Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1806 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 137 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 | C22×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85539 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #85538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85537 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85534 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #85521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #85507 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C2×#5421 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #60374 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×2−1+4⋊C3 | — | 2 | 4 | no | — |
| 14 | C2×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×2−1+4⋊C3 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C22×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C23×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 19 | #5926 | — | 2 | 4 | no | — |
| 20 | C2×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#985 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 23 | C22×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 24 | D4×#67 | — | 4 | 1 | no | maximal |
| 25 | #5427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #5427 | C22 | 1 | 2 | yes | complemented |
| 27 | #5426 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5425 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #5424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5421 | C22 | 1 | 2 | yes | complemented |
| 32 | #5421 | C22 | 1 | 2 | yes | complemented |
| 33 | #5421 | C22 | 1 | 2 | yes | complemented |
| 34 | #5421 | C22 | 1 | 2 | yes | complemented |
| 35 | #5420 | C22 | 1 | 2 | yes | complemented |
| 36 | #5419 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #5419 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#859 | C22 | 1 | 2 | yes | complemented |
| 39 | C22×2−1+4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | C2×#577 | — | 3 | 1 | no | — |
| 41 | C2×#577 | — | 3 | 1 | no | — |
| 42 | #3488 | — | 3 | 1 | no | — |
| 43 | #3013 | — | 3 | 1 | no | — |
| 44 | #3013 | — | 3 | 2 | no | — |
| 45 | #3013 | — | 3 | 1 | no | — |
| 46 | #3013 | — | 3 | 2 | no | — |
| 47 | #3010 | — | 3 | 1 | no | — |
| 48 | #3010 | — | 3 | 2 | no | — |
| 49 | #3010 | — | 3 | 2 | no | — |
| 50 | #3010 | — | 3 | 1 | no | — |
| 51 | #3006 | — | 3 | 2 | no | — |
| 52 | #3006 | — | 3 | 1 | no | — |
| 53 | #3004 | — | 3 | 1 | no | — |
| 54 | #3004 | — | 3 | 2 | no | — |
| 55 | #3002 | — | 3 | 2 | no | — |
| 56 | #3002 | — | 3 | 1 | no | — |
| 57 | C2×#448 | — | 3 | 1 | no | — |
| 58 | C2×#448 | — | 3 | 2 | no | — |
| 59 | #2898 | — | 3 | 1 | no | — |
| 60 | #2898 | — | 3 | 1 | no | — |
| 61 | #2880 | — | 3 | 1 | no | — |
| 62 | C22×C3×D4 | — | 4 | 1 | no | — |
| 63 | C22×#67 | — | 4 | 2 | no | — |
| 64 | C2×D3×D4 | — | 4 | 1 | no | — |
| 65 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 66 | 2−1+4⋊C3 | — | 2 | 4 | no | — |
| 67 | 2−1+4⋊C3 | D4 | 1 | 4 | yes | complemented |
| 68 | C2×#41⋊C3 | — | 2 | 2 | no | — |
| 69 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×SL(2,𝔽3) | — | 2 | 4 | no | — |
| 72 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 74 | C22×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 75 | #986 | — | 2 | 2 | no | — |
| 76 | #985 | — | 2 | 2 | no | — |
| 77 | #983 | — | 2 | 4 | no | — |
| 78 | C2×GL(2,𝔽3) | — | 2 | 4 | no | — |
| 79 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 81 | C2×#226 | C23 | 1 | 1 | yes | characteristic |
| 82 | #953 | — | 4 | 2 | no | — |
| 83 | #940 | — | 4 | 1 | no | — |
| 84 | #939 | — | 4 | 2 | no | — |
| 85 | #938 | — | 4 | 1 | no | — |
| 86 | #937 | — | 4 | 2 | no | — |
| 87 | D4×Dic3 | — | 4 | 1 | no | — |
| 88 | #930 | — | 4 | 1 | no | — |
| 89 | C4×#67 | — | 4 | 1 | no | — |
| 90 | #859 | C23 | 1 | 1 | yes | characteristic |
| 91 | #859 | C23 | 1 | 2 | yes | — |
| 92 | #859 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×2−1+4 | — | 2 | 4 | no | — |
| 94 | C2×2−1+4 | — | 3 | 1 | no | — |
| 95 | C2×2−1+4 | — | 3 | 2 | no | — |
| 96 | C2×2−1+4 | — | 3 | 1 | no | — |
| 97 | C2×2−1+4 | — | 6 | 4 | no | — |
