Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1482 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 121 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 | 2 | yes | maximal, complemented |
| 2 | #3497⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85539 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #85410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85407 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #85399 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D4×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85384 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #85380 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #85331 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×C4×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61085 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×2−1+4⋊C3 | C22 | 1 | 2 | yes | complemented |
| 14 | #5926 | — | 2 | 8 | no | — |
| 15 | C2×#986 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#985 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 19 | C22×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | C22×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 21 | D3×#121 | — | 4 | 1 | no | maximal |
| 22 | C4⋊(#41⋊C3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | D4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #548⋊C3 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×C4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #5427 | C22 | 1 | 2 | yes | complemented |
| 27 | #5425 | C22 | 1 | 2 | yes | complemented |
| 28 | #5421 | C22 | 1 | 2 | yes | complemented |
| 29 | #5419 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×#859 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5395 | C22 | 1 | 2 | yes | complemented |
| 32 | C4⋊GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C4⋊#226 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×#577 | — | 3 | 2 | no | — |
| 39 | #3497 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #3496 | — | 3 | 1 | no | — |
| 41 | #3284 | — | 3 | 1 | no | — |
| 42 | #3284 | — | 3 | 1 | no | — |
| 43 | #3282 | — | 3 | 2 | no | — |
| 44 | #3282 | — | 3 | 2 | no | — |
| 45 | D4×SD16 | — | 3 | 1 | no | — |
| 46 | D4×SD16 | — | 3 | 1 | no | — |
| 47 | #3276 | — | 3 | 1 | no | — |
| 48 | #3276 | — | 3 | 1 | no | — |
| 49 | #3275 | — | 3 | 2 | no | — |
| 50 | #3275 | — | 3 | 2 | no | — |
| 51 | #3274 | — | 3 | 1 | no | — |
| 52 | #3274 | — | 3 | 1 | no | — |
| 53 | #3147 | — | 3 | 1 | no | — |
| 54 | #3060 | — | 3 | 2 | no | — |
| 55 | #3037 | — | 3 | 1 | no | — |
| 56 | #3036 | — | 3 | 1 | no | — |
| 57 | #3013 | — | 3 | 2 | no | — |
| 58 | #3012 | — | 3 | 2 | no | — |
| 59 | C2×C4×SD16 | — | 3 | 1 | no | — |
| 60 | #2931 | — | 3 | 1 | no | — |
| 61 | C2×D3×D4 | — | 4 | 1 | no | — |
| 62 | C2×D3×D4 | — | 4 | 2 | no | — |
| 63 | C22×C4×D3 | — | 4 | 1 | no | — |
| 64 | 2−1+4⋊C3 | — | 2 | 4 | no | — |
| 65 | C2×#41⋊C3 | C23 | 1 | 2 | yes | — |
| 66 | C22×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 67 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 68 | #986 | — | 2 | 4 | no | — |
| 69 | #985 | — | 2 | 4 | no | — |
| 70 | #983 | — | 2 | 4 | no | — |
| 71 | #983 | — | 2 | 4 | no | — |
| 72 | C2×GL(2,𝔽3) | — | 2 | 4 | no | — |
| 73 | C2×GL(2,𝔽3) | D4 | 1 | 4 | yes | complemented |
| 74 | C2×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 75 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#226 | C23 | 1 | 2 | yes | — |
| 78 | C3×#121 | — | 4 | 1 | no | — |
| 79 | #939 | — | 4 | 2 | no | — |
| 80 | #938 | — | 4 | 1 | no | — |
| 81 | #930 | — | 4 | 1 | no | — |
| 82 | #895 | — | 4 | 1 | no | — |
| 83 | D3×C4⋊C4 | — | 4 | 1 | no | — |
| 84 | #884 | — | 4 | 2 | no | — |
| 85 | D3×C22⋊C4 | — | 4 | 2 | no | — |
| 86 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 87 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 88 | #859 | C23 | 1 | 1 | yes | characteristic |
