Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
10199784 conjugacy classes of subgroups.
The subgroup lattice has 405 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C24×#380 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | C25×#121 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C24×#386 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C23×#2847 | C2 | 1 | 240 | yes | maximal, direct product factor |
| 5 | C25×#120 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C28×C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C29 | C22 | 1 | 1 | yes | characteristic |
| 8 | C26×D4 | C22 | 1 | 6 | yes | — |
| 9 | C26×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C27×C4 | — | 2 | 192 | no | — |
| 11 | C27×C4 | C22 | 1 | 3 | yes | — |
| 12 | C27×C4 | C22 | 1 | 3 | yes | — |
| 13 | C27×C4 | C22 | 1 | 120 | yes | complemented |
| 14 | C24×#121 | — | 2 | 192 | no | — |
| 15 | C24×#121 | C22 | 1 | 360 | yes | complemented |
| 16 | C24×#120 | — | 2 | 128 | no | — |
| 17 | C24×#120 | C22 | 1 | 240 | yes | complemented |
| 18 | C25×C4⋊C4 | C22 | 1 | 3 | yes | complemented |
| 19 | C25×C22⋊C4 | C22 | 1 | 6 | yes | — |
| 20 | C25×C22⋊C4 | C22 | 1 | 6 | yes | complemented |
| 21 | C22×#2847 | C22 | 1 | 8960 | yes | direct product factor |
| 22 | C23×#386 | C22 | 1 | 720 | yes | complemented |
| 23 | C23×#380 | C22 | 1 | 360 | yes | complemented |
| 24 | C24×#95 | C22 | 1 | 6 | yes | complemented |
| 25 | C28 | — | 2 | 96 | no | — |
| 26 | C28 | — | 2 | 96 | no | — |
| 27 | C28 | D4 | 1 | 64 | yes | complemented |
| 28 | C28 | C23 | 1 | 2 | yes | — |
| 29 | C28 | C23 | 1 | 60 | yes | — |
| 30 | C28 | C23 | 1 | 3 | yes | — |
| 31 | C25×D4 | — | 2 | 192 | no | — |
| 32 | C25×D4 | — | 2 | 192 | no | — |
| 33 | C25×D4 | — | 2 | 192 | no | — |
| 34 | C25×D4 | — | 2 | 96 | no | — |
| 35 | C25×D4 | C23 | 1 | 360 | yes | — |
| 36 | C25×D4 | C23 | 1 | 60 | yes | complemented |
| 37 | C26×C4 | — | 2 | 8192 | no | — |
| 38 | C26×C4 | — | 2 | 96 | no | — |
| 39 | C26×C4 | — | 2 | 192 | no | — |
| 40 | C26×C4 | — | 2 | 192 | no | — |
| 41 | C26×C4 | — | 2 | 11520 | no | — |
| 42 | C26×C4 | D4 | 1 | 192 | yes | complemented |
| 43 | C26×C4 | C23 | 1 | 180 | yes | — |
| 44 | C26×C4 | C23 | 1 | 6 | yes | — |
| 45 | C26×C4 | C23 | 1 | 3 | yes | — |
| 46 | C26×C4 | C23 | 1 | 180 | yes | — |
| 47 | C26×C4 | C23 | 1 | 1 | yes | characteristic |
| 48 | C26×C4 | C23 | 1 | 2240 | yes | complemented |
| 49 | C23×#121 | — | 2 | 11520 | no | — |
| 50 | C23×#121 | C23 | 1 | 6720 | yes | complemented |
| 51 | C23×#120 | — | 2 | 7680 | no | — |