| 98 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 100 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | complemented |
| 101 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 102 | C22×#41 | — | 3 | 1 | no | — |
| 103 | C22×#41 | — | 3 | 2 | no | — |
| 104 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 105 | C23×Q8 | — | 3 | 1 | no | — |
| 106 | C23×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 107 | #577 | — | 6 | 4 | no | — |
| 108 | #577 | — | 6 | 8 | no | — |
| 109 | #577 | — | 6 | 4 | no | — |
| 110 | C2×#137 | — | 3 | 2 | no | — |
| 111 | C2×#137 | — | 3 | 1 | no | — |
| 112 | C2×#137 | — | 3 | 1 | no | — |
| 113 | C2×#137 | — | 3 | 2 | no | — |
| 114 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 115 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 116 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 117 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 118 | C2×#135 | — | 3 | 1 | no | — |
| 119 | C2×#135 | — | 3 | 2 | no | — |
| 120 | C2×#135 | — | 3 | 2 | no | — |
| 121 | C2×#135 | — | 3 | 1 | no | — |
| 122 | C22×SD16 | — | 3 | 2 | no | — |
| 123 | C22×SD16 | — | 3 | 1 | no | — |
| 124 | C22×SD16 | — | 3 | 1 | no | — |
| 125 | C22×SD16 | — | 3 | 2 | no | — |
| 126 | C2×#131 | — | 3 | 1 | no | — |
| 127 | C2×#131 | — | 3 | 1 | no | — |
| 128 | #550 | — | 6 | 1 | no | — |
| 129 | #548 | — | 6 | 1 | no | — |
| 130 | #546 | — | 6 | 2 | no | — |
| 131 | #546 | — | 6 | 1 | no | — |
| 132 | D42 | — | 6 | 2 | no | — |
| 133 | D42 | — | 6 | 1 | no | — |
| 134 | #537 | — | 3 | 1 | no | — |
| 135 | #537 | — | 3 | 2 | no | — |
| 136 | #535 | — | 3 | 1 | no | — |
| 137 | #535 | — | 3 | 2 | no | — |
| 138 | #525 | — | 3 | 2 | no | — |
| 139 | #525 | — | 3 | 1 | no | — |
| 140 | C2×#121 | — | 3 | 2 | no | — |
| 141 | C2×#121 | — | 3 | 1 | no | — |
| 142 | #520 | — | 3 | 1 | no | — |
| 143 | #452 | — | 3 | 1 | no | — |
| 144 | #452 | — | 3 | 2 | no | — |
| 145 | #452 | — | 3 | 2 | no | — |
| 146 | #452 | — | 3 | 1 | no | — |
| 147 | #451 | — | 3 | 2 | no | — |
| 148 | #451 | — | 3 | 2 | no | — |
| 149 | #451 | — | 3 | 2 | no | — |
| 150 | #451 | — | 3 | 1 | no | — |
| 151 | #451 | — | 3 | 2 | no | — |
| 152 | #450 | — | 3 | 1 | no | — |
| 153 | #449 | — | 3 | 1 | no | — |
| 154 | #449 | — | 3 | 2 | no | — |
| 155 | #449 | — | 3 | 2 | no | — |
| 156 | #449 | — | 3 | 2 | no | — |
| 157 | #449 | — | 3 | 2 | no | — |
| 158 | #449 | — | 3 | 2 | no | — |
| 159 | #449 | — | 3 | 2 | no | — |
| 160 | #449 | — | 3 | 2 | no | — |
| 161 | #449 | — | 3 | 1 | no | — |
| 162 | #449 | — | 3 | 2 | no | — |
| 163 | #448 | — | 3 | 2 | no | — |
| 164 | #448 | — | 3 | 2 | no | — |
| 165 | #448 | — | 3 | 2 | no | — |
| 166 | #448 | — | 3 | 2 | no | — |
| 167 | #448 | — | 3 | 2 | no | — |
| 168 | #448 | — | 3 | 2 | no | — |
| 169 | #448 | — | 3 | 2 | no | — |
| 170 | #448 | — | 3 | 2 | no | — |
| 171 | #448 | — | 3 | 2 | no | — |
| 172 | #448 | — | 3 | 1 | no | — |
| 173 | #448 | — | 3 | 2 | no | — |
| 174 | #448 | — | 3 | 2 | no | — |
| 175 | #448 | — | 3 | 2 | no | — |
| 176 | #448 | — | 3 | 2 | no | — |
| 177 | #447 | — | 3 | 2 | no | — |
| 178 | #447 | — | 3 | 1 | no | — |
| 179 | #419 | — | 3 | 2 | no | — |
| 180 | #419 | — | 3 | 1 | no | — |
| 181 | #419 | — | 3 | 1 | no | — |
| 182 | #419 | — | 3 | 2 | no | — |
| 183 | #417 | — | 3 | 1 | no | — |
| 184 | #417 | — | 3 | 2 | no | — |
| 185 | #417 | — | 3 | 2 | no | — |
| 186 | #417 | — | 3 | 1 | no | — |
| 187 | #416 | — | 3 | 1 | no | — |
| 188 | #416 | — | 3 | 2 | no | — |
| 189 | #416 | — | 3 | 2 | no | — |
| 190 | #416 | — | 3 | 1 | no | — |
| 191 | C2×#103 | — | 3 | 2 | no | — |
| 192 | C2×#103 | — | 3 | 1 | no | — |
| 193 | C2×#103 | — | 3 | 1 | no | — |
| 194 | C2×#103 | — | 3 | 2 | no | — |
| 195 | #408 | — | 3 | 1 | no | — |
| 196 | #408 | — | 3 | 2 | no | — |
| 197 | #408 | — | 3 | 2 | no | — |
| 198 | #408 | — | 3 | 1 | no | — |
| 199 | #407 | — | 3 | 2 | no | — |
| 200 | #407 | — | 3 | 1 | no | — |
| 201 | C2×C22⋊C8 | — | 3 | 2 | no | — |
| 202 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 203 | C24×C3 | — | 4 | 2 | no | — |
| 204 | C23×D3 | — | 4 | 2 | no | — |
| 205 | C2×C3×D4 | — | 4 | 1 | no | — |
| 206 | C2×C3×D4 | — | 4 | 2 | no | — |
| 207 | C2×C3×D4 | — | 4 | 1 | no | — |