| 89 | #859 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | complemented |
| 91 | C2×H(5,𝔽2) | — | 3 | 2 | no | — |
| 92 | #577 | — | 6 | 8 | no | — |
| 93 | #577 | — | 6 | 8 | no | — |
| 94 | C2×#137 | — | 3 | 2 | no | — |
| 95 | C2×#137 | — | 3 | 2 | no | — |
| 96 | C2×#137 | — | 3 | 2 | no | — |
| 97 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 98 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 99 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 100 | C2×#135 | — | 3 | 2 | no | — |
| 101 | C2×#135 | — | 3 | 2 | no | — |
| 102 | C2×#135 | — | 3 | 2 | no | — |
| 103 | C2×#135 | — | 3 | 2 | no | — |
| 104 | C22×SD16 | — | 3 | 1 | no | — |
| 105 | C22×SD16 | — | 3 | 2 | no | — |
| 106 | C22×SD16 | — | 3 | 2 | no | — |
| 107 | C2×#131 | — | 3 | 2 | no | — |
| 108 | #550 | — | 3 | 1 | no | — |
| 109 | #550 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | D4×Q8 | — | 3 | 1 | no | — |
| 111 | D4×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | #548 | — | 3 | 2 | no | — |
| 113 | #548 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | #547 | — | 3 | 1 | no | — |
| 115 | #547 | — | 3 | 1 | no | — |
| 116 | #547 | — | 6 | 1 | no | — |
| 117 | #546 | — | 3 | 2 | no | — |
| 118 | #546 | — | 3 | 2 | no | — |
| 119 | #546 | — | 6 | 2 | no | — |
| 120 | D42 | — | 3 | 1 | no | — |
| 121 | D42 | — | 3 | 1 | no | — |
| 122 | D42 | — | 6 | 1 | no | — |
| 123 | #537 | — | 3 | 2 | no | — |
| 124 | #537 | — | 3 | 2 | no | — |
| 125 | #534 | — | 6 | 2 | no | — |
| 126 | #532 | — | 3 | 1 | no | — |
| 127 | #532 | — | 3 | 1 | no | — |
| 128 | #532 | — | 3 | 1 | no | — |
| 129 | C2×#121 | — | 6 | 1 | no | — |
| 130 | C2×#121 | — | 6 | 1 | no | — |
| 131 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 132 | C2×C4×D4 | — | 3 | 1 | no | — |
| 133 | #495 | — | 3 | 2 | no | — |
| 134 | #495 | — | 3 | 2 | no | — |
| 135 | #494 | — | 3 | 1 | no | — |
| 136 | #493 | — | 3 | 1 | no | — |
| 137 | #492 | — | 3 | 1 | no | — |
| 138 | #492 | — | 3 | 1 | no | — |
| 139 | #470 | — | 3 | 2 | no | — |
| 140 | #470 | — | 3 | 2 | no | — |
| 141 | #469 | — | 3 | 2 | no | — |
| 142 | #469 | — | 3 | 2 | no | — |
| 143 | #465 | — | 3 | 2 | no | — |
| 144 | #465 | — | 3 | 2 | no | — |
| 145 | #465 | — | 3 | 2 | no | — |
| 146 | #465 | — | 3 | 2 | no | — |
| 147 | #464 | — | 3 | 2 | no | — |
| 148 | #464 | — | 3 | 2 | no | — |
| 149 | #463 | — | 3 | 2 | no | — |
| 150 | #463 | — | 3 | 2 | no | — |
| 151 | #462 | — | 3 | 1 | no | — |
| 152 | #462 | — | 3 | 1 | no | — |
| 153 | #461 | — | 3 | 1 | no | — |
| 154 | #461 | — | 3 | 1 | no | — |
| 155 | #460 | — | 3 | 1 | no | — |
| 156 | #460 | — | 3 | 1 | no | — |
| 157 | #459 | — | 3 | 1 | no | — |
| 158 | #459 | — | 3 | 1 | no | — |
| 159 | #452 | — | 3 | 2 | no | — |
| 160 | #452 | — | 3 | 2 | no | — |
| 161 | #452 | — | 3 | 2 | no | — |
| 162 | #452 | — | 3 | 2 | no | — |
| 163 | #451 | — | 3 | 2 | no | — |
| 164 | #451 | — | 3 | 2 | no | — |
| 165 | #450 | — | 3 | 2 | no | — |
| 166 | #450 | — | 3 | 2 | no | — |
| 167 | #449 | — | 3 | 2 | no | — |
| 168 | #449 | — | 3 | 2 | no | — |
| 169 | #449 | — | 3 | 2 | no | — |
| 170 | #449 | — | 3 | 2 | no | — |
| 171 | #448 | — | 3 | 2 | no | — |
| 172 | #448 | — | 3 | 2 | no | — |
| 173 | #447 | — | 3 | 2 | no | — |
| 174 | #447 | — | 3 | 2 | no | — |
| 175 | C4×SD16 | — | 3 | 1 | no | — |
| 176 | C4×SD16 | — | 3 | 1 | no | — |
| 177 | C4×SD16 | — | 3 | 1 | no | — |
| 178 | C4×SD16 | — | 3 | 1 | no | — |
| 179 | C4×SD16 | — | 3 | 1 | no | — |
| 180 | C4×SD16 | — | 3 | 1 | no | — |
| 181 | C4×SD16 | — | 3 | 1 | no | — |
| 182 | C4×SD16 | — | 3 | 1 | no | — |
| 183 | #436 | — | 3 | 1 | no | — |
| 184 | #436 | — | 3 | 1 | no | — |
| 185 | #436 | — | 3 | 2 | no | — |
| 186 | C8×D4 | — | 3 | 1 | no | — |
