Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
7106 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 7106 conjugacy classes of subgroups — too many to draw. Only its 62 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 | C2×#87521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11715711 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 3 | C2×#85566 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#87548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#32895 | — | 3 | 1 | no | maximal, Sylow |
| 6 | #87548 | — | 2 | 1 | no | — |
| 7 | #87548 | C22 | 1 | 2 | yes | complemented |
| 8 | C2×#5950 | — | 2 | 1 | no | — |
| 9 | C2×#5950 | C22 | 1 | 1 | yes | characteristic |
| 10 | #87521 | — | 2 | 1 | no | — |
| 11 | #87521 | C22 | 1 | 2 | yes | complemented |
| 12 | C2×#5934 | — | 2 | 1 | no | — |
| 13 | #85566 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×#5417 | — | 4 | 3 | no | maximal |
| 15 | C2×2−1+6 | D3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#3027 | — | 3 | 1 | no | — |
| 17 | C2×#3021 | — | 3 | 3 | no | — |
| 18 | C2×#3010 | — | 3 | 3 | no | — |
| 19 | #32895 | — | 3 | 12 | no | — |
| 20 | #32895 | — | 3 | 4 | no | — |
| 21 | C2×#1796 | — | 3 | 3 | no | — |
| 22 | C2×#1794 | — | 3 | 3 | no | — |
| 23 | C2×#1791 | — | 3 | 1 | no | — |
| 24 | #5950 | — | 2 | 2 | no | — |
| 25 | #5950 | D4 | 1 | 1 | yes | characteristic |
| 26 | #5950 | C23 | 1 | 1 | yes | characteristic |
| 27 | C2×#997 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#994 | — | 8 | 1 | no | — |
| 29 | C2×Q8×A4 | — | 4 | 3 | no | — |
| 30 | #5934 | — | 2 | 2 | no | — |
| 31 | C2×C4⋊S4 | — | 4 | 3 | no | — |
| 32 | #5417 | — | 4 | 12 | no | — |
| 33 | C2×A4⋊C8 | — | 4 | 3 | no | — |
| 34 | 2−1+6 | — | 2 | 1 | no | — |
| 35 | 2−1+6 | — | 3 | 6 | no | — |
| 36 | 2−1+6 | — | 6 | 2 | no | — |
| 37 | 2−1+6 | — | 6 | 2 | no | — |
| 38 | 2−1+6 | — | 6 | 3 | no | — |
| 39 | 2−1+6 | C2×D3 | 1 | 2 | yes | complemented |
| 40 | C2×#585 | — | 2 | 1 | no | — |
| 41 | C2×#585 | — | 3 | 3 | no | — |
| 42 | C2×#585 | — | 6 | 1 | no | — |
| 43 | C2×#585 | — | 6 | 3 | no | — |
| 44 | C2×#585 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C22×2−1+4 | — | 3 | 3 | no | — |
| 46 | C22×2−1+4 | — | 6 | 1 | no | — |
| 47 | C22×2−1+4 | — | 6 | 2 | no | — |
| 48 | C22×AGL(1,ℤ/8) | — | 3 | 3 | no | — |
| 49 | C23×SD16 | — | 3 | 1 | no | — |
| 50 | C2×#535 | — | 3 | 3 | no | — |
| 51 | #3027 | — | 3 | 6 | no | — |
| 52 | #3027 | — | 3 | 2 | no | — |
| 53 | #3027 | — | 6 | 3 | no | — |
| 54 | #3027 | — | 6 | 1 | no | — |
| 55 | C2×B(4,𝔽2) | — | 6 | 3 | no | — |
| 56 | C2×B(4,𝔽2) | — | 6 | 1 | no | — |
| 57 | #3021 | — | 3 | 12 | no | — |
| 58 | #3021 | — | 3 | 12 | no | — |
| 59 | #3021 | — | 6 | 6 | no | — |
| 60 | #3021 | — | 6 | 6 | no | — |
| 61 | C2×#454 | — | 6 | 6 | no | — |
| 62 | C2×#453 | — | 6 | 6 | no | — |
| 63 | #3010 | — | 3 | 12 | no | — |
| 64 | #3010 | — | 3 | 12 | no | — |
| 65 | #3010 | — | 6 | 6 | no | — |
| 66 | #3010 | — | 6 | 6 | no | — |
| 67 | C2×#449 | — | 6 | 3 | no | — |
| 68 | C2×#449 | — | 6 | 3 | no | — |
| 69 | C2×#448 | — | 6 | 3 | no | — |
| 70 | C2×#448 | — | 6 | 3 | no | — |
| 71 | C2×#421 | — | 3 | 6 | no | — |
| 72 | C2×#419 | — | 3 | 3 | no | — |
| 73 | C2×#416 | — | 3 | 3 | no | — |
| 74 | C2×#413 | — | 3 | 3 | no | — |
| 75 | C2×#410 | — | 3 | 3 | no | — |
| 76 | C2×#408 | — | 3 | 3 | no | — |
| 77 | #1796 | — | 3 | 12 | no | — |
| 78 | #1796 | — | 3 | 12 | no | — |
| 79 | #1794 | — | 3 | 12 | no | — |
| 80 | #1794 | — | 3 | 12 | no | — |
| 81 | #1791 | — | 3 | 6 | no | — |
| 82 | #1791 | — | 3 | 2 | no | — |
| 83 | C22×S4 | — | 8 | 3 | no | — |
| 84 | #997 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | #994 | — | 8 | 2 | no | — |
| 86 | #994 | — | 8 | 2 | no | — |
| 87 | C2×#41⋊C3 | — | 8 | 1 | no | — |
| 88 | C2×#41⋊C3 | — | 8 | 2 | no | — |
| 89 | Q8×A4 | — | 4 | 6 | no | — |
| 90 | Q8×A4 | — | 8 | 3 | no | — |
| 91 | C2×C4×A4 | — | 4 | 3 | no | — |
| 92 | C2×C4×A4 | — | 8 | 3 | no | — |
| 93 | C4⋊S4 | — | 4 | 6 | no | — |
| 94 | C4⋊S4 | — | 8 | 3 | no | — |
| 95 | C2×#215 | — | 16 | 1 | no | — |
| 96 | A4⋊C8 | — | 4 | 6 | no | — |
| 97 | #585 | — | 2 | 2 | no | — |
| 98 | #585 | — | 3 | 3 | no | — |
| 99 | #585 | — | 3 | 3 | no | — |
| 100 | #585 | — | 3 | 6 | no | — |
| 101 | #585 | — | 3 | 6 | no | — |
| 102 | #585 | — | 3 | 6 | no | — |
| 103 | #585 | — | 3 | 6 | no | — |
| 104 | #585 | — | 6 | 2 | no | — |
| 105 | #585 | — | 6 | 3 | no | — |
| 106 | #585 | — | 6 | 1 | no | — |
| 107 | #585 | — | 6 | 1 | no | — |
| 108 | #585 | — | 6 | 12 | no | — |
| 109 | #585 | — | 6 | 6 | no | — |
| 110 | #585 | — | 6 | 3 | no | — |
| 111 | #585 | — | 6 | 3 | no | — |
| 112 | #585 | — | 6 | 12 | no | — |
| 113 | #585 | — | 6 | 6 | no | — |
| 114 | #585 | — | 6 | 3 | no | — |
| 115 | #585 | — | 6 | 2 | no | — |
| 116 | #585 | — | 6 | 2 | no | — |
| 117 | #585 | — | 6 | 2 | no | — |
| 118 | #585 | — | 6 | 12 | no | — |
| 119 | #585 | — | 6 | 12 | no | — |
| 120 | #585 | — | 6 | 24 | no | — |
| 121 | #585 | — | 6 | 6 | no | — |
| 122 | #585 | — | 6 | 6 | no | — |
| 123 | #585 | — | 6 | 24 | no | — |
| 124 | #585 | — | 6 | 12 | no | — |
| 125 | #585 | — | 6 | 6 | no | — |
| 126 | #585 | — | 6 | 6 | no | — |
| 127 | #585 | — | 6 | 6 | no | — |
| 128 | #585 | — | 6 | 4 | no | — |
| 129 | #585 | #67 | 1 | 1 | yes | characteristic |
| 130 | #585 | C22×D3 | 1 | 1 | yes | characteristic |