| 208 | C2×C3×D4 | — | 8 | 4 | no | — |
| 209 | C22×C3×C4 | — | 4 | 1 | no | — |
| 210 | C2×#67 | — | 4 | 1 | no | — |
| 211 | C2×#67 | — | 4 | 2 | no | — |
| 212 | C2×#67 | — | 4 | 2 | no | — |
| 213 | C2×#67 | — | 4 | 2 | no | — |
| 214 | C2×#67 | — | 4 | 2 | no | — |
| 215 | C2×#67 | — | 4 | 2 | no | — |
| 216 | C2×#67 | — | 8 | 8 | no | — |
| 217 | C22×Dic3 | — | 4 | 2 | no | — |
| 218 | D3×D4 | — | 8 | 4 | no | — |
| 219 | C2×D12 | — | 4 | 1 | no | — |
| 220 | C2×C4×D3 | — | 4 | 1 | no | — |
| 221 | #41⋊C3 | — | 2 | 1 | no | — |
| 222 | #41⋊C3 | C2×D4 | 1 | 2 | yes | complemented |
| 223 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 224 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 225 | C2×SL(2,𝔽3) | C2×D4 | 1 | 4 | yes | complemented |
| 226 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 227 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 228 | GL(2,𝔽3) | — | 2 | 2 | no | — |
| 229 | #226 | — | 2 | 1 | no | — |
| 230 | #217 | — | 4 | 1 | no | — |
| 231 | #217 | — | 4 | 2 | no | — |
| 232 | #217 | — | 4 | 2 | no | — |
| 233 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 234 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 235 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 236 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 237 | C4×Dic3 | — | 4 | 1 | no | — |
| 238 | 2−1+4 | — | 2 | 2 | no | — |
| 239 | 2−1+4 | — | 2 | 4 | no | — |
| 240 | 2−1+4 | — | 3 | 4 | no | — |
| 241 | 2−1+4 | — | 3 | 8 | no | — |
| 242 | 2−1+4 | — | 6 | 2 | no | — |
| 243 | 2−1+4 | — | 6 | 4 | no | — |
| 244 | 2−1+4 | — | 6 | 4 | no | — |
| 245 | 2−1+4 | — | 6 | 8 | no | — |
| 246 | 2−1+4 | — | 6 | 4 | no | — |
| 247 | 2−1+4 | — | 6 | 8 | no | — |
| 248 | 2−1+4 | — | 6 | 4 | no | — |
| 249 | 2−1+4 | #67 | 1 | 4 | yes | complemented |
| 250 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 251 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 252 | C2×#41 | — | 2 | 2 | no | — |
| 253 | C2×#41 | — | 3 | 1 | no | — |
| 254 | C2×#41 | — | 3 | 2 | no | — |
| 255 | C2×#41 | — | 3 | 1 | no | — |
| 256 | C2×#41 | — | 3 | 1 | no | — |
| 257 | C2×#41 | — | 3 | 2 | no | — |
| 258 | C2×#41 | — | 3 | 1 | no | — |
| 259 | C2×#41 | — | 3 | 1 | no | — |
| 260 | C2×#41 | — | 3 | 1 | no | — |
| 261 | C2×#41 | — | 3 | 2 | no | — |
| 262 | C2×#41 | — | 3 | 2 | no | — |
| 263 | C2×#41 | — | 3 | 2 | no | — |
| 264 | C2×#41 | — | 3 | 2 | no | — |
| 265 | C2×#41 | — | 3 | 2 | no | — |
| 266 | C2×#41 | — | 3 | 1 | no | — |
| 267 | C2×#41 | — | 6 | 2 | no | — |
| 268 | C2×#41 | — | 6 | 2 | no | — |
| 269 | C2×#41 | — | 6 | 4 | no | — |
| 270 | C2×#41 | — | 6 | 4 | no | — |
| 271 | C2×#41 | — | 6 | 1 | no | — |
| 272 | C2×#41 | — | 6 | 8 | no | — |
| 273 | C2×#41 | — | 6 | 8 | no | — |
| 274 | C2×#41 | — | 6 | 2 | no | — |
| 275 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 276 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 277 | C22×Q8 | — | 2 | 4 | no | — |
| 278 | C22×Q8 | — | 3 | 1 | no | — |
| 279 | C22×Q8 | — | 3 | 2 | no | — |
| 280 | C22×Q8 | — | 3 | 2 | no | — |
| 281 | C22×Q8 | — | 3 | 2 | no | — |
| 282 | C22×Q8 | — | 3 | 1 | no | — |
| 283 | C22×Q8 | — | 3 | 1 | no | — |
| 284 | C22×Q8 | — | 3 | 2 | no | — |
| 285 | C22×Q8 | — | 6 | 1 | no | — |
| 286 | C22×Q8 | — | 6 | 1 | no | — |
| 287 | C22×Q8 | — | 6 | 4 | no | — |
| 288 | C22×Q8 | — | 6 | 4 | no | — |
| 289 | C22×Q8 | — | 6 | 4 | no | — |
| 290 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 291 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 292 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 293 | C22×D4 | — | 3 | 2 | no | — |
| 294 | C22×D4 | — | 3 | 1 | no | — |
| 295 | C22×D4 | — | 3 | 2 | no | — |
| 296 | C22×D4 | — | 3 | 1 | no | — |
| 297 | C22×D4 | — | 6 | 2 | no | — |
| 298 | C22×D4 | — | 6 | 1 | no | — |
| 299 | C22×D4 | — | 6 | 2 | no | — |
| 300 | C22×D4 | — | 6 | 1 | no | — |
| 301 | C22×D4 | S4 | 1 | 1 | yes | characteristic |
| 302 | C23×C4 | — | 3 | 2 | no | — |
| 303 | C23×C4 | — | 3 | 1 | no | — |
| 304 | C23×C4 | — | 6 | 1 | no | — |
| 305 | #137 | — | 6 | 4 | no | — |
| 306 | #137 | — | 6 | 4 | no | — |
| 307 | #137 | — | 6 | 8 | no | — |
| 308 | #137 | — | 6 | 4 | no | — |
| 309 | #137 | — | 6 | 4 | no | — |