| 187 | C8×D4 | — | 3 | 1 | no | — |
| 188 | C8×D4 | — | 3 | 2 | no | — |
| 189 | C2×#106 | — | 3 | 1 | no | — |
| 190 | #423 | — | 3 | 1 | no | — |
| 191 | #417 | — | 3 | 2 | no | — |
| 192 | #417 | — | 3 | 2 | no | — |
| 193 | C2×#103 | — | 3 | 1 | no | — |
| 194 | C2×#102 | — | 3 | 1 | no | — |
| 195 | #408 | — | 3 | 2 | no | — |
| 196 | C2×C4×C8 | — | 3 | 1 | no | — |
| 197 | C23×D3 | — | 4 | 1 | no | — |
| 198 | C23×D3 | — | 4 | 2 | no | — |
| 199 | C2×C3×D4 | — | 4 | 2 | no | — |
| 200 | C2×C3×D4 | — | 4 | 1 | no | — |
| 201 | C22×C3×C4 | — | 4 | 1 | no | — |
| 202 | C2×#67 | — | 4 | 2 | no | — |
| 203 | C2×#67 | — | 4 | 2 | no | — |
| 204 | C2×#67 | — | 4 | 2 | no | — |
| 205 | C22×Dic3 | — | 4 | 1 | no | — |
| 206 | D3×D4 | — | 8 | 8 | no | — |
| 207 | D3×D4 | — | 8 | 4 | no | — |
| 208 | C2×D12 | — | 4 | 1 | no | — |
| 209 | C2×D12 | — | 4 | 2 | no | — |
| 210 | C2×C4×D3 | — | 4 | 1 | no | — |
| 211 | C2×C4×D3 | — | 4 | 1 | no | — |
| 212 | C2×C4×D3 | — | 4 | 1 | no | — |
| 213 | C2×C4×D3 | — | 4 | 1 | no | — |
| 214 | C2×C4×D3 | — | 4 | 2 | no | — |
| 215 | C2×C4×D3 | — | 8 | 4 | no | — |
| 216 | #41⋊C3 | — | 2 | 2 | no | — |
| 217 | C2×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 218 | C2×SL(2,𝔽3) | C2×D4 | 1 | 2 | yes | complemented |
| 219 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 220 | GL(2,𝔽3) | — | 2 | 2 | no | — |
| 221 | GL(2,𝔽3) | C2×D4 | 1 | 2 | yes | complemented |
| 222 | GL(2,𝔽3) | C2×D4 | 1 | 2 | yes | complemented |
| 223 | #226 | — | 2 | 2 | no | — |
| 224 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 225 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 226 | #217 | — | 4 | 2 | no | — |
| 227 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 228 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 229 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 230 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 231 | 2−1+4 | — | 2 | 4 | no | — |
| 232 | 2−1+4 | — | 6 | 4 | no | — |
| 233 | H(5,𝔽2) | — | 6 | 8 | no | — |
| 234 | H(5,𝔽2) | — | 12 | 4 | no | — |
| 235 | C2×#41 | — | 3 | 2 | no | — |
| 236 | C2×#41 | — | 3 | 2 | no | — |
| 237 | C2×#41 | — | 3 | 2 | no | — |
| 238 | C2×#41 | — | 3 | 2 | no | — |
| 239 | C2×#41 | — | 3 | 2 | no | — |
| 240 | C2×#41 | — | 3 | 2 | no | — |
| 241 | C2×#41 | — | 6 | 2 | no | — |
| 242 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 243 | C22×Q8 | — | 3 | 2 | no | — |
| 244 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 245 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 246 | C22×D4 | — | 3 | 1 | no | — |
| 247 | C22×D4 | — | 3 | 2 | no | — |
| 248 | C22×D4 | — | 3 | 2 | no | — |
| 249 | C22×D4 | — | 6 | 2 | no | — |
| 250 | C22×D4 | — | 6 | 2 | no | — |
| 251 | C22×D4 | — | 6 | 1 | no | — |
| 252 | C22×D4 | — | 6 | 2 | no | — |
| 253 | C22×D4 | — | 6 | 1 | no | — |
| 254 | C23×C4 | — | 6 | 1 | no | — |
| 255 | #137 | — | 6 | 4 | no | — |
| 256 | #137 | — | 6 | 4 | no | — |
| 257 | #137 | — | 6 | 8 | no | — |
| 258 | #137 | — | 6 | 4 | no | — |
| 259 | #137 | — | 6 | 4 | no | — |
| 260 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 261 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 262 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 263 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 264 | #135 | — | 6 | 8 | no | — |
| 265 | #135 | — | 6 | 4 | no | — |
| 266 | #135 | — | 6 | 4 | no | — |
| 267 | #135 | — | 6 | 8 | no | — |
| 268 | #135 | — | 12 | 4 | no | — |
| 269 | C2×Q16 | — | 3 | 2 | no | — |
| 270 | C2×Q16 | — | 3 | 2 | no | — |
| 271 | C2×Q16 | — | 3 | 2 | no | — |
| 272 | C2×Q16 | — | 3 | 2 | no | — |
| 273 | C2×SD16 | — | 3 | 1 | no | — |
| 274 | C2×SD16 | — | 3 | 1 | no | — |
| 275 | C2×SD16 | — | 3 | 4 | no | — |
| 276 | C2×SD16 | — | 3 | 4 | no | — |
| 277 | C2×SD16 | — | 3 | 1 | no | — |
| 278 | C2×SD16 | — | 3 | 1 | no | — |
