Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
54775 conjugacy classes of subgroups.
The subgroup lattice has 748 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11715776 | C2 | 1 | 16 | yes | maximal, complemented |
| 2 | S4×H(5,𝔽2) | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | #11715774 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | C2×#87477 | C2 | 1 | 18 | yes | maximal, complemented |
| 5 | C2×A4×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10586066 | — | 3 | 1 | no | maximal, Sylow |
| 7 | #87568 | — | 4 | 1 | no | maximal |
| 8 | A4×H(5,𝔽2) | C22 | 1 | 16 | yes | complemented |
| 9 | C2×A4×#41 | C22 | 1 | 6 | yes | complemented |
| 10 | C22×D4×A4 | C22 | 1 | 9 | yes | complemented |
| 11 | C22×GL(2,ℤ/4) | C22 | 1 | 24 | yes | complemented |
| 12 | #87490 | C22 | 1 | 48 | yes | complemented |
| 13 | #87489 | C22 | 1 | 48 | yes | complemented |
| 14 | #41×S4 | C22 | 1 | 96 | yes | complemented |
| 15 | #87483 | C22 | 1 | 8 | yes | complemented |
| 16 | #87477 | C22 | 1 | 72 | yes | complemented |
| 17 | #87477 | C22 | 1 | 144 | yes | complemented |
| 18 | C2×#5914 | C22 | 1 | 72 | yes | complemented |
| 19 | C2×D4×S4 | C22 | 1 | 72 | yes | complemented |
| 20 | C2×#5912 | C22 | 1 | 36 | yes | complemented |
| 21 | C2×H(7,𝔽2) | — | 3 | 1 | no | — |
| 22 | C23×H(5,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #62987 | — | 3 | 16 | no | — |
| 24 | #62987 | — | 3 | 16 | no | — |
| 25 | D4×H(5,𝔽2) | — | 3 | 16 | no | — |
| 26 | D4×H(5,𝔽2) | — | 3 | 16 | no | — |
| 27 | #62852 | — | 3 | 12 | no | — |
| 28 | #62842 | — | 3 | 18 | no | — |
| 29 | #62811 | — | 3 | 12 | no | — |
| 30 | C2×#3484 | — | 3 | 18 | no | — |
| 31 | #62652 | — | 3 | 1 | no | — |
| 32 | C24×A4 | C23 | 1 | 6 | yes | complemented |
| 33 | C23×S4 | C23 | 1 | 24 | yes | complemented |
| 34 | C2×C3×H(5,𝔽2) | — | 4 | 1 | no | — |
| 35 | #5966 | — | 4 | 16 | no | — |
| 36 | D3×H(5,𝔽2) | — | 4 | 16 | no | — |
| 37 | #5964 | — | 4 | 12 | no | — |
| 38 | C2×#1004 | — | 4 | 18 | no | — |
| 39 | A4×#41 | C23 | 1 | 48 | yes | complemented |
| 40 | C2×Q8×A4 | C23 | 1 | 2 | yes | complemented |
| 41 | C2×D4×A4 | C23 | 1 | 72 | yes | complemented |
| 42 | C2×D4×A4 | C23 | 1 | 18 | yes | complemented |
| 43 | C22×C4×A4 | C23 | 1 | 9 | yes | complemented |
| 44 | C2×GL(2,ℤ/4) | C23 | 1 | 72 | yes | complemented |
| 45 | C2×GL(2,ℤ/4) | C23 | 1 | 144 | yes | complemented |
| 46 | C22×SL(2,ℤ/4) | C23 | 1 | 24 | yes | complemented |
| 47 | #5919 | C23 | 1 | 32 | yes | complemented |