| 310 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 311 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 312 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 313 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 314 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 315 | #135 | — | 6 | 2 | no | — |
| 316 | #135 | — | 6 | 8 | no | — |
| 317 | #135 | — | 6 | 8 | no | — |
| 318 | #135 | — | 6 | 4 | no | — |
| 319 | #135 | — | 6 | 2 | no | — |
| 320 | C2×Q16 | — | 3 | 2 | no | — |
| 321 | C2×Q16 | — | 3 | 1 | no | — |
| 322 | C2×Q16 | — | 3 | 2 | no | — |
| 323 | C2×Q16 | — | 3 | 1 | no | — |
| 324 | C2×SD16 | — | 3 | 2 | no | — |
| 325 | C2×SD16 | — | 3 | 1 | no | — |
| 326 | C2×SD16 | — | 3 | 2 | no | — |
| 327 | C2×SD16 | — | 3 | 2 | no | — |
| 328 | C2×SD16 | — | 3 | 2 | no | — |
| 329 | C2×SD16 | — | 3 | 2 | no | — |
| 330 | C2×SD16 | — | 3 | 2 | no | — |
| 331 | C2×SD16 | — | 3 | 2 | no | — |
| 332 | C2×SD16 | — | 3 | 1 | no | — |
| 333 | C2×SD16 | — | 3 | 1 | no | — |
| 334 | C2×SD16 | — | 3 | 1 | no | — |
| 335 | C2×SD16 | — | 3 | 2 | no | — |
| 336 | C2×SD16 | — | 6 | 4 | no | — |
| 337 | C2×SD16 | — | 6 | 4 | no | — |
| 338 | C2×SD16 | — | 6 | 8 | no | — |
| 339 | C2×SD16 | — | 6 | 4 | no | — |
| 340 | C2×SD16 | — | 6 | 4 | no | — |
| 341 | C2×D8 | — | 3 | 2 | no | — |
| 342 | C2×D8 | — | 3 | 1 | no | — |
| 343 | C2×D8 | — | 3 | 2 | no | — |
| 344 | C2×D8 | — | 3 | 1 | no | — |
| 345 | #131 | — | 6 | 4 | no | — |
| 346 | #131 | — | 6 | 4 | no | — |
| 347 | C2×M16 | — | 3 | 2 | no | — |
| 348 | C2×M16 | — | 3 | 2 | no | — |
| 349 | C2×M16 | — | 3 | 1 | no | — |
| 350 | C2×M16 | — | 3 | 1 | no | — |
| 351 | C22×C8 | — | 3 | 2 | no | — |
| 352 | C22×C8 | — | 3 | 2 | no | — |
| 353 | C22×C8 | — | 3 | 1 | no | — |
| 354 | C22×C8 | — | 3 | 1 | no | — |
| 355 | #127 | — | 6 | 2 | no | — |
| 356 | #127 | — | 6 | 1 | no | — |
| 357 | #124 | — | 6 | 2 | no | — |
| 358 | #124 | — | 6 | 1 | no | — |
| 359 | #123 | — | 6 | 2 | no | — |
| 360 | #123 | — | 6 | 1 | no | — |
| 361 | C22⋊Q8 | — | 3 | 1 | no | — |
| 362 | C22⋊Q8 | — | 3 | 1 | no | — |
| 363 | C22⋊Q8 | — | 3 | 2 | no | — |
| 364 | C22⋊Q8 | — | 6 | 1 | no | — |
| 365 | C22⋊Q8 | — | 6 | 2 | no | — |
| 366 | #121 | — | 3 | 2 | no | — |
| 367 | #121 | — | 3 | 1 | no | — |
| 368 | #121 | — | 3 | 2 | no | — |
| 369 | #121 | — | 3 | 2 | no | — |
| 370 | #121 | — | 3 | 2 | no | — |
| 371 | #121 | — | 3 | 2 | no | — |
| 372 | #121 | — | 3 | 1 | no | — |
| 373 | #121 | — | 6 | 2 | no | — |
| 374 | #121 | — | 6 | 2 | no | — |
| 375 | #121 | — | 6 | 1 | no | — |
| 376 | #121 | — | 6 | 2 | no | — |
| 377 | #121 | — | 6 | 2 | no | — |
| 378 | #121 | — | 6 | 2 | no | — |
| 379 | #121 | — | 6 | 2 | no | — |
| 380 | #121 | — | 6 | 1 | no | — |
| 381 | #121 | — | 6 | 1 | no | — |
| 382 | #120 | — | 6 | 2 | no | — |
| 383 | #120 | — | 6 | 2 | no | — |
| 384 | #120 | — | 6 | 1 | no | — |
| 385 | #120 | — | 6 | 2 | no | — |
| 386 | #120 | — | 6 | 2 | no | — |
| 387 | C4×Q8 | — | 6 | 1 | no | — |
| 388 | C4×D4 | — | 6 | 2 | no | — |
| 389 | C4×D4 | — | 6 | 2 | no | — |
| 390 | C4×D4 | — | 6 | 1 | no | — |
| 391 | C4×D4 | — | 6 | 2 | no | — |
| 392 | C4×D4 | — | 6 | 1 | no | — |
| 393 | C4×D4 | — | 6 | 1 | no | — |
| 394 | #117 | — | 3 | 2 | no | — |
| 395 | #117 | — | 3 | 1 | no | — |
| 396 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 397 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 398 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 399 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 400 | #103 | — | 3 | 2 | no | — |
| 401 | #103 | — | 3 | 1 | no | — |
| 402 | #103 | — | 3 | 2 | no | — |
| 403 | #103 | — | 3 | 2 | no | — |
| 404 | #103 | — | 3 | 2 | no | — |
| 405 | #103 | — | 3 | 2 | no | — |
| 406 | #103 | — | 3 | 2 | no | — |
| 407 | #103 | — | 3 | 2 | no | — |
| 408 | #103 | — | 3 | 1 | no | — |
| 409 | #103 | — | 3 | 2 | no | — |
| 410 | #103 | — | 3 | 2 | no | — |
| 411 | #103 | — | 3 | 1 | no | — |
| 412 | #103 | — | 3 | 2 | no | — |
| 413 | #103 | — | 3 | 1 | no | — |
| 414 | #102 | — | 3 | 1 | no | — |
| 415 | #102 | — | 3 | 1 | no | — |
| 416 | #102 | — | 3 | 1 | no | — |
| 417 | #102 | — | 3 | 2 | no | — |
| 418 | #102 | — | 3 | 2 | no | — |
| 419 | #102 | — | 3 | 1 | no | — |
