Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 76 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 | #22626868 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22626098 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22625459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22625332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22624795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22624781 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22620945 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #17989638 | — | 2 | 1 | no | — |
| 9 | #17989619 | — | 2 | 1 | no | — |
| 10 | #17989618 | — | 2 | 1 | no | — |
| 11 | #17989614 | — | 2 | 1 | no | — |
| 12 | #17989611 | — | 2 | 1 | no | — |
| 13 | #17989610 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17989610 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17989593 | — | 2 | 1 | no | — |
| 16 | #17989588 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14556653 | — | 2 | 1 | no | — |
| 18 | C2×#14556653 | — | 2 | 1 | no | — |
| 19 | C4×C4⋊#64408 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17989445 | — | 2 | 1 | no | — |
| 21 | #17989445 | — | 2 | 1 | no | — |
| 22 | #17989441 | — | 2 | 1 | no | — |
| 23 | #17989438 | — | 2 | 1 | no | — |
| 24 | #127×D73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #17989116 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17988977 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #17988952 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #17988951 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #17988785 | — | 2 | 1 | no | — |
| 30 | #17988780 | — | 2 | 1 | no | — |
| 31 | #17988736 | — | 2 | 1 | no | — |
| 32 | #17988719 | — | 2 | 1 | no | — |
| 33 | #17988642 | C22 | 1 | 1 | yes | characteristic |
| 34 | #496×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#11924037 | — | 2 | 1 | no | — |
| 36 | C2×#11924036 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#11924036 | D4 | 1 | 1 | yes | characteristic |
| 38 | C22×#10596833 | — | 2 | 1 | no | — |
| 39 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 40 | C2×C4×#64408 | — | 2 | 1 | no | — |
| 41 | #14556658 | — | 2 | 1 | no | — |
| 42 | #14556658 | — | 2 | 1 | no | — |
| 43 | #14556658 | — | 2 | 1 | no | — |
| 44 | #14556658 | D4 | 1 | 1 | yes | characteristic |
| 45 | #14556658 | D4 | 1 | 1 | yes | characteristic |
| 46 | C4⋊#10596833 | — | 2 | 1 | no | — |
| 47 | C4⋊#10596833 | — | 2 | 1 | no | — |
| 48 | #14556653 | — | 4 | 2 | no | — |
| 49 | #14556653 | — | 4 | 2 | no | — |
| 50 | #14556648 | — | 2 | 1 | no | — |
| 51 | #14556648 | — | 2 | 1 | no | — |
| 52 | C22⋊#10596833 | — | 2 | 1 | no | — |
| 53 | C22⋊#10596833 | — | 2 | 1 | no | — |
| 54 | #14556646 | — | 2 | 1 | no | — |
| 55 | #14556646 | — | 2 | 1 | no | — |
| 56 | #14556646 | — | 2 | 1 | no | — |
| 57 | C4×#10596833 | — | 2 | 1 | no | — |
| 58 | (C2×#64408)⋊C4 | — | 2 | 1 | no | — |
| 59 | C2×D4×D73 | — | 2 | 1 | no | — |
