Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
749 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 749 conjugacy classes of subgroups — too many to draw. Only its 138 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 | C2×#2238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#2190 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #21538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #21241 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13467 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13445 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13143 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13037 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #12875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12739 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#575 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#509 | C22 | 1 | 2 | yes | — |
| 14 | C2×#469 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#442 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#430 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#104 | — | 2 | 1 | no | — |
| 18 | #2879 | — | 2 | 1 | no | — |
| 19 | C2×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#121 | — | 2 | 1 | no | — |
| 21 | #2238 | — | 2 | 4 | no | — |
| 22 | #2190 | — | 2 | 4 | no | — |
| 23 | C2×#365 | C22 | 1 | 2 | yes | complemented |
| 24 | C2×#364 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#361 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×#360 | C22 | 1 | 2 | yes | — |
| 27 | C2×#360 | C22 | 1 | 2 | yes | — |
| 28 | #2139 | C22 | 1 | 2 | yes | — |
| 29 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#349 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1975 | — | 2 | 1 | no | — |
| 32 | #1975 | C22 | 1 | 2 | yes | — |
| 33 | #1974 | — | 2 | 1 | no | — |
| 34 | #1974 | C22 | 1 | 2 | yes | — |
| 35 | #1970 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #1941 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #1934 | — | 2 | 1 | no | — |
| 38 | #1895 | — | 2 | 1 | no | — |
| 39 | #1809 | C22 | 1 | 1 | yes | characteristic |
| 40 | #1776 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #1762 | — | 2 | 1 | no | — |
| 42 | #1387 | C22 | 1 | 2 | yes | complemented |
| 43 | #1383 | C22 | 1 | 2 | yes | complemented |
| 44 | #1375 | C22 | 1 | 2 | yes | complemented |
| 45 | C22×#41 | — | 2 | 1 | no | — |
| 46 | #575 | — | 2 | 2 | no | — |
| 47 | #575 | — | 2 | 2 | no | — |
| 48 | #575 | — | 4 | 2 | no | — |
| 49 | C2×#137 | — | 2 | 2 | no | — |
| 50 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 51 | C2×#135 | — | 2 | 1 | no | — |
| 52 | C2×#135 | C23 | 1 | 2 | yes | — |
| 53 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×M16 | — | 2 | 1 | no | — |
| 55 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×M16 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×#121 | — | 2 | 1 | no | — |
| 58 | C2×C4×D4 | — | 2 | 1 | no | — |
| 59 | C2×C4×D4 | — | 4 | 1 | no | — |
| 60 | C22×C42 | D4 | 1 | 1 | yes | characteristic |
