Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1409 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1409 conjugacy classes of subgroups — too many to draw. Only its 119 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×#5926 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3489⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85536 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85399 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85398 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #85383 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #85380 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85370 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #85366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61073 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×2−1+4⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×#41⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #5926 | — | 2 | 4 | no | — |
| 16 | #5923 | — | 2 | 4 | no | — |
| 17 | C2×#986 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#985 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#985 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 22 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 23 | C22×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 24 | #5612 | — | 4 | 1 | no | maximal |
| 25 | D4×SL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 26 | #548⋊C3 | C22 | 1 | 2 | yes | complemented |
| 27 | #520⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #5425 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #5424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #5419 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5419 | C22 | 1 | 2 | yes | complemented |
| 34 | #5419 | C22 | 1 | 2 | yes | complemented |
| 35 | #5395 | C22 | 1 | 2 | yes | complemented |
| 36 | #5394 | C22 | 1 | 2 | yes | complemented |
| 37 | C4×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 38 | C4⋊#226 | C22 | 1 | 2 | yes | complemented |
| 39 | C2×#577 | — | 3 | 1 | no | — |
| 40 | C2×#575 | — | 3 | 1 | no | — |
| 41 | #3489 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #3485 | — | 3 | 1 | no | — |
| 43 | #3283 | — | 3 | 2 | no | — |
| 44 | #3282 | — | 3 | 2 | no | — |
| 45 | #3276 | — | 3 | 2 | no | — |
| 46 | #3273 | — | 3 | 2 | no | — |
| 47 | #3269 | — | 3 | 2 | no | — |
| 48 | #3267 | — | 3 | 2 | no | — |
| 49 | #3267 | — | 3 | 2 | no | — |
| 50 | #3266 | — | 3 | 2 | no | — |
| 51 | #3156 | — | 3 | 1 | no | — |
| 52 | #3063 | — | 3 | 1 | no | — |
| 53 | #3056 | — | 3 | 1 | no | — |
| 54 | #3046 | — | 3 | 1 | no | — |
| 55 | #3042 | — | 3 | 1 | no | — |
| 56 | #3012 | — | 3 | 1 | no | — |
| 57 | #3011 | — | 3 | 1 | no | — |
| 58 | #3002 | — | 3 | 1 | no | — |
| 59 | C2×#452 | — | 3 | 1 | no | — |
| 60 | #2946 | — | 3 | 1 | no | — |
| 61 | #2933 | — | 3 | 1 | no | — |
| 62 | C2×D3×D4 | — | 4 | 1 | no | — |
| 63 | C2×#235 | — | 4 | 1 | no | — |
| 64 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 65 | C2×#41⋊C3 | — | 2 | 2 | no | — |
| 66 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 69 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 70 | #986 | D4 | 1 | 4 | yes | complemented |
| 71 | #985 | — | 2 | 2 | no | — |
| 72 | #985 | — | 2 | 4 | no | — |
| 73 | #984 | — | 2 | 2 | no | — |
| 74 | #983 | — | 2 | 4 | no | — |
| 75 | #983 | — | 2 | 4 | no | — |
| 76 | C2×GL(2,𝔽3) | — | 2 | 4 | no | — |
| 77 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 79 | C2×#226 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#226 | C23 | 1 | 2 | yes | — |
| 81 | C3×#121 | — | 4 | 1 | no | — |
| 82 | #938 | — | 4 | 2 | no | — |
| 83 | #937 | — | 4 | 2 | no | — |
| 84 | #936 | — | 4 | 1 | no | — |
| 85 | C4×#67 | — | 4 | 1 | no | — |
| 86 | #897 | — | 4 | 1 | no | — |
| 87 | #893 | — | 4 | 1 | no | — |
| 88 | #883 | — | 4 | 2 | no | — |
| 89 | D3×C22⋊C4 | — | 4 | 2 | no | — |
