Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2326 conjugacy classes of subgroups.
The subgroup lattice has 648 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13076609 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13075641 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13074306 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13074302 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13073686 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13073684 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13072238 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13072230 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #13071728 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #13071723 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #13071105 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13071103 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C11×#2733 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C22×#4343 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#4341 | C22 | 1 | 2 | yes | — |
| 16 | C2×C11×#124 | C22 | 1 | 2 | yes | — |
| 17 | C2×#66993 | C22 | 1 | 2 | yes | — |
| 18 | C2×#66992 | C22 | 1 | 4 | yes | — |
| 19 | C2×#66991 | C22 | 1 | 2 | yes | — |
| 20 | C2×#66989 | C22 | 1 | 2 | yes | — |
| 21 | C2×#66945 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#66945 | C22 | 1 | 2 | yes | — |
| 23 | C2×#66938 | C22 | 1 | 4 | yes | — |
| 24 | C2×#66938 | C22 | 1 | 4 | yes | — |
| 25 | C2×C42×D11 | C22 | 1 | 1 | yes | characteristic |
| 26 | C11×#394 | C22 | 1 | 2 | yes | — |
| 27 | C11×#392 | C22 | 1 | 4 | yes | — |
| 28 | C11×#391 | C22 | 1 | 1 | yes | characteristic |
| 29 | C11×#390 | C22 | 1 | 2 | yes | — |
| 30 | C11×#388 | C22 | 1 | 4 | yes | — |
| 31 | #10622843 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10622843 | C22 | 1 | 2 | yes | — |
| 33 | #10622836 | C22 | 1 | 4 | yes | — |
| 34 | #10622836 | C22 | 1 | 2 | yes | — |
| 35 | #10622834 | C22 | 1 | 2 | yes | — |
| 36 | #10622833 | C22 | 1 | 4 | yes | — |
| 37 | #10622603 | C22 | 1 | 4 | yes | — |
| 38 | #10622601 | C22 | 1 | 1 | yes | characteristic |
| 39 | #10622592 | C22 | 1 | 2 | yes | — |
| 40 | #10622587 | C22 | 1 | 2 | yes | — |
| 41 | #10622574 | C22 | 1 | 4 | yes | — |
| 42 | #10622573 | C22 | 1 | 4 | yes | — |
| 43 | #10622573 | C22 | 1 | 4 | yes | — |
| 44 | #10622571 | C22 | 1 | 4 | yes | — |
| 45 | #10622570 | C22 | 1 | 4 | yes | — |
| 46 | #10622569 | C22 | 1 | 4 | yes | — |
| 47 | #10622569 | C22 | 1 | 4 | yes | — |
| 48 | #10622569 | C22 | 1 | 4 | yes | — |
| 49 | #10622564 | C22 | 1 | 4 | yes | — |
| 50 | #10622564 | C22 | 1 | 4 | yes | — |
| 51 | #10622558 | C22 | 1 | 4 | yes | — |
| 52 | C22⋊C4×Dic11 | C22 | 1 | 4 | yes | — |
| 53 | C22⋊C4×Dic11 | C22 | 1 | 4 | yes | — |
| 54 | C22⋊C4×Dic11 | C22 | 1 | 4 | yes | — |
| 55 | #10622552 | C22 | 1 | 1 | yes | characteristic |
| 56 | #10622552 | C22 | 1 | 2 | yes | — |
| 57 | C4×(C2×D11)⋊C4 | C22 | 1 | 2 | yes | — |
| 58 | #10622545 | C22 | 1 | 4 | yes | — |
| 59 | #10622542 | C22 | 1 | 2 | yes | — |
| 60 | #10622286 | C22 | 1 | 2 | yes | — |
| 61 | #10622282 | C22 | 1 | 4 | yes | — |
| 62 | #10622279 | C22 | 1 | 4 | yes | — |
| 63 | #10622278 | C22 | 1 | 4 | yes | — |
| 64 | #10622269 | C22 | 1 | 4 | yes | — |
| 65 | #10622261 | C22 | 1 | 2 | yes | — |
| 66 | #10622259 | C22 | 1 | 4 | yes | — |
| 67 | C22×Q8×C11 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×D4×C11 | C23 | 1 | 2 | yes | — |
| 69 | C22×D4×C11 | C23 | 1 | 2 | yes | — |
| 70 | C22×D4×C11 | C23 | 1 | 2 | yes | — |
