Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
1429 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 1429 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #72342732 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72342710 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72342703 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72342693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#2177 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72227128 | — | 3 | 1 | no | maximal, Sylow |
| 7 | D4×A4⋊C8 | — | 2 | 2 | no | — |
| 8 | #11711481 | C22 | 1 | 1 | yes | characteristic |
| 9 | #11711066 | C22 | 1 | 2 | yes | — |
| 10 | D4⋊(A4⋊C8) | — | 2 | 2 | no | — |
| 11 | #11710984 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×A4×D16 | C4 | 1 | 1 | yes | characteristic |
| 13 | C4×A4×D8 | C22 | 1 | 2 | yes | — |
| 14 | A4×#367 | C4 | 1 | 1 | yes | characteristic |
| 15 | A4×#357 | C4 | 1 | 2 | yes | — |
| 16 | A4×#346 | C22 | 1 | 1 | yes | characteristic |
| 17 | #10707072 | — | 4 | 1 | no | maximal |
| 18 | C22×#2177 | D3 | 1 | 1 | yes | characteristic |
| 19 | C2×#12067 | — | 3 | 1 | no | — |
| 20 | C2×#12067 | — | 3 | 1 | no | — |
| 21 | #220116 | — | 3 | 2 | no | — |
| 22 | #140751 | — | 3 | 1 | no | — |
| 23 | #140751 | — | 3 | 1 | no | — |
| 24 | #136707 | — | 3 | 2 | no | — |
| 25 | #136707 | — | 3 | 2 | no | — |
| 26 | #134657 | — | 3 | 1 | no | — |
| 27 | #129503 | — | 3 | 2 | no | — |
| 28 | #128255 | — | 3 | 1 | no | — |
| 29 | C2×A4×D8 | C2×C4 | 1 | 2 | yes | — |
| 30 | C4×D4×A4 | — | 2 | 2 | no | — |
| 31 | C22×A4⋊C8 | — | 4 | 2 | no | — |
| 32 | A4×D16 | C8 | 1 | 4 | yes | complemented |
| 33 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×A4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | A4×#107 | C2×C4 | 1 | 2 | yes | — |
| 36 | A4×#102 | — | 2 | 2 | no | — |
| 37 | C4×C8×A4 | C23 | 1 | 1 | yes | characteristic |
| 38 | #73141 | — | 4 | 2 | no | — |
| 39 | C2×A4⋊C16 | — | 2 | 1 | no | — |
| 40 | C4⋊(A4⋊C8) | — | 2 | 2 | no | — |
| 41 | C4×A4⋊C8 | D4 | 1 | 2 | yes | — |
| 42 | C3×#2177 | — | 4 | 1 | no | — |
| 43 | #70878 | — | 4 | 2 | no | — |
| 44 | #67762 | — | 4 | 2 | no | — |
| 45 | #67513 | — | 4 | 1 | no | — |
| 46 | #67511 | — | 4 | 1 | no | — |
| 47 | C23×D16 | Dic3 | 1 | 1 | yes | characteristic |
| 48 | C22×C4×D8 | C2×D3 | 1 | 2 | yes | — |
| 49 | C2×#2177 | — | 3 | 1 | no | — |
| 50 | C2×#2177 | — | 3 | 2 | no | — |
| 51 | C2×#2177 | — | 3 | 1 | no | — |
| 52 | C2×#2177 | — | 3 | 2 | no | — |
| 53 | C2×#2177 | — | 3 | 1 | no | — |
| 54 | C2×#2177 | — | 3 | 1 | no | — |
| 55 | C22×#367 | Dic3 | 1 | 1 | yes | characteristic |
| 56 | C22×#357 | Dic3 | 1 | 2 | yes | — |
| 57 | C22×#346 | C2×D3 | 1 | 1 | yes | characteristic |
| 58 | D4×C22⋊C8 | — | 6 | 2 | no | — |
| 59 | C2×#1580 | — | 3 | 2 | no | — |
| 60 | C2×#1580 | — | 3 | 2 | no | — |
| 61 | #12599 | — | 3 | 1 | no | — |
| 62 | #12067 | — | 6 | 1 | no | — |
| 63 | #12067 | — | 6 | 1 | no | — |
| 64 | #12067 | — | 6 | 2 | no | — |
| 65 | #12067 | — | 6 | 2 | no | — |
| 66 | #12067 | — | 6 | 1 | no | — |
| 67 | #12067 | — | 6 | 1 | no | — |
| 68 | C2×#1368 | — | 3 | 1 | no | — |
| 69 | C2×#1368 | — | 3 | 1 | no | — |
| 70 | C2×#1333 | — | 3 | 2 | no | — |
| 71 | C2×#1333 | — | 3 | 2 | no | — |
| 72 | C2×#1333 | — | 3 | 2 | no | — |
| 73 | C2×#1333 | — | 3 | 2 | no | — |
| 74 | C2×#1313 | — | 3 | 1 | no | — |
| 75 | C2×#1313 | — | 3 | 1 | no | — |
| 76 | #9659 | — | 3 | 2 | no | — |
| 77 | #9659 | — | 3 | 2 | no | — |
| 78 | #8947 | — | 6 | 2 | no | — |
| 79 | #8947 | — | 6 | 2 | no | — |
| 80 | #8595 | — | 3 | 2 | no | — |
| 81 | #8310 | — | 6 | 2 | no | — |
| 82 | #8144 | — | 3 | 1 | no | — |
| 83 | #7156 | — | 3 | 2 | no | — |
| 84 | #7137 | — | 3 | 1 | no | — |
| 85 | #7137 | — | 3 | 1 | no | — |
| 86 | C2×D4×A4 | — | 2 | 2 | no | — |
| 87 | C22×C4×A4 | — | 4 | 2 | no | — |
