Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #22619278 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22611595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22608521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22608083 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22608082 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22608081 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C73×#1404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17989424 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #17989383 | — | 2 | 1 | no | — |
| 10 | #17989136 | C22 | 1 | 1 | yes | characteristic |
| 11 | #17988772 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #17988770 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #17988766 | — | 2 | 1 | no | — |
| 14 | #17988759 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17988753 | — | 2 | 1 | no | — |
| 16 | #104×D73 | — | 2 | 1 | no | — |
| 17 | #17988570 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #17988559 | — | 2 | 1 | no | — |
| 19 | #17988539 | — | 2 | 1 | no | — |
| 20 | #17988382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #17988379 | — | 2 | 1 | no | — |
| 22 | #17988327 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #17988326 | — | 2 | 1 | no | — |
| 24 | #454×C73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #354×C73 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #329×C73 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #14556639 | — | 4 | 1 | no | — |
| 28 | #14556639 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #14556637 | — | 2 | 1 | no | — |
| 30 | #14556637 | — | 4 | 1 | no | — |
| 31 | #14556637 | — | 4 | 1 | no | — |
| 32 | C2×#11924029 | — | 4 | 1 | no | — |
| 33 | C2×#11924029 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#11924027 | D4 | 1 | 1 | yes | characteristic |
| 35 | #41×D73 | — | 2 | 1 | no | — |
| 36 | #41×D73 | — | 4 | 1 | no | — |
| 37 | #41×D73 | — | 4 | 1 | no | — |
| 38 | #14556624 | — | 2 | 1 | no | — |
| 39 | #14556621 | — | 2 | 1 | no | — |
| 40 | #14556620 | — | 4 | 1 | no | — |
| 41 | #14556617 | — | 2 | 1 | no | — |
| 42 | #14556615 | — | 4 | 1 | no | — |
| 43 | #14556612 | — | 4 | 1 | no | — |
| 44 | #14556610 | — | 4 | 1 | no | — |
| 45 | C2×#11924011 | — | 4 | 1 | no | — |
| 46 | M16×D73 | — | 2 | 1 | no | — |
| 47 | #14556589 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #14556587 | D4 | 1 | 1 | yes | characteristic |
| 49 | #14556579 | D4 | 1 | 1 | yes | characteristic |
| 50 | #14556564 | — | 4 | 1 | no | — |
| 51 | #14556551 | — | 4 | 1 | no | — |
| 52 | #14556547 | — | 4 | 1 | no | — |
| 53 | C42×D73 | D4 | 1 | 1 | yes | characteristic |
| 54 | #14556519 | — | 2 | 1 | no | — |
| 55 | #14556518 | — | 2 | 1 | no | — |
