Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1104 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 110 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 | D3×#3802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724398 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11724340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724305 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11724304 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#64224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11724255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11724139 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11724138 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11724129 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11724127 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10596501 | — | 3 | 1 | no | maximal |
| 13 | C2×D33 | — | 2 | 1 | no | — |
| 14 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #89042 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #89026 | — | 2 | 1 | no | — |
| 17 | C4×D3×C3⋊D3 | — | 2 | 1 | no | — |
| 18 | C4×D3×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#3802 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×D3×D12 | — | 2 | 1 | no | — |
| 21 | C3×#3798 | — | 2 | 1 | no | — |
| 22 | C3×#3798 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #88989 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×#3788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #88964 | — | 2 | 1 | no | — |
| 26 | #88964 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #88963 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #88958 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88954 | — | 2 | 1 | no | — |
| 30 | #88954 | C22 | 1 | 2 | yes | — |
| 31 | #88954 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #88953 | — | 2 | 1 | no | — |
| 33 | D3×#625 | C22 | 1 | 2 | yes | complemented |
| 34 | #88942 | C22 | 1 | 2 | yes | complemented |
| 35 | #88941 | C22 | 1 | 2 | yes | complemented |
| 36 | #88937 | C22 | 1 | 2 | yes | complemented |
| 37 | #88936 | C22 | 1 | 2 | yes | complemented |
| 38 | #88935 | C22 | 1 | 2 | yes | complemented |
| 39 | #88935 | C22 | 1 | 2 | yes | complemented |
| 40 | C3×#3775 | C22 | 1 | 2 | yes | complemented |
| 41 | C3×#3774 | C22 | 1 | 2 | yes | complemented |
| 42 | #88925 | C22 | 1 | 2 | yes | complemented |
| 43 | #88924 | C22 | 1 | 2 | yes | complemented |
| 44 | D32×D4 | — | 6 | 1 | no | — |
| 45 | #64306 | — | 3 | 1 | no | — |
| 46 | #64306 | — | 6 | 1 | no | — |
| 47 | C2×#3802 | — | 3 | 1 | no | — |
| 48 | #64283 | — | 3 | 1 | no | — |
| 49 | #64236 | — | 3 | 2 | no | — |
| 50 | #64236 | — | 3 | 2 | no | — |
| 51 | #64227 | — | 3 | 2 | no | — |
| 52 | #64225 | — | 3 | 2 | no | — |
| 53 | #64224 | — | 3 | 1 | no | — |
| 54 | #64224 | — | 3 | 1 | no | — |
| 55 | #64224 | — | 3 | 1 | no | — |
| 56 | #64224 | D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | C2×#1113 | — | 2 | 1 | no | — |
| 58 | C2×D3×C3⋊D3 | — | 2 | 2 | no | — |
| 59 | C2×D3×C3⋊D3 | — | 2 | 1 | no | — |
| 60 | C2×D3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×C3×D32 | — | 2 | 1 | no | — |
| 62 | C2×C3×D32 | — | 2 | 2 | no | — |
| 63 | D33 | — | 4 | 4 | no | — |
| 64 | C4×C3⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 65 | C3×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 66 | C3×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 67 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 68 | C32×D12 | — | 2 | 1 | no | — |
| 69 | C32×C4×D3 | — | 2 | 1 | no | — |
| 70 | C32×C4×D3 | D4 | 1 | 1 | yes | characteristic |
| 71 | #6296 | C23 | 1 | 1 | yes | characteristic, complemented |
| 72 | #6295 | — | 2 | 1 | no | — |
| 73 | #6295 | C23 | 1 | 2 | yes | — |
| 74 | #6295 | C23 | 1 | 1 | yes | characteristic, complemented |
| 75 | #6290 | — | 2 | 2 | no | — |
| 76 | #6289 | — | 2 | 1 | no | — |
| 77 | #6289 | C23 | 1 | 1 | yes | characteristic |
| 78 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 79 | Dic3×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 80 | D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 81 | D3×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×#627 | — | 2 | 1 | no | — |
| 83 | C3×#627 | C23 | 1 | 1 | yes | characteristic, complemented |
