Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
576 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 56 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×#73035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11711663 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11711662 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11711655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #512830 | — | 3 | 1 | no | maximal, Sylow |
| 7 | A4×#135 | — | 2 | 1 | no | — |
| 8 | C2×#5402 | — | 2 | 1 | no | — |
| 9 | A4×Q32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | A4×SD32 | — | 2 | 1 | no | — |
| 11 | A4×D16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×A4×C16 | C22 | 1 | 1 | yes | characteristic |
| 13 | #73035 | — | 2 | 1 | no | — |
| 14 | #73035 | C22 | 1 | 2 | yes | — |
| 15 | #71509 | — | 4 | 1 | no | maximal |
| 16 | A4⋊C32 | C22 | 1 | 2 | yes | complemented |
| 17 | C22×#508 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×#2263 | — | 3 | 1 | no | — |
| 19 | C2×#2263 | — | 3 | 1 | no | — |
| 20 | C2×#2215 | — | 3 | 1 | no | — |
| 21 | #13663 | — | 3 | 2 | no | — |
| 22 | #13663 | — | 3 | 2 | no | — |
| 23 | #13662 | — | 3 | 2 | no | — |
| 24 | #13661 | — | 3 | 2 | no | — |
| 25 | #13616 | — | 3 | 1 | no | — |
| 26 | #13616 | — | 3 | 1 | no | — |
| 27 | #13553 | — | 3 | 1 | no | — |
| 28 | A4×#41 | — | 4 | 1 | no | — |
| 29 | C2×C4⋊S4 | — | 4 | 1 | no | — |
| 30 | A4×Q16 | — | 2 | 1 | no | — |
| 31 | A4×SD16 | — | 4 | 1 | no | — |
| 32 | A4×D8 | — | 2 | 1 | no | — |
| 33 | C2×C8×A4 | D4 | 1 | 1 | yes | characteristic |
| 34 | #5402 | — | 2 | 2 | no | — |
| 35 | #5402 | — | 4 | 1 | no | — |
| 36 | C3×#508 | — | 4 | 1 | no | — |
| 37 | C2×D48 | — | 4 | 1 | no | — |
| 38 | A4×C16 | D4 | 1 | 1 | yes | characteristic |
| 39 | A4×C16 | C23 | 1 | 1 | yes | characteristic |
| 40 | #4521 | — | 4 | 2 | no | — |
| 41 | #4519 | — | 4 | 2 | no | — |
| 42 | #4499 | — | 4 | 1 | no | — |
| 43 | C22×#135 | — | 2 | 1 | no | — |
| 44 | C2×#508 | — | 3 | 1 | no | — |
| 45 | C2×#508 | — | 3 | 1 | no | — |
| 46 | C2×#508 | — | 3 | 1 | no | — |
| 47 | C2×#508 | — | 3 | 1 | no | — |
| 48 | C2×#508 | — | 6 | 1 | no | — |
| 49 | C2×#508 | — | 6 | 1 | no | — |
| 50 | C22×Q32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×SD32 | — | 2 | 1 | no | — |
| 52 | C22×D16 | — | 3 | 1 | no | — |