| 88 | A4×D8 | — | 2 | 2 | no | — |
| 89 | A4×D8 | C2×C8 | 1 | 4 | yes | complemented |
| 90 | C2×C8×A4 | C22×C4 | 1 | 1 | yes | characteristic |
| 91 | C2×C8×A4 | #41 | 1 | 1 | yes | characteristic |
| 92 | A4×C4⋊C4 | — | 2 | 2 | no | — |
| 93 | A4×C22⋊C4 | — | 4 | 2 | no | — |
| 94 | C42×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 95 | C2×A4⋊C8 | — | 2 | 2 | no | — |
| 96 | C2×A4⋊C8 | — | 4 | 2 | no | — |
| 97 | C2×A4⋊C8 | — | 8 | 4 | no | — |
| 98 | C2×C3×D16 | — | 4 | 1 | no | — |
| 99 | C3×C4×D8 | — | 4 | 2 | no | — |
| 100 | D4×C3⋊C8 | — | 8 | 2 | no | — |
| 101 | A4×C16 | — | 2 | 1 | no | — |
| 102 | A4×C16 | C2×C8 | 1 | 2 | yes | complemented |
| 103 | A4⋊C16 | — | 4 | 1 | no | — |
| 104 | C3×#367 | — | 4 | 1 | no | — |
| 105 | C3×#357 | — | 4 | 2 | no | — |
| 106 | C3×#346 | — | 4 | 1 | no | — |
| 107 | D4⋊(C3⋊C8) | — | 8 | 2 | no | — |
| 108 | #4461 | — | 4 | 1 | no | — |
| 109 | #4457 | — | 4 | 2 | no | — |
| 110 | #4455 | — | 4 | 1 | no | — |
| 111 | C23×D8 | C2×Dic3 | 1 | 2 | yes | — |
| 112 | C22×C4×D4 | — | 2 | 2 | no | — |
| 113 | C22×D16 | — | 3 | 1 | no | — |
| 114 | C22×D16 | — | 3 | 4 | no | — |
| 115 | C22×D16 | — | 3 | 2 | no | — |
| 116 | C22×D16 | — | 3 | 1 | no | — |
| 117 | C22×D16 | C3⋊C8 | 1 | 4 | yes | complemented |
| 118 | C23×C16 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 119 | C23×C16 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×D8 | — | 3 | 2 | no | — |
| 121 | C2×C4×D8 | — | 3 | 2 | no | — |
| 122 | C2×C4×D8 | — | 3 | 2 | no | — |
| 123 | C2×C4×D8 | — | 3 | 2 | no | — |
| 124 | C2×C4×D8 | — | 6 | 2 | no | — |
| 125 | C2×C4×D8 | — | 6 | 2 | no | — |
| 126 | C2×C8×D4 | — | 6 | 2 | no | — |
| 127 | C2×C8×D4 | — | 6 | 2 | no | — |
| 128 | C22×#107 | C2×Dic3 | 1 | 2 | yes | — |
| 129 | C22×#102 | — | 2 | 2 | no | — |
| 130 | C22×C22⋊C8 | — | 12 | 2 | no | — |
| 131 | C22×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 132 | #2177 | — | 3 | 1 | no | — |
| 133 | #2177 | — | 3 | 2 | no | — |
| 134 | #2177 | — | 3 | 1 | no | — |
| 135 | #2177 | — | 3 | 2 | no | — |
| 136 | #2177 | — | 3 | 1 | no | — |
| 137 | #2177 | — | 6 | 1 | no | — |
| 138 | #2177 | — | 6 | 1 | no | — |
| 139 | #2177 | — | 6 | 1 | no | — |
| 140 | #2177 | — | 6 | 2 | no | — |
| 141 | #2177 | — | 6 | 2 | no | — |
| 142 | #2177 | S4 | 1 | 1 | yes | characteristic |
| 143 | C2×#367 | — | 3 | 1 | no | — |
| 144 | C2×#367 | — | 3 | 1 | no | — |
| 145 | C2×#367 | — | 3 | 2 | no | — |
| 146 | C2×#357 | — | 3 | 2 | no | — |
| 147 | C2×#357 | — | 3 | 2 | no | — |
| 148 | C2×#357 | — | 3 | 2 | no | — |
| 149 | C2×#357 | — | 3 | 2 | no | — |
| 150 | C2×C22⋊C16 | — | 6 | 1 | no | — |
| 151 | C2×#346 | — | 3 | 1 | no | — |
| 152 | C2×#346 | — | 3 | 1 | no | — |
| 153 | C2×#346 | — | 3 | 1 | no | — |
| 154 | C2×#346 | — | 3 | 1 | no | — |
| 155 | C2×#346 | — | 3 | 1 | no | — |
| 156 | C2×#346 | — | 3 | 1 | no | — |
| 157 | #1954 | — | 6 | 2 | no | — |
| 158 | #1954 | — | 6 | 2 | no | — |
| 159 | #1869 | — | 12 | 2 | no | — |
| 160 | #1869 | — | 12 | 2 | no | — |
| 161 | #1797 | — | 6 | 2 | no | — |
| 162 | #1779 | — | 12 | 2 | no | — |
| 163 | C4×C22⋊C8 | — | 3 | 2 | no | — |
| 164 | #1580 | — | 6 | 2 | no | — |
| 165 | #1580 | — | 6 | 2 | no | — |
| 166 | #1580 | — | 6 | 2 | no | — |
| 167 | #1580 | — | 6 | 2 | no | — |
| 168 | #1580 | — | 12 | 2 | no | — |
| 169 | #1580 | — | 12 | 2 | no | — |
| 170 | C2×#334 | — | 3 | 2 | no | — |
| 171 | C2×#334 | — | 3 | 2 | no | — |
| 172 | C2×D4⋊C8 | — | 6 | 2 | no | — |
| 173 | C2×D4⋊C8 | — | 6 | 2 | no | — |
| 174 | C2×D4⋊C8 | — | 6 | 2 | no | — |
| 175 | C2×D4⋊C8 | — | 6 | 2 | no | — |
| 176 | C2×#322 | — | 3 | 1 | no | — |
| 177 | C2×#322 | — | 3 | 1 | no | — |
| 178 | #1374 | — | 6 | 1 | no | — |
| 179 | #1368 | — | 6 | 1 | no | — |
| 180 | #1368 | — | 6 | 1 | no | — |
| 181 | #1368 | — | 6 | 1 | no | — |
| 182 | #1368 | — | 6 | 1 | no | — |
| 183 | #1333 | — | 6 | 2 | no | — |