| 84 | C3×#626 | — | 2 | 1 | no | — |
| 85 | C3×#626 | — | 2 | 1 | no | — |
| 86 | C3×#626 | — | 2 | 2 | no | — |
| 87 | C3×#626 | — | 2 | 1 | no | — |
| 88 | C3×#625 | — | 2 | 1 | no | — |
| 89 | C3×#625 | C23 | 1 | 2 | yes | — |
| 90 | C3×#625 | C23 | 1 | 1 | yes | characteristic, complemented |
| 91 | C3⋊#622 | C23 | 1 | 2 | yes | complemented |
| 92 | C3×#622 | C23 | 1 | 2 | yes | complemented |
| 93 | D3×AGL(1,ℤ/8) | — | 9 | 1 | no | maximal |
| 94 | C22×D32 | — | 6 | 1 | no | — |
| 95 | C22×D32 | — | 6 | 2 | no | — |
| 96 | D4×C3⋊D3 | — | 6 | 1 | no | — |
| 97 | C2×C4×C3⋊D3 | — | 3 | 1 | no | — |
| 98 | C2×C4×C3⋊D3 | — | 6 | 1 | no | — |
| 99 | C3×D3×D4 | — | 6 | 1 | no | — |
| 100 | C3×D3×D4 | — | 6 | 1 | no | — |
| 101 | C3×#235 | — | 6 | 1 | no | — |
| 102 | C3×#235 | — | 6 | 1 | no | — |
| 103 | C3×#235 | — | 6 | 1 | no | — |
| 104 | C2×C3×D12 | — | 6 | 1 | no | — |
| 105 | #3811 | — | 6 | 1 | no | — |
| 106 | #3811 | — | 6 | 1 | no | — |
| 107 | #3811 | — | 6 | 2 | no | — |
| 108 | #3811 | — | 6 | 1 | no | — |
| 109 | D3×#67 | — | 6 | 2 | no | — |
| 110 | D3×#67 | — | 6 | 2 | no | — |
| 111 | C2×#625 | — | 3 | 2 | no | — |
| 112 | #3805 | — | 3 | 1 | no | — |
| 113 | #3805 | — | 3 | 1 | no | — |
| 114 | #3805 | — | 6 | 1 | no | — |
| 115 | #3805 | — | 6 | 1 | no | — |
| 116 | #3802 | — | 3 | 1 | no | — |
| 117 | #3802 | — | 3 | 2 | no | — |
| 118 | #3802 | — | 3 | 1 | no | — |
| 119 | #3802 | — | 6 | 1 | no | — |
| 120 | #3802 | — | 6 | 1 | no | — |
| 121 | #3802 | — | 6 | 1 | no | — |
| 122 | #3802 | — | 6 | 1 | no | — |
| 123 | #3802 | — | 12 | 1 | no | — |
| 124 | #3802 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 125 | D3×D12 | — | 2 | 1 | no | — |
| 126 | D3×D12 | — | 6 | 1 | no | — |
| 127 | C4×D32 | — | 6 | 1 | no | — |
| 128 | C4×D32 | — | 6 | 1 | no | — |
| 129 | C4×D32 | — | 6 | 1 | no | — |
| 130 | C4×D32 | — | 6 | 1 | no | — |
| 131 | C4×D32 | — | 12 | 1 | no | — |
| 132 | #3798 | — | 2 | 1 | no | — |
| 133 | #3798 | — | 3 | 1 | no | — |
| 134 | #3798 | — | 6 | 1 | no | — |
| 135 | #3798 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 136 | #3797 | — | 3 | 1 | no | — |
| 137 | #3797 | — | 6 | 1 | no | — |
| 138 | #3796 | — | 6 | 1 | no | — |
| 139 | #3796 | — | 6 | 1 | no | — |
| 140 | #3796 | — | 6 | 1 | no | — |
| 141 | #3792 | — | 3 | 2 | no | — |
| 142 | #3788 | — | 3 | 1 | no | — |
| 143 | #3788 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 144 | #3787 | — | 3 | 2 | no | — |
| 145 | #3775 | — | 3 | 2 | no | — |
| 146 | #3775 | — | 3 | 2 | no | — |
| 147 | #3775 | — | 3 | 2 | no | — |
| 148 | #3775 | C2×D3 | 1 | 2 | yes | complemented |
| 149 | #3774 | — | 3 | 2 | no | — |
| 150 | #3774 | — | 3 | 2 | no | — |
| 151 | #3774 | — | 3 | 2 | no | — |
| 152 | #3774 | C2×D3 | 1 | 2 | yes | complemented |
| 153 | C2×C3⋊(C3⋊D3) | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 155 | C2×C3×C3⋊D3 | — | 2 | 2 | no | — |
| 156 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C32×D3 | — | 2 | 1 | no | — |
| 158 | C2×C32×D3 | — | 2 | 2 | no | — |
| 159 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | #1113 | — | 4 | 2 | no | — |
| 161 | D3×C3⋊D3 | — | 2 | 2 | no | — |
| 162 | D3×C3⋊D3 | — | 4 | 2 | no | — |
| 163 | D3×C3⋊D3 | — | 4 | 4 | no | — |
| 164 | C3×D32 | — | 4 | 4 | no | — |
| 165 | C3×D32 | — | 4 | 2 | no | — |
| 166 | C33×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C3⋊(C3⋊Dic3) | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 169 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 170 | C32×Dic3 | — | 2 | 1 | no | — |
| 171 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | D3×#41 | — | 9 | 1 | no | — |
| 173 | D3×#41 | — | 18 | 1 | no | — |
| 174 | C2×D3×D4 | — | 9 | 1 | no | — |
| 175 | C2×D3×D4 | — | 18 | 1 | no | — |
| 176 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 177 | #949 | — | 9 | 1 | no | — |
| 178 | #932 | — | 9 | 1 | no | — |
| 179 | #914 | — | 9 | 2 | no | — |
| 180 | D3×SD16 | — | 9 | 2 | no | — |
| 181 | #911 | — | 9 | 2 | no | — |
| 182 | D3×D8 | — | 9 | 2 | no | — |
| 183 | #908 | — | 9 | 1 | no | — |
| 184 | D3×M16 | — | 9 | 1 | no | — |
| 185 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 186 | C22×C3⋊D3 | — | 6 | 2 | no | — |
| 187 | C22×C3⋊D3 | — | 6 | 1 | no | — |