| 90 | C4×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 91 | #859 | C23 | 1 | 1 | yes | characteristic |
| 92 | #859 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 94 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 95 | C22×#41 | — | 3 | 1 | no | — |
| 96 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 97 | #577 | — | 6 | 4 | no | — |
| 98 | #577 | — | 6 | 4 | no | — |
| 99 | #575 | — | 6 | 4 | no | — |
| 100 | #575 | — | 6 | 4 | no | — |
| 101 | C2×#137 | — | 3 | 1 | no | — |
| 102 | C2×#137 | — | 3 | 1 | no | — |
| 103 | C2×#137 | — | 3 | 1 | no | — |
| 104 | C2×#137 | — | 3 | 2 | no | — |
| 105 | C2×#137 | — | 3 | 2 | no | — |
| 106 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 107 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 108 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 109 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 110 | C2×#135 | — | 3 | 2 | no | — |
| 111 | C2×#135 | — | 3 | 2 | no | — |
| 112 | C2×#135 | — | 3 | 1 | no | — |
| 113 | C2×#135 | — | 3 | 2 | no | — |
| 114 | C2×#135 | — | 3 | 1 | no | — |
| 115 | C22×Q16 | — | 3 | 1 | no | — |
| 116 | C22×SD16 | — | 3 | 1 | no | — |
| 117 | C22×SD16 | — | 3 | 2 | no | — |
| 118 | C2×#131 | — | 3 | 1 | no | — |
| 119 | C22×M16 | — | 3 | 1 | no | — |
| 120 | D4×Q8 | C2×D3 | 1 | 2 | yes | complemented |
| 121 | #548 | C2×D3 | 1 | 2 | yes | complemented |
| 122 | #547 | — | 3 | 2 | no | — |
| 123 | #547 | — | 3 | 2 | no | — |
| 124 | #547 | — | 3 | 2 | no | — |
| 125 | #547 | — | 6 | 1 | no | — |
| 126 | #547 | — | 6 | 1 | no | — |
| 127 | #546 | — | 3 | 2 | no | — |
| 128 | #546 | — | 3 | 2 | no | — |
| 129 | #546 | — | 3 | 2 | no | — |
| 130 | #546 | — | 6 | 1 | no | — |
| 131 | #546 | — | 6 | 1 | no | — |
| 132 | #537 | — | 3 | 1 | no | — |
| 133 | #536 | — | 3 | 1 | no | — |
| 134 | #536 | — | 3 | 1 | no | — |
| 135 | #536 | — | 3 | 1 | no | — |
| 136 | #534 | — | 6 | 2 | no | — |
| 137 | #525 | — | 3 | 1 | no | — |
| 138 | #525 | — | 3 | 1 | no | — |
| 139 | C2×#123 | — | 6 | 2 | no | — |
| 140 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 141 | #520 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 142 | #518 | — | 3 | 1 | no | — |
| 143 | #497 | — | 3 | 2 | no | — |
| 144 | #497 | — | 3 | 2 | no | — |
| 145 | #495 | — | 3 | 2 | no | — |
| 146 | #494 | — | 3 | 2 | no | — |
| 147 | #470 | — | 3 | 2 | no | — |
| 148 | #470 | — | 3 | 2 | no | — |
| 149 | #468 | — | 3 | 2 | no | — |
| 150 | #468 | — | 3 | 2 | no | — |
| 151 | #467 | — | 3 | 2 | no | — |
| 152 | #467 | — | 3 | 2 | no | — |
| 153 | #465 | — | 3 | 2 | no | — |
| 154 | #465 | — | 3 | 2 | no | — |
| 155 | #464 | — | 3 | 2 | no | — |
| 156 | #463 | — | 3 | 2 | no | — |
| 157 | #463 | — | 3 | 2 | no | — |
| 158 | #463 | — | 3 | 2 | no | — |
| 159 | #462 | — | 3 | 2 | no | — |
| 160 | #461 | — | 3 | 2 | no | — |
| 161 | #461 | — | 3 | 2 | no | — |
| 162 | #461 | — | 3 | 2 | no | — |
| 163 | #452 | — | 3 | 2 | no | — |
| 164 | #452 | — | 3 | 2 | no | — |
| 165 | #452 | — | 3 | 2 | no | — |
| 166 | #452 | — | 3 | 2 | no | — |
| 167 | #452 | — | 3 | 1 | no | — |
| 168 | #452 | — | 3 | 2 | no | — |
| 169 | #452 | — | 3 | 2 | no | — |
| 170 | #452 | — | 3 | 2 | no | — |
| 171 | #452 | — | 3 | 1 | no | — |
| 172 | #451 | — | 3 | 1 | no | — |
| 173 | #451 | — | 3 | 2 | no | — |
| 174 | #451 | — | 3 | 2 | no | — |
| 175 | #450 | — | 3 | 1 | no | — |
| 176 | #450 | — | 3 | 2 | no | — |
| 177 | #449 | — | 3 | 1 | no | — |
| 178 | #449 | — | 3 | 2 | no | — |
| 179 | #449 | — | 3 | 1 | no | — |
| 180 | #448 | — | 3 | 1 | no | — |
| 181 | #447 | — | 3 | 1 | no | — |
| 182 | #447 | — | 3 | 2 | no | — |
| 183 | #442 | — | 3 | 2 | no | — |
| 184 | #440 | — | 3 | 2 | no | — |
| 185 | C4×SD16 | — | 3 | 2 | no | — |
| 186 | C4×D8 | — | 3 | 2 | no | — |
| 187 | #436 | — | 3 | 2 | no | — |
| 188 | #435 | — | 3 | 2 | no | — |
| 189 | #435 | — | 3 | 2 | no | — |