| 52 | C23×#120 | C23 | 1 | 4480 | yes | complemented |
| 53 | C24×C4⋊C4 | — | 2 | 96 | no | — |
| 54 | C24×C4⋊C4 | C23 | 1 | 180 | yes | complemented |
| 55 | C24×C22⋊C4 | — | 2 | 192 | no | — |
| 56 | C24×C22⋊C4 | — | 2 | 192 | no | — |
| 57 | C24×C22⋊C4 | C23 | 1 | 360 | yes | — |
| 58 | C24×C22⋊C4 | C23 | 1 | 360 | yes | complemented |
| 59 | C2×#2847 | C23 | 1 | 61440 | yes | direct product factor |
| 60 | C22×#386 | C23 | 1 | 13440 | yes | complemented |
| 61 | C22×#380 | C23 | 1 | 6720 | yes | complemented |
| 62 | C23×#95 | C23 | 1 | 360 | yes | complemented |
| 63 | C27 | — | 2 | 2048 | no | — |
| 64 | C27 | — | 2 | 6144 | no | — |
| 65 | C27 | — | 2 | 6144 | no | — |
| 66 | C27 | — | 2 | 2880 | no | — |
| 67 | C27 | — | 2 | 96 | no | — |
| 68 | C27 | — | 2 | 2880 | no | — |
| 69 | C27 | — | 2 | 96 | no | — |
| 70 | C27 | — | 2 | 32 | no | — |
| 71 | C27 | — | 2 | 96 | no | — |
| 72 | C27 | — | 2 | 96 | no | — |
| 73 | C27 | C2×D4 | 1 | 96 | yes | — |
| 74 | C27 | C2×D4 | 1 | 96 | yes | — |
| 75 | C27 | C2×D4 | 1 | 1920 | yes | complemented |
| 76 | C27 | #41 | 1 | 96 | yes | — |
| 77 | C27 | C24 | 1 | 60 | yes | — |
| 78 | C27 | C24 | 1 | 560 | yes | — |
| 79 | C27 | C24 | 1 | 90 | yes | — |
| 80 | C27 | C24 | 1 | 1 | yes | characteristic |
| 81 | C24×D4 | — | 2 | 5760 | no | — |
| 82 | C24×D4 | — | 2 | 5760 | no | — |
| 83 | C24×D4 | — | 2 | 5760 | no | — |
| 84 | C24×D4 | — | 2 | 2880 | no | — |
| 85 | C24×D4 | — | 4 | 6144 | no | — |
| 86 | C24×D4 | — | 4 | 1024 | no | — |
| 87 | C24×D4 | C24 | 1 | 3360 | yes | — |
| 88 | C24×D4 | C24 | 1 | 560 | yes | complemented |
| 89 | C25×C4 | — | 2 | 6144 | no | — |
| 90 | C25×C4 | — | 2 | 245760 | no | — |
| 91 | C25×C4 | — | 2 | 2880 | no | — |
| 92 | C25×C4 | — | 2 | 96 | no | — |
| 93 | C25×C4 | — | 2 | 6144 | no | — |
| 94 | C25×C4 | — | 2 | 5760 | no | — |
| 95 | C25×C4 | — | 2 | 5760 | no | — |
| 96 | C25×C4 | — | 2 | 107520 | no | — |
| 97 | C25×C4 | — | 2 | 96 | no | — |
| 98 | C25×C4 | — | 2 | 96 | no | — |
| 99 | C25×C4 | — | 2 | 96 | no | — |
| 100 | C25×C4 | C2×D4 | 1 | 96 | yes | — |
| 101 | C25×C4 | C2×D4 | 1 | 96 | yes | — |
| 102 | C25×C4 | C2×D4 | 1 | 5760 | yes | complemented |
| 103 | C25×C4 | C24 | 1 | 1680 | yes | — |
| 104 | C25×C4 | C24 | 1 | 180 | yes | — |
| 105 | C25×C4 | C24 | 1 | 90 | yes | — |
| 106 | C25×C4 | C24 | 1 | 1680 | yes | — |
| 107 | C25×C4 | C24 | 1 | 30 | yes | — |
| 108 | C25×C4 | C24 | 1 | 7680 | yes | complemented |
| 109 | C22×#121 | — | 2 | 107520 | no | — |
| 110 | C22×#121 | C24 | 1 | 23040 | yes | complemented |
| 111 | C22×#120 | — | 2 | 71680 | no | — |