| 184 | #1333 | — | 6 | 2 | no | — |
| 185 | #1333 | — | 6 | 2 | no | — |
| 186 | #1333 | — | 6 | 2 | no | — |
| 187 | #1333 | — | 12 | 2 | no | — |
| 188 | #1333 | — | 12 | 2 | no | — |
| 189 | #1313 | — | 6 | 1 | no | — |
| 190 | #1313 | — | 6 | 1 | no | — |
| 191 | #1313 | — | 6 | 1 | no | — |
| 192 | #1313 | — | 6 | 1 | no | — |
| 193 | #1277 | — | 6 | 2 | no | — |
| 194 | #1273 | — | 3 | 2 | no | — |
| 195 | C23×A4 | — | 4 | 2 | no | — |
| 196 | D4×A4 | — | 2 | 4 | no | — |
| 197 | D4×A4 | — | 4 | 2 | no | — |
| 198 | C2×C4×A4 | — | 4 | 2 | no | — |
| 199 | C2×C4×A4 | — | 8 | 2 | no | — |
| 200 | C2×C4×A4 | — | 8 | 2 | no | — |
| 201 | C2×C4×A4 | C4×D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×A4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 203 | C2×C3×D8 | — | 4 | 2 | no | — |
| 204 | C3×C4×D4 | — | 8 | 2 | no | — |
| 205 | C22×C3⋊C8 | — | 16 | 2 | no | — |
| 206 | C8×A4 | — | 2 | 1 | no | — |
| 207 | C8×A4 | C22×C8 | 1 | 1 | yes | characteristic |
| 208 | C8×A4 | #131 | 1 | 1 | yes | characteristic |
| 209 | A4⋊C8 | — | 4 | 2 | no | — |
| 210 | A4⋊C8 | — | 8 | 2 | no | — |
| 211 | C3×D16 | — | 4 | 4 | no | — |
| 212 | C2×C3×C16 | — | 4 | 1 | no | — |
| 213 | C2×C3×C16 | — | 4 | 1 | no | — |
| 214 | C3×#107 | — | 4 | 2 | no | — |
| 215 | C3×#102 | — | 8 | 2 | no | — |
| 216 | C3×C4×C8 | — | 4 | 1 | no | — |
| 217 | #830 | — | 16 | 2 | no | — |
| 218 | C2×C3⋊C16 | — | 8 | 1 | no | — |
| 219 | C4⋊(C3⋊C8) | — | 8 | 2 | no | — |
| 220 | C4×C3⋊C8 | — | 4 | 2 | no | — |
| 221 | C23×D4 | — | 2 | 2 | no | — |
| 222 | C24×C4 | — | 4 | 2 | no | — |
| 223 | C22×D8 | — | 2 | 2 | no | — |
| 224 | C22×D8 | — | 3 | 2 | no | — |
| 225 | C22×D8 | — | 3 | 2 | no | — |
| 226 | C22×D8 | — | 3 | 4 | no | — |
| 227 | C22×D8 | — | 6 | 2 | no | — |
| 228 | C22×D8 | — | 6 | 2 | no | — |
| 229 | C22×D8 | C2×C3⋊C8 | 1 | 4 | yes | complemented |
| 230 | C23×C8 | — | 12 | 2 | no | — |
| 231 | C23×C8 | — | 12 | 2 | no | — |
| 232 | C23×C8 | #237 | 1 | 1 | yes | characteristic |
| 233 | C23×C8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×D4 | — | 6 | 2 | no | — |
| 235 | C2×C4×D4 | — | 6 | 2 | no | — |
| 236 | C2×C4×D4 | — | 6 | 2 | no | — |
| 237 | C2×C4×D4 | — | 6 | 2 | no | — |
| 238 | C2×C4×D4 | — | 12 | 2 | no | — |
| 239 | C2×C4×D4 | — | 12 | 2 | no | — |
| 240 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 241 | C22×C22⋊C4 | — | 4 | 2 | no | — |
| 242 | C22×C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×D16 | — | 3 | 2 | no | — |
| 244 | C2×D16 | — | 3 | 4 | no | — |
| 245 | C2×D16 | — | 3 | 4 | no | — |
| 246 | C2×D16 | — | 3 | 4 | no | — |
| 247 | C2×D16 | — | 3 | 8 | no | — |
| 248 | C2×D16 | — | 3 | 1 | no | — |
| 249 | C2×D16 | — | 6 | 2 | no | — |
| 250 | C2×D16 | — | 6 | 1 | no | — |
| 251 | C2×D16 | — | 6 | 4 | no | — |
| 252 | C2×D16 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 253 | C22×C16 | — | 2 | 1 | no | — |
| 254 | C22×C16 | — | 3 | 1 | no | — |
| 255 | C22×C16 | — | 3 | 1 | no | — |
| 256 | C22×C16 | — | 3 | 2 | no | — |
| 257 | C22×C16 | — | 3 | 1 | no | — |
| 258 | C22×C16 | — | 3 | 1 | no | — |
| 259 | C22×C16 | — | 6 | 1 | no | — |
| 260 | C22×C16 | — | 6 | 1 | no | — |
| 261 | C22×C16 | — | 6 | 1 | no | — |
| 262 | C22×C16 | C2×C3⋊C8 | 1 | 2 | yes | complemented |
| 263 | C4×D8 | — | 3 | 2 | no | — |
| 264 | C4×D8 | — | 3 | 2 | no | — |
| 265 | C4×D8 | — | 3 | 2 | no | — |
| 266 | C4×D8 | — | 6 | 2 | no | — |
| 267 | C4×D8 | — | 6 | 2 | no | — |
| 268 | C4×D8 | — | 6 | 2 | no | — |
| 269 | C4×D8 | — | 6 | 2 | no | — |
| 270 | C4×D8 | — | 6 | 2 | no | — |
| 271 | C4×D8 | — | 12 | 2 | no | — |
| 272 | C4×D8 | — | 12 | 2 | no | — |
| 273 | C4×D8 | C2×S4 | 1 | 2 | yes | — |
| 274 | C8×D4 | — | 12 | 2 | no | — |
| 275 | C8×D4 | — | 12 | 2 | no | — |
| 276 | C8×D4 | — | 12 | 2 | no | — |
| 277 | C8×D4 | — | 12 | 2 | no | — |
| 278 | C8×D4 | — | 24 | 2 | no | — |