| 420 | C22⋊C8 | — | 3 | 1 | no | — |
| 421 | C22⋊C8 | — | 3 | 1 | no | — |
| 422 | C22⋊C8 | — | 3 | 2 | no | — |
| 423 | C22⋊C8 | — | 3 | 2 | no | — |
| 424 | C22⋊C8 | — | 3 | 2 | no | — |
| 425 | C22⋊C8 | — | 3 | 1 | no | — |
| 426 | C22⋊C8 | — | 3 | 1 | no | — |
| 427 | C22⋊C8 | — | 3 | 2 | no | — |
| 428 | C22⋊C8 | — | 3 | 2 | no | — |
| 429 | C22⋊C8 | — | 3 | 2 | no | — |
| 430 | C23×C3 | — | 4 | 2 | no | — |
| 431 | C23×C3 | — | 4 | 1 | no | — |
| 432 | C23×C3 | — | 4 | 2 | no | — |
| 433 | C23×C3 | — | 8 | 4 | no | — |
| 434 | C23×C3 | — | 8 | 4 | no | — |
| 435 | C23×C3 | — | 16 | 2 | no | — |
| 436 | C22×D3 | — | 4 | 1 | no | — |
| 437 | C22×D3 | — | 4 | 2 | no | — |
| 438 | C22×D3 | — | 8 | 4 | no | — |
| 439 | C22×D3 | — | 8 | 4 | no | — |
| 440 | C22×D3 | — | 16 | 2 | no | — |
| 441 | C3×D4 | — | 4 | 4 | no | — |
| 442 | C3×D4 | — | 8 | 2 | no | — |
| 443 | C3×D4 | — | 8 | 4 | no | — |
| 444 | C2×C3×C4 | — | 4 | 1 | no | — |
| 445 | C2×C3×C4 | — | 4 | 1 | no | — |
| 446 | C2×C3×C4 | — | 8 | 2 | no | — |
| 447 | #67 | — | 4 | 4 | no | — |
| 448 | #67 | — | 8 | 4 | no | — |
| 449 | #67 | — | 8 | 4 | no | — |
| 450 | #67 | — | 8 | 4 | no | — |
| 451 | #67 | — | 8 | 4 | no | — |
| 452 | #67 | — | 16 | 2 | no | — |
| 453 | C2×Dic3 | — | 4 | 1 | no | — |
| 454 | C2×Dic3 | — | 4 | 1 | no | — |
| 455 | C2×Dic3 | — | 4 | 2 | no | — |
| 456 | C2×Dic3 | — | 4 | 1 | no | — |
| 457 | C2×Dic3 | — | 8 | 4 | no | — |
| 458 | D12 | — | 8 | 2 | no | — |
| 459 | C4×D3 | — | 8 | 2 | no | — |
| 460 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 461 | C24 | — | 3 | 1 | no | — |
| 462 | C24 | — | 6 | 1 | no | — |
| 463 | C24 | — | 6 | 2 | no | — |
| 464 | C24 | C2×S4 | 1 | 2 | yes | — |
| 465 | #41 | — | 2 | 1 | no | — |
| 466 | #41 | — | 3 | 4 | no | — |
| 467 | #41 | — | 3 | 4 | no | — |
| 468 | #41 | — | 3 | 2 | no | — |
| 469 | #41 | — | 3 | 8 | no | — |
| 470 | #41 | — | 3 | 8 | no | — |
| 471 | #41 | — | 3 | 4 | no | — |
| 472 | #41 | — | 6 | 4 | no | — |
| 473 | #41 | — | 6 | 2 | no | — |
| 474 | #41 | — | 6 | 4 | no | — |
| 475 | #41 | — | 6 | 2 | no | — |
| 476 | #41 | — | 6 | 4 | no | — |
| 477 | #41 | — | 6 | 4 | no | — |
| 478 | #41 | — | 6 | 2 | no | — |
| 479 | #41 | — | 6 | 4 | no | — |
| 480 | #41 | — | 6 | 4 | no | — |
| 481 | #41 | — | 6 | 2 | no | — |
| 482 | #41 | — | 6 | 2 | no | — |
| 483 | #41 | — | 6 | 8 | no | — |
| 484 | #41 | — | 6 | 4 | no | — |
| 485 | #41 | — | 6 | 4 | no | — |
| 486 | #41 | — | 6 | 16 | no | — |
| 487 | #41 | — | 6 | 4 | no | — |
| 488 | #41 | — | 6 | 2 | no | — |
| 489 | #41 | — | 6 | 4 | no | — |
| 490 | #41 | — | 6 | 16 | no | — |
| 491 | #41 | — | 6 | 4 | no | — |
| 492 | #41 | — | 6 | 4 | no | — |
| 493 | #41 | — | 6 | 1 | no | — |
| 494 | #41 | — | 6 | 2 | no | — |
| 495 | #41 | — | 12 | 4 | no | — |
| 496 | #41 | C2×#67 | 1 | 2 | yes | complemented |
| 497 | C2×Q8 | — | 2 | 1 | no | — |
| 498 | C2×Q8 | — | 2 | 2 | no | — |
| 499 | C2×Q8 | — | 3 | 1 | no | — |
| 500 | C2×Q8 | — | 3 | 2 | no | — |
| 501 | C2×Q8 | — | 3 | 1 | no | — |
| 502 | C2×Q8 | — | 3 | 2 | no | — |
| 503 | C2×Q8 | — | 3 | 1 | no | — |
| 504 | C2×Q8 | — | 3 | 2 | no | — |
| 505 | C2×Q8 | — | 3 | 4 | no | — |
| 506 | C2×Q8 | — | 3 | 4 | no | — |
| 507 | C2×Q8 | — | 3 | 8 | no | — |
| 508 | C2×Q8 | — | 3 | 4 | no | — |
| 509 | C2×Q8 | — | 3 | 1 | no | — |
| 510 | C2×Q8 | — | 6 | 4 | no | — |
| 511 | C2×Q8 | — | 6 | 2 | no | — |
| 512 | C2×Q8 | — | 6 | 2 | no | — |
| 513 | C2×Q8 | — | 6 | 2 | no | — |
| 514 | C2×Q8 | — | 6 | 4 | no | — |
| 515 | C2×Q8 | — | 6 | 4 | no | — |
| 516 | C2×Q8 | — | 6 | 4 | no | — |
| 517 | C2×Q8 | — | 6 | 4 | no | — |
| 518 | C2×Q8 | — | 6 | 4 | no | — |
| 519 | C2×Q8 | — | 6 | 8 | no | — |
| 520 | C2×Q8 | — | 6 | 8 | no | — |
| 521 | C2×Q8 | — | 6 | 1 | no | — |
| 522 | C2×Q8 | — | 6 | 2 | no | — |
| 523 | C2×Q8 | — | 6 | 4 | no | — |
| 524 | C2×Q8 | — | 6 | 4 | no | — |
| 525 | C2×Q8 | C2×#67 | 1 | 4 | yes | complemented |
| 526 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 527 | C2×D4 | — | 2 | 4 | no | — |
| 528 | C2×D4 | — | 3 | 2 | no | — |
| 529 | C2×D4 | — | 3 | 1 | no | — |
| 530 | C2×D4 | — | 3 | 1 | no | — |
| 531 | C2×D4 | — | 3 | 2 | no | — |
| 532 | C2×D4 | — | 3 | 2 | no | — |
| 533 | C2×D4 | — | 3 | 2 | no | — |
