1 | no | — |
| 566 | C2×C8 | — | 18 | 1 | no | — |
| 567 | C2×C8 | — | 18 | 1 | no | — |
| 568 | C4⋊C4 | — | 36 | 1 | no | — |
| 569 | C22⋊C4 | — | 36 | 1 | no | — |
| 570 | C42 | — | 9 | 1 | no | — |
| 571 | C22×C3 | — | 4 | 1 | no | — |
| 572 | C22×C3 | — | 4 | 1 | no | — |
| 573 | C22×C3 | — | 6 | 1 | no | — |
| 574 | C22×C3 | — | 6 | 1 | no | — |
| 575 | C22×C3 | — | 12 | 1 | no | — |
| 576 | C2×D3 | — | 2 | 1 | no | — |
| 577 | C2×D3 | — | 2 | 1 | no | — |
| 578 | C2×D3 | — | 4 | 1 | no | — |
| 579 | C2×D3 | — | 6 | 1 | no | — |
| 580 | C2×D3 | — | 6 | 1 | no | — |
| 581 | C2×D3 | — | 12 | 1 | no | — |
| 582 | C2×D3 | — | 12 | 1 | no | — |
| 583 | C2×D3 | — | 48 | 1 | no | — |
| 584 | C2×D3 | — | 48 | 1 | no | — |
| 585 | C2×D3 | — | 48 | 1 | no | — |
| 586 | C3×C4 | — | 2 | 1 | no | — |
| 587 | C3×C4 | — | 2 | 1 | no | — |
| 588 | C3×C4 | — | 4 | 1 | no | — |
| 589 | C3×C4 | — | 4 | 1 | no | — |
| 590 | C3×C4 | — | 6 | 1 | no | — |
| 591 | C3×C4 | — | 6 | 1 | no | — |
| 592 | C3×C4 | — | 12 | 1 | no | — |
| 593 | C3×C4 | — | 12 | 1 | no | — |
| 594 | C3×C4 | — | 12 | 1 | no | — |
| 595 | Dic3 | — | 2 | 1 | no | — |
| 596 | Dic3 | — | 2 | 1 | no | — |
| 597 | Dic3 | — | 4 | 1 | no | — |
| 598 | Dic3 | — | 4 | 1 | no | — |
| 599 | Dic3 | — | 4 | 1 | no | — |
| 600 | Dic3 | — | 6 | 1 | no | — |
| 601 | Dic3 | — | 6 | 1 | no | — |
| 602 | Dic3 | — | 12 | 1 | no | — |
| 603 | Dic3 | — | 12 | 1 | no | — |
| 604 | C32 | #3289 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 605 | C23 | — | 18 | 1 | no | — |
| 606 | C23 | — | 36 | 1 | no | — |
| 607 | Q8 | — | 6 | 1 | no | — |
| 608 | Q8 | — | 6 | 1 | no | — |
| 609 | Q8 | — | 6 | 1 | no | — |
| 610 | Q8 | — | 9 | 1 | no | — |
| 611 | Q8 | — | 9 | 1 | no | — |
| 612 | Q8 | — | 9 | 1 | no | — |
| 613 | Q8 | — | 12 | 1 | no | — |
| 614 | Q8 | — | 18 | 1 | no | — |
| 615 | Q8 | — | 18 | 1 | no | — |
| 616 | Q8 | — | 18 | 1 | no | — |
| 617 | Q8 | — | 36 | 1 | no | — |
| 618 | Q8 | — | 36 | 1 | no | — |
| 619 | Q8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 620 | D4 | — | 6 | 1 | no | — |
| 621 | D4 | — | 9 | 1 | no | — |
| 622 | D4 | — | 9 | 1 | no | — |
| 623 | D4 | — | 9 | 1 | no | — |
| 624 | D4 | — | 12 | 1 | no | — |
| 625 | D4 | — | 12 | 1 | no | — |
| 626 | D4 | — | 12 | 1 | no | — |
| 627 | D4 | — | 18 | 1 | no | — |
| 628 | D4 | — | 18 | 1 | no | — |
| 629 | D4 | — | 18 | 1 | no | — |
| 630 | D4 | — | 18 | 1 | no | — |
| 631 | D4 | — | 18 | 1 | no | — |
| 632 | D4 | — | 36 | 1 | no | — |
| 633 | D4 | — | 36 | 1 | no | — |
| 634 | D4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 635 | C2×C4 | — | 6 | 1 | no | — |
| 636 | C2×C4 | — | 6 | 1 | no | — |
| 637 | C2×C4 | — | 9 | 1 | no | — |
| 638 | C2×C4 | — | 12 | 1 | no | — |
| 639 | C2×C4 | — | 12 | 1 | no | — |
| 640 | C2×C4 | — | 12 | 1 | no | — |
| 641 | C2×C4 | — | 12 | 1 | no | — |
| 642 | C2×C4 | — | 18 | 1 | no | — |
| 643 | C2×C4 | — | 18 | 1 | no | — |
| 644 | C2×C4 | — | 18 | 1 | no | — |
| 645 | C2×C4 | — | 18 | 1 | no | — |
| 646 | C2×C4 | — | 18 | 1 | no | — |
| 647 | C2×C4 | — | 18 | 1 | no | — |
| 648 | C2×C4 | — | 36 | 1 | no | — |
| 649 | C2×C4 | — | 36 | 1 | no | — |
| 650 | C2×C4 | — | 36 | 1 | no | — |