| 60 | C2×D4×D73 | — | 2 | 1 | no | — |
| 61 | C2×D4×D73 | — | 2 | 1 | no | — |
| 62 | C2×#11924015 | — | 2 | 1 | no | — |
| 63 | C2×#11924013 | — | 2 | 1 | no | — |
| 64 | #14556588 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | #14556587 | — | 2 | 1 | no | — |
| 66 | #14556587 | — | 2 | 1 | no | — |
| 67 | #14556587 | — | 2 | 1 | no | — |
| 68 | #14556584 | — | 2 | 1 | no | — |
| 69 | #14556583 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #14556573 | — | 2 | 1 | no | — |
| 71 | #14556567 | D4 | 1 | 1 | yes | characteristic |
| 72 | #14556562 | D4 | 1 | 1 | yes | characteristic |
| 73 | Q8×Dic73 | D4 | 1 | 1 | yes | characteristic |
| 74 | D4×Dic73 | D4 | 1 | 1 | yes | characteristic |
| 75 | #14556551 | — | 2 | 1 | no | — |
| 76 | #14556547 | — | 2 | 1 | no | — |
| 77 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 78 | #14556520 | — | 2 | 1 | no | — |
| 79 | #14556513 | — | 2 | 1 | no | — |
| 80 | #14556513 | — | 2 | 1 | no | — |
| 81 | #14556512 | — | 2 | 1 | no | — |
| 82 | #14556512 | — | 2 | 1 | no | — |
| 83 | #14556503 | — | 2 | 1 | no | — |
| 84 | #14556502 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C2×SD16×C73 | — | 2 | 1 | no | — |
| 86 | C2×D8×C73 | — | 2 | 1 | no | — |
| 87 | #127×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | #124×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | #97×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | C22×#64408 | — | 4 | 1 | no | — |
| 91 | #11924037 | — | 8 | 1 | no | — |
| 92 | #11924036 | — | 4 | 1 | no | — |
| 93 | #11924036 | — | 4 | 1 | no | — |
| 94 | C2×#10596833 | — | 2 | 1 | no | — |
| 95 | C2×#10596833 | — | 2 | 1 | no | — |
| 96 | C2×#10596833 | — | 2 | 1 | no | — |
| 97 | C2×#10596833 | — | 2 | 1 | no | — |
| 98 | C2×#10596833 | — | 4 | 1 | no | — |
| 99 | C2×#10596833 | — | 8 | 1 | no | — |
| 100 | C4⋊#64408 | — | 2 | 2 | no | — |
| 101 | C4⋊#64408 | — | 4 | 1 | no | — |
| 102 | C4×#64408 | — | 8 | 1 | no | — |
| 103 | C23×D73 | — | 4 | 1 | no | — |
| 104 | C2×D292 | — | 2 | 1 | no | — |
| 105 | C2×D292 | — | 2 | 1 | no | — |
| 106 | C2×D292 | — | 2 | 1 | no | — |
| 107 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 108 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 109 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 110 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 111 | D4×D73 | — | 4 | 1 | no | — |
| 112 | D4×D73 | — | 4 | 1 | no | — |
| 113 | D4×D73 | — | 4 | 1 | no | — |
| 114 | D4×D73 | — | 4 | 1 | no | — |
| 115 | D4×D73 | — | 8 | 1 | no | — |
| 116 | D4×D73 | — | 8 | 1 | no | — |
| 117 | D4×D73 | — | 8 | 1 | no | — |
| 118 | D4×D73 | — | 8 | 1 | no | — |
| 119 | C22×Dic73 | — | 2 | 1 | no | — |
| 120 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×D73 | #41 | 1 | 1 | yes | characteristic |
| 123 | #11924015 | — | 8 | 1 | no | — |
| 124 | #11924013 | — | 8 | 1 | no | — |
| 125 | C2×#10596831 | — | 2 | 1 | no | — |
| 126 | C4⋊Dic73 | — | 2 | 1 | no | — |
