Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2759560 conjugacy classes of subgroups.
The subgroup lattice has 395 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C24×#382 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C24×#376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C24×#390 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C25×#127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C24×#386 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | C25×C4×D4 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C23×#2328 | C2 | 1 | 240 | yes | maximal, direct product factor |
| 8 | C26×D4 | C22 | 1 | 2 | yes | — |
| 9 | C26×D4 | C22 | 1 | 4 | yes | — |
| 10 | C27×C4 | C22 | 1 | 4 | yes | — |
| 11 | C24×#127 | C4 | 1 | 128 | yes | complemented |
| 12 | C24×#127 | C22 | 1 | 120 | yes | — |
| 13 | C24×C4×D4 | — | 2 | 128 | no | — |
| 14 | C24×C4×D4 | C22 | 1 | 240 | yes | complemented |
| 15 | C25×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 16 | C25×C22⋊C4 | C22 | 1 | 4 | yes | — |
| 17 | C25×C22⋊C4 | C22 | 1 | 8 | yes | — |
| 18 | C25×C42 | C22 | 1 | 1 | yes | characteristic |
| 19 | C25×C42 | C22 | 1 | 1 | yes | characteristic |
| 20 | C25×C42 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×#2328 | C22 | 1 | 8960 | yes | direct product factor |
| 22 | C23×#390 | C22 | 1 | 240 | yes | complemented |
| 23 | C23×#386 | C22 | 1 | 960 | yes | complemented |
| 24 | C23×#382 | C22 | 1 | 120 | yes | complemented |
| 25 | C23×#376 | C22 | 1 | 120 | yes | complemented |
| 26 | C24×#95 | C22 | 1 | 4 | yes | — |
| 27 | C24×#95 | C22 | 1 | 4 | yes | — |
| 28 | C28 | C23 | 1 | 4 | yes | — |
| 29 | C25×D4 | — | 2 | 64 | no | — |
| 30 | C25×D4 | — | 2 | 64 | no | — |
| 31 | C25×D4 | — | 4 | 128 | no | — |
| 32 | C25×D4 | C2×C4 | 1 | 128 | yes | complemented |
| 33 | C25×D4 | C2×C4 | 1 | 256 | yes | complemented |
| 34 | C25×D4 | C23 | 1 | 120 | yes | — |
| 35 | C25×D4 | C23 | 1 | 240 | yes | — |
| 36 | C26×C4 | — | 2 | 128 | no | — |
| 37 | C26×C4 | — | 4 | 128 | no | — |
| 38 | C26×C4 | C23 | 1 | 2 | yes | — |
| 39 | C26×C4 | C23 | 1 | 4 | yes | — |
| 40 | C26×C4 | C23 | 1 | 2 | yes | — |
| 41 | C26×C4 | C23 | 1 | 2 | yes | — |
| 42 | C26×C4 | C23 | 1 | 240 | yes | — |
| 43 | C26×C4 | C23 | 1 | 1 | yes | characteristic |
| 44 | C23×#127 | C2×C4 | 1 | 7680 | yes | complemented |
| 45 | C23×#127 | C23 | 1 | 2240 | yes | — |
| 46 | C23×C4×D4 | — | 2 | 7680 | no | — |
| 47 | C23×C4×D4 | C23 | 1 | 4480 | yes | complemented |
| 48 | C24×C4⋊C4 | — | 2 | 64 | no | — |
