Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
225155 conjugacy classes of subgroups; only the 2294 normal subgroups are shown.
This group has 225155 conjugacy classes of subgroups — too many to draw. Only its 2294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72228233 | C2 | 1 | 15 | yes | maximal, complemented |
| 2 | H(5,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72211144 | C2 | 1 | 15 | yes | maximal, complemented |
| 4 | #10586807 | — | 2 | 90 | no | — |
| 5 | #10586796 | — | 2 | 30 | no | — |
| 6 | #10586796 | C22 | 1 | 15 | yes | — |
| 7 | #6499867 | C22 | 1 | 30 | yes | complemented |
| 8 | #5021138 | C22 | 1 | 5 | yes | complemented |
| 9 | #347045 | — | 2 | 90 | no | — |
| 10 | #347042 | — | 2 | 30 | no | — |
| 11 | #188062 | C22 | 1 | 15 | yes | complemented |
| 12 | #187949 | C22 | 1 | 90 | yes | complemented |
| 13 | #63069 | — | 2 | 360 | no | — |
| 14 | #63069 | — | 2 | 360 | no | — |
| 15 | #63069 | — | 2 | 360 | no | — |
| 16 | #63048 | — | 2 | 120 | no | — |
| 17 | #63048 | — | 2 | 60 | no | — |
| 18 | #63048 | — | 2 | 120 | no | — |
| 19 | #63046 | — | 2 | 720 | no | — |
| 20 | #63046 | — | 2 | 360 | no | — |
| 21 | #63046 | — | 2 | 360 | no | — |
| 22 | #63046 | — | 2 | 360 | no | — |
| 23 | #63045 | — | 2 | 360 | no | — |
| 24 | #63045 | — | 2 | 180 | no | — |
| 25 | #63045 | — | 2 | 360 | no | — |
| 26 | #62841 | — | 2 | 360 | no | — |
| 27 | #62841 | — | 2 | 90 | no | — |
| 28 | #62824 | — | 2 | 360 | no | — |
| 29 | #62824 | — | 2 | 180 | no | — |
| 30 | #62824 | — | 2 | 90 | no | — |
| 31 | #62824 | D4 | 1 | 90 | yes | complemented |
| 32 | #62817 | — | 2 | 60 | no | — |
| 33 | #62817 | — | 2 | 30 | no | — |
| 34 | #62817 | — | 2 | 30 | no | — |
| 35 | #62817 | D4 | 1 | 30 | yes | complemented |
| 36 | #62817 | C23 | 1 | 30 | yes | — |
| 37 | #62694 | — | 2 | 30 | no | — |
| 38 | C22×H(3,𝔽4) | — | 2 | 10 | no | — |
| 39 | C22×H(3,𝔽4) | C23 | 1 | 5 | yes | — |
| 40 | C2×#2846 | C23 | 1 | 15 | yes | complemented |
| 41 | #23984 | — | 2 | 180 | no | — |
| 42 | #23900 | — | 2 | 180 | no | — |
| 43 | #21746 | C23 | 1 | 90 | yes | complemented |
| 44 | #15947 | — | 2 | 15 | no | — |
| 45 | #15259 | — | 2 | 45 | no | — |
| 46 | #14657 | C23 | 1 | 15 | yes | complemented |
| 47 | #8544 | — | 2 | 45 | no | — |
| 48 | #8541 | — | 2 | 15 | no | — |
| 49 | #8535 | — | 2 | 180 | no | — |
| 50 | #8534 | — | 2 | 180 | no | — |
| 51 | C27 | C24 | 1 | 1 | yes | characteristic, complemented |
| 52 | #3568 | — | 2 | 720 | no | — |
| 53 | #3568 | — | 2 | 720 | no | — |
| 54 | #3568 | — | 2 | 720 | no | — |
| 55 | #3568 | — | 2 | 720 | no | — |
| 56 | #3568 | — | 2 | 720 | no | — |
| 57 | #3561 | — | 2 | 720 | no | — |
| 58 | #3561 | — | 2 | 720 | no | — |
| 59 | #3561 | — | 2 | 720 | no | — |
| 60 | #3561 | — | 2 | 720 | no | — |
| 61 | #3561 | — | 2 | 720 | no | — |
| 62 | #3561 | — | 2 | 720 | no | — |
| 63 | #3561 | — | 2 | 360 | no | — |
| 64 | #3561 | — | 2 | 360 | no | — |
| 65 | #3561 | — | 2 | 360 | no | — |
| 66 | #3558 | — | 2 | 720 | no | — |
| 67 | #3558 | — | 2 | 720 | no | — |
| 68 | #3558 | — | 2 | 720 | no | — |
| 69 | #3558 | — | 2 | 720 | no | — |
| 70 | #3558 | — | 2 | 720 | no | — |
| 71 | #3558 | — | 2 | 720 | no | — |
| 72 | #3558 | — | 2 | 360 | no | — |
| 73 | #3558 | — | 2 | 360 | no | — |
| 74 | #3558 | — | 2 | 360 | no | — |
| 75 | #3550 | — | 2 | 720 | no | — |
| 76 | #3550 | — | 2 | 360 | no | — |
| 77 | #3550 | — | 2 | 90 | no | — |
| 78 | #3550 | — | 2 | 180 | no | — |
| 79 | #3549 | — | 2 | 90 | no | — |
| 80 | #3549 | — | 2 | 360 | no | — |
| 81 | #3545 | — | 2 | 720 | no | — |
