← #72340804
Subgroups — #72340804
Order 2048.
Only the 6580 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 398 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72340803 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #72340789 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72312790 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #72286397 | C2 | 1 | 24 | yes | maximal, complemented |
| 5 | #72286264 | C2 | 1 | 24 | yes | maximal, complemented |
| 6 | #72279737 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #72279481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72279371 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C22×#63011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#63011 | C22 | 1 | 24 | yes | — |
| 11 | C22×#3549 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×#3498 | C22 | 1 | 3 | yes | — |
| 13 | C22×#3481 | C22 | 1 | 3 | yes | — |
| 14 | #10575509 | C22 | 1 | 3 | yes | complemented |
| 15 | #10575094 | C22 | 1 | 3 | yes | complemented |
| 16 | #7641973 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #6487514 | C22 | 1 | 24 | yes | complemented |
| 18 | #6487513 | C22 | 1 | 24 | yes | complemented |
| 19 | #6446716 | C22 | 1 | 12 | yes | complemented |
| 20 | #6443311 | C22 | 1 | 12 | yes | complemented |
| 21 | #6374317 | C22 | 1 | 3 | yes | complemented |
| 22 | C2×#21797 | C22 | 1 | 3 | yes | complemented |
| 23 | #6370997 | C22 | 1 | 3 | yes | complemented |
| 24 | #6351567 | C22 | 1 | 12 | yes | complemented |
| 25 | #6351560 | C22 | 1 | 12 | yes | complemented |
| 26 | #6348972 | C22 | 1 | 24 | yes | complemented |
| 27 | #6348971 | C22 | 1 | 24 | yes | complemented |
| 28 | #6348078 | C22 | 1 | 12 | yes | complemented |
| 29 | #6348073 | C22 | 1 | 12 | yes | complemented |
| 30 | #6344053 | C22 | 1 | 3 | yes | complemented |
| 31 | #6343804 | C22 | 1 | 3 | yes | complemented |
| 32 | #6342924 | C22 | 1 | 6 | yes | complemented |
| 33 | #347190 | C22 | 1 | 192 | yes | complemented |
| 34 | #346934 | C22 | 1 | 64 | yes | complemented |
| 35 | #187899 | C22 | 1 | 24 | yes | complemented |
| 36 | #187081 | C22 | 1 | 24 | yes | complemented |
| 37 | #187042 | C22 | 1 | 48 | yes | complemented |
| 38 | #186576 | C22 | 1 | 24 | yes | complemented |
| 39 | #186563 | C22 | 1 | 48 | yes | complemented |
| 40 | C23×H(5,𝔽2) | D4 | 1 | 6 | yes | — |
| 41 | #63011 | C23 | 1 | 64 | yes | — |
| 42 | C2×#3498 | D4 | 1 | 12 | yes | — |
| 43 | C2×#3498 | D4 | 1 | 24 | yes | — |
| 44 | C2×#3498 | C23 | 1 | 12 | yes | — |
| 45 | C2×#3498 | C23 | 1 | 24 | yes | — |
| 46 | C2×#3549 | D4 | 1 | 12 | yes | complemented |
| 47 | C2×#3549 | C23 | 1 | 12 | yes | — |
| 48 | C2×#3481 | D4 | 1 | 12 | yes | complemented |
| 49 | C2×#3481 | D4 | 1 | 24 | yes | complemented |