| 48 | Q8×S4 | C23 | 1 | 32 | yes | complemented |
| 49 | #5914 | C23 | 1 | 288 | yes | complemented |
| 50 | D4×S4 | C23 | 1 | 288 | yes | complemented |
| 51 | #5912 | C23 | 1 | 48 | yes | complemented |
| 52 | #5912 | C23 | 1 | 144 | yes | complemented |
| 53 | C2×C4⋊S4 | C23 | 1 | 36 | yes | complemented |
| 54 | C2×C4×S4 | C23 | 1 | 72 | yes | complemented |
| 55 | C2×A4⋊Q8 | C23 | 1 | 36 | yes | complemented |
| 56 | H(7,𝔽2) | — | 6 | 16 | no | — |
| 57 | H(7,𝔽2) | — | 6 | 6 | no | — |
| 58 | H(7,𝔽2) | — | 6 | 9 | no | — |
| 59 | H(7,𝔽2) | — | 6 | 1 | no | — |
| 60 | C2×#585 | — | 3 | 16 | no | — |
| 61 | C2×#585 | — | 3 | 12 | no | — |
| 62 | C22×H(5,𝔽2) | — | 3 | 1 | no | — |
| 63 | C22×H(5,𝔽2) | — | 3 | 16 | no | — |
| 64 | C22×H(5,𝔽2) | — | 3 | 9 | no | — |
| 65 | C22×H(5,𝔽2) | — | 3 | 6 | no | — |
| 66 | C22×H(5,𝔽2) | — | 3 | 16 | no | — |
| 67 | C22×H(5,𝔽2) | — | 3 | 18 | no | — |
| 68 | C22×H(5,𝔽2) | C2×D3 | 1 | 16 | yes | complemented |
| 69 | C23×#41 | C2×D3 | 1 | 6 | yes | complemented |
| 70 | C24×D4 | C2×D3 | 1 | 9 | yes | complemented |
| 71 | #3500 | — | 3 | 96 | no | — |
| 72 | #3498 | — | 3 | 96 | no | — |
| 73 | #3496 | — | 3 | 144 | no | — |
| 74 | #3496 | — | 3 | 144 | no | — |
| 75 | #3489 | — | 3 | 48 | no | — |
| 76 | #3489 | — | 3 | 48 | no | — |
| 77 | #3488 | — | 3 | 48 | no | — |
| 78 | #3488 | — | 3 | 96 | no | — |
| 79 | #3488 | — | 3 | 96 | no | — |
| 80 | #3488 | — | 3 | 48 | no | — |
| 81 | #3487 | — | 3 | 24 | no | — |
| 82 | #3486 | — | 3 | 8 | no | — |
| 83 | #3485 | — | 3 | 144 | no | — |
| 84 | #3485 | — | 3 | 72 | no | — |
| 85 | #3484 | — | 3 | 144 | no | — |
| 86 | #3484 | — | 3 | 144 | no | — |
| 87 | #3484 | — | 3 | 144 | no | — |
| 88 | #3484 | — | 3 | 144 | no | — |
| 89 | #3484 | — | 3 | 72 | no | — |
| 90 | D4×#41 | — | 3 | 96 | no | — |
| 91 | D4×#41 | — | 3 | 96 | no | — |
| 92 | C2×#546 | — | 3 | 72 | no | — |
| 93 | C2×#546 | — | 3 | 72 | no | — |
| 94 | C2×D42 | — | 3 | 72 | no | — |
| 95 | C2×D42 | — | 3 | 72 | no | — |
| 96 | #3449 | — | 3 | 72 | no | — |
| 97 | C2×#535 | — | 3 | 36 | no | — |
| 98 | C2×#534 | — | 3 | 72 | no | — |
| 99 | C2×#525 | — | 3 | 36 | no | — |
| 100 | C22×#120 | — | 3 | 24 | no | — |
| 101 | C4×H(5,𝔽2) | — | 3 | 16 | no | — |
| 102 | C4×H(5,𝔽2) | — | 3 | 16 | no | — |
| 103 | #3428 | — | 3 | 12 | no | — |
| 104 | C2×#518 | — | 3 | 18 | no | — |
| 105 | C23×A4 | — | 8 | 6 | no | — |
| 106 | C23×A4 | C24 | 1 | 24 | yes | — |
| 107 | C23×A4 | C24 | 1 | 9 | yes | — |
| 108 | C22×S4 | — | 8 | 24 | no | — |
