Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4886 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#66948 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C22×#66937 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #13074719 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 4 | C2×#10622605 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C2×#10622284 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#10622573 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×D11×#95 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×C11×#399 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C23×C22⋊D11 | C22 | 1 | 1 | yes | characteristic |
| 10 | C23×C22⋊D11 | C22 | 1 | 3 | yes | — |
| 11 | C23×D44 | C22 | 1 | 3 | yes | — |
| 12 | C23×D44 | C22 | 1 | 3 | yes | — |
| 13 | C23×C4×D11 | C22 | 1 | 3 | yes | — |
| 14 | C22×C11×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 15 | C22×C11×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 16 | C22×(C2×D11)⋊C4 | C22 | 1 | 6 | yes | — |
| 17 | C22×(C2×D11)⋊C4 | C22 | 1 | 3 | yes | — |
| 18 | C22×Dic11⋊C4 | C22 | 1 | 3 | yes | — |
| 19 | C2×#66948 | — | 2 | 24 | no | — |
| 20 | C2×#66948 | C22 | 1 | 24 | yes | complemented |
| 21 | C2×#66937 | — | 2 | 24 | no | — |
| 22 | C2×#66937 | C22 | 1 | 24 | yes | complemented |
| 23 | C11×#399 | C22 | 1 | 8 | yes | complemented |
| 24 | C2×C11×#95 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C11⋊#95 | C22 | 1 | 3 | yes | — |
| 26 | #10622605 | C22 | 1 | 24 | yes | complemented |
| 27 | #10622573 | C22 | 1 | 24 | yes | complemented |
| 28 | #10622284 | C22 | 1 | 8 | yes | complemented |
| 29 | D11×#95 | C22 | 1 | 8 | yes | complemented |
| 30 | C25×C11 | C23 | 1 | 1 | yes | characteristic |
| 31 | C24×D11 | C23 | 1 | 3 | yes | — |
| 32 | C24×D11 | C23 | 1 | 1 | yes | characteristic |
| 33 | C23×C4×C11 | C23 | 1 | 3 | yes | — |
| 34 | C23×C4×C11 | C23 | 1 | 3 | yes | — |
| 35 | C22×C22⋊D11 | — | 2 | 12 | no | — |
| 36 | C22×C22⋊D11 | — | 2 | 12 | no | — |
| 37 | C22×C22⋊D11 | — | 4 | 12 | no | — |
| 38 | C22×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 39 | C22×C22⋊D11 | C23 | 1 | 12 | yes | — |
| 40 | C23×Dic11 | C23 | 1 | 1 | yes | characteristic |
| 41 | C23×Dic11 | C23 | 1 | 3 | yes | — |
| 42 | C22×D44 | — | 2 | 12 | no | — |
| 43 | C22×D44 | — | 2 | 24 | no | — |
| 44 | C22×D44 | — | 2 | 12 | no | — |
| 45 | C22×D44 | — | 4 | 12 | no | — |