| 50 | C2×#3481 | C23 | 1 | 12 | yes | — |
| 51 | C2×#3481 | C23 | 1 | 24 | yes | — |
| 52 | C22×#559 | D4 | 1 | 3 | yes | complemented |
| 53 | C22×#554 | D4 | 1 | 6 | yes | complemented |
| 54 | C22×D42 | D4 | 1 | 3 | yes | complemented |
| 55 | C22×H(3,𝔽4) | D4 | 1 | 4 | yes | complemented |
| 56 | C22×#535 | D4 | 1 | 6 | yes | — |
| 57 | C2×#3444 | C23 | 1 | 1 | yes | characteristic, complemented |
| 58 | C22×#532 | C23 | 1 | 3 | yes | — |
| 59 | C23×#127 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×C4×#41 | C23 | 1 | 3 | yes | — |
| 61 | #60804 | C23 | 1 | 12 | yes | complemented |
| 62 | #60803 | C23 | 1 | 12 | yes | complemented |
| 63 | #60639 | C23 | 1 | 6 | yes | complemented |
| 64 | #60618 | C23 | 1 | 6 | yes | complemented |
| 65 | #60562 | C23 | 1 | 12 | yes | complemented |
| 66 | #60561 | C23 | 1 | 12 | yes | complemented |
| 67 | #60484 | C23 | 1 | 6 | yes | complemented |
| 68 | #60415 | C23 | 1 | 6 | yes | complemented |
| 69 | C2×#2920 | C23 | 1 | 3 | yes | complemented |
| 70 | C2×#2920 | C23 | 1 | 3 | yes | complemented |
| 71 | #35285 | C23 | 1 | 6 | yes | complemented |
| 72 | #35274 | C23 | 1 | 6 | yes | complemented |
| 73 | #34012 | C23 | 1 | 1 | yes | characteristic, complemented |
| 74 | #25875 | C23 | 1 | 96 | yes | complemented |
| 75 | #25747 | C23 | 1 | 48 | yes | complemented |
| 76 | #25744 | C23 | 1 | 48 | yes | complemented |
| 77 | #21815 | C23 | 1 | 24 | yes | complemented |
| 78 | #21797 | C23 | 1 | 24 | yes | complemented |
| 79 | C2×#1965 | C23 | 1 | 12 | yes | complemented |
| 80 | #21209 | C23 | 1 | 12 | yes | complemented |
| 81 | #20747 | C23 | 1 | 24 | yes | complemented |
| 82 | C4×#421 | C23 | 1 | 12 | yes | complemented |
| 83 | #19074 | C23 | 1 | 48 | yes | complemented |
| 84 | #19073 | C23 | 1 | 16 | yes | complemented |
| 85 | #18532 | C23 | 1 | 96 | yes | complemented |
| 86 | #18528 | C23 | 1 | 48 | yes | complemented |
| 87 | #18527 | C23 | 1 | 48 | yes | complemented |
| 88 | #17750 | C23 | 1 | 24 | yes | complemented |
| 89 | #17738 | C23 | 1 | 12 | yes | complemented |
| 90 | #17663 | C23 | 1 | 12 | yes | complemented |
| 91 | #17647 | C23 | 1 | 24 | yes | complemented |
| 92 | #17451 | C23 | 1 | 24 | yes | complemented |
| 93 | #17450 | C23 | 1 | 24 | yes | complemented |
| 94 | #17447 | C23 | 1 | 24 | yes | complemented |
| 95 | #8530 | C23 | 1 | 64 | yes | complemented |
| 96 | #8469 | C23 | 1 | 192 | yes | complemented |
| 97 | #8440 | C23 | 1 | 192 | yes | complemented |
| 98 | C22×H(5,𝔽2) | C2×D4 | 1 | 24 | yes | — |
| 99 | C22×H(5,𝔽2) | C2×D4 | 1 | 48 | yes | — |
| 100 | C23×#41 | C2×D4 | 1 | 3 | yes | — |
| 101 | C23×#41 | C2×D4 | 1 | 6 | yes | — |
| 102 | C24×D4 | C2×D4 | 1 | 6 | yes | — |
| 103 | #3549 | C2×D4 | 1 | 48 | yes | — |
