Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
972 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 972 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 | #3502⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #85431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #85423 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #85418 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85418 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #85353 | C2 | 1 | 2 | yes | maximal |
| 9 | #85351 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C4×GL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #85318 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #61371 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C22×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 14 | D3×C22⋊Q8 | — | 4 | 1 | no | maximal |
| 15 | Q8×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | #557⋊C3 | C22 | 1 | 2 | yes | complemented |
| 17 | #557⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #519⋊C3 | C22 | 1 | 2 | yes | — |
| 19 | C2×C4×SL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 20 | #5420 | C22 | 1 | 2 | yes | — |
| 21 | C2×#859 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5394 | C22 | 1 | 2 | yes | — |
| 23 | #5394 | C22 | 1 | 2 | yes | — |
| 24 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 26 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×GL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 29 | C4×GL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 30 | #5391 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #5391 | C22 | 1 | 2 | yes | complemented |
| 32 | #5389 | C22 | 1 | 2 | yes | complemented |
| 33 | #5389 | C22 | 1 | 2 | yes | complemented |
| 34 | #5389 | C22 | 1 | 2 | yes | complemented |
| 35 | #5386 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #5386 | C22 | 1 | 2 | yes | complemented |
| 37 | #3502 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #3501 | — | 3 | 1 | no | — |
| 39 | #3388 | — | 3 | 2 | no | — |
| 40 | #3388 | — | 3 | 2 | no | — |
| 41 | #3386 | — | 3 | 1 | no | — |
| 42 | #3386 | — | 3 | 1 | no | — |
| 43 | #3385 | — | 3 | 1 | no | — |
| 44 | #3385 | — | 3 | 1 | no | — |
| 45 | #3381 | — | 3 | 1 | no | — |
| 46 | #3381 | — | 3 | 2 | no | — |
| 47 | #3381 | — | 3 | 1 | no | — |
| 48 | #3381 | — | 3 | 2 | no | — |
| 49 | Q8×SD16 | — | 3 | 1 | no | — |
| 50 | Q8×SD16 | — | 3 | 1 | no | — |
| 51 | #3163 | — | 3 | 2 | no | — |
| 52 | #3160 | — | 3 | 1 | no | — |
| 53 | #3082 | — | 3 | 2 | no | — |
| 54 | #3081 | — | 3 | 2 | no | — |
| 55 | #3078 | — | 3 | 1 | no | — |
| 56 | #3077 | — | 3 | 1 | no | — |
| 57 | #2960 | — | 3 | 1 | no | — |
| 58 | #2949 | — | 3 | 2 | no | — |
| 59 | C2×C4×SD16 | — | 3 | 1 | no | — |
| 60 | C2×D3×Q8 | — | 4 | 1 | no | — |
| 61 | C22×C4×D3 | — | 4 | 1 | no | — |
| 62 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×GL(2,𝔽3) | Q8 | 1 | 4 | yes | complemented |
| 64 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×GL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×C22⋊Q8 | — | 4 | 1 | no | — |
| 67 | #946 | — | 4 | 1 | no | — |
| 68 | #924 | — | 4 | 1 | no | — |