| 46 | C22×D44 | C23 | 1 | 12 | yes | — |
| 47 | C22×D44 | C23 | 1 | 12 | yes | — |
| 48 | C22×C4×D11 | — | 4 | 12 | no | — |
| 49 | C22×C4×D11 | D4 | 1 | 24 | yes | complemented |
| 50 | C22×C4×D11 | C23 | 1 | 12 | yes | — |
| 51 | C2×C11×C4⋊C4 | — | 2 | 12 | no | — |
| 52 | C2×C11×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 53 | C2×C11×C22⋊C4 | — | 2 | 12 | no | — |
| 54 | C2×C11×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 55 | C2×(C2×D11)⋊C4 | — | 2 | 12 | no | — |
| 56 | C2×(C2×D11)⋊C4 | — | 2 | 24 | no | — |
| 57 | C2×(C2×D11)⋊C4 | C23 | 1 | 12 | yes | — |
| 58 | C2×(C2×D11)⋊C4 | C23 | 1 | 24 | yes | — |
| 59 | C2×Dic11⋊C4 | — | 2 | 12 | no | — |
| 60 | C2×Dic11⋊C4 | C23 | 1 | 12 | yes | — |
| 61 | #66948 | — | 2 | 96 | no | — |
| 62 | #66937 | — | 2 | 96 | no | — |
| 63 | C11×#95 | C23 | 1 | 4 | yes | — |
| 64 | C11⋊#95 | C23 | 1 | 12 | yes | — |
| 65 | C2×#2656 | — | 11 | 1 | no | maximal, Sylow |
| 66 | C24×C11 | — | 2 | 6 | no | — |
| 67 | C24×C11 | — | 2 | 6 | no | — |
| 68 | C24×C11 | — | 2 | 2 | no | — |
| 69 | C24×C11 | C24 | 1 | 2 | yes | — |
| 70 | C24×C11 | C24 | 1 | 1 | yes | characteristic |
| 71 | C23×D11 | — | 2 | 6 | no | — |
| 72 | C23×D11 | — | 2 | 2 | no | — |
| 73 | C23×D11 | — | 2 | 12 | no | — |
| 74 | C23×D11 | — | 2 | 6 | no | — |
| 75 | C23×D11 | — | 2 | 6 | no | — |
| 76 | C23×D11 | — | 2 | 12 | no | — |
| 77 | C23×D11 | — | 2 | 6 | no | — |
| 78 | C23×D11 | C2×D4 | 1 | 12 | yes | — |
| 79 | C23×D11 | C24 | 1 | 6 | yes | — |
| 80 | C23×D11 | C24 | 1 | 2 | yes | — |
| 81 | C22×C4×C11 | — | 2 | 12 | no | — |
| 82 | C22×C4×C11 | — | 2 | 6 | no | — |
| 83 | C22×C4×C11 | — | 2 | 12 | no | — |
| 84 | C22×C4×C11 | C2×D4 | 1 | 12 | yes | — |
| 85 | C22×C4×C11 | C24 | 1 | 6 | yes | — |
| 86 | C22×C4×C11 | C24 | 1 | 6 | yes | — |
| 87 | C2×C22⋊D11 | — | 2 | 24 | no | — |
| 88 | C2×C22⋊D11 | — | 2 | 24 | no | — |
| 89 | C2×C22⋊D11 | — | 4 | 24 | no | — |
| 90 | C2×C22⋊D11 | — | 4 | 48 | no | — |
| 91 | C2×C22⋊D11 | — | 4 | 16 | no | — |
| 92 | C22×Dic11 | — | 2 | 6 | no | — |
| 93 | C22×Dic11 | — | 2 | 12 | no | — |
| 94 | C22×Dic11 | C2×D4 | 1 | 12 | yes | — |
| 95 | C22×Dic11 | C24 | 1 | 2 | yes | — |
| 96 | C22×Dic11 | C24 | 1 | 6 | yes | — |
| 97 | C2×D44 | — | 2 | 24 | no | — |
| 98 | C2×D44 | — | 2 | 48 | no | — |
| 99 | C2×D44 | — | 2 | 24 | no | — |
| 100 | C2×D44 | — | 4 | 24 | no | — |
| 101 | C2×D44 | — | 4 | 48 | no | — |