| 131 | C2×2−1+4 | — | 3 | 6 | no | — |
| 132 | C2×2−1+4 | — | 3 | 6 | no | — |
| 133 | C2×2−1+4 | — | 3 | 6 | no | — |
| 134 | C2×2−1+4 | — | 3 | 6 | no | — |
| 135 | C2×2−1+4 | — | 3 | 6 | no | — |
| 136 | C2×2−1+4 | — | 6 | 3 | no | — |
| 137 | C2×2−1+4 | — | 6 | 3 | no | — |
| 138 | C2×2−1+4 | — | 6 | 2 | no | — |
| 139 | C2×2−1+4 | — | 6 | 1 | no | — |
| 140 | C2×2−1+4 | — | 6 | 3 | no | — |
| 141 | C2×2−1+4 | — | 6 | 6 | no | — |
| 142 | C2×2−1+4 | — | 6 | 12 | no | — |
| 143 | C2×2−1+4 | — | 6 | 6 | no | — |
| 144 | C2×2−1+4 | — | 6 | 6 | no | — |
| 145 | C2×2−1+4 | — | 6 | 1 | no | — |
| 146 | C2×2−1+4 | — | 6 | 2 | no | — |
| 147 | C2×2−1+4 | — | 6 | 12 | no | — |
| 148 | C2×2−1+4 | — | 6 | 3 | no | — |
| 149 | C2×2−1+4 | — | 6 | 3 | no | — |
| 150 | C2×2−1+4 | — | 6 | 12 | no | — |
| 151 | C2×2−1+4 | — | 6 | 4 | no | — |
| 152 | C2×2−1+4 | — | 6 | 24 | no | — |
| 153 | C2×2−1+4 | — | 6 | 12 | no | — |
| 154 | C2×2−1+4 | — | 6 | 2 | no | — |
| 155 | C2×2−1+4 | — | 6 | 4 | no | — |
| 156 | C2×2−1+4 | — | 6 | 6 | no | — |
| 157 | C2×2−1+4 | — | 6 | 6 | no | — |
| 158 | C2×2−1+4 | — | 6 | 6 | no | — |
| 159 | C2×2−1+4 | — | 6 | 2 | no | — |
| 160 | C2×2−1+4 | — | 6 | 2 | no | — |
| 161 | C2×2−1+4 | — | 6 | 12 | no | — |
| 162 | C2×2−1+4 | — | 6 | 8 | no | — |
| 163 | C2×2−1+4 | — | 6 | 2 | no | — |
| 164 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 165 | C2×H(5,𝔽2) | — | 3 | 3 | no | — |
| 166 | C2×H(5,𝔽2) | — | 3 | 6 | no | — |
| 167 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 168 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 169 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 170 | C2×H(5,𝔽2) | — | 6 | 6 | no | — |
| 171 | C2×H(5,𝔽2) | #67 | 1 | 1 | yes | characteristic |
| 172 | C22×#41 | — | 3 | 3 | no | — |
| 173 | C22×#41 | — | 3 | 3 | no | — |
| 174 | C22×#41 | — | 3 | 3 | no | — |
| 175 | C22×#41 | — | 3 | 3 | no | — |
| 176 | C22×#41 | — | 6 | 3 | no | — |
| 177 | C22×#41 | — | 6 | 3 | no | — |
| 178 | C22×#41 | — | 6 | 1 | no | — |
| 179 | C22×#41 | — | 6 | 3 | no | — |
| 180 | C22×#41 | — | 6 | 3 | no | — |
| 181 | C22×#41 | — | 6 | 2 | no | — |
| 182 | C22×#41 | — | 6 | 12 | no | — |
| 183 | C22×#41 | — | 6 | 6 | no | — |
| 184 | C22×#41 | — | 6 | 6 | no | — |
| 185 | C23×Q8 | — | 3 | 1 | no | — |
| 186 | C23×Q8 | — | 3 | 3 | no | — |
| 187 | C23×Q8 | — | 6 | 3 | no | — |
| 188 | C23×Q8 | — | 6 | 2 | no | — |
| 189 | C23×Q8 | S4 | 1 | 3 | yes | complemented |
| 190 | C23×D4 | — | 3 | 1 | no | — |
| 191 | C2×AGL(1,ℤ/8) | — | 3 | 12 | no | — |
| 192 | C2×AGL(1,ℤ/8) | — | 6 | 6 | no | — |
| 193 | C2×AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 194 | C2×AGL(1,ℤ/8) | — | 6 | 12 | no | — |
| 195 | C22×SD16 | — | 3 | 4 | no | — |
| 196 | C22×SD16 | — | 6 | 3 | no | — |
| 197 | C22×SD16 | — | 6 | 3 | no | — |
| 198 | C22×SD16 | — | 6 | 3 | no | — |
| 199 | C22×SD16 | — | 6 | 6 | no | — |
| 200 | C22×D8 | — | 6 | 3 | no | — |
| 201 | C22×M16 | — | 3 | 3 | no | — |
| 202 | C23×C8 | — | 3 | 1 | no | — |
| 203 | #535 | — | 3 | 6 | no | — |
| 204 | #535 | — | 3 | 6 | no | — |
| 205 | #535 | — | 6 | 3 | no | — |
| 206 | #535 | — | 6 | 3 | no | — |
| 207 | #535 | — | 6 | 3 | no | — |
| 208 | #535 | — | 6 | 3 | no | — |
| 209 | #535 | — | 6 | 3 | no | — |
| 210 | #535 | — | 6 | 3 | no | — |
| 211 | C2×#127 | — | 6 | 3 | no | — |
| 212 | C2×#124 | — | 6 | 3 | no | — |
| 213 | C2×#121 | — | 6 | 3 | no | — |
| 214 | C2×#121 | — | 6 | 3 | no | — |
| 215 | C2×#120 | — | 6 | 3 | no | — |
| 216 | C2×#120 | — | 6 | 3 | no | — |
| 217 | C2×#117 | — | 3 | 3 | no | — |
| 218 | B(4,𝔽2) | — | 6 | 6 | no | — |
| 219 | B(4,𝔽2) | — | 6 | 6 | no | — |
| 220 | B(4,𝔽2) | — | 6 | 6 | no | — |
| 221 | B(4,𝔽2) | — | 6 | 12 | no | — |
| 222 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 223 | #454 | — | 6 | 24 | no | — |
| 224 | #454 | — | 6 | 24 | no | — |
| 225 | #453 | — | 6 | 24 | no | — |
| 226 | #453 | — | 6 | 24 | no | — |
| 227 | #449 | — | 6 | 12 | no | — |
| 228 | #449 | — | 6 | 12 | no | — |
| 229 | #449 | — | 6 | 12 | no | — |
| 230 | #449 | — | 6 | 12 | no | — |
| 231 | #448 | — | 6 | 12 | no | — |
| 232 | #448 | — | 6 | 12 | no | — |
| 233 | #448 | — | 6 | 12 | no | — |
| 234 | #448 | — | 6 | 12 | no | — |
| 235 | #421 | — | 3 | 24 | no | — |
| 236 | #421 | — | 6 | 12 | no | — |
| 237 | C2×#104 | — | 6 | 12 | no | — |
| 238 | #419 | — | 3 | 12 | no | — |
| 239 | #419 | — | 6 | 6 | no | — |
| 240 | #416 | — | 3 | 12 | no | — |
| 241 | #416 | — | 6 | 6 | no | — |
| 242 | C2×#103 | — | 6 | 3 | no | — |
| 243 | C2×#103 | — | 6 | 3 | no | — |
| 244 | C2×#103 | — | 6 | 3 | no | — |
| 245 | C2×#102 | — | 6 | 3 | no | — |
| 246 | #413 | — | 3 | 6 | no | — |
| 247 | #413 | — | 3 | 6 | no | — |
| 248 | #413 | — | 6 | 3 | no | — |
| 249 | #413 | — | 6 | 3 | no | — |
| 250 | C2×#101 | — | 6 | 3 | no | — |
| 251 | C2×#100 | — | 6 | 3 | no | — |
| 252 | #410 | — | 3 | 6 | no | — |
| 253 | #410 | — | 3 | 6 | no | — |
| 254 | #410 | — | 6 | 3 | no | — |
| 255 | #410 | — | 6 | 3 | no | — |
| 256 | C2×#99 | — | 6 | 3 | no | — |
| 257 | C2×#99 | — | 6 | 3 | no | — |
| 258 | #408 | — | 3 | 6 | no | — |
| 259 | #408 | — | 3 | 6 | no | — |
| 260 | #408 | — | 6 | 3 | no | — |
| 261 | #408 | — | 6 | 3 | no | — |
| 262 | C2×C22⋊C8 | — | 6 | 3 | no | — |
| 263 | C2×C22⋊C8 | — | 6 | 3 | no | — |
| 264 | C22×A4 | — | 4 | 3 | no | — |
| 265 | C2×S4 | — | 8 | 6 | no | — |
| 266 | C2×S4 | — | 16 | 6 | no | — |