| 82 | #3545 | — | 2 | 720 | no | — |
| 83 | #3545 | — | 2 | 720 | no | — |
| 84 | #3545 | — | 2 | 720 | no | — |
| 85 | #3545 | — | 2 | 360 | no | — |
| 86 | #3545 | — | 2 | 720 | no | — |
| 87 | #3545 | — | 2 | 360 | no | — |
| 88 | #3545 | — | 2 | 720 | no | — |
| 89 | #3545 | — | 2 | 360 | no | — |
| 90 | #3540 | — | 2 | 720 | no | — |
| 91 | #3540 | — | 2 | 720 | no | — |
| 92 | #3540 | — | 2 | 720 | no | — |
| 93 | #3540 | — | 2 | 720 | no | — |
| 94 | #3540 | — | 2 | 360 | no | — |
| 95 | #3540 | — | 2 | 720 | no | — |
| 96 | #3540 | — | 2 | 360 | no | — |
| 97 | #3540 | — | 2 | 720 | no | — |
| 98 | #3540 | — | 2 | 360 | no | — |
| 99 | #3532 | — | 2 | 720 | no | — |
| 100 | #3532 | — | 2 | 360 | no | — |
| 101 | #3532 | — | 2 | 360 | no | — |
| 102 | #3532 | — | 2 | 360 | no | — |
| 103 | #3532 | — | 2 | 720 | no | — |
| 104 | #3532 | — | 2 | 360 | no | — |
| 105 | #3532 | — | 2 | 360 | no | — |
| 106 | #3532 | — | 2 | 360 | no | — |
| 107 | #3531 | — | 2 | 360 | no | — |
| 108 | #3531 | — | 2 | 180 | no | — |
| 109 | #3529 | — | 2 | 360 | no | — |
| 110 | #3529 | — | 2 | 180 | no | — |
| 111 | #3529 | — | 2 | 360 | no | — |
| 112 | C2×H(3,𝔽4) | — | 2 | 240 | no | — |
| 113 | C2×H(3,𝔽4) | — | 2 | 120 | no | — |
| 114 | C2×H(3,𝔽4) | — | 2 | 120 | no | — |
| 115 | C2×H(3,𝔽4) | — | 2 | 120 | no | — |
| 116 | #3518 | — | 2 | 720 | no | — |
| 117 | #3518 | — | 2 | 360 | no | — |
| 118 | #3518 | — | 2 | 360 | no | — |
| 119 | #3518 | — | 2 | 360 | no | — |
| 120 | #3514 | — | 2 | 720 | no | — |
| 121 | #3514 | — | 2 | 720 | no | — |
| 122 | #3514 | — | 2 | 720 | no | — |
| 123 | #3514 | — | 2 | 360 | no | — |
| 124 | #3514 | — | 2 | 360 | no | — |
| 125 | #3514 | — | 2 | 360 | no | — |
| 126 | #3514 | — | 2 | 720 | no | — |
| 127 | #3514 | — | 2 | 720 | no | — |
| 128 | #3514 | — | 2 | 720 | no | — |
| 129 | #3510 | — | 2 | 720 | no | — |
| 130 | #3510 | — | 2 | 360 | no | — |
| 131 | #3510 | — | 2 | 720 | no | — |
| 132 | #3510 | — | 2 | 360 | no | — |
| 133 | #3510 | — | 2 | 360 | no | — |
| 134 | #3510 | — | 2 | 180 | no | — |
| 135 | #3500 | — | 2 | 360 | no | — |
| 136 | #3500 | — | 2 | 360 | no | — |
| 137 | #3500 | — | 2 | 180 | no | — |
| 138 | #3490 | — | 2 | 720 | no | — |
| 139 | #3490 | — | 2 | 360 | no | — |
| 140 | #3490 | — | 2 | 180 | no | — |
| 141 | #3490 | — | 2 | 360 | no | — |
| 142 | #3490 | — | 2 | 360 | no | — |
| 143 | #3490 | — | 2 | 180 | no | — |
| 144 | #3490 | — | 2 | 180 | no | — |
| 145 | #3490 | — | 2 | 90 | no | — |
| 146 | #3490 | — | 2 | 180 | no | — |
| 147 | #3490 | C2×D4 | 1 | 180 | yes | — |
| 148 | #3486 | — | 2 | 360 | no | — |
| 149 | #3486 | — | 2 | 90 | no | — |
| 150 | #3484 | — | 2 | 180 | no | — |
| 151 | #3484 | — | 2 | 360 | no | — |
| 152 | #3484 | — | 2 | 360 | no | — |
| 153 | #3484 | — | 2 | 180 | no | — |
| 154 | #3484 | — | 2 | 180 | no | — |
| 155 | #3484 | C2×D4 | 1 | 180 | yes | — |
| 156 | #3444 | — | 2 | 360 | no | — |
| 157 | #3444 | — | 2 | 90 | no | — |
| 158 | C22×#124 | — | 2 | 90 | no | — |
| 159 | C22×#124 | C2×D4 | 1 | 45 | yes | — |
| 160 | C22×#120 | — | 2 | 30 | no | — |
| 161 | C22×#120 | — | 2 | 30 | no | — |
| 162 | C22×#120 | — | 2 | 45 | no | — |
| 163 | C22×#120 | — | 4 | 5 | no | — |
| 164 | C22×#120 | C2×D4 | 1 | 15 | yes | — |
| 165 | C22×#120 | C24 | 1 | 15 | yes | — |
| 166 | C2×B(4,𝔽2) | — | 4 | 60 | no | — |
| 167 | #2846 | — | 2 | 120 | no | — |
| 168 | C2×#393 | — | 4 | 15 | no | — |
| 169 | C2×#379 | — | 2 | 45 | no | — |
| 170 | C2×#379 | C24 | 1 | 15 | yes | complemented |
| 171 | #2029 | — | 4 | 60 | no | — |
| 172 | #2021 | — | 4 | 180 | no | — |