| 279 | C8×D4 | — | 24 | 2 | no | — |
| 280 | C2×#107 | — | 3 | 2 | no | — |
| 281 | C2×#107 | — | 3 | 2 | no | — |
| 282 | C2×#107 | — | 6 | 2 | no | — |
| 283 | C2×C4⋊C8 | — | 6 | 2 | no | — |
| 284 | C2×C4⋊C8 | — | 6 | 2 | no | — |
| 285 | C2×#102 | — | 6 | 2 | no | — |
| 286 | C2×#102 | — | 6 | 2 | no | — |
| 287 | C2×#102 | — | 6 | 2 | no | — |
| 288 | C2×#102 | — | 6 | 2 | no | — |
| 289 | C2×C22⋊C8 | — | 6 | 2 | no | — |
| 290 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 291 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 292 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 293 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 294 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 295 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 296 | C2×C22⋊C8 | — | 12 | 2 | no | — |
| 297 | C2×C22⋊C8 | — | 24 | 4 | no | — |
| 298 | C2×C22⋊C8 | — | 24 | 4 | no | — |
| 299 | C2×C4×C8 | — | 3 | 1 | no | — |
| 300 | C2×C4×C8 | — | 3 | 1 | no | — |
| 301 | C2×C4×C8 | — | 3 | 1 | no | — |
| 302 | C2×C4×C8 | — | 3 | 1 | no | — |
| 303 | C2×C4×C8 | — | 3 | 2 | no | — |
| 304 | C2×C4×C8 | — | 3 | 2 | no | — |
| 305 | #367 | — | 3 | 1 | no | — |
| 306 | #367 | — | 3 | 2 | no | — |
| 307 | #367 | — | 6 | 1 | no | — |
| 308 | #367 | SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 309 | #357 | — | 3 | 2 | no | — |
| 310 | #357 | — | 3 | 2 | no | — |
| 311 | #357 | — | 3 | 2 | no | — |
| 312 | #357 | — | 6 | 2 | no | — |
| 313 | #357 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 314 | C22⋊C16 | — | 12 | 1 | no | — |
| 315 | C22⋊C16 | — | 12 | 1 | no | — |
| 316 | #346 | — | 3 | 1 | no | — |
| 317 | #346 | — | 3 | 1 | no | — |
| 318 | #346 | — | 3 | 1 | no | — |
| 319 | #346 | — | 6 | 1 | no | — |
| 320 | #346 | — | 6 | 1 | no | — |
| 321 | #346 | — | 6 | 1 | no | — |
| 322 | #346 | — | 6 | 1 | no | — |
| 323 | #346 | — | 6 | 1 | no | — |
| 324 | #346 | C2×S4 | 1 | 1 | yes | characteristic |
| 325 | #336 | — | 6 | 2 | no | — |
| 326 | #336 | — | 12 | 2 | no | — |
| 327 | #334 | — | 6 | 2 | no | — |
| 328 | #334 | — | 6 | 2 | no | — |
| 329 | #334 | — | 6 | 2 | no | — |
| 330 | #334 | — | 6 | 2 | no | — |
| 331 | D4⋊C8 | — | 12 | 2 | no | — |
| 332 | D4⋊C8 | — | 12 | 2 | no | — |
| 333 | D4⋊C8 | — | 12 | 2 | no | — |
| 334 | D4⋊C8 | — | 12 | 2 | no | — |
| 335 | D4⋊C8 | — | 24 | 2 | no | — |
| 336 | D4⋊C8 | — | 24 | 2 | no | — |
| 337 | #322 | — | 6 | 1 | no | — |
| 338 | #322 | — | 6 | 1 | no | — |
| 339 | #322 | — | 6 | 1 | no | — |
| 340 | #322 | — | 6 | 1 | no | — |
| 341 | C22×A4 | — | 4 | 4 | no | — |
| 342 | C22×A4 | — | 8 | 2 | no | — |
| 343 | C22×A4 | — | 8 | 2 | no | — |
| 344 | C22×A4 | #442 | 1 | 1 | yes | characteristic |
| 345 | C2×C3×D4 | — | 8 | 2 | no | — |
| 346 | C22×C3×C4 | — | 16 | 2 | no | — |
| 347 | C4×A4 | — | 2 | 2 | no | — |
| 348 | C4×A4 | — | 8 | 2 | no | — |
| 349 | C4×A4 | C8×D4 | 1 | 1 | yes | characteristic |
| 350 | C4×A4 | #444 | 1 | 1 | yes | characteristic |
| 351 | C3×D8 | — | 4 | 4 | no | — |
| 352 | C3×D8 | — | 8 | 2 | no | — |
| 353 | C2×C3×C8 | — | 4 | 1 | no | — |
| 354 | C2×C3×C8 | — | 4 | 1 | no | — |
| 355 | C3×C4⋊C4 | — | 8 | 2 | no | — |
| 356 | C3×C22⋊C4 | — | 16 | 2 | no | — |
| 357 | C3×C42 | — | 4 | 1 | no | — |
| 358 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 359 | C2×C3⋊C8 | — | 16 | 2 | no | — |
| 360 | C2×C3⋊C8 | — | 32 | 4 | no | — |
| 361 | C3×C16 | — | 4 | 2 | no | — |
| 362 | C3×C16 | — | 8 | 1 | no | — |
| 363 | C3⋊C16 | — | 16 | 1 | no | — |
| 364 | C25 | — | 4 | 2 | no | — |
| 365 | C22×D4 | — | 2 | 4 | no | — |
| 366 | C22×D4 | — | 4 | 2 | no | — |
| 367 | C22×D4 | — | 6 | 2 | no | — |
| 368 | C22×D4 | — | 6 | 2 | no | — |
| 369 | C22×D4 | — | 6 | 4 | no | — |
| 370 | C22×D4 | — | 12 | 2 | no | — |
| 371 | C22×D4 | — | 12 | 2 | no | — |
| 372 | C23×C4 | — | 4 | 2 | no | — |
| 373 | C23×C4 | — | 8 | 2 | no | — |