| 279 | C2×SD16 | — | 3 | 2 | no | — |
| 280 | C2×SD16 | — | 3 | 2 | no | — |
| 281 | C2×SD16 | — | 3 | 2 | no | — |
| 282 | C2×SD16 | — | 3 | 2 | no | — |
| 283 | C2×SD16 | — | 3 | 2 | no | — |
| 284 | C2×SD16 | — | 3 | 2 | no | — |
| 285 | C2×SD16 | — | 3 | 2 | no | — |
| 286 | C2×SD16 | — | 3 | 2 | no | — |
| 287 | C2×SD16 | — | 6 | 4 | no | — |
| 288 | C2×SD16 | — | 6 | 4 | no | — |
| 289 | C2×SD16 | — | 6 | 8 | no | — |
| 290 | C2×D8 | — | 3 | 2 | no | — |
| 291 | C2×D8 | — | 3 | 2 | no | — |
| 292 | C2×D8 | — | 3 | 2 | no | — |
| 293 | C2×D8 | — | 3 | 2 | no | — |
| 294 | #131 | — | 6 | 8 | no | — |
| 295 | C2×M16 | — | 3 | 2 | no | — |
| 296 | C2×M16 | — | 3 | 2 | no | — |
| 297 | C2×M16 | — | 3 | 2 | no | — |
| 298 | C22×C8 | — | 3 | 1 | no | — |
| 299 | C22×C8 | — | 3 | 2 | no | — |
| 300 | C22×C8 | — | 3 | 2 | no | — |
| 301 | C22×C8 | — | 3 | 1 | no | — |
| 302 | C4⋊Q8 | — | 3 | 1 | no | — |
| 303 | C4⋊Q8 | — | 3 | 1 | no | — |
| 304 | C4⋊Q8 | — | 3 | 1 | no | — |
| 305 | #127 | — | 3 | 1 | no | — |
| 306 | #127 | — | 3 | 1 | no | — |
| 307 | #127 | — | 3 | 1 | no | — |
| 308 | #124 | — | 3 | 2 | no | — |
| 309 | #124 | — | 3 | 2 | no | — |
| 310 | #124 | — | 3 | 2 | no | — |
| 311 | #123 | — | 6 | 2 | no | — |
| 312 | #123 | — | 6 | 2 | no | — |
| 313 | #123 | — | 6 | 2 | no | — |
| 314 | #123 | — | 6 | 2 | no | — |
| 315 | C22⋊Q8 | — | 3 | 2 | no | — |
| 316 | C22⋊Q8 | — | 3 | 2 | no | — |
| 317 | C22⋊Q8 | — | 3 | 2 | no | — |
| 318 | C22⋊Q8 | — | 3 | 2 | no | — |
| 319 | C22⋊Q8 | — | 6 | 2 | no | — |
| 320 | C22⋊Q8 | — | 6 | 2 | no | — |
| 321 | #121 | — | 3 | 2 | no | — |
| 322 | #121 | — | 3 | 1 | no | — |
| 323 | #121 | — | 3 | 2 | no | — |
| 324 | #121 | — | 3 | 2 | no | — |
| 325 | #121 | — | 3 | 2 | no | — |
| 326 | #121 | — | 3 | 2 | no | — |
| 327 | #121 | — | 6 | 2 | no | — |
| 328 | #121 | — | 6 | 2 | no | — |
| 329 | #121 | — | 6 | 1 | no | — |
| 330 | #121 | — | 6 | 1 | no | — |
| 331 | #121 | — | 6 | 1 | no | — |
| 332 | #121 | — | 6 | 2 | no | — |
| 333 | #121 | — | 6 | 1 | no | — |
| 334 | #121 | — | 6 | 2 | no | — |
| 335 | #121 | — | 6 | 2 | no | — |
| 336 | #121 | — | 6 | 1 | no | — |
| 337 | #121 | — | 6 | 1 | no | — |
| 338 | #121 | — | 6 | 1 | no | — |
| 339 | #121 | — | 6 | 2 | no | — |
| 340 | #121 | S4 | 1 | 1 | yes | characteristic |
| 341 | #120 | — | 6 | 2 | no | — |
| 342 | #120 | — | 6 | 2 | no | — |
| 343 | #120 | — | 6 | 2 | no | — |
| 344 | #120 | — | 6 | 2 | no | — |
| 345 | C4×Q8 | — | 3 | 1 | no | — |
| 346 | C4×Q8 | — | 3 | 1 | no | — |
| 347 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 348 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 349 | C4×D4 | — | 3 | 1 | no | — |
| 350 | C4×D4 | — | 3 | 1 | no | — |
| 351 | C4×D4 | — | 3 | 2 | no | — |
| 352 | C4×D4 | — | 3 | 1 | no | — |
| 353 | C4×D4 | — | 3 | 1 | no | — |
| 354 | C4×D4 | — | 3 | 1 | no | — |
| 355 | C4×D4 | — | 3 | 1 | no | — |
| 356 | C4×D4 | — | 6 | 1 | no | — |
| 357 | C4×D4 | — | 6 | 1 | no | — |
| 358 | C4×D4 | — | 6 | 1 | no | — |
| 359 | C4×D4 | — | 6 | 1 | no | — |
| 360 | C4×D4 | — | 6 | 1 | no | — |
| 361 | C4×D4 | — | 6 | 1 | no | — |
| 362 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 363 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 364 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 365 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 366 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 367 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 368 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 369 | C2×C42 | — | 3 | 1 | no | — |
| 370 | #106 | — | 3 | 1 | no | — |
| 371 | #106 | — | 3 | 1 | no | — |
| 372 | #106 | — | 3 | 1 | no | — |
| 373 | #106 | — | 3 | 1 | no | — |
| 374 | C4⋊C8 | — | 3 | 1 | no | — |
| 375 | C4⋊C8 | — | 3 | 1 | no | — |
| 376 | C4⋊C8 | — | 3 | 2 | no | — |
| 377 | #103 | — | 3 | 1 | no | — |
