Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2078 conjugacy classes of subgroups.
The subgroup lattice has 544 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226855 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72226854 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72226852 | C22 | 1 | 2 | yes | — |
| 4 | #72226849 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #72226847 | — | 2 | 4 | no | — |
| 6 | #72226845 | — | 2 | 4 | no | — |
| 7 | #72226844 | — | 2 | 4 | no | — |
| 8 | #72225562 | — | 2 | 4 | no | — |
| 9 | #72225406 | C22 | 1 | 2 | yes | — |
| 10 | #72225366 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #72225363 | C22 | 1 | 4 | yes | — |
| 12 | #72225362 | C22 | 1 | 2 | yes | — |
| 13 | #72225344 | C22 | 1 | 4 | yes | — |
| 14 | #72225313 | C22 | 1 | 2 | yes | — |
| 15 | #72225199 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | C2×#93866 | C22 | 1 | 2 | yes | — |
| 17 | #72216534 | C22 | 1 | 4 | yes | — |
| 18 | #72216416 | C22 | 1 | 2 | yes | — |
| 19 | #72216368 | C2 | 1 | 1 | yes | maximal, characteristic |
| 20 | #72216364 | C4 | 1 | 2 | yes | complemented |
| 21 | #72216358 | C4 | 1 | 4 | yes | complemented |
| 22 | #72216275 | C22 | 1 | 4 | yes | — |
| 23 | #72216270 | C22 | 1 | 4 | yes | — |
| 24 | #72216263 | C4 | 1 | 2 | yes | complemented |
| 25 | #72216236 | C22 | 1 | 1 | yes | characteristic |
| 26 | C16×M64 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#123403 | C22 | 1 | 1 | yes | characteristic |
| 28 | #513051 | — | 2 | 4 | no | — |
| 29 | #513051 | — | 2 | 4 | no | — |
| 30 | #512781 | — | 4 | 4 | no | — |
| 31 | #498572 | — | 2 | 4 | no | — |
| 32 | #498569 | — | 2 | 4 | no | — |
| 33 | #491485 | — | 4 | 1 | no | — |
| 34 | #491465 | C23 | 1 | 2 | yes | — |
| 35 | C2×#12515 | — | 4 | 1 | no | — |
| 36 | C2×#12515 | C23 | 1 | 2 | yes | — |
| 37 | #152996 | — | 2 | 4 | no | — |
| 38 | #152994 | — | 2 | 4 | no | — |
| 39 | #152981 | — | 4 | 4 | no | — |
| 40 | #152545 | — | 4 | 4 | no | — |
| 41 | #152544 | — | 4 | 4 | no | — |
| 42 | #151998 | D4 | 1 | 2 | yes | — |
| 43 | #151989 | — | 2 | 4 | no | — |
| 44 | #151728 | — | 2 | 8 | no | — |
| 45 | #151726 | C2×C4 | 1 | 8 | yes | complemented |
| 46 | #151724 | C2×C4 | 1 | 8 | yes | complemented |
| 47 | #151040 | D4 | 1 | 2 | yes | — |
| 48 | C2×#7459 | C23 | 1 | 4 | yes | — |
| 49 | C2×#7448 | — | 2 | 4 | no | — |
| 50 | #150947 | — | 2 | 4 | no | — |
| 51 | C8×M64 | C23 | 1 | 2 | yes | — |
| 52 | #141263 | — | 2 | 4 | no | — |
| 53 | #141262 | — | 2 | 4 | no | — |
| 54 | #137551 | — | 4 | 2 | no | — |
| 55 | #137550 | — | 4 | 2 | no | — |
| 56 | #129142 | C23 | 1 | 4 | yes | — |
| 57 | #123406 | C2×C4 | 1 | 2 | yes | complemented |
| 58 | #123405 | — | 4 | 1 | no | — |