| 190 | C8×D4 | — | 3 | 2 | no | — |
| 191 | #428 | — | 3 | 1 | no | — |
| 192 | #424 | — | 3 | 1 | no | — |
| 193 | #419 | — | 3 | 1 | no | — |
| 194 | #417 | — | 3 | 1 | no | — |
| 195 | #416 | — | 3 | 1 | no | — |
| 196 | #416 | — | 3 | 1 | no | — |
| 197 | C2×#103 | — | 3 | 1 | no | — |
| 198 | C2×#102 | — | 3 | 1 | no | — |
| 199 | #408 | — | 3 | 1 | no | — |
| 200 | C2×C22⋊C8 | — | 3 | 1 | no | — |
| 201 | #405 | — | 3 | 1 | no | — |
| 202 | C23×D3 | — | 4 | 2 | no | — |
| 203 | C2×C3×D4 | — | 4 | 1 | no | — |
| 204 | C2×C3×D4 | — | 4 | 2 | no | — |
| 205 | C22×C3×C4 | — | 4 | 1 | no | — |
| 206 | C2×#67 | — | 4 | 2 | no | — |
| 207 | C2×#67 | — | 4 | 2 | no | — |
| 208 | C2×#67 | — | 4 | 1 | no | — |
| 209 | D3×D4 | — | 8 | 4 | no | — |
| 210 | #235 | — | 8 | 4 | no | — |
| 211 | C2×D12 | — | 4 | 1 | no | — |
| 212 | C2×C4×D3 | — | 4 | 1 | no | — |
| 213 | C2×C4×D3 | — | 4 | 2 | no | — |
| 214 | C2×C4×D3 | — | 4 | 2 | no | — |
| 215 | C2×Dic6 | — | 4 | 1 | no | — |
| 216 | #41⋊C3 | — | 2 | 1 | no | — |
| 217 | #41⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 218 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 219 | C2×SL(2,𝔽3) | — | 2 | 1 | no | — |
| 220 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 221 | GL(2,𝔽3) | — | 2 | 1 | no | — |
| 222 | GL(2,𝔽3) | C2×D4 | 1 | 4 | yes | — |
| 223 | #226 | — | 2 | 1 | no | — |
| 224 | #226 | — | 2 | 2 | no | — |
| 225 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 226 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 227 | #217 | — | 4 | 2 | no | — |
| 228 | #217 | — | 4 | 2 | no | — |
| 229 | #217 | — | 4 | 1 | no | — |
| 230 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 231 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 232 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 233 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 234 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 235 | C4×Dic3 | — | 4 | 1 | no | — |
| 236 | 2−1+4 | — | 2 | 2 | no | — |
| 237 | 2−1+4 | — | 6 | 2 | no | — |
| 238 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 239 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 240 | C2×#41 | — | 2 | 2 | no | — |
| 241 | C2×#41 | — | 3 | 1 | no | — |
| 242 | C2×#41 | — | 3 | 1 | no | — |
| 243 | C2×#41 | — | 3 | 1 | no | — |
| 244 | C2×#41 | — | 3 | 2 | no | — |
| 245 | C2×#41 | — | 3 | 1 | no | — |
| 246 | C2×#41 | — | 3 | 2 | no | — |
| 247 | C2×#41 | — | 3 | 2 | no | — |
| 248 | C2×#41 | — | 3 | 2 | no | — |
| 249 | C2×#41 | — | 6 | 1 | no | — |
| 250 | C2×#41 | — | 6 | 1 | no | — |
| 251 | C2×#41 | — | 6 | 1 | no | — |
| 252 | C2×#41 | — | 6 | 2 | no | — |
| 253 | C2×#41 | — | 6 | 4 | no | — |
| 254 | C2×#41 | — | 12 | 2 | no | — |
| 255 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 256 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 257 | C22×Q8 | — | 3 | 1 | no | — |
| 258 | C22×Q8 | — | 3 | 1 | no | — |
| 259 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 260 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 261 | C22×D4 | — | 3 | 1 | no | — |
| 262 | C22×D4 | — | 3 | 1 | no | — |
| 263 | C22×D4 | — | 3 | 2 | no | — |
| 264 | C22×D4 | — | 6 | 2 | no | — |
| 265 | C22×D4 | — | 6 | 1 | no | — |
| 266 | C22×D4 | — | 6 | 1 | no | — |
| 267 | C23×C4 | — | 3 | 1 | no | — |
| 268 | C23×C4 | — | 6 | 1 | no | — |
| 269 | #137 | — | 6 | 4 | no | — |
| 270 | #137 | — | 6 | 4 | no | — |
| 271 | #137 | — | 6 | 4 | no | — |
| 272 | #137 | — | 6 | 4 | no | — |
| 273 | #137 | — | 6 | 4 | no | — |
| 274 | #137 | — | 6 | 4 | no | — |
| 275 | #137 | — | 6 | 2 | no | — |
| 276 | #137 | — | 6 | 2 | no | — |
| 277 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 278 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 279 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 280 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 281 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 282 | #135 | — | 6 | 8 | no | — |