| 69 | #897 | — | 4 | 1 | no | — |
| 70 | #896 | — | 4 | 2 | no | — |
| 71 | D3×C4⋊C4 | — | 4 | 1 | no | — |
| 72 | D3×C4⋊C4 | — | 4 | 2 | no | — |
| 73 | D3×C22⋊C4 | — | 4 | 2 | no | — |
| 74 | #878 | — | 4 | 2 | no | — |
| 75 | C4×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 76 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 77 | C4×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 78 | C4×SL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 79 | #859 | C23 | 1 | 1 | yes | characteristic |
| 80 | #859 | C23 | 1 | 2 | yes | — |
| 81 | #859 | C23 | 1 | 2 | yes | — |
| 82 | #859 | C23 | 1 | 1 | yes | characteristic |
| 83 | C22×SD16 | — | 3 | 1 | no | — |
| 84 | Q82 | — | 3 | 1 | no | — |
| 85 | Q82 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | #557 | — | 3 | 2 | no | — |
| 87 | #557 | — | 3 | 1 | no | — |
| 88 | #557 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 89 | #557 | C2×D3 | 1 | 2 | yes | complemented |
| 90 | #554 | — | 3 | 1 | no | — |
| 91 | #554 | — | 3 | 1 | no | — |
| 92 | #554 | — | 3 | 2 | no | — |
| 93 | #554 | — | 3 | 2 | no | — |
| 94 | #554 | — | 6 | 2 | no | — |
| 95 | #554 | — | 6 | 1 | no | — |
| 96 | D4×Q8 | — | 3 | 1 | no | — |
| 97 | D4×Q8 | — | 3 | 1 | no | — |
| 98 | D4×Q8 | — | 6 | 1 | no | — |
| 99 | #544 | — | 3 | 2 | no | — |
| 100 | #544 | — | 3 | 2 | no | — |
| 101 | #543 | — | 6 | 2 | no | — |
| 102 | #533 | — | 3 | 1 | no | — |
| 103 | #533 | — | 3 | 1 | no | — |
| 104 | #533 | — | 3 | 1 | no | — |
| 105 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 106 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 107 | #519 | C2×D3 | 1 | 2 | yes | — |
| 108 | #518 | — | 3 | 2 | no | — |
| 109 | C2×C4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×D4 | — | 3 | 1 | no | — |
| 111 | #501 | — | 3 | 2 | no | — |
| 112 | #501 | — | 3 | 2 | no | — |
| 113 | #501 | — | 3 | 2 | no | — |
| 114 | #501 | — | 3 | 2 | no | — |
| 115 | #500 | — | 3 | 1 | no | — |
| 116 | #500 | — | 3 | 1 | no | — |
| 117 | #499 | — | 3 | 2 | no | — |
| 118 | #499 | — | 3 | 2 | no | — |
| 119 | #499 | — | 3 | 2 | no | — |
| 120 | #499 | — | 3 | 2 | no | — |
| 121 | #498 | — | 3 | 1 | no | — |
| 122 | #498 | — | 3 | 2 | no | — |
| 123 | #498 | — | 3 | 2 | no | — |
| 124 | #498 | — | 3 | 1 | no | — |
| 125 | #479 | — | 3 | 2 | no | — |
| 126 | #479 | — | 3 | 2 | no | — |
| 127 | #479 | — | 3 | 2 | no | — |
| 128 | #479 | — | 3 | 2 | no | — |
| 129 | #479 | — | 3 | 2 | no | — |
| 130 | #479 | — | 3 | 2 | no | — |
| 131 | #478 | — | 3 | 2 | no | — |
| 132 | #478 | — | 3 | 2 | no | — |
| 133 | #478 | — | 3 | 2 | no | — |
| 134 | #478 | — | 3 | 2 | no | — |
| 135 | #478 | — | 3 | 2 | no | — |
| 136 | #478 | — | 3 | 2 | no | — |
| 137 | #477 | — | 3 | 1 | no | — |
| 138 | #477 | — | 3 | 2 | no | — |
| 139 | #477 | — | 3 | 1 | no | — |
| 140 | #477 | — | 3 | 2 | no | — |
| 141 | #476 | — | 3 | 1 | no | — |
| 142 | #476 | — | 3 | 1 | no | — |
| 143 | #476 | — | 3 | 2 | no | — |
| 144 | #476 | — | 3 | 2 | no | — |
| 145 | #475 | — | 3 | 1 | no | — |
| 146 | #475 | — | 3 | 2 | no | — |
| 147 | #475 | — | 3 | 1 | no | — |
| 148 | #475 | — | 3 | 2 | no | — |