| 127 | C4⋊Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C4⋊Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | #11924007 | — | 2 | 1 | no | — |
| 130 | #11924007 | — | 2 | 1 | no | — |
| 131 | #11924007 | — | 2 | 1 | no | — |
| 132 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 133 | C22⋊Dic73 | — | 2 | 1 | no | — |
| 134 | #11924005 | — | 2 | 1 | no | — |
| 135 | C4×Dic73 | — | 2 | 1 | no | — |
| 136 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C4×Dic73 | #41 | 1 | 1 | yes | characteristic |
| 139 | C2×Q8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | C2×D4×C73 | — | 2 | 1 | no | — |
| 141 | C2×D4×C73 | — | 2 | 1 | no | — |
| 142 | C2×D4×C73 | — | 2 | 1 | no | — |
| 143 | C2×D4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | SD16×C73 | — | 8 | 1 | no | — |
| 145 | D8×C73 | — | 8 | 1 | no | — |
| 146 | C2×C8×C73 | — | 2 | 1 | no | — |
| 147 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 148 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 149 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | C23×C73 | — | 2 | 1 | no | — |
| 151 | C23×C73 | — | 4 | 1 | no | — |
| 152 | C22×D73 | — | 4 | 1 | no | — |
| 153 | C22×D73 | — | 8 | 1 | no | — |
| 154 | C22×D73 | — | 8 | 1 | no | — |
| 155 | C22×D73 | — | 8 | 1 | no | — |
| 156 | C22×D73 | — | 8 | 1 | no | — |
| 157 | C22×D73 | — | 8 | 1 | no | — |
| 158 | C22×D73 | — | 8 | 1 | no | — |
| 159 | C22×D73 | #121 | 1 | 1 | yes | characteristic |
| 160 | C2×#64408 | — | 4 | 2 | no | — |
| 161 | C2×#64408 | — | 8 | 1 | no | — |
| 162 | C2×#64408 | — | 8 | 1 | no | — |
| 163 | Q8×C73 | — | 4 | 1 | no | — |
| 164 | D4×C73 | — | 4 | 1 | no | — |
| 165 | D4×C73 | — | 4 | 1 | no | — |
| 166 | D4×C73 | — | 4 | 1 | no | — |
| 167 | D4×C73 | — | 4 | 1 | no | — |
| 168 | D4×C73 | — | 4 | 1 | no | — |
| 169 | D4×C73 | — | 8 | 1 | no | — |
| 170 | C2×C4×C73 | — | 2 | 1 | no | — |
| 171 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 174 | C22⋊D73 | — | 4 | 1 | no | — |
| 175 | C22⋊D73 | — | 4 | 1 | no | — |
| 176 | C22⋊D73 | — | 8 | 2 | no | — |
| 177 | C22⋊D73 | — | 8 | 2 | no | — |
| 178 | C22⋊D73 | — | 8 | 1 | no | — |
| 179 | C22⋊D73 | — | 8 | 1 | no | — |
| 180 | C2×Dic73 | — | 2 | 1 | no | — |
| 181 | C2×Dic73 | — | 2 | 1 | no | — |
| 182 | C2×Dic73 | — | 4 | 1 | no | — |
| 183 | C2×Dic73 | — | 4 | 1 | no | — |
| 184 | C2×Dic73 | #120 | 1 | 1 | yes | characteristic |
| 185 | C2×Dic73 | #121 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic73 | #123 | 1 | 1 | yes | characteristic |
| 187 | D292 | — | 4 | 1 | no | — |
| 188 | D292 | — | 4 | 1 | no | — |
| 189 | D292 | — | 4 | 1 | no | — |
| 190 | D292 | — | 4 | 1 | no | — |
| 191 | D292 | — | 8 | 1 | no | — |
| 192 | C4×D73 | — | 2 | 1 | no | — |
| 193 | C4×D73 | — | 2 | 1 | no | — |
| 194 | C4×D73 | — | 2 | 1 | no | — |
| 195 | C4×D73 | — | 2 | 1 | no | — |
| 196 | C4×D73 | — | 4 | 1 | no | — |
| 197 | #10596833 | — | 4 | 1 | no | — |