| 59 | #123404 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 60 | #123403 | — | 4 | 1 | no | — |
| 61 | #123403 | C2×C4 | 1 | 2 | yes | — |
| 62 | #123403 | C2×C4 | 1 | 2 | yes | — |
| 63 | #123403 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 65 | #94053 | D4 | 1 | 4 | yes | — |
| 66 | #94041 | — | 2 | 4 | no | — |
| 67 | #93885 | — | 2 | 4 | no | — |
| 68 | #93868 | — | 4 | 2 | no | — |
| 69 | #93866 | — | 4 | 2 | no | — |
| 70 | #93664 | C2×C4 | 1 | 2 | yes | complemented |
| 71 | C16×C32 | C2×C4 | 1 | 2 | yes | complemented |
| 72 | C2×#2263 | — | 4 | 4 | no | — |
| 73 | C2×#2263 | — | 4 | 4 | no | — |
| 74 | C2×#2263 | — | 8 | 4 | no | — |
| 75 | #33733 | — | 8 | 2 | no | — |
| 76 | #33713 | — | 2 | 4 | no | — |
| 77 | C2×#2246 | — | 2 | 4 | no | — |
| 78 | C2×#2246 | — | 8 | 2 | no | — |
| 79 | #33465 | — | 4 | 4 | no | — |
| 80 | #33456 | — | 4 | 4 | no | — |
| 81 | #23201 | — | 4 | 2 | no | — |
| 82 | #23196 | — | 4 | 2 | no | — |
| 83 | #19603 | — | 2 | 2 | no | — |
| 84 | C2×#1712 | — | 2 | 2 | no | — |
| 85 | #13729 | — | 4 | 8 | no | — |
| 86 | #13729 | — | 8 | 4 | no | — |
| 87 | #13727 | — | 2 | 8 | no | — |
| 88 | #13727 | — | 2 | 8 | no | — |
| 89 | #13725 | — | 2 | 8 | no | — |
| 90 | #13725 | — | 2 | 8 | no | — |
| 91 | #13658 | — | 8 | 16 | no | — |
| 92 | #13638 | D8 | 1 | 4 | yes | — |
| 93 | C2×#1422 | — | 2 | 4 | no | — |
| 94 | C2×#1419 | — | 4 | 4 | no | — |
| 95 | #13622 | — | 4 | 4 | no | — |
| 96 | #13620 | — | 4 | 4 | no | — |
| 97 | #13617 | — | 4 | 4 | no | — |
| 98 | #13551 | — | 4 | 4 | no | — |
| 99 | C4×M64 | C2×D4 | 1 | 2 | yes | — |
| 100 | C4×M64 | C2×D4 | 1 | 2 | yes | — |
| 101 | #13261 | — | 4 | 4 | no | — |
| 102 | #13259 | — | 4 | 4 | no | — |
| 103 | #13245 | — | 4 | 4 | no | — |
| 104 | #13243 | — | 4 | 4 | no | — |
| 105 | #13017 | — | 8 | 4 | no | — |
| 106 | #13016 | — | 8 | 4 | no | — |
| 107 | #12670 | C2×D4 | 1 | 4 | yes | — |
| 108 | #12664 | — | 2 | 4 | no | — |
| 109 | #12521 | — | 4 | 1 | no | — |
| 110 | #12518 | — | 2 | 4 | no | — |
| 111 | #12517 | — | 2 | 2 | no | — |
| 112 | #12516 | C22×C4 | 1 | 2 | yes | — |
| 113 | #12515 | — | 2 | 4 | no | — |
| 114 | #12515 | — | 2 | 2 | no | — |
| 115 | #12515 | — | 4 | 2 | no | — |
| 116 | #12515 | — | 4 | 2 | no | — |
| 117 | #12515 | — | 4 | 1 | no | — |
| 118 | #12515 | — | 8 | 2 | no | — |
| 119 | #12515 | C22×C4 | 1 | 4 | yes | — |
| 120 | #12515 | C22×C4 | 1 | 2 | yes | — |
| 121 | #12509 | — | 4 | 2 | no | — |
| 122 | #12503 | — | 8 | 2 | no | — |
| 123 | C2×#1373 | C2×D4 | 1 | 4 | yes | — |
| 124 | #11922 | — | 4 | 2 | no | — |
| 125 | C2×#1357 | — | 4 | 2 | no | — |
| 126 | C2×C8×C16 | — | 2 | 1 | no | — |
| 127 | C2×C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 128 | #7476 | D8 | 1 | 2 | yes | — |
| 129 | #7475 | D8 | 1 | 2 | yes | — |