| 188 | C22×C3×D3 | — | 6 | 2 | no | — |
| 189 | C22×C3×D3 | — | 6 | 2 | no | — |
| 190 | C22×C3×D3 | — | 6 | 2 | no | — |
| 191 | C2×D32 | — | 2 | 2 | no | — |
| 192 | C2×D32 | — | 2 | 1 | no | — |
| 193 | C2×D32 | — | 6 | 1 | no | — |
| 194 | C2×D32 | — | 6 | 1 | no | — |
| 195 | C2×D32 | — | 6 | 2 | no | — |
| 196 | C2×D32 | — | 6 | 1 | no | — |
| 197 | C2×D32 | — | 6 | 2 | no | — |
| 198 | C2×D32 | — | 6 | 1 | no | — |
| 199 | C2×D32 | — | 6 | 2 | no | — |
| 200 | C2×D32 | — | 6 | 1 | no | — |
| 201 | C2×D32 | — | 12 | 1 | no | — |
| 202 | C2×D32 | — | 12 | 2 | no | — |
| 203 | C2×D32 | — | 12 | 8 | no | — |
| 204 | C2×D32 | — | 12 | 4 | no | — |
| 205 | C32×D4 | — | 6 | 1 | no | — |
| 206 | C2×C32×C4 | — | 3 | 1 | no | — |
| 207 | C2×C32×C4 | — | 6 | 1 | no | — |
| 208 | #638 | — | 6 | 2 | no | — |
| 209 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 210 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 211 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 212 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 213 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 214 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 215 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 216 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 217 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 218 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 219 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 220 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 221 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 222 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 223 | C3×#67 | — | 6 | 2 | no | — |
| 224 | C3×#67 | — | 6 | 1 | no | — |
| 225 | C3×#67 | — | 6 | 1 | no | — |
| 226 | C3×#67 | — | 6 | 1 | no | — |
| 227 | C3×#67 | — | 6 | 1 | no | — |
| 228 | C3×#67 | — | 6 | 2 | no | — |
| 229 | C3×#67 | — | 6 | 1 | no | — |
| 230 | C3×#67 | — | 6 | 1 | no | — |
| 231 | C3×D12 | — | 2 | 1 | no | — |
| 232 | C3×D12 | — | 2 | 1 | no | — |
| 233 | C3×D12 | — | 4 | 1 | no | — |
| 234 | C3×D12 | — | 6 | 1 | no | — |
| 235 | C3×D12 | — | 6 | 1 | no | — |
| 236 | C3×D12 | — | 6 | 2 | no | — |
| 237 | C3×D12 | — | 6 | 1 | no | — |
| 238 | C3×D12 | — | 6 | 1 | no | — |
| 239 | C3×D12 | — | 6 | 1 | no | — |
| 240 | C3×D12 | — | 12 | 1 | no | — |
| 241 | C3×C4×D3 | — | 2 | 1 | no | — |
| 242 | C3×C4×D3 | — | 2 | 1 | no | — |
| 243 | C3×C4×D3 | — | 2 | 1 | no | — |
| 244 | C3×C4×D3 | — | 2 | 1 | no | — |
| 245 | C3×C4×D3 | — | 4 | 1 | no | — |
| 246 | C3×C4×D3 | — | 6 | 1 | no | — |
| 247 | C3×C4×D3 | — | 6 | 1 | no | — |
| 248 | C3×C4×D3 | — | 6 | 1 | no | — |
| 249 | C3×C4×D3 | — | 6 | 1 | no | — |
| 250 | C3×C4×D3 | — | 12 | 1 | no | — |
| 251 | C3×Dic6 | — | 6 | 1 | no | — |
| 252 | C3×Dic6 | — | 6 | 1 | no | — |
| 253 | C3×Dic6 | — | 6 | 1 | no | — |
| 254 | #627 | — | 2 | 1 | no | — |
| 255 | #627 | — | 3 | 1 | no | — |
| 256 | #627 | — | 6 | 1 | no | — |
| 257 | #627 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 258 | #626 | — | 2 | 1 | no | — |
| 259 | #626 | — | 2 | 1 | no | — |
| 260 | #626 | — | 2 | 2 | no | — |
| 261 | #626 | — | 2 | 1 | no | — |
| 262 | #626 | — | 6 | 2 | no | — |
| 263 | #626 | — | 6 | 1 | no | — |
| 264 | #626 | — | 6 | 1 | no | — |
| 265 | #626 | — | 6 | 1 | no | — |
| 266 | #625 | — | 2 | 1 | no | — |
| 267 | #625 | — | 3 | 2 | no | — |
| 268 | #625 | — | 3 | 1 | no | — |
| 269 | #625 | — | 6 | 1 | no | — |
| 270 | #625 | — | 6 | 2 | no | — |
| 271 | #625 | — | 6 | 2 | no | — |
| 272 | #625 | — | 12 | 2 | no | — |
| 273 | #625 | C22×D3 | 1 | 2 | yes | — |
| 274 | #625 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 275 | #624 | — | 6 | 1 | no | — |
| 276 | #624 | — | 6 | 1 | no | — |
| 277 | #624 | — | 6 | 1 | no | — |
| 278 | #624 | — | 6 | 1 | no | — |
| 279 | #624 | — | 12 | 1 | no | — |
| 280 | D3×Dic3 | — | 6 | 1 | no | — |
| 281 | D3×Dic3 | — | 6 | 1 | no | — |
| 282 | D3×Dic3 | — | 6 | 1 | no | — |
| 283 | D3×Dic3 | — | 6 | 1 | no | — |
| 284 | D3×Dic3 | — | 6 | 1 | no | — |
| 285 | D3×Dic3 | — | 6 | 1 | no | — |
| 286 | D3×Dic3 | — | 6 | 1 | no | — |
| 287 | D3×Dic3 | — | 6 | 1 | no | — |
| 288 | D3×Dic3 | — | 12 | 1 | no | — |
| 289 | D3×Dic3 | — | 12 | 1 | no | — |
| 290 | #622 | — | 3 | 2 | no | — |
| 291 | #622 | C22×D3 | 1 | 2 | yes | complemented |