| 198 | #10596833 | — | 4 | 1 | no | — |
| 199 | #10596833 | — | 4 | 1 | no | — |
| 200 | #10596833 | — | 4 | 1 | no | — |
| 201 | #10596833 | — | 8 | 1 | no | — |
| 202 | C8×C73 | — | 4 | 1 | no | — |
| 203 | #10596831 | — | 4 | 1 | no | — |
| 204 | C22×C73 | — | 4 | 1 | no | — |
| 205 | C22×C73 | — | 4 | 1 | no | — |
| 206 | C22×C73 | — | 4 | 1 | no | — |
| 207 | C22×C73 | — | 8 | 1 | no | — |
| 208 | C22×C73 | — | 8 | 1 | no | — |
| 209 | C22×C73 | — | 8 | 1 | no | — |
| 210 | C22×C73 | #386 | 1 | 1 | yes | characteristic |
| 211 | C2×D73 | — | 2 | 1 | no | — |
| 212 | C2×D73 | — | 2 | 1 | no | — |
| 213 | C2×D73 | — | 8 | 1 | no | — |
| 214 | C2×D73 | — | 8 | 1 | no | — |
| 215 | C2×D73 | — | 8 | 1 | no | — |
| 216 | C2×D73 | — | 16 | 1 | no | — |
| 217 | C2×D73 | — | 16 | 1 | no | — |
| 218 | C2×D73 | — | 16 | 1 | no | — |
| 219 | C2×D73 | — | 16 | 1 | no | — |
| 220 | C2×D73 | #471 | 1 | 1 | yes | characteristic |
| 221 | C2×D73 | #472 | 1 | 1 | yes | characteristic |
| 222 | #64408 | — | 8 | 2 | no | — |
| 223 | C4×C73 | — | 2 | 1 | no | — |
| 224 | C4×C73 | — | 2 | 1 | no | — |
| 225 | C4×C73 | — | 2 | 1 | no | — |
| 226 | C4×C73 | — | 4 | 1 | no | — |
| 227 | Dic73 | — | 2 | 1 | no | — |
| 228 | Dic73 | — | 2 | 1 | no | — |
| 229 | Dic73 | — | 4 | 1 | no | — |
| 230 | Dic73 | — | 4 | 1 | no | — |
| 231 | Dic73 | #453 | 1 | 1 | yes | characteristic |
| 232 | Dic73 | #454 | 1 | 1 | yes | characteristic |
| 233 | #9378 | — | 73 | 1 | no | maximal, Sylow |
| 234 | C2×C73 | — | 8 | 1 | no | — |
| 235 | C2×C73 | — | 16 | 1 | no | — |
| 236 | C2×C73 | #1883 | 1 | 1 | yes | characteristic |
| 237 | C2×C73 | #1907 | 1 | 1 | yes | characteristic |
| 238 | C2×C73 | #1910 | 1 | 1 | yes | characteristic |
| 239 | D73 | — | 2 | 1 | no | — |
| 240 | D73 | — | 2 | 1 | no | — |
| 241 | D73 | — | 16 | 1 | no | — |
| 242 | #3217 | — | 73 | 1 | no | — |
| 243 | #2992 | — | 73 | 1 | no | — |
| 244 | #1982 | — | 73 | 1 | no | — |
| 245 | #1555 | — | 73 | 1 | no | — |
| 246 | #1509 | — | 73 | 1 | no | — |
| 247 | #1290 | — | 73 | 1 | no | — |
| 248 | #1285 | — | 73 | 1 | no | — |
| 249 | C73 | #9378 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 250 | C2×#127 | — | 73 | 1 | no | — |
| 251 | #529 | — | 73 | 1 | no | — |
| 252 | #496 | — | 73 | 1 | no | — |
| 253 | #496 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 254 | #490 | — | 73 | 1 | no | — |
| 255 | #490 | — | 73 | 1 | no | — |
| 256 | #460 | — | 146 | 1 | no | — |
| 257 | #459 | — | 146 | 1 | no | — |
| 258 | #450 | — | 146 | 1 | no | — |
| 259 | #447 | — | 146 | 1 | no | — |
| 260 | #446 | — | 146 | 1 | no | — |
| 261 | #435 | — | 146 | 1 | no | — |
| 262 | #435 | — | 146 | 1 | no | — |
| 263 | C8×D4 | — | 146 | 1 | no | — |
| 264 | #433 | — | 146 | 1 | no | — |
| 265 | #432 | — | 73 | 1 | no | — |
| 266 | #432 | — | 73 | 1 | no | — |
| 267 | #432 | — | 73 | 1 | no | — |
| 268 | #424 | — | 146 | 1 | no | — |
| 269 | C2×C4⋊C8 | — | 73 | 1 | no | — |