| 378 | #103 | — | 3 | 1 | no | — |
| 379 | #103 | — | 3 | 2 | no | — |
| 380 | #103 | — | 3 | 2 | no | — |
| 381 | #103 | — | 3 | 2 | no | — |
| 382 | #103 | — | 3 | 2 | no | — |
| 383 | #103 | — | 3 | 1 | no | — |
| 384 | #103 | — | 3 | 1 | no | — |
| 385 | #102 | — | 3 | 1 | no | — |
| 386 | #102 | — | 3 | 1 | no | — |
| 387 | #102 | — | 3 | 1 | no | — |
| 388 | #102 | — | 3 | 1 | no | — |
| 389 | #102 | — | 3 | 2 | no | — |
| 390 | #102 | — | 3 | 2 | no | — |
| 391 | #102 | — | 3 | 2 | no | — |
| 392 | #102 | — | 3 | 2 | no | — |
| 393 | C22⋊C8 | — | 3 | 2 | no | — |
| 394 | C22⋊C8 | — | 3 | 2 | no | — |
| 395 | C22⋊C8 | — | 3 | 2 | no | — |
| 396 | C22⋊C8 | — | 3 | 2 | no | — |
| 397 | C4×C8 | — | 3 | 1 | no | — |
| 398 | C4×C8 | — | 3 | 1 | no | — |
| 399 | C4×C8 | — | 3 | 1 | no | — |
| 400 | C4×C8 | — | 3 | 1 | no | — |
| 401 | C23×C3 | — | 4 | 1 | no | — |
| 402 | C23×C3 | — | 4 | 2 | no | — |
| 403 | C22×D3 | — | 4 | 1 | no | — |
| 404 | C22×D3 | — | 4 | 4 | no | — |
| 405 | C22×D3 | — | 4 | 1 | no | — |
| 406 | C22×D3 | — | 4 | 2 | no | — |
| 407 | C22×D3 | — | 8 | 4 | no | — |
| 408 | C22×D3 | — | 8 | 2 | no | — |
| 409 | C22×D3 | — | 8 | 2 | no | — |
| 410 | C22×D3 | — | 8 | 4 | no | — |
| 411 | C22×D3 | — | 8 | 4 | no | — |
| 412 | C3×D4 | — | 8 | 2 | no | — |
| 413 | C3×D4 | — | 8 | 4 | no | — |
| 414 | C2×C3×C4 | — | 4 | 1 | no | — |
| 415 | C2×C3×C4 | — | 4 | 1 | no | — |
| 416 | C2×C3×C4 | — | 4 | 2 | no | — |
| 417 | C2×C3×C4 | — | 8 | 2 | no | — |
| 418 | #67 | — | 8 | 4 | no | — |
| 419 | #67 | — | 8 | 4 | no | — |
| 420 | #67 | — | 8 | 4 | no | — |
| 421 | C2×Dic3 | — | 4 | 1 | no | — |
| 422 | C2×Dic3 | — | 4 | 1 | no | — |
| 423 | C2×Dic3 | — | 4 | 2 | no | — |
| 424 | C2×Dic3 | — | 8 | 2 | no | — |
| 425 | D12 | — | 8 | 2 | no | — |
| 426 | D12 | — | 8 | 4 | no | — |
| 427 | C4×D3 | — | 4 | 4 | no | — |
| 428 | C4×D3 | — | 8 | 2 | no | — |
| 429 | C4×D3 | — | 8 | 4 | no | — |
| 430 | C4×D3 | — | 8 | 2 | no | — |
| 431 | C4×D3 | — | 8 | 2 | no | — |
| 432 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 433 | C24 | — | 6 | 2 | no | — |
| 434 | C24 | — | 6 | 1 | no | — |
| 435 | C24 | — | 6 | 2 | no | — |
| 436 | #41 | — | 2 | 2 | no | — |
| 437 | #41 | — | 6 | 4 | no | — |
| 438 | #41 | — | 6 | 4 | no | — |
| 439 | #41 | — | 6 | 4 | no | — |
| 440 | #41 | — | 6 | 4 | no | — |
| 441 | #41 | — | 6 | 4 | no | — |
| 442 | #41 | — | 6 | 4 | no | — |
| 443 | #41 | — | 6 | 2 | no | — |
| 444 | #41 | — | 6 | 4 | no | — |
| 445 | #41 | — | 6 | 4 | no | — |
| 446 | #41 | — | 6 | 4 | no | — |
| 447 | #41 | — | 12 | 2 | no | — |
| 448 | #41 | — | 12 | 2 | no | — |
| 449 | #41 | — | 12 | 2 | no | — |
| 450 | #41 | — | 12 | 8 | no | — |
| 451 | C2×Q8 | — | 2 | 2 | no | — |
| 452 | C2×Q8 | — | 3 | 2 | no | — |
| 453 | C2×Q8 | — | 3 | 1 | no | — |
| 454 | C2×Q8 | — | 3 | 2 | no | — |
| 455 | C2×Q8 | — | 3 | 2 | no | — |
| 456 | C2×Q8 | — | 3 | 2 | no | — |
| 457 | C2×Q8 | — | 6 | 2 | no | — |
| 458 | C2×Q8 | — | 6 | 4 | no | — |
| 459 | C2×Q8 | — | 12 | 2 | no | — |
| 460 | C2×Q8 | D3×D4 | 1 | 2 | yes | complemented |
| 461 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 462 | C2×D4 | — | 3 | 1 | no | — |
| 463 | C2×D4 | — | 3 | 1 | no | — |
| 464 | C2×D4 | — | 3 | 4 | no | — |
| 465 | C2×D4 | — | 3 | 2 | no | — |
| 466 | C2×D4 | — | 3 | 2 | no | — |
| 467 | C2×D4 | — | 3 | 2 | no | — |
| 468 | C2×D4 | — | 3 | 2 | no | — |
| 469 | C2×D4 | — | 3 | 2 | no | — |
| 470 | C2×D4 | — | 3 | 1 | no | — |
| 471 | C2×D4 | — | 6 | 1 | no | — |
| 472 | C2×D4 | — | 6 | 2 | no | — |
| 473 | C2×D4 | — | 6 | 2 | no | — |
| 474 | C2×D4 | — | 6 | 1 | no | — |
| 475 | C2×D4 | — | 6 | 1 | no | — |
| 476 | C2×D4 | — | 6 | 4 | no | — |
| 477 | C2×D4 | — | 6 | 4 | no | — |
| 478 | C2×D4 | — | 6 | 2 | no | — |
| 479 | C2×D4 | — | 6 | 2 | no | — |
| 480 | C2×D4 | — | 6 | 2 | no | — |