| 61 | #509 | — | 2 | 4 | no | — |
| 62 | #509 | — | 4 | 2 | no | — |
| 63 | C2×SD32 | — | 2 | 2 | no | — |
| 64 | C2×D16 | — | 2 | 2 | no | — |
| 65 | C2×M32 | C23 | 1 | 2 | yes | — |
| 66 | C2×M32 | C23 | 1 | 2 | yes | — |
| 67 | #469 | — | 2 | 2 | no | — |
| 68 | #469 | D4 | 1 | 4 | yes | — |
| 69 | #442 | — | 4 | 2 | no | — |
| 70 | #430 | — | 2 | 2 | no | — |
| 71 | #430 | — | 2 | 2 | no | — |
| 72 | C2×#108 | — | 2 | 1 | no | — |
| 73 | C2×#108 | C23 | 1 | 2 | yes | — |
| 74 | C2×#107 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#104 | — | 2 | 2 | no | — |
| 78 | C2×#104 | — | 2 | 2 | no | — |
| 79 | C2×#104 | — | 4 | 4 | no | — |
| 80 | C2×#102 | — | 2 | 1 | no | — |
| 81 | C2×#102 | — | 2 | 1 | no | — |
| 82 | C2×#102 | — | 2 | 1 | no | — |
| 83 | #408 | — | 2 | 2 | no | — |
| 84 | #408 | — | 2 | 2 | no | — |
| 85 | #408 | — | 4 | 2 | no | — |
| 86 | #407 | — | 4 | 2 | no | — |
| 87 | C4×M16 | — | 4 | 2 | no | — |
| 88 | C2×#97 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×C8 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 92 | #390 | — | 2 | 1 | no | — |
| 93 | #389 | — | 2 | 1 | no | — |
| 94 | #388 | — | 4 | 1 | no | — |
| 95 | #386 | — | 4 | 1 | no | — |
| 96 | #380 | — | 2 | 1 | no | — |
| 97 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 98 | C4×C22⋊C4 | — | 4 | 1 | no | — |
| 99 | #365 | — | 2 | 4 | no | — |
| 100 | #364 | — | 4 | 2 | no | — |
| 101 | #361 | — | 2 | 4 | no | — |
| 102 | #360 | — | 2 | 4 | no | — |
| 103 | #360 | — | 4 | 2 | no | — |
| 104 | #358 | — | 2 | 2 | no | — |
| 105 | #357 | — | 2 | 2 | no | — |
| 106 | #349 | — | 2 | 2 | no | — |
| 107 | #349 | — | 2 | 2 | no | — |
| 108 | #340 | — | 2 | 1 | no | — |
| 109 | #340 | — | 2 | 1 | no | — |
| 110 | #340 | — | 2 | 1 | no | — |
| 111 | C2×#41 | — | 2 | 2 | no | — |
| 112 | C2×#41 | — | 2 | 2 | no | — |
| 113 | C2×#41 | — | 4 | 1 | no | — |
| 114 | C2×#41 | — | 4 | 2 | no | — |
| 115 | C2×#41 | — | 4 | 2 | no | — |
| 116 | C2×#41 | — | 4 | 1 | no | — |
| 117 | C2×#41 | — | 4 | 2 | no | — |
| 118 | C2×#41 | — | 4 | 2 | no | — |
| 119 | C22×Q8 | — | 2 | 1 | no | — |
| 120 | C22×D4 | — | 2 | 1 | no | — |
| 121 | C22×D4 | — | 2 | 1 | no | — |
| 122 | C22×D4 | — | 4 | 1 | no | — |
| 123 | C22×D4 | — | 4 | 1 | no | — |
| 124 | C23×C4 | — | 2 | 1 | no | — |
| 125 | C23×C4 | — | 4 | 1 | no | — |
| 126 | C23×C4 | — | 4 | 1 | no | — |
| 127 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | #137 | — | 4 | 4 | no | — |
| 129 | #137 | — | 4 | 4 | no | — |
| 130 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 131 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 132 | #135 | — | 2 | 2 | no | — |
| 133 | #135 | — | 2 | 2 | no | — |
| 134 | #135 | — | 2 | 2 | no | — |
| 135 | #135 | — | 2 | 2 | no | — |
| 136 | #135 | — | 4 | 2 | no | — |
| 137 | #135 | — | 4 | 2 | no | — |
| 138 | C2×Q16 | — | 2 | 1 | no | — |
| 139 | C2×Q16 | #41 | 1 | 2 | yes | — |
| 140 | C2×SD16 | — | 2 | 2 | no | — |
| 141 | C2×SD16 | — | 2 | 2 | no | — |