| 104 | #3549 | C24 | 1 | 16 | yes | — |
| 105 | C2×H(3,𝔽4) | C2×D4 | 1 | 48 | yes | — |
| 106 | #3498 | C2×D4 | 1 | 48 | yes | — |
| 107 | #3498 | C2×D4 | 1 | 96 | yes | — |
| 108 | #3498 | C24 | 1 | 48 | yes | — |
| 109 | #3481 | C2×D4 | 1 | 48 | yes | — |
| 110 | #3481 | C2×D4 | 1 | 96 | yes | — |
| 111 | #3481 | C24 | 1 | 48 | yes | — |
| 112 | C2×#559 | C2×D4 | 1 | 12 | yes | — |
| 113 | C2×#559 | C2×D4 | 1 | 24 | yes | — |
| 114 | C2×#554 | C2×D4 | 1 | 24 | yes | — |
| 115 | C2×#554 | C2×D4 | 1 | 24 | yes | — |
| 116 | C2×#554 | C2×D4 | 1 | 24 | yes | — |
| 117 | C2×D42 | C2×D4 | 1 | 12 | yes | — |
| 118 | C2×D42 | C2×D4 | 1 | 24 | yes | — |
| 119 | C2×#535 | C2×D4 | 1 | 24 | yes | — |
| 120 | C2×#535 | C2×D4 | 1 | 48 | yes | — |
| 121 | C2×#533 | C24 | 1 | 3 | yes | complemented |
| 122 | C2×#532 | C2×D4 | 1 | 6 | yes | — |
| 123 | C2×#532 | C2×D4 | 1 | 12 | yes | — |
| 124 | C2×#532 | C2×D4 | 1 | 12 | yes | — |
| 125 | C2×#532 | C2×D4 | 1 | 6 | yes | — |
| 126 | C2×#532 | C2×D4 | 1 | 12 | yes | — |
| 127 | C2×#532 | C2×D4 | 1 | 6 | yes | — |
| 128 | C2×#532 | C24 | 1 | 12 | yes | — |
| 129 | C2×#532 | C24 | 1 | 6 | yes | — |
| 130 | C2×#532 | C24 | 1 | 3 | yes | complemented |
| 131 | C22×C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 132 | C22×#127 | C2×D4 | 1 | 3 | yes | — |
| 133 | C22×#127 | C2×D4 | 1 | 12 | yes | — |
| 134 | C22×#127 | C2×D4 | 1 | 6 | yes | — |
| 135 | C22×#127 | C24 | 1 | 6 | yes | — |
| 136 | C22×#124 | C2×D4 | 1 | 6 | yes | — |
| 137 | C2×C4×#41 | C2×D4 | 1 | 12 | yes | — |
| 138 | C2×C4×#41 | C2×D4 | 1 | 12 | yes | — |
| 139 | C2×C4×#41 | C2×D4 | 1 | 12 | yes | — |
| 140 | C2×C4×#41 | C2×D4 | 1 | 12 | yes | — |
| 141 | C2×C4×#41 | C2×D4 | 1 | 6 | yes | — |
| 142 | C2×C4×#41 | C24 | 1 | 12 | yes | — |
| 143 | C2×C4×#41 | C24 | 1 | 6 | yes | — |
| 144 | C22×C4×Q8 | C2×D4 | 1 | 6 | yes | — |
| 145 | C22×C4×D4 | C2×D4 | 1 | 6 | yes | — |
| 146 | C22×#117 | C2×D4 | 1 | 3 | yes | — |
| 147 | C23×C42 | C24 | 1 | 1 | yes | characteristic |
| 148 | #3152 | C24 | 1 | 12 | yes | complemented |
| 149 | #3151 | C24 | 1 | 12 | yes | complemented |
| 150 | #3141 | C24 | 1 | 24 | yes | complemented |
| 151 | #3079 | C24 | 1 | 24 | yes | complemented |
| 152 | #3039 | C24 | 1 | 12 | yes | complemented |
| 153 | #3038 | C24 | 1 | 12 | yes | complemented |
| 154 | #2920 | C24 | 1 | 12 | yes | complemented |
| 155 | #2920 | C24 | 1 | 12 | yes | complemented |
| 156 | C2×#423 | C24 | 1 | 6 | yes | complemented |
| 157 | C2×C4×M16 | C24 | 1 | 6 | yes | complemented |
| 158 | #2867 | C24 | 1 | 4 | yes | complemented |
| 159 | #2858 | C24 | 1 | 12 | yes | complemented |
| 160 | C4×#117 | C24 | 1 | 6 | yes | complemented |
| 161 | #1965 | C24 | 1 | 48 | yes | complemented |