| 49 | C24×C4⋊C4 | C23 | 1 | 120 | yes | — |
| 50 | C24×C22⋊C4 | — | 2 | 128 | no | — |
| 51 | C24×C22⋊C4 | — | 4 | 128 | no | — |
| 52 | C24×C22⋊C4 | C23 | 1 | 240 | yes | — |
| 53 | C24×C22⋊C4 | C23 | 1 | 480 | yes | — |
| 54 | C24×C42 | — | 2 | 32 | no | — |
| 55 | C24×C42 | C2×C4 | 1 | 64 | yes | complemented |
| 56 | C24×C42 | D4 | 1 | 64 | yes | complemented |
| 57 | C24×C42 | C23 | 1 | 60 | yes | — |
| 58 | C24×C42 | C23 | 1 | 60 | yes | — |
| 59 | C24×C42 | C23 | 1 | 60 | yes | — |
| 60 | C2×#2328 | C23 | 1 | 61440 | yes | direct product factor |
| 61 | C22×#390 | C23 | 1 | 4480 | yes | complemented |
| 62 | C22×#386 | C23 | 1 | 17920 | yes | complemented |
| 63 | C22×#382 | C23 | 1 | 2240 | yes | complemented |
| 64 | C22×#376 | C23 | 1 | 2240 | yes | complemented |
| 65 | C23×#95 | C23 | 1 | 240 | yes | — |
| 66 | C23×#95 | C23 | 1 | 240 | yes | — |
| 67 | C27 | — | 2 | 64 | no | — |
| 68 | C27 | — | 2 | 64 | no | — |
| 69 | C27 | — | 2 | 128 | no | — |
| 70 | C27 | — | 2 | 128 | no | — |
| 71 | C27 | C22×C4 | 1 | 128 | yes | — |
| 72 | C27 | C24 | 1 | 120 | yes | — |
| 73 | C27 | C24 | 1 | 1 | yes | characteristic |
| 74 | C24×D4 | — | 2 | 4096 | no | — |
| 75 | C24×D4 | — | 2 | 1920 | no | — |
| 76 | C24×D4 | — | 2 | 1920 | no | — |
| 77 | C24×D4 | — | 4 | 4096 | no | — |
| 78 | C24×D4 | — | 4 | 3840 | no | — |
| 79 | C24×D4 | C22×C4 | 1 | 3840 | yes | complemented |
| 80 | C24×D4 | C22×C4 | 1 | 7680 | yes | complemented |
| 81 | C24×D4 | C24 | 1 | 1120 | yes | — |
| 82 | C24×D4 | C24 | 1 | 2240 | yes | — |
| 83 | C25×C4 | — | 2 | 64 | no | — |
| 84 | C25×C4 | — | 2 | 64 | no | — |
| 85 | C25×C4 | — | 2 | 64 | no | — |
| 86 | C25×C4 | — | 2 | 32 | no | — |
| 87 | C25×C4 | — | 2 | 128 | no | — |
| 88 | C25×C4 | — | 2 | 64 | no | — |
| 89 | C25×C4 | — | 2 | 3840 | no | — |
| 90 | C25×C4 | — | 4 | 3840 | no | — |
| 91 | C25×C4 | — | 4 | 4096 | no | — |
| 92 | C25×C4 | C22×C4 | 1 | 64 | yes | — |
| 93 | C25×C4 | C22×C4 | 1 | 32 | yes | — |
| 94 | C25×C4 | C2×D4 | 1 | 64 | yes | — |
| 95 | C25×C4 | C2×D4 | 1 | 32 | yes | — |
| 96 | C25×C4 | #41 | 1 | 32 | yes | — |
| 97 | C25×C4 | C24 | 1 | 120 | yes | — |
| 98 | C25×C4 | C24 | 1 | 60 | yes | — |
| 99 | C25×C4 | C24 | 1 | 60 | yes | — |
| 100 | C25×C4 | C24 | 1 | 60 | yes | — |
| 101 | C25×C4 | C24 | 1 | 2240 | yes | — |
| 102 | C25×C4 | C24 | 1 | 30 | yes | — |
| 103 | C22×#127 | C22×C4 | 1 | 71680 | yes | complemented |
| 104 | C22×#127 | C24 | 1 | 7680 | yes | — |
| 105 | C22×C4×D4 | — | 2 | 71680 | no | — |