| 149 | #474 | — | 3 | 1 | no | — |
| 150 | #474 | — | 3 | 1 | no | — |
| 151 | #474 | — | 3 | 2 | no | — |
| 152 | #474 | — | 3 | 2 | no | — |
| 153 | #446 | — | 3 | 1 | no | — |
| 154 | #446 | — | 3 | 1 | no | — |
| 155 | #446 | — | 3 | 2 | no | — |
| 156 | C8×Q8 | — | 3 | 1 | no | — |
| 157 | C8×Q8 | — | 3 | 1 | no | — |
| 158 | C8×Q8 | — | 3 | 2 | no | — |
| 159 | #440 | — | 3 | 2 | no | — |
| 160 | #440 | — | 3 | 2 | no | — |
| 161 | #440 | — | 3 | 2 | no | — |
| 162 | #440 | — | 3 | 2 | no | — |
| 163 | C4×SD16 | — | 3 | 1 | no | — |
| 164 | C4×SD16 | — | 3 | 2 | no | — |
| 165 | C4×SD16 | — | 3 | 1 | no | — |
| 166 | C4×SD16 | — | 3 | 2 | no | — |
| 167 | C4×SD16 | — | 3 | 1 | no | — |
| 168 | C4×SD16 | — | 3 | 1 | no | — |
| 169 | C4×SD16 | — | 3 | 1 | no | — |
| 170 | C4×SD16 | — | 3 | 2 | no | — |
| 171 | C4×SD16 | — | 3 | 1 | no | — |
| 172 | C4×SD16 | — | 3 | 2 | no | — |
| 173 | C4×SD16 | — | 3 | 1 | no | — |
| 174 | C4×SD16 | — | 3 | 1 | no | — |
| 175 | #428 | — | 3 | 2 | no | — |
| 176 | #428 | — | 3 | 2 | no | — |
| 177 | #427 | — | 3 | 2 | no | — |
| 178 | #427 | — | 3 | 2 | no | — |
| 179 | C2×#106 | — | 3 | 1 | no | — |
| 180 | #424 | — | 3 | 2 | no | — |
| 181 | #423 | — | 3 | 1 | no | — |
| 182 | #419 | — | 3 | 2 | no | — |
| 183 | #418 | — | 3 | 2 | no | — |
| 184 | C2×#103 | — | 3 | 1 | no | — |
| 185 | C2×#102 | — | 3 | 1 | no | — |
| 186 | #405 | — | 3 | 2 | no | — |
| 187 | C2×C4×C8 | — | 3 | 1 | no | — |
| 188 | C23×D3 | — | 4 | 1 | no | — |
| 189 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 190 | C22×C3×C4 | — | 4 | 1 | no | — |
| 191 | C22×Dic3 | — | 4 | 1 | no | — |
| 192 | D3×Q8 | — | 8 | 4 | no | — |
| 193 | C2×C4×D3 | — | 4 | 1 | no | — |
| 194 | C2×C4×D3 | — | 4 | 2 | no | — |
| 195 | C2×C4×D3 | — | 4 | 2 | no | — |
| 196 | C2×C4×D3 | — | 4 | 1 | no | — |
| 197 | C2×C4×D3 | — | 4 | 1 | no | — |
| 198 | C2×C4×D3 | — | 4 | 1 | no | — |
| 199 | C2×C4×D3 | — | 8 | 4 | no | — |
| 200 | C2×Dic6 | — | 4 | 2 | no | — |
| 201 | C2×Dic6 | — | 4 | 1 | no | — |
| 202 | C2×SL(2,𝔽3) | C2×Q8 | 1 | 2 | yes | complemented |
| 203 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 204 | GL(2,𝔽3) | C2×Q8 | 1 | 2 | yes | complemented |
| 205 | GL(2,𝔽3) | C2×Q8 | 1 | 2 | yes | complemented |
| 206 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 207 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 208 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 209 | #217 | — | 4 | 2 | no | — |
| 210 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 211 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 212 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 213 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 214 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 215 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 216 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 217 | C22×Q8 | — | 6 | 1 | no | — |
| 218 | C22×Q8 | — | 6 | 1 | no | — |
| 219 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | C22×D4 | — | 3 | 1 | no | — |
| 221 | C23×C4 | — | 6 | 1 | no | — |
| 222 | C2×SD16 | — | 3 | 4 | no | — |
| 223 | C2×SD16 | — | 3 | 1 | no | — |