| 71 | C22×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 72 | C22×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 73 | C22×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 74 | C23×Dic11 | C23 | 1 | 4 | yes | — |
| 75 | C2×#4343 | — | 2 | 4 | no | — |
| 76 | C2×#4343 | — | 4 | 2 | no | — |
| 77 | C2×#4343 | — | 4 | 2 | no | — |
| 78 | C2×#4341 | — | 2 | 8 | no | — |
| 79 | C2×#4341 | — | 4 | 4 | no | — |
| 80 | C2×#4341 | — | 4 | 4 | no | — |
| 81 | C22×D44 | C23 | 1 | 2 | yes | — |
| 82 | C22×D44 | C23 | 1 | 1 | yes | characteristic |
| 83 | C22×C4×D11 | C23 | 1 | 2 | yes | — |
| 84 | C22×C4×D11 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×C4×D11 | C23 | 1 | 2 | yes | — |
| 86 | C22×Dic22 | C23 | 1 | 2 | yes | — |
| 87 | C22×Dic22 | C23 | 1 | 2 | yes | — |
| 88 | C11×#124 | — | 2 | 8 | no | — |
| 89 | C2×C11×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 90 | C2×C11×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C11×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 92 | C2×C11×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 93 | C2×C11×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 94 | C2×C11×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 95 | C2×C42×C11 | C23 | 1 | 2 | yes | — |
| 96 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C22⋊Dic11 | C23 | 1 | 4 | yes | — |
| 98 | C2×C22⋊Dic11 | C23 | 1 | 4 | yes | — |
| 99 | C2×C22⋊Dic11 | C23 | 1 | 4 | yes | — |
| 100 | C2×C22⋊Dic11 | C23 | 1 | 4 | yes | — |
| 101 | #66993 | — | 4 | 4 | no | — |
| 102 | #66992 | — | 4 | 8 | no | — |
| 103 | #66991 | — | 4 | 4 | no | — |
| 104 | #66989 | — | 4 | 4 | no | — |
| 105 | C2×(C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 106 | C2×(C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | C2×(C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 108 | C2×(C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 109 | C2×(C2×D11)⋊C4 | C23 | 1 | 2 | yes | — |
| 110 | C2×(C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 111 | C2×C4⋊Dic11 | C23 | 1 | 2 | yes | — |
| 112 | C2×C4⋊Dic11 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊Dic11 | C23 | 1 | 2 | yes | — |
| 114 | C2×Dic11⋊C4 | C23 | 1 | 4 | yes | — |
| 115 | C2×C4×Dic11 | C23 | 1 | 4 | yes | — |
| 116 | C2×C4×Dic11 | C23 | 1 | 4 | yes | — |
| 117 | C2×C4×Dic11 | C23 | 1 | 2 | yes | — |
| 118 | C2×C4×Dic11 | C23 | 1 | 2 | yes | — |
| 119 | C2×C4×Dic11 | C23 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×Dic11 | C23 | 1 | 2 | yes | — |
| 121 | #66945 | — | 4 | 4 | no | — |
| 122 | #66945 | — | 4 | 2 | no | — |
| 123 | #66938 | — | 2 | 16 | no | — |
| 124 | #66938 | — | 4 | 8 | no | — |
| 125 | C42×D11 | — | 4 | 2 | no | — |
| 126 | C11×#95 | C23 | 1 | 4 | yes | — |
| 127 | C11×#95 | C23 | 1 | 2 | yes | — |
| 128 | C11⋊#95 | C23 | 1 | 2 | yes | — |
| 129 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 130 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 131 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 132 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 133 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 134 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 135 | C11⋊#95 | C23 | 1 | 4 | yes | — |
| 136 | #60048 | — | 11 | 1 | no | maximal, Sylow |
| 137 | C24×C11 | C24 | 1 | 4 | yes | — |
| 138 | C23×D11 | C24 | 1 | 2 | yes | — |
| 139 | C23×D11 | C24 | 1 | 1 | yes | characteristic |
| 140 | C2×Q8×C11 | — | 4 | 1 | no | — |
| 141 | C2×Q8×C11 | — | 4 | 1 | no | — |
| 142 | C2×Q8×C11 | #41 | 1 | 4 | yes | complemented |
| 143 | C2×D4×C11 | — | 2 | 4 | no | — |