| 109 | C22×S4 | C24 | 1 | 72 | yes | — |
| 110 | C3×H(5,𝔽2) | — | 4 | 16 | no | — |
| 111 | C2×C3×#41 | — | 4 | 6 | no | — |
| 112 | C22×C3×D4 | — | 4 | 9 | no | — |
| 113 | C22×#67 | — | 4 | 24 | no | — |
| 114 | #1010 | — | 4 | 48 | no | — |
| 115 | #1009 | — | 4 | 48 | no | — |
| 116 | D3×#41 | — | 4 | 96 | no | — |
| 117 | #1007 | — | 4 | 8 | no | — |
| 118 | #1004 | — | 4 | 72 | no | — |
| 119 | #1004 | — | 4 | 144 | no | — |
| 120 | C2×#237 | — | 4 | 72 | no | — |
| 121 | C2×D3×D4 | — | 4 | 72 | no | — |
| 122 | C2×#235 | — | 4 | 36 | no | — |
| 123 | Q8×A4 | C24 | 1 | 8 | yes | — |
| 124 | D4×A4 | C24 | 1 | 72 | yes | — |
| 125 | C2×C4×A4 | C24 | 1 | 36 | yes | — |
| 126 | C2×C4×A4 | C24 | 1 | 6 | yes | — |
| 127 | GL(2,ℤ/4) | C24 | 1 | 16 | yes | — |
| 128 | GL(2,ℤ/4) | C24 | 1 | 144 | yes | — |
| 129 | C2×SL(2,ℤ/4) | C24 | 1 | 72 | yes | — |
| 130 | C4⋊S4 | C24 | 1 | 48 | yes | — |
| 131 | C4×S4 | C24 | 1 | 96 | yes | — |
| 132 | A4⋊Q8 | C24 | 1 | 48 | yes | — |
| 133 | C26 | C22×D3 | 1 | 6 | yes | complemented |
| 134 | #585 | — | 6 | 48 | no | — |
| 135 | #585 | — | 6 | 48 | no | — |
| 136 | #585 | — | 6 | 12 | no | — |
| 137 | #585 | — | 6 | 36 | no | — |
| 138 | #585 | — | 6 | 36 | no | — |
| 139 | #585 | — | 6 | 96 | no | — |
| 140 | #585 | — | 6 | 144 | no | — |
| 141 | #585 | — | 6 | 16 | no | — |
| 142 | #585 | — | 6 | 12 | no | — |
| 143 | C2×2−1+4 | — | 3 | 8 | no | — |
| 144 | C2×2−1+4 | — | 3 | 48 | no | — |
| 145 | C2×H(5,𝔽2) | — | 3 | 16 | no | — |
| 146 | C2×H(5,𝔽2) | — | 3 | 16 | no | — |
| 147 | C2×H(5,𝔽2) | — | 3 | 144 | no | — |
| 148 | C2×H(5,𝔽2) | — | 3 | 96 | no | — |
| 149 | C2×H(5,𝔽2) | — | 3 | 72 | no | — |
| 150 | C2×H(5,𝔽2) | — | 3 | 144 | no | — |
| 151 | C2×H(5,𝔽2) | — | 3 | 48 | no | — |
| 152 | C2×H(5,𝔽2) | — | 3 | 6 | no | — |
| 153 | C2×H(5,𝔽2) | — | 3 | 9 | no | — |
| 154 | C2×H(5,𝔽2) | — | 6 | 6 | no | — |
| 155 | C2×H(5,𝔽2) | — | 6 | 18 | no | — |
| 156 | C2×H(5,𝔽2) | — | 6 | 9 | no | — |
| 157 | C2×H(5,𝔽2) | — | 6 | 72 | no | — |
| 158 | C2×H(5,𝔽2) | — | 6 | 36 | no | — |
| 159 | C2×H(5,𝔽2) | — | 6 | 72 | no | — |
| 160 | C2×H(5,𝔽2) | — | 6 | 72 | no | — |
| 161 | C2×H(5,𝔽2) | — | 6 | 72 | no | — |
| 162 | C2×H(5,𝔽2) | — | 6 | 18 | no | — |
| 163 | C2×H(5,𝔽2) | — | 6 | 2 | no | — |
| 164 | C2×H(5,𝔽2) | — | 6 | 48 | no | — |
| 165 | C2×H(5,𝔽2) | — | 6 | 96 | no | — |
| 166 | C2×H(5,𝔽2) | — | 6 | 144 | no | — |
| 167 | C2×H(5,𝔽2) | — | 6 | 16 | no | — |
| 168 | C2×H(5,𝔽2) | — | 6 | 18 | no | — |
| 169 | C2×H(5,𝔽2) | S4 | 1 | 1 | yes | characteristic, complemented |