| 106 | C22×C4×D4 | C24 | 1 | 15360 | yes | complemented |
| 107 | C23×C4⋊C4 | — | 2 | 1920 | no | — |
| 108 | C23×C4⋊C4 | C24 | 1 | 1120 | yes | — |
| 109 | C23×C22⋊C4 | — | 2 | 3840 | no | — |
| 110 | C23×C22⋊C4 | — | 4 | 3840 | no | — |
| 111 | C23×C22⋊C4 | C24 | 1 | 2240 | yes | — |
| 112 | C23×C22⋊C4 | C24 | 1 | 4480 | yes | — |
| 113 | C23×C42 | — | 2 | 960 | no | — |
| 114 | C23×C42 | C22×C4 | 1 | 1920 | yes | complemented |
| 115 | C23×C42 | C2×D4 | 1 | 1920 | yes | complemented |
| 116 | C23×C42 | C24 | 1 | 560 | yes | — |
| 117 | C23×C42 | C24 | 1 | 560 | yes | — |
| 118 | C23×C42 | C24 | 1 | 560 | yes | — |
| 119 | #2328 | C24 | 1 | 65536 | yes | direct product factor |
| 120 | C2×#390 | C24 | 1 | 15360 | yes | complemented |
| 121 | C2×#386 | C24 | 1 | 61440 | yes | complemented |
| 122 | C2×#382 | C24 | 1 | 7680 | yes | complemented |
| 123 | C2×#376 | C24 | 1 | 7680 | yes | complemented |
| 124 | C22×#95 | C24 | 1 | 2240 | yes | — |
| 125 | C22×#95 | C24 | 1 | 2240 | yes | — |
| 126 | C26 | — | 2 | 2048 | no | — |
| 127 | C26 | — | 2 | 4096 | no | — |
| 128 | C26 | — | 2 | 960 | no | — |
| 129 | C26 | — | 2 | 960 | no | — |
| 130 | C26 | — | 2 | 1920 | no | — |
| 131 | C26 | — | 2 | 1920 | no | — |
| 132 | C26 | — | 4 | 1024 | no | — |
| 133 | C26 | — | 4 | 1024 | no | — |
| 134 | C26 | — | 4 | 2048 | no | — |
| 135 | C26 | C23×C4 | 1 | 1920 | yes | — |
| 136 | C26 | C23×C4 | 1 | 16 | yes | — |
| 137 | C26 | C22×D4 | 1 | 16 | yes | — |
| 138 | C26 | C2×#41 | 1 | 16 | yes | — |
| 139 | C26 | H(5,𝔽2) | 1 | 64 | yes | — |
| 140 | C26 | C25 | 1 | 560 | yes | — |
| 141 | C26 | C25 | 1 | 15 | yes | — |
| 142 | C23×D4 | — | 2 | 61440 | no | — |
| 143 | C23×D4 | — | 2 | 8960 | no | — |
| 144 | C23×D4 | — | 2 | 8960 | no | — |
| 145 | C23×D4 | — | 4 | 61440 | no | — |
| 146 | C23×D4 | — | 4 | 17920 | no | — |
| 147 | C23×D4 | C23×C4 | 1 | 17920 | yes | complemented |
| 148 | C23×D4 | C23×C4 | 1 | 35840 | yes | complemented |
| 149 | C23×D4 | C25 | 1 | 1920 | yes | — |
| 150 | C23×D4 | C25 | 1 | 3840 | yes | — |
| 151 | C24×C4 | — | 2 | 1024 | no | — |
| 152 | C24×C4 | — | 2 | 1024 | no | — |
| 153 | C24×C4 | — | 2 | 960 | no | — |
| 154 | C24×C4 | — | 2 | 960 | no | — |
| 155 | C24×C4 | — | 2 | 960 | no | — |
| 156 | C24×C4 | — | 2 | 480 | no | — |
| 157 | C24×C4 | — | 2 | 1920 | no | — |
| 158 | C24×C4 | — | 2 | 960 | no | — |
| 159 | C24×C4 | — | 2 | 17920 | no | — |
| 160 | C24×C4 | — | 4 | 17920 | no | — |
| 161 | C24×C4 | — | 4 | 61440 | no | — |