| 130 | #7469 | — | 4 | 4 | no | — |
| 131 | #7464 | — | 2 | 4 | no | — |
| 132 | #7459 | — | 2 | 4 | no | — |
| 133 | #7459 | — | 2 | 4 | no | — |
| 134 | #7448 | — | 8 | 4 | no | — |
| 135 | #7447 | — | 8 | 4 | no | — |
| 136 | #7329 | #41 | 1 | 4 | yes | — |
| 137 | C8×C32 | C22×C4 | 1 | 4 | yes | — |
| 138 | #7179 | — | 2 | 4 | no | — |
| 139 | C162 | — | 2 | 1 | no | — |
| 140 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 141 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×#508 | — | 4 | 4 | no | — |
| 143 | C2×#508 | — | 4 | 4 | no | — |
| 144 | C22×D16 | — | 4 | 4 | no | — |
| 145 | C22×D16 | — | 4 | 4 | no | — |
| 146 | C22×D16 | — | 16 | 4 | no | — |
| 147 | #3169 | — | 8 | 2 | no | — |
| 148 | #3147 | — | 4 | 2 | no | — |
| 149 | C2×#493 | — | 4 | 2 | no | — |
| 150 | C2×#493 | — | 8 | 2 | no | — |
| 151 | #2957 | — | 8 | 4 | no | — |
| 152 | #2948 | — | 8 | 4 | no | — |
| 153 | #2263 | — | 8 | 8 | no | — |
| 154 | #2263 | — | 8 | 8 | no | — |
| 155 | #2263 | — | 16 | 4 | no | — |
| 156 | #2263 | — | 16 | 4 | no | — |
| 157 | #2263 | — | 16 | 8 | no | — |
| 158 | #2263 | — | 16 | 8 | no | — |
| 159 | C2×SD64 | — | 4 | 8 | no | — |
| 160 | C2×SD64 | — | 4 | 8 | no | — |
| 161 | C2×SD64 | — | 8 | 8 | no | — |
| 162 | C2×D32 | — | 4 | 8 | no | — |
| 163 | C2×D32 | — | 4 | 8 | no | — |
| 164 | C2×D32 | — | 8 | 8 | no | — |
| 165 | C2×M64 | — | 2 | 2 | no | — |
| 166 | C2×M64 | — | 4 | 4 | no | — |
| 167 | C2×M64 | C2×D8 | 1 | 2 | yes | — |
| 168 | C2×M64 | C2×D8 | 1 | 2 | yes | — |
| 169 | #2252 | — | 8 | 2 | no | — |
| 170 | #2249 | — | 4 | 4 | no | — |
| 171 | #2249 | — | 4 | 4 | no | — |
| 172 | #2248 | — | 4 | 4 | no | — |
| 173 | #2247 | — | 2 | 4 | no | — |
| 174 | #2246 | — | 2 | 4 | no | — |
| 175 | #2246 | — | 2 | 8 | no | — |
| 176 | #2246 | — | 4 | 4 | no | — |
| 177 | #2246 | — | 4 | 4 | no | — |
| 178 | #2246 | — | 4 | 4 | no | — |
| 179 | #2246 | — | 8 | 4 | no | — |
| 180 | #2246 | — | 8 | 4 | no | — |
| 181 | #2246 | — | 8 | 2 | no | — |
| 182 | #2246 | — | 16 | 4 | no | — |
| 183 | #2240 | — | 8 | 4 | no | — |
| 184 | #2215 | — | 16 | 4 | no | — |
| 185 | #2179 | — | 8 | 8 | no | — |
| 186 | #2178 | — | 16 | 4 | no | — |
| 187 | #2177 | — | 8 | 8 | no | — |
| 188 | C4×D16 | — | 16 | 4 | no | — |
| 189 | C4×D16 | — | 16 | 4 | no | — |
| 190 | C2×#368 | C2×D8 | 1 | 4 | yes | — |
| 191 | #2158 | C2×D8 | 1 | 4 | yes | — |
| 192 | C2×#364 | — | 2 | 4 | no | — |
| 193 | C2×#361 | — | 8 | 4 | no | — |
| 194 | #2145 | — | 8 | 4 | no | — |
| 195 | #2143 | — | 8 | 4 | no | — |
| 196 | #2140 | — | 8 | 4 | no | — |
| 197 | #2108 | — | 4 | 4 | no | — |
| 198 | C2×C4×C16 | — | 2 | 2 | no | — |
| 199 | C2×C4×C16 | C22×D4 | 1 | 2 | yes | — |
| 200 | #1978 | — | 8 | 4 | no | — |
| 201 | #1976 | — | 8 | 4 | no | — |
| 202 | #1887 | — | 16 | 2 | no | — |