| 112 | C22×#120 | C24 | 1 | 15360 | yes | complemented |
| 113 | C23×C4⋊C4 | — | 2 | 2880 | no | — |
| 114 | C23×C4⋊C4 | C24 | 1 | 1680 | yes | complemented |
| 115 | C23×C22⋊C4 | — | 2 | 5760 | no | — |
| 116 | C23×C22⋊C4 | — | 2 | 5760 | no | — |
| 117 | C23×C22⋊C4 | C24 | 1 | 3360 | yes | — |
| 118 | C23×C22⋊C4 | C24 | 1 | 3360 | yes | complemented |
| 119 | #2847 | C24 | 1 | 65536 | yes | direct product factor |
| 120 | C2×#386 | C24 | 1 | 46080 | yes | complemented |
| 121 | C2×#380 | C24 | 1 | 23040 | yes | complemented |
| 122 | C22×#95 | C24 | 1 | 3360 | yes | complemented |
| 123 | C26 | — | 2 | 30720 | no | — |
| 124 | C26 | — | 2 | 131072 | no | — |
| 125 | C26 | — | 2 | 92160 | no | — |
| 126 | C26 | — | 2 | 1536 | no | — |
| 127 | C26 | — | 2 | 3072 | no | — |
| 128 | C26 | — | 2 | 92160 | no | — |
| 129 | C26 | — | 2 | 1536 | no | — |
| 130 | C26 | — | 2 | 3072 | no | — |
| 131 | C26 | — | 2 | 13440 | no | — |
| 132 | C26 | — | 2 | 1440 | no | — |
| 133 | C26 | — | 2 | 13440 | no | — |
| 134 | C26 | — | 2 | 1440 | no | — |
| 135 | C26 | — | 2 | 480 | no | — |
| 136 | C26 | — | 2 | 1440 | no | — |
| 137 | C26 | — | 2 | 1440 | no | — |
| 138 | C26 | — | 4 | 512 | no | — |
| 139 | C26 | — | 4 | 1536 | no | — |
| 140 | C26 | — | 4 | 1536 | no | — |
| 141 | C26 | #121 | 1 | 3072 | yes | complemented |
| 142 | C26 | C22×D4 | 1 | 1440 | yes | — |
| 143 | C26 | C22×D4 | 1 | 1440 | yes | — |
| 144 | C26 | C22×D4 | 1 | 48 | yes | — |
| 145 | C26 | C22×D4 | 1 | 16 | yes | — |
| 146 | C26 | C22×D4 | 1 | 8960 | yes | complemented |
| 147 | C26 | C2×#41 | 1 | 1440 | yes | — |
| 148 | C26 | C2×#41 | 1 | 48 | yes | — |
| 149 | C26 | C25 | 1 | 280 | yes | — |
| 150 | C26 | C25 | 1 | 960 | yes | — |
| 151 | C26 | C25 | 1 | 420 | yes | — |
| 152 | C26 | C25 | 1 | 15 | yes | — |
| 153 | C23×D4 | — | 2 | 26880 | no | — |
| 154 | C23×D4 | — | 2 | 26880 | no | — |
| 155 | C23×D4 | — | 2 | 26880 | no | — |
| 156 | C23×D4 | — | 2 | 13440 | no | — |
| 157 | C23×D4 | — | 4 | 92160 | no | — |
| 158 | C23×D4 | — | 4 | 15360 | no | — |
| 159 | C23×D4 | C25 | 1 | 5760 | yes | — |
| 160 | C23×D4 | C25 | 1 | 960 | yes | complemented |
| 161 | C24×C4 | — | 2 | 92160 | no | — |
| 162 | C24×C4 | — | 2 | 1146880 | no | — |
| 163 | C24×C4 | — | 2 | 1536 | no | — |
| 164 | C24×C4 | — | 2 | 13440 | no | — |
| 165 | C24×C4 | — | 2 | 1440 | no | — |
| 166 | C24×C4 | — | 2 | 92160 | no | — |
| 167 | C24×C4 | — | 2 | 26880 | no | — |
| 168 | C24×C4 | — | 2 | 26880 | no | — |
| 169 | C24×C4 | — | 2 | 184320 | no | — |
| 170 | C24×C4 | — | 2 | 1440 | no | — |
| 171 | C24×C4 | — | 2 | 1440 | no | — |