| 162 | C24×C4 | — | 4 | 1024 | no | — |
| 163 | C24×C4 | — | 4 | 512 | no | — |
| 164 | C24×C4 | C4×D4 | 1 | 1024 | yes | — |
| 165 | C24×C4 | C23×C4 | 1 | 960 | yes | — |
| 166 | C24×C4 | C23×C4 | 1 | 480 | yes | — |
| 167 | C24×C4 | C22×D4 | 1 | 960 | yes | — |
| 168 | C24×C4 | C22×D4 | 1 | 480 | yes | — |
| 169 | C24×C4 | C2×#41 | 1 | 480 | yes | — |
| 170 | C24×C4 | C25 | 1 | 560 | yes | — |
| 171 | C24×C4 | C25 | 1 | 280 | yes | — |
| 172 | C24×C4 | C25 | 1 | 280 | yes | — |
| 173 | C24×C4 | C25 | 1 | 280 | yes | — |
| 174 | C24×C4 | C25 | 1 | 3840 | yes | — |
| 175 | C24×C4 | C25 | 1 | 140 | yes | — |
| 176 | C2×#127 | C23×C4 | 1 | 122880 | yes | complemented |
| 177 | C2×#127 | C25 | 1 | 4096 | yes | — |
| 178 | C2×C4×D4 | — | 2 | 122880 | no | — |
| 179 | C2×C4×D4 | C25 | 1 | 8192 | yes | complemented |
| 180 | C22×C4⋊C4 | — | 2 | 8960 | no | — |
| 181 | C22×C4⋊C4 | C25 | 1 | 1920 | yes | — |
| 182 | C22×C22⋊C4 | — | 2 | 17920 | no | — |
| 183 | C22×C22⋊C4 | — | 4 | 17920 | no | — |
| 184 | C22×C22⋊C4 | C25 | 1 | 3840 | yes | — |
| 185 | C22×C22⋊C4 | C25 | 1 | 7680 | yes | — |
| 186 | C22×C42 | — | 2 | 4480 | no | — |
| 187 | C22×C42 | C23×C4 | 1 | 8960 | yes | complemented |
| 188 | C22×C42 | C22×D4 | 1 | 8960 | yes | complemented |
| 189 | C22×C42 | C25 | 1 | 960 | yes | — |
| 190 | C22×C42 | C25 | 1 | 960 | yes | — |
| 191 | C22×C42 | C25 | 1 | 960 | yes | — |
| 192 | #390 | C25 | 1 | 8192 | yes | complemented |
| 193 | #386 | C25 | 1 | 32768 | yes | complemented |
| 194 | #382 | C25 | 1 | 4096 | yes | complemented |
| 195 | #376 | C25 | 1 | 4096 | yes | complemented |
| 196 | C2×#95 | C25 | 1 | 3840 | yes | — |
| 197 | C2×#95 | C25 | 1 | 3840 | yes | — |
| 198 | C25 | — | 2 | 2240 | no | — |
| 199 | C25 | — | 2 | 2240 | no | — |
| 200 | C25 | — | 2 | 4480 | no | — |
| 201 | C25 | — | 2 | 4480 | no | — |
| 202 | C25 | — | 2 | 15360 | no | — |
| 203 | C25 | — | 2 | 30720 | no | — |
| 204 | C25 | — | 4 | 32768 | no | — |
| 205 | C25 | — | 4 | 7680 | no | — |
| 206 | C25 | — | 4 | 7680 | no | — |
| 207 | C25 | — | 4 | 15360 | no | — |
| 208 | C25 | C2×C4×D4 | 1 | 256 | yes | — |
| 209 | C25 | #518 | 1 | 512 | yes | — |
| 210 | C25 | #535 | 1 | 512 | yes | — |
| 211 | C25 | #540 | 1 | 512 | yes | — |
| 212 | C25 | C24×C4 | 1 | 4480 | yes | — |
| 213 | C25 | C24×C4 | 1 | 120 | yes | — |
| 214 | C25 | C23×D4 | 1 | 120 | yes | — |
| 215 | C25 | C22×#41 | 1 | 120 | yes | — |
| 216 | C25 | C2×H(5,𝔽2) | 1 | 480 | yes | — |
| 217 | C25 | C26 | 1 | 480 | yes | — |
| 218 | C25 | C26 | 1 | 35 | yes | — |