| 267 | C2×C3×Q8 | — | 16 | 1 | no | — |
| 268 | C2×D12 | — | 16 | 1 | no | — |
| 269 | #41⋊C3 | — | 8 | 1 | no | — |
| 270 | #41⋊C3 | — | 8 | 1 | no | — |
| 271 | #41⋊C3 | — | 8 | 4 | no | — |
| 272 | C2×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 273 | C4×A4 | — | 4 | 3 | no | — |
| 274 | C4×A4 | — | 4 | 3 | no | — |
| 275 | C4×A4 | — | 8 | 6 | no | — |
| 276 | #215 | — | 16 | 4 | no | — |
| 277 | C2×C3⋊C8 | — | 16 | 1 | no | — |
| 278 | C25 | — | 6 | 1 | no | — |
| 279 | 2−1+4 | — | 3 | 12 | no | — |
| 280 | 2−1+4 | — | 3 | 12 | no | — |
| 281 | 2−1+4 | — | 6 | 1 | no | — |
| 282 | 2−1+4 | — | 6 | 1 | no | — |
| 283 | 2−1+4 | — | 6 | 6 | no | — |
| 284 | 2−1+4 | — | 6 | 12 | no | — |
| 285 | 2−1+4 | — | 6 | 6 | no | — |
| 286 | 2−1+4 | — | 6 | 12 | no | — |
| 287 | 2−1+4 | — | 6 | 12 | no | — |
| 288 | 2−1+4 | — | 6 | 6 | no | — |
| 289 | 2−1+4 | — | 6 | 6 | no | — |
| 290 | 2−1+4 | — | 6 | 6 | no | — |
| 291 | 2−1+4 | — | 6 | 12 | no | — |
| 292 | 2−1+4 | — | 6 | 12 | no | — |
| 293 | 2−1+4 | — | 6 | 3 | no | — |
| 294 | 2−1+4 | — | 6 | 3 | no | — |
| 295 | 2−1+4 | — | 6 | 12 | no | — |
| 296 | 2−1+4 | — | 6 | 12 | no | — |
| 297 | 2−1+4 | — | 6 | 2 | no | — |
| 298 | 2−1+4 | — | 6 | 4 | no | — |
| 299 | 2−1+4 | — | 6 | 4 | no | — |
| 300 | 2−1+4 | — | 6 | 2 | no | — |
| 301 | 2−1+4 | — | 6 | 24 | no | — |
| 302 | 2−1+4 | — | 6 | 24 | no | — |
| 303 | 2−1+4 | — | 6 | 24 | no | — |
| 304 | 2−1+4 | — | 6 | 24 | no | — |
| 305 | 2−1+4 | — | 6 | 24 | no | — |
| 306 | 2−1+4 | — | 6 | 6 | no | — |
| 307 | 2−1+4 | — | 6 | 12 | no | — |
| 308 | 2−1+4 | — | 6 | 6 | no | — |
| 309 | 2−1+4 | — | 6 | 12 | no | — |
| 310 | 2−1+4 | — | 6 | 12 | no | — |
| 311 | 2−1+4 | — | 6 | 24 | no | — |
| 312 | 2−1+4 | — | 6 | 24 | no | — |
| 313 | 2−1+4 | — | 6 | 2 | no | — |
| 314 | 2−1+4 | — | 6 | 12 | no | — |
| 315 | 2−1+4 | — | 6 | 12 | no | — |
| 316 | 2−1+4 | — | 6 | 24 | no | — |
| 317 | 2−1+4 | — | 6 | 24 | no | — |
| 318 | 2−1+4 | — | 6 | 24 | no | — |
| 319 | 2−1+4 | — | 6 | 12 | no | — |
| 320 | 2−1+4 | — | 6 | 12 | no | — |
| 321 | 2−1+4 | — | 6 | 4 | no | — |
| 322 | 2−1+4 | — | 6 | 6 | no | — |
| 323 | 2−1+4 | — | 6 | 12 | no | — |
| 324 | 2−1+4 | — | 6 | 24 | no | — |
| 325 | 2−1+4 | — | 6 | 12 | no | — |
| 326 | 2−1+4 | — | 6 | 12 | no | — |
| 327 | 2−1+4 | — | 6 | 12 | no | — |
| 328 | 2−1+4 | — | 6 | 6 | no | — |
| 329 | 2−1+4 | — | 6 | 4 | no | — |
| 330 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 331 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 332 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 333 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 334 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 335 | H(5,𝔽2) | — | 3 | 6 | no | — |
| 336 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 337 | H(5,𝔽2) | — | 3 | 12 | no | — |
| 338 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 339 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 340 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 341 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 342 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 343 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 344 | H(5,𝔽2) | — | 6 | 3 | no | — |
| 345 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 346 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 347 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 348 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 349 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 350 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 351 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 352 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 353 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 354 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 355 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 356 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 357 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 358 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 359 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 360 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 361 | H(5,𝔽2) | — | 6 | 6 | no | — |
| 362 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 363 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 364 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 365 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 366 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 367 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 368 | H(5,𝔽2) | — | 6 | 24 | no | — |
| 369 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 370 | H(5,𝔽2) | C2×#67 | 1 | 1 | yes | characteristic |
| 371 | C2×#41 | — | 2 | 2 | no | — |
| 372 | C2×#41 | — | 2 | 1 | no | — |
| 373 | C2×#41 | — | 3 | 3 | no | — |
| 374 | C2×#41 | — | 3 | 3 | no | — |
| 375 | C2×#41 | — | 3 | 3 | no | — |
| 376 | C2×#41 | — | 3 | 3 | no | — |
| 377 | C2×#41 | — | 3 | 3 | no | — |
| 378 | C2×#41 | — | 3 | 3 | no | — |
| 379 | C2×#41 | — | 3 | 3 | no | — |
| 380 | C2×#41 | — | 3 | 3 | no | — |
| 381 | C2×#41 | — | 3 | 6 | no | — |
| 382 | C2×#41 | — | 3 | 12 | no | — |
| 383 | C2×#41 | — | 3 | 6 | no | — |
| 384 | C2×#41 | — | 3 | 12 | no | — |
| 385 | C2×#41 | — | 3 | 6 | no | — |
| 386 | C2×#41 | — | 3 | 6 | no | — |
| 387 | C2×#41 | — | 3 | 6 | no | — |
| 388 | C2×#41 | — | 3 | 6 | no | — |
| 389 | C2×#41 | — | 6 | 6 | no | — |
| 390 | C2×#41 | — | 6 | 6 | no | — |