| 142 | C2×D8 | — | 2 | 1 | no | — |
| 143 | C2×D8 | — | 2 | 2 | no | — |
| 144 | C2×D8 | — | 2 | 1 | no | — |
| 145 | C2×D8 | — | 2 | 2 | no | — |
| 146 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 147 | C2×D8 | #41 | 1 | 2 | yes | — |
| 148 | C2×M16 | — | 2 | 2 | no | — |
| 149 | C2×M16 | — | 2 | 2 | no | — |
| 150 | C2×M16 | — | 2 | 2 | no | — |
| 151 | C2×M16 | — | 2 | 2 | no | — |
| 152 | C2×M16 | — | 2 | 2 | no | — |
| 153 | C2×M16 | — | 4 | 1 | no | — |
| 154 | C2×M16 | — | 4 | 1 | no | — |
| 155 | C2×M16 | — | 4 | 2 | no | — |
| 156 | C2×M16 | — | 4 | 2 | no | — |
| 157 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×M16 | #41 | 1 | 2 | yes | — |
| 159 | C22×C8 | — | 4 | 1 | no | — |
| 160 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 164 | #121 | — | 2 | 4 | no | — |
| 165 | #121 | — | 4 | 2 | no | — |
| 166 | C4×D4 | — | 4 | 2 | no | — |
| 167 | C4×D4 | — | 4 | 2 | no | — |
| 168 | C4×D4 | — | 8 | 4 | no | — |
| 169 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 170 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 171 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 172 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 173 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 174 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 175 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 176 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 177 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 178 | C2×C42 | — | 2 | 2 | no | — |
| 179 | C2×C42 | — | 2 | 1 | no | — |
| 180 | C2×C42 | — | 4 | 1 | no | — |
| 181 | C2×C42 | — | 4 | 1 | no | — |
| 182 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | SD32 | — | 4 | 4 | no | — |
| 185 | D16 | — | 4 | 4 | no | — |
| 186 | M32 | — | 2 | 2 | no | — |
| 187 | M32 | — | 2 | 2 | no | — |
| 188 | M32 | — | 2 | 2 | no | — |
| 189 | M32 | — | 2 | 2 | no | — |
| 190 | C2×C16 | — | 2 | 2 | no | — |
| 191 | C2×C16 | — | 2 | 2 | no | — |
| 192 | #108 | — | 2 | 2 | no | — |
| 193 | #108 | — | 2 | 2 | no | — |
| 194 | #108 | — | 4 | 2 | no | — |
| 195 | #107 | — | 2 | 2 | no | — |
| 196 | #106 | — | 2 | 1 | no | — |
| 197 | #106 | — | 2 | 2 | no | — |
| 198 | #106 | C2×D4 | 1 | 2 | yes | — |
| 199 | #104 | — | 4 | 4 | no | — |
| 200 | #104 | — | 4 | 4 | no | — |
| 201 | #102 | — | 2 | 4 | no | — |
| 202 | #102 | — | 4 | 2 | no | — |
| 203 | #102 | — | 4 | 2 | no | — |
| 204 | C22⋊C8 | — | 4 | 4 | no | — |
| 205 | C22⋊C8 | — | 4 | 4 | no | — |
| 206 | #97 | — | 2 | 2 | no | — |
| 207 | #97 | — | 4 | 1 | no | — |
| 208 | C4×C8 | — | 2 | 2 | no | — |
| 209 | C4×C8 | — | 4 | 1 | no | — |
| 210 | #95 | — | 4 | 1 | no | — |
| 211 | #95 | — | 4 | 1 | no | — |
| 212 | #95 | — | 4 | 1 | no | — |
| 213 | C24 | — | 4 | 1 | no | — |
| 214 | C24 | — | 4 | 1 | no | — |
| 215 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 216 | #41 | — | 4 | 4 | no | — |
| 217 | #41 | — | 4 | 4 | no | — |
| 218 | #41 | — | 4 | 2 | no | — |
| 219 | #41 | — | 4 | 2 | no | — |
| 220 | #41 | — | 4 | 2 | no | — |