| 172 | C24×C4 | — | 2 | 1440 | no | — |
| 173 | C24×C4 | — | 4 | 1536 | no | — |
| 174 | C24×C4 | #120 | 1 | 1024 | yes | complemented |
| 175 | C24×C4 | C22×D4 | 1 | 1440 | yes | — |
| 176 | C24×C4 | C22×D4 | 1 | 1440 | yes | — |
| 177 | C24×C4 | C22×D4 | 1 | 26880 | yes | complemented |
| 178 | C24×C4 | C25 | 1 | 2880 | yes | — |
| 179 | C24×C4 | C25 | 1 | 840 | yes | — |
| 180 | C24×C4 | C25 | 1 | 420 | yes | — |
| 181 | C24×C4 | C25 | 1 | 2880 | yes | — |
| 182 | C24×C4 | C25 | 1 | 140 | yes | — |
| 183 | C24×C4 | C25 | 1 | 4096 | yes | complemented |
| 184 | C2×#121 | — | 2 | 184320 | no | — |
| 185 | C2×#121 | C25 | 1 | 12288 | yes | complemented |
| 186 | C2×#120 | — | 2 | 122880 | no | — |
| 187 | C2×#120 | C25 | 1 | 8192 | yes | complemented |
| 188 | C22×C4⋊C4 | — | 2 | 13440 | no | — |
| 189 | C22×C4⋊C4 | C25 | 1 | 2880 | yes | complemented |
| 190 | C22×C22⋊C4 | — | 2 | 26880 | no | — |
| 191 | C22×C22⋊C4 | — | 2 | 26880 | no | — |
| 192 | C22×C22⋊C4 | C25 | 1 | 5760 | yes | — |
| 193 | C22×C22⋊C4 | C25 | 1 | 5760 | yes | complemented |
| 194 | #386 | C25 | 1 | 24576 | yes | complemented |
| 195 | #380 | C25 | 1 | 12288 | yes | complemented |
| 196 | C2×#95 | C25 | 1 | 5760 | yes | complemented |
| 197 | C25 | — | 2 | 71680 | no | — |
| 198 | C25 | — | 2 | 983040 | no | — |
| 199 | C25 | — | 2 | 215040 | no | — |
| 200 | C25 | — | 2 | 11520 | no | — |
| 201 | C25 | — | 2 | 3360 | no | — |
| 202 | C25 | — | 2 | 11520 | no | — |
| 203 | C25 | — | 2 | 3360 | no | — |
| 204 | C25 | — | 2 | 49152 | no | — |
| 205 | C25 | — | 2 | 11520 | no | — |
| 206 | C25 | — | 2 | 23040 | no | — |
| 207 | C25 | — | 2 | 215040 | no | — |
| 208 | C25 | — | 2 | 11520 | no | — |
| 209 | C25 | — | 2 | 23040 | no | — |
| 210 | C25 | — | 2 | 3360 | no | — |
| 211 | C25 | — | 2 | 1120 | no | — |
| 212 | C25 | — | 2 | 3360 | no | — |
| 213 | C25 | — | 4 | 3840 | no | — |
| 214 | C25 | — | 4 | 11520 | no | — |
| 215 | C25 | — | 4 | 11520 | no | — |
| 216 | C25 | — | 8 | 8192 | no | — |
| 217 | C25 | C2×#120 | 1 | 256 | yes | — |
| 218 | C25 | C2×#121 | 1 | 768 | yes | — |
| 219 | C25 | C2×#121 | 1 | 23040 | yes | complemented |
| 220 | C25 | #525 | 1 | 768 | yes | — |
| 221 | C25 | C23×D4 | 1 | 3360 | yes | — |
| 222 | C25 | C23×D4 | 1 | 3360 | yes | — |
| 223 | C25 | C23×D4 | 1 | 360 | yes | — |
| 224 | C25 | C23×D4 | 1 | 120 | yes | — |
| 225 | C25 | C23×D4 | 1 | 7680 | yes | complemented |
| 226 | C25 | C22×#41 | 1 | 3360 | yes | — |
| 227 | C25 | C22×#41 | 1 | 360 | yes | — |
| 228 | C25 | C26 | 1 | 240 | yes | — |
| 229 | C25 | C26 | 1 | 256 | yes | — |