| 292 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | Sylow |
| 293 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 294 | C3⋊(C3⋊D3) | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 295 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 296 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 297 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 298 | C32×D3 | — | 2 | 1 | no | — |
| 299 | C32×D3 | — | 4 | 1 | no | — |
| 300 | C32×D3 | — | 4 | 2 | no | — |
| 301 | C23×D3 | — | 18 | 1 | no | — |
| 302 | C23×D3 | — | 18 | 2 | no | — |
| 303 | C3×#41 | — | 9 | 1 | no | — |
| 304 | C3×#41 | — | 18 | 1 | no | — |
| 305 | C2×C3×D4 | — | 9 | 1 | no | — |
| 306 | C2×C3×D4 | — | 18 | 1 | no | — |
| 307 | C2×#67 | — | 18 | 2 | no | — |
| 308 | C2×#67 | — | 18 | 1 | no | — |
| 309 | #239 | — | 9 | 1 | no | — |
| 310 | #239 | — | 18 | 1 | no | — |
| 311 | D3×Q8 | — | 9 | 1 | no | — |
| 312 | D3×Q8 | — | 18 | 1 | no | — |
| 313 | #237 | — | 9 | 1 | no | — |
| 314 | #237 | — | 18 | 1 | no | — |
| 315 | #237 | — | 18 | 1 | no | — |
| 316 | #237 | — | 18 | 1 | no | — |
| 317 | #237 | — | 18 | 1 | no | — |
| 318 | D3×D4 | — | 6 | 1 | no | — |
| 319 | D3×D4 | — | 6 | 1 | no | — |
| 320 | D3×D4 | — | 9 | 1 | no | — |
| 321 | D3×D4 | — | 9 | 2 | no | — |
| 322 | D3×D4 | — | 9 | 2 | no | — |
| 323 | D3×D4 | — | 18 | 1 | no | — |
| 324 | D3×D4 | — | 18 | 2 | no | — |
| 325 | D3×D4 | — | 18 | 1 | no | — |
| 326 | D3×D4 | — | 18 | 1 | no | — |
| 327 | D3×D4 | — | 18 | 1 | no | — |
| 328 | D3×D4 | — | 18 | 1 | no | — |
| 329 | D3×D4 | — | 18 | 1 | no | — |
| 330 | D3×D4 | — | 18 | 1 | no | — |
| 331 | D3×D4 | — | 18 | 2 | no | — |
| 332 | D3×D4 | — | 18 | 1 | no | — |
| 333 | D3×D4 | — | 36 | 1 | no | — |
| 334 | #235 | — | 6 | 1 | no | — |
| 335 | #235 | — | 6 | 1 | no | — |
| 336 | #235 | — | 6 | 1 | no | — |
| 337 | #235 | — | 9 | 1 | no | — |
| 338 | #235 | — | 18 | 1 | no | — |
| 339 | C2×D12 | — | 6 | 1 | no | — |
| 340 | C2×D12 | — | 9 | 1 | no | — |
| 341 | C2×C4×D3 | — | 9 | 1 | no | — |
| 342 | C2×C4×D3 | — | 18 | 1 | no | — |
| 343 | C2×C4×D3 | — | 18 | 1 | no | — |
| 344 | C2×C4×D3 | — | 18 | 1 | no | — |
| 345 | C2×C4×D3 | — | 18 | 1 | no | — |
| 346 | C2×C4×D3 | — | 18 | 1 | no | — |
| 347 | C2×C4×D3 | — | 36 | 1 | no | — |
| 348 | C3×SD16 | — | 9 | 2 | no | — |
| 349 | C3×D8 | — | 9 | 2 | no | — |
| 350 | C3×M16 | — | 9 | 1 | no | — |
| 351 | #215 | — | 9 | 2 | no | — |
| 352 | #214 | — | 9 | 2 | no | — |
| 353 | #213 | — | 9 | 2 | no | — |
| 354 | #213 | — | 9 | 2 | no | — |
| 355 | #208 | — | 9 | 1 | no | — |
| 356 | D24 | — | 9 | 2 | no | — |
| 357 | #204 | — | 9 | 2 | no | — |
| 358 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 359 | D3×C8 | — | 9 | 2 | no | — |
| 360 | C22×C32 | — | 3 | 1 | no | — |
| 361 | C22×C32 | — | 6 | 1 | no | — |
| 362 | C22×C32 | — | 6 | 2 | no | — |
| 363 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 364 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 365 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 366 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 367 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 368 | C2×C3⋊D3 | — | 6 | 2 | no | — |
| 369 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 370 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 371 | C2×C3⋊D3 | — | 12 | 2 | no | — |
| 372 | C2×C3⋊D3 | — | 12 | 4 | no | — |
| 373 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C3×D3 | — | 2 | 1 | no | — |
| 375 | C2×C3×D3 | — | 2 | 2 | no | — |
| 376 | C2×C3×D3 | — | 2 | 1 | no | — |
| 377 | C2×C3×D3 | — | 2 | 2 | no | — |
| 378 | C2×C3×D3 | — | 2 | 1 | no | — |
| 379 | C2×C3×D3 | — | 2 | 1 | no | — |
| 380 | C2×C3×D3 | — | 4 | 1 | no | — |
| 381 | C2×C3×D3 | — | 4 | 2 | no | — |
| 382 | C2×C3×D3 | — | 6 | 1 | no | — |
| 383 | C2×C3×D3 | — | 6 | 1 | no | — |
| 384 | C2×C3×D3 | — | 6 | 1 | no | — |
| 385 | C2×C3×D3 | — | 6 | 2 | no | — |
| 386 | C2×C3×D3 | — | 6 | 1 | no | — |
| 387 | C2×C3×D3 | — | 6 | 2 | no | — |
| 388 | C2×C3×D3 | — | 12 | 1 | no | — |
| 389 | C2×C3×D3 | — | 12 | 2 | no | — |
| 390 | C2×C3×D3 | — | 12 | 4 | no | — |
| 391 | C2×C3×D3 | — | 12 | 4 | no | — |
| 392 | C2×C3×D3 | — | 12 | 4 | no | — |
| 393 | D32 | — | 4 | 4 | no | — |
| 394 | D32 | — | 4 | 2 | no | — |