| 102 | C2×D44 | — | 4 | 48 | no | — |
| 103 | C2×C4×D11 | — | 4 | 48 | no | — |
| 104 | C2×C4×D11 | — | 4 | 24 | no | — |
| 105 | C2×C4×D11 | C2×D4 | 1 | 48 | yes | complemented |
| 106 | C11×C4⋊C4 | — | 2 | 24 | no | — |
| 107 | C11×C22⋊C4 | — | 2 | 24 | no | — |
| 108 | (C2×D11)⋊C4 | — | 2 | 48 | no | — |
| 109 | (C2×D11)⋊C4 | — | 2 | 24 | no | — |
| 110 | Dic11⋊C4 | — | 2 | 24 | no | — |
| 111 | C22×#121 | — | 11 | 3 | no | — |
| 112 | C22×#121 | — | 11 | 3 | no | — |
| 113 | #2656 | — | 11 | 16 | no | — |
| 114 | C2×#399 | — | 11 | 3 | no | — |
| 115 | C2×#399 | D11 | 1 | 1 | yes | characteristic, complemented |
| 116 | C2×#392 | — | 11 | 1 | no | — |
| 117 | C2×#392 | — | 11 | 3 | no | — |
| 118 | C22×#95 | — | 11 | 1 | no | — |
| 119 | C23×C11 | — | 2 | 6 | no | — |
| 120 | C23×C11 | — | 2 | 6 | no | — |
| 121 | C23×C11 | — | 2 | 2 | no | — |
| 122 | C23×C11 | — | 4 | 4 | no | — |
| 123 | C23×C11 | — | 4 | 12 | no | — |
| 124 | C23×C11 | — | 4 | 12 | no | — |
| 125 | C23×C11 | C22×D4 | 1 | 6 | yes | — |
| 126 | C23×C11 | H(5,𝔽2) | 1 | 6 | yes | — |
| 127 | C23×C11 | 2−1+4 | 1 | 2 | yes | — |
| 128 | C23×C11 | C25 | 1 | 1 | yes | characteristic |
| 129 | C22×D11 | — | 2 | 24 | no | — |
| 130 | C22×D11 | — | 2 | 24 | no | — |
| 131 | C22×D11 | — | 2 | 6 | no | — |
| 132 | C22×D11 | — | 2 | 2 | no | — |
| 133 | C22×D11 | — | 2 | 12 | no | — |
| 134 | C22×D11 | — | 2 | 6 | no | — |
| 135 | C22×D11 | — | 2 | 6 | no | — |
| 136 | C22×D11 | — | 2 | 12 | no | — |
| 137 | C22×D11 | — | 2 | 6 | no | — |
| 138 | C22×D11 | — | 4 | 12 | no | — |
| 139 | C22×D11 | — | 4 | 24 | no | — |
| 140 | C22×D11 | — | 4 | 12 | no | — |
| 141 | C22×D11 | — | 4 | 24 | no | — |
| 142 | C22×D11 | — | 4 | 12 | no | — |
| 143 | C22×D11 | #127 | 1 | 16 | yes | — |
| 144 | C22×D11 | C22×D4 | 1 | 12 | yes | — |
| 145 | C2×C4×C11 | — | 2 | 24 | no | — |
| 146 | C2×C4×C11 | — | 2 | 12 | no | — |
| 147 | C2×C4×C11 | — | 2 | 6 | no | — |
| 148 | C2×C4×C11 | — | 2 | 12 | no | — |
| 149 | C2×C4×C11 | — | 4 | 12 | no | — |
| 150 | C2×C4×C11 | C22×D4 | 1 | 12 | yes | — |
| 151 | C22⋊D11 | — | 4 | 48 | no | — |
| 152 | C22⋊D11 | — | 4 | 16 | no | — |
| 153 | C2×Dic11 | — | 2 | 24 | no | — |
| 154 | C2×Dic11 | — | 2 | 12 | no | — |
| 155 | C2×Dic11 | — | 2 | 6 | no | — |
| 156 | C2×Dic11 | — | 4 | 4 | no | — |
| 157 | C2×Dic11 | C22×D4 | 1 | 12 | yes | — |
| 158 | D44 | — | 4 | 48 | no | — |
| 159 | D44 | — | 4 | 48 | no | — |