| 56 | #14556517 | — | 2 | 1 | no | — |
| 57 | #14556510 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #14556507 | — | 2 | 1 | no | — |
| 59 | #14556506 | — | 2 | 1 | no | — |
| 60 | #14556505 | — | 4 | 1 | no | — |
| 61 | #14556502 | — | 2 | 1 | no | — |
| 62 | C8×Dic73 | — | 4 | 1 | no | — |
| 63 | 2−1+4×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | AGL(1,ℤ/8)×C73 | — | 2 | 1 | no | — |
| 65 | #124×C73 | C23 | 1 | 1 | yes | characteristic |
| 66 | #104×C73 | — | 2 | 1 | no | — |
| 67 | #101×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | #99×C73 | — | 2 | 1 | no | — |
| 69 | #97×C73 | — | 2 | 1 | no | — |
| 70 | #11924029 | — | 2 | 1 | no | — |
| 71 | #11924029 | — | 4 | 1 | no | — |
| 72 | #11924029 | — | 4 | 1 | no | — |
| 73 | #11924029 | — | 4 | 1 | no | — |
| 74 | #11924029 | — | 4 | 1 | no | — |
| 75 | #11924029 | — | 4 | 2 | no | — |
| 76 | #11924029 | — | 4 | 1 | no | — |
| 77 | #11924028 | — | 2 | 1 | no | — |
| 78 | #11924028 | — | 4 | 1 | no | — |
| 79 | #11924028 | — | 4 | 1 | no | — |
| 80 | #11924028 | — | 4 | 2 | no | — |
| 81 | #11924028 | — | 4 | 2 | no | — |
| 82 | #11924028 | — | 4 | 1 | no | — |
| 83 | #11924027 | — | 2 | 1 | no | — |
| 84 | #11924027 | — | 4 | 1 | no | — |
| 85 | #11924027 | — | 4 | 1 | no | — |
| 86 | #11924027 | — | 4 | 1 | no | — |
| 87 | #11924027 | — | 4 | 1 | no | — |
| 88 | C2×Dic146 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 89 | Q8×D73 | — | 2 | 1 | no | — |
| 90 | Q8×D73 | — | 4 | 1 | no | — |
| 91 | Q8×D73 | — | 4 | 1 | no | — |
| 92 | C2×D292 | — | 2 | 1 | no | — |
| 93 | C2×D292 | — | 4 | 1 | no | — |
| 94 | C2×D292 | — | 4 | 2 | no | — |
| 95 | C2×D292 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×C22⋊D73 | — | 2 | 1 | no | — |
| 97 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 98 | D4×D73 | — | 2 | 1 | no | — |
| 99 | D4×D73 | — | 4 | 1 | no | — |
| 100 | D4×D73 | — | 4 | 2 | no | — |
| 101 | D4×D73 | — | 4 | 2 | no | — |
| 102 | D4×D73 | — | 4 | 1 | no | — |
| 103 | D4×D73 | — | 4 | 1 | no | — |
| 104 | C22×Dic73 | — | 2 | 1 | no | — |
| 105 | C2×C4×D73 | — | 2 | 1 | no | — |
| 106 | C2×C4×D73 | — | 2 | 1 | no | — |
| 107 | C2×C4×D73 | — | 4 | 1 | no | — |
| 108 | C2×C4×D73 | — | 4 | 2 | no | — |
| 109 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 110 | Dic292 | — | 4 | 1 | no | — |
| 111 | #11924018 | — | 4 | 1 | no | — |
| 112 | #11924017 | — | 4 | 1 | no | — |
| 113 | #11924016 | — | 4 | 1 | no | — |
| 114 | #11924016 | — | 4 | 1 | no | — |
| 115 | #11924013 | — | 4 | 1 | no | — |
| 116 | #11924012 | — | 2 | 1 | no | — |
| 117 | #11924011 | — | 4 | 1 | no | — |
| 118 | #11924011 | — | 4 | 4 | no | — |
| 119 | C2×#10596831 | — | 4 | 1 | no | — |
| 120 | C8×D73 | — | 4 | 1 | no | — |
| 121 | #11924007 | — | 4 | 1 | no | — |