| 534 | C2×D4 | — | 3 | 2 | no | — |
| 535 | C2×D4 | — | 3 | 1 | no | — |
| 536 | C2×D4 | — | 6 | 1 | no | — |
| 537 | C2×D4 | — | 6 | 4 | no | — |
| 538 | C2×D4 | — | 6 | 4 | no | — |
| 539 | C2×D4 | — | 6 | 2 | no | — |
| 540 | C2×D4 | — | 6 | 2 | no | — |
| 541 | C2×D4 | — | 6 | 2 | no | — |
| 542 | C2×D4 | — | 6 | 8 | no | — |
| 543 | C2×D4 | — | 6 | 2 | no | — |
| 544 | C2×D4 | — | 6 | 2 | no | — |
| 545 | C2×D4 | — | 6 | 1 | no | — |
| 546 | C2×D4 | — | 6 | 1 | no | — |
| 547 | C2×D4 | — | 6 | 2 | no | — |
| 548 | C2×D4 | — | 6 | 2 | no | — |
| 549 | C2×D4 | — | 6 | 1 | no | — |
| 550 | C2×D4 | — | 6 | 2 | no | — |
| 551 | C2×D4 | — | 6 | 2 | no | — |
| 552 | C2×D4 | — | 6 | 2 | no | — |
| 553 | C2×D4 | — | 6 | 2 | no | — |
| 554 | C2×D4 | — | 6 | 1 | no | — |
| 555 | C2×D4 | — | 12 | 8 | no | — |
| 556 | C2×D4 | — | 12 | 4 | no | — |
| 557 | C2×D4 | — | 24 | 4 | no | — |
| 558 | C2×D4 | — | 24 | 2 | no | — |
| 559 | C2×D4 | C2×S4 | 1 | 2 | yes | — |
| 560 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 561 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 562 | C22×C4 | — | 3 | 2 | no | — |
| 563 | C22×C4 | — | 3 | 1 | no | — |
| 564 | C22×C4 | — | 3 | 1 | no | — |
| 565 | C22×C4 | — | 3 | 2 | no | — |
| 566 | C22×C4 | — | 3 | 2 | no | — |
| 567 | C22×C4 | — | 3 | 2 | no | — |
| 568 | C22×C4 | — | 3 | 2 | no | — |
| 569 | C22×C4 | — | 3 | 1 | no | — |
| 570 | C22×C4 | — | 3 | 1 | no | — |
| 571 | C22×C4 | — | 3 | 1 | no | — |
| 572 | C22×C4 | — | 6 | 2 | no | — |
| 573 | C22×C4 | — | 6 | 2 | no | — |
| 574 | C22×C4 | — | 6 | 1 | no | — |
| 575 | C22×C4 | — | 6 | 2 | no | — |
| 576 | C22×C4 | — | 6 | 1 | no | — |
| 577 | C22×C4 | — | 6 | 4 | no | — |
| 578 | C22×C4 | — | 6 | 4 | no | — |
| 579 | C22×C4 | — | 6 | 2 | no | — |
| 580 | C22×C4 | — | 6 | 8 | no | — |
| 581 | C22×C4 | — | 6 | 1 | no | — |
| 582 | C22×C4 | — | 6 | 2 | no | — |
| 583 | C22×C4 | — | 6 | 1 | no | — |
| 584 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 585 | Q16 | — | 6 | 4 | no | — |
| 586 | Q16 | — | 6 | 1 | no | — |
| 587 | Q16 | — | 6 | 4 | no | — |
| 588 | Q16 | — | 6 | 2 | no | — |
| 589 | Q16 | — | 6 | 1 | no | — |
| 590 | SD16 | — | 6 | 2 | no | — |
| 591 | SD16 | — | 6 | 2 | no | — |
| 592 | SD16 | — | 6 | 4 | no | — |
| 593 | SD16 | — | 6 | 1 | no | — |
| 594 | SD16 | — | 6 | 4 | no | — |
| 595 | SD16 | — | 6 | 2 | no | — |
| 596 | SD16 | — | 6 | 4 | no | — |
| 597 | SD16 | — | 6 | 4 | no | — |
| 598 | SD16 | — | 6 | 2 | no | — |
| 599 | SD16 | — | 6 | 4 | no | — |
| 600 | SD16 | — | 6 | 4 | no | — |
| 601 | SD16 | — | 6 | 4 | no | — |
| 602 | SD16 | — | 6 | 1 | no | — |
| 603 | SD16 | — | 6 | 2 | no | — |
| 604 | D8 | — | 6 | 4 | no | — |
| 605 | D8 | — | 6 | 2 | no | — |
| 606 | D8 | — | 6 | 4 | no | — |
| 607 | D8 | — | 6 | 2 | no | — |
| 608 | M16 | — | 6 | 4 | no | — |
| 609 | M16 | — | 6 | 4 | no | — |
| 610 | M16 | — | 6 | 2 | no | — |
| 611 | M16 | — | 6 | 2 | no | — |
| 612 | C2×C8 | — | 3 | 1 | no | — |
| 613 | C2×C8 | — | 3 | 1 | no | — |
| 614 | C2×C8 | — | 3 | 1 | no | — |
| 615 | C2×C8 | — | 3 | 2 | no | — |
| 616 | C2×C8 | — | 3 | 1 | no | — |
| 617 | C2×C8 | — | 3 | 2 | no | — |
| 618 | C2×C8 | — | 6 | 4 | no | — |
| 619 | C2×C8 | — | 6 | 4 | no | — |
| 620 | C2×C8 | — | 6 | 2 | no | — |
| 621 | C2×C8 | — | 6 | 2 | no | — |
| 622 | C4⋊C4 | — | 3 | 2 | no | — |
| 623 | C4⋊C4 | — | 3 | 1 | no | — |
| 624 | C4⋊C4 | — | 3 | 1 | no | — |
| 625 | C4⋊C4 | — | 6 | 2 | no | — |
| 626 | C4⋊C4 | — | 6 | 1 | no | — |
| 627 | C4⋊C4 | — | 6 | 2 | no | — |
| 628 | C4⋊C4 | — | 6 | 1 | no | — |
| 629 | C4⋊C4 | — | 6 | 1 | no | — |
| 630 | C22⋊C4 | — | 6 | 1 | no | — |
| 631 | C22⋊C4 | — | 6 | 2 | no | — |
| 632 | C22⋊C4 | — | 6 | 2 | no | — |
| 633 | C22⋊C4 | — | 6 | 2 | no | — |
| 634 | C22⋊C4 | — | 6 | 2 | no | — |
| 635 | C22⋊C4 | — | 6 | 1 | no | — |
| 636 | C22⋊C4 | — | 6 | 1 | no | — |
| 637 | C22⋊C4 | — | 6 | 2 | no | — |
| 638 | C22⋊C4 | — | 6 | 1 | no | — |
| 639 | C22⋊C4 | — | 6 | 2 | no | — |
| 640 | C22⋊C4 | — | 6 | 2 | no | — |
| 641 | C22⋊C4 | — | 6 | 1 | no | — |
| 642 | C42 | — | 6 | 2 | no | — |
| 643 | C42 | — | 6 | 1 | no | — |
| 644 | C22×C3 | — | 4 | 2 | no | — |
| 645 | C22×C3 | — | 4 | 4 | no | — |
| 646 | C22×C3 | — | 4 | 1 | no | — |