| 53 | C22×D16 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C23×C16 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | C2×#466 | — | 6 | 1 | no | — |
| 56 | #2263 | — | 6 | 2 | no | — |
| 57 | #2263 | — | 6 | 2 | no | — |
| 58 | #2263 | — | 6 | 1 | no | — |
| 59 | #2263 | — | 6 | 1 | no | — |
| 60 | #2263 | — | 6 | 1 | no | — |
| 61 | #2263 | — | 6 | 1 | no | — |
| 62 | C2×SD64 | — | 3 | 2 | no | — |
| 63 | C2×SD64 | — | 3 | 2 | no | — |
| 64 | C2×D32 | — | 3 | 2 | no | — |
| 65 | C2×D32 | — | 3 | 2 | no | — |
| 66 | C2×M64 | — | 3 | 1 | no | — |
| 67 | C2×M64 | — | 3 | 1 | no | — |
| 68 | #2215 | — | 3 | 2 | no | — |
| 69 | #2215 | — | 3 | 2 | no | — |
| 70 | #2215 | — | 6 | 1 | no | — |
| 71 | #2215 | — | 6 | 1 | no | — |
| 72 | C2×#366 | — | 3 | 1 | no | — |
| 73 | C2×#357 | — | 6 | 1 | no | — |
| 74 | #1416 | — | 3 | 2 | no | — |
| 75 | #1416 | — | 3 | 2 | no | — |
| 76 | #1415 | — | 3 | 2 | no | — |
| 77 | #1415 | — | 3 | 2 | no | — |
| 78 | C22⋊C32 | — | 3 | 2 | no | — |
| 79 | C22⋊C32 | — | 3 | 2 | no | — |
| 80 | C22×S4 | — | 8 | 1 | no | — |
| 81 | Q8×A4 | — | 4 | 1 | no | — |
| 82 | D4×A4 | — | 4 | 1 | no | — |
| 83 | D4×A4 | — | 8 | 1 | no | — |
| 84 | C2×C4×A4 | — | 8 | 1 | no | — |
| 85 | C2×C4×A4 | D8 | 1 | 1 | yes | characteristic |
| 86 | C4⋊S4 | — | 4 | 2 | no | — |
| 87 | C4⋊S4 | — | 8 | 1 | no | — |
| 88 | C3×#135 | — | 8 | 1 | no | — |
| 89 | C2×D24 | — | 8 | 1 | no | — |
| 90 | C8×A4 | D8 | 1 | 1 | yes | characteristic |
| 91 | C8×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C3×Q32 | — | 4 | 1 | no | — |
| 93 | C3×SD32 | — | 8 | 1 | no | — |
| 94 | C3×D16 | — | 4 | 1 | no | — |
| 95 | C2×C3×C16 | — | 4 | 1 | no | — |
| 96 | D48 | — | 4 | 2 | no | — |
| 97 | D48 | — | 8 | 1 | no | — |
| 98 | C3⋊C32 | — | 4 | 2 | no | — |
| 99 | C22×#41 | — | 4 | 1 | no | — |
| 100 | C2×#135 | — | 6 | 1 | no | — |
| 101 | C2×#135 | — | 6 | 1 | no | — |
| 102 | C2×#135 | — | 6 | 1 | no | — |
| 103 | C2×#135 | — | 6 | 1 | no | — |
| 104 | C2×#135 | — | 12 | 1 | no | — |
| 105 | C2×#135 | — | 12 | 1 | no | — |
| 106 | C22×Q16 | — | 2 | 1 | no | — |
| 107 | C22×SD16 | — | 4 | 1 | no | — |
| 108 | C22×D8 | — | 2 | 1 | no | — |
| 109 | C22×D8 | — | 6 | 1 | no | — |
| 110 | C23×C8 | #67 | 1 | 1 | yes | characteristic |
| 111 | C2×#121 | — | 12 | 1 | no | — |
| 112 | #508 | — | 3 | 2 | no | — |
| 113 | #508 | — | 3 | 2 | no | — |
| 114 | #508 | — | 3 | 1 | no | — |
| 115 | #508 | — | 3 | 1 | no | — |
| 116 | #508 | — | 3 | 1 | no | — |
| 117 | #508 | — | 6 | 1 | no | — |
| 118 | #508 | — | 6 | 1 | no | — |
| 119 | #508 | — | 6 | 1 | no | — |
| 120 | #508 | — | 6 | 2 | no | — |
| 121 | #508 | — | 6 | 2 | no | — |
| 122 | #508 | S4 | 1 | 1 | yes | characteristic, complemented |
| 123 | C2×Q32 | — | 3 | 1 | no | — |
| 124 | C2×Q32 | — | 3 | 1 | no | — |
| 125 | C2×Q32 | — | 6 | 1 | no | — |
| 126 | C2×SD32 | — | 6 | 1 | no | — |
| 127 | C2×SD32 | — | 6 | 1 | no | — |
| 128 | C2×SD32 | — | 6 | 1 | no | — |
| 129 | C2×SD32 | — | 6 | 1 | no | — |
| 130 | C2×D16 | — | 3 | 1 | no | — |
| 131 | C2×D16 | — | 3 | 1 | no | — |
| 132 | C2×D16 | — | 3 | 2 | no | — |
| 133 | C2×D16 | — | 6 | 1 | no | — |
| 134 | C2×D16 | — | 6 | 1 | no | — |
| 135 | C2×D16 | — | 6 | 1 | no | — |
| 136 | C2×D16 | — | 6 | 1 | no | — |
| 137 | C2×D16 | — | 6 | 1 | no | — |
| 138 | C2×D16 | — | 6 | 1 | no | — |
| 139 | C22×C16 | — | 3 | 1 | no | — |
| 140 | C22×C16 | — | 3 | 1 | no | — |
| 141 | C22×C16 | — | 3 | 1 | no | — |
| 142 | C22×C16 | — | 3 | 1 | no | — |
| 143 | C22×C16 | #67 | 1 | 1 | yes | characteristic |
| 144 | C22×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 145 | #466 | — | 6 | 2 | no | — |
| 146 | #466 | — | 6 | 2 | no | — |
| 147 | #466 | — | 12 | 1 | no | — |
| 148 | #466 | — | 12 | 1 | no | — |
| 149 | C2×#107 | — | 6 | 1 | no | — |
| 150 | C2×#102 | — | 12 | 1 | no | — |
| 151 | SD64 | — | 6 | 4 | no | — |
| 152 | SD64 | — | 6 | 2 | no | — |
| 153 | SD64 | — | 6 | 2 | no | — |
| 154 | D32 | — | 6 | 4 | no | — |
| 155 | D32 | — | 6 | 2 | no | — |
| 156 | D32 | — | 6 | 2 | no | — |
| 157 | M64 | — | 6 | 1 | no | — |
| 158 | M64 | — | 6 | 1 | no | — |
| 159 | M64 | — | 6 | 1 | no | — |
| 160 | M64 | — | 6 | 1 | no | — |
| 161 | C2×C32 | — | 3 | 2 | no | — |
| 162 | C2×C32 | — | 3 | 2 | no | — |
| 163 | #366 | — | 3 | 2 | no | — |
| 164 | #366 | — | 6 | 1 | no | — |
| 165 | #357 | — | 6 | 2 | no | — |
| 166 | #357 | — | 6 | 2 | no | — |
| 167 | C22×A4 | — | 8 | 1 | no | — |
| 168 | C22×A4 | D16 | 1 | 1 | yes | characteristic |
| 169 | C2×S4 | — | 8 | 2 | no | — |
| 170 | C2×S4 | — | 16 | 2 | no | — |
| 171 | C3×#41 | — | 16 | 1 | no | — |
| 172 | C2×D12 | — | 16 | 1 | no | — |
| 173 | C4×A4 | — | 8 | 1 | no | — |
| 174 | C4×A4 | D16 | 1 | 1 | yes | characteristic |
| 175 | C4×A4 | C2×D8 | 1 | 1 | yes | characteristic |
| 176 | C3×Q16 | — | 8 | 1 | no | — |
| 177 | C3×SD16 | — | 16 | 1 | no | — |
| 178 | C3×D8 | — | 8 | 1 | no | — |
