Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
480 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 61 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 | #24918250 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #24909394 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #24909374 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #24908462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #24905474 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #24905386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C83×#1347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D664 | C22 | 1 | 1 | yes | characteristic |
| 9 | #19128211 | — | 2 | 1 | no | — |
| 10 | C2×#14581767 | — | 2 | 1 | no | — |
| 11 | C2×#14581737 | — | 2 | 1 | no | — |
| 12 | C2×#14581733 | — | 2 | 1 | no | — |
| 13 | #19128044 | — | 2 | 1 | no | — |
| 14 | #19128023 | — | 2 | 1 | no | — |
| 15 | #19127942 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19127928 | — | 2 | 1 | no | — |
| 17 | #19127864 | — | 2 | 1 | no | — |
| 18 | #19127843 | — | 2 | 1 | no | — |
| 19 | C2×#14581712 | — | 2 | 1 | no | — |
| 20 | C2×(C2×D83)⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | #19127503 | — | 2 | 1 | no | — |
| 22 | #19127501 | — | 2 | 1 | no | — |
| 23 | C22⋊(C83⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 24 | #466×C83 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22⋊C16×C83 | C22 | 1 | 1 | yes | characteristic |
| 26 | #340×C83 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#13050589 | — | 2 | 1 | no | — |
| 28 | C22×D332 | — | 2 | 1 | no | — |
| 29 | C22×D332 | — | 4 | 1 | no | — |
| 30 | C22×C4×D83 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×Dic332 | D4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C2×#13050578 | — | 2 | 1 | no | — |
| 33 | C2×D664 | — | 2 | 1 | no | — |
| 34 | C2×D664 | — | 2 | 1 | no | — |
| 35 | C2×D664 | — | 4 | 2 | no | — |
| 36 | C22×C83⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 37 | #14581774 | — | 4 | 1 | no | — |
| 38 | #14581772 | — | 2 | 1 | no | — |
| 39 | #14581771 | — | 2 | 1 | no | — |
| 40 | #14581767 | — | 4 | 2 | no | — |
| 41 | #14581767 | — | 4 | 2 | no | — |
| 42 | #14581763 | — | 2 | 1 | no | — |
| 43 | #14581760 | — | 4 | 1 | no | — |
| 44 | D4×Dic83 | — | 4 | 1 | no | — |
| 45 | (C22⋊D83)⋊C4 | — | 4 | 1 | no | — |
| 46 | #14581750 | — | 2 | 1 | no | — |
| 47 | C2×(C2×D83)⋊C4 | — | 4 | 1 | no | — |
| 48 | #14581737 | — | 4 | 2 | no | — |
| 49 | #14581733 | — | 4 | 2 | no | — |