| 230 | C25 | C26 | 1 | 360 | yes | — |
| 231 | C25 | C26 | 1 | 35 | yes | — |
| 232 | C22×D4 | — | 2 | 23040 | no | — |
| 233 | C22×D4 | — | 2 | 23040 | no | — |
| 234 | C22×D4 | — | 2 | 23040 | no | — |
| 235 | C22×D4 | — | 2 | 11520 | no | — |
| 236 | C22×D4 | — | 4 | 215040 | no | — |
| 237 | C22×D4 | — | 4 | 35840 | no | — |
| 238 | C22×D4 | C26 | 1 | 1536 | yes | — |
| 239 | C22×D4 | C26 | 1 | 256 | yes | complemented |
| 240 | C23×C4 | — | 2 | 215040 | no | — |
| 241 | C23×C4 | — | 2 | 983040 | no | — |
| 242 | C23×C4 | — | 2 | 11520 | no | — |
| 243 | C23×C4 | — | 2 | 3360 | no | — |
| 244 | C23×C4 | — | 2 | 11520 | no | — |
| 245 | C23×C4 | — | 2 | 23040 | no | — |
| 246 | C23×C4 | — | 2 | 23040 | no | — |
| 247 | C23×C4 | — | 2 | 49152 | no | — |
| 248 | C23×C4 | — | 2 | 215040 | no | — |
| 249 | C23×C4 | — | 2 | 3360 | no | — |
| 250 | C23×C4 | — | 2 | 3360 | no | — |
| 251 | C23×C4 | — | 2 | 3360 | no | — |
| 252 | C23×C4 | — | 4 | 11520 | no | — |
| 253 | C23×C4 | C2×#120 | 1 | 7680 | yes | complemented |
| 254 | C23×C4 | C23×D4 | 1 | 3360 | yes | — |
| 255 | C23×C4 | C23×D4 | 1 | 3360 | yes | — |
| 256 | C23×C4 | C23×D4 | 1 | 23040 | yes | complemented |
| 257 | C23×C4 | C26 | 1 | 720 | yes | — |
| 258 | C23×C4 | C26 | 1 | 768 | yes | — |
| 259 | C23×C4 | C26 | 1 | 360 | yes | — |
| 260 | C23×C4 | C26 | 1 | 768 | yes | — |
| 261 | C23×C4 | C26 | 1 | 120 | yes | — |
| 262 | #121 | — | 2 | 49152 | no | — |
| 263 | #120 | — | 2 | 32768 | no | — |
| 264 | C2×C4⋊C4 | — | 2 | 11520 | no | — |
| 265 | C2×C4⋊C4 | C26 | 1 | 768 | yes | complemented |
| 266 | C2×C22⋊C4 | — | 2 | 23040 | no | — |
| 267 | C2×C22⋊C4 | — | 2 | 23040 | no | — |
| 268 | C2×C22⋊C4 | C26 | 1 | 1536 | yes | — |
| 269 | C2×C22⋊C4 | C26 | 1 | 1536 | yes | complemented |
| 270 | #95 | C26 | 1 | 1536 | yes | complemented |
| 271 | C24 | — | 2 | 30720 | no | — |
| 272 | C24 | — | 2 | 92160 | no | — |
| 273 | C24 | — | 2 | 1146880 | no | — |
| 274 | C24 | — | 2 | 184320 | no | — |
| 275 | C24 | — | 2 | 1536 | no | — |
| 276 | C24 | — | 2 | 1440 | no | — |
| 277 | C24 | — | 2 | 1536 | no | — |
| 278 | C24 | — | 2 | 1440 | no | — |
| 279 | C24 | — | 2 | 13440 | no | — |
| 280 | C24 | — | 2 | 26880 | no | — |
| 281 | C24 | — | 2 | 92160 | no | — |
| 282 | C24 | — | 2 | 13440 | no | — |
| 283 | C24 | — | 2 | 26880 | no | — |
| 284 | C24 | — | 2 | 1440 | no | — |
| 285 | C24 | — | 2 | 480 | no | — |
| 286 | C24 | — | 2 | 1440 | no | — |
| 287 | C24 | — | 4 | 4480 | no | — |
| 288 | C24 | — | 4 | 13440 | no | — |
| 289 | C24 | — | 4 | 13440 | no | — |
| 290 | C24 | — | 8 | 30720 | no | — |