| 374 | C23×C4 | — | 8 | 2 | no | — |
| 375 | C23×C4 | — | 12 | 2 | no | — |
| 376 | C23×C4 | — | 12 | 2 | no | — |
| 377 | C23×C4 | — | 12 | 2 | no | — |
| 378 | C23×C4 | — | 12 | 2 | no | — |
| 379 | C23×C4 | — | 24 | 2 | no | — |
| 380 | C23×C4 | — | 24 | 2 | no | — |
| 381 | C23×C4 | #911 | 1 | 2 | yes | — |
| 382 | C23×C4 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 383 | C2×D8 | — | 3 | 4 | no | — |
| 384 | C2×D8 | — | 3 | 4 | no | — |
| 385 | C2×D8 | — | 3 | 4 | no | — |
| 386 | C2×D8 | — | 3 | 2 | no | — |
| 387 | C2×D8 | — | 6 | 2 | no | — |
| 388 | C2×D8 | — | 6 | 2 | no | — |
| 389 | C2×D8 | — | 6 | 2 | no | — |
| 390 | C2×D8 | — | 6 | 2 | no | — |
| 391 | C2×D8 | — | 6 | 2 | no | — |
| 392 | C2×D8 | — | 6 | 2 | no | — |
| 393 | C2×D8 | — | 6 | 4 | no | — |
| 394 | C2×D8 | — | 6 | 2 | no | — |
| 395 | C2×D8 | — | 6 | 4 | no | — |
| 396 | C2×D8 | — | 12 | 4 | no | — |
| 397 | C2×D8 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 398 | C22×C8 | — | 2 | 1 | no | — |
| 399 | C22×C8 | — | 3 | 1 | no | — |
| 400 | C22×C8 | — | 3 | 1 | no | — |
| 401 | C22×C8 | — | 3 | 1 | no | — |
| 402 | C22×C8 | — | 3 | 1 | no | — |
| 403 | C22×C8 | — | 3 | 1 | no | — |
| 404 | C22×C8 | — | 3 | 1 | no | — |
| 405 | C22×C8 | — | 6 | 1 | no | — |
| 406 | C22×C8 | — | 6 | 2 | no | — |
| 407 | C22×C8 | — | 6 | 2 | no | — |
| 408 | C22×C8 | — | 12 | 2 | no | — |
| 409 | C22×C8 | — | 12 | 2 | no | — |
| 410 | C22×C8 | — | 24 | 2 | no | — |
| 411 | C22×C8 | — | 24 | 2 | no | — |
| 412 | C22×C8 | — | 24 | 2 | no | — |
| 413 | C22×C8 | — | 24 | 2 | no | — |
| 414 | C22×C8 | — | 24 | 4 | no | — |
| 415 | C22×C8 | — | 24 | 4 | no | — |
| 416 | C22×C8 | — | 48 | 2 | no | — |
| 417 | C22×C8 | — | 48 | 2 | no | — |
| 418 | C22×C8 | C22×C3⋊C8 | 1 | 1 | yes | characteristic |
| 419 | C22×C8 | #948 | 1 | 1 | yes | characteristic |
| 420 | C4×D4 | — | 2 | 2 | no | — |
| 421 | C4×D4 | — | 6 | 2 | no | — |
| 422 | C4×D4 | — | 6 | 2 | no | — |
| 423 | C4×D4 | — | 6 | 2 | no | — |
| 424 | C4×D4 | — | 12 | 2 | no | — |
| 425 | C4×D4 | — | 12 | 2 | no | — |
| 426 | C4×D4 | — | 12 | 2 | no | — |
| 427 | C4×D4 | — | 12 | 2 | no | — |
| 428 | C4×D4 | — | 12 | 2 | no | — |
| 429 | C4×D4 | — | 24 | 2 | no | — |
| 430 | C4×D4 | — | 24 | 2 | no | — |
| 431 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 432 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 433 | C2×C4⋊C4 | — | 12 | 2 | no | — |
| 434 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 435 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 436 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 437 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 438 | C2×C42 | — | 3 | 1 | no | — |
| 439 | C2×C42 | — | 3 | 1 | no | — |
| 440 | C2×C42 | — | 3 | 2 | no | — |
| 441 | D16 | — | 3 | 8 | no | — |
| 442 | D16 | — | 3 | 4 | no | — |
| 443 | D16 | — | 6 | 4 | no | — |
| 444 | D16 | A4⋊C8 | 1 | 4 | yes | complemented |
| 445 | C2×C16 | — | 3 | 1 | no | — |
| 446 | C2×C16 | — | 3 | 2 | no | — |
| 447 | C2×C16 | — | 3 | 2 | no | — |
| 448 | C2×C16 | — | 3 | 2 | no | — |
| 449 | C2×C16 | — | 3 | 1 | no | — |
| 450 | C2×C16 | — | 6 | 1 | no | — |
| 451 | C2×C16 | — | 6 | 1 | no | — |
| 452 | C2×C16 | — | 6 | 1 | no | — |
| 453 | C2×C16 | — | 6 | 1 | no | — |
| 454 | C2×C16 | — | 6 | 1 | no | — |
| 455 | C2×C16 | — | 12 | 1 | no | — |
| 456 | C2×C16 | — | 12 | 1 | no | — |
| 457 | C2×C16 | — | 12 | 1 | no | — |
| 458 | C2×C16 | — | 12 | 1 | no | — |
| 459 | C2×C16 | — | 12 | 1 | no | — |
| 460 | C2×C16 | — | 12 | 1 | no | — |
| 461 | C2×C16 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 462 | C2×C16 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 463 | #107 | — | 3 | 2 | no | — |
| 464 | #107 | — | 6 | 2 | no | — |
| 465 | #107 | — | 6 | 2 | no | — |
| 466 | #107 | C2×SL(2,ℤ/4) | 1 | 2 | yes | — |
| 467 | C4⋊C8 | — | 12 | 2 | no | — |