| 283 | #135 | — | 6 | 8 | no | — |
| 284 | #135 | — | 6 | 4 | no | — |
| 285 | #135 | — | 6 | 4 | no | — |
| 286 | #135 | — | 6 | 2 | no | — |
| 287 | #135 | — | 6 | 2 | no | — |
| 288 | #135 | — | 12 | 2 | no | — |
| 289 | C2×Q16 | — | 3 | 2 | no | — |
| 290 | C2×Q16 | — | 3 | 2 | no | — |
| 291 | C2×Q16 | — | 3 | 2 | no | — |
| 292 | C2×Q16 | — | 3 | 1 | no | — |
| 293 | C2×Q16 | — | 3 | 2 | no | — |
| 294 | C2×Q16 | — | 3 | 2 | no | — |
| 295 | C2×Q16 | — | 3 | 1 | no | — |
| 296 | C2×Q16 | — | 12 | 2 | no | — |
| 297 | C2×SD16 | — | 3 | 2 | no | — |
| 298 | C2×SD16 | — | 3 | 2 | no | — |
| 299 | C2×SD16 | — | 3 | 2 | no | — |
| 300 | C2×SD16 | — | 3 | 2 | no | — |
| 301 | C2×SD16 | — | 3 | 1 | no | — |
| 302 | C2×SD16 | — | 3 | 2 | no | — |
| 303 | C2×SD16 | — | 3 | 2 | no | — |
| 304 | C2×SD16 | — | 3 | 2 | no | — |
| 305 | C2×SD16 | — | 3 | 1 | no | — |
| 306 | C2×SD16 | — | 3 | 1 | no | — |
| 307 | C2×SD16 | — | 3 | 1 | no | — |
| 308 | C2×SD16 | — | 6 | 4 | no | — |
| 309 | C2×SD16 | — | 6 | 4 | no | — |
| 310 | C2×SD16 | — | 6 | 4 | no | — |
| 311 | C2×D8 | — | 3 | 2 | no | — |
| 312 | C2×D8 | — | 3 | 1 | no | — |
| 313 | C2×D8 | — | 3 | 2 | no | — |
| 314 | C2×D8 | — | 3 | 1 | no | — |
| 315 | #131 | — | 6 | 4 | no | — |
| 316 | C2×M16 | — | 3 | 1 | no | — |
| 317 | C2×M16 | — | 3 | 1 | no | — |
| 318 | C2×M16 | — | 3 | 2 | no | — |
| 319 | C2×M16 | — | 3 | 2 | no | — |
| 320 | C2×M16 | — | 6 | 4 | no | — |
| 321 | C22×C8 | — | 3 | 2 | no | — |
| 322 | C22×C8 | — | 3 | 1 | no | — |
| 323 | C22×C8 | — | 3 | 2 | no | — |
| 324 | C22×C8 | — | 3 | 1 | no | — |
| 325 | C4⋊Q8 | — | 3 | 2 | no | — |
| 326 | C4⋊Q8 | — | 3 | 2 | no | — |
| 327 | C4⋊Q8 | — | 6 | 1 | no | — |
| 328 | #124 | — | 3 | 2 | no | — |
| 329 | #124 | — | 3 | 2 | no | — |
| 330 | #124 | — | 6 | 1 | no | — |
| 331 | #123 | — | 3 | 2 | no | — |
| 332 | #123 | — | 6 | 2 | no | — |
| 333 | #123 | — | 6 | 2 | no | — |
| 334 | #123 | — | 6 | 2 | no | — |
| 335 | #123 | — | 6 | 2 | no | — |
| 336 | #123 | — | 6 | 2 | no | — |
| 337 | #123 | — | 6 | 2 | no | — |
| 338 | #123 | — | 6 | 2 | no | — |
| 339 | #123 | — | 6 | 1 | no | — |
| 340 | #123 | — | 6 | 2 | no | — |
| 341 | #123 | — | 6 | 2 | no | — |
| 342 | C22⋊Q8 | — | 3 | 1 | no | — |
| 343 | C22⋊Q8 | — | 3 | 1 | no | — |
| 344 | C22⋊Q8 | — | 3 | 2 | no | — |
| 345 | C22⋊Q8 | — | 3 | 2 | no | — |
| 346 | C22⋊Q8 | — | 3 | 2 | no | — |
| 347 | C22⋊Q8 | — | 3 | 1 | no | — |
| 348 | C22⋊Q8 | — | 3 | 1 | no | — |
| 349 | C22⋊Q8 | — | 3 | 2 | no | — |
| 350 | C22⋊Q8 | — | 3 | 2 | no | — |
| 351 | C22⋊Q8 | — | 6 | 1 | no | — |
| 352 | C22⋊Q8 | — | 6 | 1 | no | — |
| 353 | C22⋊Q8 | — | 6 | 1 | no | — |
| 354 | #121 | — | 3 | 1 | no | — |
| 355 | #121 | — | 3 | 2 | no | — |
| 356 | #121 | — | 3 | 1 | no | — |
| 357 | #121 | — | 3 | 1 | no | — |
| 358 | #121 | — | 6 | 2 | no | — |
| 359 | #121 | — | 6 | 2 | no | — |
| 360 | #121 | — | 6 | 2 | no | — |
| 361 | #121 | — | 6 | 2 | no | — |
| 362 | #121 | — | 6 | 2 | no | — |
| 363 | #121 | S4 | 1 | 1 | yes | characteristic |
| 364 | #120 | — | 3 | 2 | no | — |
| 365 | #120 | — | 6 | 2 | no | — |
| 366 | #120 | — | 6 | 1 | no | — |
| 367 | #120 | — | 6 | 2 | no | — |
| 368 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 369 | C4×D4 | — | 3 | 2 | no | — |
| 370 | C4×D4 | — | 3 | 2 | no | — |
| 371 | C4×D4 | — | 3 | 2 | no | — |
| 372 | C4×D4 | — | 3 | 2 | no | — |
| 373 | C4×D4 | — | 3 | 2 | no | — |
| 374 | C4×D4 | — | 6 | 1 | no | — |
| 375 | C4×D4 | — | 6 | 1 | no | — |
| 376 | C4×D4 | — | 6 | 1 | no | — |
| 377 | C4×D4 | — | 6 | 1 | no | — |
| 378 | #117 | — | 3 | 1 | no | — |
| 379 | #117 | — | 3 | 1 | no | — |
| 380 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 381 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 382 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 383 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 384 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 385 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 386 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 387 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 388 | #107 | — | 3 | 2 | no | — |