| 647 | C22×C3 | — | 8 | 2 | no | — |
| 648 | C22×C3 | — | 8 | 1 | no | — |
| 649 | C22×C3 | — | 8 | 2 | no | — |
| 650 | C22×C3 | — | 8 | 1 | no | — |
| 651 | C22×C3 | — | 8 | 2 | no | — |
| 652 | C22×C3 | — | 8 | 2 | no | — |
| 653 | C22×C3 | — | 8 | 2 | no | — |
| 654 | C22×C3 | — | 16 | 8 | no | — |
| 655 | C2×D3 | — | 4 | 2 | no | — |
| 656 | C2×D3 | — | 8 | 1 | no | — |
| 657 | C2×D3 | — | 8 | 1 | no | — |
| 658 | C2×D3 | — | 8 | 2 | no | — |
| 659 | C2×D3 | — | 8 | 2 | no | — |
| 660 | C2×D3 | — | 8 | 2 | no | — |
| 661 | C2×D3 | — | 16 | 8 | no | — |
| 662 | C3×C4 | — | 4 | 2 | no | — |
| 663 | C3×C4 | — | 8 | 1 | no | — |
| 664 | Dic3 | — | 4 | 2 | no | — |
| 665 | Dic3 | — | 8 | 1 | no | — |
| 666 | Dic3 | — | 8 | 2 | no | — |
| 667 | Dic3 | — | 8 | 1 | no | — |
| 668 | C23 | — | 2 | 4 | no | — |
| 669 | C23 | — | 2 | 4 | no | — |
| 670 | C23 | — | 3 | 1 | no | — |
| 671 | C23 | — | 3 | 1 | no | — |
| 672 | C23 | — | 4 | 2 | no | — |
| 673 | C23 | — | 6 | 2 | no | — |
| 674 | C23 | — | 6 | 2 | no | — |
| 675 | C23 | — | 6 | 1 | no | — |
| 676 | C23 | — | 6 | 2 | no | — |
| 677 | C23 | — | 12 | 1 | no | — |
| 678 | C23 | — | 12 | 2 | no | — |
| 679 | C23 | — | 12 | 4 | no | — |
| 680 | C23 | — | 24 | 2 | no | — |
| 681 | C23 | — | 24 | 2 | no | — |
| 682 | C23 | — | 24 | 1 | no | — |
| 683 | C23 | — | 24 | 1 | no | — |
| 684 | C23 | C22×S4 | 1 | 2 | yes | — |
| 685 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 686 | C23 | C22×S4 | 1 | 2 | yes | — |
| 687 | Q8 | — | 3 | 4 | no | — |
| 688 | Q8 | — | 3 | 1 | no | — |
| 689 | Q8 | — | 3 | 4 | no | — |
| 690 | Q8 | — | 3 | 4 | no | — |
| 691 | Q8 | — | 3 | 2 | no | — |
| 692 | Q8 | — | 6 | 4 | no | — |
| 693 | Q8 | — | 6 | 2 | no | — |
| 694 | Q8 | — | 6 | 1 | no | — |
| 695 | Q8 | — | 6 | 2 | no | — |
| 696 | Q8 | — | 6 | 8 | no | — |
| 697 | Q8 | — | 6 | 1 | no | — |
| 698 | Q8 | — | 6 | 1 | no | — |
| 699 | Q8 | — | 6 | 2 | no | — |
| 700 | Q8 | C22×#67 | 1 | 1 | yes | characteristic |
| 701 | D4 | — | 2 | 4 | no | — |
| 702 | D4 | — | 2 | 2 | no | — |
| 703 | D4 | — | 3 | 2 | no | — |
| 704 | D4 | — | 3 | 8 | no | — |
| 705 | D4 | — | 3 | 2 | no | — |
| 706 | D4 | — | 6 | 4 | no | — |
| 707 | D4 | — | 6 | 1 | no | — |
| 708 | D4 | — | 6 | 1 | no | — |
| 709 | D4 | — | 6 | 1 | no | — |
| 710 | D4 | — | 6 | 2 | no | — |
| 711 | D4 | — | 6 | 2 | no | — |
| 712 | D4 | — | 6 | 1 | no | — |
| 713 | D4 | — | 6 | 4 | no | — |
| 714 | D4 | — | 6 | 4 | no | — |
| 715 | D4 | — | 6 | 4 | no | — |
| 716 | D4 | — | 12 | 4 | no | — |
| 717 | D4 | — | 12 | 2 | no | — |
| 718 | D4 | — | 12 | 2 | no | — |
| 719 | D4 | — | 12 | 4 | no | — |
| 720 | D4 | — | 12 | 4 | no | — |
| 721 | D4 | — | 12 | 2 | no | — |
| 722 | D4 | — | 24 | 2 | no | — |
| 723 | D4 | — | 24 | 2 | no | — |
| 724 | D4 | — | 24 | 2 | no | — |
| 725 | D4 | — | 24 | 1 | no | — |
| 726 | D4 | — | 24 | 2 | no | — |
| 727 | D4 | GL(2,ℤ/4) | 1 | 4 | yes | — |
| 728 | C2×C4 | — | 2 | 2 | no | — |
| 729 | C2×C4 | — | 3 | 4 | no | — |
| 730 | C2×C4 | — | 3 | 4 | no | — |
| 731 | C2×C4 | — | 3 | 2 | no | — |
| 732 | C2×C4 | — | 3 | 1 | no | — |
| 733 | C2×C4 | — | 3 | 2 | no | — |
| 734 | C2×C4 | — | 3 | 2 | no | — |
| 735 | C2×C4 | — | 3 | 1 | no | — |
| 736 | C2×C4 | — | 3 | 2 | no | — |
| 737 | C2×C4 | — | 6 | 1 | no | — |
| 738 | C2×C4 | — | 6 | 1 | no | — |
| 739 | C2×C4 | — | 6 | 2 | no | — |
| 740 | C2×C4 | — | 6 | 4 | no | — |
| 741 | C2×C4 | — | 6 | 1 | no | — |
| 742 | C2×C4 | — | 6 | 1 | no | — |
| 743 | C2×C4 | — | 6 | 4 | no | — |
| 744 | C2×C4 | — | 6 | 2 | no | — |
| 745 | C2×C4 | — | 6 | 2 | no | — |
| 746 | C2×C4 | — | 6 | 4 | no | — |
| 747 | C2×C4 | — | 6 | 8 | no | — |
| 748 | C2×C4 | — | 6 | 4 | no | — |
| 749 | C2×C4 | — | 6 | 4 | no | — |
| 750 | C2×C4 | — | 6 | 2 | no | — |
| 751 | C2×C4 | — | 6 | 1 | no | — |
| 752 | C2×C4 | — | 6 | 1 | no | — |
| 753 | C2×C4 | — | 6 | 2 | no | — |
| 754 | C2×C4 | — | 6 | 1 | no | — |
| 755 | C2×C4 | — | 12 | 4 | no | — |
| 756 | C2×C4 | — | 12 | 2 | no | — |
| 757 | C2×C4 | — | 24 | 2 | no | — |
| 758 | C2×C4 | — | 24 | 1 | no | — |
| 759 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 760 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 761 | C8 | — | 6 | 1 | no | — |