| 481 | C2×D4 | — | 6 | 2 | no | — |
| 482 | C2×D4 | — | 6 | 2 | no | — |
| 483 | C2×D4 | — | 6 | 1 | no | — |
| 484 | C2×D4 | — | 6 | 2 | no | — |
| 485 | C2×D4 | — | 12 | 2 | no | — |
| 486 | C2×D4 | — | 12 | 2 | no | — |
| 487 | C2×D4 | — | 12 | 8 | no | — |
| 488 | C2×D4 | — | 12 | 8 | no | — |
| 489 | C2×D4 | — | 12 | 8 | no | — |
| 490 | C2×D4 | — | 24 | 2 | no | — |
| 491 | C2×D4 | — | 24 | 2 | no | — |
| 492 | C2×D4 | C2×S4 | 1 | 1 | yes | characteristic |
| 493 | C2×D4 | C2×S4 | 1 | 2 | yes | — |
| 494 | C22×C4 | — | 3 | 1 | no | — |
| 495 | C22×C4 | — | 3 | 2 | no | — |
| 496 | C22×C4 | — | 3 | 1 | no | — |
| 497 | C22×C4 | — | 3 | 2 | no | — |
| 498 | C22×C4 | — | 6 | 2 | no | — |
| 499 | C22×C4 | — | 6 | 2 | no | — |
| 500 | C22×C4 | — | 6 | 2 | no | — |
| 501 | C22×C4 | — | 6 | 1 | no | — |
| 502 | C22×C4 | — | 6 | 2 | no | — |
| 503 | C22×C4 | — | 6 | 1 | no | — |
| 504 | C22×C4 | — | 6 | 1 | no | — |
| 505 | C22×C4 | — | 6 | 1 | no | — |
| 506 | C22×C4 | — | 6 | 1 | no | — |
| 507 | C22×C4 | — | 24 | 2 | no | — |
| 508 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 509 | Q16 | — | 6 | 4 | no | — |
| 510 | Q16 | — | 6 | 4 | no | — |
| 511 | Q16 | — | 6 | 2 | no | — |
| 512 | Q16 | — | 6 | 2 | no | — |
| 513 | Q16 | — | 12 | 2 | no | — |
| 514 | SD16 | — | 3 | 4 | no | — |
| 515 | SD16 | — | 3 | 2 | no | — |
| 516 | SD16 | — | 3 | 4 | no | — |
| 517 | SD16 | — | 3 | 2 | no | — |
| 518 | SD16 | — | 3 | 2 | no | — |
| 519 | SD16 | — | 3 | 2 | no | — |
| 520 | SD16 | — | 6 | 4 | no | — |
| 521 | SD16 | — | 6 | 4 | no | — |
| 522 | SD16 | — | 6 | 4 | no | — |
| 523 | SD16 | — | 6 | 4 | no | — |
| 524 | SD16 | — | 6 | 4 | no | — |
| 525 | SD16 | — | 6 | 2 | no | — |
| 526 | SD16 | — | 6 | 2 | no | — |
| 527 | SD16 | — | 12 | 2 | no | — |
| 528 | SD16 | — | 12 | 2 | no | — |
| 529 | D8 | — | 6 | 4 | no | — |
| 530 | D8 | — | 6 | 4 | no | — |
| 531 | D8 | — | 6 | 4 | no | — |
| 532 | D8 | — | 12 | 2 | no | — |
| 533 | M16 | — | 6 | 4 | no | — |
| 534 | M16 | — | 6 | 4 | no | — |
| 535 | M16 | — | 6 | 4 | no | — |
| 536 | C2×C8 | — | 3 | 1 | no | — |
| 537 | C2×C8 | — | 3 | 1 | no | — |
| 538 | C2×C8 | — | 3 | 4 | no | — |
| 539 | C2×C8 | — | 3 | 1 | no | — |
| 540 | C2×C8 | — | 3 | 1 | no | — |
| 541 | C2×C8 | — | 3 | 2 | no | — |
| 542 | C2×C8 | — | 3 | 2 | no | — |
| 543 | C2×C8 | — | 6 | 4 | no | — |
| 544 | C2×C8 | — | 6 | 4 | no | — |
| 545 | C2×C8 | — | 6 | 2 | no | — |
| 546 | C4⋊C4 | — | 3 | 1 | no | — |
| 547 | C4⋊C4 | — | 3 | 1 | no | — |
| 548 | C4⋊C4 | — | 3 | 1 | no | — |
| 549 | C4⋊C4 | — | 3 | 2 | no | — |
| 550 | C4⋊C4 | — | 3 | 1 | no | — |
| 551 | C4⋊C4 | — | 3 | 1 | no | — |
| 552 | C4⋊C4 | — | 6 | 1 | no | — |
| 553 | C4⋊C4 | — | 6 | 1 | no | — |
| 554 | C4⋊C4 | — | 6 | 1 | no | — |
| 555 | C4⋊C4 | — | 6 | 2 | no | — |
| 556 | C4⋊C4 | — | 6 | 1 | no | — |
| 557 | C4⋊C4 | — | 6 | 1 | no | — |
| 558 | C4⋊C4 | — | 6 | 2 | no | — |
| 559 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 560 | C22⋊C4 | — | 3 | 2 | no | — |
| 561 | C22⋊C4 | — | 3 | 2 | no | — |
| 562 | C22⋊C4 | — | 3 | 2 | no | — |
| 563 | C22⋊C4 | — | 6 | 2 | no | — |
| 564 | C22⋊C4 | — | 6 | 1 | no | — |
| 565 | C22⋊C4 | — | 6 | 1 | no | — |
| 566 | C22⋊C4 | — | 6 | 1 | no | — |
| 567 | C22⋊C4 | — | 6 | 1 | no | — |
| 568 | C22⋊C4 | — | 6 | 2 | no | — |
| 569 | C22⋊C4 | — | 6 | 2 | no | — |
| 570 | C22⋊C4 | — | 6 | 2 | no | — |
| 571 | C22⋊C4 | — | 6 | 2 | no | — |
| 572 | C22⋊C4 | — | 6 | 2 | no | — |
| 573 | C22⋊C4 | — | 6 | 2 | no | — |
| 574 | C22⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 575 | C42 | — | 3 | 1 | no | — |
| 576 | C42 | — | 3 | 1 | no | — |
| 577 | C42 | — | 3 | 1 | no | — |
| 578 | C42 | — | 3 | 1 | no | — |
| 579 | C22×C3 | — | 4 | 2 | no | — |
| 580 | C22×C3 | — | 4 | 1 | no | — |
| 581 | C22×C3 | — | 8 | 1 | no | — |
| 582 | C22×C3 | — | 8 | 1 | no | — |