| 468 | C4⋊C8 | — | 12 | 2 | no | — |
| 469 | C4⋊C8 | — | 12 | 2 | no | — |
| 470 | C4⋊C8 | — | 12 | 2 | no | — |
| 471 | #102 | — | 2 | 2 | no | — |
| 472 | #102 | — | 6 | 2 | no | — |
| 473 | #102 | — | 6 | 2 | no | — |
| 474 | #102 | — | 6 | 2 | no | — |
| 475 | #102 | — | 12 | 2 | no | — |
| 476 | C22⋊C8 | — | 12 | 2 | no | — |
| 477 | C22⋊C8 | — | 12 | 2 | no | — |
| 478 | C22⋊C8 | — | 24 | 2 | no | — |
| 479 | C22⋊C8 | — | 24 | 2 | no | — |
| 480 | C22⋊C8 | — | 24 | 2 | no | — |
| 481 | C22⋊C8 | — | 24 | 2 | no | — |
| 482 | C22⋊C8 | — | 24 | 4 | no | — |
| 483 | C22⋊C8 | — | 24 | 4 | no | — |
| 484 | C22⋊C8 | — | 24 | 2 | no | — |
| 485 | C22⋊C8 | — | 24 | 2 | no | — |
| 486 | C22⋊C8 | — | 48 | 2 | no | — |
| 487 | C22⋊C8 | — | 48 | 2 | no | — |
| 488 | C4×C8 | — | 3 | 1 | no | — |
| 489 | C4×C8 | — | 3 | 1 | no | — |
| 490 | C4×C8 | — | 3 | 1 | no | — |
| 491 | C4×C8 | — | 6 | 1 | no | — |
| 492 | C4×C8 | — | 6 | 2 | no | — |
| 493 | C4×C8 | — | 6 | 2 | no | — |
| 494 | C4×C8 | — | 6 | 2 | no | — |
| 495 | C4×C8 | — | 6 | 2 | no | — |
| 496 | C4×C8 | C22×S4 | 1 | 1 | yes | characteristic |
| 497 | C23×C3 | — | 16 | 2 | no | — |
| 498 | C2×A4 | — | 8 | 4 | no | — |
| 499 | C2×A4 | #1580 | 1 | 1 | yes | characteristic |
| 500 | C2×A4 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 501 | C3×D4 | — | 8 | 4 | no | — |
| 502 | C3×D4 | — | 16 | 2 | no | — |
| 503 | C2×C3×C4 | — | 4 | 2 | no | — |
| 504 | C2×C3×C4 | — | 4 | 1 | no | — |
| 505 | C2×C3×C4 | — | 16 | 2 | no | — |
| 506 | C2×C3×C4 | — | 32 | 2 | no | — |
| 507 | C2×C3×C4 | — | 32 | 2 | no | — |
| 508 | C3×C8 | — | 4 | 1 | no | — |
| 509 | C3×C8 | — | 4 | 1 | no | — |
| 510 | C3×C8 | — | 8 | 1 | no | — |
| 511 | C3⋊C8 | — | 16 | 2 | no | — |
| 512 | C3⋊C8 | — | 32 | 2 | no | — |
| 513 | C24 | — | 4 | 4 | no | — |
| 514 | C24 | — | 8 | 2 | no | — |
| 515 | C24 | — | 8 | 2 | no | — |
| 516 | C24 | — | 12 | 2 | no | — |
| 517 | C24 | — | 12 | 2 | no | — |
| 518 | C24 | — | 12 | 4 | no | — |
| 519 | C24 | — | 24 | 2 | no | — |
| 520 | C24 | — | 24 | 2 | no | — |
| 521 | C24 | #5152 | 1 | 1 | yes | characteristic |
| 522 | C2×D4 | — | 2 | 2 | no | — |
| 523 | C2×D4 | — | 6 | 4 | no | — |
| 524 | C2×D4 | — | 6 | 4 | no | — |
| 525 | C2×D4 | — | 6 | 4 | no | — |
| 526 | C2×D4 | — | 6 | 2 | no | — |
| 527 | C2×D4 | — | 12 | 2 | no | — |
| 528 | C2×D4 | — | 12 | 2 | no | — |
| 529 | C2×D4 | — | 12 | 2 | no | — |
| 530 | C2×D4 | — | 12 | 2 | no | — |
| 531 | C2×D4 | — | 12 | 2 | no | — |
| 532 | C2×D4 | — | 12 | 2 | no | — |
| 533 | C2×D4 | — | 12 | 4 | no | — |
| 534 | C2×D4 | — | 12 | 2 | no | — |
| 535 | C2×D4 | — | 12 | 4 | no | — |
| 536 | C2×D4 | — | 24 | 4 | no | — |
| 537 | C22×C4 | — | 2 | 2 | no | — |
| 538 | C22×C4 | — | 3 | 1 | no | — |
| 539 | C22×C4 | — | 3 | 1 | no | — |
| 540 | C22×C4 | — | 3 | 1 | no | — |
| 541 | C22×C4 | — | 3 | 1 | no | — |
| 542 | C22×C4 | — | 3 | 2 | no | — |
| 543 | C22×C4 | — | 3 | 2 | no | — |
| 544 | C22×C4 | — | 4 | 2 | no | — |
| 545 | C22×C4 | — | 6 | 2 | no | — |
| 546 | C22×C4 | — | 8 | 2 | no | — |
| 547 | C22×C4 | — | 12 | 2 | no | — |
| 548 | C22×C4 | — | 12 | 2 | no | — |
| 549 | C22×C4 | — | 12 | 2 | no | — |
| 550 | C22×C4 | — | 12 | 2 | no | — |
| 551 | C22×C4 | — | 12 | 2 | no | — |
| 552 | C22×C4 | — | 24 | 2 | no | — |
| 553 | C22×C4 | — | 24 | 2 | no | — |
| 554 | C22×C4 | — | 24 | 2 | no | — |
| 555 | C22×C4 | — | 24 | 2 | no | — |
| 556 | C22×C4 | — | 24 | 2 | no | — |
| 557 | C22×C4 | — | 24 | 2 | no | — |
| 558 | C22×C4 | — | 24 | 2 | no | — |
| 559 | C22×C4 | — | 24 | 2 | no | — |
| 560 | C22×C4 | — | 24 | 2 | no | — |
| 561 | C22×C4 | — | 24 | 2 | no | — |
| 562 | C22×C4 | — | 24 | 2 | no | — |
| 563 | C22×C4 | — | 24 | 2 | no | — |
| 564 | C22×C4 | — | 24 | 2 | no | — |
| 565 | C22×C4 | — | 24 | 2 | no | — |
| 566 | C22×C4 | — | 48 | 2 | no | — |
| 567 | C22×C4 | — | 48 | 2 | no | — |