| 162 | #1962 | C24 | 1 | 48 | yes | complemented |
| 163 | C4×#104 | C24 | 1 | 48 | yes | complemented |
| 164 | #1560 | C24 | 1 | 48 | yes | complemented |
| 165 | #1525 | C24 | 1 | 48 | yes | complemented |
| 166 | #1489 | C24 | 1 | 96 | yes | complemented |
| 167 | C26 | #120 | 1 | 4 | yes | — |
| 168 | C2×H(5,𝔽2) | C22×D4 | 1 | 96 | yes | — |
| 169 | C22×#41 | #120 | 1 | 12 | yes | — |
| 170 | C22×#41 | #120 | 1 | 6 | yes | — |
| 171 | C22×#41 | #120 | 1 | 24 | yes | — |
| 172 | C22×#41 | #120 | 1 | 12 | yes | — |
| 173 | C22×#41 | C22×D4 | 1 | 12 | yes | — |
| 174 | C22×#41 | C22×D4 | 1 | 6 | yes | — |
| 175 | C22×#41 | C22×D4 | 1 | 24 | yes | — |
| 176 | C22×#41 | C22×D4 | 1 | 12 | yes | — |
| 177 | C23×Q8 | #120 | 1 | 3 | yes | — |
| 178 | C23×Q8 | #120 | 1 | 6 | yes | — |
| 179 | C23×D4 | #120 | 1 | 3 | yes | — |
| 180 | C23×D4 | #120 | 1 | 6 | yes | — |
| 181 | C23×D4 | #120 | 1 | 24 | yes | — |
| 182 | C23×D4 | #120 | 1 | 12 | yes | — |
| 183 | C23×D4 | C22×D4 | 1 | 12 | yes | — |
| 184 | C23×D4 | C22×D4 | 1 | 24 | yes | — |
| 185 | C24×C4 | C22×D4 | 1 | 3 | yes | — |
| 186 | H(3,𝔽4) | C22×D4 | 1 | 64 | yes | — |
| 187 | #559 | C22×D4 | 1 | 48 | yes | — |
| 188 | #554 | C22×D4 | 1 | 96 | yes | — |
| 189 | D42 | C22×D4 | 1 | 48 | yes | — |
| 190 | #535 | C22×D4 | 1 | 96 | yes | — |
| 191 | #532 | #120 | 1 | 24 | yes | — |
| 192 | #532 | #120 | 1 | 24 | yes | — |
| 193 | #532 | #120 | 1 | 24 | yes | — |
| 194 | #532 | C22×D4 | 1 | 24 | yes | — |
| 195 | #532 | C22×D4 | 1 | 12 | yes | — |
| 196 | #532 | C22×D4 | 1 | 24 | yes | — |
| 197 | #532 | C22×D4 | 1 | 12 | yes | — |
| 198 | #532 | C22×D4 | 1 | 24 | yes | — |
| 199 | #532 | C22×D4 | 1 | 12 | yes | — |
| 200 | #532 | C25 | 1 | 12 | yes | — |
| 201 | C2×C4⋊Q8 | #120 | 1 | 6 | yes | — |
| 202 | C2×C4⋊Q8 | #120 | 1 | 12 | yes | — |
| 203 | C2×C4⋊Q8 | C22×D4 | 1 | 12 | yes | — |
| 204 | C2×C4⋊Q8 | C22×D4 | 1 | 6 | yes | — |
| 205 | C2×C4⋊Q8 | C25 | 1 | 3 | yes | complemented |
| 206 | C2×#127 | #120 | 1 | 6 | yes | — |
| 207 | C2×#127 | #120 | 1 | 12 | yes | — |
| 208 | C2×#127 | #120 | 1 | 4 | yes | — |
| 209 | C2×#127 | #120 | 1 | 12 | yes | — |
| 210 | C2×#127 | #120 | 1 | 8 | yes | — |
| 211 | C2×#127 | C22×D4 | 1 | 12 | yes | — |
| 212 | C2×#127 | C22×D4 | 1 | 6 | yes | — |
| 213 | C2×#127 | C22×D4 | 1 | 12 | yes | — |
| 214 | C2×#127 | C22×D4 | 1 | 24 | yes | — |
| 215 | C2×#127 | C25 | 1 | 4 | yes | — |
| 216 | C2×#127 | C25 | 1 | 1 | yes | characteristic, complemented |
| 217 | C2×#124 | #120 | 1 | 12 | yes | — |
| 218 | C2×#124 | #120 | 1 | 24 | yes | — |
| 219 | C2×#124 | C22×D4 | 1 | 24 | yes | — |
| 220 | C2×#124 | C22×D4 | 1 | 12 | yes | — |
| 221 | C4×#41 | #120 | 1 | 12 | yes | — |
| 222 | C4×#41 | #120 | 1 | 24 | yes | — |