| 179 | C2×C3×C8 | — | 4 | 1 | no | — |
| 180 | D24 | — | 8 | 2 | no | — |
| 181 | D24 | — | 16 | 1 | no | — |
| 182 | C3×C16 | — | 4 | 1 | no | — |
| 183 | C3×C16 | — | 4 | 1 | no | — |
| 184 | C2×#41 | — | 12 | 1 | no | — |
| 185 | C2×#41 | — | 12 | 1 | no | — |
| 186 | C2×#41 | — | 12 | 1 | no | — |
| 187 | C2×#41 | — | 12 | 1 | no | — |
| 188 | C2×#41 | — | 24 | 1 | no | — |
| 189 | C2×#41 | — | 24 | 1 | no | — |
| 190 | C22×Q8 | — | 4 | 1 | no | — |
| 191 | C22×D4 | — | 4 | 1 | no | — |
| 192 | C22×D4 | — | 8 | 1 | no | — |
| 193 | C22×D4 | — | 12 | 1 | no | — |
| 194 | C22×D4 | — | 24 | 1 | no | — |
| 195 | C23×C4 | — | 8 | 1 | no | — |
| 196 | C23×C4 | #213 | 1 | 1 | yes | characteristic |
| 197 | #135 | — | 2 | 1 | no | — |
| 198 | #135 | — | 6 | 1 | no | — |
| 199 | #135 | — | 6 | 1 | no | — |
| 200 | #135 | — | 6 | 2 | no | — |
| 201 | #135 | — | 6 | 1 | no | — |
| 202 | #135 | — | 12 | 1 | no | — |
| 203 | #135 | — | 12 | 1 | no | — |
| 204 | #135 | — | 12 | 1 | no | — |
| 205 | #135 | — | 12 | 1 | no | — |
| 206 | #135 | — | 12 | 2 | no | — |
| 207 | #135 | — | 12 | 2 | no | — |
| 208 | C2×Q16 | — | 6 | 1 | no | — |
| 209 | C2×Q16 | — | 6 | 1 | no | — |
| 210 | C2×Q16 | — | 12 | 1 | no | — |
| 211 | C2×SD16 | — | 12 | 1 | no | — |
| 212 | C2×SD16 | — | 12 | 1 | no | — |
| 213 | C2×SD16 | — | 12 | 1 | no | — |
| 214 | C2×SD16 | — | 12 | 1 | no | — |
| 215 | C2×D8 | — | 6 | 1 | no | — |
| 216 | C2×D8 | — | 6 | 1 | no | — |
| 217 | C2×D8 | — | 6 | 2 | no | — |
| 218 | C2×D8 | — | 12 | 1 | no | — |
| 219 | C2×D8 | — | 12 | 1 | no | — |
| 220 | C2×D8 | — | 12 | 1 | no | — |
| 221 | C2×D8 | — | 12 | 1 | no | — |
| 222 | C2×D8 | — | 12 | 1 | no | — |
| 223 | C2×D8 | — | 12 | 1 | no | — |
| 224 | C22×C8 | — | 3 | 1 | no | — |
| 225 | C22×C8 | — | 3 | 1 | no | — |
| 226 | C22×C8 | — | 3 | 1 | no | — |
| 227 | C22×C8 | — | 3 | 1 | no | — |
| 228 | C22×C8 | #213 | 1 | 1 | yes | characteristic |
| 229 | C22×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 230 | #121 | — | 12 | 2 | no | — |
| 231 | #121 | — | 12 | 2 | no | — |
| 232 | #121 | — | 24 | 1 | no | — |
| 233 | #121 | — | 24 | 1 | no | — |
| 234 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 235 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 236 | Q32 | — | 3 | 2 | no | — |
| 237 | Q32 | — | 3 | 1 | no | — |
| 238 | Q32 | — | 6 | 1 | no | — |
| 239 | Q32 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 240 | SD32 | — | 2 | 1 | no | — |
| 241 | SD32 | — | 6 | 1 | no | — |
| 242 | SD32 | — | 6 | 1 | no | — |
| 243 | SD32 | — | 6 | 2 | no | — |
| 244 | SD32 | — | 6 | 1 | no | — |
| 245 | D16 | — | 3 | 2 | no | — |
| 246 | D16 | — | 3 | 1 | no | — |
| 247 | D16 | — | 6 | 1 | no | — |
| 248 | D16 | — | 6 | 2 | no | — |
| 249 | D16 | — | 6 | 2 | no | — |
| 250 | D16 | — | 12 | 1 | no | — |
| 251 | D16 | — | 12 | 1 | no | — |
| 252 | D16 | C2×S4 | 1 | 1 | yes | characteristic, complemented |
| 253 | C2×C16 | — | 3 | 1 | no | — |
| 254 | C2×C16 | — | 3 | 1 | no | — |
| 255 | C2×C16 | — | 3 | 1 | no | — |
| 256 | C2×C16 | — | 3 | 1 | no | — |
| 257 | C2×C16 | — | 3 | 1 | no | — |
| 258 | C2×C16 | — | 3 | 1 | no | — |
| 259 | C2×C16 | — | 3 | 1 | no | — |
| 260 | C2×C16 | — | 6 | 1 | no | — |
| 261 | C2×C16 | C2×S4 | 1 | 1 | yes | characteristic |
| 262 | #107 | — | 6 | 2 | no | — |
| 263 | #107 | — | 12 | 1 | no | — |
| 264 | #102 | — | 12 | 2 | no | — |
| 265 | #102 | — | 12 | 2 | no | — |
| 266 | C32 | — | 6 | 2 | no | — |
| 267 | C32 | — | 6 | 2 | no | — |
| 268 | C22×D3 | — | 32 | 1 | no | — |
| 269 | C2×A4 | — | 2 | 1 | no | — |
| 270 | C2×A4 | — | 16 | 1 | no | — |
| 271 | C2×A4 | C2×D16 | 1 | 1 | yes | characteristic |
| 272 | S4 | — | 16 | 2 | no | — |
| 273 | C3×Q8 | — | 16 | 1 | no | — |
| 274 | C3×D4 | — | 16 | 1 | no | — |
| 275 | C3×D4 | — | 32 | 1 | no | — |
| 276 | C2×C3×C4 | — | 4 | 1 | no | — |
| 277 | C2×C3×C4 | — | 32 | 1 | no | — |
| 278 | D12 | — | 16 | 2 | no | — |
| 279 | D12 | — | 32 | 1 | no | — |
| 280 | C3×C8 | — | 4 | 1 | no | — |
| 281 | C3×C8 | — | 4 | 1 | no | — |
| 282 | C24 | — | 8 | 1 | no | — |
| 283 | C24 | — | 24 | 1 | no | — |
| 284 | C24 | #826 | 1 | 1 | yes | characteristic |
| 285 | #41 | — | 4 | 1 | no | — |
| 286 | #41 | — | 12 | 1 | no | — |
| 287 | #41 | — | 12 | 1 | no | — |
| 288 | #41 | — | 12 | 2 | no | — |
| 289 | #41 | — | 12 | 1 | no | — |
| 290 | #41 | — | 24 | 1 | no | — |
| 291 | #41 | — | 24 | 1 | no | — |
| 292 | #41 | — | 24 | 1 | no | — |
| 293 | #41 | — | 24 | 1 | no | — |
| 294 | #41 | — | 24 | 2 | no | — |
| 295 | #41 | — | 24 | 2 | no | — |
| 296 | C2×Q8 | — | 12 | 1 | no | — |
| 297 | C2×Q8 | — | 12 | 1 | no | — |
| 298 | C2×Q8 | — | 24 | 1 | no | — |
| 299 | C2×D4 | — | 12 | 1 | no | — |
| 300 | C2×D4 | — | 12 | 1 | no | — |
| 301 | C2×D4 | — | 12 | 2 | no | — |
| 302 | C2×D4 | — | 24 | 1 | no | — |
| 303 | C2×D4 | — | 24 | 1 | no | — |
| 304 | C2×D4 | — | 24 | 1 | no | — |
| 305 | C2×D4 | — | 24 | 1 | no | — |
| 306 | C2×D4 | — | 24 | 1 | no | — |
| 307 | C2×D4 | — | 24 | 1 | no | — |
| 308 | C2×D4 | — | 24 | 1 | no | — |
| 309 | C2×D4 | — | 24 | 1 | no | — |
| 310 | C2×D4 | — | 24 | 1 | no | — |
| 311 | C2×D4 | — | 24 | 2 | no | — |
| 312 | C2×D4 | — | 24 | 2 | no | — |
| 313 | C2×D4 | — | 24 | 1 | no | — |
| 314 | C2×D4 | — | 48 | 2 | no | — |
| 315 | C2×D4 | — | 48 | 2 | no | — |
| 316 | C22×C4 | — | 3 | 1 | no | — |
| 317 | C22×C4 | — | 3 | 1 | no | — |
| 318 | C22×C4 | — | 3 | 1 | no | — |
| 319 | C22×C4 | — | 3 | 1 | no | — |
| 320 | C22×C4 | — | 8 | 1 | no | — |
| 321 | C22×C4 | — | 24 | 1 | no | — |
| 322 | C22×C4 | — | 24 | 1 | no | — |
| 323 | C22×C4 | — | 24 | 1 | no | — |
| 324 | C22×C4 | — | 24 | 1 | no | — |
| 325 | C22×C4 | — | 24 | 1 | no | — |
| 326 | C22×C4 | #826 | 1 | 1 | yes | characteristic |
| 327 | C22×C4 | C2×#213 | 1 | 1 | yes | characteristic |
| 328 | Q16 | — | 2 | 1 | no | — |
| 329 | Q16 | — | 6 | 1 | no | — |
| 330 | Q16 | — | 12 | 1 | no | — |
| 331 | Q16 | — | 12 | 1 | no | — |
| 332 | SD16 | — | 4 | 1 | no | — |
| 333 | SD16 | — | 12 | 1 | no | — |
| 334 | SD16 | — | 12 | 1 | no | — |
| 335 | SD16 | — | 12 | 2 | no | — |
| 336 | SD16 | — | 12 | 1 | no | — |
| 337 | D8 | — | 2 | 1 | no | — |
| 338 | D8 | — | 6 | 1 | no | — |
| 339 | D8 | — | 12 | 1 | no | — |
| 340 | D8 | — | 12 | 1 | no | — |
| 341 | D8 | — | 12 | 2 | no | — |
| 342 | D8 | — | 12 | 2 | no | — |
| 343 | D8 | — | 24 | 1 | no | — |
| 344 | D8 | — | 24 | 1 | no | — |
| 345 | C2×C8 | — | 3 | 1 | no | — |
| 346 | C2×C8 | — | 3 | 1 | no | — |
| 347 | C2×C8 | — | 3 | 1 | no | — |
| 348 | C2×C8 | — | 3 | 1 | no | — |
| 349 | C2×C8 | — | 3 | 1 | no | — |
| 350 | C2×C8 | — | 3 | 1 | no | — |
| 351 | C2×C8 | — | 3 | 1 | no | — |
| 352 | C2×C8 | — | 6 | 1 | no | — |
| 353 | C2×C8 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 354 | C4⋊C4 | — | 12 | 2 | no | — |
| 355 | C4⋊C4 | — | 24 | 1 | no | — |
| 356 | C22⋊C4 | — | 24 | 2 | no | — |
| 357 | C22⋊C4 | — | 24 | 2 | no | — |
| 358 | C16 | — | 3 | 1 | no | — |
| 359 | C16 | — | 3 | 1 | no | — |
| 360 | C16 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 361 | C16 | C22×S4 | 1 | 1 | yes | characteristic |
| 362 | C22×C3 | — | 4 | 1 | no | — |
| 363 | C22×C3 | — | 32 | 1 | no | — |
| 364 | C2×D3 | — | 32 | 2 | no | — |
| 365 | C2×D3 | — | 64 | 2 | no | — |
| 366 | A4 | #2263 | 1 | 1 | yes | characteristic, complemented |
| 367 | C3×C4 | — | 4 | 1 | no | — |
| 368 | C3×C4 | — | 4 | 1 | no | — |
| 369 | C3×C4 | — | 32 | 1 | no | — |
| 370 | C23 | — | 2 | 1 | no | — |
| 371 | C23 | — | 3 | 1 | no | — |
| 372 | C23 | — | 3 | 1 | no | — |
| 373 | C23 | — | 6 | 1 | no | — |
| 374 | C23 | — | 16 | 1 | no | — |
| 375 | C23 | — | 24 | 1 | no | — |
| 376 | C23 | — | 24 | 1 | no | — |
| 377 | C23 | — | 24 | 2 | no | — |
| 378 | C23 | — | 48 | 1 | no | — |
| 379 | C23 | — | 48 | 1 | no | — |
| 380 | C23 | — | 48 | 2 | no | — |
| 381 | C23 | — | 48 | 2 | no | — |
| 382 | C23 | — | 48 | 1 | no | — |
| 383 | C23 | C2×#826 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 4 | 1 | no | — |
| 385 | Q8 | — | 12 | 1 | no | — |
| 386 | Q8 | — | 24 | 1 | no | — |
| 387 | Q8 | — | 24 | 1 | no | — |
| 388 | D4 | — | 4 | 1 | no | — |
| 389 | D4 | — | 8 | 1 | no | — |
| 390 | D4 | — | 12 | 1 | no | — |
| 391 | D4 | — | 24 | 1 | no | — |
| 392 | D4 | — | 24 | 1 | no | — |
| 393 | D4 | — | 24 | 2 | no | — |
| 394 | D4 | — | 24 | 1 | no | — |
| 395 | D4 | — | 24 | 1 | no | — |
| 396 | D4 | — | 24 | 2 | no | — |
| 397 | D4 | — | 24 | 1 | no | — |
| 398 | D4 | — | 24 | 2 | no | — |
| 399 | D4 | — | 48 | 1 | no | — |
| 400 | D4 | — | 48 | 2 | no | — |
| 401 | D4 | — | 48 | 4 | no | — |
| 402 | D4 | — | 48 | 2 | no | — |
| 403 | D4 | — | 48 | 1 | no | — |
| 404 | C2×C4 | — | 3 | 1 | no | — |
| 405 | C2×C4 | — | 3 | 1 | no | — |
| 406 | C2×C4 | — | 3 | 1 | no | — |
| 407 | C2×C4 | — | 3 | 1 | no | — |
| 408 | C2×C4 | — | 3 | 1 | no | — |
| 409 | C2×C4 | — | 3 | 1 | no | — |
| 410 | C2×C4 | — | 3 | 1 | no | — |
| 411 | C2×C4 | — | 6 | 1 | no | — |
| 412 | C2×C4 | — | 8 | 1 | no | — |
| 413 | C2×C4 | — | 24 | 1 | no | — |
| 414 | C2×C4 | — | 24 | 1 | no | — |
| 415 | C2×C4 | — | 24 | 2 | no | — |
| 416 | C2×C4 | — | 24 | 1 | no | — |
| 417 | C2×C4 | — | 24 | 1 | no | — |
| 418 | C2×C4 | — | 24 | 1 | no | — |
| 419 | C2×C4 | — | 24 | 2 | no | — |
| 420 | C2×C4 | — | 48 | 2 | no | — |
| 421 | C2×C4 | #5415 | 1 | 1 | yes | characteristic |
| 422 | C8 | — | 3 | 1 | no | — |
| 423 | C8 | — | 3 | 1 | no | — |
| 424 | C8 | #5415 | 1 | 1 | yes | characteristic |
| 425 | C8 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 426 | C2×C3 | — | 4 | 1 | no | — |
| 427 | C2×C3 | — | 8 | 1 | no | — |
| 428 | C2×C3 | — | 64 | 1 | no | — |
| 429 | D3 | — | 64 | 2 | no | — |