| 173 | #1898 | — | 2 | 360 | no | — |
| 174 | #1889 | — | 4 | 180 | no | — |
| 175 | #1819 | — | 2 | 90 | no | — |
| 176 | #1781 | — | 2 | 90 | no | — |
| 177 | #1440 | — | 2 | 45 | no | — |
| 178 | #1438 | — | 2 | 45 | no | — |
| 179 | #1438 | — | 4 | 45 | no | — |
| 180 | #1437 | — | 4 | 15 | no | — |
| 181 | C26 | — | 2 | 2 | no | — |
| 182 | C26 | — | 2 | 15 | no | — |
| 183 | C26 | — | 16 | 6 | no | — |
| 184 | C26 | #120 | 1 | 5 | yes | complemented |
| 185 | C26 | C25 | 1 | 1 | yes | characteristic |
| 186 | C2×2−1+4 | — | 2 | 90 | no | — |
| 187 | C2×H(5,𝔽2) | — | 2 | 60 | no | — |
| 188 | C2×H(5,𝔽2) | — | 2 | 60 | no | — |
| 189 | C2×H(5,𝔽2) | #120 | 1 | 60 | yes | complemented |
| 190 | C23×Q8 | — | 2 | 30 | no | — |
| 191 | C23×Q8 | #120 | 1 | 15 | yes | complemented |
| 192 | C23×D4 | — | 2 | 90 | no | — |
| 193 | C23×D4 | — | 4 | 15 | no | — |
| 194 | C23×D4 | C22×D4 | 1 | 45 | yes | — |
| 195 | #564 | — | 2 | 24 | no | — |
| 196 | #564 | — | 2 | 12 | no | — |
| 197 | #563 | — | 2 | 360 | no | — |
| 198 | #563 | — | 2 | 720 | no | — |
| 199 | #563 | — | 2 | 360 | no | — |
| 200 | #563 | — | 2 | 180 | no | — |
| 201 | #563 | — | 2 | 720 | no | — |
| 202 | #563 | — | 2 | 360 | no | — |
| 203 | #562 | — | 2 | 360 | no | — |
| 204 | #562 | — | 2 | 180 | no | — |
| 205 | #562 | — | 2 | 720 | no | — |
| 206 | #562 | — | 2 | 720 | no | — |
| 207 | #562 | — | 2 | 720 | no | — |
| 208 | H(3,𝔽4) | — | 2 | 40 | no | — |
| 209 | H(3,𝔽4) | — | 2 | 20 | no | — |
| 210 | H(3,𝔽4) | — | 2 | 40 | no | — |
| 211 | H(3,𝔽4) | — | 2 | 240 | no | — |
| 212 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 213 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 214 | H(3,𝔽4) | — | 2 | 240 | no | — |
| 215 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 216 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 217 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 218 | H(3,𝔽4) | — | 2 | 120 | no | — |
| 219 | H(3,𝔽4) | — | 2 | 360 | no | — |
| 220 | H(3,𝔽4) | — | 2 | 720 | no | — |
| 221 | H(3,𝔽4) | — | 2 | 360 | no | — |
| 222 | H(3,𝔽4) | — | 2 | 360 | no | — |
| 223 | #560 | — | 2 | 360 | no | — |
| 224 | #560 | — | 2 | 720 | no | — |
| 225 | #560 | — | 2 | 360 | no | — |
| 226 | #560 | — | 2 | 360 | no | — |
| 227 | #559 | — | 2 | 360 | no | — |
| 228 | #559 | — | 2 | 180 | no | — |
| 229 | #559 | — | 2 | 720 | no | — |
| 230 | #559 | — | 2 | 720 | no | — |
| 231 | #559 | — | 2 | 720 | no | — |
| 232 | Q82 | — | 2 | 120 | no | — |
| 233 | Q82 | — | 2 | 60 | no | — |
| 234 | Q82 | — | 2 | 120 | no | — |
| 235 | #556 | — | 2 | 720 | no | — |
| 236 | #556 | — | 2 | 720 | no | — |
| 237 | #556 | — | 2 | 720 | no | — |
| 238 | #556 | — | 2 | 360 | no | — |
| 239 | #556 | — | 2 | 360 | no | — |
| 240 | #556 | — | 2 | 360 | no | — |
| 241 | #556 | — | 2 | 720 | no | — |
| 242 | #556 | — | 2 | 720 | no | — |
| 243 | #556 | — | 2 | 720 | no | — |
| 244 | #555 | — | 2 | 180 | no | — |
| 245 | #555 | — | 2 | 360 | no | — |
| 246 | #555 | — | 2 | 720 | no | — |
| 247 | #555 | — | 2 | 720 | no | — |
| 248 | #555 | — | 2 | 720 | no | — |
| 249 | #551 | — | 2 | 720 | no | — |
| 250 | #551 | — | 2 | 360 | no | — |
| 251 | #551 | — | 2 | 720 | no | — |
| 252 | #551 | — | 2 | 720 | no | — |
| 253 | #551 | — | 2 | 720 | no | — |
| 254 | #551 | — | 2 | 360 | no | — |
| 255 | #551 | — | 2 | 720 | no | — |
| 256 | #551 | — | 2 | 720 | no | — |
| 257 | #551 | — | 2 | 720 | no | — |
| 258 | #551 | — | 2 | 720 | no | — |
| 259 | #551 | — | 2 | 360 | no | — |
| 260 | #551 | — | 2 | 360 | no | — |
| 261 | #551 | — | 2 | 720 | no | — |
| 262 | #551 | — | 2 | 720 | no | — |