| 203 | #1884 | — | 16 | 2 | no | — |
| 204 | #1772 | — | 2 | 4 | no | — |
| 205 | #1713 | — | 2 | 2 | no | — |
| 206 | #1712 | — | 2 | 4 | no | — |
| 207 | #1712 | — | 2 | 2 | no | — |
| 208 | #1712 | — | 4 | 2 | no | — |
| 209 | #1712 | — | 8 | 2 | no | — |
| 210 | #1709 | — | 4 | 2 | no | — |
| 211 | #1706 | — | 8 | 2 | no | — |
| 212 | C2×C82 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 213 | #1426 | — | 2 | 8 | no | — |
| 214 | #1422 | — | 4 | 4 | no | — |
| 215 | #1422 | — | 4 | 4 | no | — |
| 216 | #1419 | — | 8 | 8 | no | — |
| 217 | #1418 | — | 8 | 8 | no | — |
| 218 | #1417 | — | 16 | 4 | no | — |
| 219 | #1415 | — | 16 | 4 | no | — |
| 220 | #1398 | — | 8 | 8 | no | — |
| 221 | #1397 | — | 2 | 2 | no | — |
| 222 | #1397 | #135 | 1 | 4 | yes | — |
| 223 | C4×C32 | C4×D4 | 1 | 4 | yes | — |
| 224 | C4×C32 | C4×D4 | 1 | 4 | yes | — |
| 225 | #1382 | — | 2 | 4 | no | — |
| 226 | #1379 | — | 4 | 4 | no | — |
| 227 | #1373 | — | 2 | 4 | no | — |
| 228 | #1373 | — | 2 | 4 | no | — |
| 229 | #1359 | — | 16 | 2 | no | — |
| 230 | #1357 | — | 16 | 2 | no | — |
| 231 | C8×C16 | — | 2 | 2 | no | — |
| 232 | C8×C16 | — | 2 | 1 | no | — |
| 233 | C8×C16 | — | 2 | 1 | no | — |
| 234 | C8×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 235 | C8×C16 | C2×#41 | 1 | 2 | yes | — |
| 236 | C8×C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 237 | C2×#135 | — | 8 | 4 | no | — |
| 238 | C22×D8 | — | 8 | 4 | no | — |
| 239 | C22×D8 | — | 16 | 4 | no | — |
| 240 | #568 | — | 16 | 2 | no | — |
| 241 | #532 | — | 8 | 2 | no | — |
| 242 | C2×#127 | — | 8 | 2 | no | — |
| 243 | #518 | — | 16 | 2 | no | — |
| 244 | #508 | — | 8 | 4 | no | — |
| 245 | #508 | — | 8 | 4 | no | — |
| 246 | #508 | — | 8 | 4 | no | — |
| 247 | #508 | — | 8 | 4 | no | — |
| 248 | #508 | — | 16 | 4 | no | — |
| 249 | #508 | — | 16 | 4 | no | — |
| 250 | C2×Q32 | — | 4 | 4 | no | — |
| 251 | C2×Q32 | — | 4 | 4 | no | — |
| 252 | C2×SD32 | — | 8 | 4 | no | — |
| 253 | C2×SD32 | — | 8 | 4 | no | — |
| 254 | C2×D16 | — | 4 | 8 | no | — |
| 255 | C2×D16 | — | 4 | 4 | no | — |
| 256 | C2×D16 | — | 4 | 8 | no | — |
| 257 | C2×D16 | — | 4 | 4 | no | — |
| 258 | C2×D16 | — | 8 | 4 | no | — |
| 259 | C2×D16 | — | 8 | 4 | no | — |
| 260 | C2×D16 | — | 8 | 4 | no | — |
| 261 | C2×D16 | — | 8 | 4 | no | — |
| 262 | C2×D16 | — | 8 | 4 | no | — |
| 263 | C2×D16 | — | 8 | 4 | no | — |
| 264 | C2×D16 | — | 16 | 4 | no | — |
| 265 | C2×D16 | — | 16 | 4 | no | — |
| 266 | C2×D16 | — | 16 | 8 | no | — |
| 267 | C2×D16 | — | 16 | 8 | no | — |
| 268 | C2×D16 | — | 16 | 4 | no | — |
| 269 | C2×D16 | — | 32 | 16 | no | — |
| 270 | C2×M32 | — | 4 | 4 | no | — |
| 271 | C22×C16 | — | 2 | 4 | no | — |
| 272 | C22×C16 | C22×D8 | 1 | 2 | yes | — |
| 273 | C22×C16 | #576 | 1 | 2 | yes | — |