| 144 | C2×D4×C11 | — | 2 | 4 | no | — |
| 145 | C2×D4×C11 | — | 4 | 2 | no | — |
| 146 | C2×D4×C11 | — | 4 | 2 | no | — |
| 147 | C2×D4×C11 | — | 4 | 2 | no | — |
| 148 | C2×D4×C11 | — | 4 | 2 | no | — |
| 149 | C2×D4×C11 | — | 4 | 4 | no | — |
| 150 | C2×D4×C11 | — | 4 | 2 | no | — |
| 151 | C22×C4×C11 | C24 | 1 | 4 | yes | — |
| 152 | C22×C4×C11 | C24 | 1 | 2 | yes | — |
| 153 | C22×C4×C11 | C24 | 1 | 2 | yes | — |
| 154 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 155 | C22×C4×C11 | C24 | 1 | 2 | yes | — |
| 156 | C2×C22⋊D11 | — | 2 | 8 | no | — |
| 157 | C2×C22⋊D11 | — | 2 | 8 | no | — |
| 158 | C2×C22⋊D11 | — | 2 | 8 | no | — |
| 159 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 160 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 161 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 162 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 163 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 164 | C2×C22⋊D11 | — | 4 | 4 | no | — |
| 165 | C22×Dic11 | — | 2 | 8 | no | — |
| 166 | C22×Dic11 | — | 2 | 8 | no | — |
| 167 | C22×Dic11 | — | 4 | 4 | no | — |
| 168 | C22×Dic11 | C24 | 1 | 2 | yes | — |
| 169 | C22×Dic11 | C24 | 1 | 4 | yes | — |
| 170 | C22×Dic11 | C24 | 1 | 4 | yes | — |
| 171 | C22×Dic11 | C24 | 1 | 2 | yes | — |
| 172 | C22×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 173 | #4343 | — | 4 | 16 | no | — |
| 174 | #4341 | — | 4 | 32 | no | — |
| 175 | C2×D44 | — | 2 | 4 | no | — |
| 176 | C2×D44 | — | 2 | 4 | no | — |
| 177 | C2×D44 | — | 2 | 2 | no | — |
| 178 | C2×D44 | — | 4 | 1 | no | — |
| 179 | C2×D44 | — | 4 | 1 | no | — |
| 180 | C2×D44 | — | 4 | 2 | no | — |
| 181 | C2×C4×D11 | — | 2 | 4 | no | — |
| 182 | C2×C4×D11 | — | 2 | 2 | no | — |
| 183 | C2×C4×D11 | — | 2 | 4 | no | — |
| 184 | C2×C4×D11 | — | 2 | 4 | no | — |
| 185 | C2×C4×D11 | — | 2 | 2 | no | — |
| 186 | C2×C4×D11 | — | 2 | 4 | no | — |
| 187 | C2×C4×D11 | — | 2 | 2 | no | — |
| 188 | C2×C4×D11 | — | 2 | 4 | no | — |
| 189 | C2×C4×D11 | — | 4 | 2 | no | — |
| 190 | C2×Dic22 | — | 4 | 2 | no | — |
| 191 | C2×Dic22 | — | 4 | 2 | no | — |
| 192 | C2×Dic22 | — | 4 | 4 | no | — |
| 193 | C2×Dic22 | — | 4 | 2 | no | — |
| 194 | C2×Dic22 | #41 | 1 | 8 | yes | complemented |
| 195 | C11×C4⋊C4 | — | 4 | 2 | no | — |
| 196 | C11×C4⋊C4 | — | 4 | 1 | no | — |
| 197 | C11×C22⋊C4 | — | 2 | 8 | no | — |
| 198 | C11×C22⋊C4 | — | 2 | 8 | no | — |
| 199 | C11×C22⋊C4 | — | 2 | 8 | no | — |
| 200 | C11×C22⋊C4 | — | 4 | 4 | no | — |
| 201 | C42×C11 | — | 2 | 4 | no | — |
| 202 | C42×C11 | — | 4 | 1 | no | — |
| 203 | C22⋊Dic11 | — | 2 | 8 | no | — |
| 204 | C22⋊Dic11 | — | 2 | 8 | no | — |
| 205 | C22⋊Dic11 | — | 2 | 8 | no | — |
| 206 | C22⋊Dic11 | — | 4 | 4 | no | — |
| 207 | (C2×D11)⋊C4 | — | 2 | 8 | no | — |
| 208 | (C2×D11)⋊C4 | — | 2 | 8 | no | — |
| 209 | (C2×D11)⋊C4 | — | 2 | 8 | no | — |
| 210 | (C2×D11)⋊C4 | — | 4 | 4 | no | — |
| 211 | (C2×D11)⋊C4 | — | 4 | 4 | no | — |
| 212 | (C2×D11)⋊C4 | — | 4 | 2 | no | — |
| 213 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 214 | C4⋊Dic11 | — | 4 | 1 | no | — |
| 215 | C4⋊Dic11 | — | 4 | 2 | no | — |
| 216 | Dic11⋊C4 | — | 4 | 4 | no | — |
| 217 | C4×Dic11 | — | 2 | 8 | no | — |
| 218 | C4×Dic11 | — | 2 | 8 | no | — |
| 219 | C4×Dic11 | — | 2 | 4 | no | — |
| 220 | C4×Dic11 | — | 4 | 2 | no | — |
| 221 | C4×Dic11 | — | 4 | 1 | no | — |
| 222 | C4×Dic11 | — | 4 | 2 | no | — |
| 223 | #2811 | — | 11 | 1 | no | — |
| 224 | #2733 | — | 11 | 2 | no | — |
| 225 | #2733 | D11 | 1 | 1 | yes | characteristic, complemented |
| 226 | #2610 | — | 11 | 2 | no | — |