| 263 | #551 | — | 2 | 360 | no | — |
| 264 | #551 | — | 2 | 720 | no | — |
| 265 | #551 | — | 2 | 360 | no | — |
| 266 | #551 | — | 2 | 720 | no | — |
| 267 | D4×Q8 | — | 2 | 360 | no | — |
| 268 | D4×Q8 | — | 2 | 360 | no | — |
| 269 | D4×Q8 | — | 2 | 360 | no | — |
| 270 | D4×Q8 | — | 2 | 720 | no | — |
| 271 | #548 | — | 2 | 720 | no | — |
| 272 | #548 | — | 2 | 720 | no | — |
| 273 | #548 | — | 2 | 720 | no | — |
| 274 | #548 | — | 2 | 720 | no | — |
| 275 | #548 | — | 2 | 720 | no | — |
| 276 | #546 | — | 2 | 720 | no | — |
| 277 | #546 | — | 2 | 720 | no | — |
| 278 | #546 | — | 2 | 720 | no | — |
| 279 | #546 | — | 2 | 720 | no | — |
| 280 | #546 | — | 2 | 720 | no | — |
| 281 | #546 | — | 2 | 720 | no | — |
| 282 | #546 | — | 2 | 720 | no | — |
| 283 | #546 | — | 2 | 720 | no | — |
| 284 | #546 | — | 2 | 720 | no | — |
| 285 | #546 | — | 2 | 720 | no | — |
| 286 | #546 | — | 2 | 720 | no | — |
| 287 | #546 | — | 2 | 720 | no | — |
| 288 | #546 | — | 2 | 720 | no | — |
| 289 | #546 | — | 2 | 720 | no | — |
| 290 | #546 | — | 2 | 720 | no | — |
| 291 | D42 | — | 2 | 360 | no | — |
| 292 | D42 | — | 2 | 180 | no | — |
| 293 | D42 | — | 2 | 720 | no | — |
| 294 | D42 | — | 2 | 360 | no | — |
| 295 | D42 | — | 2 | 360 | no | — |
| 296 | D42 | — | 2 | 720 | no | — |
| 297 | #543 | — | 2 | 180 | no | — |
| 298 | #543 | — | 2 | 120 | no | — |
| 299 | #543 | — | 2 | 240 | no | — |
| 300 | #543 | — | 2 | 180 | no | — |
| 301 | #543 | — | 2 | 90 | no | — |
| 302 | #543 | — | 2 | 60 | no | — |
| 303 | #543 | #120 | 1 | 60 | yes | complemented |
| 304 | #542 | — | 2 | 720 | no | — |
| 305 | #542 | — | 2 | 720 | no | — |
| 306 | #542 | — | 2 | 720 | no | — |
| 307 | #542 | — | 2 | 720 | no | — |
| 308 | #542 | — | 2 | 720 | no | — |
| 309 | #542 | — | 2 | 720 | no | — |
| 310 | #542 | — | 2 | 720 | no | — |
| 311 | #542 | — | 2 | 720 | no | — |
| 312 | #542 | — | 2 | 720 | no | — |
| 313 | #542 | — | 2 | 720 | no | — |
| 314 | #542 | — | 2 | 720 | no | — |
| 315 | #542 | — | 2 | 720 | no | — |
| 316 | #542 | — | 2 | 720 | no | — |
| 317 | #542 | — | 2 | 720 | no | — |
| 318 | #542 | — | 2 | 720 | no | — |
| 319 | #538 | — | 2 | 720 | no | — |
| 320 | #538 | — | 2 | 720 | no | — |
| 321 | #538 | — | 2 | 720 | no | — |
| 322 | #538 | — | 2 | 720 | no | — |
| 323 | #538 | — | 2 | 720 | no | — |
| 324 | #538 | — | 2 | 720 | no | — |
| 325 | #538 | — | 2 | 720 | no | — |
| 326 | #538 | — | 2 | 720 | no | — |
| 327 | #538 | — | 2 | 720 | no | — |
| 328 | #538 | — | 2 | 720 | no | — |
| 329 | #538 | — | 2 | 720 | no | — |
| 330 | #538 | — | 2 | 720 | no | — |
| 331 | #538 | — | 2 | 360 | no | — |
| 332 | #538 | — | 2 | 360 | no | — |
| 333 | #538 | — | 2 | 360 | no | — |
| 334 | #538 | — | 2 | 360 | no | — |
| 335 | #538 | — | 2 | 360 | no | — |
| 336 | #538 | — | 2 | 360 | no | — |
| 337 | #536 | — | 2 | 720 | no | — |
| 338 | #536 | — | 2 | 360 | no | — |
| 339 | #536 | — | 2 | 720 | no | — |
| 340 | #536 | — | 2 | 360 | no | — |
| 341 | #536 | — | 2 | 360 | no | — |
| 342 | #536 | — | 2 | 180 | no | — |
| 343 | #535 | — | 2 | 720 | no | — |
| 344 | #535 | — | 2 | 720 | no | — |
| 345 | #535 | — | 2 | 360 | no | — |
| 346 | #535 | — | 2 | 360 | no | — |
| 347 | #535 | — | 2 | 360 | no | — |
| 348 | #535 | — | 2 | 180 | no | — |
| 349 | #534 | — | 2 | 180 | no | — |
| 350 | #534 | — | 2 | 360 | no | — |
| 351 | #534 | — | 2 | 720 | no | — |
| 352 | #534 | — | 2 | 360 | no | — |
| 353 | #534 | — | 2 | 360 | no | — |
| 354 | #534 | — | 2 | 90 | no | — |
| 355 | #534 | — | 2 | 180 | no | — |
| 356 | #534 | — | 2 | 180 | no | — |
| 357 | #534 | — | 2 | 180 | no | — |
