Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
107453 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#46996 | C2 | 1 | 96 | yes | maximal, direct product factor |
| 2 | C22×#2760 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C22×#2840 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#2404 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | C22×#2403 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C22×#2308 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C24×#41 | C22 | 1 | 4 | yes | complemented |
| 8 | C25×D4 | C22 | 1 | 3 | yes | — |
| 9 | C23×#120 | C22 | 1 | 12 | yes | complemented |
| 10 | C24×C22⋊C4 | C22 | 1 | 6 | yes | complemented |
| 11 | C2×#2760 | C22 | 1 | 576 | yes | complemented |
| 12 | #46996 | C22 | 1 | 1024 | yes | direct product factor |
| 13 | C2×#2840 | C22 | 1 | 48 | yes | complemented |
| 14 | C2×#2404 | C22 | 1 | 576 | yes | complemented |
| 15 | C2×#2403 | C22 | 1 | 144 | yes | complemented |
| 16 | C22×#401 | C22 | 1 | 8 | yes | complemented |
| 17 | C22×#393 | C22 | 1 | 12 | yes | complemented |
| 18 | C22×#393 | C22 | 1 | 12 | yes | complemented |
| 19 | C22×#392 | C22 | 1 | 12 | yes | — |
| 20 | C22×#392 | C22 | 1 | 4 | yes | complemented |
| 21 | C2×#2308 | C22 | 1 | 144 | yes | complemented |
| 22 | C22×#386 | C22 | 1 | 12 | yes | complemented |
| 23 | C22×#386 | C22 | 1 | 24 | yes | complemented |
| 24 | C22×#386 | C22 | 1 | 24 | yes | complemented |
| 25 | C22×#381 | C22 | 1 | 6 | yes | complemented |
| 26 | C22×#381 | C22 | 1 | 12 | yes | complemented |
| 27 | C22×#379 | C22 | 1 | 3 | yes | — |
| 28 | C22×#379 | C22 | 1 | 1 | yes | characteristic |
| 29 | C27 | C23 | 1 | 3 | yes | — |
| 30 | C27 | C23 | 1 | 1 | yes | characteristic |
| 31 | C23×#41 | — | 4 | 96 | no | — |
| 32 | C23×#41 | C23 | 1 | 96 | yes | complemented |
| 33 | C24×Q8 | C23 | 1 | 4 | yes | — |
| 34 | C24×D4 | — | 2 | 48 | no | — |
| 35 | C24×D4 | — | 4 | 48 | no | — |
| 36 | C24×D4 | C23 | 1 | 12 | yes | — |
| 37 | C24×D4 | C23 | 1 | 12 | yes | — |
| 38 | C24×D4 | C23 | 1 | 72 | yes | — |
| 39 | C25×C4 | C23 | 1 | 3 | yes | — |
| 40 | C25×C4 | C23 | 1 | 12 | yes | — |
| 41 | C22×#120 | — | 4 | 96 | no | — |
| 42 | C22×#120 | C23 | 1 | 288 | yes | complemented |
| 43 | C23×C22⋊C4 | — | 4 | 48 | no | — |
| 44 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 45 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 46 | C23×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 47 | C23×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 48 | C23×C22⋊C4 | C23 | 1 | 24 | yes | — |
| 49 | C23×C22⋊C4 | C23 | 1 | 144 | yes | complemented |
| 50 | #2840 | C23 | 1 | 256 | yes | complemented |
| 51 | #2760 | C23 | 1 | 3072 | yes | complemented |
| 52 | #2404 | C23 | 1 | 3072 | yes | complemented |
