Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1491 conjugacy classes of subgroups.
The subgroup lattice has 603 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11876971 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #11876968 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11874466 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11874454 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11782902 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11782669 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11782663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11782584 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11782414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11773693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C9×#1721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10784427 | — | 3 | 1 | no | maximal |
| 13 | C2×#63476 | — | 2 | 2 | no | — |
| 14 | C2×#63473 | — | 2 | 4 | no | — |
| 15 | #10589827 | C22 | 1 | 1 | yes | characteristic |
| 16 | #10589818 | C22 | 1 | 2 | yes | — |
| 17 | D9×#127 | C22 | 1 | 1 | yes | characteristic |
| 18 | C9×#493 | C22 | 1 | 2 | yes | — |
| 19 | C9×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C9×#492 | C22 | 1 | 1 | yes | characteristic |
| 21 | C9×#486 | C22 | 1 | 2 | yes | complemented |
| 22 | #10588856 | — | 2 | 2 | no | — |
| 23 | #10588839 | — | 2 | 2 | no | — |
| 24 | #10588834 | — | 2 | 4 | no | — |
| 25 | #10588832 | — | 2 | 2 | no | — |
| 26 | #10588770 | C22 | 1 | 1 | yes | characteristic |
| 27 | #10588760 | C22 | 1 | 2 | yes | complemented |
| 28 | #10588755 | C22 | 1 | 2 | yes | — |
| 29 | #10588755 | C22 | 1 | 1 | yes | characteristic |
| 30 | #10588755 | C22 | 1 | 2 | yes | complemented |
| 31 | #10588753 | C22 | 1 | 2 | yes | — |
| 32 | #10588750 | C22 | 1 | 2 | yes | complemented |
| 33 | #10588465 | — | 2 | 4 | no | — |
| 34 | #10588462 | — | 2 | 4 | no | — |
| 35 | #10588377 | C22 | 1 | 1 | yes | characteristic |
| 36 | #10588376 | C22 | 1 | 2 | yes | complemented |
| 37 | #10588375 | C22 | 1 | 2 | yes | — |
| 38 | C4×#3663 | C22 | 1 | 1 | yes | characteristic |
| 39 | C4×#3663 | C22 | 1 | 2 | yes | — |
| 40 | #10588360 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C9×#322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #10588131 | C22 | 1 | 2 | yes | complemented |
| 43 | C8×C9⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #81783 | — | 3 | 2 | no | — |
| 45 | #81777 | — | 3 | 1 | no | — |
| 46 | #81761 | — | 3 | 1 | no | — |
| 47 | #81560 | — | 3 | 2 | no | — |
| 48 | C3×#1721 | D3 | 1 | 1 | yes | characteristic |
| 49 | #71279 | — | 3 | 2 | no | — |
| 50 | #71276 | — | 3 | 1 | no | — |
| 51 | #71254 | — | 3 | 1 | no | — |
| 52 | #71185 | — | 3 | 2 | no | — |
| 53 | #68091 | — | 3 | 1 | no | — |
| 54 | #68075 | — | 3 | 1 | no | — |
| 55 | C2×#3701 | — | 2 | 1 | no | — |
| 56 | C2×#3699 | — | 2 | 2 | no | — |
| 57 | C2×D4×D9 | — | 2 | 2 | no | — |
| 58 | C2×D4×D9 | — | 2 | 1 | no | — |
| 59 | C2×C9×SD16 | — | 2 | 2 | no | — |
| 60 | C2×C9×D8 | — | 2 | 4 | no | — |
| 61 | C2×C9×D8 | — | 2 | 2 | no | — |
| 62 | C9×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C9×#127 | C23 | 1 | 2 | yes | — |
| 64 | C9×#127 | C23 | 1 | 1 | yes | characteristic |
| 65 | #63509 | — | 2 | 1 | no | — |