| 583 | C22×C3 | — | 8 | 2 | no | — |
| 584 | C22×C3 | — | 8 | 2 | no | — |
| 585 | C22×C3 | — | 8 | 2 | no | — |
| 586 | C2×D3 | — | 4 | 2 | no | — |
| 587 | C2×D3 | — | 4 | 2 | no | — |
| 588 | C2×D3 | — | 4 | 2 | no | — |
| 589 | C2×D3 | — | 4 | 2 | no | — |
| 590 | C2×D3 | — | 8 | 1 | no | — |
| 591 | C2×D3 | — | 8 | 1 | no | — |
| 592 | C2×D3 | — | 8 | 2 | no | — |
| 593 | C2×D3 | — | 8 | 2 | no | — |
| 594 | C2×D3 | — | 8 | 2 | no | — |
| 595 | C2×D3 | — | 8 | 8 | no | — |
| 596 | C2×D3 | — | 16 | 8 | no | — |
| 597 | C3×C4 | — | 4 | 2 | no | — |
| 598 | C3×C4 | — | 8 | 1 | no | — |
| 599 | C3×C4 | — | 8 | 2 | no | — |
| 600 | Dic3 | — | 4 | 2 | no | — |
| 601 | Dic3 | — | 8 | 1 | no | — |
| 602 | Dic3 | — | 8 | 2 | no | — |
| 603 | C23 | — | 3 | 2 | no | — |
| 604 | C23 | — | 6 | 1 | no | — |
| 605 | C23 | — | 6 | 1 | no | — |
| 606 | C23 | — | 6 | 4 | no | — |
| 607 | C23 | — | 6 | 2 | no | — |
| 608 | C23 | — | 12 | 4 | no | — |
| 609 | C23 | — | 12 | 4 | no | — |
| 610 | C23 | — | 24 | 1 | no | — |
| 611 | C23 | — | 24 | 1 | no | — |
| 612 | C23 | — | 24 | 2 | no | — |
| 613 | C23 | — | 24 | 2 | no | — |
| 614 | C23 | — | 24 | 2 | no | — |
| 615 | C23 | — | 24 | 2 | no | — |
| 616 | C23 | C22×S4 | 1 | 2 | yes | — |
| 617 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 618 | Q8 | — | 3 | 2 | no | — |
| 619 | Q8 | — | 3 | 1 | no | — |
| 620 | Q8 | — | 6 | 4 | no | — |
| 621 | Q8 | — | 6 | 1 | no | — |
| 622 | Q8 | — | 6 | 2 | no | — |
| 623 | Q8 | — | 6 | 2 | no | — |
| 624 | Q8 | — | 6 | 2 | no | — |
| 625 | Q8 | — | 6 | 2 | no | — |
| 626 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 627 | D4 | — | 2 | 4 | no | — |
| 628 | D4 | — | 2 | 2 | no | — |
| 629 | D4 | — | 3 | 2 | no | — |
| 630 | D4 | — | 3 | 2 | no | — |
| 631 | D4 | — | 6 | 4 | no | — |
| 632 | D4 | — | 6 | 2 | no | — |
| 633 | D4 | — | 6 | 2 | no | — |
| 634 | D4 | — | 6 | 1 | no | — |
| 635 | D4 | — | 6 | 1 | no | — |
| 636 | D4 | — | 6 | 4 | no | — |
| 637 | D4 | — | 6 | 2 | no | — |
| 638 | D4 | — | 6 | 2 | no | — |
| 639 | D4 | — | 6 | 4 | no | — |
| 640 | D4 | — | 6 | 2 | no | — |
| 641 | D4 | — | 12 | 4 | no | — |
| 642 | D4 | — | 12 | 2 | no | — |
| 643 | D4 | — | 12 | 4 | no | — |
| 644 | D4 | — | 12 | 4 | no | — |
| 645 | D4 | — | 12 | 4 | no | — |
| 646 | D4 | — | 12 | 4 | no | — |
| 647 | D4 | — | 12 | 2 | no | — |
| 648 | D4 | — | 24 | 1 | no | — |
| 649 | D4 | — | 24 | 1 | no | — |
| 650 | D4 | — | 24 | 2 | no | — |
| 651 | D4 | — | 24 | 2 | no | — |
| 652 | C2×C4 | — | 2 | 2 | no | — |
| 653 | C2×C4 | — | 3 | 2 | no | — |
| 654 | C2×C4 | — | 3 | 2 | no | — |
| 655 | C2×C4 | — | 3 | 1 | no | — |
| 656 | C2×C4 | — | 3 | 1 | no | — |
| 657 | C2×C4 | — | 3 | 1 | no | — |
| 658 | C2×C4 | — | 3 | 1 | no | — |
| 659 | C2×C4 | — | 3 | 2 | no | — |
| 660 | C2×C4 | — | 6 | 2 | no | — |
| 661 | C2×C4 | — | 6 | 2 | no | — |
| 662 | C2×C4 | — | 6 | 2 | no | — |
| 663 | C2×C4 | — | 6 | 2 | no | — |
| 664 | C2×C4 | — | 6 | 1 | no | — |
| 665 | C2×C4 | — | 6 | 1 | no | — |
| 666 | C2×C4 | — | 6 | 2 | no | — |
| 667 | C2×C4 | — | 12 | 4 | no | — |
| 668 | C2×C4 | — | 12 | 4 | no | — |
| 669 | C2×C4 | — | 12 | 4 | no | — |
| 670 | C2×C4 | — | 12 | 1 | no | — |
| 671 | C2×C4 | — | 12 | 4 | no | — |
| 672 | C2×C4 | — | 12 | 2 | no | — |
| 673 | C2×C4 | — | 12 | 2 | no | — |
| 674 | C2×C4 | — | 24 | 1 | no | — |
| 675 | C2×C4 | — | 24 | 1 | no | — |
| 676 | C2×C4 | — | 24 | 1 | no | — |
| 677 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 678 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 679 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 680 | C8 | — | 3 | 2 | no | — |
| 681 | C8 | — | 3 | 2 | no | — |
| 682 | C8 | — | 6 | 2 | no | — |
| 683 | C8 | — | 6 | 2 | no | — |
| 684 | C8 | — | 6 | 1 | no | — |
| 685 | C8 | — | 6 | 1 | no | — |
| 686 | C2×C3 | — | 4 | 1 | no | — |