| 219 | C22×D4 | — | 2 | 7680 | no | — |
| 220 | C22×D4 | — | 2 | 7680 | no | — |
| 221 | C22×D4 | — | 2 | 143360 | no | — |
| 222 | C22×D4 | — | 4 | 143360 | no | — |
| 223 | C22×D4 | — | 4 | 15360 | no | — |
| 224 | C22×D4 | C24×C4 | 1 | 15360 | yes | complemented |
| 225 | C22×D4 | C24×C4 | 1 | 30720 | yes | complemented |
| 226 | C22×D4 | C26 | 1 | 512 | yes | — |
| 227 | C22×D4 | C26 | 1 | 1024 | yes | — |
| 228 | C23×C4 | — | 2 | 2240 | no | — |
| 229 | C23×C4 | — | 2 | 2240 | no | — |
| 230 | C23×C4 | — | 2 | 7680 | no | — |
| 231 | C23×C4 | — | 2 | 7680 | no | — |
| 232 | C23×C4 | — | 2 | 2240 | no | — |
| 233 | C23×C4 | — | 2 | 1120 | no | — |
| 234 | C23×C4 | — | 2 | 2240 | no | — |
| 235 | C23×C4 | — | 2 | 4480 | no | — |
| 236 | C23×C4 | — | 2 | 15360 | no | — |
| 237 | C23×C4 | — | 4 | 15360 | no | — |
| 238 | C23×C4 | — | 4 | 143360 | no | — |
| 239 | C23×C4 | — | 4 | 7680 | no | — |
| 240 | C23×C4 | — | 4 | 3840 | no | — |
| 241 | C23×C4 | C2×C4×D4 | 1 | 7680 | yes | — |
| 242 | C23×C4 | C24×C4 | 1 | 2240 | yes | — |
| 243 | C23×C4 | C24×C4 | 1 | 1120 | yes | — |
| 244 | C23×C4 | C23×D4 | 1 | 2240 | yes | — |
| 245 | C23×C4 | C23×D4 | 1 | 1120 | yes | — |
| 246 | C23×C4 | C22×#41 | 1 | 1120 | yes | — |
| 247 | C23×C4 | C26 | 1 | 240 | yes | — |
| 248 | C23×C4 | C26 | 1 | 480 | yes | — |
| 249 | C23×C4 | C26 | 1 | 240 | yes | — |
| 250 | C23×C4 | C26 | 1 | 240 | yes | — |
| 251 | C23×C4 | C26 | 1 | 1024 | yes | — |
| 252 | C23×C4 | C26 | 1 | 120 | yes | — |
| 253 | #127 | C24×C4 | 1 | 32768 | yes | complemented |
| 254 | C4×D4 | — | 2 | 32768 | no | — |
| 255 | C2×C4⋊C4 | — | 2 | 7680 | no | — |
| 256 | C2×C4⋊C4 | C26 | 1 | 512 | yes | — |
| 257 | C2×C22⋊C4 | — | 2 | 15360 | no | — |
| 258 | C2×C22⋊C4 | — | 4 | 15360 | no | — |
| 259 | C2×C22⋊C4 | C26 | 1 | 1024 | yes | — |
| 260 | C2×C22⋊C4 | C26 | 1 | 2048 | yes | — |
| 261 | C2×C42 | — | 2 | 3840 | no | — |
| 262 | C2×C42 | C24×C4 | 1 | 7680 | yes | complemented |
| 263 | C2×C42 | C23×D4 | 1 | 7680 | yes | complemented |
| 264 | C2×C42 | C26 | 1 | 256 | yes | — |
| 265 | C2×C42 | C26 | 1 | 256 | yes | — |
| 266 | C2×C42 | C26 | 1 | 256 | yes | — |
| 267 | #95 | C26 | 1 | 1024 | yes | — |
| 268 | #95 | C26 | 1 | 1024 | yes | — |
| 269 | C24 | — | 2 | 960 | no | — |
| 270 | C24 | — | 2 | 960 | no | — |
| 271 | C24 | — | 2 | 1920 | no | — |
| 272 | C24 | — | 2 | 1920 | no | — |
| 273 | C24 | — | 2 | 17920 | no | — |
| 274 | C24 | — | 2 | 35840 | no | — |
| 275 | C24 | — | 4 | 122880 | no | — |