| 651 | C8 | — | 6 | 1 | no | — |
| 652 | C8 | — | 6 | 1 | no | — |
| 653 | C8 | — | 9 | 1 | no | — |
| 654 | C8 | — | 9 | 1 | no | — |
| 655 | C8 | — | 9 | 1 | no | — |
| 656 | C8 | — | 18 | 1 | no | — |
| 657 | C8 | — | 18 | 1 | no | — |
| 658 | C8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 659 | C2×C3 | — | 2 | 1 | no | — |
| 660 | C2×C3 | — | 2 | 1 | no | — |
| 661 | C2×C3 | — | 8 | 1 | no | — |
| 662 | C2×C3 | — | 8 | 1 | no | — |
| 663 | C2×C3 | — | 12 | 1 | no | — |
| 664 | C2×C3 | — | 12 | 1 | no | — |
| 665 | C2×C3 | — | 24 | 1 | no | — |
| 666 | D3 | — | 4 | 1 | no | — |
| 667 | D3 | — | 4 | 1 | no | — |
| 668 | D3 | — | 8 | 1 | no | — |
| 669 | D3 | — | 12 | 1 | no | — |
| 670 | D3 | — | 12 | 1 | no | — |
| 671 | D3 | — | 24 | 1 | no | — |
| 672 | D3 | — | 24 | 1 | no | — |
| 673 | C22 | — | 2 | 1 | no | — |
| 674 | C22 | — | 6 | 1 | no | — |
| 675 | C22 | — | 6 | 1 | no | — |
| 676 | C22 | — | 9 | 1 | no | — |
| 677 | C22 | — | 12 | 1 | no | — |
| 678 | C22 | — | 18 | 1 | no | — |
| 679 | C22 | — | 72 | 1 | no | — |
| 680 | C22 | — | 144 | 1 | no | — |
| 681 | C4 | — | 2 | 1 | no | — |
| 682 | C4 | — | 6 | 1 | no | — |
| 683 | C4 | — | 6 | 1 | no | — |
| 684 | C4 | — | 9 | 1 | no | — |
| 685 | C4 | — | 12 | 1 | no | — |
| 686 | C4 | — | 12 | 1 | no | — |
| 687 | C4 | — | 12 | 1 | no | — |
| 688 | C4 | — | 18 | 1 | no | — |
| 689 | C4 | — | 36 | 1 | no | — |
| 690 | C4 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 691 | C3 | — | 2 | 1 | no | — |
| 692 | C3 | — | 2 | 1 | no | — |
| 693 | C2 | — | 4 | 1 | no | — |
| 694 | C2 | — | 12 | 1 | no | — |
| 695 | C2 | — | 12 | 1 | no | — |
| 696 | C2 | — | 18 | 1 | no | — |
| 697 | C2 | — | 24 | 1 | no | — |
| 698 | C2 | — | 36 | 1 | no | — |
| 699 | C2 | D4×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596521 | C2 | semidirect |
| 2. #10596516 | C2 | semidirect |
| 3. #10594757 | C2 | semidirect |
| 4. #10594752 | C2 | semidirect |
| 5. #10593784 | C2 | semidirect |
| 6. #10593484 | C2 | semidirect |
| 7. #10593482 | C2 | semidirect |
| 8. #10593473 | C2 | semidirect |
| 9. #10593470 | C2 | semidirect |
| 10. #10593469 | C2 | semidirect |
| 11. #10593467 | C2 | semidirect |
| 12. #10593304 | C2 | semidirect |
| 13. #10593302 | C2 | semidirect |
| 14. #10593298 | C2 | semidirect |
| 15. #10593291 | C2 | semidirect |
| 19. #64309 | C22 | semidirect |
| 21. #64287 | C22 | semidirect |
| 26. #64228 | C22 | semidirect |
| 32. #64226 | C22 | semidirect |
| 37. #64222 | C22 | semidirect |
| 47. #63931 | C22 | semidirect |
| 50. #63805 | C22 | semidirect |
| 52. #63802 | C22 | semidirect |
| 57. #63783 | C22 | semidirect |
| 58. #63771 | C22 | semidirect |
| 59. #63767 | C22 | semidirect |
| 60. #63733 | C22 | semidirect |
| 62. #63731 | C22 | semidirect |
| 63. #63728 | C22 | semidirect |
| 64. #63728 | C22 | semidirect |
| 65. #63728 | C22 | semidirect |
| 604. C32 | #3289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596521 | 2 |
| #10596516 | 2 |
| #10594757 | 2 |
| #10594752 | 2 |
| #10593784 | 2 |
| #10593484 | 2 |
| #10593482 | 2 |
| #10593473 | 2 |
| #10593470 | 2 |
| #10593469 | 2 |
| #10593467 | 2 |
| #10593304 | 2 |
| #10593302 | 2 |
| #10593298 | 2 |
| #10593291 | 2 |
| #3289 | 9 |