| 395 | D32 | — | 6 | 4 | no | — |
| 396 | D32 | — | 12 | 2 | no | — |
| 397 | D32 | — | 12 | 2 | no | — |
| 398 | D32 | — | 12 | 4 | no | — |
| 399 | D32 | — | 12 | 2 | no | — |
| 400 | D32 | — | 12 | 4 | no | — |
| 401 | D32 | — | 12 | 4 | no | — |
| 402 | D32 | — | 12 | 4 | no | — |
| 403 | D32 | — | 12 | 2 | no | — |
| 404 | D32 | — | 24 | 4 | no | — |
| 405 | C32×C4 | — | 2 | 1 | no | — |
| 406 | C32×C4 | — | 2 | 1 | no | — |
| 407 | C32×C4 | — | 3 | 1 | no | — |
| 408 | C32×C4 | — | 4 | 1 | no | — |
| 409 | C32×C4 | — | 4 | 1 | no | — |
| 410 | C32×C4 | — | 6 | 1 | no | — |
| 411 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 412 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 413 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 414 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 415 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 416 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 417 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 418 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 419 | C3×Dic3 | — | 2 | 1 | no | — |
| 420 | C3×Dic3 | — | 2 | 1 | no | — |
| 421 | C3×Dic3 | — | 2 | 1 | no | — |
| 422 | C3×Dic3 | — | 2 | 1 | no | — |
| 423 | C3×Dic3 | — | 4 | 1 | no | — |
| 424 | C3×Dic3 | — | 6 | 1 | no | — |
| 425 | C3×Dic3 | — | 6 | 1 | no | — |
| 426 | C3×Dic3 | — | 6 | 1 | no | — |
| 427 | C3×Dic3 | — | 6 | 1 | no | — |
| 428 | C3×Dic3 | — | 12 | 1 | no | — |
| 429 | C2×#41 | — | 27 | 1 | no | — |
| 430 | C22×D4 | — | 27 | 1 | no | — |
| 431 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 432 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 433 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 434 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 435 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 436 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 437 | C2×SD16 | — | 27 | 2 | no | — |
| 438 | C2×D8 | — | 27 | 2 | no | — |
| 439 | C2×M16 | — | 27 | 1 | no | — |
| 440 | C33 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 441 | C23×C3 | — | 18 | 1 | no | — |
| 442 | C23×C3 | — | 18 | 2 | no | — |
| 443 | C22×D3 | — | 6 | 2 | no | — |
| 444 | C22×D3 | — | 6 | 2 | no | — |
| 445 | C22×D3 | — | 6 | 2 | no | — |
| 446 | C22×D3 | — | 9 | 1 | no | — |
| 447 | C22×D3 | — | 18 | 1 | no | — |
| 448 | C22×D3 | — | 18 | 1 | no | — |
| 449 | C22×D3 | — | 18 | 1 | no | — |
| 450 | C22×D3 | — | 18 | 2 | no | — |
| 451 | C22×D3 | — | 18 | 1 | no | — |
| 452 | C22×D3 | — | 18 | 2 | no | — |
| 453 | C22×D3 | — | 18 | 1 | no | — |
| 454 | C22×D3 | — | 18 | 2 | no | — |
| 455 | C22×D3 | — | 18 | 1 | no | — |
| 456 | C22×D3 | — | 18 | 2 | no | — |
| 457 | C22×D3 | — | 36 | 1 | no | — |
| 458 | C22×D3 | — | 36 | 2 | no | — |
| 459 | C22×D3 | — | 36 | 4 | no | — |
| 460 | C22×D3 | — | 36 | 8 | no | — |
| 461 | C3×Q8 | — | 9 | 1 | no | — |
| 462 | C3×Q8 | — | 18 | 1 | no | — |
| 463 | C3×D4 | — | 6 | 1 | no | — |
| 464 | C3×D4 | — | 6 | 1 | no | — |
| 465 | C3×D4 | — | 9 | 1 | no | — |
| 466 | C3×D4 | — | 9 | 2 | no | — |
| 467 | C3×D4 | — | 12 | 1 | no | — |
| 468 | C3×D4 | — | 18 | 1 | no | — |
| 469 | C3×D4 | — | 18 | 1 | no | — |
| 470 | C3×D4 | — | 18 | 2 | no | — |
| 471 | C3×D4 | — | 18 | 1 | no | — |
| 472 | C3×D4 | — | 18 | 1 | no | — |
| 473 | C3×D4 | — | 18 | 1 | no | — |
| 474 | C2×C3×C4 | — | 6 | 1 | no | — |
| 475 | C2×C3×C4 | — | 6 | 1 | no | — |
| 476 | C2×C3×C4 | — | 6 | 1 | no | — |
| 477 | C2×C3×C4 | — | 6 | 1 | no | — |
| 478 | C2×C3×C4 | — | 9 | 1 | no | — |
| 479 | C2×C3×C4 | — | 12 | 1 | no | — |
| 480 | C2×C3×C4 | — | 18 | 1 | no | — |
| 481 | #67 | — | 6 | 2 | no | — |
| 482 | #67 | — | 6 | 1 | no | — |
| 483 | #67 | — | 6 | 1 | no | — |
| 484 | #67 | — | 6 | 1 | no | — |
| 485 | #67 | — | 6 | 1 | no | — |
| 486 | #67 | — | 6 | 1 | no | — |
| 487 | #67 | — | 6 | 1 | no | — |
| 488 | #67 | — | 6 | 2 | no | — |
| 489 | #67 | — | 18 | 1 | no | — |
| 490 | #67 | — | 18 | 2 | no | — |
| 491 | #67 | — | 18 | 1 | no | — |
| 492 | #67 | — | 18 | 1 | no | — |
| 493 | #67 | — | 18 | 2 | no | — |
| 494 | #67 | — | 18 | 2 | no | — |
| 495 | #67 | — | 18 | 2 | no | — |
| 496 | #67 | — | 36 | 2 | no | — |
| 497 | C2×Dic3 | — | 9 | 1 | no | — |
| 498 | C2×Dic3 | — | 18 | 1 | no | — |
| 499 | C2×Dic3 | — | 18 | 1 | no | — |