| 391 | C2×#41 | — | 6 | 6 | no | — |
| 392 | C2×#41 | — | 6 | 6 | no | — |
| 393 | C2×#41 | — | 6 | 1 | no | — |
| 394 | C2×#41 | — | 6 | 1 | no | — |
| 395 | C2×#41 | — | 6 | 1 | no | — |
| 396 | C2×#41 | — | 6 | 3 | no | — |
| 397 | C2×#41 | — | 6 | 6 | no | — |
| 398 | C2×#41 | — | 6 | 6 | no | — |
| 399 | C2×#41 | — | 6 | 6 | no | — |
| 400 | C2×#41 | — | 6 | 3 | no | — |
| 401 | C2×#41 | — | 6 | 3 | no | — |
| 402 | C2×#41 | — | 6 | 6 | no | — |
| 403 | C2×#41 | — | 6 | 6 | no | — |
| 404 | C2×#41 | — | 6 | 6 | no | — |
| 405 | C2×#41 | — | 6 | 6 | no | — |
| 406 | C2×#41 | — | 6 | 3 | no | — |
| 407 | C2×#41 | — | 6 | 6 | no | — |
| 408 | C2×#41 | — | 6 | 3 | no | — |
| 409 | C2×#41 | — | 6 | 3 | no | — |
| 410 | C2×#41 | — | 6 | 3 | no | — |
| 411 | C2×#41 | — | 6 | 3 | no | — |
| 412 | C2×#41 | — | 6 | 3 | no | — |
| 413 | C2×#41 | — | 6 | 6 | no | — |
| 414 | C2×#41 | — | 6 | 3 | no | — |
| 415 | C2×#41 | — | 6 | 6 | no | — |
| 416 | C2×#41 | — | 6 | 6 | no | — |
| 417 | C2×#41 | — | 6 | 3 | no | — |
| 418 | C2×#41 | — | 6 | 6 | no | — |
| 419 | C2×#41 | — | 6 | 6 | no | — |
| 420 | C2×#41 | — | 6 | 6 | no | — |
| 421 | C2×#41 | — | 6 | 6 | no | — |
| 422 | C2×#41 | — | 6 | 6 | no | — |
| 423 | C2×#41 | — | 6 | 6 | no | — |
| 424 | C2×#41 | — | 6 | 6 | no | — |
| 425 | C2×#41 | — | 6 | 6 | no | — |
| 426 | C2×#41 | — | 6 | 6 | no | — |
| 427 | C2×#41 | — | 6 | 6 | no | — |
| 428 | C2×#41 | — | 6 | 6 | no | — |
| 429 | C2×#41 | — | 6 | 6 | no | — |
| 430 | C2×#41 | — | 6 | 6 | no | — |
| 431 | C2×#41 | — | 6 | 3 | no | — |
| 432 | C2×#41 | — | 6 | 6 | no | — |
| 433 | C2×#41 | — | 6 | 12 | no | — |
| 434 | C2×#41 | — | 6 | 4 | no | — |
| 435 | C2×#41 | — | 6 | 1 | no | — |
| 436 | C2×#41 | — | 6 | 1 | no | — |
| 437 | C2×#41 | — | 6 | 4 | no | — |
| 438 | C2×#41 | — | 6 | 24 | no | — |
| 439 | C2×#41 | — | 6 | 24 | no | — |
| 440 | C2×#41 | — | 6 | 24 | no | — |
| 441 | C2×#41 | — | 6 | 24 | no | — |
| 442 | C2×#41 | — | 6 | 6 | no | — |
| 443 | C2×#41 | — | 6 | 12 | no | — |
| 444 | C2×#41 | — | 6 | 6 | no | — |
| 445 | C2×#41 | — | 6 | 12 | no | — |
| 446 | C2×#41 | — | 6 | 12 | no | — |
| 447 | C2×#41 | — | 6 | 6 | no | — |
| 448 | C2×#41 | — | 6 | 6 | no | — |
| 449 | C2×#41 | — | 6 | 6 | no | — |
| 450 | C2×#41 | — | 6 | 6 | no | — |
| 451 | C2×#41 | — | 6 | 6 | no | — |
| 452 | C2×#41 | — | 6 | 24 | no | — |
| 453 | C2×#41 | — | 6 | 24 | no | — |
| 454 | C2×#41 | — | 6 | 12 | no | — |
| 455 | C2×#41 | — | 6 | 12 | no | — |
| 456 | C2×#41 | — | 6 | 24 | no | — |
| 457 | C2×#41 | — | 6 | 24 | no | — |
| 458 | C2×#41 | — | 6 | 24 | no | — |
| 459 | C2×#41 | — | 6 | 12 | no | — |
| 460 | C2×#41 | — | 6 | 12 | no | — |
| 461 | C2×#41 | — | 6 | 24 | no | — |
| 462 | C2×#41 | — | 6 | 12 | no | — |
| 463 | C2×#41 | — | 6 | 12 | no | — |
| 464 | C2×#41 | — | 6 | 24 | no | — |
| 465 | C2×#41 | — | 6 | 24 | no | — |
| 466 | C2×#41 | — | 6 | 24 | no | — |
| 467 | C2×#41 | — | 6 | 24 | no | — |
| 468 | C2×#41 | — | 6 | 12 | no | — |
| 469 | C2×#41 | — | 6 | 24 | no | — |
| 470 | C2×#41 | — | 6 | 12 | no | — |
| 471 | C2×#41 | — | 6 | 12 | no | — |
| 472 | C2×#41 | — | 6 | 12 | no | — |
| 473 | C2×#41 | — | 6 | 1 | no | — |
| 474 | C2×#41 | — | 6 | 3 | no | — |
| 475 | C22×Q8 | — | 2 | 3 | no | — |
| 476 | C22×Q8 | — | 3 | 3 | no | — |
| 477 | C22×Q8 | — | 3 | 3 | no | — |
| 478 | C22×Q8 | — | 3 | 2 | no | — |
| 479 | C22×Q8 | — | 3 | 3 | no | — |
| 480 | C22×Q8 | — | 3 | 6 | no | — |
| 481 | C22×Q8 | — | 3 | 3 | no | — |
| 482 | C22×Q8 | — | 3 | 6 | no | — |
| 483 | C22×Q8 | — | 3 | 6 | no | — |
| 484 | C22×Q8 | — | 3 | 6 | no | — |
| 485 | C22×Q8 | — | 6 | 3 | no | — |
| 486 | C22×Q8 | — | 6 | 3 | no | — |
| 487 | C22×Q8 | — | 6 | 3 | no | — |
| 488 | C22×Q8 | — | 6 | 3 | no | — |
| 489 | C22×Q8 | — | 6 | 1 | no | — |
| 490 | C22×Q8 | — | 6 | 3 | no | — |
| 491 | C22×Q8 | — | 6 | 3 | no | — |
| 492 | C22×Q8 | — | 6 | 3 | no | — |
| 493 | C22×Q8 | — | 6 | 1 | no | — |
| 494 | C22×Q8 | — | 6 | 2 | no | — |
| 495 | C22×Q8 | — | 6 | 3 | no | — |
| 496 | C22×Q8 | — | 6 | 6 | no | — |
| 497 | C22×Q8 | — | 6 | 6 | no | — |
| 498 | C22×Q8 | — | 6 | 6 | no | — |
| 499 | C22×Q8 | — | 6 | 12 | no | — |
| 500 | C22×Q8 | — | 6 | 6 | no | — |
| 501 | C22×Q8 | — | 6 | 6 | no | — |
| 502 | C22×Q8 | — | 6 | 6 | no | — |
| 503 | C22×Q8 | — | 6 | 6 | no | — |
| 504 | C22×Q8 | — | 6 | 6 | no | — |
| 505 | C22×Q8 | — | 6 | 24 | no | — |
| 506 | C22×Q8 | — | 6 | 4 | no | — |
| 507 | C22×Q8 | — | 6 | 4 | no | — |
| 508 | C22×Q8 | — | 6 | 12 | no | — |
| 509 | C22×Q8 | — | 6 | 12 | no | — |
| 510 | C22×Q8 | C2×S4 | 1 | 6 | yes | complemented |
| 511 | C22×D4 | — | 3 | 3 | no | — |
| 512 | C22×D4 | — | 3 | 3 | no | — |
| 513 | C22×D4 | — | 3 | 3 | no | — |
| 514 | C22×D4 | — | 3 | 3 | no | — |
| 515 | C22×D4 | — | 3 | 2 | no | — |
| 516 | C22×D4 | — | 6 | 3 | no | — |
| 517 | C22×D4 | — | 6 | 3 | no | — |
| 518 | C22×D4 | — | 6 | 3 | no | — |
| 519 | C22×D4 | — | 6 | 3 | no | — |
| 520 | C22×D4 | — | 6 | 1 | no | — |
| 521 | C22×D4 | — | 6 | 12 | no | — |
| 522 | C22×D4 | — | 6 | 3 | no | — |
| 523 | C22×D4 | — | 6 | 3 | no | — |
| 524 | C22×D4 | — | 6 | 3 | no | — |
| 525 | C22×D4 | — | 6 | 6 | no | — |
| 526 | C22×D4 | — | 6 | 6 | no | — |
| 527 | C22×D4 | — | 6 | 3 | no | — |
| 528 | C22×D4 | — | 6 | 2 | no | — |
| 529 | C22×D4 | — | 6 | 1 | no | — |
| 530 | C22×D4 | — | 12 | 3 | no | — |
| 531 | C22×D4 | — | 12 | 3 | no | — |