| 568 | C22×C4 | D4×C3⋊C8 | 1 | 1 | yes | characteristic |
| 569 | C22×C4 | #5197 | 1 | 1 | yes | characteristic |
| 570 | D8 | — | 2 | 2 | no | — |
| 571 | D8 | — | 3 | 4 | no | — |
| 572 | D8 | — | 6 | 4 | no | — |
| 573 | D8 | — | 6 | 4 | no | — |
| 574 | D8 | — | 6 | 4 | no | — |
| 575 | D8 | — | 6 | 2 | no | — |
| 576 | D8 | — | 12 | 2 | no | — |
| 577 | D8 | C2×A4⋊C8 | 1 | 4 | yes | complemented |
| 578 | C2×C8 | — | 3 | 1 | no | — |
| 579 | C2×C8 | — | 3 | 1 | no | — |
| 580 | C2×C8 | — | 3 | 1 | no | — |
| 581 | C2×C8 | — | 3 | 1 | no | — |
| 582 | C2×C8 | — | 3 | 1 | no | — |
| 583 | C2×C8 | — | 3 | 1 | no | — |
| 584 | C2×C8 | — | 3 | 1 | no | — |
| 585 | C2×C8 | — | 3 | 1 | no | — |
| 586 | C2×C8 | — | 6 | 1 | no | — |
| 587 | C2×C8 | — | 6 | 1 | no | — |
| 588 | C2×C8 | — | 6 | 1 | no | — |
| 589 | C2×C8 | — | 6 | 1 | no | — |
| 590 | C2×C8 | — | 6 | 1 | no | — |
| 591 | C2×C8 | — | 12 | 2 | no | — |
| 592 | C2×C8 | — | 12 | 2 | no | — |
| 593 | C2×C8 | — | 12 | 2 | no | — |
| 594 | C2×C8 | — | 12 | 2 | no | — |
| 595 | C2×C8 | — | 12 | 2 | no | — |
| 596 | C2×C8 | — | 12 | 2 | no | — |
| 597 | C2×C8 | — | 24 | 2 | no | — |
| 598 | C2×C8 | — | 24 | 2 | no | — |
| 599 | C2×C8 | — | 24 | 2 | no | — |
| 600 | C2×C8 | — | 24 | 2 | no | — |
| 601 | C2×C8 | — | 24 | 2 | no | — |
| 602 | C2×C8 | — | 24 | 2 | no | — |
| 603 | C2×C8 | — | 48 | 4 | no | — |
| 604 | C2×C8 | — | 48 | 4 | no | — |
| 605 | C2×C8 | — | 48 | 4 | no | — |
| 606 | C2×C8 | — | 48 | 4 | no | — |
| 607 | C2×C8 | #5914 | 1 | 1 | yes | characteristic |
| 608 | C2×C8 | C22×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 609 | C4⋊C4 | — | 2 | 2 | no | — |
| 610 | C4⋊C4 | — | 6 | 2 | no | — |
| 611 | C4⋊C4 | — | 12 | 2 | no | — |
| 612 | C4⋊C4 | — | 12 | 2 | no | — |
| 613 | C22⋊C4 | — | 4 | 2 | no | — |
| 614 | C22⋊C4 | — | 12 | 2 | no | — |
| 615 | C22⋊C4 | — | 12 | 2 | no | — |
| 616 | C22⋊C4 | — | 12 | 2 | no | — |
| 617 | C22⋊C4 | — | 24 | 2 | no | — |
| 618 | C42 | — | 3 | 2 | no | — |
| 619 | C42 | — | 3 | 1 | no | — |
| 620 | C42 | — | 6 | 1 | no | — |
| 621 | C42 | D4×S4 | 1 | 1 | yes | characteristic |
| 622 | C16 | — | 2 | 1 | no | — |
| 623 | C16 | — | 3 | 2 | no | — |
| 624 | C16 | — | 6 | 1 | no | — |
| 625 | C16 | — | 24 | 1 | no | — |
| 626 | C16 | — | 24 | 1 | no | — |
| 627 | C16 | C2×A4⋊C8 | 1 | 2 | yes | complemented |
| 628 | C22×C3 | — | 4 | 1 | no | — |
| 629 | C22×C3 | — | 16 | 4 | no | — |
| 630 | C22×C3 | — | 32 | 2 | no | — |
| 631 | C22×C3 | — | 32 | 2 | no | — |
| 632 | A4 | #12067 | 1 | 1 | yes | characteristic, complemented |
| 633 | C3×C4 | — | 4 | 1 | no | — |
| 634 | C3×C4 | — | 4 | 1 | no | — |
| 635 | C3×C4 | — | 8 | 2 | no | — |
| 636 | C3×C4 | — | 32 | 2 | no | — |
| 637 | C23 | — | 3 | 1 | no | — |
| 638 | C23 | — | 3 | 1 | no | — |
| 639 | C23 | — | 3 | 2 | no | — |
| 640 | C23 | — | 4 | 2 | no | — |
| 641 | C23 | — | 8 | 4 | no | — |
| 642 | C23 | — | 12 | 4 | no | — |
| 643 | C23 | — | 12 | 4 | no | — |
| 644 | C23 | — | 12 | 4 | no | — |
| 645 | C23 | — | 12 | 2 | no | — |
| 646 | C23 | — | 24 | 2 | no | — |
| 647 | C23 | — | 24 | 2 | no | — |
| 648 | C23 | — | 24 | 2 | no | — |
| 649 | C23 | — | 24 | 2 | no | — |
| 650 | C23 | — | 24 | 2 | no | — |
| 651 | C23 | — | 24 | 4 | no | — |
| 652 | C23 | — | 24 | 2 | no | — |
| 653 | C23 | — | 24 | 2 | no | — |
| 654 | C23 | — | 24 | 4 | no | — |
| 655 | C23 | — | 24 | 4 | no | — |
| 656 | C23 | — | 24 | 2 | no | — |
| 657 | C23 | — | 24 | 2 | no | — |
| 658 | C23 | — | 48 | 4 | no | — |
| 659 | C23 | #70878 | 1 | 1 | yes | characteristic |
| 660 | C23 | #71515 | 1 | 2 | yes | — |
| 661 | D4 | — | 2 | 4 | no | — |
| 662 | D4 | — | 4 | 2 | no | — |
| 663 | D4 | — | 6 | 4 | no | — |
| 664 | D4 | — | 12 | 4 | no | — |
| 665 | D4 | — | 12 | 4 | no | — |
| 666 | D4 | — | 12 | 4 | no | — |
| 667 | D4 | — | 12 | 2 | no | — |
| 668 | D4 | — | 24 | 2 | no | — |
| 669 | C2×C4 | — | 3 | 1 | no | — |