| 66 | C2×#3675 | — | 2 | 2 | no | — |
| 67 | #63502 | — | 2 | 2 | no | — |
| 68 | #63502 | — | 2 | 1 | no | — |
| 69 | #63500 | — | 2 | 2 | no | — |
| 70 | #63500 | — | 2 | 2 | no | — |
| 71 | #63498 | — | 2 | 2 | no | — |
| 72 | D4×Dic9 | — | 2 | 2 | no | — |
| 73 | D4×Dic9 | — | 2 | 2 | no | — |
| 74 | C2×#3673 | — | 2 | 4 | no | — |
| 75 | C2×#3673 | — | 2 | 4 | no | — |
| 76 | C2×#3673 | — | 2 | 2 | no | — |
| 77 | C2×#3672 | — | 2 | 4 | no | — |
| 78 | #63476 | — | 4 | 8 | no | — |
| 79 | #63473 | — | 4 | 16 | no | — |
| 80 | C2×D72 | — | 2 | 2 | no | — |
| 81 | C2×#3664 | — | 2 | 4 | no | — |
| 82 | C2×#3663 | D4 | 1 | 4 | yes | — |
| 83 | C2×#3663 | D4 | 1 | 2 | yes | — |
| 84 | #63457 | — | 2 | 2 | no | — |
| 85 | #63455 | — | 2 | 2 | no | — |
| 86 | #63436 | C23 | 1 | 1 | yes | characteristic |
| 87 | #63436 | C23 | 1 | 1 | yes | characteristic |
| 88 | C42×D9 | C23 | 1 | 1 | yes | characteristic |
| 89 | #63431 | C23 | 1 | 2 | yes | — |
| 90 | C9×#102 | — | 2 | 4 | no | — |
| 91 | C4×C8×C9 | C23 | 1 | 2 | yes | — |
| 92 | C4×C8×C9 | C23 | 1 | 1 | yes | characteristic |
| 93 | #63392 | — | 2 | 4 | no | — |
| 94 | #63380 | — | 2 | 4 | no | — |
| 95 | #63377 | — | 2 | 2 | no | — |
| 96 | #63375 | D4 | 1 | 4 | yes | — |
| 97 | #63375 | D4 | 1 | 2 | yes | — |
| 98 | #63367 | — | 2 | 4 | no | — |
| 99 | C4×C9⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×C9⋊C8 | C23 | 1 | 2 | yes | — |
| 101 | #19745 | — | 9 | 1 | no | Sylow |
| 102 | C2×#914 | — | 6 | 2 | no | — |
| 103 | C2×#911 | — | 6 | 4 | no | — |
| 104 | #5725 | — | 3 | 1 | no | — |
| 105 | #5716 | — | 3 | 2 | no | — |
| 106 | D3×#127 | — | 3 | 1 | no | — |
| 107 | C3×#493 | C2×D3 | 1 | 2 | yes | — |
| 108 | C3×#493 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | C3×#492 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | C3×#486 | C2×D3 | 1 | 2 | yes | — |
| 111 | #5176 | — | 6 | 2 | no | — |
| 112 | #5159 | — | 6 | 2 | no | — |
| 113 | #5154 | — | 6 | 4 | no | — |
| 114 | #5152 | — | 6 | 2 | no | — |
| 115 | #5085 | — | 3 | 1 | no | — |
| 116 | #5080 | — | 3 | 2 | no | — |
| 117 | #5076 | — | 3 | 2 | no | — |
| 118 | #5073 | — | 3 | 2 | no | — |
| 119 | #5073 | — | 3 | 1 | no | — |
| 120 | #5073 | — | 3 | 2 | no | — |
| 121 | #5070 | — | 3 | 2 | no | — |
| 122 | #4785 | — | 6 | 4 | no | — |
| 123 | #4782 | — | 6 | 4 | no | — |
| 124 | #4695 | — | 3 | 1 | no | — |
| 125 | #4694 | — | 3 | 2 | no | — |
| 126 | #4693 | — | 3 | 2 | no | — |
| 127 | C4×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 128 | C4×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 129 | #4680 | — | 3 | 1 | no | — |
| 130 | C3×#322 | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | #4454 | — | 3 | 2 | no | — |
| 132 | C8×C3⋊C8 | — | 3 | 1 | no | — |
| 133 | C23×D9 | — | 4 | 1 | no | — |
| 134 | C2×Q8×C9 | — | 2 | 1 | no | — |
| 135 | C2×D4×C9 | — | 2 | 2 | no | — |
| 136 | C2×D4×C9 | — | 2 | 2 | no | — |
| 137 | C2×D4×C9 | — | 2 | 2 | no | — |
| 138 | C2×D4×C9 | — | 2 | 1 | no | — |
| 139 | C2×D4×C9 | — | 2 | 2 | no | — |
| 140 | C2×#611 | — | 4 | 2 | no | — |
| 141 | C2×#611 | — | 4 | 2 | no | — |
| 142 | C2×#611 | — | 4 | 1 | no | — |
| 143 | C22×Dic9 | — | 4 | 2 | no | — |
| 144 | #3701 | — | 4 | 4 | no | — |
| 145 | #3699 | — | 4 | 8 | no | — |
| 146 | D4×D9 | — | 4 | 8 | no | — |