| 532 | C23×C4 | — | 2 | 3 | no | — |
| 533 | C23×C4 | — | 3 | 1 | no | — |
| 534 | C23×C4 | — | 3 | 3 | no | — |
| 535 | C23×C4 | — | 6 | 3 | no | — |
| 536 | C23×C4 | — | 6 | 3 | no | — |
| 537 | C23×C4 | — | 6 | 3 | no | — |
| 538 | C23×C4 | — | 6 | 1 | no | — |
| 539 | C23×C4 | — | 6 | 3 | no | — |
| 540 | C23×C4 | — | 6 | 6 | no | — |
| 541 | C23×C4 | C2×S4 | 1 | 3 | yes | — |
| 542 | AGL(1,ℤ/8) | — | 6 | 48 | no | — |
| 543 | AGL(1,ℤ/8) | — | 12 | 24 | no | — |
| 544 | C2×SD16 | — | 6 | 12 | no | — |
| 545 | C2×SD16 | — | 6 | 12 | no | — |
| 546 | C2×SD16 | — | 6 | 12 | no | — |
| 547 | C2×SD16 | — | 12 | 6 | no | — |
| 548 | C2×SD16 | — | 12 | 6 | no | — |
| 549 | C2×SD16 | — | 12 | 3 | no | — |
| 550 | C2×SD16 | — | 12 | 6 | no | — |
| 551 | C2×SD16 | — | 12 | 6 | no | — |
| 552 | C2×SD16 | — | 12 | 1 | no | — |
| 553 | C2×D8 | — | 6 | 12 | no | — |
| 554 | C2×D8 | — | 12 | 6 | no | — |
| 555 | C2×D8 | — | 12 | 6 | no | — |
| 556 | C2×M16 | — | 3 | 6 | no | — |
| 557 | C2×M16 | — | 6 | 3 | no | — |
| 558 | C2×M16 | — | 6 | 6 | no | — |
| 559 | C2×M16 | — | 6 | 6 | no | — |
| 560 | C22×C8 | — | 3 | 2 | no | — |
| 561 | C22×C8 | — | 6 | 3 | no | — |
| 562 | C22×C8 | — | 6 | 3 | no | — |
| 563 | C22×C8 | — | 6 | 3 | no | — |
| 564 | #127 | — | 6 | 6 | no | — |
| 565 | #127 | — | 6 | 6 | no | — |
| 566 | #127 | — | 12 | 3 | no | — |
| 567 | #127 | — | 12 | 3 | no | — |
| 568 | #124 | — | 6 | 6 | no | — |
| 569 | #124 | — | 6 | 6 | no | — |
| 570 | #124 | — | 12 | 3 | no | — |
| 571 | #124 | — | 12 | 3 | no | — |
| 572 | #121 | — | 6 | 6 | no | — |
| 573 | #121 | — | 6 | 6 | no | — |
| 574 | #121 | — | 6 | 6 | no | — |
| 575 | #121 | — | 6 | 6 | no | — |
| 576 | #121 | — | 12 | 3 | no | — |
| 577 | #121 | — | 12 | 3 | no | — |
| 578 | #121 | — | 12 | 3 | no | — |
| 579 | #121 | — | 12 | 3 | no | — |
| 580 | #120 | — | 6 | 6 | no | — |
| 581 | #120 | — | 6 | 6 | no | — |
| 582 | #120 | — | 6 | 6 | no | — |
| 583 | #120 | — | 6 | 6 | no | — |
| 584 | #120 | — | 12 | 3 | no | — |
| 585 | #120 | — | 12 | 3 | no | — |
| 586 | #120 | — | 12 | 3 | no | — |
| 587 | #120 | — | 12 | 3 | no | — |
| 588 | #117 | — | 3 | 6 | no | — |
| 589 | #117 | — | 6 | 3 | no | — |
| 590 | #117 | — | 6 | 3 | no | — |
| 591 | #117 | — | 6 | 3 | no | — |
| 592 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 593 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 594 | C2×C22⋊C4 | — | 12 | 3 | no | — |
| 595 | C2×C22⋊C4 | — | 12 | 3 | no | — |
| 596 | C2×C42 | — | 6 | 3 | no | — |
| 597 | #104 | — | 6 | 48 | no | — |
| 598 | #103 | — | 6 | 12 | no | — |
| 599 | #103 | — | 6 | 12 | no | — |
| 600 | #103 | — | 6 | 12 | no | — |
| 601 | #102 | — | 6 | 12 | no | — |
| 602 | #101 | — | 6 | 6 | no | — |
| 603 | #101 | — | 6 | 6 | no | — |
| 604 | #100 | — | 6 | 6 | no | — |
| 605 | #100 | — | 6 | 6 | no | — |
| 606 | #99 | — | 6 | 6 | no | — |
| 607 | #99 | — | 6 | 6 | no | — |
| 608 | #99 | — | 6 | 6 | no | — |
| 609 | #99 | — | 6 | 6 | no | — |
| 610 | C22⋊C8 | — | 6 | 6 | no | — |
| 611 | C22⋊C8 | — | 6 | 6 | no | — |
| 612 | C22⋊C8 | — | 6 | 6 | no | — |
| 613 | C22⋊C8 | — | 6 | 6 | no | — |
| 614 | C22×D3 | — | 32 | 1 | no | — |
| 615 | C2×A4 | — | 4 | 6 | no | — |
| 616 | C2×A4 | — | 4 | 3 | no | — |
| 617 | S4 | — | 16 | 6 | no | — |
| 618 | C3×Q8 | — | 16 | 2 | no | — |
| 619 | C3×Q8 | — | 32 | 1 | no | — |
| 620 | C2×C3×C4 | — | 16 | 1 | no | — |
| 621 | C2×C3×C4 | — | 32 | 1 | no | — |
| 622 | D12 | — | 16 | 2 | no | — |
| 623 | D12 | — | 32 | 1 | no | — |
| 624 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 625 | C3⋊C8 | — | 16 | 2 | no | — |
| 626 | C24 | — | 3 | 1 | no | — |
| 627 | C24 | — | 3 | 3 | no | — |
| 628 | C24 | — | 6 | 3 | no | — |
| 629 | C24 | — | 6 | 2 | no | — |
| 630 | C24 | — | 6 | 2 | no | — |
| 631 | C24 | — | 12 | 3 | no | — |
| 632 | C24 | — | 12 | 3 | no | — |
| 633 | C24 | — | 48 | 2 | no | — |
| 634 | C24 | GL(2,ℤ/4) | 1 | 3 | yes | — |
| 635 | #41 | — | 2 | 4 | no | — |
| 636 | #41 | — | 2 | 1 | no | — |
| 637 | #41 | — | 2 | 1 | no | — |
| 638 | #41 | — | 3 | 24 | no | — |
| 639 | #41 | — | 3 | 24 | no | — |
| 640 | #41 | — | 6 | 1 | no | — |
| 641 | #41 | — | 6 | 3 | no | — |
| 642 | #41 | — | 6 | 6 | no | — |
| 643 | #41 | — | 6 | 3 | no | — |
| 644 | #41 | — | 6 | 3 | no | — |
| 645 | #41 | — | 6 | 6 | no | — |
| 646 | #41 | — | 6 | 3 | no | — |
| 647 | #41 | — | 6 | 6 | no | — |
| 648 | #41 | — | 6 | 6 | no | — |
| 649 | #41 | — | 6 | 6 | no | — |
| 650 | #41 | — | 6 | 6 | no | — |
| 651 | #41 | — | 6 | 3 | no | — |
| 652 | #41 | — | 6 | 12 | no | — |
| 653 | #41 | — | 6 | 12 | no | — |
| 654 | #41 | — | 6 | 12 | no | — |
| 655 | #41 | — | 6 | 6 | no | — |
| 656 | #41 | — | 6 | 6 | no | — |
| 657 | #41 | — | 6 | 12 | no | — |
| 658 | #41 | — | 6 | 6 | no | — |
| 659 | #41 | — | 6 | 6 | no | — |
| 660 | #41 | — | 6 | 12 | no | — |
| 661 | #41 | — | 6 | 12 | no | — |
| 662 | #41 | — | 6 | 12 | no | — |
| 663 | #41 | — | 6 | 3 | no | — |
| 664 | #41 | — | 6 | 3 | no | — |
| 665 | #41 | — | 6 | 6 | no | — |
| 666 | #41 | — | 6 | 3 | no | — |
| 667 | #41 | — | 6 | 12 | no | — |
| 668 | #41 | — | 6 | 12 | no | — |
| 669 | #41 | — | 6 | 12 | no | — |
| 670 | #41 | — | 6 | 12 | no | — |
| 671 | #41 | — | 6 | 12 | no | — |
| 672 | #41 | — | 6 | 12 | no | — |
| 673 | #41 | — | 6 | 12 | no | — |
| 674 | #41 | — | 6 | 24 | no | — |
| 675 | #41 | — | 6 | 2 | no | — |
| 676 | #41 | — | 6 | 2 | no | — |