| 358 | #534 | #120 | 1 | 180 | yes | complemented |
| 359 | #533 | — | 2 | 720 | no | — |
| 360 | #533 | — | 2 | 360 | no | — |
| 361 | #533 | — | 2 | 180 | no | — |
| 362 | #533 | — | 2 | 90 | no | — |
| 363 | #532 | — | 2 | 720 | no | — |
| 364 | #532 | — | 2 | 360 | no | — |
| 365 | #532 | — | 2 | 90 | no | — |
| 366 | #532 | — | 2 | 180 | no | — |
| 367 | #529 | — | 2 | 720 | no | — |
| 368 | #529 | — | 2 | 720 | no | — |
| 369 | #529 | — | 2 | 720 | no | — |
| 370 | #529 | — | 2 | 720 | no | — |
| 371 | #529 | — | 2 | 720 | no | — |
| 372 | #529 | — | 2 | 720 | no | — |
| 373 | #529 | — | 2 | 360 | no | — |
| 374 | #529 | — | 2 | 360 | no | — |
| 375 | #529 | — | 2 | 360 | no | — |
| 376 | C2×#124 | — | 2 | 360 | no | — |
| 377 | C2×#124 | — | 2 | 720 | no | — |
| 378 | C2×#124 | — | 2 | 720 | no | — |
| 379 | C2×#124 | — | 2 | 360 | no | — |
| 380 | C2×#124 | — | 2 | 180 | no | — |
| 381 | C2×#124 | — | 2 | 360 | no | — |
| 382 | #525 | — | 2 | 360 | no | — |
| 383 | #525 | — | 2 | 720 | no | — |
| 384 | #525 | — | 2 | 720 | no | — |
| 385 | #525 | — | 2 | 360 | no | — |
| 386 | #525 | — | 2 | 360 | no | — |
| 387 | #525 | — | 2 | 180 | no | — |
| 388 | C2×#120 | — | 2 | 120 | no | — |
| 389 | C2×#120 | — | 2 | 240 | no | — |
| 390 | C2×#120 | — | 2 | 240 | no | — |
| 391 | C2×#120 | — | 2 | 120 | no | — |
| 392 | C2×#120 | — | 2 | 360 | no | — |
| 393 | C2×#120 | — | 2 | 180 | no | — |
| 394 | C2×#120 | — | 2 | 180 | no | — |
| 395 | C2×#120 | — | 2 | 120 | no | — |
| 396 | C2×#120 | — | 2 | 180 | no | — |
| 397 | C2×#120 | — | 4 | 180 | no | — |
| 398 | C2×#120 | — | 16 | 90 | no | — |
| 399 | C2×#120 | — | 16 | 30 | no | — |
| 400 | C2×#120 | C22×D4 | 1 | 120 | yes | — |
| 401 | #519 | — | 2 | 360 | no | — |
| 402 | #519 | — | 2 | 90 | no | — |
| 403 | #518 | — | 2 | 360 | no | — |
| 404 | #518 | — | 2 | 180 | no | — |
| 405 | #518 | — | 2 | 360 | no | — |
| 406 | #518 | — | 2 | 180 | no | — |
| 407 | #518 | — | 2 | 180 | no | — |
| 408 | #518 | #120 | 1 | 180 | yes | complemented |
| 409 | C4×#41 | — | 2 | 360 | no | — |
| 410 | C4×#41 | — | 2 | 360 | no | — |
| 411 | C4×#41 | — | 2 | 180 | no | — |
| 412 | C22×C22⋊C4 | — | 2 | 90 | no | — |
| 413 | C22×C22⋊C4 | — | 2 | 90 | no | — |
| 414 | C22×C22⋊C4 | — | 2 | 45 | no | — |
| 415 | C22×C22⋊C4 | — | 4 | 45 | no | — |
| 416 | C22×C22⋊C4 | — | 4 | 15 | no | — |
| 417 | C22×C22⋊C4 | #120 | 1 | 45 | yes | complemented |
| 418 | C22×C22⋊C4 | C22×D4 | 1 | 45 | yes | — |
| 419 | C22×C42 | — | 2 | 30 | no | — |
| 420 | C22×C42 | #120 | 1 | 15 | yes | complemented |
| 421 | B(4,𝔽2) | — | 16 | 120 | no | — |
| 422 | C2×#99 | — | 4 | 180 | no | — |
| 423 | #393 | — | 16 | 30 | no | — |
| 424 | #379 | — | 2 | 60 | no | — |
| 425 | #379 | — | 4 | 180 | no | — |
| 426 | C2×#95 | — | 4 | 45 | no | — |
| 427 | #342 | — | 4 | 180 | no | — |
| 428 | C25 | — | 2 | 30 | no | — |
| 429 | C25 | — | 2 | 30 | no | — |
| 430 | C25 | — | 4 | 5 | no | — |
| 431 | C25 | — | 4 | 30 | no | — |
| 432 | C25 | — | 8 | 90 | no | — |
| 433 | C25 | — | 16 | 3 | no | — |
| 434 | C25 | — | 16 | 45 | no | — |
| 435 | C25 | — | 16 | 15 | no | — |
| 436 | C25 | — | 16 | 40 | no | — |
| 437 | C25 | — | 16 | 24 | no | — |
| 438 | C25 | — | 32 | 6 | no | — |
| 439 | C25 | C2×#120 | 1 | 15 | yes | — |
| 440 | C25 | C23×D4 | 1 | 15 | yes | — |
| 441 | 2−1+4 | — | 32 | 90 | no | — |
| 442 | H(5,𝔽2) | — | 16 | 60 | no | — |
| 443 | H(5,𝔽2) | — | 32 | 60 | no | — |
| 444 | H(5,𝔽2) | — | 32 | 60 | no | — |
| 445 | C2×#41 | — | 2 | 360 | no | — |
| 446 | C2×#41 | — | 2 | 360 | no | — |
| 447 | C2×#41 | — | 2 | 180 | no | — |