| 276 | C24 | — | 4 | 8960 | no | — |
| 277 | C24 | — | 4 | 8960 | no | — |
| 278 | C24 | — | 4 | 17920 | no | — |
| 279 | C24 | #2328 | 1 | 4096 | yes | direct product factor |
| 280 | C24 | C22×C4×D4 | 1 | 960 | yes | — |
| 281 | C24 | C2×#518 | 1 | 1920 | yes | — |
| 282 | C24 | C2×#535 | 1 | 1920 | yes | — |
| 283 | C24 | C2×#540 | 1 | 1920 | yes | — |
| 284 | C24 | C25×C4 | 1 | 1920 | yes | — |
| 285 | C24 | C25×C4 | 1 | 140 | yes | — |
| 286 | C24 | C24×D4 | 1 | 140 | yes | — |
| 287 | C24 | C23×#41 | 1 | 140 | yes | — |
| 288 | C24 | C22×H(5,𝔽2) | 1 | 560 | yes | — |
| 289 | C24 | C27 | 1 | 64 | yes | — |
| 290 | C24 | C27 | 1 | 15 | yes | — |
| 291 | C2×D4 | — | 2 | 1024 | no | — |
| 292 | C2×D4 | — | 2 | 1024 | no | — |
| 293 | C2×D4 | — | 2 | 61440 | no | — |
| 294 | C2×D4 | — | 4 | 61440 | no | — |
| 295 | C2×D4 | — | 4 | 2048 | no | — |
| 296 | C2×D4 | C25×C4 | 1 | 2048 | yes | complemented |
| 297 | C2×D4 | C25×C4 | 1 | 4096 | yes | complemented |
| 298 | C22×C4 | — | 2 | 960 | no | — |
| 299 | C22×C4 | — | 2 | 960 | no | — |
| 300 | C22×C4 | — | 2 | 8960 | no | — |
| 301 | C22×C4 | — | 2 | 8960 | no | — |
| 302 | C22×C4 | — | 2 | 960 | no | — |
| 303 | C22×C4 | — | 2 | 480 | no | — |
| 304 | C22×C4 | — | 2 | 960 | no | — |
| 305 | C22×C4 | — | 2 | 1920 | no | — |
| 306 | C22×C4 | — | 2 | 2048 | no | — |
| 307 | C22×C4 | — | 4 | 2048 | no | — |
| 308 | C22×C4 | — | 4 | 61440 | no | — |
| 309 | C22×C4 | — | 4 | 8960 | no | — |
| 310 | C22×C4 | — | 4 | 4480 | no | — |
| 311 | C22×C4 | C22×C4×D4 | 1 | 8960 | yes | — |
| 312 | C22×C4 | C25×C4 | 1 | 960 | yes | — |
| 313 | C22×C4 | C25×C4 | 1 | 480 | yes | — |
| 314 | C22×C4 | C24×D4 | 1 | 960 | yes | — |
| 315 | C22×C4 | C24×D4 | 1 | 480 | yes | — |
| 316 | C22×C4 | C23×#41 | 1 | 480 | yes | — |
| 317 | C22×C4 | C27 | 1 | 32 | yes | — |
| 318 | C22×C4 | C27 | 1 | 64 | yes | — |
| 319 | C22×C4 | C27 | 1 | 32 | yes | — |
| 320 | C22×C4 | C27 | 1 | 32 | yes | — |
| 321 | C22×C4 | C27 | 1 | 16 | yes | — |
| 322 | C4⋊C4 | — | 2 | 1024 | no | — |
| 323 | C22⋊C4 | — | 2 | 2048 | no | — |
| 324 | C22⋊C4 | — | 4 | 2048 | no | — |
| 325 | C42 | — | 2 | 512 | no | — |
| 326 | C42 | C25×C4 | 1 | 1024 | yes | complemented |
| 327 | C42 | C24×D4 | 1 | 1024 | yes | complemented |
| 328 | C23 | — | 2 | 3840 | no | — |
| 329 | C23 | — | 2 | 7680 | no | — |
| 330 | C23 | — | 2 | 64 | no | — |
| 331 | C23 | — | 2 | 64 | no | — |
| 332 | C23 | — | 2 | 128 | no | — |
| 333 | C23 | — | 2 | 128 | no | — |
| 334 | C23 | — | 4 | 1920 | no | — |