| 677 | #41 | — | 6 | 1 | no | — |
| 678 | #41 | — | 6 | 6 | no | — |
| 679 | #41 | — | 6 | 6 | no | — |
| 680 | #41 | — | 6 | 24 | no | — |
| 681 | #41 | — | 6 | 24 | no | — |
| 682 | #41 | — | 6 | 12 | no | — |
| 683 | #41 | — | 6 | 24 | no | — |
| 684 | #41 | — | 6 | 24 | no | — |
| 685 | #41 | — | 6 | 24 | no | — |
| 686 | #41 | — | 6 | 12 | no | — |
| 687 | #41 | — | 6 | 24 | no | — |
| 688 | #41 | — | 6 | 24 | no | — |
| 689 | #41 | — | 6 | 12 | no | — |
| 690 | #41 | — | 6 | 12 | no | — |
| 691 | #41 | — | 6 | 12 | no | — |
| 692 | #41 | — | 6 | 3 | no | — |
| 693 | #41 | — | 6 | 3 | no | — |
| 694 | #41 | — | 6 | 6 | no | — |
| 695 | #41 | — | 6 | 12 | no | — |
| 696 | #41 | — | 6 | 12 | no | — |
| 697 | #41 | — | 6 | 12 | no | — |
| 698 | #41 | — | 6 | 12 | no | — |
| 699 | #41 | — | 6 | 12 | no | — |
| 700 | #41 | — | 6 | 24 | no | — |
| 701 | #41 | — | 6 | 24 | no | — |
| 702 | #41 | — | 6 | 24 | no | — |
| 703 | #41 | — | 6 | 24 | no | — |
| 704 | #41 | — | 6 | 24 | no | — |
| 705 | #41 | — | 6 | 24 | no | — |
| 706 | #41 | — | 6 | 12 | no | — |
| 707 | #41 | — | 6 | 12 | no | — |
| 708 | #41 | — | 6 | 24 | no | — |
| 709 | #41 | — | 6 | 24 | no | — |
| 710 | #41 | — | 6 | 24 | no | — |
| 711 | #41 | — | 6 | 24 | no | — |
| 712 | #41 | — | 6 | 12 | no | — |
| 713 | #41 | — | 6 | 12 | no | — |
| 714 | #41 | — | 6 | 24 | no | — |
| 715 | #41 | — | 6 | 6 | no | — |
| 716 | #41 | — | 6 | 6 | no | — |
| 717 | #41 | — | 6 | 2 | no | — |
| 718 | #41 | — | 6 | 2 | no | — |
| 719 | #41 | — | 6 | 4 | no | — |
| 720 | #41 | — | 6 | 1 | no | — |
| 721 | #41 | — | 6 | 1 | no | — |
| 722 | C2×Q8 | — | 2 | 1 | no | — |
| 723 | C2×Q8 | — | 3 | 3 | no | — |
| 724 | C2×Q8 | — | 3 | 3 | no | — |
| 725 | C2×Q8 | — | 3 | 3 | no | — |
| 726 | C2×Q8 | — | 3 | 3 | no | — |
| 727 | C2×Q8 | — | 3 | 6 | no | — |
| 728 | C2×Q8 | — | 3 | 6 | no | — |
| 729 | C2×Q8 | — | 3 | 6 | no | — |
| 730 | C2×Q8 | — | 3 | 6 | no | — |
| 731 | C2×Q8 | — | 3 | 6 | no | — |
| 732 | C2×Q8 | — | 3 | 6 | no | — |
| 733 | C2×Q8 | — | 3 | 6 | no | — |
| 734 | C2×Q8 | — | 3 | 3 | no | — |
| 735 | C2×Q8 | — | 6 | 3 | no | — |
| 736 | C2×Q8 | — | 6 | 3 | no | — |
| 737 | C2×Q8 | — | 6 | 3 | no | — |
| 738 | C2×Q8 | — | 6 | 3 | no | — |
| 739 | C2×Q8 | — | 6 | 6 | no | — |
| 740 | C2×Q8 | — | 6 | 3 | no | — |
| 741 | C2×Q8 | — | 6 | 3 | no | — |
| 742 | C2×Q8 | — | 6 | 6 | no | — |
| 743 | C2×Q8 | — | 6 | 3 | no | — |
| 744 | C2×Q8 | — | 6 | 6 | no | — |
| 745 | C2×Q8 | — | 6 | 6 | no | — |
| 746 | C2×Q8 | — | 6 | 12 | no | — |
| 747 | C2×Q8 | — | 6 | 6 | no | — |
| 748 | C2×Q8 | — | 6 | 3 | no | — |
| 749 | C2×Q8 | — | 6 | 3 | no | — |
| 750 | C2×Q8 | — | 6 | 6 | no | — |
| 751 | C2×Q8 | — | 6 | 6 | no | — |
| 752 | C2×Q8 | — | 6 | 1 | no | — |
| 753 | C2×Q8 | — | 6 | 1 | no | — |
| 754 | C2×Q8 | — | 6 | 4 | no | — |
| 755 | C2×Q8 | — | 6 | 6 | no | — |
| 756 | C2×Q8 | — | 6 | 6 | no | — |
| 757 | C2×Q8 | — | 6 | 12 | no | — |
| 758 | C2×Q8 | — | 6 | 12 | no | — |
| 759 | C2×Q8 | — | 6 | 12 | no | — |
| 760 | C2×Q8 | — | 6 | 24 | no | — |
| 761 | C2×Q8 | — | 6 | 24 | no | — |
| 762 | C2×Q8 | — | 6 | 6 | no | — |
| 763 | C2×Q8 | — | 6 | 12 | no | — |
| 764 | C2×Q8 | — | 6 | 12 | no | — |
| 765 | C2×Q8 | — | 6 | 24 | no | — |
| 766 | C2×Q8 | — | 6 | 3 | no | — |
| 767 | C2×Q8 | — | 6 | 3 | no | — |
| 768 | C2×Q8 | — | 6 | 12 | no | — |
| 769 | C2×Q8 | — | 6 | 12 | no | — |
| 770 | C2×Q8 | — | 6 | 24 | no | — |
| 771 | C2×Q8 | — | 6 | 24 | no | — |
| 772 | C2×Q8 | — | 6 | 12 | no | — |
| 773 | C2×Q8 | — | 6 | 12 | no | — |
| 774 | C2×Q8 | — | 6 | 6 | no | — |
| 775 | C2×Q8 | — | 6 | 6 | no | — |
| 776 | C2×Q8 | #1020 | 1 | 1 | yes | characteristic |
| 777 | C2×D4 | — | 3 | 6 | no | — |
| 778 | C2×D4 | — | 3 | 6 | no | — |
| 779 | C2×D4 | — | 3 | 6 | no | — |
| 780 | C2×D4 | — | 3 | 3 | no | — |
| 781 | C2×D4 | — | 3 | 3 | no | — |
| 782 | C2×D4 | — | 3 | 3 | no | — |
| 783 | C2×D4 | — | 3 | 3 | no | — |
| 784 | C2×D4 | — | 3 | 3 | no | — |
| 785 | C2×D4 | — | 3 | 3 | no | — |
| 786 | C2×D4 | — | 3 | 3 | no | — |
| 787 | C2×D4 | — | 3 | 3 | no | — |
| 788 | C2×D4 | — | 3 | 3 | no | — |
| 789 | C2×D4 | — | 3 | 3 | no | — |
| 790 | C2×D4 | — | 3 | 3 | no | — |
| 791 | C2×D4 | — | 3 | 3 | no | — |
| 792 | C2×D4 | — | 6 | 2 | no | — |
| 793 | C2×D4 | — | 6 | 6 | no | — |
| 794 | C2×D4 | — | 6 | 6 | no | — |
| 795 | C2×D4 | — | 6 | 3 | no | — |
| 796 | C2×D4 | — | 6 | 3 | no | — |
| 797 | C2×D4 | — | 6 | 6 | no | — |
| 798 | C2×D4 | — | 6 | 6 | no | — |
| 799 | C2×D4 | — | 6 | 24 | no | — |
| 800 | C2×D4 | — | 6 | 24 | no | — |
| 801 | C2×D4 | — | 6 | 3 | no | — |
| 802 | C2×D4 | — | 6 | 6 | no | — |
| 803 | C2×D4 | — | 6 | 3 | no | — |
| 804 | C2×D4 | — | 6 | 3 | no | — |
| 805 | C2×D4 | — | 6 | 6 | no | — |
| 806 | C2×D4 | — | 6 | 12 | no | — |
| 807 | C2×D4 | — | 6 | 6 | no | — |
| 808 | C2×D4 | — | 6 | 6 | no | — |
| 809 | C2×D4 | — | 6 | 12 | no | — |
| 810 | C2×D4 | — | 6 | 6 | no | — |
| 811 | C2×D4 | — | 6 | 6 | no | — |
| 812 | C2×D4 | — | 6 | 6 | no | — |
| 813 | C2×D4 | — | 6 | 6 | no | — |
| 814 | C2×D4 | — | 6 | 6 | no | — |
| 815 | C2×D4 | — | 6 | 12 | no | — |
| 816 | C2×D4 | — | 6 | 12 | no | — |
| 817 | C2×D4 | — | 6 | 12 | no | — |
| 818 | C2×D4 | — | 6 | 2 | no | — |
| 819 | C2×D4 | — | 6 | 1 | no | — |
| 820 | C2×D4 | — | 6 | 6 | no | — |
| 821 | C2×D4 | — | 6 | 12 | no | — |
| 822 | C2×D4 | — | 6 | 8 | no | — |
| 823 | C2×D4 | — | 6 | 3 | no | — |
| 824 | C2×D4 | — | 6 | 3 | no | — |