| 762 | C8 | — | 6 | 1 | no | — |
| 763 | C8 | — | 6 | 1 | no | — |
| 764 | C8 | — | 6 | 2 | no | — |
| 765 | C8 | — | 6 | 1 | no | — |
| 766 | C8 | — | 6 | 2 | no | — |
| 767 | C2×C3 | — | 4 | 1 | no | — |
| 768 | C2×C3 | — | 4 | 1 | no | — |
| 769 | C2×C3 | — | 4 | 1 | no | — |
| 770 | C2×C3 | — | 8 | 4 | no | — |
| 771 | C2×C3 | — | 8 | 2 | no | — |
| 772 | C2×C3 | — | 16 | 2 | no | — |
| 773 | D3 | — | 8 | 2 | no | — |
| 774 | D3 | — | 16 | 2 | no | — |
| 775 | C22 | — | 2 | 2 | no | — |
| 776 | C22 | — | 2 | 1 | no | — |
| 777 | C22 | — | 2 | 2 | no | — |
| 778 | C22 | — | 2 | 1 | no | — |
| 779 | C22 | — | 2 | 2 | no | — |
| 780 | C22 | — | 2 | 2 | no | — |
| 781 | C22 | — | 2 | 2 | no | — |
| 782 | C22 | — | 3 | 2 | no | — |
| 783 | C22 | — | 4 | 8 | no | — |
| 784 | C22 | — | 6 | 1 | no | — |
| 785 | C22 | — | 6 | 1 | no | — |
| 786 | C22 | — | 6 | 1 | no | — |
| 787 | C22 | — | 6 | 1 | no | — |
| 788 | C22 | — | 6 | 1 | no | — |
| 789 | C22 | — | 12 | 4 | no | — |
| 790 | C22 | — | 12 | 1 | no | — |
| 791 | C22 | — | 12 | 2 | no | — |
| 792 | C22 | — | 12 | 1 | no | — |
| 793 | C22 | — | 12 | 2 | no | — |
| 794 | C22 | — | 12 | 1 | no | — |
| 795 | C22 | — | 12 | 2 | no | — |
| 796 | C22 | — | 48 | 4 | no | — |
| 797 | C22 | — | 48 | 2 | no | — |
| 798 | C22 | #5926 | 1 | 2 | yes | complemented |
| 799 | C22 | C2×GL(2,ℤ/4) | 1 | 4 | yes | — |
| 800 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 801 | C4 | — | 2 | 1 | no | — |
| 802 | C4 | — | 3 | 1 | no | — |
| 803 | C4 | — | 3 | 1 | no | — |
| 804 | C4 | — | 3 | 4 | no | — |
| 805 | C4 | — | 6 | 1 | no | — |
| 806 | C4 | — | 6 | 2 | no | — |
| 807 | C4 | — | 12 | 1 | no | — |
| 808 | C4 | — | 12 | 2 | no | — |
| 809 | C4 | — | 12 | 1 | no | — |
| 810 | C4 | — | 12 | 1 | no | — |
| 811 | C4 | C2×GL(2,ℤ/4) | 1 | 2 | yes | — |
| 812 | C3 | — | 4 | 1 | no | Sylow |
| 813 | C2 | — | 2 | 2 | no | — |
| 814 | C2 | — | 2 | 4 | no | — |
| 815 | C2 | — | 4 | 2 | no | — |
| 816 | C2 | — | 6 | 2 | no | — |
| 817 | C2 | — | 12 | 1 | no | — |
| 818 | C2 | — | 24 | 1 | no | — |
| 819 | C2 | — | 24 | 2 | no | — |
| 820 | C2 | C2×#5926 | 1 | 1 | yes | characteristic |
| 821 | C2 | #87496 | 1 | 1 | yes | characteristic |
| 822 | C2 | C22×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C23×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Fitting | C22×2−1+4 | D3 |
| hypercenter | C22×D4 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×2−1+4⋊C3 | C2 | semidirect |
| 2. C2×#5926 | C2 | semidirect |
| 3. #85540 | C2 | semidirect |
| 4. #85539 | C2 | semidirect |
| 5. #85538 | C2 | semidirect |
| 6. #85537 | C2 | semidirect |
| 7. #85534 | C2 | semidirect |
| 8. #85523 | C2 | semidirect |
| 9. #85521 | C2 | semidirect |
| 10. #85507 | C2 | semidirect |
| 11. C2×#5421 | C2 | semidirect |
| 15. C2×2−1+4⋊C3 | C22 | semidirect |
| 16. C2×2−1+4⋊C3 | C22 | semidirect |
| 17. C22×#41⋊C3 | C22 | semidirect |
| 18. C23×SL(2,𝔽3) | C22 | semidirect |
| 20. C2×#986 | C22 | semidirect |
| 21. C2×#985 | C22 | semidirect |
| 22. C2×#983 | C22 | semidirect |
| 23. C22×GL(2,𝔽3) | C22 | semidirect |
| 25. #5427 | C22 | semidirect |
| 26. #5427 | C22 | semidirect |
| 27. #5426 | C22 | semidirect |
| 28. #5425 | C22 | semidirect |
| 29. #5424 | C22 | semidirect |
| 30. #5421 | C22 | semidirect |
| 31. #5421 | C22 | semidirect |
| 32. #5421 | C22 | semidirect |
| 33. #5421 | C22 | semidirect |
| 34. #5421 | C22 | semidirect |
| 35. #5420 | C22 | semidirect |
| 36. #5419 | C22 | semidirect |
| 37. #5419 | C22 | semidirect |
| 38. C2×#859 | C22 | semidirect |
| 39. C22×2−1+4 | D3 | semidirect |
| 67. 2−1+4⋊C3 | D4 | semidirect |
| 99. C2×2−1+4 | C2×D3 | semidirect |
| 100. C2×2−1+4 | C2×D3 | semidirect |
| 104. C22×#41 | C2×D3 | semidirect |
| 106. C23×Q8 | C2×D3 | semidirect |
| 222. #41⋊C3 | C2×D4 | semidirect |
| 225. C2×SL(2,𝔽3) | C2×D4 | semidirect |
| 249. 2−1+4 | #67 | semidirect |
| 496. #41 | C2×#67 | semidirect |
| 525. C2×Q8 | C2×#67 | semidirect |
| 798. C22 | #5926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4⋊C3 | 2 |
| C2×#5926 | 2 |
| #85540 | 2 |
| #85539 | 2 |
| #85538 | 2 |
| #85537 | 2 |
| #85534 | 2 |
| #85523 | 2 |
| #85521 | 2 |
| #85507 | 2 |
| C2×#5421 | 2 |
| #60374 | 3 |
| D4×#67 | 4 |