| 223 | C4×#41 | #120 | 1 | 24 | yes | — |
| 224 | C4×#41 | #120 | 1 | 12 | yes | — |
| 225 | C4×#41 | C22×D4 | 1 | 24 | yes | — |
| 226 | C4×#41 | C22×D4 | 1 | 24 | yes | — |
| 227 | C4×#41 | C22×D4 | 1 | 24 | yes | — |
| 228 | C4×#41 | C22×D4 | 1 | 24 | yes | — |
| 229 | C4×#41 | C22×D4 | 1 | 12 | yes | — |
| 230 | C4×#41 | C25 | 1 | 12 | yes | — |
| 231 | C2×C4×Q8 | #120 | 1 | 12 | yes | — |
| 232 | C2×C4×Q8 | #120 | 1 | 12 | yes | — |
| 233 | C2×C4×Q8 | #120 | 1 | 12 | yes | — |
| 234 | C2×C4×Q8 | C22×D4 | 1 | 12 | yes | — |
| 235 | C2×C4×Q8 | C22×D4 | 1 | 12 | yes | — |
| 236 | C2×C4×Q8 | C22×D4 | 1 | 12 | yes | — |
| 237 | C2×C4×D4 | #120 | 1 | 12 | yes | — |
| 238 | C2×C4×D4 | #120 | 1 | 12 | yes | — |
| 239 | C2×C4×D4 | #120 | 1 | 12 | yes | — |
| 240 | C2×C4×D4 | C22×D4 | 1 | 12 | yes | — |
| 241 | C2×C4×D4 | C22×D4 | 1 | 12 | yes | — |
| 242 | C2×C4×D4 | C22×D4 | 1 | 12 | yes | — |
| 243 | C2×#117 | #120 | 1 | 6 | yes | — |
| 244 | C2×#117 | #120 | 1 | 12 | yes | — |
| 245 | C2×#117 | C22×D4 | 1 | 12 | yes | — |
| 246 | C2×#117 | C22×D4 | 1 | 6 | yes | — |
| 247 | C22×C4⋊C4 | #120 | 1 | 6 | yes | — |
| 248 | C22×C42 | C22×D4 | 1 | 3 | yes | — |
| 249 | C22×C42 | C22×D4 | 1 | 6 | yes | — |
| 250 | C22×C42 | C22×D4 | 1 | 3 | yes | — |
| 251 | C22×C42 | C22×D4 | 1 | 6 | yes | — |
| 252 | C22×C42 | C22×D4 | 1 | 3 | yes | — |
| 253 | C22×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C22×C42 | C22×D4 | 1 | 3 | yes | — |
| 255 | C22×C42 | C25 | 1 | 3 | yes | — |
| 256 | #423 | C25 | 1 | 12 | yes | complemented |
| 257 | C4×M16 | C25 | 1 | 12 | yes | complemented |
| 258 | C43 | C25 | 1 | 4 | yes | complemented |
| 259 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 260 | C25 | C2×#120 | 1 | 24 | yes | — |
| 261 | C2×#41 | C2×#120 | 1 | 24 | yes | — |
| 262 | C2×#41 | C2×#120 | 1 | 12 | yes | — |
| 263 | C2×#41 | C2×#120 | 1 | 24 | yes | — |
| 264 | C2×#41 | C2×#120 | 1 | 48 | yes | — |
| 265 | C2×#41 | C23×D4 | 1 | 12 | yes | — |
| 266 | C2×#41 | C23×D4 | 1 | 24 | yes | — |
| 267 | C22×Q8 | C2×#120 | 1 | 6 | yes | — |
| 268 | C22×Q8 | C2×#120 | 1 | 12 | yes | — |
| 269 | C22×Q8 | C2×#120 | 1 | 24 | yes | — |
| 270 | C22×Q8 | C2×#120 | 1 | 12 | yes | — |
| 271 | C22×D4 | C2×#120 | 1 | 12 | yes | — |
| 272 | C22×D4 | C2×#120 | 1 | 24 | yes | — |
| 273 | C22×D4 | C2×#120 | 1 | 12 | yes | — |
| 274 | C22×D4 | C2×#120 | 1 | 6 | yes | — |
| 275 | C22×D4 | C2×#120 | 1 | 24 | yes | — |
| 276 | C22×D4 | C2×#120 | 1 | 48 | yes | — |
| 277 | C22×D4 | C23×D4 | 1 | 24 | yes | — |
| 278 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 279 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 280 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 281 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 282 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 283 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 284 | C23×C4 | C2×#120 | 1 | 6 | yes | — |