| 227 | #2610 | — | 11 | 4 | no | — |
| 228 | #2555 | — | 11 | 2 | no | — |
| 229 | #2555 | — | 11 | 4 | no | — |
| 230 | #2431 | — | 11 | 4 | no | — |
| 231 | #2431 | — | 11 | 2 | no | — |
| 232 | #2372 | — | 11 | 4 | no | — |
| 233 | #2372 | — | 11 | 2 | no | — |
| 234 | #2297 | — | 11 | 1 | no | — |
| 235 | #2297 | — | 11 | 2 | no | — |
| 236 | C23×C11 | — | 2 | 4 | no | — |
| 237 | C23×C11 | — | 2 | 4 | no | — |
| 238 | C23×C11 | — | 2 | 4 | no | — |
| 239 | C23×C11 | — | 2 | 4 | no | — |
| 240 | C23×C11 | — | 2 | 4 | no | — |
| 241 | C23×C11 | — | 2 | 4 | no | — |
| 242 | C23×C11 | — | 2 | 4 | no | — |
| 243 | C23×C11 | C25 | 1 | 1 | yes | characteristic |
| 244 | C22×D11 | — | 2 | 1 | no | — |
| 245 | C22×D11 | — | 2 | 2 | no | — |
| 246 | C22×D11 | — | 2 | 1 | no | — |
| 247 | C22×D11 | — | 2 | 2 | no | — |
| 248 | C22×D11 | — | 2 | 4 | no | — |
| 249 | C22×D11 | — | 2 | 2 | no | — |
| 250 | C22×D11 | — | 2 | 4 | no | — |
| 251 | C22×D11 | — | 2 | 2 | no | — |
| 252 | C22×D11 | — | 2 | 2 | no | — |
| 253 | C22×D11 | H(5,𝔽2) | 1 | 2 | yes | — |
| 254 | Q8×C11 | — | 4 | 4 | no | — |
| 255 | D4×C11 | — | 4 | 8 | no | — |
| 256 | D4×C11 | — | 8 | 4 | no | — |
| 257 | D4×C11 | — | 8 | 4 | no | — |
| 258 | C2×C4×C11 | — | 2 | 2 | no | — |
| 259 | C2×C4×C11 | — | 2 | 1 | no | — |
| 260 | C2×C4×C11 | — | 2 | 2 | no | — |
| 261 | C2×C4×C11 | — | 2 | 2 | no | — |
| 262 | C2×C4×C11 | — | 2 | 1 | no | — |
| 263 | C2×C4×C11 | — | 2 | 2 | no | — |
| 264 | C2×C4×C11 | — | 2 | 4 | no | — |
| 265 | C2×C4×C11 | — | 2 | 4 | no | — |
| 266 | C2×C4×C11 | — | 2 | 4 | no | — |
| 267 | C2×C4×C11 | — | 2 | 2 | no | — |
| 268 | C2×C4×C11 | — | 2 | 4 | no | — |
| 269 | C2×C4×C11 | C2×#41 | 1 | 4 | yes | — |
| 270 | C2×C4×C11 | C2×#41 | 1 | 2 | yes | — |
| 271 | C2×C4×C11 | C2×#41 | 1 | 4 | yes | — |
| 272 | C22⋊D11 | — | 4 | 16 | no | — |
| 273 | C22⋊D11 | — | 8 | 8 | no | — |
| 274 | C22⋊D11 | — | 8 | 8 | no | — |
| 275 | C2×Dic11 | — | 2 | 1 | no | — |
| 276 | C2×Dic11 | — | 2 | 2 | no | — |
| 277 | C2×Dic11 | — | 2 | 1 | no | — |
| 278 | C2×Dic11 | — | 2 | 2 | no | — |
| 279 | C2×Dic11 | — | 2 | 4 | no | — |
| 280 | C2×Dic11 | — | 2 | 4 | no | — |
| 281 | C2×Dic11 | — | 2 | 4 | no | — |
| 282 | C2×Dic11 | — | 2 | 2 | no | — |
| 283 | C2×Dic11 | — | 2 | 4 | no | — |
| 284 | C2×Dic11 | — | 2 | 4 | no | — |
| 285 | C2×Dic11 | — | 2 | 4 | no | — |
| 286 | C2×Dic11 | — | 4 | 16 | no | — |
| 287 | C2×Dic11 | C2×#41 | 1 | 8 | yes | — |
| 288 | C2×Dic11 | H(5,𝔽2) | 1 | 4 | yes | — |
| 289 | C2×Dic11 | H(5,𝔽2) | 1 | 2 | yes | — |
| 290 | D44 | — | 4 | 8 | no | — |
| 291 | D44 | — | 4 | 4 | no | — |
| 292 | C4×D11 | — | 2 | 16 | no | — |
| 293 | C4×D11 | — | 2 | 8 | no | — |
| 294 | C4×D11 | — | 4 | 8 | no | — |
| 295 | Dic22 | — | 4 | 8 | no | — |
| 296 | Dic22 | — | 8 | 4 | no | — |
| 297 | C22×#41 | — | 11 | 1 | no | — |
| 298 | C22×#41 | — | 11 | 2 | no | — |
| 299 | C2×#127 | — | 11 | 2 | no | — |
| 300 | C2×#124 | — | 11 | 2 | no | — |
| 301 | C2×#124 | — | 11 | 4 | no | — |
| 302 | C2×#124 | — | 11 | 4 | no | — |
| 303 | C2×#124 | C2×D11 | 1 | 2 | yes | — |
| 304 | C2×#121 | — | 11 | 2 | no | — |
| 305 | C2×#121 | — | 11 | 4 | no | — |
| 306 | C2×#117 | — | 11 | 1 | no | — |
| 307 | C2×#117 | — | 11 | 2 | no | — |
| 308 | C22×C42 | — | 11 | 1 | no | — |
| 309 | #395 | — | 11 | 2 | no | — |
| 310 | #395 | — | 11 | 4 | no | — |
| 311 | #394 | — | 11 | 4 | no | — |
| 312 | #394 | C2×D11 | 1 | 2 | yes | — |
| 313 | #393 | — | 11 | 2 | no | — |
| 314 | #392 | — | 11 | 2 | no | — |
| 315 | #392 | — | 11 | 4 | no | — |
| 316 | #392 | — | 11 | 4 | no | — |