| 291 | C24 | #2847 | 1 | 4096 | yes | direct product factor |
| 292 | C24 | C22×#120 | 1 | 960 | yes | — |
| 293 | C24 | C22×#121 | 1 | 2880 | yes | — |
| 294 | C24 | C22×#121 | 1 | 26880 | yes | complemented |
| 295 | C24 | C2×#525 | 1 | 2880 | yes | — |
| 296 | C24 | C24×D4 | 1 | 1440 | yes | — |
| 297 | C24 | C24×D4 | 1 | 1440 | yes | — |
| 298 | C24 | C24×D4 | 1 | 420 | yes | — |
| 299 | C24 | C24×D4 | 1 | 140 | yes | — |
| 300 | C24 | C24×D4 | 1 | 1024 | yes | complemented |
| 301 | C24 | C23×#41 | 1 | 1440 | yes | — |
| 302 | C24 | C23×#41 | 1 | 420 | yes | — |
| 303 | C24 | C27 | 1 | 32 | yes | — |
| 304 | C24 | C27 | 1 | 48 | yes | — |
| 305 | C24 | C27 | 1 | 15 | yes | — |
| 306 | C2×D4 | — | 2 | 3072 | no | — |
| 307 | C2×D4 | — | 2 | 3072 | no | — |
| 308 | C2×D4 | — | 2 | 3072 | no | — |
| 309 | C2×D4 | — | 2 | 1536 | no | — |
| 310 | C2×D4 | — | 4 | 92160 | no | — |
| 311 | C2×D4 | — | 4 | 15360 | no | — |
| 312 | C22×C4 | — | 2 | 92160 | no | — |
| 313 | C22×C4 | — | 2 | 131072 | no | — |
| 314 | C22×C4 | — | 2 | 1536 | no | — |
| 315 | C22×C4 | — | 2 | 1440 | no | — |
| 316 | C22×C4 | — | 2 | 13440 | no | — |
| 317 | C22×C4 | — | 2 | 3072 | no | — |
| 318 | C22×C4 | — | 2 | 3072 | no | — |
| 319 | C22×C4 | — | 2 | 92160 | no | — |
| 320 | C22×C4 | — | 2 | 1440 | no | — |
| 321 | C22×C4 | — | 2 | 1440 | no | — |
| 322 | C22×C4 | — | 2 | 1440 | no | — |
| 323 | C22×C4 | — | 4 | 13440 | no | — |
| 324 | C22×C4 | C22×#120 | 1 | 8960 | yes | complemented |
| 325 | C22×C4 | C24×D4 | 1 | 1440 | yes | — |
| 326 | C22×C4 | C24×D4 | 1 | 1440 | yes | — |
| 327 | C22×C4 | C24×D4 | 1 | 3072 | yes | complemented |
| 328 | C22×C4 | C27 | 1 | 96 | yes | — |
| 329 | C22×C4 | C27 | 1 | 48 | yes | — |
| 330 | C22×C4 | C27 | 1 | 16 | yes | — |
| 331 | C4⋊C4 | — | 2 | 1536 | no | — |
| 332 | C22⋊C4 | — | 2 | 3072 | no | — |
| 333 | C22⋊C4 | — | 2 | 3072 | no | — |
| 334 | C23 | — | 2 | 2048 | no | — |
| 335 | C23 | — | 2 | 245760 | no | — |
| 336 | C23 | — | 2 | 6144 | no | — |
| 337 | C23 | — | 2 | 2880 | no | — |
| 338 | C23 | — | 2 | 5760 | no | — |
| 339 | C23 | — | 2 | 6144 | no | — |
| 340 | C23 | — | 2 | 2880 | no | — |
| 341 | C23 | — | 2 | 5760 | no | — |
| 342 | C23 | — | 2 | 96 | no | — |
| 343 | C23 | — | 2 | 96 | no | — |
| 344 | C23 | — | 2 | 107520 | no | — |
| 345 | C23 | — | 2 | 96 | no | — |
| 346 | C23 | — | 2 | 32 | no | — |
| 347 | C23 | — | 2 | 96 | no | — |
| 348 | C23 | — | 4 | 960 | no | — |
| 349 | C23 | — | 4 | 2880 | no | — |
| 350 | C23 | — | 4 | 2880 | no | — |
| 351 | C23 | — | 8 | 17920 | no | — |