| 500 | C2×Dic3 | — | 18 | 1 | no | — |
| 501 | C2×Dic3 | — | 18 | 1 | no | — |
| 502 | C2×Dic3 | — | 18 | 1 | no | — |
| 503 | C2×Dic3 | — | 36 | 1 | no | — |
| 504 | D12 | — | 2 | 1 | no | — |
| 505 | D12 | — | 6 | 1 | no | — |
| 506 | D12 | — | 6 | 2 | no | — |
| 507 | D12 | — | 6 | 1 | no | — |
| 508 | D12 | — | 6 | 1 | no | — |
| 509 | D12 | — | 6 | 1 | no | — |
| 510 | D12 | — | 6 | 1 | no | — |
| 511 | D12 | — | 9 | 2 | no | — |
| 512 | D12 | — | 9 | 1 | no | — |
| 513 | D12 | — | 12 | 1 | no | — |
| 514 | D12 | — | 18 | 1 | no | — |
| 515 | C4×D3 | — | 2 | 1 | no | — |
| 516 | C4×D3 | — | 6 | 1 | no | — |
| 517 | C4×D3 | — | 6 | 1 | no | — |
| 518 | C4×D3 | — | 6 | 1 | no | — |
| 519 | C4×D3 | — | 6 | 1 | no | — |
| 520 | C4×D3 | — | 9 | 1 | no | — |
| 521 | C4×D3 | — | 9 | 1 | no | — |
| 522 | C4×D3 | — | 9 | 1 | no | — |
| 523 | C4×D3 | — | 12 | 1 | no | — |
| 524 | C4×D3 | — | 18 | 1 | no | — |
| 525 | C4×D3 | — | 18 | 1 | no | — |
| 526 | C4×D3 | — | 18 | 1 | no | — |
| 527 | C4×D3 | — | 18 | 1 | no | — |
| 528 | C4×D3 | — | 18 | 1 | no | — |
| 529 | C4×D3 | — | 18 | 1 | no | — |
| 530 | C4×D3 | — | 18 | 1 | no | — |
| 531 | C4×D3 | — | 18 | 1 | no | — |
| 532 | C4×D3 | — | 18 | 1 | no | — |
| 533 | C4×D3 | — | 18 | 1 | no | — |
| 534 | C4×D3 | — | 18 | 1 | no | — |
| 535 | C4×D3 | — | 18 | 1 | no | — |
| 536 | C4×D3 | — | 36 | 1 | no | — |
| 537 | C4×D3 | — | 36 | 1 | no | — |
| 538 | C4×D3 | — | 36 | 1 | no | — |
| 539 | C4×D3 | — | 36 | 1 | no | — |
| 540 | C4×D3 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 541 | Dic6 | — | 6 | 1 | no | — |
| 542 | Dic6 | — | 6 | 1 | no | — |
| 543 | Dic6 | — | 6 | 1 | no | — |
| 544 | Dic6 | — | 9 | 1 | no | — |
| 545 | Dic6 | — | 18 | 1 | no | — |
| 546 | C3×C8 | — | 9 | 2 | no | — |
| 547 | C3⋊C8 | — | 9 | 2 | no | — |
| 548 | C2×C32 | — | 2 | 1 | no | — |
| 549 | C2×C32 | — | 2 | 1 | no | — |
| 550 | C2×C32 | — | 4 | 1 | no | — |
| 551 | C2×C32 | — | 4 | 1 | no | — |
| 552 | C2×C32 | — | 6 | 1 | no | — |
| 553 | C2×C32 | — | 12 | 1 | no | — |
| 554 | C2×C32 | — | 12 | 2 | no | — |
| 555 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 556 | C3⋊D3 | — | 2 | 1 | no | — |
| 557 | C3⋊D3 | — | 3 | 2 | no | — |
| 558 | C3⋊D3 | — | 4 | 1 | no | — |
| 559 | C3⋊D3 | — | 4 | 2 | no | — |
| 560 | C3⋊D3 | — | 6 | 2 | no | — |
| 561 | C3⋊D3 | — | 6 | 2 | no | — |
| 562 | C3⋊D3 | — | 12 | 2 | no | — |
| 563 | C3⋊D3 | — | 12 | 2 | no | — |
| 564 | C3×D3 | — | 2 | 2 | no | — |
| 565 | C3×D3 | — | 4 | 1 | no | — |
| 566 | C3×D3 | — | 4 | 2 | no | — |
| 567 | C3×D3 | — | 4 | 1 | no | — |
| 568 | C3×D3 | — | 4 | 2 | no | — |
| 569 | C3×D3 | — | 4 | 2 | no | — |
| 570 | C3×D3 | — | 4 | 1 | no | — |
| 571 | C3×D3 | — | 6 | 2 | no | — |
| 572 | C3×D3 | — | 8 | 2 | no | — |
| 573 | C3×D3 | — | 12 | 1 | no | — |
| 574 | C3×D3 | — | 12 | 2 | no | — |
| 575 | C3×D3 | — | 12 | 1 | no | — |
| 576 | C3×D3 | — | 12 | 2 | no | — |
| 577 | C3×D3 | — | 12 | 2 | no | — |
| 578 | C3×D3 | — | 12 | 1 | no | — |
| 579 | C3×D3 | — | 24 | 2 | no | — |
| 580 | C24 | — | 54 | 1 | no | — |
| 581 | #41 | — | 9 | 1 | no | — |
| 582 | #41 | — | 18 | 1 | no | — |
| 583 | #41 | — | 27 | 1 | no | — |
| 584 | #41 | — | 27 | 1 | no | — |
| 585 | #41 | — | 27 | 1 | no | — |
| 586 | #41 | — | 54 | 1 | no | — |
| 587 | C2×Q8 | — | 27 | 1 | no | — |
| 588 | C2×D4 | — | 9 | 1 | no | — |
| 589 | C2×D4 | — | 18 | 1 | no | — |
| 590 | C2×D4 | — | 27 | 1 | no | — |
| 591 | C2×D4 | — | 27 | 1 | no | — |
| 592 | C2×D4 | — | 27 | 2 | no | — |
| 593 | C2×D4 | — | 27 | 2 | no | — |
| 594 | C2×D4 | — | 54 | 1 | no | — |
| 595 | C2×D4 | — | 54 | 1 | no | — |
| 596 | C2×D4 | — | 54 | 1 | no | — |
| 597 | C22×C4 | — | 27 | 1 | no | — |
| 598 | C22×C4 | — | 54 | 1 | no | — |
| 599 | SD16 | — | 9 | 2 | no | — |
| 600 | SD16 | — | 27 | 2 | no | — |
| 601 | SD16 | — | 27 | 2 | no | — |
| 602 | SD16 | — | 27 | 2 | no | — |
| 603 | D8 | — | 9 | 2 | no | — |
| 604 | D8 | — | 27 | 2 | no | — |
| 605 | D8 | — | 27 | 2 | no | — |
| 606 | D8 | — | 27 | 2 | no | — |
| 607 | M16 | — | 9 | 1 | no | — |
| 608 | M16 | — | 27 | 2 | no | — |
| 609 | M16 | — | 27 | 1 | no | — |
| 610 | C2×C8 | — | 27 | 2 | no | — |
| 611 | C22×C3 | — | 6 | 1 | no | — |
| 612 | C22×C3 | — | 6 | 1 | no | — |
| 613 | C22×C3 | — | 6 | 1 | no | — |