| 221 | #41 | — | 4 | 2 | no | — |
| 222 | #41 | — | 8 | 2 | no | — |
| 223 | #41 | — | 8 | 2 | no | — |
| 224 | #41 | — | 8 | 2 | no | — |
| 225 | #41 | — | 8 | 2 | no | — |
| 226 | C2×Q8 | — | 2 | 2 | no | — |
| 227 | C2×Q8 | — | 4 | 1 | no | — |
| 228 | C2×Q8 | — | 4 | 2 | no | — |
| 229 | C2×Q8 | — | 4 | 2 | no | — |
| 230 | C2×D4 | — | 2 | 2 | no | — |
| 231 | C2×D4 | — | 2 | 2 | no | — |
| 232 | C2×D4 | — | 4 | 2 | no | — |
| 233 | C2×D4 | — | 4 | 2 | no | — |
| 234 | C2×D4 | — | 4 | 1 | no | — |
| 235 | C2×D4 | — | 4 | 2 | no | — |
| 236 | C2×D4 | — | 4 | 2 | no | — |
| 237 | C2×D4 | — | 4 | 4 | no | — |
| 238 | C2×D4 | — | 4 | 1 | no | — |
| 239 | C2×D4 | — | 4 | 1 | no | — |
| 240 | C2×D4 | — | 4 | 1 | no | — |
| 241 | C2×D4 | — | 4 | 1 | no | — |
| 242 | C2×D4 | — | 4 | 1 | no | — |
| 243 | C2×D4 | — | 8 | 2 | no | — |
| 244 | C2×D4 | — | 8 | 2 | no | — |
| 245 | C2×D4 | — | 8 | 2 | no | — |
| 246 | C2×D4 | — | 8 | 2 | no | — |
| 247 | C22×C4 | — | 2 | 1 | no | — |
| 248 | C22×C4 | — | 2 | 1 | no | — |
| 249 | C22×C4 | — | 2 | 1 | no | — |
| 250 | C22×C4 | — | 2 | 1 | no | — |
| 251 | C22×C4 | — | 2 | 1 | no | — |
| 252 | C22×C4 | — | 2 | 1 | no | — |
| 253 | C22×C4 | — | 4 | 2 | no | — |
| 254 | C22×C4 | — | 4 | 2 | no | — |
| 255 | C22×C4 | — | 4 | 2 | no | — |
| 256 | C22×C4 | — | 4 | 1 | no | — |
| 257 | C22×C4 | — | 4 | 1 | no | — |
| 258 | C22×C4 | — | 4 | 2 | no | — |
| 259 | C22×C4 | — | 4 | 1 | no | — |
| 260 | C22×C4 | — | 4 | 1 | no | — |
| 261 | C22×C4 | — | 8 | 2 | no | — |
| 262 | C22×C4 | — | 8 | 2 | no | — |
| 263 | C22×C4 | — | 8 | 2 | no | — |
| 264 | C22×C4 | — | 8 | 1 | no | — |
| 265 | C22×C4 | — | 8 | 2 | no | — |
| 266 | C22×C4 | — | 8 | 2 | no | — |
| 267 | C22×C4 | #121 | 1 | 2 | yes | — |
| 268 | C22×C4 | #135 | 1 | 2 | yes | — |
| 269 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 270 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 271 | Q16 | — | 2 | 2 | no | — |
| 272 | Q16 | — | 2 | 2 | no | — |
| 273 | Q16 | — | 4 | 2 | no | — |
| 274 | SD16 | — | 4 | 4 | no | — |
| 275 | SD16 | — | 4 | 2 | no | — |
| 276 | SD16 | — | 4 | 2 | no | — |
| 277 | D8 | — | 2 | 2 | no | — |
| 278 | D8 | — | 2 | 4 | no | — |
| 279 | D8 | — | 2 | 2 | no | — |
| 280 | D8 | — | 4 | 2 | no | — |
| 281 | D8 | — | 4 | 2 | no | — |
| 282 | M16 | — | 2 | 4 | no | — |
| 283 | M16 | — | 2 | 4 | no | — |
| 284 | M16 | — | 4 | 4 | no | — |
| 285 | M16 | — | 4 | 2 | no | — |
| 286 | M16 | — | 4 | 2 | no | — |
| 287 | M16 | — | 8 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 1 | no | — |
| 289 | C2×C8 | — | 2 | 1 | no | — |
| 290 | C2×C8 | — | 2 | 1 | no | — |
| 291 | C2×C8 | — | 2 | 1 | no | — |
| 292 | C2×C8 | — | 2 | 1 | no | — |
| 293 | C2×C8 | — | 2 | 1 | no | — |
| 294 | C2×C8 | — | 2 | 1 | no | — |
| 295 | C2×C8 | — | 4 | 2 | no | — |
| 296 | C2×C8 | — | 8 | 2 | no | — |
| 297 | C2×C8 | #121 | 1 | 2 | yes | — |