| 147 | D4×D9 | — | 4 | 4 | no | — |
| 148 | C2×D36 | — | 2 | 2 | no | — |
| 149 | C2×D36 | — | 2 | 1 | no | — |
| 150 | C2×D36 | — | 2 | 2 | no | — |
| 151 | C2×D36 | — | 2 | 1 | no | — |
| 152 | C2×D36 | — | 4 | 1 | no | — |
| 153 | C2×C4×D9 | — | 4 | 1 | no | — |
| 154 | C2×C4×D9 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×D9 | C2×D4 | 1 | 2 | yes | — |
| 156 | C2×Dic18 | — | 2 | 2 | no | — |
| 157 | C9×SD16 | — | 4 | 4 | no | — |
| 158 | C9×D8 | — | 4 | 8 | no | — |
| 159 | C9×D8 | — | 4 | 4 | no | — |
| 160 | C2×C8×C9 | C2×D4 | 1 | 4 | yes | — |
| 161 | C2×C8×C9 | C2×D4 | 1 | 2 | yes | — |
| 162 | C9×C4⋊C4 | — | 2 | 2 | no | — |
| 163 | C42×C9 | C24 | 1 | 1 | yes | characteristic |
| 164 | #3676 | — | 4 | 2 | no | — |
| 165 | #3676 | — | 4 | 2 | no | — |
| 166 | #3675 | — | 4 | 4 | no | — |
| 167 | #3673 | — | 4 | 4 | no | — |
| 168 | #3673 | — | 4 | 8 | no | — |
| 169 | #3673 | — | 4 | 8 | no | — |
| 170 | #3672 | — | 4 | 8 | no | — |
| 171 | (C2×D9)⋊C4 | — | 4 | 2 | no | — |
| 172 | C4⋊Dic9 | — | 2 | 2 | no | — |
| 173 | C4⋊Dic9 | — | 2 | 2 | no | — |
| 174 | C4×Dic9 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C4×Dic9 | C2×D4 | 1 | 2 | yes | — |
| 176 | C2×C9⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 177 | C2×C9⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 178 | D72 | — | 4 | 4 | no | — |
| 179 | #3664 | — | 4 | 8 | no | — |
| 180 | #3663 | — | 2 | 4 | no | — |
| 181 | #3663 | — | 2 | 8 | no | — |
| 182 | #3184 | — | 9 | 1 | no | — |
| 183 | #3184 | — | 9 | 2 | no | — |
| 184 | #3151 | — | 9 | 2 | no | — |
| 185 | #3151 | — | 9 | 1 | no | — |
| 186 | #1721 | — | 9 | 2 | no | — |
| 187 | #1721 | D9 | 1 | 1 | yes | characteristic, complemented |
| 188 | #1715 | — | 9 | 2 | no | — |
| 189 | #1715 | — | 9 | 1 | no | — |
| 190 | #1712 | — | 9 | 1 | no | — |
| 191 | #1705 | — | 9 | 1 | no | — |
| 192 | #1455 | — | 9 | 1 | no | — |
| 193 | C2×#239 | — | 6 | 1 | no | — |
| 194 | C2×#237 | — | 6 | 2 | no | — |
| 195 | C2×D3×D4 | — | 6 | 2 | no | — |
| 196 | C2×D3×D4 | — | 6 | 1 | no | — |
| 197 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 198 | C2×C3×D8 | — | 2 | 2 | no | — |
| 199 | C2×C3×D8 | — | 2 | 4 | no | — |
| 200 | C3×C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | C3×#127 | C22×D3 | 1 | 1 | yes | characteristic |
| 202 | C3×#127 | C22×D3 | 1 | 2 | yes | — |
| 203 | #947 | — | 6 | 1 | no | — |
| 204 | C2×#215 | — | 6 | 2 | no | — |
| 205 | #940 | — | 6 | 2 | no | — |
| 206 | #940 | — | 6 | 1 | no | — |
| 207 | #938 | — | 6 | 2 | no | — |
| 208 | #938 | — | 6 | 2 | no | — |
| 209 | #936 | — | 6 | 2 | no | — |
| 210 | D4×Dic3 | — | 6 | 2 | no | — |
| 211 | D4×Dic3 | — | 6 | 2 | no | — |
| 212 | C2×#214 | — | 6 | 4 | no | — |
| 213 | C2×#213 | — | 6 | 4 | no | — |
| 214 | C2×#213 | — | 6 | 2 | no | — |
| 215 | C2×#213 | — | 6 | 4 | no | — |
| 216 | #914 | — | 12 | 8 | no | — |
| 217 | #911 | — | 12 | 16 | no | — |
| 218 | C2×D24 | — | 6 | 2 | no | — |
| 219 | C2×#204 | — | 6 | 4 | no | — |
| 220 | C2×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 221 | C2×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 222 | #895 | — | 6 | 2 | no | — |
| 223 | #893 | — | 6 | 2 | no | — |
| 224 | #874 | — | 3 | 1 | no | — |
| 225 | #874 | — | 3 | 1 | no | — |
| 226 | C42×D3 | — | 3 | 1 | no | — |