| 160 | C4×D11 | — | 4 | 48 | no | — |
| 161 | C23×D4 | — | 11 | 1 | no | — |
| 162 | C23×D4 | — | 11 | 3 | no | — |
| 163 | C23×D4 | — | 11 | 3 | no | — |
| 164 | C23×D4 | — | 11 | 3 | no | — |
| 165 | C24×C4 | — | 11 | 3 | no | — |
| 166 | C2×#121 | — | 11 | 24 | no | — |
| 167 | C2×#121 | — | 11 | 24 | no | — |
| 168 | C2×#121 | — | 22 | 24 | no | — |
| 169 | C2×#121 | — | 22 | 24 | no | — |
| 170 | C22×C4⋊C4 | — | 11 | 3 | no | — |
| 171 | C22×C4⋊C4 | C2×D11 | 1 | 3 | yes | — |
| 172 | C22×C22⋊C4 | — | 11 | 6 | no | — |
| 173 | C22×C22⋊C4 | — | 11 | 3 | no | — |
| 174 | C22×C22⋊C4 | C2×D11 | 1 | 3 | yes | — |
| 175 | #399 | — | 11 | 24 | no | — |
| 176 | #399 | C2×D11 | 1 | 8 | yes | complemented |
| 177 | #392 | — | 11 | 24 | no | — |
| 178 | #392 | — | 11 | 8 | no | — |
| 179 | C2×#95 | — | 11 | 3 | no | — |
| 180 | C2×#95 | — | 11 | 8 | no | — |
| 181 | C2×#95 | C2×D11 | 1 | 1 | yes | characteristic |
| 182 | C22×C11 | — | 4 | 2 | no | — |
| 183 | C22×C11 | — | 4 | 6 | no | — |
| 184 | C22×C11 | — | 4 | 6 | no | — |
| 185 | C22×C11 | — | 8 | 8 | no | — |
| 186 | C22×C11 | C2×#127 | 1 | 4 | yes | — |
| 187 | C22×C11 | #534 | 1 | 12 | yes | — |
| 188 | C22×C11 | #537 | 1 | 12 | yes | — |
| 189 | C22×C11 | C23×D4 | 1 | 3 | yes | — |
| 190 | C22×C11 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 191 | C22×C11 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 192 | C2×D11 | — | 2 | 32 | no | — |
| 193 | C2×D11 | — | 2 | 12 | no | — |
| 194 | C2×D11 | — | 2 | 12 | no | — |
| 195 | C2×D11 | — | 4 | 6 | no | — |
| 196 | C2×D11 | — | 4 | 12 | no | — |
| 197 | C2×D11 | — | 4 | 6 | no | — |
| 198 | C2×D11 | — | 4 | 12 | no | — |
| 199 | C2×D11 | — | 4 | 6 | no | — |
| 200 | C2×D11 | — | 8 | 24 | no | — |
| 201 | C2×D11 | C2×#127 | 1 | 8 | yes | — |
| 202 | C4×C11 | — | 2 | 12 | no | — |
| 203 | C4×C11 | — | 4 | 6 | no | — |
| 204 | Dic11 | — | 2 | 12 | no | — |
| 205 | Dic11 | — | 4 | 2 | no | — |
| 206 | C25 | — | 11 | 1 | no | — |
| 207 | C25 | — | 11 | 3 | no | — |
| 208 | C25 | C22×D11 | 1 | 1 | yes | characteristic |
| 209 | C22×D4 | — | 11 | 4 | no | — |
| 210 | C22×D4 | — | 11 | 12 | no | — |
| 211 | C22×D4 | — | 11 | 12 | no | — |
| 212 | C22×D4 | — | 11 | 12 | no | — |
| 213 | C22×D4 | — | 22 | 12 | no | — |
| 214 | C22×D4 | — | 22 | 24 | no | — |
| 215 | C22×D4 | — | 22 | 12 | no | — |
| 216 | C22×D4 | — | 22 | 12 | no | — |
| 217 | C22×D4 | — | 22 | 12 | no | — |