| 352 | C23 | C2×#2847 | 1 | 7680 | yes | direct product factor |
| 353 | C23 | C23×#120 | 1 | 560 | yes | — |
| 354 | C23 | C23×#121 | 1 | 1680 | yes | — |
| 355 | C23 | C23×#121 | 1 | 5760 | yes | complemented |
| 356 | C23 | C22×#525 | 1 | 1680 | yes | — |
| 357 | C23 | C25×D4 | 1 | 96 | yes | — |
| 358 | C23 | C25×D4 | 1 | 96 | yes | — |
| 359 | C23 | C25×D4 | 1 | 90 | yes | — |
| 360 | C23 | C25×D4 | 1 | 30 | yes | — |
| 361 | C23 | C24×#41 | 1 | 96 | yes | — |
| 362 | C23 | C24×#41 | 1 | 90 | yes | — |
| 363 | C23 | C28 | 1 | 1 | yes | characteristic |
| 364 | D4 | — | 4 | 6144 | no | — |
| 365 | D4 | — | 4 | 1024 | no | — |
| 366 | C2×C4 | — | 2 | 6144 | no | — |
| 367 | C2×C4 | — | 2 | 2880 | no | — |
| 368 | C2×C4 | — | 2 | 96 | no | — |
| 369 | C2×C4 | — | 2 | 6144 | no | — |
| 370 | C2×C4 | — | 2 | 96 | no | — |
| 371 | C2×C4 | — | 2 | 96 | no | — |
| 372 | C2×C4 | — | 2 | 96 | no | — |
| 373 | C2×C4 | — | 4 | 2880 | no | — |
| 374 | C2×C4 | C23×#120 | 1 | 1920 | yes | complemented |
| 375 | C2×C4 | C25×D4 | 1 | 96 | yes | — |
| 376 | C2×C4 | C25×D4 | 1 | 96 | yes | — |
| 377 | C22 | — | 2 | 8192 | no | — |
| 378 | C22 | — | 2 | 96 | no | — |
| 379 | C22 | — | 2 | 11520 | no | — |
| 380 | C22 | — | 2 | 192 | no | — |
| 381 | C22 | — | 2 | 96 | no | — |
| 382 | C22 | — | 2 | 192 | no | — |
| 383 | C22 | — | 4 | 32 | no | — |
| 384 | C22 | — | 4 | 96 | no | — |
| 385 | C22 | — | 4 | 96 | no | — |
| 386 | C22 | — | 8 | 1920 | no | — |
| 387 | C22 | C22×#2847 | 1 | 2240 | yes | direct product factor |
| 388 | C22 | C24×#120 | 1 | 60 | yes | — |
| 389 | C22 | C24×#121 | 1 | 180 | yes | — |
| 390 | C22 | C24×#121 | 1 | 192 | yes | complemented |
| 391 | C22 | C23×#525 | 1 | 180 | yes | — |
| 392 | C22 | C26×D4 | 1 | 3 | yes | — |
| 393 | C22 | C26×D4 | 1 | 1 | yes | characteristic |
| 394 | C22 | C25×#41 | 1 | 3 | yes | — |
| 395 | C4 | — | 2 | 96 | no | — |
| 396 | C4 | — | 4 | 96 | no | — |
| 397 | C4 | C24×#120 | 1 | 64 | yes | complemented |
| 398 | C2 | — | 2 | 192 | no | — |
| 399 | C2 | — | 8 | 32 | no | — |
| 400 | C2 | C25×#120 | 1 | 1 | yes | characteristic |
| 401 | C2 | C23×#2847 | 1 | 120 | yes | direct product factor |
| 402 | C2 | C24×#525 | 1 | 3 | yes | — |
| 403 | C2 | C25×#121 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C27 | C24 |
| commutator, Frattini, cosocle | C23 | C28 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C27 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#380 | C2 | semidirect |
| 2. C25×#121 | C2 | semidirect |
| 3. C24×#386 | C2 | semidirect |
| 4. C23×#2847 | C2 | direct (N × H) |
| 5. C25×#120 | C2 | semidirect |