| 389 | #106 | — | 3 | 2 | no | — |
| 390 | C4⋊C8 | — | 3 | 2 | no | — |
| 391 | C4⋊C8 | — | 3 | 2 | no | — |
| 392 | #103 | — | 3 | 2 | no | — |
| 393 | #103 | — | 3 | 2 | no | — |
| 394 | #103 | — | 3 | 1 | no | — |
| 395 | #103 | — | 3 | 1 | no | — |
| 396 | #103 | — | 3 | 2 | no | — |
| 397 | #103 | — | 3 | 2 | no | — |
| 398 | #103 | — | 3 | 2 | no | — |
| 399 | #103 | — | 3 | 1 | no | — |
| 400 | #103 | — | 3 | 1 | no | — |
| 401 | #102 | — | 3 | 2 | no | — |
| 402 | #102 | — | 3 | 2 | no | — |
| 403 | #102 | — | 3 | 1 | no | — |
| 404 | #102 | — | 3 | 1 | no | — |
| 405 | #102 | — | 3 | 1 | no | — |
| 406 | #102 | — | 3 | 1 | no | — |
| 407 | #102 | — | 3 | 2 | no | — |
| 408 | C22⋊C8 | — | 3 | 1 | no | — |
| 409 | C22⋊C8 | — | 3 | 1 | no | — |
| 410 | C22⋊C8 | — | 3 | 1 | no | — |
| 411 | C22⋊C8 | — | 3 | 1 | no | — |
| 412 | C22⋊C8 | — | 3 | 2 | no | — |
| 413 | C22⋊C8 | — | 3 | 2 | no | — |
| 414 | #97 | — | 3 | 2 | no | — |
| 415 | C4×C8 | — | 3 | 2 | no | — |
| 416 | C23×C3 | — | 4 | 2 | no | — |
| 417 | C23×C3 | — | 4 | 1 | no | — |
| 418 | C22×D3 | — | 4 | 1 | no | — |
| 419 | C22×D3 | — | 4 | 2 | no | — |
| 420 | C22×D3 | — | 8 | 4 | no | — |
| 421 | C22×D3 | — | 8 | 4 | no | — |
| 422 | C22×D3 | — | 16 | 2 | no | — |
| 423 | C3×D4 | — | 8 | 2 | no | — |
| 424 | C3×D4 | — | 16 | 2 | no | — |
| 425 | C2×C3×C4 | — | 4 | 1 | no | — |
| 426 | C2×C3×C4 | — | 4 | 2 | no | — |
| 427 | C2×C3×C4 | — | 4 | 1 | no | — |
| 428 | C2×C3×C4 | — | 8 | 2 | no | — |
| 429 | #67 | — | 8 | 4 | no | — |
| 430 | #67 | — | 8 | 4 | no | — |
| 431 | #67 | — | 8 | 2 | no | — |
| 432 | C2×Dic3 | — | 4 | 1 | no | — |
| 433 | C2×Dic3 | — | 4 | 1 | no | — |
| 434 | C2×Dic3 | — | 4 | 1 | no | — |
| 435 | C2×Dic3 | — | 4 | 2 | no | — |
| 436 | D12 | — | 4 | 4 | no | — |
| 437 | C4×D3 | — | 8 | 2 | no | — |
| 438 | C4×D3 | — | 8 | 4 | no | — |
| 439 | C4×D3 | — | 16 | 2 | no | — |
| 440 | Dic6 | — | 8 | 2 | no | — |
| 441 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 442 | C24 | — | 3 | 1 | no | — |
| 443 | C24 | — | 6 | 1 | no | — |
| 444 | C24 | — | 6 | 2 | no | — |
| 445 | #41 | — | 2 | 1 | no | — |
| 446 | #41 | — | 3 | 2 | no | — |
| 447 | #41 | — | 6 | 2 | no | — |
| 448 | #41 | — | 6 | 2 | no | — |
| 449 | #41 | — | 6 | 2 | no | — |
| 450 | #41 | — | 6 | 2 | no | — |
| 451 | #41 | — | 6 | 2 | no | — |
| 452 | #41 | — | 6 | 2 | no | — |
| 453 | #41 | — | 6 | 2 | no | — |
| 454 | #41 | — | 6 | 1 | no | — |
| 455 | #41 | — | 6 | 4 | no | — |
| 456 | #41 | — | 6 | 4 | no | — |
| 457 | #41 | — | 6 | 4 | no | — |
| 458 | #41 | — | 6 | 4 | no | — |
| 459 | #41 | — | 12 | 4 | no | — |
| 460 | #41 | — | 12 | 1 | no | — |
| 461 | #41 | — | 12 | 2 | no | — |
| 462 | #41 | — | 12 | 2 | no | — |
| 463 | #41 | — | 12 | 2 | no | — |
| 464 | #41 | — | 12 | 2 | no | — |
| 465 | #41 | — | 12 | 4 | no | — |
| 466 | #41 | — | 12 | 4 | no | — |
| 467 | #41 | D3×D4 | 1 | 2 | yes | — |
| 468 | C2×Q8 | — | 2 | 2 | no | — |
| 469 | C2×Q8 | — | 2 | 1 | no | — |
| 470 | C2×Q8 | — | 3 | 1 | no | — |
| 471 | C2×Q8 | — | 3 | 2 | no | — |
| 472 | C2×Q8 | — | 3 | 1 | no | — |
| 473 | C2×Q8 | — | 3 | 2 | no | — |
| 474 | C2×Q8 | — | 3 | 1 | no | — |
| 475 | C2×Q8 | — | 6 | 2 | no | — |
| 476 | C2×Q8 | — | 6 | 2 | no | — |
| 477 | C2×Q8 | — | 6 | 2 | no | — |
| 478 | C2×Q8 | — | 6 | 2 | no | — |
| 479 | C2×Q8 | — | 6 | 1 | no | — |
| 480 | C2×Q8 | — | 6 | 2 | no | — |
| 481 | C2×Q8 | — | 6 | 1 | no | — |
| 482 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 483 | C2×D4 | — | 3 | 1 | no | — |
| 484 | C2×D4 | — | 3 | 2 | no | — |
| 485 | C2×D4 | — | 3 | 4 | no | — |
| 486 | C2×D4 | — | 3 | 1 | no | — |
| 487 | C2×D4 | — | 3 | 2 | no | — |