| 122 | #11924007 | — | 8 | 1 | no | — |
| 123 | C22⋊Dic73 | — | 4 | 1 | no | — |
| 124 | #11924005 | — | 4 | 1 | no | — |
| 125 | C4×Dic73 | — | 2 | 1 | no | — |
| 126 | C4×Dic73 | — | 8 | 1 | no | — |
| 127 | C4×Dic73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | #41×C73 | — | 2 | 1 | no | — |
| 129 | #41×C73 | — | 4 | 1 | no | — |
| 130 | #41×C73 | — | 4 | 1 | no | — |
| 131 | C2×Q8×C73 | — | 4 | 1 | no | — |
| 132 | C2×Q8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 133 | C2×D4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | SD16×C73 | — | 4 | 1 | no | — |
| 135 | D8×C73 | — | 4 | 1 | no | — |
| 136 | M16×C73 | — | 2 | 1 | no | — |
| 137 | C2×C8×C73 | — | 4 | 1 | no | — |
| 138 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 139 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 140 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C23×C73 | — | 2 | 1 | no | — |
| 142 | C22×D73 | — | 2 | 1 | no | — |
| 143 | C22×D73 | — | 4 | 1 | no | — |
| 144 | C22×D73 | — | 4 | 2 | no | — |
| 145 | C22×D73 | #99 | 1 | 1 | yes | characteristic |
| 146 | Q8×C73 | — | 2 | 1 | no | — |
| 147 | Q8×C73 | — | 4 | 1 | no | — |
| 148 | Q8×C73 | — | 4 | 1 | no | — |
| 149 | D4×C73 | — | 2 | 1 | no | — |
| 150 | D4×C73 | — | 4 | 1 | no | — |
| 151 | D4×C73 | — | 4 | 1 | no | — |
| 152 | D4×C73 | — | 4 | 1 | no | — |
| 153 | C2×C4×C73 | — | 2 | 1 | no | — |
| 154 | C2×C4×C73 | — | 2 | 1 | no | — |
| 155 | C2×C4×C73 | — | 4 | 1 | no | — |
| 156 | C2×C4×C73 | — | 4 | 2 | no | — |
| 157 | C2×C4×C73 | — | 8 | 1 | no | — |
| 158 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | C22⋊D73 | — | 4 | 1 | no | — |
| 160 | C22⋊D73 | — | 4 | 2 | no | — |
| 161 | C22⋊D73 | — | 4 | 1 | no | — |
| 162 | C22⋊D73 | — | 4 | 1 | no | — |
| 163 | C22⋊D73 | — | 8 | 2 | no | — |
| 164 | C22⋊D73 | — | 8 | 1 | no | — |
| 165 | C2×Dic73 | — | 2 | 1 | no | — |
| 166 | C2×Dic73 | — | 2 | 1 | no | — |
| 167 | C2×Dic73 | — | 4 | 1 | no | — |
| 168 | C2×Dic73 | — | 4 | 1 | no | — |
| 169 | C2×Dic73 | — | 4 | 1 | no | — |
| 170 | C2×Dic73 | — | 8 | 1 | no | — |
| 171 | C2×Dic73 | #99 | 1 | 1 | yes | characteristic |
| 172 | D292 | — | 2 | 1 | no | — |
| 173 | D292 | — | 4 | 1 | no | — |
| 174 | D292 | — | 4 | 2 | no | — |
| 175 | D292 | — | 4 | 1 | no | — |
| 176 | D292 | — | 4 | 1 | no | — |
| 177 | D292 | — | 4 | 2 | no | — |
| 178 | C4×D73 | — | 2 | 1 | no | — |
| 179 | C4×D73 | — | 2 | 1 | no | — |
| 180 | C4×D73 | — | 4 | 2 | no | — |
| 181 | C4×D73 | — | 4 | 1 | no | — |
| 182 | C4×D73 | — | 4 | 1 | no | — |
| 183 | C4×D73 | — | 4 | 2 | no | — |
| 184 | C4×D73 | — | 4 | 2 | no | — |
| 185 | C4×D73 | — | 4 | 1 | no | — |
| 186 | C4×D73 | — | 4 | 1 | no | — |
| 187 | C4×D73 | — | 4 | 1 | no | — |
| 188 | Dic146 | — | 2 | 1 | no | — |