| 224 | C2×SD16 | — | 3 | 1 | no | — |
| 225 | C2×SD16 | — | 3 | 4 | no | — |
| 226 | C2×SD16 | — | 3 | 1 | no | — |
| 227 | C2×SD16 | — | 3 | 1 | no | — |
| 228 | C2×M16 | — | 3 | 2 | no | — |
| 229 | C22×C8 | — | 3 | 1 | no | — |
| 230 | C22×C8 | — | 3 | 1 | no | — |
| 231 | C4⋊Q8 | — | 3 | 1 | no | — |
| 232 | C4⋊Q8 | — | 3 | 1 | no | — |
| 233 | C4⋊Q8 | — | 3 | 1 | no | — |
| 234 | C4⋊Q8 | — | 3 | 2 | no | — |
| 235 | C4⋊Q8 | — | 3 | 1 | no | — |
| 236 | C4⋊Q8 | — | 3 | 2 | no | — |
| 237 | C4⋊Q8 | — | 3 | 1 | no | — |
| 238 | C4⋊Q8 | — | 3 | 1 | no | — |
| 239 | C4⋊Q8 | — | 3 | 2 | no | — |
| 240 | C4⋊Q8 | — | 3 | 2 | no | — |
| 241 | C4⋊Q8 | — | 6 | 2 | no | — |
| 242 | C4⋊Q8 | — | 6 | 2 | no | — |
| 243 | #125 | — | 3 | 2 | no | — |
| 244 | #125 | — | 3 | 2 | no | — |
| 245 | #125 | — | 3 | 2 | no | — |
| 246 | #125 | — | 3 | 2 | no | — |
| 247 | #125 | — | 3 | 2 | no | — |
| 248 | #125 | — | 3 | 2 | no | — |
| 249 | #125 | — | 3 | 2 | no | — |
| 250 | #125 | — | 6 | 2 | no | — |
| 251 | #125 | — | 6 | 2 | no | — |
| 252 | C22⋊Q8 | — | 3 | 1 | no | — |
| 253 | C22⋊Q8 | — | 3 | 2 | no | — |
| 254 | C22⋊Q8 | — | 6 | 1 | no | — |
| 255 | C22⋊Q8 | — | 6 | 2 | no | — |
| 256 | C22⋊Q8 | — | 6 | 1 | no | — |
| 257 | C22⋊Q8 | — | 6 | 2 | no | — |
| 258 | C22⋊Q8 | — | 6 | 2 | no | — |
| 259 | C22⋊Q8 | — | 6 | 2 | no | — |
| 260 | C22⋊Q8 | — | 6 | 2 | no | — |
| 261 | C22⋊Q8 | — | 6 | 2 | no | — |
| 262 | C22⋊Q8 | — | 6 | 2 | no | — |
| 263 | C22⋊Q8 | — | 6 | 2 | no | — |
| 264 | C22⋊Q8 | — | 6 | 1 | no | — |
| 265 | C22⋊Q8 | — | 6 | 1 | no | — |
| 266 | C22⋊Q8 | — | 6 | 2 | no | — |
| 267 | C22⋊Q8 | — | 6 | 2 | no | — |
| 268 | C22⋊Q8 | — | 6 | 1 | no | — |
| 269 | C22⋊Q8 | — | 6 | 1 | no | — |
| 270 | C22⋊Q8 | — | 6 | 1 | no | — |
| 271 | C22⋊Q8 | — | 6 | 2 | no | — |
| 272 | C22⋊Q8 | — | 6 | 2 | no | — |
| 273 | C22⋊Q8 | S4 | 1 | 1 | yes | characteristic |
| 274 | C4×Q8 | — | 3 | 1 | no | — |
| 275 | C4×Q8 | — | 3 | 1 | no | — |
| 276 | C4×Q8 | — | 3 | 2 | no | — |
| 277 | C4×Q8 | — | 3 | 1 | no | — |
| 278 | C4×Q8 | — | 3 | 1 | no | — |
| 279 | C4×Q8 | — | 3 | 2 | no | — |
| 280 | C4×Q8 | — | 3 | 2 | no | — |
| 281 | C4×Q8 | — | 6 | 1 | no | — |
| 282 | C4×Q8 | — | 6 | 1 | no | — |
| 283 | C4×Q8 | — | 6 | 1 | no | — |
| 284 | C4×Q8 | — | 6 | 1 | no | — |
| 285 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 286 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 287 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 288 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 289 | C4×D4 | — | 3 | 1 | no | — |
| 290 | C4×D4 | — | 3 | 1 | no | — |
| 291 | C4×D4 | — | 3 | 1 | no | — |
| 292 | C4×D4 | — | 3 | 1 | no | — |
| 293 | C4×D4 | — | 3 | 2 | no | — |
| 294 | C4×D4 | — | 3 | 2 | no | — |
| 295 | C4×D4 | — | 3 | 2 | no | — |
| 296 | C4×D4 | — | 3 | 2 | no | — |
| 297 | C4×D4 | — | 6 | 1 | no | — |
| 298 | C4×D4 | — | 6 | 1 | no | — |
| 299 | C4×D4 | — | 6 | 2 | no | — |
| 300 | C4×D4 | — | 6 | 2 | no | — |
| 301 | #117 | — | 3 | 2 | no | — |
| 302 | #117 | — | 3 | 2 | no | — |
| 303 | #117 | — | 3 | 2 | no | — |