| 448 | C22×Q8 | — | 2 | 360 | no | — |
| 449 | C22×Q8 | — | 2 | 90 | no | — |
| 450 | C22×Q8 | — | 16 | 15 | no | — |
| 451 | C22×Q8 | — | 32 | 30 | no | — |
| 452 | C22×D4 | — | 2 | 180 | no | — |
| 453 | C22×D4 | — | 2 | 360 | no | — |
| 454 | C22×D4 | — | 2 | 360 | no | — |
| 455 | C22×D4 | — | 2 | 180 | no | — |
| 456 | C22×D4 | — | 2 | 180 | no | — |
| 457 | C22×D4 | — | 8 | 30 | no | — |
| 458 | C22×D4 | — | 8 | 90 | no | — |
| 459 | C22×D4 | — | 16 | 45 | no | — |
| 460 | C22×D4 | — | 16 | 45 | no | — |
| 461 | C22×D4 | — | 32 | 90 | no | — |
| 462 | C22×D4 | C2×#120 | 1 | 180 | yes | — |
| 463 | C23×C4 | — | 2 | 90 | no | — |
| 464 | C23×C4 | — | 4 | 15 | no | — |
| 465 | C23×C4 | C2×#120 | 1 | 45 | yes | — |
| 466 | C4⋊Q8 | — | 2 | 360 | no | — |
| 467 | C4⋊Q8 | — | 2 | 720 | no | — |
| 468 | C4⋊Q8 | — | 2 | 90 | no | — |
| 469 | C4⋊Q8 | — | 2 | 180 | no | — |
| 470 | #127 | — | 2 | 90 | no | — |
| 471 | #127 | — | 2 | 360 | no | — |
| 472 | #126 | — | 2 | 720 | no | — |
| 473 | #126 | — | 2 | 720 | no | — |
| 474 | #126 | — | 2 | 720 | no | — |
| 475 | #126 | — | 2 | 720 | no | — |
| 476 | #126 | — | 2 | 720 | no | — |
| 477 | #125 | — | 2 | 360 | no | — |
| 478 | #125 | — | 2 | 180 | no | — |
| 479 | #124 | — | 2 | 360 | no | — |
| 480 | #124 | — | 2 | 180 | no | — |
| 481 | #124 | — | 2 | 360 | no | — |
| 482 | #124 | — | 2 | 720 | no | — |
| 483 | #124 | — | 2 | 720 | no | — |
| 484 | #124 | — | 2 | 360 | no | — |
| 485 | #124 | — | 2 | 720 | no | — |
| 486 | #124 | — | 2 | 720 | no | — |
| 487 | #124 | — | 2 | 720 | no | — |
| 488 | #124 | — | 2 | 360 | no | — |
| 489 | #124 | — | 2 | 720 | no | — |
| 490 | #124 | — | 2 | 360 | no | — |
| 491 | #123 | — | 2 | 720 | no | — |
| 492 | #123 | — | 2 | 720 | no | — |
| 493 | #123 | — | 2 | 360 | no | — |
| 494 | #123 | — | 2 | 720 | no | — |
| 495 | #123 | — | 2 | 720 | no | — |
| 496 | #123 | — | 2 | 720 | no | — |
| 497 | #123 | — | 2 | 720 | no | — |
| 498 | #123 | — | 2 | 360 | no | — |
| 499 | #123 | — | 2 | 360 | no | — |
| 500 | C22⋊Q8 | — | 2 | 720 | no | — |
| 501 | C22⋊Q8 | — | 2 | 720 | no | — |
| 502 | C22⋊Q8 | — | 2 | 720 | no | — |
| 503 | C22⋊Q8 | — | 2 | 720 | no | — |
| 504 | C22⋊Q8 | — | 2 | 720 | no | — |
| 505 | C22⋊Q8 | — | 2 | 720 | no | — |
| 506 | C22⋊Q8 | — | 2 | 360 | no | — |
| 507 | C22⋊Q8 | — | 2 | 360 | no | — |
| 508 | C22⋊Q8 | — | 2 | 360 | no | — |
| 509 | #121 | — | 2 | 720 | no | — |
| 510 | #121 | — | 2 | 720 | no | — |
| 511 | #121 | — | 2 | 720 | no | — |
| 512 | #121 | — | 2 | 360 | no | — |
| 513 | #121 | — | 2 | 360 | no | — |
| 514 | #121 | — | 2 | 720 | no | — |
| 515 | #121 | — | 2 | 720 | no | — |
| 516 | #121 | — | 2 | 720 | no | — |
| 517 | #121 | — | 2 | 360 | no | — |
| 518 | #120 | — | 2 | 240 | no | — |
| 519 | #120 | — | 2 | 120 | no | — |
| 520 | #120 | — | 2 | 120 | no | — |
| 521 | #120 | — | 2 | 360 | no | — |
| 522 | #120 | — | 2 | 360 | no | — |
| 523 | #120 | — | 2 | 720 | no | — |
| 524 | #120 | — | 2 | 360 | no | — |
| 525 | #120 | — | 2 | 360 | no | — |
| 526 | #120 | — | 2 | 720 | no | — |
| 527 | #120 | — | 2 | 360 | no | — |
| 528 | #120 | — | 2 | 120 | no | — |
| 529 | #120 | — | 2 | 360 | no | — |
| 530 | #120 | — | 8 | 360 | no | — |
| 531 | #120 | — | 16 | 180 | no | — |
| 532 | #120 | — | 16 | 80 | no | — |
| 533 | C4×Q8 | — | 2 | 720 | no | — |
| 534 | C4×Q8 | — | 2 | 360 | no | — |
| 535 | C4×Q8 | — | 2 | 360 | no | — |
| 536 | C4×Q8 | — | 2 | 360 | no | — |
| 537 | C4×D4 | — | 2 | 720 | no | — |
| 538 | C4×D4 | — | 2 | 720 | no | — |
| 539 | C4×D4 | — | 2 | 720 | no | — |
| 540 | C4×D4 | — | 2 | 360 | no | — |