| 227 | #869 | — | 3 | 2 | no | — |
| 228 | C3×#102 | — | 2 | 4 | no | — |
| 229 | C3×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 230 | C3×C4×C8 | C22×D3 | 1 | 2 | yes | — |
| 231 | #832 | — | 6 | 4 | no | — |
| 232 | #821 | — | 6 | 4 | no | — |
| 233 | #817 | — | 6 | 2 | no | — |
| 234 | #815 | — | 3 | 2 | no | — |
| 235 | #815 | — | 3 | 4 | no | — |
| 236 | #808 | — | 6 | 4 | no | — |
| 237 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 238 | C4×C3⋊C8 | — | 3 | 1 | no | — |
| 239 | C23×C9 | — | 4 | 2 | no | — |
| 240 | C23×C9 | — | 4 | 1 | no | — |
| 241 | C22×D9 | — | 4 | 1 | no | — |
| 242 | C22×D9 | — | 4 | 1 | no | — |
| 243 | C22×D9 | — | 8 | 2 | no | — |
| 244 | C22×D9 | — | 8 | 4 | no | — |
| 245 | C22×D9 | #127 | 1 | 1 | yes | characteristic |
| 246 | Q8×C9 | — | 4 | 2 | no | — |
| 247 | D4×C9 | — | 4 | 4 | no | — |
| 248 | D4×C9 | — | 4 | 4 | no | — |
| 249 | D4×C9 | — | 4 | 2 | no | — |
| 250 | D4×C9 | — | 4 | 4 | no | — |
| 251 | D4×C9 | — | 4 | 4 | no | — |
| 252 | C2×C4×C9 | — | 4 | 1 | no | — |
| 253 | C2×C4×C9 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C9 | C22×D4 | 1 | 2 | yes | — |
| 255 | #611 | — | 8 | 2 | no | — |
| 256 | #611 | — | 8 | 4 | no | — |
| 257 | #611 | — | 8 | 4 | no | — |
| 258 | C2×Dic9 | — | 4 | 2 | no | — |
| 259 | C2×Dic9 | — | 8 | 4 | no | — |
| 260 | C2×Dic9 | #127 | 1 | 2 | yes | — |
| 261 | C2×Dic9 | #127 | 1 | 1 | yes | characteristic |
| 262 | D36 | — | 4 | 4 | no | — |
| 263 | D36 | — | 4 | 2 | no | — |
| 264 | D36 | — | 4 | 2 | no | — |
| 265 | D36 | — | 4 | 4 | no | — |
| 266 | D36 | — | 8 | 2 | no | — |
| 267 | C4×D9 | — | 2 | 4 | no | — |
| 268 | C4×D9 | — | 2 | 2 | no | — |
| 269 | C4×D9 | — | 8 | 2 | no | — |
| 270 | Dic18 | — | 4 | 4 | no | — |
| 271 | C8×C9 | — | 2 | 4 | no | — |
| 272 | C8×C9 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 273 | C9⋊C8 | — | 2 | 2 | no | — |
| 274 | C9⋊C8 | AGL(1,ℤ/8) | 1 | 8 | yes | complemented |
| 275 | C2×AGL(1,ℤ/8) | — | 18 | 4 | no | — |
| 276 | C2×AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 277 | #532 | — | 9 | 1 | no | — |
| 278 | #532 | — | 9 | 2 | no | — |
| 279 | C2×#127 | — | 9 | 1 | no | — |
| 280 | #498 | — | 9 | 2 | no | — |
| 281 | #498 | — | 9 | 1 | no | — |
| 282 | #496 | — | 18 | 4 | no | — |
| 283 | #496 | — | 18 | 2 | no | — |
| 284 | #493 | — | 9 | 2 | no | — |
| 285 | #493 | — | 9 | 1 | no | — |
| 286 | #493 | — | 9 | 2 | no | — |
| 287 | #493 | — | 9 | 1 | no | — |
| 288 | #493 | C2×D9 | 1 | 2 | yes | — |
| 289 | #493 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 290 | #492 | — | 9 | 1 | no | — |
| 291 | #492 | — | 9 | 2 | no | — |
| 292 | #492 | — | 9 | 2 | no | — |
| 293 | #492 | C2×D9 | 1 | 1 | yes | characteristic |
| 294 | #486 | — | 9 | 2 | no | — |
| 295 | #486 | — | 9 | 2 | no | — |
| 296 | #486 | C2×D9 | 1 | 2 | yes | complemented |
| 297 | #469 | — | 18 | 4 | no | — |
| 298 | #469 | — | 18 | 2 | no | — |
| 299 | #442 | — | 18 | 4 | no | — |
| 300 | #442 | — | 18 | 2 | no | — |
| 301 | C4×M16 | — | 9 | 2 | no | — |
| 302 | C4×M16 | — | 9 | 1 | no | — |
| 303 | #322 | — | 9 | 2 | no | — |
| 304 | #322 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 305 | C82 | — | 9 | 1 | no | — |
| 306 | C23×D3 | — | 12 | 1 | no | — |
| 307 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 308 | C2×C3×D4 | — | 2 | 2 | no | — |
| 309 | C2×C3×D4 | — | 2 | 2 | no | — |
| 310 | C2×C3×D4 | — | 2 | 2 | no | — |
| 311 | C2×C3×D4 | — | 2 | 1 | no | — |
| 312 | C2×C3×D4 | — | 2 | 2 | no | — |
| 313 | C2×#67 | — | 12 | 2 | no | — |
| 314 | C2×#67 | — | 12 | 1 | no | — |
| 315 | C2×#67 | — | 12 | 2 | no | — |
| 316 | C22×Dic3 | — | 12 | 2 | no | — |
| 317 | #239 | — | 12 | 4 | no | — |
| 318 | #237 | — | 12 | 8 | no | — |
| 319 | D3×D4 | — | 12 | 8 | no | — |
| 320 | D3×D4 | — | 12 | 4 | no | — |
| 321 | C2×D12 | — | 6 | 2 | no | — |
| 322 | C2×D12 | — | 6 | 2 | no | — |
| 323 | C2×D12 | — | 6 | 1 | no | — |
| 324 | C2×D12 | — | 6 | 1 | no | — |
| 325 | C2×D12 | — | 12 | 1 | no | — |
| 326 | C2×C4×D3 | — | 3 | 2 | no | — |
| 327 | C2×C4×D3 | — | 3 | 1 | no | — |
| 328 | C2×C4×D3 | — | 12 | 1 | no | — |
| 329 | C2×Dic6 | — | 6 | 2 | no | — |
| 330 | C3×SD16 | — | 4 | 4 | no | — |
| 331 | C3×D8 | — | 4 | 8 | no | — |
| 332 | C3×D8 | — | 4 | 4 | no | — |
| 333 | C2×C3×C8 | D3×D4 | 1 | 4 | yes | — |
| 334 | C2×C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 335 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 336 | C3×C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 337 | #217 | — | 12 | 2 | no | — |
| 338 | #217 | — | 12 | 2 | no | — |
| 339 | #215 | — | 12 | 4 | no | — |
| 340 | #214 | — | 12 | 8 | no | — |
| 341 | #213 | — | 12 | 8 | no | — |
| 342 | #213 | — | 12 | 8 | no | — |
| 343 | #213 | — | 12 | 4 | no | — |
| 344 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 345 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 346 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 347 | C4×Dic3 | — | 3 | 2 | no | — |
| 348 | C4×Dic3 | — | 3 | 1 | no | — |
| 349 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 350 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 351 | D24 | — | 12 | 4 | no | — |
| 352 | #204 | — | 12 | 8 | no | — |
| 353 | ΓL(1,𝔽25) | — | 6 | 8 | no | — |
| 354 | ΓL(1,𝔽25) | — | 6 | 4 | no | — |
| 355 | C22×C9 | — | 8 | 2 | no | — |
| 356 | C22×C9 | — | 8 | 1 | no | — |
| 357 | C22×C9 | — | 8 | 2 | no | — |
| 358 | C22×C9 | — | 8 | 2 | no | — |
| 359 | C22×C9 | — | 8 | 2 | no | — |
| 360 | C22×C9 | C2×#127 | 1 | 1 | yes | characteristic |
| 361 | C2×D9 | — | 2 | 1 | no | — |
| 362 | C2×D9 | — | 2 | 2 | no | — |
| 363 | C2×D9 | — | 8 | 1 | no | — |
| 364 | C2×D9 | — | 8 | 1 | no | — |
| 365 | C2×D9 | — | 8 | 2 | no | — |
| 366 | C2×D9 | — | 8 | 2 | no | — |
| 367 | C2×D9 | — | 16 | 4 | no | — |
| 368 | C4×C9 | — | 8 | 1 | no | — |
| 369 | C4×C9 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 370 | C4×C9 | C2×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 371 | Dic9 | — | 2 | 1 | no | — |
| 372 | Dic9 | — | 2 | 2 | no | — |
| 373 | Dic9 | — | 8 | 2 | no | — |
| 374 | C2×#41 | — | 18 | 2 | no | — |
| 375 | C2×#41 | — | 18 | 1 | no | — |
| 376 | C22×D4 | — | 18 | 2 | no | — |
| 377 | C22×D4 | — | 18 | 1 | no | — |
| 378 | AGL(1,ℤ/8) | — | 36 | 16 | no | — |
| 379 | AGL(1,ℤ/8) | — | 36 | 8 | no | — |
| 380 | C2×SD16 | — | 2 | 2 | no | — |
| 381 | C2×SD16 | — | 18 | 4 | no | — |
| 382 | C2×SD16 | — | 18 | 2 | no | — |
| 383 | C2×SD16 | — | 18 | 4 | no | — |
| 384 | C2×D8 | — | 2 | 4 | no | — |
| 385 | C2×D8 | — | 2 | 2 | no | — |
| 386 | C2×D8 | — | 18 | 4 | no | — |
| 387 | C2×D8 | — | 18 | 2 | no | — |
| 388 | C2×D8 | — | 18 | 4 | no | — |
| 389 | C2×D8 | — | 18 | 2 | no | — |
| 390 | C2×M16 | — | 9 | 4 | no | — |
| 391 | C2×M16 | — | 9 | 2 | no | — |
| 392 | C4⋊Q8 | — | 9 | 2 | no | — |
| 393 | C4⋊Q8 | C22×D9 | 1 | 1 | yes | characteristic |
| 394 | #127 | — | 9 | 1 | no | — |
| 395 | #127 | — | 9 | 1 | no | — |
| 396 | #127 | — | 18 | 2 | no | — |
| 397 | #127 | — | 18 | 1 | no | — |
| 398 | #127 | C22×D9 | 1 | 1 | yes | characteristic |
| 399 | #127 | C22×D9 | 1 | 2 | yes | — |
| 400 | #124 | — | 18 | 2 | no | — |
| 401 | #124 | — | 18 | 1 | no | — |
| 402 | #121 | — | 18 | 2 | no | — |
| 403 | #121 | — | 18 | 2 | no | — |
| 404 | #121 | — | 18 | 2 | no | — |
| 405 | C4×D4 | — | 18 | 2 | no | — |
| 406 | C4×D4 | — | 18 | 2 | no | — |
| 407 | C4×D4 | — | 18 | 2 | no | — |
| 408 | C2×C42 | — | 9 | 1 | no | — |
| 409 | #106 | — | 18 | 4 | no | — |
| 410 | #106 | — | 18 | 2 | no | — |
| 411 | #102 | — | 2 | 4 | no | — |
| 412 | #102 | — | 18 | 4 | no | — |
| 413 | #102 | — | 18 | 4 | no | — |
| 414 | #97 | — | 9 | 4 | no | — |
| 415 | #97 | — | 9 | 2 | no | — |
| 416 | C4×C8 | — | 9 | 2 | no | — |
| 417 | C4×C8 | — | 9 | 1 | no | — |
| 418 | C4×C8 | C22×D9 | 1 | 1 | yes | characteristic |
| 419 | C4×C8 | C22×D9 | 1 | 2 | yes | — |
| 420 | C23×C3 | — | 4 | 2 | no | — |
| 421 | C23×C3 | — | 4 | 1 | no | — |
| 422 | C22×D3 | — | 3 | 1 | no | — |
| 423 | C22×D3 | — | 12 | 1 | no | — |
| 424 | C22×D3 | — | 12 | 1 | no | — |
| 425 | C22×D3 | — | 24 | 2 | no | — |
| 426 | C22×D3 | — | 24 | 4 | no | — |
| 427 | C3×Q8 | — | 4 | 2 | no | — |
| 428 | C3×D4 | — | 4 | 2 | no | — |
| 429 | C3×D4 | — | 4 | 4 | no | — |
| 430 | C3×D4 | — | 4 | 4 | no | — |
| 431 | C3×D4 | — | 4 | 4 | no | — |
| 432 | C3×D4 | — | 4 | 4 | no | — |
| 433 | C2×C3×C4 | — | 4 | 1 | no | — |
| 434 | C2×C3×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 435 | C2×C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 436 | #67 | — | 24 | 2 | no | — |
| 437 | #67 | — | 24 | 4 | no | — |
| 438 | #67 | — | 24 | 4 | no | — |
| 439 | C2×Dic3 | — | 3 | 2 | no | — |
| 440 | C2×Dic3 | — | 3 | 1 | no | — |
| 441 | C2×Dic3 | — | 12 | 2 | no | — |
| 442 | C2×Dic3 | — | 24 | 4 | no | — |
| 443 | D12 | — | 12 | 2 | no | — |
| 444 | D12 | — | 12 | 2 | no | — |
| 445 | D12 | — | 12 | 4 | no | — |
| 446 | D12 | — | 12 | 4 | no | — |
| 447 | D12 | — | 24 | 2 | no | — |
| 448 | C4×D3 | — | 6 | 2 | no | — |
| 449 | C4×D3 | — | 6 | 4 | no | — |
| 450 | C4×D3 | — | 24 | 2 | no | — |
| 451 | Dic6 | — | 12 | 4 | no | — |
| 452 | C3×C8 | — | 2 | 4 | no | — |
| 453 | C3×C8 | #911 | 1 | 4 | yes | — |
| 454 | C3⋊C8 | — | 3 | 8 | no | — |
| 455 | C3⋊C8 | — | 6 | 2 | no | — |
| 456 | C2×C9 | — | 16 | 1 | no | — |
| 457 | C2×C9 | — | 16 | 2 | no | — |
| 458 | C2×C9 | #3151 | 1 | 1 | yes | characteristic |
| 459 | C2×C9 | #3151 | 1 | 2 | yes | — |
| 460 | D9 | — | 4 | 1 | no | — |
| 461 | D9 | — | 16 | 1 | no | — |
| 462 | D9 | — | 16 | 1 | no | — |
| 463 | C24 | — | 36 | 1 | no | — |
| 464 | #41 | — | 36 | 8 | no | — |
| 465 | #41 | — | 36 | 4 | no | — |
| 466 | C2×Q8 | — | 2 | 1 | no | — |
| 467 | C2×Q8 | — | 18 | 2 | no | — |
| 468 | C2×D4 | — | 2 | 2 | no | — |
| 469 | C2×D4 | — | 2 | 2 | no | — |
| 470 | C2×D4 | — | 2 | 2 | no | — |
| 471 | C2×D4 | — | 2 | 2 | no | — |
| 472 | C2×D4 | — | 2 | 1 | no | — |
| 473 | C2×D4 | — | 18 | 2 | no | — |
| 474 | C2×D4 | — | 18 | 1 | no | — |
| 475 | C2×D4 | — | 18 | 1 | no | — |
| 476 | C2×D4 | — | 18 | 2 | no | — |
| 477 | C2×D4 | — | 36 | 1 | no | — |
| 478 | C2×D4 | — | 36 | 2 | no | — |
| 479 | C2×D4 | — | 36 | 1 | no | — |
| 480 | C2×D4 | — | 36 | 4 | no | — |
| 481 | C2×D4 | — | 36 | 8 | no | — |
| 482 | C2×D4 | — | 36 | 2 | no | — |
| 483 | C22×C4 | — | 9 | 1 | no | — |
| 484 | C22×C4 | — | 9 | 2 | no | — |
| 485 | C22×C4 | — | 36 | 1 | no | — |
| 486 | C22×C4 | — | 36 | 2 | no | — |
| 487 | SD16 | — | 4 | 4 | no | — |
| 488 | SD16 | — | 36 | 8 | no | — |
| 489 | SD16 | — | 36 | 8 | no | — |
| 490 | SD16 | — | 36 | 4 | no | — |
| 491 | D8 | — | 4 | 8 | no | — |
| 492 | D8 | — | 4 | 4 | no | — |
| 493 | D8 | — | 36 | 8 | no | — |
| 494 | D8 | — | 36 | 8 | no | — |
| 495 | D8 | — | 36 | 4 | no | — |
| 496 | D8 | — | 36 | 4 | no | — |
| 497 | M16 | — | 18 | 8 | no | — |
| 498 | M16 | — | 18 | 4 | no | — |
| 499 | C2×C8 | — | 9 | 4 | no | — |
| 500 | C2×C8 | — | 9 | 2 | no | — |
| 501 | C2×C8 | D4×D9 | 1 | 4 | yes | — |
| 502 | C2×C8 | D4×D9 | 1 | 2 | yes | — |
| 503 | C4⋊C4 | — | 2 | 2 | no | — |
| 504 | C4⋊C4 | — | 18 | 2 | no | — |
| 505 | C4⋊C4 | — | 18 | 2 | no | — |
| 506 | C22⋊C4 | — | 36 | 2 | no | — |
| 507 | C22⋊C4 | — | 36 | 2 | no | — |
| 508 | C22⋊C4 | — | 36 | 2 | no | — |
| 509 | C42 | — | 9 | 1 | no | — |
| 510 | C42 | — | 9 | 2 | no | — |
| 511 | C42 | C23×D9 | 1 | 1 | yes | characteristic |
| 512 | C22×C3 | — | 8 | 1 | no | — |
| 513 | C22×C3 | — | 8 | 2 | no | — |
| 514 | C22×C3 | — | 8 | 2 | no | — |
| 515 | C22×C3 | — | 8 | 2 | no | — |
| 516 | C22×C3 | — | 8 | 2 | no | — |
| 517 | C22×C3 | D3×#127 | 1 | 1 | yes | characteristic |
| 518 | C2×D3 | — | 6 | 1 | no | — |
| 519 | C2×D3 | — | 6 | 2 | no | — |
| 520 | C2×D3 | — | 24 | 1 | no | — |
| 521 | C2×D3 | — | 24 | 1 | no | — |
| 522 | C2×D3 | — | 24 | 2 | no | — |
| 523 | C2×D3 | — | 24 | 2 | no | — |
| 524 | C2×D3 | — | 48 | 4 | no | — |
| 525 | C3×C4 | — | 8 | 1 | no | — |
| 526 | C3×C4 | C2×#911 | 1 | 2 | yes | — |
| 527 | C3×C4 | D3×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 528 | Dic3 | — | 6 | 1 | no | — |
| 529 | Dic3 | — | 6 | 2 | no | — |
| 530 | Dic3 | — | 24 | 2 | no | — |
| 531 | C9 | #19745 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 532 | C23 | — | 4 | 2 | no | — |
| 533 | C23 | — | 4 | 1 | no | — |
| 534 | C23 | — | 9 | 1 | no | — |
| 535 | C23 | — | 36 | 1 | no | — |
| 536 | C23 | — | 36 | 1 | no | — |
| 537 | C23 | — | 72 | 4 | no | — |
| 538 | C23 | — | 72 | 2 | no | — |
| 539 | Q8 | — | 4 | 2 | no | — |
| 540 | Q8 | — | 36 | 4 | no | — |
| 541 | D4 | — | 4 | 4 | no | — |
| 542 | D4 | — | 4 | 2 | no | — |
| 543 | D4 | — | 4 | 4 | no | — |
| 544 | D4 | — | 4 | 4 | no | — |
| 545 | D4 | — | 4 | 4 | no | — |
| 546 | D4 | — | 36 | 2 | no | — |
| 547 | D4 | — | 36 | 2 | no | — |
| 548 | D4 | — | 36 | 4 | no | — |
| 549 | D4 | — | 36 | 4 | no | — |
| 550 | D4 | — | 72 | 2 | no | — |
| 551 | D4 | — | 72 | 4 | no | — |
| 552 | D4 | — | 72 | 2 | no | — |
| 553 | D4 | — | 72 | 4 | no | — |
| 554 | C2×C4 | — | 4 | 1 | no | — |
| 555 | C2×C4 | — | 9 | 2 | no | — |
| 556 | C2×C4 | — | 9 | 1 | no | — |
| 557 | C2×C4 | — | 18 | 2 | no | — |
| 558 | C2×C4 | — | 18 | 4 | no | — |
| 559 | C2×C4 | — | 36 | 2 | no | — |