| 170 | C22×#41 | — | 3 | 6 | no | — |
| 171 | C22×#41 | — | 3 | 18 | no | — |
| 172 | C22×#41 | — | 3 | 48 | no | — |
| 173 | C22×#41 | — | 3 | 18 | no | — |
| 174 | C22×#41 | — | 3 | 6 | no | — |
| 175 | C22×#41 | — | 3 | 36 | no | — |
| 176 | C22×#41 | — | 3 | 72 | no | — |
| 177 | C22×#41 | — | 3 | 96 | no | — |
| 178 | C22×#41 | C22×D3 | 1 | 48 | yes | complemented |
| 179 | C23×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 180 | C23×D4 | — | 3 | 9 | no | — |
| 181 | C23×D4 | — | 3 | 18 | no | — |
| 182 | C23×D4 | — | 3 | 9 | no | — |
| 183 | C23×D4 | — | 3 | 72 | no | — |
| 184 | C23×D4 | — | 3 | 36 | no | — |
| 185 | C23×D4 | — | 3 | 24 | no | — |
| 186 | C23×D4 | — | 3 | 72 | no | — |
| 187 | C23×D4 | — | 3 | 24 | no | — |
| 188 | C23×D4 | — | 3 | 24 | no | — |
| 189 | C23×D4 | C22×D3 | 1 | 18 | yes | complemented |
| 190 | C23×D4 | C22×D3 | 1 | 72 | yes | complemented |
| 191 | C24×C4 | C22×D3 | 1 | 9 | yes | complemented |
| 192 | #550 | — | 3 | 96 | no | — |
| 193 | #550 | — | 3 | 96 | no | — |
| 194 | D4×Q8 | — | 3 | 32 | no | — |
| 195 | D4×Q8 | — | 3 | 32 | no | — |
| 196 | #548 | — | 3 | 32 | no | — |
| 197 | #548 | — | 3 | 96 | no | — |
| 198 | #548 | — | 3 | 96 | no | — |
| 199 | #548 | — | 3 | 32 | no | — |
| 200 | #547 | — | 3 | 288 | no | — |
| 201 | #547 | — | 3 | 288 | no | — |
| 202 | #546 | — | 3 | 288 | no | — |
| 203 | #546 | — | 3 | 576 | no | — |
| 204 | #546 | — | 3 | 576 | no | — |
| 205 | #546 | — | 3 | 288 | no | — |
| 206 | #546 | — | 3 | 288 | no | — |
| 207 | #546 | — | 3 | 288 | no | — |
| 208 | D42 | — | 3 | 288 | no | — |
| 209 | D42 | — | 3 | 576 | no | — |
| 210 | D42 | — | 3 | 576 | no | — |
| 211 | D42 | — | 3 | 288 | no | — |
| 212 | #537 | — | 3 | 144 | no | — |
| 213 | #537 | — | 3 | 144 | no | — |
| 214 | #536 | — | 3 | 48 | no | — |
| 215 | #536 | — | 3 | 144 | no | — |
| 216 | #535 | — | 3 | 144 | no | — |
| 217 | #535 | — | 3 | 288 | no | — |
| 218 | #535 | — | 3 | 144 | no | — |
| 219 | #534 | — | 3 | 288 | no | — |
| 220 | #534 | — | 3 | 576 | no | — |
| 221 | #532 | — | 3 | 288 | no | — |
| 222 | C2×#127 | — | 3 | 72 | no | — |
| 223 | C2×#124 | — | 3 | 72 | no | — |
| 224 | #525 | — | 3 | 144 | no | — |
| 225 | #525 | — | 3 | 144 | no | — |
| 226 | #525 | — | 3 | 288 | no | — |
| 227 | #525 | — | 3 | 48 | no | — |
| 228 | #525 | — | 3 | 144 | no | — |
| 229 | C2×#123 | — | 3 | 72 | no | — |
| 230 | C2×#123 | — | 3 | 144 | no | — |
| 231 | C2×C22⋊Q8 | — | 3 | 36 | no | — |
| 232 | C2×C22⋊Q8 | — | 3 | 36 | no | — |