| 614 | C22×C3 | — | 6 | 2 | no | — |
| 615 | C22×C3 | — | 6 | 1 | no | — |
| 616 | C22×C3 | — | 6 | 2 | no | — |
| 617 | C22×C3 | — | 9 | 1 | no | — |
| 618 | C22×C3 | — | 12 | 1 | no | — |
| 619 | C22×C3 | — | 12 | 2 | no | — |
| 620 | C22×C3 | — | 18 | 1 | no | — |
| 621 | C22×C3 | — | 18 | 2 | no | — |
| 622 | C22×C3 | — | 36 | 4 | no | — |
| 623 | C22×C3 | — | 36 | 2 | no | — |
| 624 | C2×D3 | — | 2 | 1 | no | — |
| 625 | C2×D3 | — | 2 | 2 | no | — |
| 626 | C2×D3 | — | 6 | 1 | no | — |
| 627 | C2×D3 | — | 6 | 1 | no | — |
| 628 | C2×D3 | — | 6 | 1 | no | — |
| 629 | C2×D3 | — | 6 | 2 | no | — |
| 630 | C2×D3 | — | 6 | 1 | no | — |
| 631 | C2×D3 | — | 6 | 2 | no | — |
| 632 | C2×D3 | — | 9 | 1 | no | — |
| 633 | C2×D3 | — | 12 | 1 | no | — |
| 634 | C2×D3 | — | 12 | 2 | no | — |
| 635 | C2×D3 | — | 12 | 4 | no | — |
| 636 | C2×D3 | — | 12 | 4 | no | — |
| 637 | C2×D3 | — | 12 | 4 | no | — |
| 638 | C2×D3 | — | 18 | 1 | no | — |
| 639 | C2×D3 | — | 18 | 1 | no | — |
| 640 | C2×D3 | — | 18 | 2 | no | — |
| 641 | C2×D3 | — | 18 | 4 | no | — |
| 642 | C2×D3 | — | 36 | 1 | no | — |
| 643 | C2×D3 | — | 36 | 1 | no | — |
| 644 | C2×D3 | — | 36 | 2 | no | — |
| 645 | C2×D3 | — | 36 | 4 | no | — |
| 646 | C2×D3 | — | 36 | 2 | no | — |
| 647 | C2×D3 | — | 36 | 4 | no | — |
| 648 | C2×D3 | — | 36 | 4 | no | — |
| 649 | C2×D3 | — | 36 | 2 | no | — |
| 650 | C2×D3 | — | 36 | 2 | no | — |
| 651 | C2×D3 | — | 36 | 4 | no | — |
| 652 | C2×D3 | — | 36 | 2 | no | — |
| 653 | C2×D3 | — | 36 | 4 | no | — |
| 654 | C2×D3 | — | 72 | 4 | no | — |
| 655 | C2×D3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 656 | C3×C4 | — | 2 | 1 | no | — |
| 657 | C3×C4 | — | 2 | 1 | no | — |
| 658 | C3×C4 | — | 4 | 1 | no | — |
| 659 | C3×C4 | — | 4 | 1 | no | — |
| 660 | C3×C4 | — | 6 | 1 | no | — |
| 661 | C3×C4 | — | 6 | 1 | no | — |
| 662 | C3×C4 | — | 6 | 1 | no | — |
| 663 | C3×C4 | — | 6 | 1 | no | — |
| 664 | C3×C4 | — | 9 | 1 | no | — |
| 665 | C3×C4 | — | 12 | 1 | no | — |
| 666 | C3×C4 | — | 18 | 1 | no | — |
| 667 | C3×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 668 | Dic3 | — | 2 | 1 | no | — |
| 669 | Dic3 | — | 6 | 1 | no | — |
| 670 | Dic3 | — | 6 | 1 | no | — |
| 671 | Dic3 | — | 6 | 1 | no | — |
| 672 | Dic3 | — | 6 | 1 | no | — |
| 673 | Dic3 | — | 9 | 1 | no | — |
| 674 | Dic3 | — | 12 | 1 | no | — |
| 675 | Dic3 | — | 18 | 1 | no | — |
| 676 | Dic3 | — | 18 | 1 | no | — |
| 677 | Dic3 | — | 36 | 1 | no | — |
| 678 | Dic3 | — | 36 | 1 | no | — |
| 679 | Dic3 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 680 | C32 | — | 2 | 1 | no | — |
| 681 | C32 | — | 2 | 1 | no | — |
| 682 | C32 | — | 4 | 1 | no | — |
| 683 | C32 | — | 4 | 1 | no | — |
| 684 | C32 | D3×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented |
| 685 | C23 | — | 18 | 2 | no | — |
| 686 | C23 | — | 18 | 1 | no | — |
| 687 | C23 | — | 27 | 1 | no | — |
| 688 | C23 | — | 54 | 1 | no | — |
| 689 | C23 | — | 54 | 2 | no | — |
| 690 | C23 | — | 54 | 1 | no | — |
| 691 | C23 | — | 108 | 4 | no | — |
| 692 | Q8 | — | 9 | 1 | no | — |
| 693 | Q8 | — | 18 | 1 | no | — |
| 694 | Q8 | — | 27 | 1 | no | — |
| 695 | D4 | — | 6 | 1 | no | — |
| 696 | D4 | — | 9 | 1 | no | — |
| 697 | D4 | — | 9 | 2 | no | — |
| 698 | D4 | — | 18 | 2 | no | — |
| 699 | D4 | — | 18 | 1 | no | — |
| 700 | D4 | — | 18 | 1 | no | — |
| 701 | D4 | — | 18 | 1 | no | — |
| 702 | D4 | — | 18 | 1 | no | — |
| 703 | D4 | — | 18 | 1 | no | — |
| 704 | D4 | — | 27 | 1 | no | — |
| 705 | D4 | — | 27 | 2 | no | — |
| 706 | D4 | — | 54 | 1 | no | — |
| 707 | D4 | — | 54 | 2 | no | — |
| 708 | C2×C4 | — | 3 | 1 | no | — |
| 709 | C2×C4 | — | 6 | 1 | no | — |
| 710 | C2×C4 | — | 9 | 1 | no | — |
| 711 | C2×C4 | — | 18 | 1 | no | — |
| 712 | C2×C4 | — | 27 | 1 | no | — |
| 713 | C2×C4 | — | 27 | 1 | no | — |
| 714 | C2×C4 | — | 27 | 1 | no | — |
| 715 | C2×C4 | — | 27 | 1 | no | — |
| 716 | C2×C4 | — | 54 | 1 | no | — |
| 717 | C2×C4 | — | 54 | 1 | no | — |
| 718 | C2×C4 | — | 54 | 1 | no | — |
| 719 | C8 | — | 9 | 2 | no | — |
| 720 | C8 | — | 27 | 2 | no | — |
| 721 | C2×C3 | — | 2 | 1 | no | — |
| 722 | C2×C3 | — | 2 | 1 | no | — |
| 723 | C2×C3 | — | 4 | 1 | no | — |
| 724 | C2×C3 | — | 4 | 1 | no | — |
| 725 | C2×C3 | — | 6 | 2 | no | — |