| 270 | C2×#102 | — | 146 | 1 | no | — |
| 271 | C2×#102 | — | 146 | 1 | no | — |
| 272 | C4×C4⋊C4 | — | 73 | 1 | no | — |
| 273 | #331 | — | 146 | 1 | no | — |
| 274 | #331 | — | 146 | 1 | no | — |
| 275 | #328 | — | 146 | 1 | no | — |
| 276 | #327 | — | 146 | 1 | no | — |
| 277 | C22×D4 | — | 146 | 1 | no | — |
| 278 | C22×D4 | — | 146 | 1 | no | — |
| 279 | C22×D4 | — | 146 | 1 | no | — |
| 280 | C2×SD16 | — | 2 | 1 | no | — |
| 281 | C2×SD16 | — | 146 | 1 | no | — |
| 282 | C2×D8 | — | 2 | 1 | no | — |
| 283 | C2×D8 | — | 146 | 1 | no | — |
| 284 | C2×M16 | — | 146 | 1 | no | — |
| 285 | C22×C8 | — | 73 | 1 | no | — |
| 286 | C22×C8 | — | 73 | 1 | no | — |
| 287 | C22×C8 | — | 146 | 1 | no | — |
| 288 | #127 | — | 73 | 1 | no | — |
| 289 | #127 | — | 146 | 1 | no | — |
| 290 | #127 | — | 146 | 1 | no | — |
| 291 | #127 | — | 146 | 1 | no | — |
| 292 | #127 | C2×#64408 | 1 | 1 | yes | characteristic |
| 293 | #126 | — | 146 | 1 | no | — |
| 294 | #125 | — | 73 | 1 | no | — |
| 295 | #124 | C2×#64408 | 1 | 1 | yes | characteristic |
| 296 | #123 | — | 146 | 1 | no | — |
| 297 | C22⋊Q8 | — | 73 | 1 | no | — |
| 298 | #121 | — | 73 | 1 | no | — |
| 299 | C4×Q8 | — | 73 | 1 | no | — |
| 300 | C4×D4 | — | 73 | 1 | no | — |
| 301 | C4×D4 | — | 146 | 1 | no | — |
| 302 | #117 | — | 146 | 1 | no | — |
| 303 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 304 | C2×C42 | — | 73 | 1 | no | — |
| 305 | C2×C42 | — | 146 | 1 | no | — |
| 306 | C4⋊C8 | — | 73 | 1 | no | — |
| 307 | C4⋊C8 | — | 73 | 1 | no | — |
| 308 | C4⋊C8 | — | 146 | 1 | no | — |
| 309 | C4⋊C8 | — | 146 | 1 | no | — |
| 310 | C4⋊C8 | — | 146 | 1 | no | — |
| 311 | C4⋊C8 | — | 146 | 1 | no | — |
| 312 | C4⋊C8 | — | 146 | 1 | no | — |
| 313 | C4⋊C8 | — | 146 | 1 | no | — |
| 314 | #102 | — | 292 | 2 | no | — |
| 315 | #102 | — | 292 | 2 | no | — |
| 316 | #102 | — | 146 | 1 | no | — |
| 317 | #102 | — | 146 | 1 | no | — |
| 318 | #102 | — | 146 | 1 | no | — |
| 319 | #102 | — | 146 | 1 | no | — |
| 320 | C22⋊C8 | — | 146 | 1 | no | — |
| 321 | C22⋊C8 | — | 146 | 1 | no | — |
| 322 | C22⋊C8 | — | 146 | 1 | no | — |
| 323 | C22⋊C8 | — | 146 | 1 | no | — |
| 324 | C22⋊C8 | — | 146 | 1 | no | — |
| 325 | #97 | — | 73 | 1 | no | — |
| 326 | #97 | — | 146 | 1 | no | — |
| 327 | #97 | — | 146 | 1 | no | — |
| 328 | #97 | — | 146 | 1 | no | — |
| 329 | #97 | C2×#64408 | 1 | 1 | yes | characteristic |
| 330 | C4×C8 | — | 146 | 1 | no | — |
| 331 | #95 | — | 146 | 1 | no | — |
| 332 | C24 | — | 292 | 1 | no | — |
| 333 | C2×Q8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 334 | C2×D4 | — | 2 | 1 | no | — |
| 335 | C2×D4 | — | 2 | 1 | no | — |
| 336 | C2×D4 | — | 2 | 1 | no | — |
| 337 | C2×D4 | — | 292 | 1 | no | — |
| 338 | C2×D4 | — | 292 | 1 | no | — |
| 339 | C2×D4 | — | 292 | 1 | no | — |
| 340 | C2×D4 | — | 292 | 1 | no | — |
| 341 | C2×D4 | — | 292 | 1 | no | — |
| 342 | C2×D4 | — | 292 | 1 | no | — |
| 343 | C2×D4 | — | 292 | 1 | no | — |