| 541 | C4×D4 | — | 2 | 360 | no | — |
| 542 | C4×D4 | — | 2 | 360 | no | — |
| 543 | C4×D4 | — | 2 | 720 | no | — |
| 544 | C4×D4 | — | 2 | 720 | no | — |
| 545 | C4×D4 | — | 2 | 720 | no | — |
| 546 | #117 | — | 2 | 720 | no | — |
| 547 | #117 | — | 2 | 360 | no | — |
| 548 | #117 | — | 2 | 360 | no | — |
| 549 | #117 | — | 2 | 720 | no | — |
| 550 | #117 | — | 2 | 360 | no | — |
| 551 | #117 | — | 2 | 180 | no | — |
| 552 | C2×C22⋊C4 | — | 2 | 180 | no | — |
| 553 | C2×C22⋊C4 | — | 2 | 360 | no | — |
| 554 | C2×C22⋊C4 | — | 2 | 360 | no | — |
| 555 | C2×C22⋊C4 | — | 2 | 720 | no | — |
| 556 | C2×C22⋊C4 | — | 2 | 360 | no | — |
| 557 | C2×C22⋊C4 | — | 2 | 180 | no | — |
| 558 | C2×C22⋊C4 | — | 2 | 90 | no | — |
| 559 | C2×C22⋊C4 | — | 2 | 180 | no | — |
| 560 | C2×C22⋊C4 | — | 2 | 180 | no | — |
| 561 | C2×C22⋊C4 | — | 4 | 90 | no | — |
| 562 | C2×C22⋊C4 | — | 8 | 90 | no | — |
| 563 | C2×C22⋊C4 | — | 8 | 90 | no | — |
| 564 | C2×C22⋊C4 | — | 16 | 45 | no | — |
| 565 | C2×C22⋊C4 | — | 16 | 45 | no | — |
| 566 | C2×C22⋊C4 | — | 16 | 45 | no | — |
| 567 | C2×C22⋊C4 | C2×#120 | 1 | 180 | yes | — |
| 568 | C2×C42 | — | 2 | 360 | no | — |
| 569 | C2×C42 | — | 2 | 90 | no | — |
| 570 | #99 | — | 16 | 180 | no | — |
| 571 | #95 | — | 16 | 45 | no | — |
| 572 | C24 | — | 2 | 30 | no | — |
| 573 | C24 | — | 2 | 60 | no | — |
| 574 | C24 | — | 2 | 10 | no | — |
| 575 | C24 | — | 2 | 30 | no | — |
| 576 | C24 | — | 4 | 30 | no | — |
| 577 | C24 | — | 4 | 60 | no | — |
| 578 | C24 | — | 8 | 45 | no | — |
| 579 | C24 | — | 8 | 45 | no | — |
| 580 | C24 | — | 8 | 45 | no | — |
| 581 | C24 | — | 8 | 90 | no | — |
| 582 | C24 | — | 8 | 15 | no | — |
| 583 | C24 | — | 16 | 90 | no | — |
| 584 | C24 | — | 16 | 120 | no | — |
| 585 | C24 | — | 16 | 60 | no | — |
| 586 | C24 | — | 16 | 90 | no | — |
| 587 | C24 | — | 16 | 180 | no | — |
| 588 | C24 | — | 16 | 180 | no | — |
| 589 | C24 | — | 16 | 10 | no | — |
| 590 | C24 | — | 16 | 6 | no | — |
| 591 | C24 | — | 16 | 60 | no | — |
| 592 | C24 | — | 16 | 20 | no | — |
| 593 | C24 | — | 32 | 30 | no | — |
| 594 | C24 | — | 32 | 32 | no | — |
| 595 | C24 | #2846 | 1 | 30 | yes | — |
| 596 | C24 | C22×#120 | 1 | 30 | yes | — |
| 597 | C24 | C22×#120 | 1 | 5 | yes | — |
| 598 | #41 | — | 16 | 180 | no | — |
| 599 | #41 | — | 16 | 360 | no | — |
| 600 | #41 | — | 16 | 360 | no | — |
| 601 | C2×Q8 | — | 2 | 60 | no | — |
| 602 | C2×Q8 | — | 2 | 120 | no | — |
| 603 | C2×Q8 | — | 2 | 120 | no | — |
| 604 | C2×Q8 | — | 16 | 90 | no | — |
| 605 | C2×Q8 | — | 16 | 360 | no | — |
| 606 | C2×D4 | — | 2 | 180 | no | — |
| 607 | C2×D4 | — | 2 | 360 | no | — |
| 608 | C2×D4 | — | 2 | 360 | no | — |
| 609 | C2×D4 | — | 8 | 180 | no | — |
| 610 | C2×D4 | — | 16 | 180 | no | — |
| 611 | C2×D4 | — | 16 | 180 | no | — |
| 612 | C2×D4 | — | 16 | 360 | no | — |
| 613 | C2×D4 | — | 16 | 180 | no | — |
| 614 | C2×D4 | — | 16 | 360 | no | — |
| 615 | C2×D4 | — | 16 | 180 | no | — |
| 616 | C2×D4 | — | 16 | 60 | no | — |
| 617 | C2×D4 | — | 32 | 90 | no | — |
| 618 | C22×C4 | — | 2 | 180 | no | — |
| 619 | C22×C4 | — | 2 | 360 | no | — |
| 620 | C22×C4 | — | 2 | 90 | no | — |
| 621 | C22×C4 | — | 8 | 45 | no | — |
| 622 | C22×C4 | — | 8 | 45 | no | — |
| 623 | C22×C4 | — | 8 | 45 | no | — |
| 624 | C22×C4 | — | 8 | 15 | no | — |
| 625 | C22×C4 | — | 16 | 90 | no | — |
| 626 | C22×C4 | #2846 | 1 | 90 | yes | — |
| 627 | C4⋊C4 | — | 2 | 360 | no | — |
| 628 | C4⋊C4 | — | 2 | 360 | no | — |
| 629 | C4⋊C4 | — | 2 | 360 | no | — |
| 630 | C22⋊C4 | — | 2 | 720 | no | — |
| 631 | C22⋊C4 | — | 2 | 360 | no | — |
| 632 | C22⋊C4 | — | 2 | 360 | no | — |