| 50 | C2×C83⋊C16 | — | 2 | 1 | no | — |
| 51 | #14581726 | D4 | 1 | 1 | yes | characteristic, complemented |
| 52 | #14581723 | — | 2 | 1 | no | — |
| 53 | #14581717 | — | 2 | 1 | no | — |
| 54 | #14581715 | — | 2 | 1 | no | — |
| 55 | #14581713 | — | 2 | 1 | no | — |
| 56 | #14581712 | — | 4 | 2 | no | — |
| 57 | (C2×D83)⋊C8 | — | 2 | 1 | no | — |
| 58 | (C2×D83)⋊C8 | — | 2 | 1 | no | — |
| 59 | C2×D8×C83 | D4 | 1 | 1 | yes | characteristic, complemented |
| 60 | C22×C8×C83 | C23 | 1 | 1 | yes | characteristic |
| 61 | #121×C83 | — | 2 | 1 | no | — |
| 62 | C2×C4⋊C4×C83 | — | 2 | 1 | no | — |
| 63 | C2×C16×C83 | — | 2 | 1 | no | — |
| 64 | #107×C83 | D4 | 1 | 1 | yes | characteristic, complemented |
| 65 | #102×C83 | — | 2 | 1 | no | — |
| 66 | C23×D83 | — | 4 | 1 | no | — |
| 67 | C23×D83 | D8 | 1 | 1 | yes | characteristic |
| 68 | #13050589 | — | 8 | 1 | no | — |
| 69 | #13050589 | — | 8 | 1 | no | — |
| 70 | C2×Dic166 | — | 2 | 1 | no | — |
| 71 | C2×D332 | — | 2 | 2 | no | — |
| 72 | C2×D332 | — | 4 | 1 | no | — |
| 73 | C2×D332 | — | 4 | 1 | no | — |
| 74 | C2×D332 | — | 4 | 1 | no | — |
| 75 | C2×D332 | — | 4 | 1 | no | — |
| 76 | C2×D332 | — | 4 | 1 | no | — |
| 77 | C2×D332 | — | 4 | 4 | no | — |
| 78 | C2×D332 | — | 8 | 2 | no | — |
| 79 | C2×D332 | — | 8 | 2 | no | — |
| 80 | C2×C22⋊D83 | — | 4 | 1 | no | — |
| 81 | C2×C22⋊D83 | — | 4 | 1 | no | — |
| 82 | C22×Dic83 | — | 4 | 1 | no | — |
| 83 | C22×Dic83 | D8 | 1 | 1 | yes | characteristic |
| 84 | C2×C4×D83 | — | 2 | 1 | no | — |
| 85 | C2×C4×D83 | — | 2 | 1 | no | — |
| 86 | C2×C4×D83 | — | 4 | 1 | no | — |
| 87 | C2×C4×D83 | — | 4 | 1 | no | — |
| 88 | Dic332 | — | 4 | 1 | no | — |
| 89 | #13050578 | — | 8 | 1 | no | — |
| 90 | D664 | — | 2 | 2 | no | — |
| 91 | D664 | — | 2 | 2 | no | — |
| 92 | D664 | — | 4 | 1 | no | — |
| 93 | D664 | — | 4 | 1 | no | — |
| 94 | C2×C83⋊C8 | — | 2 | 1 | no | — |
| 95 | C2×C83⋊C8 | — | 4 | 1 | no | — |
| 96 | C4⋊Dic83 | — | 2 | 1 | no | — |
| 97 | C4⋊Dic83 | — | 4 | 1 | no | — |
| 98 | Dic83⋊C4 | — | 4 | 1 | no | — |
| 99 | C22⋊Dic83 | — | 4 | 1 | no | — |
| 100 | C22⋊Dic83 | — | 4 | 1 | no | — |
| 101 | (C2×D83)⋊C4 | — | 4 | 1 | no | — |
| 102 | (C2×D83)⋊C4 | — | 4 | 1 | no | — |
| 103 | (C2×D83)⋊C4 | — | 4 | 4 | no | — |
| 104 | C4×Dic83 | — | 4 | 1 | no | — |
| 105 | C83⋊C16 | — | 4 | 1 | no | — |
| 106 | C2×D4×C83 | — | 2 | 1 | no | — |
| 107 | C2×D4×C83 | — | 4 | 1 | no | — |
| 108 | C22×C4×C83 | — | 4 | 1 | no | — |