| 298 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 299 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 301 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 302 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 303 | C4⋊C4 | — | 2 | 2 | no | — |
| 304 | C4⋊C4 | — | 4 | 1 | no | — |
| 305 | C4⋊C4 | — | 4 | 1 | no | — |
| 306 | C4⋊C4 | — | 4 | 1 | no | — |
| 307 | C4⋊C4 | — | 4 | 1 | no | — |
| 308 | C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4⋊C4 | — | 8 | 2 | no | — |
| 310 | C22⋊C4 | — | 4 | 4 | no | — |
| 311 | C22⋊C4 | — | 8 | 2 | no | — |
| 312 | C22⋊C4 | — | 8 | 2 | no | — |
| 313 | C22⋊C4 | — | 8 | 2 | no | — |
| 314 | C22⋊C4 | — | 8 | 2 | no | — |
| 315 | C42 | — | 2 | 1 | no | — |
| 316 | C42 | — | 2 | 1 | no | — |
| 317 | C42 | — | 2 | 1 | no | — |
| 318 | C42 | — | 4 | 2 | no | — |
| 319 | C42 | — | 8 | 2 | no | — |
| 320 | C42 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 321 | C16 | — | 4 | 2 | no | — |
| 322 | C16 | — | 4 | 2 | no | — |
| 323 | C23 | — | 2 | 1 | no | — |
| 324 | C23 | — | 2 | 1 | no | — |
| 325 | C23 | — | 4 | 1 | no | — |
| 326 | C23 | — | 4 | 1 | no | — |
| 327 | C23 | — | 4 | 2 | no | — |
| 328 | C23 | — | 4 | 2 | no | — |
| 329 | C23 | — | 8 | 1 | no | — |
| 330 | C23 | — | 8 | 1 | no | — |
| 331 | C23 | — | 8 | 2 | no | — |
| 332 | C23 | — | 8 | 1 | no | — |
| 333 | C23 | — | 8 | 1 | no | — |
| 334 | C23 | — | 8 | 1 | no | — |
| 335 | C23 | — | 8 | 1 | no | — |
| 336 | C23 | — | 16 | 1 | no | — |
| 337 | C23 | — | 16 | 1 | no | — |
| 338 | C23 | #463 | 1 | 2 | yes | — |
| 339 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 340 | Q8 | — | 4 | 2 | no | — |
| 341 | Q8 | — | 4 | 2 | no | — |
| 342 | Q8 | — | 8 | 2 | no | — |
| 343 | D4 | — | 4 | 2 | no | — |
| 344 | D4 | — | 4 | 2 | no | — |
| 345 | D4 | — | 4 | 2 | no | — |
| 346 | D4 | — | 4 | 2 | no | — |
| 347 | D4 | — | 8 | 2 | no | — |
| 348 | D4 | — | 8 | 4 | no | — |
| 349 | D4 | — | 8 | 8 | no | — |
| 350 | D4 | — | 8 | 2 | no | — |
| 351 | D4 | — | 8 | 2 | no | — |
| 352 | D4 | — | 8 | 1 | no | — |
| 353 | D4 | — | 8 | 1 | no | — |
| 354 | C2×C4 | — | 2 | 1 | no | — |
| 355 | C2×C4 | — | 2 | 1 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 2 | no | — |
| 359 | C2×C4 | — | 2 | 2 | no | — |
| 360 | C2×C4 | — | 2 | 2 | no | — |
| 361 | C2×C4 | — | 2 | 2 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 1 | no | — |
| 365 | C2×C4 | — | 4 | 1 | no | — |
| 366 | C2×C4 | — | 4 | 2 | no | — |
| 367 | C2×C4 | — | 4 | 2 | no | — |
| 368 | C2×C4 | — | 8 | 4 | no | — |
| 369 | C2×C4 | — | 8 | 4 | no | — |
| 370 | C2×C4 | — | 8 | 1 | no | — |
| 371 | C2×C4 | — | 8 | 2 | no | — |
| 372 | C2×C4 | — | 8 | 1 | no | — |
| 373 | C2×C4 | — | 8 | 2 | no | — |
| 374 | C2×C4 | — | 8 | 2 | no | — |
| 375 | C2×C4 | — | 8 | 1 | no | — |
| 376 | C2×C4 | — | 8 | 1 | no | — |
| 377 | C2×C4 | — | 8 | 1 | no | — |
| 378 | C2×C4 | — | 8 | 1 | no | — |
| 379 | C2×C4 | — | 8 | 1 | no | — |
| 380 | C2×C4 | — | 8 | 1 | no | — |
| 381 | C2×C4 | — | 16 | 4 | no | — |
| 382 | C2×C4 | #463 | 1 | 2 | yes | — |