| 218 | C22×D4 | — | 44 | 12 | no | — |
| 219 | C22×D4 | — | 44 | 12 | no | — |
| 220 | C23×C4 | — | 11 | 3 | no | — |
| 221 | C23×C4 | — | 11 | 24 | no | — |
| 222 | C23×C4 | — | 11 | 12 | no | — |
| 223 | C23×C4 | — | 11 | 1 | no | — |
| 224 | C23×C4 | — | 44 | 12 | no | — |
| 225 | C23×C4 | C22×D11 | 1 | 3 | yes | — |
| 226 | C23×C4 | C22×D11 | 1 | 3 | yes | — |
| 227 | #121 | — | 22 | 96 | no | — |
| 228 | #121 | — | 22 | 96 | no | — |
| 229 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 230 | C2×C4⋊C4 | — | 11 | 12 | no | — |
| 231 | C2×C4⋊C4 | — | 22 | 12 | no | — |
| 232 | C2×C4⋊C4 | C22×D11 | 1 | 12 | yes | — |
| 233 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 234 | C2×C22⋊C4 | — | 11 | 24 | no | — |
| 235 | C2×C22⋊C4 | — | 11 | 12 | no | — |
| 236 | C2×C22⋊C4 | — | 22 | 24 | no | — |
| 237 | C2×C22⋊C4 | — | 22 | 12 | no | — |
| 238 | C2×C22⋊C4 | C22×D11 | 1 | 12 | yes | — |
| 239 | #95 | — | 11 | 12 | no | — |
| 240 | #95 | C22×D11 | 1 | 4 | yes | — |
| 241 | C2×C11 | — | 8 | 2 | no | — |
| 242 | C2×C11 | #2656 | 1 | 8 | yes | complemented |
| 243 | C2×C11 | C22×#127 | 1 | 1 | yes | characteristic |
| 244 | C2×C11 | C2×#534 | 1 | 3 | yes | — |
| 245 | C2×C11 | C2×#537 | 1 | 3 | yes | — |
| 246 | D11 | — | 2 | 8 | no | — |
| 247 | D11 | — | 8 | 6 | no | — |
| 248 | C24 | — | 2 | 6 | no | — |
| 249 | C24 | — | 2 | 2 | no | — |
| 250 | C24 | — | 2 | 6 | no | — |
| 251 | C24 | — | 11 | 12 | no | — |
| 252 | C24 | — | 11 | 2 | no | — |
| 253 | C24 | — | 11 | 6 | no | — |
| 254 | C24 | — | 22 | 2 | no | — |
| 255 | C24 | — | 22 | 6 | no | — |
| 256 | C24 | — | 22 | 12 | no | — |
| 257 | C24 | — | 22 | 6 | no | — |
| 258 | C24 | — | 22 | 6 | no | — |
| 259 | C24 | — | 22 | 6 | no | — |
| 260 | C24 | — | 22 | 12 | no | — |
| 261 | C24 | C23×D11 | 1 | 2 | yes | — |
| 262 | C24 | C23×D11 | 1 | 1 | yes | characteristic |
| 263 | C2×D4 | — | 22 | 24 | no | — |
| 264 | C2×D4 | — | 22 | 48 | no | — |
| 265 | C2×D4 | — | 22 | 24 | no | — |
| 266 | C2×D4 | — | 22 | 24 | no | — |
| 267 | C2×D4 | — | 22 | 24 | no | — |
| 268 | C2×D4 | — | 44 | 24 | no | — |
| 269 | C2×D4 | — | 44 | 48 | no | — |
| 270 | C2×D4 | — | 44 | 48 | no | — |
| 271 | C2×D4 | — | 44 | 24 | no | — |
| 272 | C2×D4 | — | 44 | 48 | no | — |
| 273 | C2×D4 | — | 44 | 16 | no | — |
| 274 | C22×C4 | — | 2 | 12 | no | — |
| 275 | C22×C4 | — | 2 | 6 | no | — |
| 276 | C22×C4 | — | 2 | 12 | no | — |