| 633 | C22⋊C4 | — | 2 | 360 | no | — |
| 634 | C22⋊C4 | — | 8 | 180 | no | — |
| 635 | C22⋊C4 | — | 16 | 180 | no | — |
| 636 | C22⋊C4 | — | 16 | 60 | no | — |
| 637 | C42 | — | 2 | 30 | no | — |
| 638 | C42 | — | 2 | 360 | no | — |
| 639 | C42 | — | 2 | 90 | no | — |
| 640 | C23 | — | 2 | 30 | no | — |
| 641 | C23 | — | 4 | 15 | no | — |
| 642 | C23 | — | 4 | 30 | no | — |
| 643 | C23 | — | 4 | 60 | no | — |
| 644 | C23 | — | 4 | 90 | no | — |
| 645 | C23 | — | 4 | 20 | no | — |
| 646 | C23 | — | 8 | 90 | no | — |
| 647 | C23 | — | 8 | 90 | no | — |
| 648 | C23 | — | 8 | 30 | no | — |
| 649 | C23 | — | 8 | 60 | no | — |
| 650 | C23 | — | 8 | 90 | no | — |
| 651 | C23 | — | 8 | 120 | no | — |
| 652 | C23 | — | 8 | 90 | no | — |
| 653 | C23 | — | 16 | 45 | no | — |
| 654 | C23 | — | 16 | 15 | no | — |
| 655 | C23 | — | 16 | 15 | no | — |
| 656 | C23 | — | 16 | 45 | no | — |
| 657 | C23 | — | 16 | 15 | no | — |
| 658 | C23 | — | 16 | 15 | no | — |
| 659 | C23 | — | 16 | 45 | no | — |
| 660 | C23 | — | 16 | 120 | no | — |
| 661 | C23 | — | 16 | 360 | no | — |
| 662 | C23 | — | 16 | 1 | no | — |
| 663 | C23 | — | 32 | 120 | no | — |
| 664 | C23 | — | 32 | 120 | no | — |
| 665 | C23 | C2×#2846 | 1 | 15 | yes | — |
| 666 | Q8 | — | 8 | 120 | no | — |
| 667 | Q8 | — | 8 | 60 | no | — |
| 668 | Q8 | — | 8 | 120 | no | — |
| 669 | D4 | — | 8 | 360 | no | — |
| 670 | D4 | — | 8 | 180 | no | — |
| 671 | D4 | — | 8 | 360 | no | — |
| 672 | D4 | — | 32 | 120 | no | — |
| 673 | C2×C4 | — | 2 | 90 | no | — |
| 674 | C2×C4 | — | 4 | 90 | no | — |
| 675 | C2×C4 | — | 8 | 90 | no | — |
| 676 | C2×C4 | — | 8 | 180 | no | — |
| 677 | C2×C4 | — | 8 | 360 | no | — |
| 678 | C2×C4 | — | 16 | 45 | no | — |
| 679 | C2×C4 | — | 16 | 15 | no | — |
| 680 | C2×C4 | — | 16 | 45 | no | — |
| 681 | C22 | — | 2 | 45 | no | — |
| 682 | C22 | — | 4 | 5 | no | — |
| 683 | C22 | — | 4 | 15 | no | — |
| 684 | C22 | — | 4 | 90 | no | — |
| 685 | C22 | — | 8 | 60 | no | — |
| 686 | C22 | — | 8 | 40 | no | — |
| 687 | C22 | — | 16 | 30 | no | — |
| 688 | C22 | — | 16 | 30 | no | — |
| 689 | C22 | — | 16 | 90 | no | — |
| 690 | C22 | — | 16 | 6 | no | — |
| 691 | C22 | — | 32 | 30 | no | — |
| 692 | C22 | — | 32 | 30 | no | — |
| 693 | C22 | — | 32 | 60 | no | — |
| 694 | C22 | #6342371 | 1 | 1 | yes | characteristic |
| 695 | C4 | — | 4 | 90 | no | — |
| 696 | C4 | — | 32 | 15 | no | — |
| 697 | C2 | — | 4 | 15 | no | — |
| 698 | C2 | — | 8 | 30 | no | — |
| 699 | C2 | — | 16 | 4 | no | — |
| 700 | C2 | #72210025 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #6342371 |
| commutator, Frattini, cosocle | C26 | C25 |
| LCS | G ▷ C26 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C26 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72228233 | C2 | semidirect |
| 2. H(5,𝔽4) | C2 | semidirect |
| 3. #72211144 | C2 | semidirect |
| 7. #6499867 | C22 | semidirect |
| 8. #5021138 | C22 | semidirect |
| 11. #188062 | C22 | semidirect |
| 12. #187949 | C22 | semidirect |
| 31. #62824 | D4 | semidirect |
| 35. #62817 | D4 | semidirect |
| 40. C2×#2846 | C23 | semidirect |
| 43. #21746 | C23 | semidirect |
| 46. #14657 | C23 | semidirect |
| 51. C27 | C24 | semidirect |
| 170. C2×#379 | C24 | semidirect |
| 184. C26 | #120 | semidirect |
| 189. C2×H(5,𝔽2) | #120 | semidirect |
| 191. C23×Q8 | #120 | semidirect |
| 303. #543 | #120 | semidirect |
| 358. #534 | #120 | semidirect |
| 408. #518 | #120 | semidirect |
| 417. C22×C22⋊C4 | #120 | semidirect |
| 420. C22×C42 | #120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72228233 | 2 |
| H(5,𝔽4) | 2 |
| #72211144 | 2 |