| 189 | Dic146 | — | 4 | 1 | no | — |
| 190 | Dic146 | — | 4 | 1 | no | — |
| 191 | Dic146 | — | 4 | 1 | no | — |
| 192 | C8×C73 | — | 4 | 1 | no | — |
| 193 | C8×C73 | — | 4 | 2 | no | — |
| 194 | #10596831 | — | 4 | 1 | no | — |
| 195 | #10596831 | — | 4 | 2 | no | — |
| 196 | C22×C73 | — | 4 | 1 | no | — |
| 197 | C22×C73 | — | 4 | 1 | no | — |
| 198 | C22×C73 | — | 8 | 1 | no | — |
| 199 | C22×C73 | C2×#99 | 1 | 1 | yes | characteristic |
| 200 | C2×D73 | — | 2 | 1 | no | — |
| 201 | C2×D73 | — | 4 | 1 | no | — |
| 202 | C2×D73 | — | 4 | 1 | no | — |
| 203 | C2×D73 | — | 4 | 1 | no | — |
| 204 | C2×D73 | — | 8 | 1 | no | — |
| 205 | C2×D73 | — | 16 | 1 | no | — |
| 206 | C2×D73 | — | 16 | 2 | no | — |
| 207 | C4×C73 | — | 2 | 1 | no | — |
| 208 | C4×C73 | — | 4 | 1 | no | — |
| 209 | C4×C73 | — | 4 | 1 | no | — |
| 210 | C4×C73 | — | 4 | 1 | no | — |
| 211 | C4×C73 | — | 16 | 1 | no | — |
| 212 | Dic73 | — | 2 | 2 | no | — |
| 213 | Dic73 | — | 4 | 1 | no | — |
| 214 | Dic73 | — | 4 | 1 | no | — |
| 215 | Dic73 | — | 16 | 1 | no | — |
| 216 | Dic73 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 217 | Dic73 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 218 | #13568 | — | 73 | 1 | no | maximal, Sylow |
| 219 | C2×C73 | — | 2 | 1 | no | — |
| 220 | C2×C73 | — | 8 | 1 | no | — |
| 221 | C2×C73 | — | 8 | 1 | no | — |
| 222 | C2×C73 | C2×AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 223 | D73 | — | 4 | 1 | no | — |
| 224 | D73 | — | 8 | 1 | no | — |
| 225 | D73 | — | 8 | 1 | no | — |
| 226 | #3018 | — | 73 | 1 | no | — |
| 227 | #2126 | — | 73 | 1 | no | — |
| 228 | #1525 | — | 73 | 1 | no | — |
| 229 | #1404 | — | 73 | 1 | no | — |
| 230 | #1404 | — | 73 | 1 | no | — |
| 231 | #1404 | — | 73 | 1 | no | — |
| 232 | #1404 | D73 | 1 | 1 | yes | characteristic, complemented |
| 233 | C73 | #13568 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 234 | #585 | — | 73 | 1 | no | — |
| 235 | #575 | — | 146 | 1 | no | — |
| 236 | #532 | — | 73 | 1 | no | — |
| 237 | #456 | — | 73 | 1 | no | — |
| 238 | #456 | — | 73 | 1 | no | — |
| 239 | #455 | — | 146 | 1 | no | — |
| 240 | #454 | — | 73 | 1 | no | — |
| 241 | #454 | C2×D73 | 1 | 1 | yes | characteristic |
| 242 | #453 | — | 146 | 1 | no | — |
| 243 | C2×#104 | — | 146 | 1 | no | — |
| 244 | #413 | — | 73 | 1 | no | — |
| 245 | #410 | — | 146 | 1 | no | — |
| 246 | C4×M16 | — | 146 | 1 | no | — |
| 247 | #354 | — | 73 | 1 | no | — |
| 248 | #354 | C2×D73 | 1 | 1 | yes | characteristic, complemented |
| 249 | #353 | — | 146 | 1 | no | — |
| 250 | #329 | — | 73 | 1 | no | — |
| 251 | #329 | — | 146 | 1 | no | — |
| 252 | #329 | C2×D73 | 1 | 1 | yes | characteristic, complemented |
| 253 | 2−1+4 | — | 292 | 1 | no | — |
| 254 | 2−1+4 | — | 73 | 1 | no | — |