| 233 | C2×#121 | — | 3 | 36 | no | — |
| 234 | C2×#121 | — | 3 | 144 | no | — |
| 235 | C2×#121 | — | 3 | 144 | no | — |
| 236 | C2×#121 | — | 3 | 72 | no | — |
| 237 | C2×#121 | — | 3 | 72 | no | — |
| 238 | C2×#121 | — | 3 | 36 | no | — |
| 239 | C2×#120 | — | 3 | 144 | no | — |
| 240 | C2×#120 | — | 3 | 144 | no | — |
| 241 | C2×#120 | — | 3 | 144 | no | — |
| 242 | C2×#120 | — | 3 | 72 | no | — |
| 243 | C2×#120 | — | 3 | 144 | no | — |
| 244 | #520 | — | 3 | 48 | no | — |
| 245 | #520 | — | 3 | 48 | no | — |
| 246 | #519 | — | 3 | 8 | no | — |
| 247 | #518 | — | 3 | 72 | no | — |
| 248 | #518 | — | 3 | 144 | no | — |
| 249 | C4×#41 | — | 3 | 96 | no | — |
| 250 | C2×C4×D4 | — | 3 | 72 | no | — |
| 251 | C2×C4×D4 | — | 3 | 72 | no | — |
| 252 | C2×C4×D4 | — | 3 | 72 | no | — |
| 253 | C2×C4×D4 | — | 3 | 72 | no | — |
| 254 | C2×#117 | — | 3 | 36 | no | — |
| 255 | C22×C22⋊C4 | — | 3 | 24 | no | — |
| 256 | C22×C22⋊C4 | — | 3 | 24 | no | — |
| 257 | C22×C22⋊C4 | — | 3 | 24 | no | — |
| 258 | C24×C3 | — | 4 | 6 | no | — |
| 259 | C23×D3 | — | 4 | 24 | no | — |
| 260 | C22×A4 | — | 4 | 24 | no | — |
| 261 | C22×A4 | — | 4 | 9 | no | — |
| 262 | C22×A4 | C25 | 1 | 18 | yes | — |
| 263 | C22×A4 | C25 | 1 | 1 | yes | characteristic |
| 264 | C2×S4 | — | 4 | 72 | no | — |
| 265 | C2×S4 | C25 | 1 | 16 | yes | — |
| 266 | C3×#41 | — | 4 | 48 | no | — |
| 267 | C2×C3×Q8 | — | 4 | 2 | no | — |
| 268 | C2×C3×D4 | — | 4 | 72 | no | — |
| 269 | C2×C3×D4 | — | 4 | 18 | no | — |
| 270 | C22×C3×C4 | — | 4 | 9 | no | — |
| 271 | C2×#67 | — | 4 | 72 | no | — |
| 272 | C2×#67 | — | 4 | 144 | no | — |
| 273 | C22×Dic3 | — | 4 | 24 | no | — |
| 274 | #239 | — | 4 | 32 | no | — |
| 275 | D3×Q8 | — | 4 | 32 | no | — |
| 276 | #237 | — | 4 | 288 | no | — |
| 277 | D3×D4 | — | 4 | 288 | no | — |
| 278 | #235 | — | 4 | 48 | no | — |
| 279 | #235 | — | 4 | 144 | no | — |
| 280 | C2×D12 | — | 4 | 36 | no | — |
| 281 | C2×C4×D3 | — | 4 | 72 | no | — |
| 282 | C2×Dic6 | — | 4 | 36 | no | — |
| 283 | C4×A4 | C25 | 1 | 12 | yes | — |
| 284 | SL(2,ℤ/4) | C25 | 1 | 16 | yes | — |
| 285 | C25 | — | 3 | 6 | no | — |
| 286 | C25 | — | 3 | 24 | no | — |
| 287 | C25 | — | 3 | 18 | no | — |
| 288 | C25 | — | 3 | 24 | no | — |
| 289 | C25 | — | 8 | 6 | no | — |
| 290 | C25 | — | 24 | 6 | no | — |
| 291 | C25 | C23×D3 | 1 | 24 | yes | — |
| 292 | C25 | C23×D3 | 1 | 9 | yes | — |
| 293 | 2−1+4 | — | 6 | 32 | no | — |
| 294 | 2−1+4 | — | 6 | 24 | no | — |
| 295 | 2−1+4 | — | 6 | 144 | no | — |
| 296 | 2−1+4 | — | 6 | 48 | no | — |