| 383 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | #525 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | C2×#135 | 1 | 1 | yes | characteristic |
| 387 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 389 | C8 | — | 2 | 2 | no | — |
| 390 | C8 | — | 2 | 2 | no | — |
| 391 | C8 | — | 4 | 1 | no | — |
| 392 | C8 | — | 8 | 2 | no | — |
| 393 | C8 | #546 | 1 | 2 | yes | — |
| 394 | C8 | #551 | 1 | 2 | yes | — |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | — | 2 | 1 | no | — |
| 397 | C22 | — | 2 | 2 | no | — |
| 398 | C22 | — | 4 | 2 | no | — |
| 399 | C22 | — | 4 | 1 | no | — |
| 400 | C22 | — | 4 | 1 | no | — |
| 401 | C22 | — | 8 | 1 | no | — |
| 402 | C22 | — | 8 | 2 | no | — |
| 403 | C22 | — | 8 | 2 | no | — |
| 404 | C22 | — | 8 | 2 | no | — |
| 405 | C22 | — | 8 | 2 | no | — |
| 406 | C22 | — | 8 | 2 | no | — |
| 407 | C22 | — | 8 | 2 | no | — |
| 408 | C22 | — | 16 | 1 | no | — |
| 409 | C22 | — | 16 | 1 | no | — |
| 410 | C22 | — | 16 | 4 | no | — |
| 411 | C22 | — | 16 | 1 | no | — |
| 412 | C22 | — | 16 | 1 | no | — |
| 413 | C22 | C2×#463 | 1 | 1 | yes | characteristic |
| 414 | C22 | #3109 | 1 | 1 | yes | characteristic |
| 415 | C22 | #3192 | 1 | 1 | yes | characteristic |
| 416 | C4 | — | 2 | 2 | no | — |
| 417 | C4 | — | 4 | 2 | no | — |
| 418 | C4 | — | 4 | 2 | no | — |
| 419 | C4 | — | 8 | 2 | no | — |
| 420 | C4 | — | 8 | 2 | no | — |
| 421 | C4 | — | 16 | 1 | no | — |
| 422 | C4 | — | 16 | 1 | no | — |
| 423 | C4 | #2534 | 1 | 1 | yes | characteristic |
| 424 | C4 | #3038 | 1 | 1 | yes | characteristic |
| 425 | C4 | #3105 | 1 | 1 | yes | characteristic |
| 426 | C4 | #3188 | 1 | 1 | yes | characteristic |
| 427 | C2 | — | 2 | 1 | no | — |
| 428 | C2 | — | 2 | 1 | no | — |
| 429 | C2 | — | 4 | 2 | no | — |
| 430 | C2 | — | 16 | 2 | no | — |
| 431 | C2 | — | 16 | 2 | no | — |
| 432 | C2 | #28117 | 1 | 1 | yes | characteristic |
| 433 | C2 | #33688 | 1 | 1 | yes | characteristic |
| 434 | C2 | #33690 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #3109 |
| commutator, Frattini, cosocle | C22×C8 | C24 |
| prime radical | C2×#2190 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×C4×M16 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#2238 | C2 | semidirect |
| 3. #21538 | C2 | semidirect |
| 4. #21241 | C2 | semidirect |
| 5. #13467 | C2 | semidirect |
| 6. #13445 | C2 | semidirect |
| 7. #13143 | C2 | semidirect |
| 8. #13037 | C2 | semidirect |
| 9. #12875 | C2 | semidirect |
| 10. #12791 | C2 | semidirect |
| 11. #12739 | C2 | semidirect |
| 15. C2×#442 | C22 | semidirect |
| 23. C2×#365 | C22 | semidirect |
| 24. C2×#364 | C22 | semidirect |
| 25. C2×#361 | C22 | semidirect |
| 35. #1970 | C22 | semidirect |
| 36. #1941 | C22 | semidirect |
| 40. #1776 | C22 | semidirect |
| 42. #1387 | C22 | semidirect |
| 43. #1383 | C22 | semidirect |
| 44. #1375 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2238 | 2 |
| C2×#2190 | 2 |
| #21538 | 2 |
| #21241 | 2 |
| #13467 | 2 |
| #13445 | 2 |
| #13143 | 2 |
| #13037 | 2 |
| #12875 | 2 |
| #12791 | 2 |
| #12739 | 2 |