| 304 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 305 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 306 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 307 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 308 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 309 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 310 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 311 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 312 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 313 | C2×C42 | — | 3 | 1 | no | — |
| 314 | #107 | — | 3 | 2 | no | — |
| 315 | #107 | — | 3 | 2 | no | — |
| 316 | #107 | — | 3 | 2 | no | — |
| 317 | #107 | — | 3 | 2 | no | — |
| 318 | #107 | — | 3 | 2 | no | — |
| 319 | #107 | — | 3 | 2 | no | — |
| 320 | #107 | — | 3 | 2 | no | — |
| 321 | #107 | — | 3 | 2 | no | — |
| 322 | #106 | — | 3 | 1 | no | — |
| 323 | #106 | — | 3 | 1 | no | — |
| 324 | #106 | — | 3 | 1 | no | — |
| 325 | #106 | — | 3 | 1 | no | — |
| 326 | #106 | — | 3 | 2 | no | — |
| 327 | #106 | — | 3 | 2 | no | — |
| 328 | #106 | — | 3 | 2 | no | — |
| 329 | #106 | — | 3 | 2 | no | — |
| 330 | #106 | — | 3 | 2 | no | — |
| 331 | #106 | — | 3 | 2 | no | — |
| 332 | #106 | — | 3 | 2 | no | — |
| 333 | #106 | — | 3 | 2 | no | — |
| 334 | C4⋊C8 | — | 3 | 1 | no | — |
| 335 | C4⋊C8 | — | 3 | 1 | no | — |
| 336 | C4⋊C8 | — | 3 | 2 | no | — |
| 337 | C4⋊C8 | — | 3 | 2 | no | — |
| 338 | C4⋊C8 | — | 3 | 2 | no | — |
| 339 | C4⋊C8 | — | 3 | 2 | no | — |
| 340 | C4⋊C8 | — | 3 | 2 | no | — |
| 341 | #103 | — | 3 | 1 | no | — |
| 342 | #103 | — | 3 | 1 | no | — |
| 343 | #103 | — | 3 | 2 | no | — |
| 344 | #103 | — | 3 | 2 | no | — |
| 345 | #103 | — | 3 | 1 | no | — |
| 346 | #103 | — | 3 | 1 | no | — |
| 347 | #103 | — | 3 | 2 | no | — |
| 348 | #103 | — | 3 | 2 | no | — |
| 349 | #102 | — | 3 | 1 | no | — |
| 350 | #102 | — | 3 | 1 | no | — |
| 351 | #102 | — | 3 | 1 | no | — |
| 352 | #102 | — | 3 | 1 | no | — |
| 353 | #102 | — | 3 | 2 | no | — |
| 354 | #102 | — | 3 | 2 | no | — |
| 355 | #102 | — | 3 | 2 | no | — |
| 356 | #102 | — | 3 | 2 | no | — |
| 357 | #97 | — | 3 | 2 | no | — |
| 358 | #97 | — | 3 | 2 | no | — |
| 359 | C4×C8 | — | 3 | 1 | no | — |
| 360 | C4×C8 | — | 3 | 1 | no | — |
| 361 | C4×C8 | — | 3 | 1 | no | — |
| 362 | C4×C8 | — | 3 | 1 | no | — |
| 363 | C4×C8 | — | 3 | 2 | no | — |
| 364 | C4×C8 | — | 3 | 2 | no | — |
| 365 | C23×C3 | — | 4 | 1 | no | — |
| 366 | C22×D3 | — | 4 | 1 | no | — |
| 367 | C22×D3 | — | 4 | 1 | no | — |
| 368 | C22×D3 | — | 4 | 4 | no | — |
| 369 | C22×D3 | — | 8 | 2 | no | — |
| 370 | C22×D3 | — | 8 | 2 | no | — |
| 371 | C3×Q8 | — | 8 | 2 | no | — |
| 372 | C2×C3×C4 | — | 4 | 1 | no | — |
| 373 | C2×C3×C4 | — | 4 | 1 | no | — |
| 374 | C2×C3×C4 | — | 4 | 2 | no | — |
| 375 | C2×C3×C4 | — | 4 | 2 | no | — |
| 376 | C2×C3×C4 | — | 8 | 2 | no | — |
| 377 | C2×Dic3 | — | 4 | 1 | no | — |
| 378 | C2×Dic3 | — | 4 | 2 | no | — |
| 379 | C2×Dic3 | — | 4 | 1 | no | — |
| 380 | C2×Dic3 | — | 4 | 2 | no | — |
| 381 | C2×Dic3 | — | 8 | 2 | no | — |
| 382 | C4×D3 | — | 4 | 4 | no | — |
| 383 | C4×D3 | — | 8 | 2 | no | — |
| 384 | C4×D3 | — | 8 | 2 | no | — |
| 385 | C4×D3 | — | 8 | 4 | no | — |