| 53 | #2403 | C23 | 1 | 768 | yes | complemented |
| 54 | C2×#401 | C23 | 1 | 192 | yes | complemented |
| 55 | C2×#393 | C23 | 1 | 288 | yes | complemented |
| 56 | C2×#393 | C23 | 1 | 288 | yes | complemented |
| 57 | C2×#392 | C23 | 1 | 288 | yes | — |
| 58 | C2×#392 | C23 | 1 | 96 | yes | complemented |
| 59 | #2308 | C23 | 1 | 768 | yes | complemented |
| 60 | C2×#386 | C23 | 1 | 288 | yes | complemented |
| 61 | C2×#386 | C23 | 1 | 576 | yes | complemented |
| 62 | C2×#386 | C23 | 1 | 576 | yes | complemented |
| 63 | C2×#381 | C23 | 1 | 288 | yes | complemented |
| 64 | C2×#381 | C23 | 1 | 144 | yes | complemented |
| 65 | C2×#379 | C23 | 1 | 72 | yes | — |
| 66 | C2×#379 | C23 | 1 | 24 | yes | — |
| 67 | C22×#95 | C23 | 1 | 4 | yes | — |
| 68 | C22×#95 | C23 | 1 | 24 | yes | — |
| 69 | C22×#95 | C23 | 1 | 12 | yes | — |
| 70 | C22×#95 | C23 | 1 | 8 | yes | — |
| 71 | C26 | — | 2 | 24 | no | — |
| 72 | C26 | — | 2 | 48 | no | — |
| 73 | C26 | — | 4 | 24 | no | — |
| 74 | C26 | — | 4 | 48 | no | — |
| 75 | C26 | #41 | 1 | 16 | yes | complemented |
| 76 | C26 | C24 | 1 | 3 | yes | — |
| 77 | C26 | C24 | 1 | 6 | yes | — |
| 78 | C26 | C24 | 1 | 36 | yes | — |
| 79 | C26 | C24 | 1 | 12 | yes | — |
| 80 | C22×#41 | — | 4 | 1152 | no | — |
| 81 | C22×#41 | — | 4 | 1024 | no | — |
| 82 | C22×#41 | C24 | 1 | 256 | yes | complemented |
| 83 | C23×Q8 | — | 4 | 48 | no | — |
| 84 | C23×Q8 | C24 | 1 | 48 | yes | — |
| 85 | C23×D4 | — | 2 | 96 | no | — |
| 86 | C23×D4 | — | 2 | 576 | no | — |
| 87 | C23×D4 | — | 2 | 96 | no | — |
| 88 | C23×D4 | — | 2 | 192 | no | — |
| 89 | C23×D4 | — | 4 | 48 | no | — |
| 90 | C23×D4 | — | 4 | 48 | no | — |
| 91 | C23×D4 | — | 4 | 576 | no | — |
| 92 | C23×D4 | — | 4 | 768 | no | — |
| 93 | C23×D4 | C24 | 1 | 144 | yes | — |
| 94 | C23×D4 | C24 | 1 | 144 | yes | — |
| 95 | C23×D4 | C24 | 1 | 192 | yes | — |
| 96 | C24×C4 | — | 2 | 24 | no | — |
| 97 | C24×C4 | — | 2 | 96 | no | — |
| 98 | C24×C4 | — | 4 | 24 | no | — |
| 99 | C24×C4 | — | 4 | 96 | no | — |
| 100 | C24×C4 | C24 | 1 | 4 | yes | — |
| 101 | C24×C4 | C24 | 1 | 6 | yes | — |
| 102 | C24×C4 | C24 | 1 | 12 | yes | — |
| 103 | C24×C4 | C24 | 1 | 36 | yes | — |
| 104 | C24×C4 | C24 | 1 | 144 | yes | — |
| 105 | C2×#120 | — | 4 | 1152 | no | — |
| 106 | C2×#120 | C24 | 1 | 768 | yes | complemented |
| 107 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 108 | C22×C22⋊C4 | — | 4 | 48 | no | — |
| 109 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 110 | C22×C22⋊C4 | — | 4 | 576 | no | — |
| 111 | C22×C22⋊C4 | — | 4 | 96 | no | — |
| 112 | C22×C22⋊C4 | — | 4 | 48 | no | — |
| 113 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 114 | C22×C22⋊C4 | C24 | 1 | 288 | yes | — |
| 115 | C22×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 116 | C22×C22⋊C4 | C24 | 1 | 144 | yes | — |