| 297 | 2−1+4 | — | 6 | 144 | no | — |
| 298 | 2−1+4 | — | 6 | 48 | no | — |
| 299 | 2−1+4 | — | 6 | 8 | no | — |
| 300 | H(5,𝔽2) | — | 3 | 96 | no | — |
| 301 | H(5,𝔽2) | — | 3 | 144 | no | — |
| 302 | H(5,𝔽2) | — | 6 | 96 | no | — |
| 303 | H(5,𝔽2) | — | 6 | 288 | no | — |
| 304 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 305 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 306 | H(5,𝔽2) | — | 6 | 288 | no | — |
| 307 | H(5,𝔽2) | — | 6 | 288 | no | — |
| 308 | H(5,𝔽2) | — | 6 | 576 | no | — |
| 309 | H(5,𝔽2) | — | 6 | 72 | no | — |
| 310 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 311 | H(5,𝔽2) | — | 6 | 32 | no | — |
| 312 | H(5,𝔽2) | — | 6 | 48 | no | — |
| 313 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 314 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 315 | H(5,𝔽2) | — | 6 | 48 | no | — |
| 316 | H(5,𝔽2) | — | 6 | 72 | no | — |
| 317 | H(5,𝔽2) | — | 6 | 144 | no | — |
| 318 | H(5,𝔽2) | C2×S4 | 1 | 16 | yes | complemented |
| 319 | C2×#41 | — | 3 | 48 | no | — |
| 320 | C2×#41 | — | 3 | 48 | no | — |
| 321 | C2×#41 | — | 3 | 144 | no | — |
| 322 | C2×#41 | — | 3 | 144 | no | — |
| 323 | C2×#41 | — | 3 | 48 | no | — |
| 324 | C2×#41 | — | 3 | 48 | no | — |
| 325 | C2×#41 | — | 3 | 144 | no | — |
| 326 | C2×#41 | — | 3 | 288 | no | — |
| 327 | C2×#41 | — | 3 | 32 | no | — |
| 328 | C2×#41 | — | 3 | 6 | no | — |
| 329 | C2×#41 | — | 3 | 18 | no | — |
| 330 | C2×#41 | — | 3 | 18 | no | — |
| 331 | C2×#41 | — | 6 | 6 | no | — |
| 332 | C2×#41 | — | 6 | 18 | no | — |
| 333 | C2×#41 | — | 6 | 18 | no | — |
| 334 | C2×#41 | — | 6 | 72 | no | — |
| 335 | C2×#41 | — | 6 | 36 | no | — |
| 336 | C2×#41 | — | 6 | 72 | no | — |
| 337 | C2×#41 | — | 6 | 72 | no | — |
| 338 | C2×#41 | — | 6 | 36 | no | — |
| 339 | C2×#41 | — | 6 | 36 | no | — |
| 340 | C2×#41 | — | 6 | 72 | no | — |
| 341 | C2×#41 | — | 6 | 288 | no | — |
| 342 | C2×#41 | — | 6 | 144 | no | — |
| 343 | C2×#41 | — | 6 | 72 | no | — |
| 344 | C2×#41 | — | 6 | 24 | no | — |
| 345 | C2×#41 | — | 6 | 96 | no | — |
| 346 | C2×#41 | — | 6 | 288 | no | — |
| 347 | C2×#41 | — | 6 | 288 | no | — |
| 348 | C2×#41 | — | 6 | 96 | no | — |
| 349 | C2×#41 | — | 6 | 72 | no | — |
| 350 | C2×#41 | — | 6 | 36 | no | — |
| 351 | C2×#41 | C2×S4 | 1 | 6 | yes | complemented |
| 352 | C22×Q8 | — | 3 | 2 | no | — |
| 353 | C22×Q8 | — | 3 | 6 | no | — |
| 354 | C22×Q8 | — | 3 | 8 | no | — |
| 355 | C22×Q8 | — | 3 | 36 | no | — |
| 356 | C22×Q8 | — | 3 | 32 | no | — |
| 357 | C22×Q8 | C23×D3 | 1 | 8 | yes | — |