| 255 | 2−1+4 | C4×D73 | 1 | 1 | yes | characteristic |
| 256 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 257 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 258 | H(5,𝔽2) | — | 146 | 1 | no | — |
| 259 | C2×#41 | — | 292 | 1 | no | — |
| 260 | C2×#41 | — | 292 | 1 | no | — |
| 261 | C2×#41 | — | 292 | 1 | no | — |
| 262 | C2×#41 | — | 73 | 1 | no | — |
| 263 | C2×#41 | — | 73 | 1 | no | — |
| 264 | C2×#41 | — | 146 | 1 | no | — |
| 265 | #137 | — | 292 | 1 | no | — |
| 266 | #137 | — | 146 | 1 | no | — |
| 267 | #137 | — | 146 | 1 | no | — |
| 268 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 269 | AGL(1,ℤ/8) | — | 292 | 1 | no | — |
| 270 | AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 271 | #135 | — | 292 | 1 | no | — |
| 272 | #135 | — | 292 | 1 | no | — |
| 273 | C2×M16 | — | 292 | 1 | no | — |
| 274 | C2×M16 | — | 146 | 1 | no | — |
| 275 | C4⋊Q8 | — | 73 | 1 | no | — |
| 276 | #127 | — | 73 | 1 | no | — |
| 277 | #124 | — | 73 | 1 | no | — |
| 278 | #124 | C22×D73 | 1 | 1 | yes | characteristic |
| 279 | #121 | — | 292 | 1 | no | — |
| 280 | C4×D4 | — | 292 | 1 | no | — |
| 281 | #117 | — | 292 | 1 | no | — |
| 282 | C2×C42 | — | 73 | 1 | no | — |
| 283 | #104 | — | 2 | 1 | no | — |
| 284 | #104 | — | 146 | 1 | no | — |
| 285 | #104 | — | 146 | 1 | no | — |
| 286 | #104 | — | 146 | 1 | no | — |
| 287 | #101 | — | 73 | 1 | no | — |
| 288 | #101 | C4×D73 | 1 | 1 | yes | characteristic |
| 289 | #100 | — | 146 | 1 | no | — |
| 290 | #99 | — | 2 | 1 | no | — |
| 291 | #99 | — | 292 | 1 | no | — |
| 292 | #99 | — | 146 | 1 | no | — |
| 293 | #97 | — | 2 | 1 | no | — |
| 294 | #97 | — | 146 | 1 | no | — |
| 295 | C4×C8 | — | 292 | 1 | no | — |
| 296 | #41 | — | 2 | 1 | no | — |
| 297 | #41 | — | 4 | 1 | no | — |
| 298 | #41 | — | 4 | 1 | no | — |
| 299 | #41 | — | 292 | 1 | no | — |
| 300 | #41 | — | 292 | 2 | no | — |
| 301 | #41 | — | 292 | 2 | no | — |
| 302 | #41 | — | 292 | 1 | no | — |
| 303 | #41 | — | 292 | 1 | no | — |
| 304 | #41 | — | 292 | 1 | no | — |
| 305 | #41 | — | 292 | 2 | no | — |
| 306 | #41 | — | 292 | 1 | no | — |
| 307 | #41 | — | 292 | 1 | no | — |
| 308 | #41 | — | 292 | 1 | no | — |
| 309 | #41 | — | 292 | 1 | no | — |
| 310 | #41 | — | 292 | 1 | no | — |
| 311 | #41 | — | 292 | 1 | no | — |
| 312 | #41 | — | 292 | 1 | no | — |
| 313 | #41 | — | 292 | 1 | no | — |
| 314 | #41 | — | 146 | 1 | no | — |
| 315 | #41 | — | 146 | 1 | no | — |
| 316 | #41 | — | 146 | 1 | no | — |
| 317 | C2×Q8 | — | 4 | 1 | no | — |
| 318 | C2×Q8 | — | 292 | 1 | no | — |
| 319 | C2×Q8 | — | 292 | 1 | no | — |
| 320 | C2×Q8 | — | 73 | 1 | no | — |
| 321 | C2×Q8 | — | 146 | 1 | no | — |
| 322 | C2×Q8 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 323 | C2×D4 | — | 292 | 2 | no | — |
| 324 | C2×D4 | — | 292 | 1 | no | — |
| 325 | C2×D4 | — | 292 | 1 | no | — |
| 326 | C2×D4 | — | 292 | 2 | no | — |
| 327 | C2×D4 | — | 292 | 1 | no | — |
| 328 | C2×D4 | — | 292 | 2 | no | — |
| 329 | C2×D4 | — | 292 | 1 | no | — |
| 330 | C2×D4 | — | 292 | 1 | no | — |
| 331 | C2×D4 | — | 73 | 1 | no | — |
| 332 | C2×D4 | — | 146 | 1 | no | — |
| 333 | C2×D4 | — | 146 | 1 | no | — |
| 334 | C2×D4 | — | 146 | 1 | no | — |
| 335 | C2×D4 | D4×D73 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | — | 292 | 2 | no | — |
| 337 | C22×C4 | — | 292 | 1 | no | — |
| 338 | C22×C4 | — | 73 | 1 | no | — |
| 339 | C22×C4 | — | 146 | 1 | no | — |
| 340 | C22×C4 | — | 146 | 1 | no | — |
| 341 | C22×C4 | — | 146 | 1 | no | — |
| 342 | Q16 | — | 292 | 1 | no | — |
| 343 | Q16 | — | 292 | 1 | no | — |
| 344 | SD16 | — | 4 | 1 | no | — |
| 345 | SD16 | — | 292 | 1 | no | — |
| 346 | SD16 | — | 292 | 1 | no | — |
| 347 | SD16 | — | 292 | 1 | no | — |
| 348 | D8 | — | 4 | 1 | no | — |
| 349 | D8 | — | 292 | 1 | no | — |
| 350 | M16 | — | 2 | 1 | no | — |
| 351 | M16 | — | 292 | 4 | no | — |
| 352 | M16 | — | 292 | 1 | no | — |
| 353 | M16 | — | 146 | 1 | no | — |
| 354 | C2×C8 | — | 4 | 1 | no | — |
| 355 | C2×C8 | — | 292 | 1 | no | — |
| 356 | C2×C8 | — | 292 | 1 | no | — |
| 357 | C4⋊C4 | — | 292 | 1 | no | — |
| 358 | C4⋊C4 | — | 584 | 1 | no | — |
| 359 | C22⋊C4 | — | 4 | 1 | no | — |
| 360 | C22⋊C4 | — | 4 | 1 | no | — |
| 361 | C22⋊C4 | — | 292 | 1 | no | — |
| 362 | C22⋊C4 | — | 292 | 1 | no | — |
| 363 | C42 | — | 584 | 1 | no | — |
| 364 | C42 | — | 73 | 1 | no | — |
| 365 | C42 | — | 146 | 1 | no | — |
| 366 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 367 | C23 | — | 2 | 1 | no | — |
| 368 | C23 | — | 292 | 2 | no | — |
| 369 | C23 | — | 292 | 1 | no | — |
| 370 | C23 | — | 73 | 1 | no | — |
| 371 | C23 | — | 146 | 1 | no | — |
| 372 | Q8 | — | 2 | 1 | no | — |
| 373 | Q8 | — | 4 | 1 | no | — |
| 374 | Q8 | — | 4 | 1 | no | — |
| 375 | Q8 | — | 292 | 1 | no | — |
| 376 | Q8 | — | 292 | 1 | no | — |
| 377 | Q8 | — | 292 | 1 | no | — |
| 378 | Q8 | — | 146 | 1 | no | — |
| 379 | D4 | — | 2 | 1 | no | — |
| 380 | D4 | — | 4 | 1 | no | — |
| 381 | D4 | — | 4 | 1 | no | — |
| 382 | D4 | — | 4 | 1 | no | — |
| 383 | D4 | — | 292 | 1 | no | — |
| 384 | D4 | — | 292 | 1 | no | — |
| 385 | D4 | — | 292 | 2 | no | — |
| 386 | D4 | — | 292 | 1 | no | — |
| 387 | D4 | — | 292 | 2 | no | — |
| 388 | D4 | — | 292 | 2 | no | — |
| 389 | D4 | — | 292 | 1 | no | — |
| 390 | D4 | — | 292 | 1 | no | — |
| 391 | D4 | — | 292 | 1 | no | — |
| 392 | D4 | — | 584 | 1 | no | — |
| 393 | D4 | — | 584 | 2 | no | — |
| 394 | D4 | — | 146 | 1 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 4 | 1 | no | — |
| 398 | C2×C4 | — | 4 | 2 | no | — |
| 399 | C2×C4 | — | 8 | 1 | no | — |
| 400 | C2×C4 | — | 292 | 1 | no | — |
| 401 | C2×C4 | — | 292 | 2 | no | — |
| 402 | C2×C4 | — | 292 | 2 | no | — |
| 403 | C2×C4 | — | 292 | 1 | no | — |
| 404 | C2×C4 | — | 292 | 1 | no | — |
| 405 | C2×C4 | — | 292 | 1 | no | — |
| 406 | C2×C4 | — | 292 | 1 | no | — |
| 407 | C2×C4 | — | 292 | 2 | no | — |
| 408 | C2×C4 | — | 292 | 1 | no | — |
| 409 | C2×C4 | — | 292 | 1 | no | — |
| 410 | C2×C4 | — | 292 | 1 | no | — |
| 411 | C2×C4 | — | 584 | 1 | no | — |
| 412 | C2×C4 | — | 73 | 1 | no | — |
| 413 | C2×C4 | — | 146 | 1 | no | — |
| 414 | C2×C4 | — | 146 | 1 | no | — |
| 415 | C2×C4 | — | 146 | 1 | no | — |
| 416 | C2×C4 | — | 146 | 1 | no | — |
| 417 | C2×C4 | C22⋊C4×D73 | 1 | 1 | yes | characteristic |
| 418 | C8 | — | 4 | 1 | no | — |
| 419 | C8 | — | 4 | 2 | no | — |
| 420 | C8 | — | 292 | 1 | no | — |
| 421 | C8 | — | 292 | 2 | no | — |
| 422 | C22 | — | 4 | 1 | no | — |
| 423 | C22 | — | 4 | 1 | no | — |
| 424 | C22 | — | 8 | 1 | no | — |
| 425 | C22 | — | 292 | 1 | no | — |
| 426 | C22 | — | 292 | 1 | no | — |
| 427 | C22 | — | 292 | 1 | no | — |
| 428 | C22 | — | 584 | 1 | no | — |
| 429 | C22 | — | 1168 | 1 | no | — |
| 430 | C22 | — | 1168 | 2 | no | — |
| 431 | C22 | — | 146 | 1 | no | — |
| 432 | C22 | #99×D73 | 1 | 1 | yes | characteristic |
| 433 | C4 | — | 2 | 1 | no | — |
| 434 | C4 | — | 4 | 1 | no | — |
| 435 | C4 | — | 4 | 1 | no | — |
| 436 | C4 | — | 4 | 1 | no | — |
| 437 | C4 | — | 16 | 1 | no | — |
| 438 | C4 | — | 292 | 1 | no | — |
| 439 | C4 | — | 292 | 1 | no | — |
| 440 | C4 | — | 73 | 1 | no | — |
| 441 | C4 | — | 73 | 1 | no | — |
| 442 | C4 | — | 1168 | 1 | no | — |
| 443 | C4 | — | 146 | 2 | no | — |
| 444 | C2 | — | 2 | 1 | no | — |
| 445 | C2 | — | 8 | 1 | no | — |
| 446 | C2 | — | 8 | 1 | no | — |
| 447 | C2 | — | 292 | 1 | no | — |
| 448 | C2 | — | 584 | 1 | no | — |
| 449 | C2 | — | 584 | 1 | no | — |
| 450 | C2 | AΣL(1,𝔽16)×D73 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22611595 | C2 | semidirect |
| 3. #22608521 | C2 | semidirect |
| 4. #22608083 | C2 | semidirect |
| 5. #22608082 | C2 | semidirect |
| 6. #22608081 | C2 | semidirect |
| 7. C73×#1404 | C2 | semidirect |
| 8. #17989424 | C4 | semidirect |
| 11. #17988772 | C4 | semidirect |
| 12. #17988770 | C4 | semidirect |
| 17. #17988570 | C4 | semidirect |
| 20. #17988382 | C22 | semidirect |
| 22. #17988327 | C22 | semidirect |
| 25. #354×C73 | C22 | semidirect |
| 26. #329×C73 | C22 | semidirect |
| 232. #1404 | D73 | semidirect |
| 233. C73 | #13568 | semidirect |
| 248. #354 | C2×D73 | semidirect |
| 252. #329 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619278 | 2 |
| #22611595 | 2 |
| #22608521 | 2 |
| #22608083 | 2 |
| #22608082 | 2 |
| #22608081 | 2 |
| C73×#1404 | 2 |
| #13568 | 73 |