| 825 | C2×D4 | — | 6 | 24 | no | — |
| 826 | C2×D4 | — | 6 | 24 | no | — |
| 827 | C2×D4 | — | 6 | 12 | no | — |
| 828 | C2×D4 | — | 6 | 12 | no | — |
| 829 | C2×D4 | — | 6 | 24 | no | — |
| 830 | C2×D4 | — | 6 | 12 | no | — |
| 831 | C2×D4 | — | 6 | 12 | no | — |
| 832 | C2×D4 | — | 6 | 2 | no | — |
| 833 | C2×D4 | — | 6 | 2 | no | — |
| 834 | C2×D4 | — | 6 | 6 | no | — |
| 835 | C2×D4 | — | 6 | 4 | no | — |
| 836 | C2×D4 | — | 6 | 4 | no | — |
| 837 | C2×D4 | — | 6 | 2 | no | — |
| 838 | C2×D4 | — | 6 | 2 | no | — |
| 839 | C2×D4 | — | 6 | 1 | no | — |
| 840 | C2×D4 | — | 12 | 3 | no | — |
| 841 | C2×D4 | — | 12 | 3 | no | — |
| 842 | C2×D4 | — | 12 | 3 | no | — |
| 843 | C2×D4 | — | 12 | 6 | no | — |
| 844 | C2×D4 | — | 12 | 3 | no | — |
| 845 | C2×D4 | — | 12 | 3 | no | — |
| 846 | C2×D4 | — | 12 | 6 | no | — |
| 847 | C2×D4 | — | 12 | 6 | no | — |
| 848 | C2×D4 | — | 12 | 6 | no | — |
| 849 | C2×D4 | — | 12 | 6 | no | — |
| 850 | C2×D4 | — | 12 | 1 | no | — |
| 851 | C2×D4 | — | 48 | 6 | no | — |
| 852 | C2×D4 | — | 48 | 6 | no | — |
| 853 | C22×C4 | — | 2 | 6 | no | — |
| 854 | C22×C4 | — | 3 | 3 | no | — |
| 855 | C22×C4 | — | 3 | 1 | no | — |
| 856 | C22×C4 | — | 3 | 1 | no | — |
| 857 | C22×C4 | — | 3 | 3 | no | — |
| 858 | C22×C4 | — | 3 | 3 | no | — |
| 859 | C22×C4 | — | 3 | 3 | no | — |
| 860 | C22×C4 | — | 3 | 3 | no | — |
| 861 | C22×C4 | — | 3 | 3 | no | — |
| 862 | C22×C4 | — | 3 | 3 | no | — |
| 863 | C22×C4 | — | 3 | 3 | no | — |
| 864 | C22×C4 | — | 3 | 3 | no | — |
| 865 | C22×C4 | — | 3 | 3 | no | — |
| 866 | C22×C4 | — | 3 | 3 | no | — |
| 867 | C22×C4 | — | 3 | 3 | no | — |
| 868 | C22×C4 | — | 6 | 3 | no | — |
| 869 | C22×C4 | — | 6 | 2 | no | — |
| 870 | C22×C4 | — | 6 | 3 | no | — |
| 871 | C22×C4 | — | 6 | 3 | no | — |
| 872 | C22×C4 | — | 6 | 3 | no | — |
| 873 | C22×C4 | — | 6 | 12 | no | — |
| 874 | C22×C4 | — | 6 | 6 | no | — |
| 875 | C22×C4 | — | 6 | 6 | no | — |
| 876 | C22×C4 | — | 6 | 12 | no | — |
| 877 | C22×C4 | — | 6 | 6 | no | — |
| 878 | C22×C4 | — | 6 | 6 | no | — |
| 879 | C22×C4 | — | 6 | 6 | no | — |
| 880 | C22×C4 | — | 6 | 6 | no | — |
| 881 | C22×C4 | — | 6 | 3 | no | — |
| 882 | C22×C4 | — | 6 | 2 | no | — |
| 883 | C22×C4 | — | 6 | 6 | no | — |
| 884 | C22×C4 | — | 6 | 6 | no | — |
| 885 | C22×C4 | — | 6 | 6 | no | — |
| 886 | C22×C4 | — | 6 | 6 | no | — |
| 887 | C22×C4 | — | 6 | 6 | no | — |
| 888 | C22×C4 | — | 6 | 12 | no | — |
| 889 | C22×C4 | — | 6 | 12 | no | — |
| 890 | C22×C4 | — | 6 | 12 | no | — |
| 891 | C22×C4 | — | 6 | 12 | no | — |
| 892 | C22×C4 | — | 6 | 12 | no | — |
| 893 | C22×C4 | — | 6 | 12 | no | — |
| 894 | C22×C4 | — | 6 | 12 | no | — |
| 895 | C22×C4 | — | 6 | 1 | no | — |
| 896 | C22×C4 | — | 6 | 3 | no | — |
| 897 | C22×C4 | — | 6 | 6 | no | — |
| 898 | C22×C4 | — | 12 | 3 | no | — |
| 899 | C22×C4 | GL(2,ℤ/4) | 1 | 3 | yes | — |
| 900 | C22×C4 | C22×S4 | 1 | 3 | yes | — |
| 901 | SD16 | — | 12 | 12 | no | — |
| 902 | SD16 | — | 12 | 24 | no | — |
| 903 | SD16 | — | 12 | 4 | no | — |
| 904 | D8 | — | 12 | 24 | no | — |
| 905 | M16 | — | 6 | 12 | no | — |
| 906 | M16 | — | 12 | 6 | no | — |
| 907 | C2×C8 | — | 6 | 6 | no | — |
| 908 | C2×C8 | — | 6 | 6 | no | — |
| 909 | C2×C8 | — | 12 | 3 | no | — |
| 910 | C2×C8 | — | 12 | 3 | no | — |
| 911 | C2×C8 | — | 12 | 3 | no | — |
| 912 | C2×C8 | — | 12 | 1 | no | — |
| 913 | C4⋊C4 | — | 6 | 6 | no | — |
| 914 | C4⋊C4 | — | 12 | 3 | no | — |
| 915 | C22⋊C4 | — | 6 | 6 | no | — |
| 916 | C22⋊C4 | — | 12 | 6 | no | — |
| 917 | C22⋊C4 | — | 12 | 6 | no | — |
| 918 | C22⋊C4 | — | 12 | 6 | no | — |
| 919 | C22⋊C4 | — | 12 | 6 | no | — |
| 920 | C22⋊C4 | — | 12 | 3 | no | — |
| 921 | C42 | — | 6 | 6 | no | — |
| 922 | C42 | — | 12 | 3 | no | — |
| 923 | C22×C3 | — | 16 | 1 | no | — |
| 924 | C2×D3 | — | 32 | 2 | no | — |
| 925 | C2×D3 | — | 64 | 2 | no | — |
| 926 | A4 | — | 4 | 3 | no | — |
| 927 | C3×C4 | — | 16 | 1 | no | — |
| 928 | C3×C4 | — | 16 | 1 | no | — |
| 929 | C3×C4 | — | 32 | 2 | no | — |
| 930 | C23 | — | 3 | 1 | no | — |
| 931 | C23 | — | 3 | 3 | no | — |
| 932 | C23 | — | 3 | 3 | no | — |
| 933 | C23 | — | 3 | 3 | no | — |
| 934 | C23 | — | 3 | 3 | no | — |
| 935 | C23 | — | 3 | 3 | no | — |
| 936 | C23 | — | 4 | 6 | no | — |
| 937 | C23 | — | 6 | 6 | no | — |
| 938 | C23 | — | 6 | 6 | no | — |
| 939 | C23 | — | 6 | 3 | no | — |
| 940 | C23 | — | 6 | 4 | no | — |
| 941 | C23 | — | 6 | 4 | no | — |
| 942 | C23 | — | 6 | 2 | no | — |
| 943 | C23 | — | 6 | 1 | no | — |
| 944 | C23 | — | 12 | 6 | no | — |
| 945 | C23 | — | 12 | 2 | no | — |
| 946 | C23 | — | 12 | 6 | no | — |
| 947 | C23 | — | 24 | 3 | no | — |
| 948 | C23 | — | 24 | 6 | no | — |
| 949 | C23 | — | 24 | 6 | no | — |
| 950 | C23 | — | 24 | 6 | no | — |
| 951 | C23 | — | 24 | 4 | no | — |
| 952 | C23 | — | 24 | 1 | no | — |
| 953 | C23 | — | 48 | 2 | no | — |
| 954 | C23 | — | 48 | 6 | no | — |
| 955 | C23 | C2×GL(2,ℤ/4) | 1 | 3 | yes | — |
| 956 | Q8 | — | 2 | 1 | no | — |
| 957 | Q8 | — | 2 | 1 | no | — |
| 958 | Q8 | — | 3 | 12 | no | — |
| 959 | Q8 | — | 3 | 6 | no | — |
| 960 | Q8 | — | 6 | 6 | no | — |
| 961 | Q8 | — | 6 | 6 | no | — |
| 962 | Q8 | — | 6 | 3 | no | — |
| 963 | Q8 | — | 6 | 6 | no | — |
| 964 | Q8 | — | 6 | 3 | no | — |
| 965 | Q8 | — | 6 | 6 | no | — |
| 966 | Q8 | — | 6 | 6 | no | — |
| 967 | Q8 | — | 6 | 6 | no | — |
| 968 | Q8 | — | 6 | 1 | no | — |
| 969 | Q8 | — | 6 | 12 | no | — |