| 277 | C22×C4 | — | 11 | 12 | no | — |
| 278 | C22×C4 | — | 11 | 6 | no | — |
| 279 | C22×C4 | — | 11 | 48 | no | — |
| 280 | C22×C4 | — | 11 | 2 | no | — |
| 281 | C22×C4 | — | 22 | 12 | no | — |
| 282 | C22×C4 | — | 22 | 6 | no | — |
| 283 | C22×C4 | — | 44 | 48 | no | — |
| 284 | C22×C4 | — | 44 | 24 | no | — |
| 285 | C22×C4 | D4×D11 | 1 | 12 | yes | — |
| 286 | C22×C4 | C23×D11 | 1 | 6 | yes | — |
| 287 | C22×C4 | C23×D11 | 1 | 6 | yes | — |
| 288 | C4⋊C4 | — | 2 | 24 | no | — |
| 289 | C4⋊C4 | — | 22 | 24 | no | — |
| 290 | C22⋊C4 | — | 2 | 24 | no | — |
| 291 | C22⋊C4 | — | 22 | 48 | no | — |
| 292 | C22⋊C4 | — | 22 | 24 | no | — |
| 293 | C11 | C2×#2656 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 294 | C23 | — | 2 | 6 | no | — |
| 295 | C23 | — | 2 | 2 | no | — |
| 296 | C23 | — | 2 | 6 | no | — |
| 297 | C23 | — | 4 | 4 | no | — |
| 298 | C23 | — | 4 | 12 | no | — |
| 299 | C23 | — | 4 | 12 | no | — |
| 300 | C23 | — | 11 | 16 | no | — |
| 301 | C23 | — | 11 | 12 | no | — |
| 302 | C23 | — | 22 | 24 | no | — |
| 303 | C23 | — | 22 | 24 | no | — |
| 304 | C23 | — | 22 | 2 | no | — |
| 305 | C23 | — | 22 | 6 | no | — |
| 306 | C23 | — | 22 | 12 | no | — |
| 307 | C23 | — | 22 | 6 | no | — |
| 308 | C23 | — | 22 | 6 | no | — |
| 309 | C23 | — | 22 | 6 | no | — |
| 310 | C23 | — | 22 | 12 | no | — |
| 311 | C23 | — | 44 | 12 | no | — |
| 312 | C23 | — | 44 | 24 | no | — |
| 313 | C23 | — | 44 | 12 | no | — |
| 314 | C23 | — | 44 | 24 | no | — |
| 315 | C23 | — | 44 | 12 | no | — |
| 316 | C23 | C2×D4×D11 | 1 | 6 | yes | — |
| 317 | C23 | #67040 | 1 | 2 | yes | — |
| 318 | C23 | #67042 | 1 | 6 | yes | — |
| 319 | C23 | C24×D11 | 1 | 1 | yes | characteristic |
| 320 | D4 | — | 44 | 48 | no | — |
| 321 | D4 | — | 44 | 48 | no | — |
| 322 | D4 | — | 44 | 48 | no | — |
| 323 | D4 | — | 44 | 16 | no | — |
| 324 | C2×C4 | — | 2 | 24 | no | — |
| 325 | C2×C4 | — | 2 | 12 | no | — |
| 326 | C2×C4 | — | 2 | 6 | no | — |
| 327 | C2×C4 | — | 2 | 12 | no | — |
| 328 | C2×C4 | — | 4 | 12 | no | — |
| 329 | C2×C4 | — | 11 | 12 | no | — |
| 330 | C2×C4 | — | 22 | 24 | no | — |
| 331 | C2×C4 | — | 22 | 12 | no | — |
| 332 | C2×C4 | — | 22 | 6 | no | — |
| 333 | C2×C4 | — | 44 | 48 | no | — |
| 334 | C2×C4 | — | 44 | 4 | no | — |
| 335 | C2×C4 | C2×D4×D11 | 1 | 12 | yes | — |
| 336 | C22 | — | 4 | 2 | no | — |
| 337 | C22 | — | 4 | 6 | no | — |
| 338 | C22 | — | 4 | 6 | no | — |