| 335 | C23 | — | 4 | 1920 | no | — |
| 336 | C23 | — | 4 | 3840 | no | — |
| 337 | C23 | — | 4 | 71680 | no | — |
| 338 | C23 | C2×#2328 | 1 | 7680 | yes | direct product factor |
| 339 | C23 | C23×C4×D4 | 1 | 560 | yes | — |
| 340 | C23 | C22×#518 | 1 | 1120 | yes | — |
| 341 | C23 | C22×#535 | 1 | 1120 | yes | — |
| 342 | C23 | C22×#540 | 1 | 1120 | yes | — |
| 343 | C23 | C26×C4 | 1 | 128 | yes | — |
| 344 | C23 | C26×C4 | 1 | 30 | yes | — |
| 345 | C23 | C25×D4 | 1 | 30 | yes | — |
| 346 | C23 | C24×#41 | 1 | 30 | yes | — |
| 347 | C23 | C23×H(5,𝔽2) | 1 | 120 | yes | — |
| 348 | C23 | C28 | 1 | 1 | yes | characteristic |
| 349 | D4 | — | 2 | 4096 | no | — |
| 350 | D4 | — | 4 | 4096 | no | — |
| 351 | C2×C4 | — | 2 | 1920 | no | — |
| 352 | C2×C4 | — | 2 | 1920 | no | — |
| 353 | C2×C4 | — | 2 | 64 | no | — |
| 354 | C2×C4 | — | 2 | 64 | no | — |
| 355 | C2×C4 | — | 2 | 64 | no | — |
| 356 | C2×C4 | — | 2 | 32 | no | — |
| 357 | C2×C4 | — | 2 | 64 | no | — |
| 358 | C2×C4 | — | 2 | 128 | no | — |
| 359 | C2×C4 | — | 4 | 4096 | no | — |
| 360 | C2×C4 | — | 4 | 1920 | no | — |
| 361 | C2×C4 | — | 4 | 960 | no | — |
| 362 | C2×C4 | C23×C4×D4 | 1 | 1920 | yes | — |
| 363 | C2×C4 | C26×C4 | 1 | 64 | yes | — |
| 364 | C2×C4 | C26×C4 | 1 | 32 | yes | — |
| 365 | C2×C4 | C25×D4 | 1 | 64 | yes | — |
| 366 | C2×C4 | C25×D4 | 1 | 32 | yes | — |
| 367 | C2×C4 | C24×#41 | 1 | 32 | yes | — |
| 368 | C22 | — | 2 | 256 | no | — |
| 369 | C22 | — | 2 | 128 | no | — |
| 370 | C22 | — | 4 | 128 | no | — |
| 371 | C22 | — | 4 | 64 | no | — |
| 372 | C22 | — | 4 | 64 | no | — |
| 373 | C22 | — | 4 | 7680 | no | — |
| 374 | C22 | C22×#2328 | 1 | 2240 | yes | direct product factor |
| 375 | C22 | C24×C4×D4 | 1 | 60 | yes | — |
| 376 | C22 | C23×#518 | 1 | 120 | yes | — |
| 377 | C22 | C23×#535 | 1 | 120 | yes | — |
| 378 | C22 | C23×#540 | 1 | 120 | yes | — |
| 379 | C22 | C27×C4 | 1 | 1 | yes | characteristic |
| 380 | C22 | C26×D4 | 1 | 1 | yes | characteristic |
| 381 | C22 | C25×#41 | 1 | 1 | yes | characteristic |
| 382 | C22 | C24×H(5,𝔽2) | 1 | 4 | yes | — |
| 383 | C4 | — | 2 | 64 | no | — |
| 384 | C4 | — | 2 | 64 | no | — |
| 385 | C4 | — | 4 | 32 | no | — |
| 386 | C4 | — | 4 | 64 | no | — |
| 387 | C4 | C24×C4×D4 | 1 | 64 | yes | — |
| 388 | C2 | — | 4 | 128 | no | — |
| 389 | C2 | C23×#2328 | 1 | 120 | yes | direct product factor |
| 390 | C2 | C25×C4×D4 | 1 | 1 | yes | characteristic |
| 391 | C2 | C24×#518 | 1 | 2 | yes | — |
| 392 | C2 | C24×#535 | 1 | 2 | yes | — |