| 274 | #500 | — | 8 | 2 | no | — |
| 275 | #495 | — | 8 | 4 | no | — |
| 276 | #494 | — | 4 | 2 | no | — |
| 277 | #493 | — | 4 | 4 | no | — |
| 278 | #493 | — | 4 | 2 | no | — |
| 279 | #493 | — | 8 | 4 | no | — |
| 280 | #493 | — | 8 | 2 | no | — |
| 281 | #493 | — | 8 | 4 | no | — |
| 282 | #493 | — | 8 | 2 | no | — |
| 283 | #493 | — | 16 | 2 | no | — |
| 284 | #493 | — | 16 | 4 | no | — |
| 285 | #492 | — | 8 | 2 | no | — |
| 286 | #486 | — | 16 | 2 | no | — |
| 287 | #466 | — | 16 | 4 | no | — |
| 288 | #444 | — | 32 | 4 | no | — |
| 289 | #443 | — | 16 | 8 | no | — |
| 290 | #442 | — | 32 | 4 | no | — |
| 291 | C4×D8 | — | 16 | 4 | no | — |
| 292 | C4×D8 | — | 16 | 8 | no | — |
| 293 | C2×#108 | — | 2 | 4 | no | — |
| 294 | #427 | — | 2 | 4 | no | — |
| 295 | #421 | — | 16 | 4 | no | — |
| 296 | #418 | — | 16 | 4 | no | — |
| 297 | C2×#100 | — | 16 | 2 | no | — |
| 298 | #410 | — | 16 | 2 | no | — |
| 299 | #405 | — | 4 | 4 | no | — |
| 300 | C2×C4×C8 | — | 2 | 1 | no | — |
| 301 | C2×C4×C8 | D42 | 1 | 1 | yes | characteristic |
| 302 | SD64 | — | 8 | 16 | no | — |
| 303 | SD64 | — | 16 | 8 | no | — |
| 304 | SD64 | — | 16 | 16 | no | — |
| 305 | D32 | — | 8 | 16 | no | — |
| 306 | D32 | — | 16 | 8 | no | — |
| 307 | D32 | — | 16 | 16 | no | — |
| 308 | M64 | — | 2 | 8 | no | — |
| 309 | M64 | — | 2 | 4 | no | — |
| 310 | M64 | — | 8 | 4 | no | — |
| 311 | M64 | — | 8 | 4 | no | — |
| 312 | M64 | #509 | 1 | 8 | yes | — |
| 313 | C2×C32 | — | 2 | 4 | no | — |
| 314 | C2×C32 | — | 8 | 4 | no | — |
| 315 | C2×C32 | C4×D8 | 1 | 4 | yes | — |
| 316 | C2×C32 | C4×D8 | 1 | 4 | yes | — |
| 317 | #368 | — | 2 | 4 | no | — |
| 318 | #368 | — | 2 | 4 | no | — |
| 319 | #367 | — | 2 | 4 | no | — |
| 320 | #366 | — | 2 | 4 | no | — |
| 321 | #366 | — | 16 | 4 | no | — |
| 322 | #364 | — | 4 | 4 | no | — |
| 323 | #364 | — | 4 | 4 | no | — |
| 324 | #361 | — | 32 | 4 | no | — |
| 325 | #360 | — | 32 | 4 | no | — |
| 326 | #359 | — | 16 | 8 | no | — |
| 327 | #357 | — | 16 | 8 | no | — |
| 328 | #357 | — | 16 | 8 | no | — |
| 329 | #346 | — | 8 | 4 | no | — |
| 330 | C4×C16 | — | 2 | 2 | no | — |
| 331 | C4×C16 | — | 2 | 2 | no | — |
| 332 | C4×C16 | — | 2 | 4 | no | — |
| 333 | C4×C16 | — | 8 | 4 | no | — |
| 334 | C4×C16 | C2×C4×D4 | 1 | 2 | yes | — |
| 335 | C4×C16 | #550 | 1 | 2 | yes | — |
| 336 | C4×C16 | C2×#135 | 1 | 2 | yes | — |
| 337 | C4×C16 | #576 | 1 | 2 | yes | — |
| 338 | #339 | — | 4 | 4 | no | — |
| 339 | C82 | — | 2 | 1 | no | — |
| 340 | C82 | #518 | 1 | 1 | yes | characteristic |
| 341 | C82 | #559 | 1 | 1 | yes | characteristic |
| 342 | C2×#41 | — | 16 | 2 | no | — |
| 343 | C22×D4 | — | 16 | 2 | no | — |
| 344 | C22×D4 | — | 32 | 2 | no | — |
| 345 | #135 | — | 16 | 4 | no | — |
| 346 | #135 | — | 16 | 4 | no | — |
| 347 | #135 | — | 16 | 4 | no | — |
| 348 | #135 | — | 16 | 4 | no | — |
| 349 | C2×Q16 | — | 8 | 4 | no | — |
| 350 | C2×SD16 | — | 16 | 4 | no | — |
| 351 | C2×D8 | — | 8 | 8 | no | — |
| 352 | C2×D8 | — | 8 | 4 | no | — |
| 353 | C2×D8 | — | 16 | 8 | no | — |
| 354 | C2×D8 | — | 16 | 4 | no | — |
| 355 | C2×D8 | — | 16 | 4 | no | — |
| 356 | C2×D8 | — | 16 | 4 | no | — |
| 357 | C2×D8 | — | 16 | 4 | no | — |
| 358 | C2×D8 | — | 16 | 4 | no | — |
| 359 | C2×D8 | — | 16 | 4 | no | — |
| 360 | C2×D8 | — | 32 | 4 | no | — |
| 361 | C2×D8 | — | 32 | 16 | no | — |
| 362 | #131 | — | 32 | 8 | no | — |
| 363 | C2×M16 | — | 4 | 4 | no | — |
| 364 | C2×M16 | — | 64 | 2 | no | — |
| 365 | C22×C8 | — | 2 | 2 | no | — |
| 366 | C22×C8 | D4×D8 | 1 | 2 | yes | — |
| 367 | C4⋊Q8 | — | 8 | 2 | no | — |
| 368 | #127 | — | 8 | 4 | no | — |
| 369 | #127 | — | 8 | 2 | no | — |
| 370 | #127 | — | 16 | 2 | no | — |
| 371 | #127 | — | 32 | 2 | no | — |
| 372 | #124 | — | 16 | 2 | no | — |
| 373 | #121 | — | 32 | 2 | no | — |
| 374 | C4×D4 | — | 32 | 2 | no | — |
| 375 | C4×D4 | — | 32 | 8 | no | — |
| 376 | #117 | — | 4 | 4 | no | — |
| 377 | C2×C22⋊C4 | — | 64 | 2 | no | — |
| 378 | C2×C42 | #3292 | 1 | 1 | yes | characteristic |
| 379 | Q32 | — | 8 | 4 | no | — |
| 380 | Q32 | — | 8 | 4 | no | — |
| 381 | Q32 | — | 16 | 4 | no | — |
| 382 | SD32 | — | 16 | 4 | no | — |
| 383 | SD32 | — | 16 | 4 | no | — |
| 384 | SD32 | — | 32 | 4 | no | — |
| 385 | D16 | — | 8 | 4 | no | — |
| 386 | D16 | — | 8 | 8 | no | — |
| 387 | D16 | — | 8 | 4 | no | — |
| 388 | D16 | — | 8 | 8 | no | — |
| 389 | D16 | — | 16 | 4 | no | — |
| 390 | D16 | — | 16 | 8 | no | — |
| 391 | D16 | — | 16 | 4 | no | — |
| 392 | D16 | — | 16 | 4 | no | — |
| 393 | D16 | — | 32 | 4 | no | — |
| 394 | D16 | — | 32 | 8 | no | — |
| 395 | D16 | — | 32 | 16 | no | — |
| 396 | D16 | — | 32 | 16 | no | — |
| 397 | M32 | — | 8 | 4 | no | — |
| 398 | M32 | — | 8 | 4 | no | — |
| 399 | C2×C16 | — | 2 | 4 | no | — |
| 400 | C2×C16 | — | 2 | 4 | no | — |
| 401 | C2×C16 | — | 2 | 4 | no | — |
| 402 | C2×C16 | — | 4 | 8 | no | — |
| 403 | C2×C16 | — | 8 | 4 | no | — |
| 404 | C2×C16 | C2×C4×D8 | 1 | 2 | yes | — |
| 405 | C2×C16 | #2948 | 1 | 2 | yes | — |
| 406 | C2×C16 | #3391 | 1 | 2 | yes | — |
| 407 | C2×C16 | #3396 | 1 | 2 | yes | — |
| 408 | C2×C16 | C2×#509 | 1 | 4 | yes | — |
| 409 | C2×C16 | #3415 | 1 | 4 | yes | — |
| 410 | #108 | — | 4 | 4 | no | — |
| 411 | #108 | — | 4 | 4 | no | — |
| 412 | #107 | — | 4 | 4 | no | — |
| 413 | #107 | — | 16 | 4 | no | — |
| 414 | #106 | — | 4 | 4 | no | — |
| 415 | #104 | — | 32 | 8 | no | — |
| 416 | #102 | — | 32 | 8 | no | — |
| 417 | #102 | — | 32 | 4 | no | — |
| 418 | #100 | — | 64 | 2 | no | — |
| 419 | #99 | — | 64 | 2 | no | — |
| 420 | #97 | — | 8 | 4 | no | — |
| 421 | C4×C8 | — | 2 | 2 | no | — |
| 422 | C4×C8 | — | 2 | 1 | no | — |
| 423 | C4×C8 | — | 2 | 1 | no | — |
| 424 | C4×C8 | — | 8 | 4 | no | — |
| 425 | C4×C8 | #2366 | 1 | 1 | yes | characteristic |
| 426 | C4×C8 | #3287 | 1 | 2 | yes | — |
| 427 | C4×C8 | #3292 | 1 | 1 | yes | characteristic |
| 428 | C32 | — | 2 | 8 | no | — |
| 429 | C32 | — | 2 | 4 | no | — |
| 430 | C32 | — | 16 | 4 | no | — |
| 431 | C32 | #2177 | 1 | 8 | yes | — |
| 432 | C24 | — | 32 | 2 | no | — |
| 433 | #41 | — | 32 | 4 | no | — |
| 434 | #41 | — | 32 | 4 | no | — |
| 435 | C2×Q8 | — | 16 | 2 | no | — |
| 436 | C2×D4 | — | 16 | 2 | no | — |
| 437 | C2×D4 | — | 16 | 4 | no | — |
| 438 | C2×D4 | — | 32 | 2 | no | — |
| 439 | C2×D4 | — | 32 | 4 | no | — |
| 440 | C2×D4 | — | 32 | 2 | no | — |
| 441 | C2×D4 | — | 32 | 4 | no | — |
| 442 | C2×D4 | — | 32 | 4 | no | — |
| 443 | C2×D4 | — | 32 | 2 | no | — |
| 444 | C2×D4 | — | 64 | 2 | no | — |
| 445 | C2×D4 | — | 64 | 8 | no | — |
| 446 | C22×C4 | — | 2 | 1 | no | — |
| 447 | C22×C4 | — | 32 | 2 | no | — |
| 448 | C22×C4 | — | 64 | 4 | no | — |
| 449 | C22×C4 | D82 | 1 | 1 | yes | characteristic |
| 450 | Q16 | — | 16 | 4 | no | — |
| 451 | Q16 | — | 16 | 4 | no | — |
| 452 | SD16 | — | 32 | 4 | no | — |
| 453 | SD16 | — | 32 | 4 | no | — |
| 454 | D8 | — | 16 | 8 | no | — |
| 455 | D8 | — | 16 | 4 | no | — |
| 456 | D8 | — | 16 | 8 | no | — |
| 457 | D8 | — | 16 | 4 | no | — |
| 458 | D8 | — | 32 | 16 | no | — |
| 459 | D8 | — | 32 | 8 | no | — |
| 460 | D8 | — | 32 | 4 | no | — |
| 461 | D8 | — | 32 | 4 | no | — |
| 462 | D8 | — | 64 | 8 | no | — |
| 463 | M16 | — | 8 | 4 | no | — |
| 464 | M16 | — | 8 | 4 | no | — |
| 465 | M16 | — | 64 | 4 | no | — |
| 466 | C2×C8 | — | 2 | 2 | no | — |
| 467 | C2×C8 | — | 2 | 2 | no | — |
| 468 | C2×C8 | — | 4 | 4 | no | — |
| 469 | C2×C8 | — | 8 | 4 | no | — |
| 470 | C2×C8 | — | 64 | 4 | no | — |
| 471 | C2×C8 | #19975 | 1 | 2 | yes | — |
| 472 | C2×C8 | #23185 | 1 | 2 | yes | — |
| 473 | C2×C8 | #33840 | 1 | 4 | yes | — |
| 474 | C2×C8 | #33858 | 1 | 4 | yes | — |
| 475 | C4⋊C4 | — | 8 | 4 | no | — |
| 476 | C4⋊C4 | — | 32 | 2 | no | — |
| 477 | C22⋊C4 | — | 8 | 4 | no | — |
| 478 | C22⋊C4 | — | 64 | 2 | no | — |
| 479 | C22⋊C4 | — | 64 | 4 | no | — |
| 480 | C42 | — | 2 | 1 | no | — |
| 481 | C42 | — | 8 | 4 | no | — |
| 482 | C42 | #20021 | 1 | 1 | yes | characteristic |
| 483 | C42 | #23201 | 1 | 1 | yes | characteristic |
| 484 | C16 | — | 2 | 8 | no | — |
| 485 | C16 | — | 2 | 2 | no | — |
| 486 | C16 | — | 2 | 2 | no | — |
| 487 | C16 | — | 4 | 4 | no | — |
| 488 | C16 | — | 16 | 4 | no | — |
| 489 | C16 | C2×#2177 | 1 | 2 | yes | — |
| 490 | C16 | #33456 | 1 | 2 | yes | — |
| 491 | C16 | #33966 | 1 | 4 | yes | — |
| 492 | C23 | — | 32 | 2 | no | — |