| 339 | C22 | — | 8 | 8 | no | — |
| 340 | C22 | — | 11 | 8 | no | — |
| 341 | C22 | — | 22 | 32 | no | — |
| 342 | C22 | — | 22 | 12 | no | — |
| 343 | C22 | — | 22 | 12 | no | — |
| 344 | C22 | — | 44 | 6 | no | — |
| 345 | C22 | — | 44 | 12 | no | — |
| 346 | C22 | — | 44 | 6 | no | — |
| 347 | C22 | — | 44 | 12 | no | — |
| 348 | C22 | — | 44 | 6 | no | — |
| 349 | C22 | — | 88 | 24 | no | — |
| 350 | C22 | #10623160 | 1 | 12 | yes | — |
| 351 | C22 | #10623184 | 1 | 12 | yes | — |
| 352 | C22 | D11×#127 | 1 | 4 | yes | — |
| 353 | C22 | C22×D4×D11 | 1 | 3 | yes | — |
| 354 | C22 | C2×#67040 | 1 | 1 | yes | characteristic |
| 355 | C22 | C2×#67042 | 1 | 3 | yes | — |
| 356 | C4 | — | 2 | 12 | no | — |
| 357 | C4 | — | 4 | 6 | no | — |
| 358 | C4 | — | 22 | 12 | no | — |
| 359 | C4 | — | 44 | 2 | no | — |
| 360 | C2 | — | 8 | 2 | no | — |
| 361 | C2 | — | 22 | 8 | no | — |
| 362 | C2 | — | 88 | 6 | no | — |
| 363 | C2 | #13074719 | 1 | 8 | yes | direct product factor |
| 364 | C2 | C2×D11×#127 | 1 | 1 | yes | characteristic |
| 365 | C2 | C2×#10623184 | 1 | 3 | yes | — |
| 366 | C2 | C2×#10623160 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D11 |
| commutator, cosocle | C23×C11 | C25 |
| Frattini | C23 | C24×D11 |
| Fitting | C2×C11×#399 | C2 |
| socle | C24×C11 | C24 |
| hypercenter | C2×#399 | D11 |
| hypocenter | C11 | C2×#2656 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#66948 | C2 | semidirect |
| 2. C22×#66937 | C2 | semidirect |
| 3. #13074719 | C2 | direct (N × H) |
| 4. C2×#10622605 | C2 | semidirect |
| 5. C2×#10622284 | C2 | semidirect |
| 6. C2×#10622573 | C2 | semidirect |
| 7. C2×D11×#95 | C2 | semidirect |
| 8. C2×C11×#399 | C2 | semidirect |
| 20. C2×#66948 | C22 | semidirect |
| 22. C2×#66937 | C22 | semidirect |
| 23. C11×#399 | C22 | semidirect |
| 26. #10622605 | C22 | semidirect |
| 27. #10622573 | C22 | semidirect |
| 28. #10622284 | C22 | semidirect |
| 29. D11×#95 | C22 | semidirect |
| 49. C22×C4×D11 | D4 | semidirect |
| 105. C2×C4×D11 | C2×D4 | semidirect |
| 115. C2×#399 | D11 | semidirect |
| 176. #399 | C2×D11 | semidirect |
| 242. C2×C11 | #2656 | semidirect |
| 293. C11 | C2×#2656 | semidirect |
| 363. C2 | #13074719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66948 | 2 |
| C22×#66937 | 2 |
| #13074719 | 2 |
| C2×#10622605 | 2 |
| C2×#10622284 | 2 |
| C2×#10622573 | 2 |
| C2×D11×#95 | 2 |
| C2×C11×#399 | 2 |
| C2×#2656 | 11 |