| 317 | #392 | — | 11 | 4 | no | — |
| 318 | #392 | C2×D11 | 1 | 4 | yes | — |
| 319 | #391 | — | 11 | 1 | no | — |
| 320 | #391 | — | 11 | 2 | no | — |
| 321 | #391 | — | 11 | 2 | no | — |
| 322 | #391 | — | 11 | 2 | no | — |
| 323 | #391 | — | 11 | 4 | no | — |
| 324 | #391 | C2×D11 | 1 | 1 | yes | characteristic |
| 325 | #390 | — | 11 | 2 | no | — |
| 326 | #390 | — | 11 | 1 | no | — |
| 327 | #390 | — | 11 | 4 | no | — |
| 328 | #390 | — | 11 | 2 | no | — |
| 329 | #390 | — | 11 | 1 | no | — |
| 330 | #390 | C2×D11 | 1 | 2 | yes | — |
| 331 | #388 | — | 11 | 4 | no | — |
| 332 | #388 | — | 11 | 4 | no | — |
| 333 | #388 | — | 11 | 4 | no | — |
| 334 | #388 | — | 11 | 4 | no | — |
| 335 | #388 | — | 11 | 4 | no | — |
| 336 | #388 | C2×D11 | 1 | 4 | yes | — |
| 337 | #386 | — | 11 | 4 | no | — |
| 338 | #386 | — | 11 | 4 | no | — |
| 339 | #386 | — | 11 | 4 | no | — |
| 340 | #386 | — | 11 | 4 | no | — |
| 341 | #386 | — | 11 | 4 | no | — |
| 342 | #386 | — | 11 | 4 | no | — |
| 343 | C4×C22⋊C4 | — | 11 | 4 | no | — |
| 344 | C4×C22⋊C4 | — | 11 | 4 | no | — |
| 345 | C4×C22⋊C4 | — | 11 | 4 | no | — |
| 346 | C4×C22⋊C4 | — | 11 | 2 | no | — |
| 347 | C4×C22⋊C4 | — | 11 | 4 | no | — |
| 348 | #376 | — | 11 | 4 | no | — |
| 349 | #376 | — | 11 | 2 | no | — |
| 350 | C22×C11 | — | 4 | 4 | no | — |
| 351 | C22×C11 | — | 4 | 4 | no | — |
| 352 | C22×C11 | — | 4 | 4 | no | — |
| 353 | C22×C11 | — | 4 | 4 | no | — |
| 354 | C22×C11 | — | 4 | 4 | no | — |
| 355 | C22×C11 | — | 4 | 4 | no | — |
| 356 | C22×C11 | — | 4 | 4 | no | — |
| 357 | C22×C11 | C22×#41 | 1 | 1 | yes | characteristic |
| 358 | C22×C11 | C22×#41 | 1 | 2 | yes | — |
| 359 | C22×C11 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 360 | C22×C11 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 361 | C22×C11 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 362 | C2×D11 | — | 2 | 2 | no | — |
| 363 | C2×D11 | — | 2 | 4 | no | — |
| 364 | C2×D11 | — | 4 | 2 | no | — |
| 365 | C2×D11 | — | 4 | 1 | no | — |
| 366 | C2×D11 | — | 4 | 1 | no | — |
| 367 | C2×D11 | — | 4 | 4 | no | — |
| 368 | C2×D11 | — | 4 | 2 | no | — |
| 369 | C2×D11 | — | 4 | 2 | no | — |
| 370 | C2×D11 | — | 4 | 4 | no | — |
| 371 | C2×D11 | — | 4 | 2 | no | — |
| 372 | C4×C11 | — | 2 | 4 | no | — |
| 373 | C4×C11 | — | 2 | 4 | no | — |
| 374 | C4×C11 | — | 2 | 2 | no | — |
| 375 | C4×C11 | — | 4 | 4 | no | — |
| 376 | C4×C11 | — | 4 | 2 | no | — |
| 377 | Dic11 | — | 2 | 8 | no | — |
| 378 | Dic11 | — | 2 | 2 | no | — |
| 379 | Dic11 | — | 2 | 4 | no | — |
| 380 | Dic11 | — | 4 | 2 | no | — |
| 381 | Dic11 | — | 4 | 4 | no | — |
| 382 | C2×#41 | — | 22 | 8 | no | — |
| 383 | C2×#41 | — | 22 | 4 | no | — |
| 384 | C2×#41 | — | 44 | 4 | no | — |
| 385 | C2×#41 | — | 44 | 2 | no | — |
| 386 | C2×#41 | — | 44 | 4 | no | — |
| 387 | C2×#41 | — | 44 | 2 | no | — |
| 388 | C22×Q8 | — | 11 | 2 | no | — |
| 389 | C22×Q8 | — | 11 | 2 | no | — |
| 390 | C22×Q8 | C22×D11 | 1 | 1 | yes | characteristic |
| 391 | C22×D4 | — | 11 | 4 | no | — |
| 392 | C22×D4 | — | 11 | 4 | no | — |
| 393 | C22×D4 | — | 11 | 4 | no | — |
| 394 | C22×D4 | — | 11 | 2 | no | — |
| 395 | C22×D4 | — | 11 | 1 | no | — |
| 396 | C22×D4 | C22×D11 | 1 | 2 | yes | — |
| 397 | C22×D4 | C22×D11 | 1 | 2 | yes | — |
| 398 | C22×D4 | C22×D11 | 1 | 2 | yes | — |
| 399 | C23×C4 | — | 11 | 4 | no | — |
| 400 | C23×C4 | — | 11 | 1 | no | — |
| 401 | C23×C4 | — | 11 | 2 | no | — |
| 402 | C23×C4 | — | 11 | 2 | no | — |
| 403 | #127 | — | 44 | 4 | no | — |
| 404 | #124 | — | 2 | 8 | no | — |
| 405 | #124 | — | 22 | 16 | no | — |