| 386 | C4×D3 | — | 8 | 2 | no | — |
| 387 | C4×D3 | — | 8 | 4 | no | — |
| 388 | Dic6 | — | 8 | 2 | no | — |
| 389 | Dic6 | — | 8 | 4 | no | — |
| 390 | SL(2,𝔽3) | C22×Q8 | 1 | 1 | yes | characteristic |
| 391 | C24 | — | 6 | 1 | no | — |
| 392 | C2×Q8 | — | 3 | 1 | no | — |
| 393 | C2×Q8 | — | 3 | 2 | no | — |
| 394 | C2×Q8 | — | 3 | 1 | no | — |
| 395 | C2×Q8 | — | 3 | 2 | no | — |
| 396 | C2×Q8 | — | 6 | 1 | no | — |
| 397 | C2×Q8 | — | 6 | 1 | no | — |
| 398 | C2×Q8 | — | 6 | 2 | no | — |
| 399 | C2×Q8 | — | 6 | 1 | no | — |
| 400 | C2×Q8 | — | 6 | 2 | no | — |
| 401 | C2×Q8 | — | 24 | 2 | no | — |
| 402 | C2×Q8 | — | 24 | 2 | no | — |
| 403 | C2×Q8 | D3×Q8 | 1 | 2 | yes | complemented |
| 404 | C2×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 405 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 406 | C2×D4 | — | 3 | 1 | no | — |
| 407 | C2×D4 | — | 3 | 1 | no | — |
| 408 | C2×D4 | — | 3 | 4 | no | — |
| 409 | C2×D4 | — | 6 | 1 | no | — |
| 410 | C2×D4 | — | 6 | 2 | no | — |
| 411 | C22×C4 | — | 3 | 1 | no | — |
| 412 | C22×C4 | — | 3 | 1 | no | — |
| 413 | C22×C4 | — | 6 | 2 | no | — |
| 414 | C22×C4 | — | 6 | 2 | no | — |
| 415 | C22×C4 | — | 6 | 1 | no | — |
| 416 | C22×C4 | — | 6 | 1 | no | — |
| 417 | C22×C4 | — | 6 | 1 | no | — |
| 418 | C22×C4 | — | 6 | 2 | no | — |
| 419 | C22×C4 | — | 6 | 2 | no | — |
| 420 | C22×C4 | — | 6 | 1 | no | — |
| 421 | C22×C4 | — | 6 | 1 | no | — |
| 422 | C22×C4 | — | 24 | 2 | no | — |
| 423 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 424 | SD16 | — | 3 | 4 | no | — |
| 425 | SD16 | — | 3 | 4 | no | — |
| 426 | SD16 | — | 3 | 2 | no | — |
| 427 | SD16 | — | 3 | 2 | no | — |
| 428 | SD16 | — | 3 | 2 | no | — |
| 429 | SD16 | — | 3 | 2 | no | — |
| 430 | M16 | — | 6 | 4 | no | — |
| 431 | C2×C8 | — | 3 | 1 | no | — |
| 432 | C2×C8 | — | 3 | 1 | no | — |
| 433 | C2×C8 | — | 3 | 4 | no | — |
| 434 | C2×C8 | — | 3 | 1 | no | — |
| 435 | C2×C8 | — | 3 | 1 | no | — |
| 436 | C2×C8 | — | 3 | 2 | no | — |
| 437 | C2×C8 | — | 3 | 2 | no | — |
| 438 | C2×C8 | — | 6 | 2 | no | — |
| 439 | C4⋊C4 | — | 3 | 1 | no | — |
| 440 | C4⋊C4 | — | 3 | 1 | no | — |
| 441 | C4⋊C4 | — | 3 | 2 | no | — |
| 442 | C4⋊C4 | — | 3 | 2 | no | — |
| 443 | C4⋊C4 | — | 3 | 2 | no | — |
| 444 | C4⋊C4 | — | 3 | 1 | no | — |
| 445 | C4⋊C4 | — | 3 | 2 | no | — |
| 446 | C4⋊C4 | — | 3 | 2 | no | — |
| 447 | C4⋊C4 | — | 3 | 2 | no | — |
| 448 | C4⋊C4 | — | 3 | 2 | no | — |
| 449 | C4⋊C4 | — | 3 | 2 | no | — |
| 450 | C4⋊C4 | — | 3 | 1 | no | — |
| 451 | C4⋊C4 | — | 3 | 1 | no | — |
| 452 | C4⋊C4 | — | 3 | 2 | no | — |
| 453 | C4⋊C4 | — | 3 | 2 | no | — |
| 454 | C4⋊C4 | — | 6 | 1 | no | — |
| 455 | C4⋊C4 | — | 6 | 1 | no | — |
| 456 | C4⋊C4 | — | 6 | 2 | no | — |
| 457 | C4⋊C4 | — | 6 | 1 | no | — |
| 458 | C4⋊C4 | — | 6 | 2 | no | — |
| 459 | C4⋊C4 | — | 6 | 2 | no | — |
| 460 | C4⋊C4 | — | 6 | 2 | no | — |
| 461 | C4⋊C4 | — | 6 | 2 | no | — |
| 462 | C4⋊C4 | — | 6 | 1 | no | — |
| 463 | C4⋊C4 | — | 6 | 2 | no | — |
| 464 | C4⋊C4 | — | 6 | 1 | no | — |
| 465 | C4⋊C4 | — | 6 | 2 | no | — |
| 466 | C4⋊C4 | — | 6 | 2 | no | — |
| 467 | C4⋊C4 | — | 6 | 2 | no | — |