| 726 | C2×C3 | — | 12 | 1 | no | — |
| 727 | C2×C3 | — | 12 | 2 | no | — |
| 728 | C2×C3 | — | 12 | 1 | no | — |
| 729 | C2×C3 | — | 12 | 2 | no | — |
| 730 | C2×C3 | — | 12 | 2 | no | — |
| 731 | C2×C3 | — | 12 | 1 | no | — |
| 732 | C2×C3 | — | 18 | 1 | no | — |
| 733 | C2×C3 | — | 24 | 2 | no | — |
| 734 | C2×C3 | — | 36 | 2 | no | — |
| 735 | C2×C3 | — | 36 | 1 | no | — |
| 736 | C2×C3 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 737 | D3 | — | 2 | 1 | no | — |
| 738 | D3 | — | 4 | 2 | no | — |
| 739 | D3 | — | 4 | 1 | no | — |
| 740 | D3 | — | 6 | 2 | no | — |
| 741 | D3 | — | 9 | 2 | no | — |
| 742 | D3 | — | 12 | 1 | no | — |
| 743 | D3 | — | 12 | 2 | no | — |
| 744 | D3 | — | 12 | 1 | no | — |
| 745 | D3 | — | 12 | 2 | no | — |
| 746 | D3 | — | 12 | 2 | no | — |
| 747 | D3 | — | 12 | 1 | no | — |
| 748 | D3 | — | 18 | 2 | no | — |
| 749 | D3 | — | 18 | 2 | no | — |
| 750 | D3 | — | 24 | 2 | no | — |
| 751 | D3 | — | 36 | 2 | no | — |
| 752 | D3 | — | 36 | 2 | no | — |
| 753 | C22 | — | 3 | 1 | no | — |
| 754 | C22 | — | 6 | 1 | no | — |
| 755 | C22 | — | 6 | 2 | no | — |
| 756 | C22 | — | 9 | 1 | no | — |
| 757 | C22 | — | 18 | 1 | no | — |
| 758 | C22 | — | 18 | 2 | no | — |
| 759 | C22 | — | 27 | 1 | no | — |
| 760 | C22 | — | 36 | 4 | no | — |
| 761 | C22 | — | 36 | 2 | no | — |
| 762 | C22 | — | 54 | 2 | no | — |
| 763 | C22 | — | 108 | 4 | no | — |
| 764 | C22 | — | 108 | 2 | no | — |
| 765 | C22 | — | 108 | 2 | no | — |
| 766 | C4 | — | 3 | 1 | no | — |
| 767 | C4 | — | 6 | 1 | no | — |
| 768 | C4 | — | 9 | 1 | no | — |
| 769 | C4 | — | 18 | 1 | no | — |
| 770 | C4 | — | 27 | 1 | no | — |
| 771 | C4 | D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 772 | C3 | — | 2 | 1 | no | — |
| 773 | C3 | — | 2 | 1 | no | — |
| 774 | C3 | — | 4 | 1 | no | — |
| 775 | C3 | — | 4 | 1 | no | — |
| 776 | C3 | #10596501 | 1 | 1 | yes | characteristic, complemented |
| 777 | C2 | — | 6 | 1 | no | — |
| 778 | C2 | — | 12 | 2 | no | — |
| 779 | C2 | — | 12 | 1 | no | — |
| 780 | C2 | — | 18 | 1 | no | — |
| 781 | C2 | — | 27 | 2 | no | — |
| 782 | C2 | — | 36 | 2 | no | — |
| 783 | C2 | — | 36 | 1 | no | — |
| 784 | C2 | C2×D3×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×#3802 | C2 | semidirect |
| 2. #11724398 | C2 | semidirect |
| 3. #11724340 | C2 | semidirect |
| 4. #11724305 | C2 | semidirect |
| 5. #11724304 | C2 | semidirect |
| 6. C3×#64224 | C2 | semidirect |
| 7. #11724255 | C2 | semidirect |
| 8. #11724139 | C2 | semidirect |
| 9. #11724138 | C2 | semidirect |
| 10. #11724129 | C2 | semidirect |
| 11. #11724127 | C2 | semidirect |
| 14. C4⋊#1113 | C22 | semidirect |
| 15. #89042 | C22 | semidirect |
| 19. C3×#3802 | C22 | semidirect |
| 22. C3×#3798 | C22 | semidirect |
| 23. #88989 | C22 | semidirect |
| 24. C3×#3788 | C22 | semidirect |
| 26. #88964 | C22 | semidirect |
| 27. #88963 | C22 | semidirect |
| 28. #88958 | C22 | semidirect |
| 31. #88954 | C22 | semidirect |
| 33. D3×#625 | C22 | semidirect |
| 34. #88942 | C22 | semidirect |
| 35. #88941 | C22 | semidirect |
| 36. #88937 | C22 | semidirect |
| 37. #88936 | C22 | semidirect |
| 38. #88935 | C22 | semidirect |
| 39. #88935 | C22 | semidirect |
| 40. C3×#3775 | C22 | semidirect |
| 41. C3×#3774 | C22 | semidirect |
| 42. #88925 | C22 | semidirect |
| 43. #88924 | C22 | semidirect |
| 56. #64224 | D3 | semidirect |
| 71. #6296 | C23 | semidirect |
| 74. #6295 | C23 | semidirect |
| 83. C3×#627 | C23 | semidirect |
| 90. C3×#625 | C23 | semidirect |
| 91. C3⋊#622 | C23 | semidirect |
| 92. C3×#622 | C23 | semidirect |
| 124. #3802 | C2×D3 | semidirect |
| 135. #3798 | C2×D3 | semidirect |
| 143. #3788 | C2×D3 | semidirect |
| 148. #3775 | C2×D3 | semidirect |
| 152. #3774 | C2×D3 | semidirect |
| 257. #627 | C22×D3 | semidirect |
| 274. #625 | C22×D3 | semidirect |
| 291. #622 | C22×D3 | semidirect |
| 294. C3⋊(C3⋊D3) | AGL(1,ℤ/8) | semidirect |
| 440. C33 | C2×AGL(1,ℤ/8) | semidirect |
| 684. C32 | D3×AGL(1,ℤ/8) | semidirect |
| 776. C3 | #10596501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#3802 | 2 |
| #11724398 | 2 |
| #11724340 | 2 |
| #11724305 | 2 |
| #11724304 | 2 |
| C3×#64224 | 2 |
| #11724255 | 2 |
| #11724139 | 2 |
| #11724138 | 2 |
| #11724129 | 2 |
| #11724127 | 2 |
| #10596501 | 3 |
| D3×AGL(1,ℤ/8) | 9 |