| 406 | #124 | — | 44 | 8 | no | — |
| 407 | #124 | — | 44 | 4 | no | — |
| 408 | #121 | — | 44 | 4 | no | — |
| 409 | #121 | — | 44 | 8 | no | — |
| 410 | #117 | — | 44 | 4 | no | — |
| 411 | #117 | — | 44 | 2 | no | — |
| 412 | C2×C4⋊C4 | — | 11 | 1 | no | — |
| 413 | C2×C4⋊C4 | — | 11 | 2 | no | — |
| 414 | C2×C4⋊C4 | — | 11 | 4 | no | — |
| 415 | C2×C4⋊C4 | — | 11 | 2 | no | — |
| 416 | C2×C4⋊C4 | C22×D11 | 1 | 2 | yes | — |
| 417 | C2×C4⋊C4 | C22×D11 | 1 | 1 | yes | characteristic |
| 418 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 419 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 420 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 421 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 422 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 423 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 424 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 425 | C2×C22⋊C4 | — | 11 | 2 | no | — |
| 426 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 427 | C2×C22⋊C4 | — | 11 | 4 | no | — |
| 428 | C2×C22⋊C4 | C22×D11 | 1 | 4 | yes | — |
| 429 | C2×C22⋊C4 | C22×D11 | 1 | 4 | yes | — |
| 430 | C2×C22⋊C4 | C22×D11 | 1 | 4 | yes | — |
| 431 | C2×C22⋊C4 | C22×D11 | 1 | 4 | yes | — |
| 432 | C2×C42 | — | 11 | 2 | no | — |
| 433 | C2×C42 | — | 11 | 4 | no | — |
| 434 | C2×C42 | — | 11 | 4 | no | — |
| 435 | C2×C42 | — | 11 | 2 | no | — |
| 436 | C2×C42 | — | 11 | 1 | no | — |
| 437 | C2×C42 | — | 11 | 2 | no | — |
| 438 | C2×C42 | — | 44 | 2 | no | — |
| 439 | C2×C42 | C22×D11 | 1 | 2 | yes | — |
| 440 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 441 | #95 | — | 11 | 4 | no | — |
| 442 | #95 | — | 11 | 4 | no | — |
| 443 | #95 | — | 11 | 4 | no | — |
| 444 | #95 | — | 11 | 2 | no | — |
| 445 | #95 | — | 11 | 4 | no | — |
| 446 | #95 | — | 11 | 4 | no | — |
| 447 | #95 | — | 11 | 4 | no | — |
| 448 | #95 | — | 11 | 4 | no | — |
| 449 | #95 | C22×D11 | 1 | 2 | yes | — |
| 450 | #95 | C22×D11 | 1 | 4 | yes | — |
| 451 | C2×C11 | — | 8 | 4 | no | — |
| 452 | C2×C11 | #3483 | 1 | 2 | yes | — |
| 453 | C2×C11 | #3483 | 1 | 1 | yes | characteristic |
| 454 | C2×C11 | #3490 | 1 | 2 | yes | — |
| 455 | C2×C11 | #3490 | 1 | 1 | yes | characteristic |
| 456 | C2×C11 | #3549 | 1 | 1 | yes | characteristic |
| 457 | D11 | — | 4 | 2 | no | — |
| 458 | D11 | — | 8 | 2 | no | — |
| 459 | C24 | — | 11 | 1 | no | — |
| 460 | C24 | — | 11 | 2 | no | — |
| 461 | C24 | C23×D11 | 1 | 4 | yes | — |
| 462 | #41 | — | 44 | 32 | no | — |
| 463 | #41 | — | 44 | 16 | no | — |
| 464 | C2×Q8 | — | 4 | 1 | no | — |
| 465 | C2×Q8 | — | 4 | 1 | no | — |
| 466 | C2×Q8 | — | 11 | 8 | no | — |
| 467 | C2×Q8 | — | 44 | 2 | no | — |
| 468 | C2×Q8 | — | 44 | 2 | no | — |
| 469 | C2×Q8 | — | 44 | 2 | no | — |
| 470 | C2×Q8 | — | 44 | 4 | no | — |
| 471 | C2×Q8 | #4341 | 1 | 4 | yes | complemented |
| 472 | C2×D4 | — | 2 | 4 | no | — |
| 473 | C2×D4 | — | 2 | 4 | no | — |
| 474 | C2×D4 | — | 4 | 2 | no | — |
| 475 | C2×D4 | — | 4 | 2 | no | — |
| 476 | C2×D4 | — | 4 | 2 | no | — |
| 477 | C2×D4 | — | 4 | 4 | no | — |
| 478 | C2×D4 | — | 4 | 2 | no | — |
| 479 | C2×D4 | — | 4 | 2 | no | — |
| 480 | C2×D4 | — | 22 | 4 | no | — |
| 481 | C2×D4 | — | 22 | 8 | no | — |
| 482 | C2×D4 | — | 22 | 8 | no | — |
| 483 | C2×D4 | — | 22 | 8 | no | — |
| 484 | C2×D4 | — | 22 | 4 | no | — |
| 485 | C2×D4 | — | 22 | 2 | no | — |
| 486 | C2×D4 | — | 44 | 1 | no | — |
| 487 | C2×D4 | — | 44 | 1 | no | — |
| 488 | C2×D4 | — | 44 | 2 | no | — |
| 489 | C2×D4 | — | 44 | 4 | no | — |
| 490 | C2×D4 | — | 44 | 4 | no | — |
| 491 | C2×D4 | — | 44 | 4 | no | — |
| 492 | C2×D4 | — | 44 | 4 | no | — |
| 493 | C2×D4 | — | 44 | 4 | no | — |
| 494 | C2×D4 | — | 44 | 4 | no | — |
| 495 | C22×C4 | — | 11 | 4 | no | — |
| 496 | C22×C4 | — | 11 | 1 | no | — |
| 497 | C22×C4 | — | 11 | 2 | no | — |
| 498 | C22×C4 | — | 11 | 2 | no | — |
| 499 | C22×C4 | — | 11 | 4 | no | — |
| 500 | C22×C4 | — | 22 | 4 | no | — |
| 501 | C22×C4 | — | 22 | 2 | no | — |
| 502 | C22×C4 | — | 22 | 4 | no | — |
| 503 | C22×C4 | — | 22 | 4 | no | — |
| 504 | C22×C4 | — | 22 | 2 | no | — |
| 505 | C22×C4 | — | 22 | 8 | no | — |
| 506 | C22×C4 | — | 22 | 8 | no | — |
| 507 | C22×C4 | — | 22 | 2 | no | — |
| 508 | C22×C4 | — | 22 | 4 | no | — |
| 509 | C22×C4 | — | 22 | 4 | no | — |
| 510 | C22×C4 | — | 44 | 2 | no | — |
| 511 | C22×C4 | — | 44 | 4 | no | — |
| 512 | C22×C4 | C23×D11 | 1 | 4 | yes | — |
| 513 | C22×C4 | C23×D11 | 1 | 2 | yes | — |
| 514 | C22×C4 | C23×D11 | 1 | 2 | yes | — |
| 515 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 516 | C22×C4 | C23×D11 | 1 | 2 | yes | — |
| 517 | C4⋊C4 | — | 4 | 2 | no | — |
| 518 | C4⋊C4 | — | 4 | 1 | no | — |
| 519 | C4⋊C4 | — | 44 | 2 | no | — |
| 520 | C4⋊C4 | — | 44 | 1 | no | — |
| 521 | C4⋊C4 | — | 44 | 4 | no | — |
| 522 | C4⋊C4 | — | 44 | 2 | no | — |
| 523 | C22⋊C4 | — | 2 | 8 | no | — |
| 524 | C22⋊C4 | — | 2 | 8 | no | — |
| 525 | C22⋊C4 | — | 2 | 8 | no | — |
| 526 | C22⋊C4 | — | 4 | 4 | no | — |
| 527 | C22⋊C4 | — | 22 | 8 | no | — |
| 528 | C22⋊C4 | — | 22 | 8 | no | — |
| 529 | C22⋊C4 | — | 22 | 8 | no | — |
| 530 | C22⋊C4 | — | 22 | 8 | no | — |
| 531 | C22⋊C4 | — | 22 | 8 | no | — |
| 532 | C22⋊C4 | — | 22 | 8 | no | — |
| 533 | C22⋊C4 | — | 44 | 4 | no | — |
| 534 | C22⋊C4 | — | 44 | 2 | no | — |
| 535 | C22⋊C4 | — | 44 | 4 | no | — |
| 536 | C22⋊C4 | — | 44 | 4 | no | — |
| 537 | C42 | — | 2 | 4 | no | — |
| 538 | C42 | — | 4 | 1 | no | — |
| 539 | C42 | — | 22 | 8 | no | — |
| 540 | C42 | — | 22 | 4 | no | — |
| 541 | C42 | — | 22 | 8 | no | — |
| 542 | C42 | — | 44 | 2 | no | — |
| 543 | C42 | — | 44 | 1 | no | — |
| 544 | C42 | — | 44 | 2 | no | — |
| 545 | C11 | #60048 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 546 | C23 | — | 2 | 4 | no | — |
| 547 | C23 | — | 2 | 4 | no | — |
| 548 | C23 | — | 2 | 4 | no | — |
| 549 | C23 | — | 2 | 4 | no | — |
| 550 | C23 | — | 2 | 4 | no | — |
| 551 | C23 | — | 2 | 4 | no | — |
| 552 | C23 | — | 2 | 4 | no | — |
| 553 | C23 | — | 11 | 2 | no | — |
| 554 | C23 | — | 22 | 1 | no | — |
| 555 | C23 | — | 22 | 2 | no | — |
| 556 | C23 | — | 22 | 2 | no | — |
| 557 | C23 | — | 22 | 1 | no | — |
| 558 | C23 | — | 22 | 2 | no | — |
| 559 | C23 | — | 22 | 4 | no | — |
| 560 | C23 | — | 22 | 4 | no | — |
| 561 | C23 | — | 22 | 2 | no | — |
| 562 | C23 | — | 22 | 2 | no | — |
| 563 | C23 | C24×D11 | 1 | 1 | yes | characteristic |
| 564 | Q8 | — | 4 | 4 | no | — |
| 565 | Q8 | — | 44 | 8 | no | — |
| 566 | Q8 | — | 88 | 4 | no | — |
| 567 | D4 | — | 4 | 8 | no | — |
| 568 | D4 | — | 8 | 4 | no | — |
| 569 | D4 | — | 8 | 4 | no | — |
| 570 | D4 | — | 44 | 8 | no | — |
| 571 | D4 | — | 44 | 4 | no | — |
| 572 | D4 | — | 44 | 16 | no | — |
| 573 | D4 | — | 88 | 8 | no | — |
| 574 | D4 | — | 88 | 8 | no | — |
| 575 | C2×C4 | — | 2 | 2 | no | — |
| 576 | C2×C4 | — | 2 | 1 | no | — |
| 577 | C2×C4 | — | 2 | 2 | no | — |
| 578 | C2×C4 | — | 2 | 2 | no | — |
| 579 | C2×C4 | — | 2 | 1 | no | — |
| 580 | C2×C4 | — | 2 | 2 | no | — |
| 581 | C2×C4 | — | 2 | 4 | no | — |
| 582 | C2×C4 | — | 2 | 4 | no | — |
| 583 | C2×C4 | — | 2 | 4 | no | — |
| 584 | C2×C4 | — | 2 | 2 | no | — |
| 585 | C2×C4 | — | 2 | 4 | no | — |
| 586 | C2×C4 | — | 11 | 8 | no | — |
| 587 | C2×C4 | — | 11 | 4 | no | — |
| 588 | C2×C4 | — | 11 | 2 | no | — |
| 589 | C2×C4 | — | 22 | 16 | no | — |
| 590 | C2×C4 | — | 22 | 8 | no | — |
| 591 | C2×C4 | — | 22 | 1 | no | — |
| 592 | C2×C4 | — | 22 | 2 | no | — |
| 593 | C2×C4 | — | 22 | 2 | no | — |
| 594 | C2×C4 | — | 22 | 1 | no | — |
| 595 | C2×C4 | — | 22 | 4 | no | — |
| 596 | C2×C4 | — | 22 | 4 | no | — |
| 597 | C2×C4 | — | 22 | 4 | no | — |
| 598 | C2×C4 | — | 22 | 2 | no | — |
| 599 | C2×C4 | — | 22 | 4 | no | — |
| 600 | C2×C4 | — | 22 | 4 | no | — |
| 601 | C2×C4 | — | 22 | 4 | no | — |
| 602 | C2×C4 | — | 44 | 8 | no | — |
| 603 | C2×C4 | — | 44 | 16 | no | — |
| 604 | C2×C4 | C2×#4341 | 1 | 4 | yes | — |
| 605 | C2×C4 | C2×#4341 | 1 | 2 | yes | — |
| 606 | C2×C4 | #41×D11 | 1 | 4 | yes | — |
| 607 | C22 | — | 4 | 4 | no | — |
| 608 | C22 | — | 4 | 4 | no | — |
| 609 | C22 | — | 4 | 4 | no | — |
| 610 | C22 | — | 4 | 4 | no | — |
| 611 | C22 | — | 4 | 4 | no | — |
| 612 | C22 | — | 4 | 4 | no | — |
| 613 | C22 | — | 4 | 4 | no | — |
| 614 | C22 | — | 22 | 4 | no | — |
| 615 | C22 | — | 22 | 2 | no | — |
| 616 | C22 | — | 44 | 2 | no | — |
| 617 | C22 | — | 44 | 1 | no | — |
| 618 | C22 | — | 44 | 1 | no | — |
| 619 | C22 | — | 44 | 4 | no | — |
| 620 | C22 | — | 44 | 2 | no | — |
| 621 | C22 | — | 44 | 2 | no | — |
| 622 | C22 | — | 44 | 4 | no | — |
| 623 | C22 | — | 44 | 2 | no | — |
| 624 | C22 | C22×#4341 | 1 | 1 | yes | characteristic |
| 625 | C22 | C2×#41×D11 | 1 | 2 | yes | — |
| 626 | C22 | D11×H(5,𝔽2) | 1 | 2 | yes | — |
| 627 | C22 | D11×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 628 | C22 | D11×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 629 | C4 | — | 2 | 4 | no | — |
| 630 | C4 | — | 2 | 2 | no | — |
| 631 | C4 | — | 2 | 4 | no | — |
| 632 | C4 | — | 4 | 4 | no | — |
| 633 | C4 | — | 4 | 2 | no | — |
| 634 | C4 | — | 22 | 4 | no | — |
| 635 | C4 | — | 22 | 8 | no | — |
| 636 | C4 | — | 22 | 2 | no | — |
| 637 | C4 | — | 44 | 2 | no | — |
| 638 | C4 | — | 44 | 4 | no | — |
| 639 | C2 | — | 8 | 4 | no | — |
| 640 | C2 | — | 44 | 2 | no | — |
| 641 | C2 | — | 88 | 2 | no | — |
| 642 | C2 | #13082239 | 1 | 2 | yes | — |
| 643 | C2 | #13082241 | 1 | 1 | yes | characteristic |
| 644 | C2 | #13082302 | 1 | 2 | yes | — |
| 645 | C2 | #13082304 | 1 | 1 | yes | characteristic |
| 646 | C2 | #13083020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2733 | C2 |
| hypercenter | #2733 | D11 |
| hypocenter | C11 | #60048 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2733 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13076609 | C2 | semidirect |
| 2. #13075641 | C2 | semidirect |
| 3. #13074306 | C2 | semidirect |
| 4. #13074302 | C2 | semidirect |
| 5. #13073686 | C2 | semidirect |
| 6. #13073684 | C2 | semidirect |
| 7. #13072238 | C2 | semidirect |
| 8. #13072230 | C2 | semidirect |
| 9. #13071728 | C2 | semidirect |
| 10. #13071723 | C2 | semidirect |
| 11. #13071105 | C2 | semidirect |
| 12. #13071103 | C2 | semidirect |
| 13. C11×#2733 | C2 | semidirect |
| 142. C2×Q8×C11 | #41 | semidirect |
| 194. C2×Dic22 | #41 | semidirect |
| 225. #2733 | D11 | semidirect |
| 471. C2×Q8 | #4341 | semidirect |
| 545. C11 | #60048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13076609 | 2 |
| #13075641 | 2 |
| #13074306 | 2 |
| #13074302 | 2 |
| #13073686 | 2 |
| #13073684 | 2 |
| #13072238 | 2 |
| #13072230 | 2 |
| #13071728 | 2 |
| #13071723 | 2 |
| #13071105 | 2 |
| #13071103 | 2 |
| C11×#2733 | 2 |
| #60048 | 11 |