| 687 | C2×C3 | — | 4 | 1 | no | — |
| 688 | C2×C3 | — | 4 | 1 | no | — |
| 689 | C2×C3 | — | 8 | 2 | no | — |
| 690 | C2×C3 | — | 16 | 2 | no | — |
| 691 | D3 | — | 4 | 4 | no | — |
| 692 | D3 | — | 8 | 2 | no | — |
| 693 | D3 | — | 16 | 2 | no | — |
| 694 | C22 | — | 2 | 1 | no | — |
| 695 | C22 | — | 2 | 1 | no | — |
| 696 | C22 | — | 2 | 2 | no | — |
| 697 | C22 | — | 2 | 2 | no | — |
| 698 | C22 | — | 2 | 2 | no | — |
| 699 | C22 | — | 6 | 2 | no | — |
| 700 | C22 | — | 6 | 2 | no | — |
| 701 | C22 | — | 6 | 2 | no | — |
| 702 | C22 | — | 6 | 2 | no | — |
| 703 | C22 | — | 6 | 2 | no | — |
| 704 | C22 | — | 12 | 1 | no | — |
| 705 | C22 | — | 12 | 1 | no | — |
| 706 | C22 | — | 12 | 1 | no | — |
| 707 | C22 | — | 12 | 1 | no | — |
| 708 | C22 | — | 12 | 2 | no | — |
| 709 | C22 | — | 12 | 2 | no | — |
| 710 | C22 | — | 12 | 2 | no | — |
| 711 | C22 | — | 24 | 4 | no | — |
| 712 | C22 | — | 48 | 4 | no | — |
| 713 | C22 | — | 48 | 4 | no | — |
| 714 | C22 | D4×S4 | 1 | 2 | yes | — |
| 715 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 716 | C4 | — | 2 | 2 | no | — |
| 717 | C4 | — | 2 | 1 | no | — |
| 718 | C4 | — | 3 | 1 | no | — |
| 719 | C4 | — | 3 | 1 | no | — |
| 720 | C4 | — | 3 | 2 | no | — |
| 721 | C4 | — | 6 | 2 | no | — |
| 722 | C4 | — | 6 | 1 | no | — |
| 723 | C4 | — | 6 | 1 | no | — |
| 724 | C4 | — | 12 | 2 | no | — |
| 725 | C4 | — | 12 | 1 | no | — |
| 726 | C4 | — | 12 | 1 | no | — |
| 727 | C4 | #5926 | 1 | 2 | yes | complemented |
| 728 | C3 | — | 4 | 1 | no | Sylow |
| 729 | C2 | — | 2 | 2 | no | — |
| 730 | C2 | — | 4 | 2 | no | — |
| 731 | C2 | — | 12 | 2 | no | — |
| 732 | C2 | — | 12 | 2 | no | — |
| 733 | C2 | — | 12 | 2 | no | — |
| 734 | C2 | — | 24 | 2 | no | — |
| 735 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| 736 | C2 | C2×#5926 | 1 | 1 | yes | characteristic |
| 737 | C2 | #87497 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C23×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Fitting | #3497 | 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. #3497⋊C3 | C2 | semidirect |
| 3. #85539 | C2 | semidirect |
| 4. #85410 | C2 | semidirect |
| 5. #85407 | C2 | semidirect |
| 6. #85399 | C2 | semidirect |
| 7. D4×GL(2,𝔽3) | C2 | semidirect |
| 8. #85384 | C2 | semidirect |
| 9. #85380 | C2 | semidirect |
| 10. #85331 | C2 | semidirect |
| 11. C2×C4×GL(2,𝔽3) | C2 | semidirect |
| 13. C2×2−1+4⋊C3 | C22 | semidirect |
| 15. C2×#986 | C22 | semidirect |
| 16. C2×#985 | C22 | semidirect |
| 17. C2×#983 | C22 | semidirect |
| 18. C2×#983 | C22 | semidirect |
| 20. C22×GL(2,𝔽3) | C22 | semidirect |
| 22. C4⋊(#41⋊C3) | C22 | semidirect |
| 23. D4×SL(2,𝔽3) | C22 | semidirect |
| 24. #548⋊C3 | C22 | semidirect |
| 25. C2×C4×SL(2,𝔽3) | C22 | semidirect |
| 26. #5427 | C22 | semidirect |
| 27. #5425 | C22 | semidirect |
| 28. #5421 | C22 | semidirect |
| 29. #5419 | C22 | semidirect |
| 30. C2×#859 | C22 | semidirect |
| 31. #5395 | C22 | semidirect |
| 32. C4⋊GL(2,𝔽3) | C22 | semidirect |
| 33. C4×GL(2,𝔽3) | C22 | semidirect |
| 34. C4×GL(2,𝔽3) | C22 | semidirect |
| 35. C4×GL(2,𝔽3) | C22 | semidirect |
| 36. C4×GL(2,𝔽3) | C22 | semidirect |
| 37. C4⋊#226 | C22 | semidirect |
| 39. #3497 | D3 | semidirect |
| 73. C2×GL(2,𝔽3) | D4 | semidirect |
| 90. C2×2−1+4 | C2×D3 | semidirect |
| 109. #550 | C2×D3 | semidirect |
| 111. D4×Q8 | C2×D3 | semidirect |
| 113. #548 | C2×D3 | semidirect |
| 131. C2×C4×Q8 | C2×D3 | semidirect |
| 218. C2×SL(2,𝔽3) | C2×D4 | semidirect |
| 221. GL(2,𝔽3) | C2×D4 | semidirect |
| 222. GL(2,𝔽3) | C2×D4 | semidirect |
| 460. C2×Q8 | D3×D4 | semidirect |
| 727. C4 | #5926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5926 | 2 |
| #3497⋊C3 | 2 |
| #85539 | 2 |
| #85410 | 2 |
| #85407 | 2 |
| #85399 | 2 |
| D4×GL(2,𝔽3) | 2 |
| #85384 | 2 |
| #85380 | 2 |
| #85331 | 2 |
| C2×C4×GL(2,𝔽3) | 2 |
| #61085 | 3 |
| D3×#121 | 4 |