| 560 | C2×C4 | — | 72 | 2 | no | — |
| 561 | C2×C4 | — | 72 | 4 | no | — |
| 562 | C2×C4 | C2×D4×D9 | 1 | 1 | yes | characteristic |
| 563 | C2×C4 | C2×D4×D9 | 1 | 2 | yes | — |
| 564 | C8 | — | 2 | 4 | no | — |
| 565 | C8 | — | 9 | 8 | no | — |
| 566 | C8 | — | 18 | 2 | no | — |
| 567 | C8 | #63473 | 1 | 4 | yes | complemented |
| 568 | C2×C3 | — | 16 | 1 | no | — |
| 569 | C2×C3 | — | 16 | 2 | no | — |
| 570 | C2×C3 | #81783 | 1 | 1 | yes | characteristic |
| 571 | C2×C3 | #81845 | 1 | 2 | yes | — |
| 572 | D3 | — | 12 | 1 | no | — |
| 573 | D3 | — | 48 | 1 | no | — |
| 574 | D3 | — | 48 | 1 | no | — |
| 575 | C22 | — | 8 | 2 | no | — |
| 576 | C22 | — | 8 | 2 | no | — |
| 577 | C22 | — | 8 | 2 | no | — |
| 578 | C22 | — | 8 | 1 | no | — |
| 579 | C22 | — | 8 | 2 | no | — |
| 580 | C22 | — | 18 | 2 | no | — |
| 581 | C22 | — | 18 | 1 | no | — |
| 582 | C22 | — | 72 | 2 | no | — |
| 583 | C22 | — | 72 | 2 | no | — |
| 584 | C22 | — | 72 | 1 | no | — |
| 585 | C22 | — | 72 | 1 | no | — |
| 586 | C22 | — | 144 | 4 | no | — |
| 587 | C22 | D9×#127 | 1 | 1 | yes | characteristic |
| 588 | C4 | — | 8 | 1 | no | — |
| 589 | C4 | — | 18 | 2 | no | — |
| 590 | C4 | — | 18 | 1 | no | — |
| 591 | C4 | — | 72 | 2 | no | — |
| 592 | C4 | C2×#63473 | 1 | 2 | yes | — |
| 593 | C4 | D9×AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 594 | C3 | #10784427 | 1 | 1 | yes | characteristic |
| 595 | C2 | — | 16 | 1 | no | — |
| 596 | C2 | — | 16 | 2 | no | — |
| 597 | C2 | — | 36 | 1 | no | — |
| 598 | C2 | — | 144 | 1 | no | — |
| 599 | C2 | — | 144 | 1 | no | — |
| 600 | C2 | #11874460 | 1 | 2 | yes | — |
| 601 | C2 | #11874466 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D9×#127 |
| commutator, cosocle | C42×C9 | C24 |
| Frattini | C3×C42 | C23×D3 |
| Fitting | C9×#1721 | C2 |
| socle | C22×C3 | D3×#127 |
| hypercenter | #1721 | D9 |
| hypocenter | C9 | #19745 |
| LCS | G ▷ C42×C9 ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1721 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11876971 | C2 | semidirect |
| 2. #11876968 | C2 | semidirect |
| 3. #11874466 | C2 | semidirect |
| 4. #11874454 | C2 | semidirect |
| 5. #11782902 | C2 | semidirect |
| 6. #11782669 | C2 | semidirect |
| 7. #11782663 | C2 | semidirect |
| 8. #11782584 | C2 | semidirect |
| 9. #11782414 | C2 | semidirect |
| 10. #11773693 | C2 | semidirect |
| 11. C9×#1721 | C2 | semidirect |
| 19. C9×#493 | C22 | semidirect |
| 21. C9×#486 | C22 | semidirect |
| 27. #10588760 | C22 | semidirect |
| 30. #10588755 | C22 | semidirect |
| 32. #10588750 | C22 | semidirect |
| 36. #10588376 | C22 | semidirect |
| 40. #10588360 | C22 | semidirect |
| 41. C9×#322 | C22 | semidirect |
| 42. #10588131 | C22 | semidirect |
| 43. C8×C9⋊C8 | C22 | semidirect |
| 187. #1721 | D9 | semidirect |
| 272. C8×C9 | AGL(1,ℤ/8) | semidirect |
| 274. C9⋊C8 | AGL(1,ℤ/8) | semidirect |
| 289. #493 | C2×D9 | semidirect |
| 296. #486 | C2×D9 | semidirect |
| 304. #322 | C2×D9 | semidirect |
| 531. C9 | #19745 | semidirect |
| 567. C8 | #63473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11876971 | 2 |
| #11876968 | 2 |
| #11874466 | 2 |
| #11874454 | 2 |
| #11782902 | 2 |
| #11782669 | 2 |
| #11782663 | 2 |
| #11782584 | 2 |
| #11782414 | 2 |
| #11773693 | 2 |
| C9×#1721 | 2 |
| #10784427 | 3 |