| 468 | C4⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 469 | C4⋊C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 470 | C22⋊C4 | — | 3 | 2 | no | — |
| 471 | C22⋊C4 | — | 6 | 1 | no | — |
| 472 | C22⋊C4 | — | 6 | 1 | no | — |
| 473 | C22⋊C4 | — | 6 | 1 | no | — |
| 474 | C22⋊C4 | — | 6 | 1 | no | — |
| 475 | C22⋊C4 | — | 6 | 2 | no | — |
| 476 | C22⋊C4 | — | 6 | 2 | no | — |
| 477 | C22⋊C4 | — | 6 | 2 | no | — |
| 478 | C22⋊C4 | — | 6 | 2 | no | — |
| 479 | C22⋊C4 | — | 6 | 2 | no | — |
| 480 | C22⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 481 | C42 | — | 3 | 1 | no | — |
| 482 | C42 | — | 3 | 1 | no | — |
| 483 | C42 | — | 3 | 2 | no | — |
| 484 | C42 | — | 3 | 2 | no | — |
| 485 | C42 | — | 3 | 1 | no | — |
| 486 | C42 | — | 3 | 1 | no | — |
| 487 | C42 | — | 6 | 2 | no | — |
| 488 | C42 | — | 6 | 2 | no | — |
| 489 | C22×C3 | — | 4 | 2 | no | — |
| 490 | C22×C3 | — | 4 | 1 | no | — |
| 491 | C22×C3 | — | 8 | 1 | no | — |
| 492 | C22×C3 | — | 8 | 1 | no | — |
| 493 | C2×D3 | — | 4 | 2 | no | — |
| 494 | C2×D3 | — | 4 | 2 | no | — |
| 495 | C2×D3 | — | 4 | 2 | no | — |
| 496 | C2×D3 | — | 4 | 2 | no | — |
| 497 | C2×D3 | — | 8 | 1 | no | — |
| 498 | C2×D3 | — | 8 | 1 | no | — |
| 499 | C2×D3 | — | 8 | 8 | no | — |
| 500 | C3×C4 | — | 4 | 2 | no | — |
| 501 | C3×C4 | — | 8 | 2 | no | — |
| 502 | C3×C4 | — | 8 | 1 | no | — |
| 503 | C3×C4 | — | 8 | 2 | no | — |
| 504 | Dic3 | — | 4 | 2 | no | — |
| 505 | Dic3 | — | 8 | 2 | no | — |
| 506 | Dic3 | — | 8 | 1 | no | — |
| 507 | Dic3 | — | 8 | 2 | no | — |
| 508 | C23 | — | 6 | 1 | no | — |
| 509 | C23 | — | 6 | 1 | no | — |
| 510 | C23 | — | 6 | 4 | no | — |
| 511 | C23 | — | 24 | 1 | no | — |
| 512 | C23 | — | 24 | 1 | no | — |
| 513 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 514 | Q8 | — | 2 | 2 | no | — |
| 515 | Q8 | — | 3 | 2 | no | — |
| 516 | Q8 | — | 3 | 1 | no | — |
| 517 | Q8 | — | 6 | 1 | no | — |
| 518 | Q8 | — | 6 | 2 | no | — |
| 519 | Q8 | — | 12 | 2 | no | — |
| 520 | Q8 | — | 12 | 2 | no | — |
| 521 | Q8 | — | 24 | 2 | no | — |
| 522 | Q8 | — | 24 | 1 | no | — |
| 523 | Q8 | — | 24 | 1 | no | — |
| 524 | Q8 | — | 24 | 2 | no | — |
| 525 | Q8 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 526 | D4 | — | 3 | 2 | no | — |
| 527 | D4 | — | 3 | 2 | no | — |
| 528 | D4 | — | 6 | 1 | no | — |
| 529 | D4 | — | 6 | 1 | no | — |
| 530 | D4 | — | 6 | 4 | no | — |
| 531 | C2×C4 | — | 2 | 2 | no | — |
| 532 | C2×C4 | — | 3 | 2 | no | — |
| 533 | C2×C4 | — | 3 | 2 | no | — |
| 534 | C2×C4 | — | 3 | 1 | no | — |
| 535 | C2×C4 | — | 3 | 1 | no | — |
| 536 | C2×C4 | — | 3 | 1 | no | — |
| 537 | C2×C4 | — | 3 | 1 | no | — |
| 538 | C2×C4 | — | 3 | 2 | no | — |
| 539 | C2×C4 | — | 3 | 2 | no | — |
| 540 | C2×C4 | — | 6 | 2 | no | — |
| 541 | C2×C4 | — | 6 | 2 | no | — |
| 542 | C2×C4 | — | 6 | 1 | no | — |
| 543 | C2×C4 | — | 6 | 1 | no | — |
| 544 | C2×C4 | — | 12 | 1 | no | — |
| 545 | C2×C4 | — | 12 | 2 | no | — |
| 546 | C2×C4 | — | 12 | 2 | no | — |
| 547 | C2×C4 | — | 24 | 1 | no | — |
| 548 | C2×C4 | — | 24 | 1 | no | — |
| 549 | C2×C4 | — | 24 | 2 | no | — |
| 550 | C2×C4 | — | 24 | 2 | no | — |