| 430 | C22 | — | 3 | 1 | no | — |
| 431 | C22 | — | 3 | 1 | no | — |
| 432 | C22 | — | 3 | 1 | no | — |
| 433 | C22 | — | 6 | 1 | no | — |
| 434 | C22 | — | 6 | 1 | no | — |
| 435 | C22 | — | 6 | 1 | no | — |
| 436 | C22 | — | 6 | 1 | no | — |
| 437 | C22 | — | 8 | 1 | no | — |
| 438 | C22 | — | 24 | 1 | no | — |
| 439 | C22 | — | 48 | 1 | no | — |
| 440 | C22 | — | 48 | 1 | no | — |
| 441 | C22 | — | 48 | 1 | no | — |
| 442 | C22 | — | 48 | 1 | no | — |
| 443 | C22 | — | 48 | 2 | no | — |
| 444 | C22 | — | 48 | 2 | no | — |
| 445 | C22 | — | 48 | 2 | no | — |
| 446 | C22 | — | 96 | 2 | no | — |
| 447 | C22 | — | 96 | 2 | no | — |
| 448 | C22 | #71509 | 1 | 1 | yes | characteristic, complemented |
| 449 | C22 | #73133 | 1 | 1 | yes | characteristic |
| 450 | C4 | — | 3 | 1 | no | — |
| 451 | C4 | — | 3 | 1 | no | — |
| 452 | C4 | — | 8 | 1 | no | — |
| 453 | C4 | — | 24 | 1 | no | — |
| 454 | C4 | — | 48 | 2 | no | — |
| 455 | C4 | #73133 | 1 | 1 | yes | characteristic |
| 456 | C4 | C2×#5415 | 1 | 1 | yes | characteristic |
| 457 | C3 | — | 4 | 1 | no | Sylow |
| 458 | C2 | — | 2 | 1 | no | — |
| 459 | C2 | — | 3 | 1 | no | — |
| 460 | C2 | — | 3 | 1 | no | — |
| 461 | C2 | — | 6 | 1 | no | — |
| 462 | C2 | — | 16 | 1 | no | — |
| 463 | C2 | — | 48 | 1 | no | — |
| 464 | C2 | — | 96 | 2 | no | — |
| 465 | C2 | C2×#73133 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#73133 |
| commutator, cosocle | A4×C16 | C23 |
| Frattini | C16 | C22×S4 |
| Fitting | C22×#508 | D3 |
| socle | C23 | C2×#826 |
| hypercenter | #508 | S4 |
| hypocenter | A4 | #2263 |
| LCS | G ▷ A4×C16 ▷ C8×A4 ▷ C4×A4 ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #508 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#73035 | C2 | semidirect |
| 2. #11711663 | C2 | semidirect |
| 3. #11711662 | C2 | semidirect |
| 4. #11711655 | C2 | semidirect |
| 5. A4×#508 | C2 | semidirect |
| 9. A4×Q32 | C22 | semidirect |
| 11. A4×D16 | C22 | semidirect |
| 16. A4⋊C32 | C22 | semidirect |
| 17. C22×#508 | D3 | semidirect |
| 50. C22×Q32 | C2×D3 | semidirect |
| 53. C22×D16 | C2×D3 | semidirect |
| 122. #508 | S4 | semidirect |
| 239. Q32 | C2×S4 | semidirect |
| 252. D16 | C2×S4 | semidirect |
| 366. A4 | #2263 | semidirect |
| 448. C22 | #71509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#73035 | 2 |
| #11711663 | 2 |
| #11711662 | 2 |
| #11711655 | 2 |
| A4×#508 | 2 |
| #512830 | 3 |
| #71509 | 4 |