| 117 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 118 | C22×C22⋊C4 | C24 | 1 | 384 | yes | complemented |
| 119 | #401 | C24 | 1 | 512 | yes | complemented |
| 120 | #393 | C24 | 1 | 768 | yes | complemented |
| 121 | #393 | C24 | 1 | 768 | yes | complemented |
| 122 | #392 | C24 | 1 | 768 | yes | — |
| 123 | #392 | C24 | 1 | 256 | yes | complemented |
| 124 | #386 | C24 | 1 | 1536 | yes | complemented |
| 125 | #386 | C24 | 1 | 768 | yes | complemented |
| 126 | #386 | C24 | 1 | 1536 | yes | complemented |
| 127 | #381 | C24 | 1 | 384 | yes | complemented |
| 128 | #381 | C24 | 1 | 768 | yes | complemented |
| 129 | #379 | C24 | 1 | 64 | yes | — |
| 130 | #379 | C24 | 1 | 192 | yes | — |
| 131 | C2×#95 | C24 | 1 | 144 | yes | — |
| 132 | C2×#95 | C24 | 1 | 48 | yes | — |
| 133 | C2×#95 | C24 | 1 | 96 | yes | — |
| 134 | C2×#95 | C24 | 1 | 288 | yes | — |
| 135 | C25 | — | 2 | 384 | no | — |
| 136 | C25 | — | 2 | 24 | no | — |
| 137 | C25 | — | 2 | 24 | no | — |
| 138 | C25 | — | 2 | 24 | no | — |
| 139 | C25 | — | 2 | 96 | no | — |
| 140 | C25 | — | 2 | 48 | no | — |
| 141 | C25 | — | 2 | 144 | no | — |
| 142 | C25 | — | 2 | 288 | no | — |
| 143 | C25 | — | 4 | 192 | no | — |
| 144 | C25 | — | 4 | 144 | no | — |
| 145 | C25 | — | 4 | 288 | no | — |
| 146 | C25 | — | 8 | 192 | no | — |
| 147 | C25 | — | 8 | 384 | no | — |
| 148 | C25 | — | 8 | 128 | no | — |
| 149 | C25 | C2×#41 | 1 | 24 | yes | — |
| 150 | C25 | C2×#41 | 1 | 96 | yes | complemented |
| 151 | C25 | H(5,𝔽2) | 1 | 48 | yes | — |
| 152 | C25 | C25 | 1 | 18 | yes | — |
| 153 | C25 | C25 | 1 | 36 | yes | — |
| 154 | C25 | C25 | 1 | 48 | yes | — |
| 155 | C25 | C25 | 1 | 16 | yes | — |
| 156 | C25 | C25 | 1 | 1 | yes | characteristic |
| 157 | C2×#41 | — | 4 | 1536 | no | — |
| 158 | C2×#41 | — | 4 | 6144 | no | — |
| 159 | C22×Q8 | — | 4 | 288 | no | — |
| 160 | C22×Q8 | — | 4 | 256 | no | — |
| 161 | C22×Q8 | C25 | 1 | 64 | yes | — |
| 162 | C22×D4 | — | 2 | 576 | no | — |
| 163 | C22×D4 | — | 2 | 768 | no | — |
| 164 | C22×D4 | — | 2 | 576 | no | — |
| 165 | C22×D4 | — | 2 | 1152 | no | — |
| 166 | C22×D4 | — | 4 | 288 | no | — |
| 167 | C22×D4 | — | 4 | 288 | no | — |
| 168 | C22×D4 | — | 4 | 768 | no | — |
| 169 | C22×D4 | — | 4 | 768 | no | — |
| 170 | C22×D4 | — | 4 | 768 | no | — |
| 171 | C22×D4 | — | 4 | 4608 | no | — |
| 172 | C22×D4 | C25 | 1 | 192 | yes | — |
| 173 | C22×D4 | C25 | 1 | 192 | yes | — |
| 174 | C23×C4 | — | 2 | 144 | no | — |
| 175 | C23×C4 | — | 2 | 24 | no | — |
| 176 | C23×C4 | — | 2 | 48 | no | — |
| 177 | C23×C4 | — | 2 | 48 | no | — |
| 178 | C23×C4 | — | 2 | 576 | no | — |
| 179 | C23×C4 | — | 2 | 48 | no | — |
| 180 | C23×C4 | — | 2 | 96 | no | — |
| 181 | C23×C4 | — | 4 | 144 | no | — |
| 182 | C23×C4 | — | 4 | 576 | no | — |
| 183 | C23×C4 | — | 4 | 192 | no | — |
| 184 | C23×C4 | — | 4 | 768 | no | — |
| 185 | C23×C4 | C25 | 1 | 24 | yes | — |
| 186 | C23×C4 | C25 | 1 | 72 | yes | — |
| 187 | C23×C4 | C25 | 1 | 36 | yes | — |
| 188 | C23×C4 | C25 | 1 | 192 | yes | — |
| 189 | C23×C4 | C25 | 1 | 48 | yes | — |
| 190 | #120 | — | 4 | 1536 | no | — |
| 191 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 192 | C2×C22⋊C4 | — | 4 | 288 | no | — |
| 193 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 194 | C2×C22⋊C4 | — | 4 | 768 | no | — |
| 195 | C2×C22⋊C4 | — | 4 | 576 | no | — |
| 196 | C2×C22⋊C4 | — | 4 | 288 | no | — |
| 197 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 198 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 199 | C2×C22⋊C4 | C25 | 1 | 192 | yes | — |
| 200 | C2×C22⋊C4 | C25 | 1 | 192 | yes | — |
| 201 | C2×C22⋊C4 | C25 | 1 | 384 | yes | — |
| 202 | #95 | C25 | 1 | 64 | yes | — |
| 203 | #95 | C25 | 1 | 384 | yes | — |
| 204 | #95 | C25 | 1 | 192 | yes | — |
| 205 | #95 | C25 | 1 | 128 | yes | — |
| 206 | C24 | — | 2 | 1152 | no | — |
| 207 | C24 | — | 2 | 72 | no | — |
| 208 | C24 | — | 2 | 72 | no | — |
| 209 | C24 | — | 2 | 72 | no | — |
| 210 | C24 | — | 2 | 288 | no | — |
| 211 | C24 | — | 2 | 144 | no | — |
| 212 | C24 | — | 2 | 96 | no | — |
| 213 | C24 | — | 2 | 192 | no | — |
| 214 | C24 | — | 2 | 192 | no | — |
| 215 | C24 | — | 2 | 384 | no | — |
| 216 | C24 | — | 2 | 96 | no | — |
| 217 | C24 | — | 2 | 192 | no | — |
| 218 | C24 | — | 4 | 576 | no | — |
| 219 | C24 | — | 4 | 96 | no | — |
| 220 | C24 | — | 4 | 192 | no | — |
| 221 | C24 | — | 4 | 192 | no | — |
| 222 | C24 | — | 4 | 192 | no | — |
| 223 | C24 | — | 4 | 192 | no | — |
| 224 | C24 | — | 8 | 576 | no | — |
| 225 | C24 | — | 8 | 1152 | no | — |
| 226 | C24 | — | 8 | 1536 | no | — |
| 227 | C24 | — | 8 | 512 | no | — |
| 228 | C24 | — | 8 | 384 | no | — |
| 229 | C24 | C22×#41 | 1 | 72 | yes | — |
| 230 | C24 | C22×#41 | 1 | 4 | yes | — |
| 231 | C24 | C22×#41 | 1 | 64 | yes | complemented |
| 232 | C24 | C2×H(5,𝔽2) | 1 | 144 | yes | — |
| 233 | C24 | C2×H(5,𝔽2) | 1 | 24 | yes | — |
| 234 | C24 | C26 | 1 | 12 | yes | — |
| 235 | C24 | C26 | 1 | 24 | yes | — |
| 236 | C24 | C26 | 1 | 3 | yes | — |
| 237 | #41 | — | 4 | 4096 | no | — |
| 238 | C2×Q8 | — | 4 | 192 | no | — |
| 239 | C2×Q8 | — | 4 | 768 | no | — |
| 240 | C2×D4 | — | 2 | 384 | no | — |
| 241 | C2×D4 | — | 2 | 384 | no | — |
| 242 | C2×D4 | — | 2 | 768 | no | — |
| 243 | C2×D4 | — | 4 | 192 | no | — |
| 244 | C2×D4 | — | 4 | 192 | no | — |
| 245 | C2×D4 | — | 4 | 2304 | no | — |
| 246 | C2×D4 | — | 4 | 2304 | no | — |
| 247 | C2×D4 | — | 4 | 3072 | no | — |
| 248 | C22×C4 | — | 2 | 96 | no | — |
| 249 | C22×C4 | — | 2 | 72 | no | — |
| 250 | C22×C4 | — | 2 | 144 | no | — |
| 251 | C22×C4 | — | 2 | 144 | no | — |
| 252 | C22×C4 | — | 2 | 384 | no | — |
| 253 | C22×C4 | — | 2 | 144 | no | — |
| 254 | C22×C4 | — | 2 | 288 | no | — |
| 255 | C22×C4 | — | 4 | 96 | no | — |
| 256 | C22×C4 | — | 4 | 384 | no | — |
| 257 | C22×C4 | — | 4 | 576 | no | — |
| 258 | C22×C4 | — | 4 | 2304 | no | — |
| 259 | C22×C4 | — | 4 | 96 | no | — |
| 260 | C22×C4 | — | 4 | 64 | no | — |
| 261 | C22×C4 | — | 4 | 192 | no | — |
| 262 | C22×C4 | C26 | 1 | 24 | yes | — |
| 263 | C22×C4 | C26 | 1 | 16 | yes | — |
| 264 | C22×C4 | C26 | 1 | 48 | yes | — |
| 265 | C22⋊C4 | — | 4 | 96 | no | — |
| 266 | C22⋊C4 | — | 4 | 192 | no | — |
| 267 | C22⋊C4 | — | 4 | 96 | no | — |
| 268 | C22⋊C4 | — | 4 | 384 | no | — |
| 269 | C22⋊C4 | — | 4 | 192 | no | — |
| 270 | C23 | — | 2 | 384 | no | — |
| 271 | C23 | — | 2 | 144 | no | — |
| 272 | C23 | — | 2 | 288 | no | — |
| 273 | C23 | — | 2 | 288 | no | — |
| 274 | C23 | — | 2 | 24 | no | — |
| 275 | C23 | — | 2 | 24 | no | — |
| 276 | C23 | — | 2 | 24 | no | — |
| 277 | C23 | — | 2 | 96 | no | — |
| 278 | C23 | — | 2 | 48 | no | — |
| 279 | C23 | — | 2 | 576 | no | — |
| 280 | C23 | — | 4 | 192 | no | — |
| 281 | C23 | — | 4 | 288 | no | — |
| 282 | C23 | — | 4 | 768 | no | — |
| 283 | C23 | — | 4 | 384 | no | — |
| 284 | C23 | — | 4 | 288 | no | — |
| 285 | C23 | — | 4 | 288 | no | — |
| 286 | C23 | — | 8 | 384 | no | — |
| 287 | C23 | — | 8 | 192 | no | — |
| 288 | C23 | — | 8 | 2304 | no | — |
| 289 | C23 | — | 8 | 128 | no | — |
| 290 | C23 | — | 8 | 768 | no | — |
| 291 | C23 | #3490 | 1 | 48 | yes | — |
| 292 | C23 | #3532 | 1 | 64 | yes | — |
| 293 | C23 | C23×#41 | 1 | 24 | yes | — |
| 294 | C23 | C23×#41 | 1 | 6 | yes | — |
| 295 | C23 | C22×H(5,𝔽2) | 1 | 48 | yes | — |
| 296 | C23 | C22×H(5,𝔽2) | 1 | 36 | yes | — |
| 297 | C23 | C27 | 1 | 1 | yes | characteristic |
| 298 | Q8 | — | 4 | 256 | no | — |
| 299 | D4 | — | 4 | 768 | no | — |
| 300 | D4 | — | 4 | 768 | no | — |
| 301 | C2×C4 | — | 2 | 24 | no | — |
| 302 | C2×C4 | — | 2 | 48 | no | — |
| 303 | C2×C4 | — | 2 | 48 | no | — |
| 304 | C2×C4 | — | 2 | 48 | no | — |
| 305 | C2×C4 | — | 2 | 96 | no | — |
| 306 | C2×C4 | — | 4 | 192 | no | — |
| 307 | C2×C4 | — | 4 | 768 | no | — |
| 308 | C2×C4 | — | 4 | 144 | no | — |
| 309 | C2×C4 | — | 4 | 96 | no | — |
| 310 | C2×C4 | — | 4 | 288 | no | — |
| 311 | C22 | — | 2 | 96 | no | — |
| 312 | C22 | — | 2 | 24 | no | — |
| 313 | C22 | — | 2 | 48 | no | — |
| 314 | C22 | — | 2 | 48 | no | — |
| 315 | C22 | — | 4 | 48 | no | — |
| 316 | C22 | — | 4 | 48 | no | — |
| 317 | C22 | — | 4 | 48 | no | — |
| 318 | C22 | — | 4 | 576 | no | — |
| 319 | C22 | — | 4 | 288 | no | — |
| 320 | C22 | — | 8 | 384 | no | — |
| 321 | C22 | — | 8 | 128 | no | — |
| 322 | C22 | #46996 | 1 | 64 | yes | direct product factor |
| 323 | C22 | C2×#3532 | 1 | 48 | yes | — |
| 324 | C22 | C2×#3490 | 1 | 36 | yes | — |
| 325 | C22 | C24×#41 | 1 | 1 | yes | characteristic |
| 326 | C22 | C23×H(5,𝔽2) | 1 | 6 | yes | — |
| 327 | C4 | — | 4 | 16 | no | — |
| 328 | C4 | — | 4 | 48 | no | — |
| 329 | C4 | — | 4 | 24 | no | — |
| 330 | C2 | — | 4 | 48 | no | — |
| 331 | C2 | — | 4 | 24 | no | — |
| 332 | C2 | C2×#46996 | 1 | 24 | yes | direct product factor |
| 333 | C2 | C22×#3490 | 1 | 3 | yes | — |
| 334 | C2 | C22×#3532 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C25 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#46996 | C2 | direct (N × H) |
| 2. C22×#2760 | C2 | semidirect |
| 3. C22×#2840 | C2 | semidirect |
| 4. C22×#2404 | C2 | semidirect |
| 5. C22×#2403 | C2 | semidirect |
| 6. C22×#2308 | C2 | semidirect |
| 7. C24×#41 | C22 | semidirect |
| 9. C23×#120 | C22 | semidirect |
| 10. C24×C22⋊C4 | C22 | semidirect |
| 11. C2×#2760 | C22 | semidirect |
| 12. #46996 | C22 | direct (N × H) |
| 13. C2×#2840 | C22 | semidirect |
| 14. C2×#2404 | C22 | semidirect |
| 15. C2×#2403 | C22 | semidirect |
| 16. C22×#401 | C22 | semidirect |
| 17. C22×#393 | C22 | semidirect |
| 18. C22×#393 | C22 | semidirect |
| 20. C22×#392 | C22 | semidirect |
| 21. C2×#2308 | C22 | semidirect |
| 22. C22×#386 | C22 | semidirect |
| 23. C22×#386 | C22 | semidirect |
| 24. C22×#386 | C22 | semidirect |
| 25. C22×#381 | C22 | semidirect |
| 26. C22×#381 | C22 | semidirect |
| 32. C23×#41 | C23 | semidirect |
| 42. C22×#120 | C23 | semidirect |
| 49. C23×C22⋊C4 | C23 | semidirect |
| 50. #2840 | C23 | semidirect |
| 51. #2760 | C23 | semidirect |
| 52. #2404 | C23 | semidirect |
| 53. #2403 | C23 | semidirect |
| 54. C2×#401 | C23 | semidirect |
| 55. C2×#393 | C23 | semidirect |
| 56. C2×#393 | C23 | semidirect |
| 58. C2×#392 | C23 | semidirect |
| 59. #2308 | C23 | semidirect |
| 60. C2×#386 | C23 | semidirect |
| 61. C2×#386 | C23 | semidirect |
| 62. C2×#386 | C23 | semidirect |
| 63. C2×#381 | C23 | semidirect |
| 64. C2×#381 | C23 | semidirect |
| 75. C26 | #41 | semidirect |
| 82. C22×#41 | C24 | semidirect |
| 106. C2×#120 | C24 | semidirect |
| 118. C22×C22⋊C4 | C24 | semidirect |
| 119. #401 | C24 | semidirect |
| 120. #393 | C24 | semidirect |
| 121. #393 | C24 | semidirect |
| 123. #392 | C24 | semidirect |
| 124. #386 | C24 | semidirect |
| 125. #386 | C24 | semidirect |
| 126. #386 | C24 | semidirect |
| 127. #381 | C24 | semidirect |
| 128. #381 | C24 | semidirect |
| 150. C25 | C2×#41 | semidirect |
| 231. C24 | C22×#41 | semidirect |
| 322. C22 | #46996 | direct (N × H) |
| 332. C2 | C2×#46996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#46996 | 2 |
| C22×#2760 | 2 |
| C22×#2840 | 2 |
| C22×#2404 | 2 |
| C22×#2403 | 2 |
| C22×#2308 | 2 |