| 344 | C2×D4 | — | 584 | 1 | no | — |
| 345 | C2×D4 | — | 584 | 1 | no | — |
| 346 | C2×D4 | — | 584 | 1 | no | — |
| 347 | C2×D4 | — | 584 | 1 | no | — |
| 348 | C2×D4 | — | 146 | 1 | no | — |
| 349 | C2×D4 | — | 146 | 1 | no | — |
| 350 | C2×D4 | — | 146 | 1 | no | — |
| 351 | C2×D4 | — | 146 | 1 | no | — |
| 352 | C2×D4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 353 | C22×C4 | — | 292 | 1 | no | — |
| 354 | C22×C4 | — | 73 | 1 | no | — |
| 355 | C22×C4 | — | 73 | 1 | no | — |
| 356 | C22×C4 | — | 73 | 1 | no | — |
| 357 | C22×C4 | — | 146 | 1 | no | — |
| 358 | SD16 | — | 8 | 1 | no | — |
| 359 | SD16 | — | 584 | 1 | no | — |
| 360 | D8 | — | 8 | 1 | no | — |
| 361 | D8 | — | 584 | 1 | no | — |
| 362 | M16 | — | 584 | 1 | no | — |
| 363 | C2×C8 | — | 2 | 1 | no | — |
| 364 | C2×C8 | — | 292 | 1 | no | — |
| 365 | C2×C8 | — | 292 | 1 | no | — |
| 366 | C2×C8 | — | 292 | 1 | no | — |
| 367 | C2×C8 | — | 584 | 1 | no | — |
| 368 | C2×C8 | — | 146 | 1 | no | — |
| 369 | C2×C8 | — | 146 | 1 | no | — |
| 370 | C2×C8 | — | 146 | 1 | no | — |
| 371 | C2×C8 | — | 146 | 1 | no | — |
| 372 | C2×C8 | — | 146 | 1 | no | — |
| 373 | C4⋊C4 | — | 292 | 1 | no | — |
| 374 | C4⋊C4 | — | 73 | 1 | no | — |
| 375 | C4⋊C4 | — | 73 | 1 | no | — |
| 376 | C4⋊C4 | — | 146 | 1 | no | — |
| 377 | C4⋊C4 | — | 146 | 1 | no | — |
| 378 | C4⋊C4 | — | 146 | 2 | no | — |
| 379 | C4⋊C4 | — | 146 | 1 | no | — |
| 380 | C4⋊C4 | — | 146 | 1 | no | — |
| 381 | C22⋊C4 | — | 2 | 1 | no | — |
| 382 | C22⋊C4 | — | 2 | 1 | no | — |
| 383 | C22⋊C4 | — | 146 | 1 | no | — |
| 384 | C22⋊C4 | — | 146 | 1 | no | — |
| 385 | C22⋊C4 | — | 146 | 1 | no | — |
| 386 | C42 | — | 584 | 1 | no | — |
| 387 | C42 | — | 73 | 1 | no | — |
| 388 | C42 | — | 73 | 1 | no | — |
| 389 | C42 | — | 73 | 1 | no | — |
| 390 | C42 | — | 146 | 1 | no | — |
| 391 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 392 | C23 | — | 2 | 1 | no | — |
| 393 | C23 | — | 4 | 1 | no | — |
| 394 | C23 | — | 292 | 1 | no | — |
| 395 | C23 | — | 584 | 1 | no | — |
| 396 | C23 | — | 584 | 1 | no | — |
| 397 | C23 | — | 584 | 1 | no | — |
| 398 | C23 | — | 584 | 1 | no | — |
| 399 | C23 | — | 584 | 1 | no | — |
| 400 | C23 | — | 584 | 1 | no | — |
| 401 | C23 | — | 73 | 1 | no | — |
| 402 | Q8 | — | 4 | 1 | no | — |
| 403 | D4 | — | 4 | 1 | no | — |
| 404 | D4 | — | 4 | 1 | no | — |
| 405 | D4 | — | 4 | 1 | no | — |
| 406 | D4 | — | 4 | 1 | no | — |
| 407 | D4 | — | 4 | 1 | no | — |
| 408 | D4 | — | 8 | 1 | no | — |
| 409 | D4 | — | 292 | 1 | no | — |
| 410 | D4 | — | 292 | 1 | no | — |
| 411 | D4 | — | 292 | 1 | no | — |
| 412 | D4 | — | 292 | 1 | no | — |
| 413 | D4 | — | 292 | 1 | no | — |
| 414 | D4 | — | 292 | 1 | no | — |
| 415 | D4 | — | 584 | 1 | no | — |
| 416 | D4 | — | 584 | 1 | no | — |
| 417 | D4 | — | 584 | 1 | no | — |
| 418 | D4 | — | 584 | 2 | no | — |
| 419 | D4 | — | 584 | 2 | no | — |
| 420 | C2×C4 | — | 2 | 1 | no | — |
| 421 | C2×C4 | — | 292 | 1 | no | — |