| 488 | C2×D4 | — | 3 | 1 | no | — |
| 489 | C2×D4 | — | 3 | 2 | no | — |
| 490 | C2×D4 | — | 6 | 2 | no | — |
| 491 | C2×D4 | — | 6 | 1 | no | — |
| 492 | C2×D4 | — | 6 | 2 | no | — |
| 493 | C2×D4 | — | 6 | 2 | no | — |
| 494 | C2×D4 | — | 6 | 4 | no | — |
| 495 | C2×D4 | — | 6 | 2 | no | — |
| 496 | C2×D4 | — | 6 | 1 | no | — |
| 497 | C2×D4 | — | 6 | 2 | no | — |
| 498 | C2×D4 | — | 6 | 2 | no | — |
| 499 | C2×D4 | — | 6 | 1 | no | — |
| 500 | C2×D4 | — | 6 | 1 | no | — |
| 501 | C2×D4 | — | 6 | 1 | no | — |
| 502 | C2×D4 | — | 12 | 1 | no | — |
| 503 | C2×D4 | — | 12 | 2 | no | — |
| 504 | C2×D4 | — | 12 | 4 | no | — |
| 505 | C2×D4 | — | 12 | 8 | no | — |
| 506 | C2×D4 | — | 12 | 4 | no | — |
| 507 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 508 | C2×D4 | C2×S4 | 1 | 2 | yes | — |
| 509 | C22×C4 | — | 3 | 1 | no | — |
| 510 | C22×C4 | — | 3 | 2 | no | — |
| 511 | C22×C4 | — | 3 | 1 | no | — |
| 512 | C22×C4 | — | 3 | 1 | no | — |
| 513 | C22×C4 | — | 3 | 1 | no | — |
| 514 | C22×C4 | — | 3 | 1 | no | — |
| 515 | C22×C4 | — | 6 | 2 | no | — |
| 516 | C22×C4 | — | 6 | 2 | no | — |
| 517 | C22×C4 | — | 6 | 1 | no | — |
| 518 | C22×C4 | — | 6 | 1 | no | — |
| 519 | C22×C4 | — | 6 | 2 | no | — |
| 520 | C22×C4 | — | 6 | 2 | no | — |
| 521 | C22×C4 | — | 6 | 2 | no | — |
| 522 | C22×C4 | — | 6 | 1 | no | — |
| 523 | C22×C4 | — | 6 | 2 | no | — |
| 524 | C22×C4 | — | 6 | 1 | no | — |
| 525 | C22×C4 | — | 6 | 2 | no | — |
| 526 | C22×C4 | — | 12 | 4 | no | — |
| 527 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 528 | Q16 | — | 6 | 4 | no | — |
| 529 | Q16 | — | 6 | 4 | no | — |
| 530 | Q16 | — | 6 | 2 | no | — |
| 531 | Q16 | — | 6 | 1 | no | — |
| 532 | Q16 | — | 6 | 2 | no | — |
| 533 | Q16 | — | 6 | 1 | no | — |
| 534 | Q16 | — | 12 | 2 | no | — |
| 535 | Q16 | — | 12 | 2 | no | — |
| 536 | Q16 | — | 12 | 1 | no | — |
| 537 | SD16 | — | 3 | 4 | no | — |
| 538 | SD16 | — | 3 | 4 | no | — |
| 539 | SD16 | — | 6 | 4 | no | — |
| 540 | SD16 | — | 6 | 4 | no | — |
| 541 | SD16 | — | 6 | 4 | no | — |
| 542 | SD16 | — | 6 | 4 | no | — |
| 543 | SD16 | — | 6 | 2 | no | — |
| 544 | SD16 | — | 6 | 4 | no | — |
| 545 | SD16 | — | 6 | 4 | no | — |
| 546 | SD16 | — | 6 | 1 | no | — |
| 547 | SD16 | — | 6 | 1 | no | — |
| 548 | SD16 | — | 12 | 1 | no | — |
| 549 | SD16 | — | 12 | 1 | no | — |
| 550 | D8 | — | 3 | 8 | no | — |
| 551 | D8 | — | 6 | 2 | no | — |
| 552 | D8 | — | 6 | 4 | no | — |
| 553 | D8 | — | 12 | 1 | no | — |
| 554 | M16 | — | 3 | 4 | no | — |
| 555 | M16 | — | 6 | 4 | no | — |
| 556 | M16 | — | 6 | 4 | no | — |
| 557 | M16 | — | 6 | 2 | no | — |
| 558 | C2×C8 | — | 3 | 2 | no | — |
| 559 | C2×C8 | — | 3 | 1 | no | — |
| 560 | C2×C8 | — | 3 | 1 | no | — |
| 561 | C2×C8 | — | 3 | 1 | no | — |
| 562 | C2×C8 | — | 3 | 1 | no | — |
| 563 | C2×C8 | — | 3 | 2 | no | — |
| 564 | C2×C8 | — | 6 | 4 | no | — |
| 565 | C2×C8 | — | 6 | 4 | no | — |
| 566 | C2×C8 | — | 6 | 2 | no | — |
| 567 | C2×C8 | — | 6 | 2 | no | — |
| 568 | C4⋊C4 | — | 3 | 2 | no | — |
| 569 | C4⋊C4 | — | 3 | 1 | no | — |
| 570 | C4⋊C4 | — | 3 | 2 | no | — |
| 571 | C4⋊C4 | — | 3 | 2 | no | — |
| 572 | C4⋊C4 | — | 3 | 1 | no | — |
| 573 | C4⋊C4 | — | 3 | 1 | no | — |
| 574 | C4⋊C4 | — | 6 | 2 | no | — |
| 575 | C4⋊C4 | — | 6 | 1 | no | — |
| 576 | C4⋊C4 | — | 6 | 2 | no | — |
| 577 | C4⋊C4 | — | 6 | 2 | no | — |
| 578 | C4⋊C4 | — | 6 | 2 | no | — |
| 579 | C4⋊C4 | — | 6 | 1 | no | — |
| 580 | C4⋊C4 | — | 6 | 2 | no | — |
| 581 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 582 | C22⋊C4 | — | 3 | 2 | no | — |
| 583 | C22⋊C4 | — | 3 | 2 | no | — |
| 584 | C22⋊C4 | — | 3 | 2 | no | — |
| 585 | C22⋊C4 | — | 3 | 2 | no | — |
| 586 | C22⋊C4 | — | 6 | 2 | no | — |
| 587 | C22⋊C4 | — | 6 | 1 | no | — |
| 588 | C22⋊C4 | — | 6 | 2 | no | — |
| 589 | C22⋊C4 | — | 6 | 2 | no | — |
| 590 | C22⋊C4 | — | 6 | 1 | no | — |
| 591 | C22⋊C4 | — | 6 | 1 | no | — |