| 109 | C22×C4×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | D8×C83 | — | 4 | 1 | no | — |
| 111 | C2×C8×C83 | — | 4 | 1 | no | — |
| 112 | C2×C8×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C4⋊C4×C83 | — | 2 | 2 | no | — |
| 115 | C4⋊C4×C83 | — | 2 | 1 | no | — |
| 116 | C4⋊C4×C83 | — | 4 | 1 | no | — |
| 117 | C22⋊C4×C83 | — | 4 | 1 | no | — |
| 118 | C16×C83 | — | 4 | 1 | no | — |
| 119 | C23×C83 | — | 4 | 1 | no | — |
| 120 | C23×C83 | C2×D8 | 1 | 1 | yes | characteristic |
| 121 | C22×D83 | — | 2 | 1 | no | — |
| 122 | C22×D83 | — | 2 | 1 | no | — |
| 123 | C22×D83 | — | 2 | 1 | no | — |
| 124 | C22×D83 | — | 4 | 1 | no | — |
| 125 | C22×D83 | — | 4 | 1 | no | — |
| 126 | C22×D83 | — | 4 | 2 | no | — |
| 127 | C22×D83 | — | 8 | 1 | no | — |
| 128 | C22×D83 | — | 8 | 1 | no | — |
| 129 | C22×D83 | — | 8 | 1 | no | — |
| 130 | C22×D83 | — | 8 | 1 | no | — |
| 131 | C22×D83 | — | 8 | 1 | no | — |
| 132 | C22×D83 | — | 8 | 1 | no | — |
| 133 | D4×C83 | — | 4 | 1 | no | — |
| 134 | D4×C83 | — | 4 | 1 | no | — |
| 135 | D4×C83 | — | 8 | 1 | no | — |
| 136 | D4×C83 | — | 8 | 1 | no | — |
| 137 | C2×C4×C83 | — | 2 | 1 | no | — |
| 138 | C2×C4×C83 | — | 2 | 1 | no | — |
| 139 | C2×C4×C83 | — | 4 | 2 | no | — |
| 140 | C2×C4×C83 | — | 4 | 1 | no | — |
| 141 | C2×C4×C83 | — | 8 | 1 | no | — |
| 142 | C2×C4×C83 | — | 8 | 1 | no | — |
| 143 | C2×C4×C83 | #120 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C83 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 145 | C22⋊D83 | — | 8 | 2 | no | — |
| 146 | C22⋊D83 | — | 8 | 2 | no | — |
| 147 | C2×Dic83 | — | 2 | 1 | no | — |
| 148 | C2×Dic83 | — | 4 | 1 | no | — |
| 149 | C2×Dic83 | — | 4 | 1 | no | — |
| 150 | C2×Dic83 | — | 4 | 1 | no | — |
| 151 | C2×Dic83 | — | 8 | 2 | no | — |
| 152 | D332 | — | 4 | 2 | no | — |
| 153 | D332 | — | 4 | 2 | no | — |
| 154 | D332 | — | 8 | 1 | no | — |
| 155 | D332 | — | 8 | 8 | no | — |
| 156 | D332 | — | 8 | 1 | no | — |
| 157 | C4×D83 | — | 4 | 1 | no | — |
| 158 | C4×D83 | — | 4 | 1 | no | — |
| 159 | C4×D83 | — | 8 | 1 | no | — |
| 160 | Dic166 | — | 4 | 1 | no | — |
| 161 | Dic166 | — | 4 | 1 | no | — |
| 162 | C8×C83 | — | 2 | 1 | no | — |
| 163 | C8×C83 | — | 2 | 1 | no | — |
| 164 | C83⋊C8 | — | 4 | 1 | no | — |
| 165 | C22×C83 | — | 2 | 1 | no | — |
| 166 | C22×C83 | — | 2 | 1 | no | — |
| 167 | C22×C83 | — | 8 | 1 | no | — |
| 168 | C22×C83 | — | 8 | 1 | no | — |
| 169 | C22×C83 | — | 8 | 1 | no | — |
| 170 | C22×C83 | #447 | 1 | 1 | yes | characteristic |
| 171 | C22×C83 | #508 | 1 | 1 | yes | characteristic |