| 422 | C2×C4 | — | 292 | 1 | no | — |
| 423 | C2×C4 | — | 292 | 1 | no | — |
| 424 | C2×C4 | — | 292 | 2 | no | — |
| 425 | C2×C4 | — | 584 | 1 | no | — |
| 426 | C2×C4 | — | 584 | 1 | no | — |
| 427 | C2×C4 | — | 73 | 1 | no | — |
| 428 | C2×C4 | — | 73 | 1 | no | — |
| 429 | C2×C4 | — | 73 | 1 | no | — |
| 430 | C2×C4 | — | 146 | 1 | no | — |
| 431 | C2×C4 | — | 146 | 1 | no | — |
| 432 | C2×C4 | — | 146 | 1 | no | — |
| 433 | C2×C4 | — | 146 | 1 | no | — |
| 434 | C2×C4 | — | 146 | 1 | no | — |
| 435 | C2×C4 | — | 146 | 1 | no | — |
| 436 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 437 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 438 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 439 | C8 | — | 4 | 1 | no | — |
| 440 | C8 | — | 292 | 1 | no | — |
| 441 | C8 | — | 292 | 1 | no | — |
| 442 | C8 | — | 292 | 1 | no | — |
| 443 | C8 | — | 292 | 1 | no | — |
| 444 | C8 | — | 292 | 1 | no | — |
| 445 | C8 | — | 584 | 1 | no | — |
| 446 | C22 | — | 4 | 1 | no | — |
| 447 | C22 | — | 4 | 1 | no | — |
| 448 | C22 | — | 4 | 1 | no | — |
| 449 | C22 | — | 8 | 1 | no | — |
| 450 | C22 | — | 8 | 1 | no | — |
| 451 | C22 | — | 8 | 1 | no | — |
| 452 | C22 | — | 584 | 1 | no | — |
| 453 | C22 | — | 584 | 1 | no | — |
| 454 | C22 | — | 584 | 1 | no | — |
| 455 | C22 | — | 73 | 1 | no | — |
| 456 | C22 | — | 73 | 1 | no | — |
| 457 | C22 | — | 1168 | 1 | no | — |
| 458 | C22 | — | 1168 | 1 | no | — |
| 459 | C22 | — | 1168 | 1 | no | — |
| 460 | C22 | — | 1168 | 1 | no | — |
| 461 | C22 | — | 146 | 1 | no | — |
| 462 | C22 | — | 146 | 1 | no | — |
| 463 | C22 | #17989535 | 1 | 1 | yes | characteristic |
| 464 | C4 | — | 2 | 1 | no | — |
| 465 | C4 | — | 2 | 1 | no | — |
| 466 | C4 | — | 2 | 1 | no | — |
| 467 | C4 | — | 4 | 1 | no | — |
| 468 | C4 | — | 292 | 1 | no | — |
| 469 | C4 | — | 292 | 1 | no | — |
| 470 | C4 | — | 584 | 2 | no | — |
| 471 | C4 | — | 73 | 1 | no | — |
| 472 | C4 | — | 73 | 1 | no | — |
| 473 | C4 | — | 146 | 1 | no | — |
| 474 | C4 | — | 146 | 1 | no | — |
| 475 | C2 | — | 8 | 1 | no | — |
| 476 | C2 | — | 16 | 1 | no | — |
| 477 | C2 | — | 1168 | 1 | no | — |
| 478 | C2 | — | 146 | 1 | no | — |
| 479 | C2 | — | 146 | 1 | no | — |
| 480 | C2 | #22625931 | 1 | 1 | yes | characteristic |
| 481 | C2 | #22625970 | 1 | 1 | yes | characteristic |
| 482 | C2 | #22625974 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626868 | C2 | semidirect |
| 2. #22626098 | C2 | semidirect |
| 3. #22625459 | C2 | semidirect |
| 4. #22625332 | C2 | semidirect |
| 5. #22624795 | C2 | semidirect |
| 6. #22624781 | C2 | semidirect |
| 26. #17988977 | C4 | semidirect |
| 27. #17988952 | C4 | semidirect |
| 28. #17988951 | C4 | semidirect |
| 34. #496×C73 | C4 | semidirect |
| 249. C73 | #9378 | semidirect |
| 253. #496 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626868 | 2 |
| #22626098 | 2 |
| #22625459 | 2 |
| #22625332 | 2 |
| #22624795 | 2 |
| #22624781 | 2 |
| #22620945 | 2 |
| #9378 | 73 |