| 285 | C23×C4 | C2×#120 | 1 | 3 | yes | — |
| 286 | C23×C4 | C23×D4 | 1 | 3 | yes | — |
| 287 | C23×C4 | C23×D4 | 1 | 6 | yes | — |
| 288 | C4⋊Q8 | C2×#120 | 1 | 24 | yes | — |
| 289 | C4⋊Q8 | C2×#120 | 1 | 12 | yes | — |
| 290 | C4⋊Q8 | C23×D4 | 1 | 12 | yes | — |
| 291 | #127 | C2×#120 | 1 | 24 | yes | — |
| 292 | #127 | C2×#120 | 1 | 12 | yes | — |
| 293 | #127 | C23×D4 | 1 | 12 | yes | — |
| 294 | #124 | C2×#120 | 1 | 48 | yes | — |
| 295 | #124 | C2×#120 | 1 | 24 | yes | — |
| 296 | #124 | C23×D4 | 1 | 24 | yes | — |
| 297 | C4×Q8 | C2×#120 | 1 | 24 | yes | — |
| 298 | C4×Q8 | C2×#120 | 1 | 24 | yes | — |
| 299 | C4×Q8 | C2×#120 | 1 | 24 | yes | — |
| 300 | C4×Q8 | C23×D4 | 1 | 24 | yes | — |
| 301 | C4×D4 | C2×#120 | 1 | 24 | yes | — |
| 302 | C4×D4 | C2×#120 | 1 | 24 | yes | — |
| 303 | C4×D4 | C2×#120 | 1 | 24 | yes | — |
| 304 | C4×D4 | C23×D4 | 1 | 24 | yes | — |
| 305 | #117 | C2×#120 | 1 | 24 | yes | — |
| 306 | #117 | C2×#120 | 1 | 12 | yes | — |
| 307 | #117 | C23×D4 | 1 | 12 | yes | — |
| 308 | C2×C4⋊C4 | C2×#120 | 1 | 12 | yes | — |
| 309 | C2×C4⋊C4 | C2×#120 | 1 | 12 | yes | — |
| 310 | C2×C4⋊C4 | C2×#120 | 1 | 12 | yes | — |
| 311 | C2×C42 | C2×#120 | 1 | 1 | yes | characteristic |
| 312 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 313 | C2×C42 | C2×#120 | 1 | 2 | yes | — |
| 314 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 315 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 316 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 317 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 318 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 319 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 320 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 321 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 322 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 323 | C2×C42 | C2×#120 | 1 | 3 | yes | — |
| 324 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 325 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 326 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 327 | C2×C42 | C2×#120 | 1 | 6 | yes | — |
| 328 | C2×C42 | C23×D4 | 1 | 6 | yes | — |
| 329 | C2×C42 | C23×D4 | 1 | 3 | yes | — |
| 330 | C2×C42 | C23×D4 | 1 | 3 | yes | — |
| 331 | C2×C42 | C23×D4 | 1 | 6 | yes | — |
| 332 | C2×C42 | C23×D4 | 1 | 3 | yes | — |
| 333 | C2×C42 | C23×D4 | 1 | 3 | yes | — |
| 334 | C2×C42 | C23×D4 | 1 | 6 | yes | — |
| 335 | C2×C42 | C23×D4 | 1 | 3 | yes | — |
| 336 | C2×C42 | C26 | 1 | 1 | yes | characteristic |
| 337 | C24 | #2846 | 1 | 1 | yes | characteristic |
| 338 | C24 | #2846 | 1 | 3 | yes | — |