| 6. C28×C4 | C2 | semidirect |
| 9. C26×D4 | C22 | semidirect |
| 13. C27×C4 | C22 | semidirect |
| 15. C24×#121 | C22 | semidirect |
| 17. C24×#120 | C22 | semidirect |
| 18. C25×C4⋊C4 | C22 | semidirect |
| 20. C25×C22⋊C4 | C22 | semidirect |
| 21. C22×#2847 | C22 | direct (N × H) |
| 22. C23×#386 | C22 | semidirect |
| 23. C23×#380 | C22 | semidirect |
| 24. C24×#95 | C22 | semidirect |
| 27. C28 | D4 | semidirect |
| 36. C25×D4 | C23 | semidirect |
| 42. C26×C4 | D4 | semidirect |
| 48. C26×C4 | C23 | semidirect |
| 50. C23×#121 | C23 | semidirect |
| 52. C23×#120 | C23 | semidirect |
| 54. C24×C4⋊C4 | C23 | semidirect |
| 58. C24×C22⋊C4 | C23 | semidirect |
| 59. C2×#2847 | C23 | direct (N × H) |
| 60. C22×#386 | C23 | semidirect |
| 61. C22×#380 | C23 | semidirect |
| 62. C23×#95 | C23 | semidirect |
| 75. C27 | C2×D4 | semidirect |
| 88. C24×D4 | C24 | semidirect |
| 102. C25×C4 | C2×D4 | semidirect |
| 108. C25×C4 | C24 | semidirect |
| 110. C22×#121 | C24 | semidirect |
| 112. C22×#120 | C24 | semidirect |
| 114. C23×C4⋊C4 | C24 | semidirect |
| 118. C23×C22⋊C4 | C24 | semidirect |
| 119. #2847 | C24 | direct (N × H) |
| 120. C2×#386 | C24 | semidirect |
| 121. C2×#380 | C24 | semidirect |
| 122. C22×#95 | C24 | semidirect |
| 141. C26 | #121 | semidirect |
| 146. C26 | C22×D4 | semidirect |
| 160. C23×D4 | C25 | semidirect |
| 174. C24×C4 | #120 | semidirect |
| 177. C24×C4 | C22×D4 | semidirect |
| 183. C24×C4 | C25 | semidirect |
| 185. C2×#121 | C25 | semidirect |
| 187. C2×#120 | C25 | semidirect |
| 189. C22×C4⋊C4 | C25 | semidirect |
| 193. C22×C22⋊C4 | C25 | semidirect |
| 194. #386 | C25 | semidirect |
| 195. #380 | C25 | semidirect |
| 196. C2×#95 | C25 | semidirect |
| 219. C25 | C2×#121 | semidirect |
| 225. C25 | C23×D4 | semidirect |
| 239. C22×D4 | C26 | semidirect |
| 253. C23×C4 | C2×#120 | semidirect |
| 256. C23×C4 | C23×D4 | semidirect |
| 265. C2×C4⋊C4 | C26 | semidirect |
| 269. C2×C22⋊C4 | C26 | semidirect |
| 270. #95 | C26 | semidirect |
| 291. C24 | #2847 | direct (N × H) |
| 294. C24 | C22×#121 | semidirect |
| 300. C24 | C24×D4 | semidirect |
| 324. C22×C4 | C22×#120 | semidirect |
| 327. C22×C4 | C24×D4 | semidirect |
| 352. C23 | C2×#2847 | direct (N × H) |
| 355. C23 | C23×#121 | semidirect |
| 374. C2×C4 | C23×#120 | semidirect |
| 387. C22 | C22×#2847 | direct (N × H) |
| 390. C22 | C24×#121 | semidirect |
| 397. C4 | C24×#120 | semidirect |
| 401. C2 | C23×#2847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#380 | 2 |
| C25×#121 | 2 |
| C24×#386 | 2 |
| C23×#2847 | 2 |
| C25×#120 | 2 |
| C28×C4 | 2 |