| 172 | C22×C83 | #509 | 1 | 1 | yes | characteristic |
| 173 | C2×D83 | — | 4 | 2 | no | — |
| 174 | C2×D83 | — | 4 | 1 | no | — |
| 175 | C2×D83 | — | 4 | 1 | no | — |
| 176 | C2×D83 | — | 4 | 1 | no | — |
| 177 | C2×D83 | — | 8 | 1 | no | — |
| 178 | C2×D83 | — | 8 | 2 | no | — |
| 179 | C2×D83 | — | 8 | 2 | no | — |
| 180 | C2×D83 | — | 8 | 2 | no | — |
| 181 | C2×D83 | — | 16 | 1 | no | — |
| 182 | C2×D83 | — | 16 | 1 | no | — |
| 183 | C2×D83 | — | 16 | 1 | no | — |
| 184 | C2×D83 | — | 16 | 1 | no | — |
| 185 | C4×C83 | — | 2 | 1 | no | — |
| 186 | C4×C83 | — | 8 | 2 | no | — |
| 187 | C4×C83 | — | 8 | 1 | no | — |
| 188 | C4×C83 | #453 | 1 | 1 | yes | characteristic |
| 189 | C4×C83 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 190 | Dic83 | — | 4 | 1 | no | — |
| 191 | Dic83 | — | 8 | 1 | no | — |
| 192 | Dic83 | — | 8 | 1 | no | — |
| 193 | #12104 | — | 83 | 1 | no | maximal, Sylow |
| 194 | C2×C83 | — | 2 | 1 | no | — |
| 195 | C2×C83 | — | 2 | 1 | no | — |
| 196 | C2×C83 | — | 16 | 1 | no | — |
| 197 | C2×C83 | #1595 | 1 | 1 | yes | characteristic |
| 198 | C2×C83 | #2186 | 1 | 1 | yes | characteristic |
| 199 | C2×C83 | #2190 | 1 | 1 | yes | characteristic |
| 200 | D83 | — | 8 | 1 | no | — |
| 201 | D83 | — | 16 | 2 | no | — |
| 202 | #3191 | — | 83 | 1 | no | — |
| 203 | #2187 | — | 83 | 1 | no | — |
| 204 | #2184 | — | 83 | 1 | no | — |
| 205 | #1999 | — | 83 | 1 | no | — |
| 206 | #1348 | — | 83 | 1 | no | — |
| 207 | #1347 | D83 | 1 | 1 | yes | characteristic, complemented |
| 208 | #1314 | — | 83 | 1 | no | — |
| 209 | C83 | #12104 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 210 | C22×D8 | — | 83 | 1 | no | — |
| 211 | #525 | — | 166 | 1 | no | — |
| 212 | C2×#121 | — | 166 | 1 | no | — |
| 213 | C2×SD32 | — | 166 | 1 | no | — |
| 214 | C2×D16 | — | 166 | 1 | no | — |
| 215 | #485 | — | 166 | 1 | no | — |
| 216 | #482 | — | 166 | 1 | no | — |
| 217 | #467 | — | 83 | 1 | no | — |
| 218 | #466 | C2×D83 | 1 | 1 | yes | characteristic |
| 219 | #465 | — | 166 | 1 | no | — |
| 220 | #452 | — | 166 | 1 | no | — |
| 221 | #449 | — | 166 | 1 | no | — |
| 222 | C2×#102 | — | 166 | 1 | no | — |
| 223 | C2×C22⋊C8 | — | 83 | 1 | no | — |
| 224 | #357 | — | 166 | 1 | no | — |
| 225 | #357 | — | 166 | 1 | no | — |
| 226 | C22⋊C16 | — | 83 | 1 | no | — |
| 227 | C22⋊C16 | C2×D83 | 1 | 1 | yes | characteristic |
| 228 | #340 | C2×D83 | 1 | 1 | yes | characteristic |
| 229 | C2×#41 | — | 166 | 1 | no | — |
| 230 | C22×D4 | — | 332 | 1 | no | — |
| 231 | C22×D4 | — | 166 | 1 | no | — |
| 232 | C23×C4 | — | 83 | 1 | no | — |
| 233 | C2×Q16 | — | 83 | 1 | no | — |
| 234 | C2×SD16 | — | 166 | 1 | no | — |
| 235 | C2×D8 | — | 332 | 2 | no | — |
| 236 | C2×D8 | — | 166 | 1 | no | — |
| 237 | C2×D8 | — | 166 | 1 | no | — |
| 238 | C2×D8 | D332 | 1 | 1 | yes | characteristic, complemented |
| 239 | C22×C8 | — | 83 | 1 | no | — |
| 240 | C22×C8 | C22×D83 | 1 | 1 | yes | characteristic |
| 241 | #123 | — | 332 | 1 | no | — |
| 242 | C22⋊Q8 | — | 166 | 1 | no | — |
| 243 | C22⋊Q8 | — | 166 | 1 | no | — |
| 244 | #121 | — | 2 | 1 | no | — |
| 245 | #121 | — | 332 | 2 | no | — |
| 246 | #121 | — | 332 | 2 | no | — |
| 247 | #121 | — | 166 | 1 | no | — |
| 248 | #120 | — | 332 | 1 | no | — |
| 249 | C4×D4 | — | 332 | 1 | no | — |
| 250 | C4×D4 | — | 332 | 1 | no | — |
| 251 | #117 | — | 166 | 1 | no | — |
| 252 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 253 | C2×C22⋊C4 | — | 332 | 1 | no | — |
| 254 | SD32 | — | 332 | 2 | no | — |
| 255 | D16 | — | 332 | 2 | no | — |
| 256 | C2×C16 | — | 2 | 1 | no | — |
| 257 | C2×C16 | — | 166 | 1 | no | — |
| 258 | #107 | — | 83 | 1 | no | — |
| 259 | #107 | D332 | 1 | 1 | yes | characteristic, complemented |
| 260 | #106 | — | 166 | 1 | no | — |
| 261 | #103 | — | 166 | 1 | no | — |
| 262 | #103 | — | 166 | 1 | no | — |
| 263 | #102 | — | 2 | 1 | no | — |
| 264 | #102 | — | 332 | 2 | no | — |
| 265 | #102 | — | 166 | 1 | no | — |
| 266 | C22⋊C8 | — | 166 | 1 | no | — |
| 267 | C22⋊C8 | — | 166 | 1 | no | — |
| 268 | C24 | — | 332 | 1 | no | — |
| 269 | C24 | — | 83 | 1 | no | — |
| 270 | #41 | — | 664 | 1 | no | — |
| 271 | #41 | — | 664 | 1 | no | — |
| 272 | C2×Q8 | — | 166 | 1 | no | — |
| 273 | C2×D4 | — | 2 | 1 | no | — |
| 274 | C2×D4 | — | 4 | 1 | no | — |
| 275 | C2×D4 | — | 332 | 1 | no | — |
| 276 | C2×D4 | — | 332 | 1 | no | — |
| 277 | C2×D4 | — | 332 | 1 | no | — |
| 278 | C2×D4 | — | 332 | 4 | no | — |
| 279 | C2×D4 | — | 332 | 1 | no | — |
| 280 | C2×D4 | — | 332 | 1 | no | — |
| 281 | C2×D4 | — | 332 | 1 | no | — |
| 282 | C2×D4 | — | 332 | 1 | no | — |
| 283 | C2×D4 | — | 664 | 2 | no | — |
| 284 | C2×D4 | — | 664 | 2 | no | — |
| 285 | C2×D4 | — | 166 | 2 | no | — |
| 286 | C22×C4 | — | 4 | 1 | no | — |
| 287 | C22×C4 | — | 332 | 1 | no | — |
| 288 | C22×C4 | — | 332 | 1 | no | — |
| 289 | C22×C4 | — | 332 | 1 | no | — |
| 290 | C22×C4 | — | 83 | 1 | no | — |
| 291 | C22×C4 | — | 166 | 1 | no | — |
| 292 | C22×C4 | — | 166 | 1 | no | — |
| 293 | C22×C4 | D4×D83 | 1 | 1 | yes | characteristic |
| 294 | Q16 | — | 332 | 1 | no | — |
| 295 | SD16 | — | 664 | 1 | no | — |
| 296 | D8 | — | 4 | 1 | no | — |
| 297 | D8 | — | 332 | 1 | no | — |
| 298 | D8 | — | 332 | 1 | no | — |
| 299 | D8 | — | 166 | 2 | no | — |
| 300 | D8 | — | 166 | 2 | no | — |
| 301 | C2×C8 | — | 4 | 1 | no | — |
| 302 | C2×C8 | — | 332 | 1 | no | — |
| 303 | C2×C8 | — | 166 | 1 | no | — |
| 304 | C2×C8 | D4×D83 | 1 | 1 | yes | characteristic |
| 305 | C2×C8 | C2×D332 | 1 | 1 | yes | characteristic |
| 306 | C4⋊C4 | — | 2 | 2 | no | — |
| 307 | C4⋊C4 | — | 2 | 1 | no | — |
| 308 | C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4⋊C4 | — | 332 | 1 | no | — |
| 310 | C4⋊C4 | — | 332 | 1 | no | — |
| 311 | C4⋊C4 | — | 166 | 1 | no | — |
| 312 | C22⋊C4 | — | 4 | 1 | no | — |
| 313 | C22⋊C4 | — | 332 | 4 | no | — |
| 314 | C22⋊C4 | — | 332 | 1 | no | — |
| 315 | C22⋊C4 | — | 332 | 1 | no | — |
| 316 | C22⋊C4 | — | 332 | 1 | no | — |
| 317 | C22⋊C4 | — | 332 | 1 | no | — |
| 318 | C42 | — | 332 | 1 | no | — |
| 319 | C16 | — | 4 | 1 | no | — |
| 320 | C16 | — | 332 | 1 | no | — |
| 321 | C23 | — | 4 | 1 | no | — |
| 322 | C23 | — | 332 | 1 | no | — |
| 323 | C23 | — | 332 | 1 | no | — |
| 324 | C23 | — | 332 | 2 | no | — |
| 325 | C23 | — | 664 | 1 | no | — |
| 326 | C23 | — | 664 | 1 | no | — |
| 327 | C23 | — | 664 | 1 | no | — |
| 328 | C23 | — | 664 | 1 | no | — |
| 329 | C23 | — | 664 | 1 | no | — |
| 330 | C23 | — | 664 | 1 | no | — |
| 331 | C23 | — | 166 | 1 | no | — |
| 332 | C23 | — | 166 | 1 | no | — |
| 333 | C23 | — | 166 | 1 | no | — |
| 334 | C23 | D8×D83 | 1 | 1 | yes | characteristic |
| 335 | Q8 | — | 332 | 1 | no | — |
| 336 | Q8 | — | 332 | 1 | no | — |
| 337 | D4 | — | 4 | 1 | no | — |
| 338 | D4 | — | 4 | 1 | no | — |
| 339 | D4 | — | 8 | 1 | no | — |
| 340 | D4 | — | 8 | 1 | no | — |
| 341 | D4 | — | 332 | 2 | no | — |
| 342 | D4 | — | 332 | 2 | no | — |
| 343 | D4 | — | 664 | 1 | no | — |
| 344 | D4 | — | 664 | 8 | no | — |
| 345 | D4 | — | 664 | 2 | no | — |
| 346 | D4 | — | 664 | 2 | no | — |
| 347 | D4 | — | 664 | 1 | no | — |
| 348 | C2×C4 | — | 2 | 1 | no | — |
| 349 | C2×C4 | — | 2 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 2 | no | — |
| 351 | C2×C4 | — | 4 | 1 | no | — |
| 352 | C2×C4 | — | 8 | 1 | no | — |
| 353 | C2×C4 | — | 8 | 1 | no | — |
| 354 | C2×C4 | — | 332 | 1 | no | — |
| 355 | C2×C4 | — | 332 | 1 | no | — |
| 356 | C2×C4 | — | 332 | 1 | no | — |
| 357 | C2×C4 | — | 332 | 1 | no | — |
| 358 | C2×C4 | — | 332 | 1 | no | — |
| 359 | C2×C4 | — | 664 | 1 | no | — |
| 360 | C2×C4 | — | 664 | 2 | no | — |
| 361 | C2×C4 | — | 166 | 1 | no | — |
| 362 | C2×C4 | #14581762 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #14581819 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 2 | 1 | no | — |
| 365 | C8 | — | 2 | 1 | no | — |
| 366 | C8 | — | 332 | 1 | no | — |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 2 | 1 | no | — |
| 369 | C22 | — | 8 | 1 | no | — |
| 370 | C22 | — | 8 | 1 | no | — |
| 371 | C22 | — | 8 | 1 | no | — |
| 372 | C22 | — | 1328 | 1 | no | — |
| 373 | C22 | — | 1328 | 1 | no | — |
| 374 | C22 | — | 1328 | 1 | no | — |
| 375 | C22 | — | 1328 | 1 | no | — |
| 376 | C22 | — | 332 | 2 | no | — |
| 377 | C22 | — | 332 | 1 | no | — |
| 378 | C22 | — | 332 | 1 | no | — |
| 379 | C22 | — | 332 | 1 | no | — |
| 380 | C22 | — | 664 | 2 | no | — |
| 381 | C22 | — | 664 | 2 | no | — |
| 382 | C22 | — | 664 | 1 | no | — |
| 383 | C22 | — | 664 | 2 | no | — |
| 384 | C22 | #19127836 | 1 | 1 | yes | characteristic |
| 385 | C22 | #19128132 | 1 | 1 | yes | characteristic |
| 386 | C22 | #19128135 | 1 | 1 | yes | characteristic |
| 387 | C4 | — | 2 | 1 | no | — |
| 388 | C4 | — | 8 | 2 | no | — |
| 389 | C4 | — | 8 | 1 | no | — |
| 390 | C4 | — | 332 | 1 | no | — |
| 391 | C4 | — | 664 | 1 | no | — |
| 392 | C4 | — | 664 | 1 | no | — |
| 393 | C4 | #19127870 | 1 | 1 | yes | characteristic |
| 394 | C4 | #19127889 | 1 | 1 | yes | characteristic |
| 395 | C2 | — | 2 | 1 | no | — |
| 396 | C2 | — | 2 | 1 | no | — |
| 397 | C2 | — | 16 | 1 | no | — |
| 398 | C2 | — | 1328 | 2 | no | — |
| 399 | C2 | — | 664 | 1 | no | — |
| 400 | C2 | #24906382 | 1 | 1 | yes | characteristic |
| 401 | C2 | #24909387 | 1 | 1 | yes | characteristic |
| 402 | C2 | #24909410 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24918250 | C2 | semidirect |
| 2. #24909394 | C2 | semidirect |
| 3. #24909374 | C2 | semidirect |
| 4. #24908462 | C2 | semidirect |
| 5. #24905474 | C2 | semidirect |
| 6. #24905386 | C2 | semidirect |
| 7. C83×#1347 | C2 | semidirect |
| 31. C2×Dic332 | D4 | semidirect |
| 51. #14581726 | D4 | semidirect |
| 59. C2×D8×C83 | D4 | semidirect |
| 64. #107×C83 | D4 | semidirect |
| 207. #1347 | D83 | semidirect |
| 209. C83 | #12104 | semidirect |
| 238. C2×D8 | D332 | semidirect |
| 259. #107 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918250 | 2 |
| #24909394 | 2 |
| #24909374 | 2 |
| #24908462 | 2 |
| #24905474 | 2 |
| #24905386 | 2 |
| C83×#1347 | 2 |
| #12104 | 83 |