| 339 | C24 | C22×#120 | 1 | 3 | yes | — |
| 340 | C24 | C22×#120 | 1 | 16 | yes | — |
| 341 | C2×Q8 | C22×#120 | 1 | 12 | yes | — |
| 342 | C2×Q8 | C22×#120 | 1 | 24 | yes | — |
| 343 | C2×D4 | #3019 | 1 | 24 | yes | complemented |
| 344 | C2×D4 | C22×#120 | 1 | 24 | yes | — |
| 345 | C2×D4 | C22×#120 | 1 | 12 | yes | — |
| 346 | C22×C4 | #2846 | 1 | 6 | yes | — |
| 347 | C22×C4 | #2846 | 1 | 6 | yes | — |
| 348 | C22×C4 | #2846 | 1 | 6 | yes | — |
| 349 | C22×C4 | #2846 | 1 | 3 | yes | — |
| 350 | C22×C4 | #2846 | 1 | 3 | yes | — |
| 351 | C22×C4 | #2846 | 1 | 6 | yes | — |
| 352 | C22×C4 | #2846 | 1 | 6 | yes | — |
| 353 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 354 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 355 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 356 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 357 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 358 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 359 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 360 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 361 | C22×C4 | C22×#120 | 1 | 3 | yes | — |
| 362 | C22×C4 | C22×#120 | 1 | 6 | yes | — |
| 363 | C22×C4 | C24×D4 | 1 | 3 | yes | — |
| 364 | C4⋊C4 | C22×#120 | 1 | 24 | yes | — |
| 365 | C42 | #2846 | 1 | 3 | yes | — |
| 366 | C42 | #2846 | 1 | 6 | yes | — |
| 367 | C42 | #2846 | 1 | 3 | yes | — |
| 368 | C42 | #2846 | 1 | 6 | yes | — |
| 369 | C42 | #2846 | 1 | 1 | yes | characteristic |
| 370 | C42 | #2846 | 1 | 3 | yes | — |
| 371 | C42 | #2846 | 1 | 2 | yes | — |
| 372 | C42 | C22×#120 | 1 | 6 | yes | — |
| 373 | C42 | C22×#120 | 1 | 6 | yes | — |
| 374 | C42 | C22×#120 | 1 | 6 | yes | — |
| 375 | C42 | C22×#120 | 1 | 6 | yes | — |
| 376 | C42 | C22×#120 | 1 | 3 | yes | — |
| 377 | C42 | C22×#120 | 1 | 6 | yes | — |
| 378 | C42 | C22×#120 | 1 | 3 | yes | — |
| 379 | C42 | C24×D4 | 1 | 3 | yes | — |
| 380 | C42 | C24×D4 | 1 | 1 | yes | characteristic |
| 381 | C23 | C2×#2846 | 1 | 3 | yes | — |
| 382 | C23 | C2×#2846 | 1 | 3 | yes | — |
| 383 | C23 | C23×#120 | 1 | 1 | yes | characteristic |
| 384 | D4 | C2×#3019 | 1 | 24 | yes | — |
| 385 | C2×C4 | C2×#2846 | 1 | 3 | yes | — |
| 386 | C2×C4 | C2×#2846 | 1 | 3 | yes | — |
| 387 | C2×C4 | C2×#2846 | 1 | 6 | yes | — |
| 388 | C2×C4 | C2×#2846 | 1 | 6 | yes | — |
| 389 | C2×C4 | C2×#3019 | 1 | 12 | yes | — |
| 390 | C2×C4 | C23×#120 | 1 | 3 | yes | — |
| 391 | C2×C4 | C23×#120 | 1 | 3 | yes | — |
| 392 | C22 | #6628867 | 1 | 6 | yes | — |
| 393 | C22 | C22×#2846 | 1 | 1 | yes | characteristic |
| 394 | C4 | #6628867 | 1 | 6 | yes | — |
| 395 | C4 | C22×#3019 | 1 | 6 | yes | — |
| 396 | C2 | C2×#6628867 | 1 | 3 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta