Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #22621699 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #22611932 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22609220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22608089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22608082 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22608078 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C73×#2202 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #17989395 | — | 2 | 1 | no | — |
| 9 | #17989391 | — | 2 | 1 | no | — |
| 10 | #17988977 | — | 2 | 1 | no | — |
| 11 | #17988977 | C22 | 1 | 1 | yes | characteristic |
| 12 | #17988855 | — | 2 | 1 | no | — |
| 13 | #17988853 | — | 2 | 1 | no | — |
| 14 | #17988773 | — | 2 | 1 | no | — |
| 15 | #17988764 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988756 | — | 2 | 1 | no | — |
| 17 | #17988706 | — | 2 | 1 | no | — |
| 18 | #17988382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #17988374 | — | 2 | 1 | no | — |
| 20 | #17988327 | — | 2 | 1 | no | — |
| 21 | #17988327 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | H(3,𝔽4)×C73 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #454×C73 | — | 2 | 1 | no | — |
| 24 | #454×C73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #355×C73 | — | 2 | 1 | no | — |
| 26 | #355×C73 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #14556637 | — | 2 | 1 | no | — |
| 28 | #14556636 | D4 | 1 | 1 | yes | characteristic |
| 29 | #14556622 | — | 2 | 1 | no | — |
| 30 | #14556622 | — | 4 | 1 | no | — |
| 31 | #14556619 | — | 2 | 1 | no | — |
| 32 | #14556618 | — | 4 | 1 | no | — |
| 33 | #14556616 | — | 2 | 1 | no | — |
| 34 | #14556616 | — | 4 | 1 | no | — |
| 35 | #14556615 | — | 4 | 1 | no | — |
| 36 | #14556612 | — | 4 | 1 | no | — |
| 37 | #14556611 | — | 2 | 1 | no | — |
| 38 | #14556611 | — | 4 | 1 | no | — |
| 39 | C2×#11924015 | — | 2 | 1 | no | — |
| 40 | C2×#11924015 | — | 4 | 1 | no | — |
| 41 | C2×#11924015 | — | 4 | 1 | no | — |
| 42 | C2×#11924013 | — | 2 | 1 | no | — |
| 43 | C2×#11924013 | — | 4 | 1 | no | — |
| 44 | D8×D73 | — | 4 | 1 | no | — |
| 45 | #14556599 | — | 2 | 1 | no | — |
| 46 | #14556598 | — | 2 | 1 | no | — |
| 47 | #14556588 | D4 | 1 | 1 | yes | characteristic, complemented |
| 48 | #14556560 | — | 4 | 1 | no | — |
| 49 | #14556526 | — | 2 | 1 | no | — |
| 50 | #14556519 | — | 2 | 1 | no | — |
| 51 | #14556508 | D4 | 1 | 1 | yes | characteristic |
| 52 | #14556507 | — | 2 | 1 | no | — |
| 53 | #14556506 | — | 2 | 1 | no | — |
| 54 | #14556505 | — | 4 | 1 | no | — |
| 55 | #14556502 | — | 2 | 1 | no | — |
| 56 | #14556502 | D4 | 1 | 1 | yes | characteristic, complemented |
| 57 | 2−1+4×C73 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | AGL(1,ℤ/8)×C73 | — | 2 | 1 | no | — |
| 59 | AGL(1,ℤ/8)×C73 | — | 4 | 1 | no | — |
| 60 | #124×C73 | — | 2 | 1 | no | — |
| 61 | #124×C73 | — | 2 | 1 | no | — |
| 62 | #124×C73 | — | 4 | 1 | no | — |
| 63 | #124×C73 | C23 | 1 | 1 | yes | characteristic |
| 64 | #120×C73 | — | 2 | 1 | no | — |
| 65 | #120×C73 | — | 4 | 1 | no | — |
| 66 | #104×C73 | — | 2 | 1 | no | — |
| 67 | #104×C73 | — | 4 | 1 | no | — |
| 68 | #101×C73 | — | 2 | 1 | no | — |
| 69 | #101×C73 | D4 | 1 | 1 | yes | characteristic, complemented |
| 70 | #11924029 | — | 4 | 1 | no | — |
| 71 | #11924028 | — | 2 | 1 | no | — |
| 72 | #11924028 | — | 4 | 1 | no | — |
| 73 | #11924027 | — | 4 | 1 | no | — |
| 74 | C2×D292 | — | 2 | 1 | no | — |
| 75 | C2×D292 | — | 4 | 1 | no | — |
| 76 | C2×D292 | — | 4 | 1 | no | — |
| 77 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊D73 | — | 8 | 1 | no | — |
| 79 | D4×D73 | — | 4 | 1 | no | — |
| 80 | D4×D73 | — | 4 | 1 | no | — |
| 81 | D4×D73 | — | 8 | 1 | no | — |
| 82 | #11924018 | — | 2 | 1 | no | — |
| 83 | #11924018 | — | 4 | 1 | no | — |
| 84 | #11924017 | — | 4 | 1 | no | — |
| 85 | #11924016 | — | 2 | 1 | no | — |
| 86 | #11924015 | — | 2 | 1 | no | — |
| 87 | #11924015 | — | 4 | 1 | no | — |
| 88 | #11924015 | — | 4 | 1 | no | — |
| 89 | #11924015 | — | 4 | 1 | no | — |
| 90 | #11924015 | — | 4 | 1 | no | — |
| 91 | #11924015 | — | 8 | 2 | no | — |
| 92 | D584 | — | 4 | 1 | no | — |
| 93 | #11924013 | — | 2 | 1 | no | — |
| 94 | #11924013 | — | 4 | 1 | no | — |
| 95 | #11924013 | — | 4 | 1 | no | — |
| 96 | #11924013 | — | 4 | 1 | no | — |
| 97 | #11924013 | — | 8 | 2 | no | — |
| 98 | #11924012 | — | 2 | 1 | no | — |
| 99 | #11924012 | — | 4 | 1 | no | — |
| 100 | #11924011 | — | 4 | 1 | no | — |
| 101 | C2×#10596831 | — | 2 | 1 | no | — |
| 102 | C2×#10596831 | — | 4 | 1 | no | — |
| 103 | C2×#10596831 | — | 4 | 1 | no | — |
| 104 | C8×D73 | — | 4 | 1 | no | — |
| 105 | C22⋊Dic73 | — | 4 | 1 | no | — |
| 106 | C22⋊Dic73 | — | 8 | 1 | no | — |
| 107 | C24×C73 | — | 2 | 1 | no | — |
| 108 | #41×C73 | — | 2 | 1 | no | — |
| 109 | #41×C73 | — | 4 | 1 | no | — |
| 110 | #41×C73 | — | 4 | 1 | no | — |
| 111 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 112 | C2×Q8×C73 | — | 4 | 1 | no | — |
| 113 | C2×Q8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C2×D4×C73 | — | 2 | 1 | no | — |
| 115 | C2×D4×C73 | — | 2 | 1 | no | — |
| 116 | C2×D4×C73 | — | 4 | 1 | no | — |
| 117 | C2×D4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | SD16×C73 | — | 4 | 1 | no | — |
| 119 | SD16×C73 | — | 8 | 1 | no | — |
| 120 | D8×C73 | — | 4 | 1 | no | — |
| 121 | D8×C73 | — | 8 | 1 | no | — |
| 122 | M16×C73 | — | 2 | 1 | no | — |
| 123 | M16×C73 | — | 4 | 1 | no | — |
| 124 | C22⋊C4×C73 | — | 2 | 1 | no | — |
| 125 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 126 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 127 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 128 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 129 | C42×C73 | — | 2 | 1 | no | — |
| 130 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C23×C73 | — | 2 | 1 | no | — |
| 132 | C23×C73 | — | 4 | 1 | no | — |
| 133 | C23×C73 | — | 8 | 1 | no | — |
| 134 | C23×C73 | — | 16 | 1 | no | — |
| 135 | C22×D73 | — | 4 | 1 | no | — |
| 136 | C22×D73 | — | 4 | 1 | no | — |
| 137 | C22×D73 | — | 8 | 1 | no | — |
| 138 | Q8×C73 | — | 2 | 1 | no | — |
| 139 | Q8×C73 | — | 4 | 1 | no | — |
| 140 | Q8×C73 | — | 4 | 1 | no | — |
| 141 | Q8×C73 | — | 8 | 1 | no | — |
| 142 | D4×C73 | — | 2 | 1 | no | — |
| 143 | D4×C73 | — | 4 | 1 | no | — |
| 144 | D4×C73 | — | 4 | 1 | no | — |
| 145 | D4×C73 | — | 4 | 1 | no | — |
| 146 | D4×C73 | — | 8 | 1 | no | — |
| 147 | D4×C73 | — | 8 | 1 | no | — |
| 148 | D4×C73 | — | 16 | 1 | no | — |
| 149 | C2×C4×C73 | — | 2 | 1 | no | — |
| 150 | C2×C4×C73 | — | 2 | 1 | no | — |
| 151 | C2×C4×C73 | — | 4 | 1 | no | — |
| 152 | C2×C4×C73 | — | 4 | 1 | no | — |
| 153 | C2×C4×C73 | — | 8 | 1 | no | — |
| 154 | C2×C4×C73 | #120 | 1 | 1 | yes | characteristic |
| 155 | C22⋊D73 | — | 4 | 1 | no | — |
| 156 | C22⋊D73 | — | 8 | 1 | no | — |
| 157 | C22⋊D73 | — | 8 | 1 | no | — |
| 158 | C22⋊D73 | — | 16 | 2 | no | — |
| 159 | C2×Dic73 | — | 4 | 1 | no | — |
| 160 | C2×Dic73 | — | 8 | 1 | no | — |
| 161 | D292 | — | 2 | 1 | no | — |
| 162 | D292 | — | 4 | 1 | no | — |
| 163 | D292 | — | 4 | 1 | no | — |
| 164 | D292 | — | 8 | 1 | no | — |
| 165 | D292 | — | 8 | 1 | no | — |
| 166 | D292 | — | 8 | 1 | no | — |
| 167 | C4×D73 | — | 4 | 1 | no | — |
| 168 | C4×D73 | — | 8 | 1 | no | — |
| 169 | Dic146 | — | 2 | 1 | no | — |
| 170 | C8×C73 | — | 4 | 1 | no | — |
| 171 | C8×C73 | — | 8 | 1 | no | — |
| 172 | #10596831 | — | 2 | 1 | no | — |
| 173 | #10596831 | — | 2 | 1 | no | — |
| 174 | #10596831 | — | 4 | 1 | no | — |
| 175 | #10596831 | — | 4 | 2 | no | — |
| 176 | C22×C73 | — | 4 | 1 | no | — |
| 177 | C22×C73 | — | 4 | 1 | no | — |
| 178 | C22×C73 | — | 8 | 1 | no | — |
| 179 | C22×C73 | — | 8 | 1 | no | — |
| 180 | C22×C73 | — | 8 | 1 | no | — |
| 181 | C22×C73 | — | 8 | 2 | no | — |
| 182 | C22×C73 | — | 8 | 1 | no | — |
| 183 | C22×C73 | — | 16 | 1 | no | — |
| 184 | C22×C73 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 185 | C2×D73 | — | 4 | 1 | no | — |
| 186 | C2×D73 | — | 8 | 1 | no | — |
| 187 | C2×D73 | — | 16 | 1 | no | — |
| 188 | C2×D73 | — | 16 | 1 | no | — |
| 189 | C2×D73 | — | 32 | 1 | no | — |
| 190 | C4×C73 | — | 2 | 1 | no | — |
| 191 | C4×C73 | — | 4 | 1 | no | — |
| 192 | C4×C73 | — | 4 | 1 | no | — |
| 193 | C4×C73 | — | 4 | 1 | no | — |
| 194 | C4×C73 | — | 8 | 1 | no | — |
| 195 | Dic73 | — | 4 | 1 | no | — |
| 196 | Dic73 | — | 16 | 1 | no | — |
| 197 | #13677 | — | 73 | 1 | no | maximal, Sylow |
| 198 | C2×C73 | — | 2 | 1 | no | — |
| 199 | C2×C73 | — | 8 | 1 | no | — |
| 200 | C2×C73 | — | 8 | 1 | no | — |
| 201 | C2×C73 | — | 16 | 1 | no | — |
| 202 | C2×C73 | #2196 | 1 | 1 | yes | characteristic |
| 203 | D73 | — | 8 | 1 | no | — |
| 204 | D73 | — | 16 | 1 | no | — |
| 205 | #3288 | — | 73 | 1 | no | — |
| 206 | #2202 | D73 | 1 | 1 | yes | characteristic, complemented |
| 207 | #2199 | — | 73 | 1 | no | — |
| 208 | #1655 | — | 73 | 1 | no | — |
| 209 | #1406 | — | 73 | 1 | no | — |
| 210 | #1404 | — | 73 | 1 | no | — |
| 211 | #1403 | — | 73 | 1 | no | — |
| 212 | C73 | #13677 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 213 | #577 | — | 146 | 1 | no | — |
| 214 | #576 | — | 146 | 1 | no | — |
| 215 | H(3,𝔽4) | C2×D73 | 1 | 1 | yes | characteristic, complemented |
| 216 | #496 | — | 73 | 1 | no | — |
| 217 | #496 | — | 146 | 1 | no | — |
| 218 | #472 | — | 146 | 1 | no | — |
| 219 | #471 | — | 146 | 1 | no | — |
| 220 | B(4,𝔽2) | — | 146 | 1 | no | — |
| 221 | #455 | — | 73 | 1 | no | — |
| 222 | #454 | — | 2 | 1 | no | — |
| 223 | #454 | C2×D73 | 1 | 1 | yes | characteristic |
| 224 | #453 | — | 146 | 1 | no | — |
| 225 | #444 | — | 146 | 1 | no | — |
| 226 | #355 | — | 2 | 1 | no | — |
| 227 | #355 | C2×D73 | 1 | 1 | yes | characteristic, complemented |
| 228 | #354 | — | 73 | 1 | no | — |
| 229 | AΣL(1,𝔽16) | — | 146 | 1 | no | — |
| 230 | #329 | — | 73 | 1 | no | — |
| 231 | #329 | — | 146 | 1 | no | — |
| 232 | 2−1+4 | C22⋊D73 | 1 | 1 | yes | characteristic, complemented |
| 233 | H(5,𝔽2) | — | 73 | 1 | no | — |
| 234 | H(5,𝔽2) | — | 146 | 1 | no | — |
| 235 | #137 | — | 292 | 1 | no | — |
| 236 | #137 | — | 146 | 1 | no | — |
| 237 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 238 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 239 | AGL(1,ℤ/8) | — | 292 | 1 | no | — |
| 240 | AGL(1,ℤ/8) | — | 292 | 1 | no | — |
| 241 | AGL(1,ℤ/8) | — | 292 | 1 | no | — |
| 242 | AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 243 | AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 244 | #135 | — | 292 | 1 | no | — |
| 245 | #135 | — | 292 | 1 | no | — |
| 246 | #135 | — | 146 | 1 | no | — |
| 247 | C2×SD16 | — | 292 | 1 | no | — |
| 248 | C2×SD16 | — | 292 | 1 | no | — |
| 249 | C2×SD16 | — | 146 | 1 | no | — |
| 250 | C2×D8 | — | 292 | 1 | no | — |
| 251 | C2×D8 | — | 292 | 1 | no | — |
| 252 | C2×D8 | — | 146 | 1 | no | — |
| 253 | #131 | — | 146 | 1 | no | — |
| 254 | #131 | — | 146 | 1 | no | — |
| 255 | #127 | — | 73 | 1 | no | — |
| 256 | #124 | — | 2 | 1 | no | — |
| 257 | #124 | — | 2 | 1 | no | — |
| 258 | #124 | — | 4 | 1 | no | — |
| 259 | #124 | C22×D73 | 1 | 1 | yes | characteristic |
| 260 | #120 | — | 2 | 1 | no | — |
| 261 | #120 | — | 4 | 1 | no | — |
| 262 | #120 | — | 292 | 1 | no | — |
| 263 | #108 | — | 146 | 1 | no | — |
| 264 | #104 | — | 2 | 1 | no | — |
| 265 | #104 | — | 4 | 1 | no | — |
| 266 | #104 | — | 146 | 1 | no | — |
| 267 | #101 | — | 2 | 1 | no | — |
| 268 | #101 | C22⋊D73 | 1 | 1 | yes | characteristic, complemented |
| 269 | #100 | — | 73 | 1 | no | — |
| 270 | #100 | — | 146 | 1 | no | — |
| 271 | #99 | — | 292 | 1 | no | — |
| 272 | #99 | — | 146 | 1 | no | — |
| 273 | #97 | — | 73 | 1 | no | — |
| 274 | #97 | — | 146 | 1 | no | — |
| 275 | C24 | — | 2 | 1 | no | — |
| 276 | #41 | — | 2 | 1 | no | — |
| 277 | #41 | — | 4 | 1 | no | — |
| 278 | #41 | — | 4 | 1 | no | — |
| 279 | #41 | — | 292 | 1 | no | — |
| 280 | #41 | — | 292 | 1 | no | — |
| 281 | #41 | — | 292 | 1 | no | — |
| 282 | #41 | — | 146 | 1 | no | — |
| 283 | C2×Q8 | — | 2 | 1 | no | — |
| 284 | C2×Q8 | — | 4 | 1 | no | — |
| 285 | C2×Q8 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 286 | C2×D4 | — | 2 | 1 | no | — |
| 287 | C2×D4 | — | 2 | 1 | no | — |
| 288 | C2×D4 | — | 4 | 1 | no | — |
| 289 | C2×D4 | — | 292 | 1 | no | — |
| 290 | C2×D4 | — | 292 | 1 | no | — |
| 291 | C2×D4 | — | 292 | 1 | no | — |
| 292 | C2×D4 | — | 292 | 1 | no | — |
| 293 | C2×D4 | — | 292 | 1 | no | — |
| 294 | C2×D4 | — | 584 | 1 | no | — |
| 295 | C2×D4 | — | 584 | 1 | no | — |
| 296 | C2×D4 | — | 146 | 1 | no | — |
| 297 | C2×D4 | D4×D73 | 1 | 1 | yes | characteristic |
| 298 | Q16 | — | 292 | 1 | no | — |
| 299 | Q16 | — | 146 | 1 | no | — |
| 300 | SD16 | — | 4 | 1 | no | — |
| 301 | SD16 | — | 8 | 1 | no | — |
| 302 | SD16 | — | 292 | 1 | no | — |
| 303 | SD16 | — | 292 | 1 | no | — |
| 304 | SD16 | — | 292 | 1 | no | — |
| 305 | SD16 | — | 292 | 1 | no | — |
| 306 | SD16 | — | 292 | 1 | no | — |
| 307 | SD16 | — | 584 | 2 | no | — |
| 308 | SD16 | — | 146 | 1 | no | — |
| 309 | SD16 | — | 146 | 1 | no | — |
| 310 | D8 | — | 4 | 1 | no | — |
| 311 | D8 | — | 8 | 1 | no | — |
| 312 | D8 | — | 292 | 1 | no | — |
| 313 | D8 | — | 292 | 1 | no | — |
| 314 | D8 | — | 292 | 1 | no | — |
| 315 | D8 | — | 292 | 1 | no | — |
| 316 | D8 | — | 584 | 2 | no | — |
| 317 | D8 | — | 146 | 1 | no | — |
| 318 | M16 | — | 2 | 1 | no | — |
| 319 | M16 | — | 4 | 1 | no | — |
| 320 | M16 | — | 292 | 1 | no | — |
| 321 | M16 | — | 292 | 1 | no | — |
| 322 | M16 | — | 146 | 1 | no | — |
| 323 | C2×C8 | — | 292 | 1 | no | — |
| 324 | C2×C8 | — | 292 | 1 | no | — |
| 325 | C2×C8 | — | 292 | 1 | no | — |
| 326 | C2×C8 | — | 146 | 1 | no | — |
| 327 | C22⋊C4 | — | 2 | 1 | no | — |
| 328 | C22⋊C4 | — | 4 | 1 | no | — |
| 329 | C22⋊C4 | — | 4 | 1 | no | — |
| 330 | C22⋊C4 | — | 4 | 1 | no | — |
| 331 | C22⋊C4 | — | 4 | 1 | no | — |
| 332 | C22⋊C4 | — | 292 | 1 | no | — |
| 333 | C22⋊C4 | — | 584 | 1 | no | — |
| 334 | C42 | — | 2 | 1 | no | — |
| 335 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 336 | C23 | — | 2 | 1 | no | — |
| 337 | C23 | — | 4 | 1 | no | — |
| 338 | C23 | — | 8 | 1 | no | — |
| 339 | C23 | — | 16 | 1 | no | — |
| 340 | C23 | — | 292 | 1 | no | — |
| 341 | C23 | — | 292 | 1 | no | — |
| 342 | C23 | — | 584 | 1 | no | — |
| 343 | Q8 | — | 2 | 1 | no | — |
| 344 | Q8 | — | 4 | 1 | no | — |
| 345 | Q8 | — | 4 | 1 | no | — |
| 346 | Q8 | — | 8 | 1 | no | — |
| 347 | Q8 | — | 146 | 1 | no | — |
| 348 | D4 | — | 2 | 1 | no | — |
| 349 | D4 | — | 4 | 1 | no | — |
| 350 | D4 | — | 4 | 1 | no | — |
| 351 | D4 | — | 4 | 1 | no | — |
| 352 | D4 | — | 8 | 1 | no | — |
| 353 | D4 | — | 8 | 1 | no | — |
| 354 | D4 | — | 16 | 1 | no | — |
| 355 | D4 | — | 292 | 1 | no | — |
| 356 | D4 | — | 292 | 1 | no | — |
| 357 | D4 | — | 292 | 1 | no | — |
| 358 | D4 | — | 584 | 1 | no | — |
| 359 | D4 | — | 584 | 1 | no | — |
| 360 | D4 | — | 584 | 1 | no | — |
| 361 | D4 | — | 584 | 1 | no | — |
| 362 | D4 | — | 584 | 1 | no | — |
| 363 | D4 | — | 1168 | 2 | no | — |
| 364 | D4 | — | 146 | 1 | no | — |
| 365 | C2×C4 | — | 2 | 1 | no | — |
| 366 | C2×C4 | — | 2 | 1 | no | — |
| 367 | C2×C4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 8 | 1 | no | — |
| 370 | C2×C4 | — | 292 | 1 | no | — |
| 371 | C2×C4 | — | 292 | 1 | no | — |
| 372 | C2×C4 | — | 584 | 1 | no | — |
| 373 | C2×C4 | — | 584 | 1 | no | — |
| 374 | C2×C4 | #14556559 | 1 | 1 | yes | characteristic |
| 375 | C8 | — | 4 | 1 | no | — |
| 376 | C8 | — | 8 | 1 | no | — |
| 377 | C8 | — | 292 | 1 | no | — |
| 378 | C8 | — | 292 | 2 | no | — |
| 379 | C8 | — | 146 | 1 | no | — |
| 380 | C8 | — | 146 | 1 | no | — |
| 381 | C22 | — | 4 | 1 | no | — |
| 382 | C22 | — | 4 | 1 | no | — |
| 383 | C22 | — | 8 | 1 | no | — |
| 384 | C22 | — | 8 | 1 | no | — |
| 385 | C22 | — | 8 | 1 | no | — |
| 386 | C22 | — | 8 | 2 | no | — |
| 387 | C22 | — | 8 | 1 | no | — |
| 388 | C22 | — | 16 | 1 | no | — |
| 389 | C22 | — | 2336 | 1 | no | — |
| 390 | C22 | — | 292 | 1 | no | — |
| 391 | C22 | — | 584 | 1 | no | — |
| 392 | C22 | — | 1168 | 1 | no | — |
| 393 | C22 | — | 1168 | 1 | no | — |
| 394 | C22 | #17988773 | 1 | 1 | yes | characteristic |
| 395 | C4 | — | 2 | 1 | no | — |
| 396 | C4 | — | 4 | 1 | no | — |
| 397 | C4 | — | 4 | 1 | no | — |
| 398 | C4 | — | 4 | 1 | no | — |
| 399 | C4 | — | 8 | 1 | no | — |
| 400 | C4 | — | 292 | 1 | no | — |
| 401 | C4 | — | 1168 | 1 | no | — |
| 402 | C2 | — | 2 | 1 | no | — |
| 403 | C2 | — | 8 | 1 | no | — |
| 404 | C2 | — | 8 | 1 | no | — |
| 405 | C2 | — | 16 | 1 | no | — |
| 406 | C2 | — | 584 | 1 | no | — |
| 407 | C2 | — | 1168 | 1 | no | — |
| 408 | C2 | #22611913 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22621699 | C2 | semidirect |
| 2. #22611932 | C2 | semidirect |
| 3. #22609220 | C2 | semidirect |
| 4. #22608089 | C2 | semidirect |
| 5. #22608082 | C2 | semidirect |
| 6. #22608078 | C2 | semidirect |
| 7. C73×#2202 | C2 | semidirect |
| 18. #17988382 | C22 | semidirect |
| 21. #17988327 | C22 | semidirect |
| 22. H(3,𝔽4)×C73 | C22 | semidirect |
| 26. #355×C73 | C22 | semidirect |
| 47. #14556588 | D4 | semidirect |
| 56. #14556502 | D4 | semidirect |
| 57. 2−1+4×C73 | D4 | semidirect |
| 69. #101×C73 | D4 | semidirect |
| 206. #2202 | D73 | semidirect |
| 212. C73 | #13677 | semidirect |
| 215. H(3,𝔽4) | C2×D73 | semidirect |
| 227. #355 | C2×D73 | semidirect |
| 232. 2−1+4 | C22⋊D73 | semidirect |
| 268. #101 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621699 | 2 |
| #22611932 | 2 |
| #22609220 | 2 |
| #22608089 | 2 |
| #22608082 | 2 |
| #22608078 | 2 |
| C73×#2202 | 2 |
| #13677 | 73 |