Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 454 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 | #24917912 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #24909145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #24909127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #24905621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #24905620 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #24905619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C83×#1406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14581819 | — | 2 | 1 | no | — |
| 9 | C2×#14581816 | — | 2 | 1 | no | — |
| 10 | #19128250 | C22 | 1 | 1 | yes | characteristic |
| 11 | #127×D83 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #19128091 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19128090 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #19128088 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #19128076 | — | 2 | 1 | no | — |
| 16 | #19128072 | — | 2 | 1 | no | — |
| 17 | #19127684 | — | 2 | 1 | no | — |
| 18 | #19127673 | — | 2 | 1 | no | — |
| 19 | #19127653 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #19127499 | — | 2 | 1 | no | — |
| 21 | #19127498 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #19127496 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #19127493 | — | 2 | 1 | no | — |
| 24 | #496×C83 | C22 | 1 | 1 | yes | characteristic |
| 25 | #355×C83 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #354×C83 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#13050591 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#13050589 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×D4×D83 | — | 2 | 1 | no | — |
| 30 | C2×D4×D83 | — | 4 | 1 | no | — |
| 31 | #14581819 | — | 4 | 2 | no | — |
| 32 | #14581819 | — | 4 | 2 | no | — |
| 33 | #14581816 | — | 4 | 2 | no | — |
| 34 | #14581816 | — | 4 | 2 | no | — |
| 35 | C2×#13050579 | — | 2 | 1 | no | — |
| 36 | C2×#13050578 | — | 2 | 1 | no | — |
| 37 | C2×#13050577 | — | 2 | 1 | no | — |
| 38 | C2×D664 | — | 2 | 1 | no | — |
| 39 | C2×#13050575 | — | 2 | 1 | no | — |
| 40 | C2×#13050575 | — | 2 | 1 | no | — |
| 41 | C2×#13050573 | — | 2 | 1 | no | — |
| 42 | M16×D83 | — | 4 | 1 | no | — |
| 43 | #14581790 | D4 | 1 | 1 | yes | characteristic |
| 44 | #14581789 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #14581788 | — | 2 | 1 | no | — |
| 46 | #14581788 | — | 4 | 1 | no | — |
| 47 | #14581788 | D4 | 1 | 1 | yes | characteristic |
| 48 | #14581780 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #14581765 | — | 4 | 1 | no | — |
| 50 | (C22⋊D83)⋊C4 | — | 4 | 1 | no | — |
| 51 | #14581748 | — | 4 | 1 | no | — |
| 52 | C42×D83 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #14581711 | — | 2 | 1 | no | — |
| 54 | #14581708 | — | 4 | 1 | no | — |
| 55 | #14581707 | — | 2 | 1 | no | — |
| 56 | #14581706 | — | 4 | 1 | no | — |
| 57 | #14581703 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C8×Dic83 | — | 2 | 1 | no | — |
| 59 | C2×SD16×C83 | — | 2 | 1 | no | — |
| 60 | C2×D8×C83 | — | 2 | 1 | no | — |
| 61 | #127×C83 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | #124×C83 | C23 | 1 | 1 | yes | characteristic |
| 63 | #101×C83 | — | 2 | 1 | no | — |
| 64 | #99×C83 | — | 2 | 1 | no | — |
| 65 | #97×C83 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C23×D83 | — | 4 | 1 | no | — |
| 67 | #13050591 | — | 4 | 1 | no | — |
| 68 | #13050591 | — | 4 | 1 | no | — |
| 69 | #13050589 | — | 4 | 1 | no | — |
| 70 | #13050589 | — | 4 | 1 | no | — |
| 71 | C2×Dic166 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C2×D332 | — | 2 | 1 | no | — |
| 73 | C2×D332 | — | 2 | 1 | no | — |
| 74 | C2×D332 | — | 4 | 1 | no | — |
| 75 | C2×D332 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 76 | C2×C22⋊D83 | — | 2 | 1 | no | — |
| 77 | C2×C22⋊D83 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊D83 | — | 4 | 2 | no | — |
| 79 | C2×C22⋊D83 | — | 4 | 1 | no | — |
| 80 | D4×D83 | — | 4 | 1 | no | — |
| 81 | D4×D83 | — | 4 | 1 | no | — |
| 82 | D4×D83 | — | 4 | 1 | no | — |
| 83 | D4×D83 | — | 4 | 1 | no | — |
| 84 | D4×D83 | — | 8 | 4 | no | — |
| 85 | C22×Dic83 | — | 2 | 1 | no | — |
| 86 | C2×C4×D83 | — | 2 | 1 | no | — |
| 87 | C2×C4×D83 | — | 2 | 1 | no | — |
| 88 | C2×C4×D83 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 89 | #13050579 | — | 4 | 2 | no | — |
| 90 | #13050578 | — | 4 | 2 | no | — |
| 91 | #13050577 | — | 4 | 2 | no | — |
| 92 | D664 | — | 4 | 2 | no | — |
| 93 | #13050575 | — | 4 | 2 | no | — |
| 94 | #13050575 | — | 4 | 2 | no | — |
| 95 | #13050574 | — | 4 | 1 | no | — |
| 96 | #13050573 | — | 2 | 2 | no | — |
| 97 | #13050573 | — | 2 | 2 | no | — |
| 98 | #13050573 | — | 8 | 1 | no | — |
| 99 | C2×C83⋊C8 | — | 2 | 1 | no | — |
| 100 | C8×D83 | — | 8 | 1 | no | — |
| 101 | Dic83⋊C4 | — | 4 | 1 | no | — |
| 102 | Dic83⋊C4 | — | 8 | 1 | no | — |
| 103 | C22⋊Dic83 | — | 4 | 1 | no | — |
| 104 | (C2×D83)⋊C4 | — | 4 | 1 | no | — |
| 105 | C4×Dic83 | — | 2 | 1 | no | — |
| 106 | C4×Dic83 | — | 8 | 1 | no | — |
| 107 | C4×Dic83 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C2×Q8×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×D4×C83 | — | 2 | 1 | no | — |
| 110 | C2×D4×C83 | — | 4 | 1 | no | — |
| 111 | C2×D4×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | SD16×C83 | — | 4 | 2 | no | — |
| 113 | D8×C83 | — | 4 | 2 | no | — |
| 114 | M16×C83 | — | 4 | 1 | no | — |
| 115 | C2×C8×C83 | — | 2 | 1 | no | — |
| 116 | C22⋊C4×C83 | — | 4 | 1 | no | — |
| 117 | C22⋊C4×C83 | — | 4 | 1 | no | — |
| 118 | C42×C83 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C23×C83 | — | 2 | 1 | no | — |
| 120 | C23×C83 | — | 4 | 1 | no | — |
| 121 | C22×D83 | — | 2 | 1 | no | — |
| 122 | C22×D83 | — | 4 | 1 | no | — |
| 123 | C22×D83 | — | 8 | 1 | no | — |
| 124 | C22×D83 | — | 8 | 1 | no | — |
| 125 | C22×D83 | — | 8 | 4 | no | — |
| 126 | C22×D83 | #99 | 1 | 1 | yes | characteristic |
| 127 | Q8×C83 | — | 4 | 1 | no | — |
| 128 | D4×C83 | — | 4 | 1 | no | — |
| 129 | D4×C83 | — | 4 | 1 | no | — |
| 130 | D4×C83 | — | 4 | 1 | no | — |
| 131 | D4×C83 | — | 8 | 2 | no | — |
| 132 | C2×C4×C83 | — | 2 | 1 | no | — |
| 133 | C2×C4×C83 | — | 2 | 1 | no | — |
| 134 | C2×C4×C83 | — | 8 | 1 | no | — |
| 135 | C2×C4×C83 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C22⋊D83 | — | 8 | 4 | no | — |
| 137 | C22⋊D83 | — | 8 | 2 | no | — |
| 138 | C22⋊D83 | — | 8 | 1 | no | — |
| 139 | C22⋊D83 | — | 8 | 1 | no | — |
| 140 | C22⋊D83 | — | 8 | 1 | no | — |
| 141 | C2×Dic83 | — | 2 | 1 | no | — |
| 142 | C2×Dic83 | — | 2 | 1 | no | — |
| 143 | C2×Dic83 | — | 4 | 1 | no | — |
| 144 | C2×Dic83 | — | 4 | 1 | no | — |
| 145 | C2×Dic83 | — | 8 | 1 | no | — |
| 146 | C2×Dic83 | #99 | 1 | 1 | yes | characteristic |
| 147 | D332 | — | 4 | 1 | no | — |
| 148 | D332 | — | 4 | 1 | no | — |
| 149 | D332 | — | 4 | 1 | no | — |
| 150 | D332 | — | 8 | 1 | no | — |
| 151 | D332 | — | 8 | 2 | no | — |
| 152 | C4×D83 | — | 2 | 1 | no | — |
| 153 | C4×D83 | — | 2 | 1 | no | — |
| 154 | C4×D83 | — | 4 | 2 | no | — |
| 155 | C4×D83 | — | 4 | 1 | no | — |
| 156 | C4×D83 | — | 4 | 1 | no | — |
| 157 | Dic166 | — | 4 | 1 | no | — |
| 158 | C8×C83 | — | 2 | 2 | no | — |
| 159 | C8×C83 | — | 8 | 1 | no | — |
| 160 | C83⋊C8 | — | 2 | 2 | no | — |
| 161 | C83⋊C8 | — | 8 | 1 | no | — |
| 162 | C22×C83 | — | 4 | 1 | no | — |
| 163 | C22×C83 | — | 8 | 1 | no | — |
| 164 | C22×C83 | — | 8 | 2 | no | — |
| 165 | C22×C83 | — | 8 | 1 | no | — |
| 166 | C22×C83 | C2×#99 | 1 | 1 | yes | characteristic |
| 167 | C2×D83 | — | 2 | 1 | no | — |
| 168 | C2×D83 | — | 4 | 1 | no | — |
| 169 | C2×D83 | — | 4 | 1 | no | — |
| 170 | C2×D83 | — | 8 | 1 | no | — |
| 171 | C2×D83 | — | 8 | 2 | no | — |
| 172 | C2×D83 | — | 8 | 1 | no | — |
| 173 | C2×D83 | — | 16 | 2 | no | — |
| 174 | C2×D83 | — | 16 | 2 | no | — |
| 175 | C4×C83 | — | 2 | 1 | no | — |
| 176 | C4×C83 | — | 4 | 1 | no | — |
| 177 | C4×C83 | — | 4 | 1 | no | — |
| 178 | C4×C83 | — | 16 | 1 | no | — |
| 179 | Dic83 | — | 2 | 2 | no | — |
| 180 | Dic83 | — | 4 | 1 | no | — |
| 181 | Dic83 | — | 16 | 1 | no | — |
| 182 | Dic83 | #353 | 1 | 1 | yes | characteristic |
| 183 | Dic83 | #353 | 1 | 1 | yes | characteristic |
| 184 | #13579 | — | 83 | 1 | no | maximal, Sylow |
| 185 | C2×C83 | — | 2 | 1 | no | — |
| 186 | C2×C83 | — | 8 | 1 | no | — |
| 187 | C2×C83 | — | 16 | 1 | no | — |
| 188 | C2×C83 | C2×#353 | 1 | 1 | yes | characteristic |
| 189 | D83 | — | 4 | 1 | no | — |
| 190 | D83 | — | 8 | 1 | no | — |
| 191 | D83 | — | 16 | 1 | no | — |
| 192 | #3151 | — | 83 | 1 | no | — |
| 193 | #2132 | — | 83 | 1 | no | — |
| 194 | #2126 | — | 83 | 1 | no | — |
| 195 | #1406 | — | 83 | 1 | no | — |
| 196 | #1406 | — | 83 | 1 | no | — |
| 197 | #1406 | — | 83 | 1 | no | — |
| 198 | #1406 | D83 | 1 | 1 | yes | characteristic, complemented |
| 199 | C83 | #13579 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 200 | C2×AGL(1,ℤ/8) | — | 166 | 1 | no | — |
| 201 | C2×AGL(1,ℤ/8) | — | 166 | 1 | no | — |
| 202 | #532 | — | 83 | 1 | no | — |
| 203 | C2×#127 | — | 83 | 1 | no | — |
| 204 | #496 | — | 83 | 1 | no | — |
| 205 | #496 | — | 83 | 1 | no | — |
| 206 | #496 | — | 83 | 1 | no | — |
| 207 | #496 | C2×D83 | 1 | 1 | yes | characteristic |
| 208 | #493 | — | 166 | 1 | no | — |
| 209 | #492 | — | 166 | 1 | no | — |
| 210 | #413 | — | 166 | 1 | no | — |
| 211 | #410 | — | 166 | 1 | no | — |
| 212 | C4×M16 | — | 83 | 1 | no | — |
| 213 | #356 | — | 166 | 1 | no | — |
| 214 | #355 | — | 83 | 1 | no | — |
| 215 | #355 | C2×D83 | 1 | 1 | yes | characteristic, complemented |
| 216 | #354 | — | 83 | 1 | no | — |
| 217 | #354 | C2×D83 | 1 | 1 | yes | characteristic, complemented |
| 218 | #353 | — | 166 | 1 | no | — |
| 219 | C2×#41 | — | 83 | 1 | no | — |
| 220 | C2×#41 | — | 83 | 1 | no | — |
| 221 | C22×D4 | — | 332 | 1 | no | — |
| 222 | C22×D4 | — | 166 | 1 | no | — |
| 223 | AGL(1,ℤ/8) | — | 332 | 2 | no | — |
| 224 | AGL(1,ℤ/8) | — | 332 | 2 | no | — |
| 225 | AGL(1,ℤ/8) | — | 332 | 2 | no | — |
| 226 | AGL(1,ℤ/8) | — | 332 | 2 | no | — |
| 227 | C2×SD16 | — | 2 | 1 | no | — |
| 228 | C2×SD16 | — | 166 | 1 | no | — |
| 229 | C2×SD16 | — | 166 | 1 | no | — |
| 230 | C2×SD16 | — | 166 | 1 | no | — |
| 231 | C2×D8 | — | 2 | 1 | no | — |
| 232 | C2×D8 | — | 166 | 1 | no | — |
| 233 | C2×D8 | — | 166 | 1 | no | — |
| 234 | C2×D8 | — | 166 | 1 | no | — |
| 235 | C2×M16 | — | 332 | 1 | no | — |
| 236 | C2×M16 | — | 166 | 1 | no | — |
| 237 | C4⋊Q8 | — | 83 | 1 | no | — |
| 238 | #127 | — | 332 | 1 | no | — |
| 239 | #127 | — | 83 | 1 | no | — |
| 240 | #127 | — | 83 | 1 | no | — |
| 241 | #127 | — | 166 | 1 | no | — |
| 242 | #127 | C4×D83 | 1 | 1 | yes | characteristic |
| 243 | #124 | — | 83 | 1 | no | — |
| 244 | #124 | C22×D83 | 1 | 1 | yes | characteristic |
| 245 | #121 | — | 332 | 1 | no | — |
| 246 | C4×D4 | — | 332 | 1 | no | — |
| 247 | #117 | — | 332 | 1 | no | — |
| 248 | C2×C42 | — | 83 | 1 | no | — |
| 249 | #101 | — | 2 | 1 | no | — |
| 250 | #101 | — | 166 | 1 | no | — |
| 251 | #100 | — | 332 | 1 | no | — |
| 252 | #99 | — | 2 | 1 | no | — |
| 253 | #99 | — | 332 | 1 | no | — |
| 254 | #99 | — | 166 | 1 | no | — |
| 255 | #97 | — | 83 | 1 | no | — |
| 256 | #97 | C4×D83 | 1 | 1 | yes | characteristic |
| 257 | C4×C8 | — | 166 | 1 | no | — |
| 258 | C24 | — | 332 | 1 | no | — |
| 259 | #41 | — | 332 | 1 | no | — |
| 260 | #41 | — | 332 | 1 | no | — |
| 261 | #41 | — | 332 | 1 | no | — |
| 262 | #41 | — | 332 | 1 | no | — |
| 263 | C2×Q8 | — | 83 | 1 | no | — |
| 264 | C2×Q8 | D4×D83 | 1 | 1 | yes | characteristic |
| 265 | C2×D4 | — | 2 | 1 | no | — |
| 266 | C2×D4 | — | 4 | 1 | no | — |
| 267 | C2×D4 | — | 332 | 1 | no | — |
| 268 | C2×D4 | — | 332 | 1 | no | — |
| 269 | C2×D4 | — | 332 | 1 | no | — |
| 270 | C2×D4 | — | 332 | 1 | no | — |
| 271 | C2×D4 | — | 332 | 1 | no | — |
| 272 | C2×D4 | — | 332 | 1 | no | — |
| 273 | C2×D4 | — | 332 | 1 | no | — |
| 274 | C2×D4 | — | 332 | 2 | no | — |
| 275 | C2×D4 | — | 83 | 1 | no | — |
| 276 | C2×D4 | — | 664 | 4 | no | — |
| 277 | C2×D4 | — | 166 | 1 | no | — |
| 278 | C2×D4 | — | 166 | 1 | no | — |
| 279 | C2×D4 | — | 166 | 1 | no | — |
| 280 | C2×D4 | D4×D83 | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | — | 83 | 1 | no | — |
| 282 | C22×C4 | — | 166 | 1 | no | — |
| 283 | C22×C4 | — | 166 | 1 | no | — |
| 284 | C22×C4 | — | 166 | 1 | no | — |
| 285 | SD16 | — | 4 | 2 | no | — |
| 286 | SD16 | — | 332 | 2 | no | — |
| 287 | SD16 | — | 332 | 2 | no | — |
| 288 | SD16 | — | 332 | 2 | no | — |
| 289 | D8 | — | 4 | 2 | no | — |
| 290 | D8 | — | 332 | 2 | no | — |
| 291 | D8 | — | 332 | 2 | no | — |
| 292 | D8 | — | 332 | 2 | no | — |
| 293 | M16 | — | 4 | 1 | no | — |
| 294 | M16 | — | 332 | 1 | no | — |
| 295 | M16 | — | 664 | 1 | no | — |
| 296 | M16 | — | 166 | 2 | no | — |
| 297 | M16 | — | 166 | 2 | no | — |
| 298 | C2×C8 | — | 2 | 1 | no | — |
| 299 | C2×C8 | — | 664 | 1 | no | — |
| 300 | C2×C8 | — | 166 | 1 | no | — |
| 301 | C4⋊C4 | — | 332 | 1 | no | — |
| 302 | C4⋊C4 | — | 664 | 1 | no | — |
| 303 | C22⋊C4 | — | 4 | 1 | no | — |
| 304 | C22⋊C4 | — | 4 | 1 | no | — |
| 305 | C22⋊C4 | — | 332 | 1 | no | — |
| 306 | C22⋊C4 | — | 332 | 1 | no | — |
| 307 | C42 | — | 83 | 1 | no | — |
| 308 | C42 | — | 664 | 1 | no | — |
| 309 | C42 | — | 166 | 1 | no | — |
| 310 | C42 | C2×C4×D83 | 1 | 1 | yes | characteristic |
| 311 | C23 | — | 2 | 1 | no | — |
| 312 | C23 | — | 4 | 1 | no | — |
| 313 | C23 | — | 332 | 1 | no | — |
| 314 | C23 | — | 83 | 1 | no | — |
| 315 | C23 | — | 664 | 4 | no | — |
| 316 | C23 | — | 664 | 1 | no | — |
| 317 | C23 | — | 664 | 1 | no | — |
| 318 | C23 | — | 166 | 1 | no | — |
| 319 | Q8 | — | 4 | 1 | no | — |
| 320 | Q8 | — | 332 | 1 | no | — |
| 321 | D4 | — | 4 | 1 | no | — |
| 322 | D4 | — | 4 | 1 | no | — |
| 323 | D4 | — | 4 | 1 | no | — |
| 324 | D4 | — | 8 | 2 | no | — |
| 325 | D4 | — | 332 | 1 | no | — |
| 326 | D4 | — | 332 | 1 | no | — |
| 327 | D4 | — | 332 | 1 | no | — |
| 328 | D4 | — | 664 | 1 | no | — |
| 329 | D4 | — | 664 | 2 | no | — |
| 330 | D4 | — | 664 | 1 | no | — |
| 331 | D4 | — | 664 | 1 | no | — |
| 332 | D4 | — | 664 | 1 | no | — |
| 333 | D4 | — | 664 | 4 | no | — |
| 334 | D4 | — | 664 | 2 | no | — |
| 335 | C2×C4 | — | 2 | 1 | no | — |
| 336 | C2×C4 | — | 2 | 1 | no | — |
| 337 | C2×C4 | — | 8 | 1 | no | — |
| 338 | C2×C4 | — | 332 | 1 | no | — |
| 339 | C2×C4 | — | 332 | 1 | no | — |
| 340 | C2×C4 | — | 332 | 2 | no | — |
| 341 | C2×C4 | — | 332 | 1 | no | — |
| 342 | C2×C4 | — | 332 | 1 | no | — |
| 343 | C2×C4 | — | 83 | 1 | no | — |
| 344 | C2×C4 | — | 664 | 1 | no | — |
| 345 | C2×C4 | — | 166 | 1 | no | — |
| 346 | C2×C4 | — | 166 | 1 | no | — |
| 347 | C2×C4 | — | 166 | 1 | no | — |
| 348 | C2×C4 | — | 166 | 1 | no | — |
| 349 | C2×C4 | C22⋊C4×D83 | 1 | 1 | yes | characteristic |
| 350 | C8 | — | 2 | 2 | no | — |
| 351 | C8 | — | 8 | 1 | no | — |
| 352 | C8 | — | 664 | 1 | no | — |
| 353 | C8 | — | 166 | 2 | no | — |
| 354 | C22 | — | 4 | 1 | no | — |
| 355 | C22 | — | 8 | 1 | no | — |
| 356 | C22 | — | 8 | 2 | no | — |
| 357 | C22 | — | 8 | 1 | no | — |
| 358 | C22 | — | 1328 | 2 | no | — |
| 359 | C22 | — | 1328 | 2 | no | — |
| 360 | C22 | — | 332 | 1 | no | — |
| 361 | C22 | — | 332 | 1 | no | — |
| 362 | C22 | — | 664 | 2 | no | — |
| 363 | C22 | — | 664 | 1 | no | — |
| 364 | C22 | — | 664 | 1 | no | — |
| 365 | C22 | — | 166 | 1 | no | — |
| 366 | C22 | #99×D83 | 1 | 1 | yes | characteristic |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 4 | 1 | no | — |
| 369 | C4 | — | 4 | 1 | no | — |
| 370 | C4 | — | 16 | 1 | no | — |
| 371 | C4 | — | 1328 | 1 | no | — |
| 372 | C4 | — | 332 | 1 | no | — |
| 373 | C4 | — | 83 | 1 | no | — |
| 374 | C4 | — | 83 | 1 | no | — |
| 375 | C4 | — | 166 | 2 | no | — |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 8 | 1 | no | — |
| 378 | C2 | — | 16 | 1 | no | — |
| 379 | C2 | — | 1328 | 1 | no | — |
| 380 | C2 | — | 332 | 1 | no | — |
| 381 | C2 | — | 664 | 1 | no | — |
| 382 | C2 | #353×D83 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #24909145 | C2 | semidirect |
| 3. #24909127 | C2 | semidirect |
| 4. #24905621 | C2 | semidirect |
| 5. #24905620 | C2 | semidirect |
| 6. #24905619 | C2 | semidirect |
| 7. C83×#1406 | C2 | semidirect |
| 11. #127×D83 | C4 | semidirect |
| 13. #19128090 | C4 | semidirect |
| 14. #19128088 | C4 | semidirect |
| 19. #19127653 | C4 | semidirect |
| 21. #19127498 | C22 | semidirect |
| 22. #19127496 | C22 | semidirect |
| 25. #355×C83 | C22 | semidirect |
| 26. #354×C83 | C22 | semidirect |
| 198. #1406 | D83 | semidirect |
| 199. C83 | #13579 | semidirect |
| 215. #355 | C2×D83 | semidirect |
| 217. #354 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917912 | 2 |
| #24909145 | 2 |
| #24909127 | 2 |
| #24905621 | 2 |
| #24905620 | 2 |
| #24905619 | 2 |
| C83×#1406 | 2 |
| #13579 | 83 |