| 551 | C2×C4 | — | 24 | 2 | no | — |
| 552 | C2×C4 | — | 24 | 2 | no | — |
| 553 | C2×C4 | — | 24 | 1 | no | — |
| 554 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 556 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 557 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 558 | C8 | — | 3 | 2 | no | — |
| 559 | C8 | — | 3 | 2 | no | — |
| 560 | C8 | — | 6 | 1 | no | — |
| 561 | C8 | — | 6 | 1 | no | — |
| 562 | C8 | — | 6 | 2 | no | — |
| 563 | C8 | — | 6 | 2 | no | — |
| 564 | C2×C3 | — | 4 | 1 | no | — |
| 565 | C2×C3 | — | 4 | 1 | no | — |
| 566 | C2×C3 | — | 4 | 1 | no | — |
| 567 | C2×C3 | — | 8 | 2 | no | — |
| 568 | D3 | — | 4 | 4 | no | — |
| 569 | D3 | — | 8 | 2 | no | — |
| 570 | C22 | — | 2 | 1 | no | — |
| 571 | C22 | — | 2 | 1 | no | — |
| 572 | C22 | — | 6 | 2 | no | — |
| 573 | C22 | — | 6 | 2 | no | — |
| 574 | C22 | — | 12 | 1 | no | — |
| 575 | C22 | — | 12 | 1 | no | — |
| 576 | C22 | — | 12 | 1 | no | — |
| 577 | C22 | — | 12 | 1 | no | — |
| 578 | C22 | — | 24 | 4 | no | — |
| 579 | C22 | Q8×S4 | 1 | 2 | yes | — |
| 580 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 581 | C4 | — | 2 | 1 | no | — |
| 582 | C4 | — | 2 | 2 | no | — |
| 583 | C4 | — | 2 | 2 | no | — |
| 584 | C4 | — | 3 | 1 | no | — |
| 585 | C4 | — | 3 | 1 | no | — |
| 586 | C4 | — | 3 | 2 | no | — |
| 587 | C4 | — | 6 | 2 | no | — |
| 588 | C4 | — | 6 | 1 | no | — |
| 589 | C4 | — | 6 | 1 | no | — |
| 590 | C4 | — | 6 | 2 | no | — |
| 591 | C4 | — | 12 | 1 | no | — |
| 592 | C4 | — | 12 | 1 | no | — |
| 593 | C4 | — | 12 | 2 | no | — |
| 594 | C4 | — | 12 | 2 | no | — |
| 595 | C4 | #5926 | 1 | 2 | yes | — |
| 596 | C3 | — | 4 | 1 | no | Sylow |
| 597 | C2 | — | 2 | 2 | no | — |
| 598 | C2 | — | 12 | 2 | no | — |
| 599 | C2 | — | 12 | 2 | no | — |
| 600 | C2 | C2×Q8×S4 | 1 | 1 | yes | characteristic |
| 601 | C2 | C2×#5926 | 1 | 1 | yes | characteristic |
| 602 | C2 | #87497 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3502⋊C3 | C2 | semidirect |
| 2. #85431 | C2 | semidirect |
| 3. Q8×GL(2,𝔽3) | C2 | semidirect |
| 4. #85424 | C2 | semidirect |
| 5. #85423 | C2 | semidirect |
| 6. #85418 | C2 | semidirect |
| 7. #85418 | C2 | semidirect |
| 9. #85351 | C2 | semidirect |
| 11. #85318 | C2 | semidirect |
| 15. Q8×SL(2,𝔽3) | C22 | semidirect |
| 16. #557⋊C3 | C22 | semidirect |
| 17. #557⋊C3 | C22 | semidirect |
| 30. #5391 | C22 | semidirect |
| 31. #5391 | C22 | semidirect |
| 32. #5389 | C22 | semidirect |
| 33. #5389 | C22 | semidirect |
| 34. #5389 | C22 | semidirect |
| 35. #5386 | C22 | semidirect |
| 36. #5386 | C22 | semidirect |
| 37. #3502 | D3 | semidirect |
| 63. C2×GL(2,𝔽3) | Q8 | semidirect |
| 85. Q82 | C2×D3 | semidirect |
| 88. #557 | C2×D3 | semidirect |
| 89. #557 | C2×D3 | semidirect |
| 202. C2×SL(2,𝔽3) | C2×Q8 | semidirect |
| 204. GL(2,𝔽3) | C2×Q8 | semidirect |
| 205. GL(2,𝔽3) | C2×Q8 | semidirect |
| 403. C2×Q8 | D3×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3502⋊C3 | 2 |
| #85431 | 2 |
| Q8×GL(2,𝔽3) | 2 |
| #85424 | 2 |
| #85423 | 2 |
| #85418 | 2 |
| #85353 | 2 |
| #85351 | 2 |
| C2×C4×GL(2,𝔽3) | 2 |
| #85318 | 2 |
| #61371 | 3 |
| D3×C22⋊Q8 | 4 |