| 970 | Q8 | — | 6 | 12 | no | — |
| 971 | Q8 | — | 6 | 3 | no | — |
| 972 | Q8 | C2×#1020 | 1 | 2 | yes | — |
| 973 | D4 | — | 3 | 12 | no | — |
| 974 | D4 | — | 6 | 4 | no | — |
| 975 | D4 | — | 6 | 4 | no | — |
| 976 | D4 | — | 6 | 6 | no | — |
| 977 | D4 | — | 6 | 6 | no | — |
| 978 | D4 | — | 6 | 6 | no | — |
| 979 | D4 | — | 6 | 6 | no | — |
| 980 | D4 | — | 6 | 6 | no | — |
| 981 | D4 | — | 6 | 3 | no | — |
| 982 | D4 | — | 6 | 3 | no | — |
| 983 | D4 | — | 6 | 6 | no | — |
| 984 | D4 | — | 6 | 24 | no | — |
| 985 | D4 | — | 6 | 24 | no | — |
| 986 | D4 | — | 6 | 4 | no | — |
| 987 | D4 | — | 6 | 1 | no | — |
| 988 | D4 | — | 6 | 1 | no | — |
| 989 | D4 | — | 6 | 4 | no | — |
| 990 | D4 | — | 6 | 2 | no | — |
| 991 | D4 | — | 6 | 12 | no | — |
| 992 | D4 | — | 6 | 12 | no | — |
| 993 | D4 | — | 6 | 2 | no | — |
| 994 | D4 | — | 6 | 2 | no | — |
| 995 | D4 | — | 12 | 6 | no | — |
| 996 | D4 | — | 12 | 2 | no | — |
| 997 | D4 | — | 24 | 3 | no | — |
| 998 | D4 | — | 24 | 1 | no | — |
| 999 | D4 | — | 48 | 6 | no | — |
| 1000 | D4 | — | 48 | 6 | no | — |
| 1001 | D4 | — | 48 | 6 | no | — |
| 1002 | D4 | — | 48 | 6 | no | — |
| 1003 | C2×C4 | — | 2 | 1 | no | — |
| 1004 | C2×C4 | — | 3 | 3 | no | — |
| 1005 | C2×C4 | — | 3 | 3 | no | — |
| 1006 | C2×C4 | — | 3 | 6 | no | — |
| 1007 | C2×C4 | — | 3 | 3 | no | — |
| 1008 | C2×C4 | — | 3 | 3 | no | — |
| 1009 | C2×C4 | — | 3 | 3 | no | — |
| 1010 | C2×C4 | — | 3 | 3 | no | — |
| 1011 | C2×C4 | — | 3 | 3 | no | — |
| 1012 | C2×C4 | — | 3 | 3 | no | — |
| 1013 | C2×C4 | — | 3 | 3 | no | — |
| 1014 | C2×C4 | — | 3 | 3 | no | — |
| 1015 | C2×C4 | — | 3 | 3 | no | — |
| 1016 | C2×C4 | — | 6 | 6 | no | — |
| 1017 | C2×C4 | — | 6 | 6 | no | — |
| 1018 | C2×C4 | — | 6 | 4 | no | — |
| 1019 | C2×C4 | — | 6 | 4 | no | — |
| 1020 | C2×C4 | — | 6 | 3 | no | — |
| 1021 | C2×C4 | — | 6 | 3 | no | — |
| 1022 | C2×C4 | — | 6 | 3 | no | — |
| 1023 | C2×C4 | — | 6 | 3 | no | — |
| 1024 | C2×C4 | — | 6 | 3 | no | — |
| 1025 | C2×C4 | — | 6 | 24 | no | — |
| 1026 | C2×C4 | — | 6 | 24 | no | — |
| 1027 | C2×C4 | — | 6 | 3 | no | — |
| 1028 | C2×C4 | — | 6 | 6 | no | — |
| 1029 | C2×C4 | — | 6 | 6 | no | — |
| 1030 | C2×C4 | — | 6 | 6 | no | — |
| 1031 | C2×C4 | — | 6 | 12 | no | — |
| 1032 | C2×C4 | — | 6 | 12 | no | — |
| 1033 | C2×C4 | — | 6 | 12 | no | — |
| 1034 | C2×C4 | — | 6 | 12 | no | — |
| 1035 | C2×C4 | — | 6 | 1 | no | — |
| 1036 | C2×C4 | — | 6 | 3 | no | — |
| 1037 | C2×C4 | — | 6 | 1 | no | — |
| 1038 | C2×C4 | — | 6 | 1 | no | — |
| 1039 | C2×C4 | — | 6 | 1 | no | — |
| 1040 | C2×C4 | — | 6 | 1 | no | — |
| 1041 | C2×C4 | — | 6 | 6 | no | — |
| 1042 | C2×C4 | — | 12 | 6 | no | — |
| 1043 | C2×C4 | — | 24 | 6 | no | — |
| 1044 | C2×C4 | C2×#1020 | 1 | 1 | yes | characteristic |
| 1045 | C8 | — | 12 | 6 | no | — |
| 1046 | C8 | — | 12 | 2 | no | — |
| 1047 | C2×C3 | — | 16 | 2 | no | — |
| 1048 | C2×C3 | — | 16 | 1 | no | — |
| 1049 | D3 | — | 64 | 2 | no | — |
| 1050 | C22 | — | 3 | 3 | no | — |
| 1051 | C22 | — | 3 | 3 | no | — |
| 1052 | C22 | — | 4 | 3 | no | — |
| 1053 | C22 | — | 6 | 6 | no | — |
| 1054 | C22 | — | 6 | 4 | no | — |
| 1055 | C22 | — | 6 | 1 | no | — |
| 1056 | C22 | — | 6 | 1 | no | — |
| 1057 | C22 | — | 12 | 3 | no | — |
| 1058 | C22 | — | 12 | 1 | no | — |
| 1059 | C22 | — | 12 | 3 | no | — |
| 1060 | C22 | — | 12 | 3 | no | — |
| 1061 | C22 | — | 12 | 3 | no | — |
| 1062 | C22 | — | 12 | 2 | no | — |
| 1063 | C22 | — | 12 | 4 | no | — |
| 1064 | C22 | — | 24 | 3 | no | — |
| 1065 | C22 | — | 24 | 6 | no | — |
| 1066 | C22 | — | 24 | 6 | no | — |
| 1067 | C22 | — | 24 | 6 | no | — |
| 1068 | C22 | — | 24 | 6 | no | — |
| 1069 | C22 | — | 24 | 4 | no | — |
| 1070 | C22 | — | 24 | 4 | no | — |
| 1071 | C22 | — | 24 | 2 | no | — |
| 1072 | C22 | — | 48 | 6 | no | — |
| 1073 | C22 | — | 48 | 2 | no | — |
| 1074 | C22 | #87524 | 1 | 1 | yes | characteristic |
| 1075 | C4 | — | 2 | 2 | no | — |
| 1076 | C4 | — | 3 | 3 | no | — |
| 1077 | C4 | — | 3 | 3 | no | — |
| 1078 | C4 | — | 6 | 1 | no | — |
| 1079 | C4 | — | 6 | 1 | no | — |
| 1080 | C4 | — | 6 | 6 | no | — |
| 1081 | C4 | — | 24 | 6 | no | — |
| 1082 | C4 | #87524 | 1 | 1 | yes | characteristic |
| 1083 | C4 | C22×#1020 | 1 | 1 | yes | characteristic |
| 1084 | C3 | — | 16 | 1 | no | Sylow |
| 1085 | C2 | — | 6 | 3 | no | — |
| 1086 | C2 | — | 6 | 3 | no | — |
| 1087 | C2 | — | 12 | 1 | no | — |
| 1088 | C2 | — | 12 | 1 | no | — |
| 1089 | C2 | — | 12 | 4 | no | — |
| 1090 | C2 | — | 48 | 2 | no | — |
| 1091 | C2 | #11715711 | 1 | 2 | yes | direct product factor |
| 1092 | C2 | C2×#87524 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #87524 |
| commutator, cosocle | #5950 | C23 |
| Frattini | C4 | C22×#1020 |
| Fitting | C2×2−1+6 | D3 |
| hypercenter | C2×Q8 | #1020 |
| hypocenter | #997 | C2×D4 |
| LCS | G ▷ #5950 ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87521 | C2 | semidirect |
| 2. #11715711 | C2 | direct (N × H) |
| 3. C2×#85566 | C2 | semidirect |
| 4. C2×#87548 | C2 | semidirect |
| 7. #87548 | C22 | semidirect |
| 11. #87521 | C22 | semidirect |
| 13. #85566 | C22 | semidirect |
| 15. C2×2−1+6 | D3 | semidirect |
| 39. 2−1+6 | C2×D3 | semidirect |
| 189. C23×Q8 | S4 | semidirect |
| 510. C22×Q8 | C2×S4 | semidirect |
| 1091. C2 | #11715711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87521 | 2 |
| #11715711 | 2 |
| C2×#85566 | 2 |
| C2×#87548 | 2 |
| C2×#32895 | 3 |
| C2×#5417 | 4 |