| 493 | C23 | — | 32 | 4 | no | — |
| 494 | C23 | — | 64 | 2 | no | — |
| 495 | C23 | — | 64 | 2 | no | — |
| 496 | C23 | — | 128 | 4 | no | — |
| 497 | C23 | #492532 | 1 | 1 | yes | characteristic |
| 498 | Q8 | — | 32 | 4 | no | — |
| 499 | D4 | — | 32 | 8 | no | — |
| 500 | D4 | — | 32 | 4 | no | — |
| 501 | D4 | — | 64 | 8 | no | — |
| 502 | D4 | — | 64 | 4 | no | — |
| 503 | D4 | — | 64 | 4 | no | — |
| 504 | D4 | — | 64 | 4 | no | — |
| 505 | D4 | — | 128 | 4 | no | — |
| 506 | C2×C4 | — | 256 | 4 | no | — |
| 507 | C2×C4 | — | 2 | 1 | no | — |
| 508 | C2×C4 | — | 2 | 1 | no | — |
| 509 | C2×C4 | — | 4 | 2 | no | — |
| 510 | C2×C4 | — | 16 | 4 | no | — |
| 511 | C2×C4 | — | 32 | 2 | no | — |
| 512 | C2×C4 | — | 64 | 2 | no | — |
| 513 | C2×C4 | — | 64 | 2 | no | — |
| 514 | C2×C4 | #231561 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | #492514 | 1 | 4 | yes | — |
| 516 | C2×C4 | #492532 | 1 | 1 | yes | characteristic |
| 517 | C8 | — | 2 | 4 | no | — |
| 518 | C8 | — | 4 | 2 | no | — |
| 519 | C8 | — | 16 | 4 | no | — |
| 520 | C8 | #492817 | 1 | 4 | yes | — |
| 521 | C8 | #498562 | 1 | 2 | yes | — |
| 522 | C8 | #498572 | 1 | 2 | yes | — |
| 523 | C22 | — | 256 | 2 | no | — |
| 524 | C22 | — | 4 | 1 | no | — |
| 525 | C22 | — | 64 | 2 | no | — |
| 526 | C22 | — | 64 | 4 | no | — |
| 527 | C22 | — | 128 | 4 | no | — |
| 528 | C22 | — | 128 | 2 | no | — |
| 529 | C22 | — | 128 | 4 | no | — |
| 530 | C22 | #72216416 | 1 | 1 | yes | characteristic |
| 531 | C22 | #72226856 | 1 | 2 | yes | — |
| 532 | C4 | — | 2 | 2 | no | — |
| 533 | C4 | — | 4 | 1 | no | — |
| 534 | C4 | — | 32 | 4 | no | — |
| 535 | C4 | — | 64 | 2 | no | — |
| 536 | C4 | #72226848 | 1 | 2 | yes | — |
| 537 | C4 | #72226856 | 1 | 2 | yes | — |
| 538 | C2 | — | 2 | 1 | no | — |
| 539 | C2 | — | 2 | 2 | no | — |
| 540 | C2 | — | 128 | 4 | no | — |
| 541 | C2 | — | 128 | 2 | no | — |
| 542 | C2 | #72226857 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72226857 |
| commutator | C8×C16 | C23×C4 |
| Frattini, cosocle | C2×C8×C16 | C24 |
| prime radical | #72216368 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226855 | C2 | semidirect |
| 2. #72226854 | C2 | semidirect |
| 4. #72226849 | C2 | semidirect |
| 10. #72225366 | C2 | semidirect |
| 15. #72225199 | C2 | semidirect |
| 20. #72216364 | C4 | semidirect |
| 21. #72216358 | C4 | semidirect |
| 24. #72216263 | C4 | semidirect |
| 45. #151726 | C2×C4 | semidirect |
| 46. #151724 | C2×C4 | semidirect |
| 57. #123406 | C2×C4 | semidirect |
| 59. #123404 | C2×C4 | semidirect |
| 63. #123403 | C2×C4 | semidirect |
| 70. #93664 | C2×C4 | semidirect |
| 71. C16×C32 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226855 | 2 |
| #72226854 | 2 |
| #72226849 | 2 |
| #72225366 | 2 |
| #72225199 | 2 |
| #72216368 | 2 |