| 592 | C22⋊C4 | — | 6 | 2 | no | — |
| 593 | C22⋊C4 | — | 6 | 2 | no | — |
| 594 | C22⋊C4 | — | 6 | 1 | no | — |
| 595 | C22⋊C4 | — | 6 | 1 | no | — |
| 596 | C22⋊C4 | — | 6 | 2 | no | — |
| 597 | C22⋊C4 | — | 6 | 2 | no | — |
| 598 | C22⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 599 | C42 | — | 3 | 2 | no | — |
| 600 | C42 | — | 6 | 1 | no | — |
| 601 | C22×C3 | — | 4 | 1 | no | — |
| 602 | C22×C3 | — | 8 | 1 | no | — |
| 603 | C22×C3 | — | 8 | 2 | no | — |
| 604 | C22×C3 | — | 8 | 1 | no | — |
| 605 | C22×C3 | — | 8 | 1 | no | — |
| 606 | C22×C3 | — | 8 | 2 | no | — |
| 607 | C22×C3 | — | 8 | 2 | no | — |
| 608 | C2×D3 | — | 4 | 4 | no | — |
| 609 | C2×D3 | — | 4 | 2 | no | — |
| 610 | C2×D3 | — | 8 | 1 | no | — |
| 611 | C2×D3 | — | 8 | 2 | no | — |
| 612 | C2×D3 | — | 8 | 2 | no | — |
| 613 | C2×D3 | — | 8 | 1 | no | — |
| 614 | C2×D3 | — | 16 | 8 | no | — |
| 615 | C3×C4 | — | 4 | 2 | no | — |
| 616 | C3×C4 | — | 8 | 1 | no | — |
| 617 | C3×C4 | — | 8 | 2 | no | — |
| 618 | Dic3 | — | 8 | 2 | no | — |
| 619 | Dic3 | — | 8 | 1 | no | — |
| 620 | Dic3 | — | 8 | 1 | no | — |
| 621 | Dic3 | — | 8 | 1 | no | — |
| 622 | C23 | — | 3 | 1 | no | — |
| 623 | C23 | — | 3 | 1 | no | — |
| 624 | C23 | — | 6 | 2 | no | — |
| 625 | C23 | — | 6 | 4 | no | — |
| 626 | C23 | — | 6 | 2 | no | — |
| 627 | C23 | — | 6 | 1 | no | — |
| 628 | C23 | — | 12 | 1 | no | — |
| 629 | C23 | — | 12 | 1 | no | — |
| 630 | C23 | — | 12 | 4 | no | — |
| 631 | C23 | — | 24 | 2 | no | — |
| 632 | C23 | — | 24 | 2 | no | — |
| 633 | C23 | — | 24 | 1 | no | — |
| 634 | C23 | — | 24 | 1 | no | — |
| 635 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 636 | C23 | C22×S4 | 1 | 2 | yes | — |
| 637 | Q8 | — | 3 | 1 | no | — |
| 638 | Q8 | — | 6 | 2 | no | — |
| 639 | Q8 | — | 6 | 1 | no | — |
| 640 | Q8 | — | 6 | 1 | no | — |
| 641 | Q8 | — | 6 | 2 | no | — |
| 642 | Q8 | — | 6 | 2 | no | — |
| 643 | Q8 | — | 6 | 1 | no | — |
| 644 | Q8 | — | 6 | 1 | no | — |
| 645 | Q8 | — | 6 | 2 | no | — |
| 646 | Q8 | — | 6 | 2 | no | — |
| 647 | Q8 | — | 12 | 2 | no | — |
| 648 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 649 | D4 | — | 2 | 2 | no | — |
| 650 | D4 | — | 3 | 2 | no | — |
| 651 | D4 | — | 3 | 4 | no | — |
| 652 | D4 | — | 4 | 2 | no | — |
| 653 | D4 | — | 6 | 1 | no | — |
| 654 | D4 | — | 6 | 1 | no | — |
| 655 | D4 | — | 6 | 1 | no | — |
| 656 | D4 | — | 6 | 2 | no | — |
| 657 | D4 | — | 6 | 1 | no | — |
| 658 | D4 | — | 6 | 1 | no | — |
| 659 | D4 | — | 6 | 4 | no | — |
| 660 | D4 | — | 6 | 4 | no | — |
| 661 | D4 | — | 12 | 2 | no | — |
| 662 | D4 | — | 12 | 2 | no | — |
| 663 | D4 | — | 12 | 4 | no | — |
| 664 | D4 | — | 12 | 4 | no | — |
| 665 | D4 | — | 12 | 4 | no | — |
| 666 | D4 | — | 12 | 2 | no | — |
| 667 | D4 | — | 12 | 4 | no | — |
| 668 | D4 | — | 24 | 1 | no | — |
| 669 | D4 | — | 24 | 1 | no | — |
| 670 | C2×C4 | — | 2 | 2 | no | — |
| 671 | C2×C4 | — | 3 | 1 | no | — |
| 672 | C2×C4 | — | 3 | 2 | no | — |
| 673 | C2×C4 | — | 3 | 2 | no | — |
| 674 | C2×C4 | — | 3 | 2 | no | — |
| 675 | C2×C4 | — | 3 | 1 | no | — |
| 676 | C2×C4 | — | 3 | 2 | no | — |
| 677 | C2×C4 | — | 6 | 1 | no | — |
| 678 | C2×C4 | — | 6 | 1 | no | — |
| 679 | C2×C4 | — | 6 | 2 | no | — |
| 680 | C2×C4 | — | 6 | 2 | no | — |
| 681 | C2×C4 | — | 6 | 1 | no | — |
| 682 | C2×C4 | — | 6 | 1 | no | — |
| 683 | C2×C4 | — | 6 | 2 | no | — |
| 684 | C2×C4 | — | 6 | 2 | no | — |
| 685 | C2×C4 | — | 6 | 1 | no | — |
| 686 | C2×C4 | — | 6 | 1 | no | — |
| 687 | C2×C4 | — | 6 | 2 | no | — |
| 688 | C2×C4 | — | 6 | 1 | no | — |
| 689 | C2×C4 | — | 12 | 4 | no | — |
| 690 | C2×C4 | — | 12 | 2 | no | — |
| 691 | C2×C4 | — | 12 | 4 | no | — |
| 692 | C2×C4 | — | 12 | 4 | no | — |
| 693 | C2×C4 | — | 12 | 2 | no | — |
| 694 | C2×C4 | — | 12 | 2 | no | — |
| 695 | C2×C4 | — | 24 | 2 | no | — |
| 696 | C2×C4 | — | 24 | 1 | no | — |
| 697 | C2×C4 | — | 24 | 2 | no | — |