| 670 | C2×C4 | — | 3 | 1 | no | — |
| 671 | C2×C4 | — | 3 | 1 | no | — |
| 672 | C2×C4 | — | 3 | 1 | no | — |
| 673 | C2×C4 | — | 3 | 1 | no | — |
| 674 | C2×C4 | — | 3 | 1 | no | — |
| 675 | C2×C4 | — | 3 | 1 | no | — |
| 676 | C2×C4 | — | 3 | 2 | no | — |
| 677 | C2×C4 | — | 4 | 2 | no | — |
| 678 | C2×C4 | — | 6 | 2 | no | — |
| 679 | C2×C4 | — | 6 | 2 | no | — |
| 680 | C2×C4 | — | 6 | 1 | no | — |
| 681 | C2×C4 | — | 6 | 2 | no | — |
| 682 | C2×C4 | — | 6 | 2 | no | — |
| 683 | C2×C4 | — | 8 | 2 | no | — |
| 684 | C2×C4 | — | 8 | 2 | no | — |
| 685 | C2×C4 | — | 12 | 2 | no | — |
| 686 | C2×C4 | — | 24 | 2 | no | — |
| 687 | C2×C4 | — | 24 | 2 | no | — |
| 688 | C2×C4 | — | 24 | 2 | no | — |
| 689 | C2×C4 | — | 24 | 2 | no | — |
| 690 | C2×C4 | — | 24 | 2 | no | — |
| 691 | C2×C4 | — | 24 | 2 | no | — |
| 692 | C2×C4 | — | 24 | 2 | no | — |
| 693 | C2×C4 | — | 24 | 2 | no | — |
| 694 | C2×C4 | — | 24 | 2 | no | — |
| 695 | C2×C4 | — | 24 | 2 | no | — |
| 696 | C2×C4 | — | 48 | 2 | no | — |
| 697 | C2×C4 | — | 48 | 2 | no | — |
| 698 | C2×C4 | #85457 | 1 | 2 | yes | — |
| 699 | C2×C4 | D4×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 700 | C8 | — | 2 | 1 | no | — |
| 701 | C8 | — | 3 | 1 | no | — |
| 702 | C8 | — | 3 | 1 | no | — |
| 703 | C8 | — | 6 | 1 | no | — |
| 704 | C8 | — | 24 | 2 | no | — |
| 705 | C8 | — | 24 | 2 | no | — |
| 706 | C8 | — | 48 | 2 | no | — |
| 707 | C8 | — | 48 | 2 | no | — |
| 708 | C8 | C22×A4⋊C8 | 1 | 1 | yes | characteristic |
| 709 | C8 | #85511 | 1 | 1 | yes | characteristic |
| 710 | C2×C3 | — | 4 | 2 | no | — |
| 711 | C2×C3 | — | 4 | 1 | no | — |
| 712 | C2×C3 | — | 32 | 4 | no | — |
| 713 | C22 | — | 3 | 2 | no | — |
| 714 | C22 | — | 3 | 1 | no | — |
| 715 | C22 | — | 3 | 2 | no | — |
| 716 | C22 | — | 3 | 2 | no | — |
| 717 | C22 | — | 3 | 1 | no | — |
| 718 | C22 | — | 3 | 1 | no | — |
| 719 | C22 | — | 4 | 4 | no | — |
| 720 | C22 | — | 6 | 1 | no | — |
| 721 | C22 | — | 8 | 2 | no | — |
| 722 | C22 | — | 8 | 2 | no | — |
| 723 | C22 | — | 12 | 4 | no | — |
| 724 | C22 | — | 24 | 4 | no | — |
| 725 | C22 | — | 24 | 4 | no | — |
| 726 | C22 | — | 24 | 4 | no | — |
| 727 | C22 | — | 24 | 4 | no | — |
| 728 | C22 | — | 24 | 4 | no | — |
| 729 | C22 | — | 24 | 4 | no | — |
| 730 | C22 | — | 24 | 2 | no | — |
| 731 | C22 | — | 24 | 2 | no | — |
| 732 | C22 | — | 48 | 2 | no | — |
| 733 | C22 | — | 48 | 2 | no | — |
| 734 | C22 | #10707072 | 1 | 1 | yes | characteristic, complemented |
| 735 | C22 | #11712923 | 1 | 1 | yes | characteristic |
| 736 | C4 | — | 2 | 2 | no | — |
| 737 | C4 | — | 3 | 1 | no | — |
| 738 | C4 | — | 3 | 1 | no | — |
| 739 | C4 | — | 6 | 2 | no | — |
| 740 | C4 | — | 8 | 2 | no | — |
| 741 | C4 | — | 24 | 2 | no | — |
| 742 | C4 | D4×A4⋊C8 | 1 | 1 | yes | characteristic |
| 743 | C4 | #11712942 | 1 | 1 | yes | characteristic |
| 744 | C3 | — | 4 | 1 | no | Sylow |
| 745 | C2 | — | 3 | 1 | no | — |
| 746 | C2 | — | 3 | 1 | no | — |
| 747 | C2 | — | 3 | 2 | no | — |
| 748 | C2 | — | 8 | 4 | no | — |
| 749 | C2 | — | 24 | 4 | no | — |
| 750 | C2 | #72241436 | 1 | 2 | yes | — |
| 751 | C2 | #72342710 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72342732 | C2 | semidirect |
| 2. #72342710 | C2 | semidirect |
| 3. #72342703 | C2 | semidirect |
| 4. #72342693 | C2 | semidirect |
| 32. A4×D16 | C8 | semidirect |
| 89. A4×D8 | C2×C8 | semidirect |
| 102. A4×C16 | C2×C8 | semidirect |
| 117. C22×D16 | C3⋊C8 | semidirect |
| 229. C22×D8 | C2×C3⋊C8 | semidirect |
| 262. C22×C16 | C2×C3⋊C8 | semidirect |
| 444. D16 | A4⋊C8 | semidirect |
| 577. D8 | C2×A4⋊C8 | semidirect |
| 627. C16 | C2×A4⋊C8 | semidirect |
| 632. A4 | #12067 | semidirect |
| 734. C22 | #10707072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72342732 | 2 |
| #72342710 | 2 |
| #72342703 | 2 |
| #72342693 | 2 |
| A4×#2177 | 2 |
| #72227128 | 3 |
| #10707072 | 4 |