| 393 | C2 | C24×#540 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C27 | C24 |
| commutator | C22 | C27×C4 |
| Frattini, cosocle | C23 | C28 |
| prime radical | C25×#127 | C2 |
| LCS | G ▷ C22 ▷ 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×#382 | C2 | semidirect |
| 2. C24×#376 | C2 | semidirect |
| 3. C24×#390 | C2 | semidirect |
| 5. C24×#386 | C2 | semidirect |
| 6. C25×C4×D4 | C2 | semidirect |
| 7. C23×#2328 | C2 | direct (N × H) |
| 11. C24×#127 | C4 | semidirect |
| 14. C24×C4×D4 | C22 | semidirect |
| 21. C22×#2328 | C22 | direct (N × H) |
| 22. C23×#390 | C22 | semidirect |
| 23. C23×#386 | C22 | semidirect |
| 24. C23×#382 | C22 | semidirect |
| 25. C23×#376 | C22 | semidirect |
| 32. C25×D4 | C2×C4 | semidirect |
| 33. C25×D4 | C2×C4 | semidirect |
| 44. C23×#127 | C2×C4 | semidirect |
| 47. C23×C4×D4 | C23 | semidirect |
| 55. C24×C42 | C2×C4 | semidirect |
| 56. C24×C42 | D4 | semidirect |
| 60. C2×#2328 | C23 | direct (N × H) |
| 61. C22×#390 | C23 | semidirect |
| 62. C22×#386 | C23 | semidirect |
| 63. C22×#382 | C23 | semidirect |
| 64. C22×#376 | C23 | semidirect |
| 79. C24×D4 | C22×C4 | semidirect |
| 80. C24×D4 | C22×C4 | semidirect |
| 103. C22×#127 | C22×C4 | semidirect |
| 106. C22×C4×D4 | C24 | semidirect |
| 114. C23×C42 | C22×C4 | semidirect |
| 115. C23×C42 | C2×D4 | semidirect |
| 119. #2328 | C24 | direct (N × H) |
| 120. C2×#390 | C24 | semidirect |
| 121. C2×#386 | C24 | semidirect |
| 122. C2×#382 | C24 | semidirect |
| 123. C2×#376 | C24 | semidirect |
| 147. C23×D4 | C23×C4 | semidirect |
| 148. C23×D4 | C23×C4 | semidirect |
| 176. C2×#127 | C23×C4 | semidirect |
| 179. C2×C4×D4 | C25 | semidirect |
| 187. C22×C42 | C23×C4 | semidirect |
| 188. C22×C42 | C22×D4 | semidirect |
| 192. #390 | C25 | semidirect |
| 193. #386 | C25 | semidirect |
| 194. #382 | C25 | semidirect |
| 195. #376 | C25 | semidirect |
| 224. C22×D4 | C24×C4 | semidirect |
| 225. C22×D4 | C24×C4 | semidirect |
| 253. #127 | C24×C4 | semidirect |
| 262. C2×C42 | C24×C4 | semidirect |
| 263. C2×C42 | C23×D4 | semidirect |
| 279. C24 | #2328 | direct (N × H) |
| 296. C2×D4 | C25×C4 | semidirect |
| 297. C2×D4 | C25×C4 | semidirect |
| 326. C42 | C25×C4 | semidirect |
| 327. C42 | C24×D4 | semidirect |
| 338. C23 | C2×#2328 | direct (N × H) |
| 374. C22 | C22×#2328 | direct (N × H) |
| 389. C2 | C23×#2328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#382 | 2 |
| C24×#376 | 2 |
| C24×#390 | 2 |
| C25×#127 | 2 |
| C24×#386 | 2 |
| C25×C4×D4 | 2 |
| C23×#2328 | 2 |