| 698 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 699 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 700 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 701 | C8 | — | 3 | 4 | no | — |
| 702 | C8 | — | 6 | 1 | no | — |
| 703 | C8 | — | 6 | 2 | no | — |
| 704 | C8 | — | 6 | 1 | no | — |
| 705 | C8 | — | 6 | 1 | no | — |
| 706 | C8 | — | 6 | 1 | no | — |
| 707 | C2×C3 | — | 4 | 1 | no | — |
| 708 | C2×C3 | — | 4 | 1 | no | — |
| 709 | C2×C3 | — | 4 | 1 | no | — |
| 710 | C2×C3 | — | 16 | 2 | no | — |
| 711 | C2×C3 | — | 16 | 1 | no | — |
| 712 | D3 | — | 8 | 4 | no | — |
| 713 | D3 | — | 8 | 2 | no | — |
| 714 | C22 | — | 2 | 1 | no | — |
| 715 | C22 | — | 2 | 2 | no | — |
| 716 | C22 | — | 2 | 1 | no | — |
| 717 | C22 | — | 2 | 2 | no | — |
| 718 | C22 | — | 2 | 2 | no | — |
| 719 | C22 | — | 2 | 1 | no | — |
| 720 | C22 | — | 3 | 2 | no | — |
| 721 | C22 | — | 6 | 1 | no | — |
| 722 | C22 | — | 6 | 1 | no | — |
| 723 | C22 | — | 6 | 1 | no | — |
| 724 | C22 | — | 6 | 4 | no | — |
| 725 | C22 | — | 6 | 1 | no | — |
| 726 | C22 | — | 6 | 1 | no | — |
| 727 | C22 | — | 12 | 2 | no | — |
| 728 | C22 | — | 12 | 2 | no | — |
| 729 | C22 | — | 12 | 1 | no | — |
| 730 | C22 | — | 12 | 1 | no | — |
| 731 | C22 | — | 12 | 1 | no | — |
| 732 | C22 | — | 24 | 2 | no | — |
| 733 | C22 | — | 24 | 4 | no | — |
| 734 | C22 | — | 48 | 4 | no | — |
| 735 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 736 | C4 | — | 2 | 1 | no | — |
| 737 | C4 | — | 2 | 2 | no | — |
| 738 | C4 | — | 3 | 1 | no | — |
| 739 | C4 | — | 3 | 1 | no | — |
| 740 | C4 | — | 6 | 1 | no | — |
| 741 | C4 | — | 6 | 2 | no | — |
| 742 | C4 | — | 6 | 2 | no | — |
| 743 | C4 | — | 12 | 1 | no | — |
| 744 | C4 | — | 12 | 2 | no | — |
| 745 | C4 | — | 12 | 1 | no | — |
| 746 | C4 | — | 12 | 1 | no | — |
| 747 | C4 | D4×S4 | 1 | 2 | yes | — |
| 748 | C3 | — | 4 | 1 | no | Sylow |
| 749 | C2 | — | 4 | 1 | no | — |
| 750 | C2 | — | 4 | 2 | no | — |
| 751 | C2 | — | 6 | 2 | no | — |
| 752 | C2 | — | 12 | 1 | no | — |
| 753 | C2 | — | 12 | 4 | no | — |
| 754 | C2 | — | 24 | 1 | no | — |
| 755 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| 756 | C2 | #87496 | 1 | 1 | yes | characteristic |
| 757 | C2 | #87497 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C23×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Fitting | #3489 | D3 |
| hypercenter | #121 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5926 | C2 | semidirect |
| 2. C2×#5923 | C2 | semidirect |
| 3. #3489⋊C3 | C2 | semidirect |
| 4. #85536 | C2 | semidirect |
| 5. #85521 | C2 | semidirect |
| 6. #85399 | C2 | semidirect |
| 7. #85398 | C2 | semidirect |
| 8. #85383 | C2 | semidirect |
| 9. #85380 | C2 | semidirect |
| 10. #85370 | C2 | semidirect |
| 11. #85366 | C2 | semidirect |
| 14. C22×#41⋊C3 | C22 | semidirect |
| 19. C2×#985 | C22 | semidirect |
| 20. C2×#984 | C22 | semidirect |
| 21. C2×#983 | C22 | semidirect |
| 22. C2×#983 | C22 | semidirect |
| 23. C22×GL(2,𝔽3) | C22 | semidirect |
| 25. D4×SL(2,𝔽3) | C22 | semidirect |
| 26. #548⋊C3 | C22 | semidirect |
| 27. #520⋊C3 | C22 | semidirect |
| 28. #5427 | C22 | semidirect |
| 29. #5425 | C22 | semidirect |
| 30. #5424 | C22 | semidirect |
| 31. #5421 | C22 | semidirect |
| 32. #5419 | C22 | semidirect |
| 33. #5419 | C22 | semidirect |
| 34. #5419 | C22 | semidirect |
| 35. #5395 | C22 | semidirect |
| 36. #5394 | C22 | semidirect |
| 37. C4×GL(2,𝔽3) | C22 | semidirect |
| 38. C4⋊#226 | C22 | semidirect |
| 41. #3489 | D3 | semidirect |
| 70. #986 | D4 | semidirect |
| 96. C22×#41 | C2×D3 | semidirect |
| 120. D4×Q8 | C2×D3 | semidirect |
| 121. #548 | C2×D3 | semidirect |
| 141. #520 | C2×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5926 | 2 |
| C2×#5923 | 2 |
| #3489⋊C3 | 2 |
| #85536 | 2 |
| #85521 | 2 |
| #85399 | 2 |
| #85398 | 2 |
| #85383 | 2 |
| #85380 | 2 |
| #85370 | 2 |
| #85366 | 2 |
| #61073 | 3 |
| #5612 | 4 |