| 358 | C22×D4 | — | 3 | 18 | no | — |
| 359 | C22×D4 | — | 3 | 72 | no | — |
| 360 | C22×D4 | — | 3 | 18 | no | — |
| 361 | C22×D4 | — | 3 | 36 | no | — |
| 362 | C22×D4 | — | 3 | 72 | no | — |
| 363 | C22×D4 | — | 3 | 144 | no | — |
| 364 | C22×D4 | — | 3 | 72 | no | — |
| 365 | C22×D4 | — | 3 | 36 | no | — |
| 366 | C22×D4 | — | 3 | 18 | no | — |
| 367 | C22×D4 | — | 3 | 72 | no | — |
| 368 | C22×D4 | — | 3 | 288 | no | — |
| 369 | C22×D4 | — | 3 | 72 | no | — |
| 370 | C22×D4 | — | 3 | 144 | no | — |
| 371 | C22×D4 | — | 3 | 36 | no | — |
| 372 | C22×D4 | — | 3 | 288 | no | — |
| 373 | C22×D4 | — | 3 | 72 | no | — |
| 374 | C22×D4 | — | 3 | 72 | no | — |
| 375 | C22×D4 | — | 3 | 144 | no | — |
| 376 | C22×D4 | — | 3 | 144 | no | — |
| 377 | C22×D4 | — | 3 | 9 | no | — |
| 378 | C22×D4 | — | 6 | 18 | no | — |
| 379 | C22×D4 | — | 6 | 36 | no | — |
| 380 | C22×D4 | — | 6 | 9 | no | — |
| 381 | C22×D4 | — | 6 | 144 | no | — |
| 382 | C22×D4 | — | 6 | 36 | no | — |
| 383 | C22×D4 | — | 6 | 72 | no | — |
| 384 | C22×D4 | — | 6 | 144 | no | — |
| 385 | C22×D4 | — | 6 | 288 | no | — |
| 386 | C22×D4 | — | 6 | 72 | no | — |
| 387 | C22×D4 | — | 6 | 72 | no | — |
| 388 | C22×D4 | — | 6 | 72 | no | — |
| 389 | C22×D4 | — | 6 | 24 | no | — |
| 390 | C22×D4 | — | 6 | 24 | no | — |
| 391 | C22×D4 | — | 6 | 72 | no | — |
| 392 | C22×D4 | — | 24 | 24 | no | — |
| 393 | C22×D4 | — | 24 | 24 | no | — |
| 394 | C22×D4 | — | 24 | 48 | no | — |
| 395 | C22×D4 | C2×S4 | 1 | 9 | yes | complemented |
| 396 | C22×D4 | C23×D3 | 1 | 72 | yes | — |
| 397 | C23×C4 | — | 3 | 9 | no | — |
| 398 | C23×C4 | — | 3 | 36 | no | — |
| 399 | C23×C4 | — | 3 | 9 | no | — |
| 400 | C23×C4 | — | 3 | 18 | no | — |
| 401 | C23×C4 | — | 3 | 24 | no | — |
| 402 | C23×C4 | — | 3 | 72 | no | — |
| 403 | C23×C4 | — | 3 | 24 | no | — |
| 404 | C23×C4 | — | 3 | 24 | no | — |
| 405 | C23×C4 | C23×D3 | 1 | 36 | yes | — |
| 406 | C23×C4 | C23×D3 | 1 | 6 | yes | — |
| 407 | C4⋊Q8 | — | 3 | 96 | no | — |
| 408 | #127 | — | 3 | 288 | no | — |
| 409 | #124 | — | 3 | 288 | no | — |
| 410 | #124 | — | 3 | 96 | no | — |
| 411 | #123 | — | 3 | 96 | no | — |
| 412 | #123 | — | 3 | 576 | no | — |
| 413 | #123 | — | 3 | 288 | no | — |
| 414 | C22⋊Q8 | — | 3 | 48 | no | — |
| 415 | C22⋊Q8 | — | 3 | 144 | no | — |
| 416 | C22⋊Q8 | — | 3 | 144 | no | — |
| 417 | C22⋊Q8 | — | 3 | 96 | no | — |
| 418 | C22⋊Q8 | — | 3 | 96 | no | — |
| 419 | C22⋊Q8 | — | 3 | 48 | no | — |
| 420 | #121 | — | 3 | 48 | no | — |
| 421 | #121 | — | 3 | 288 | no | — |
| 422 | #121 | — | 3 | 288 | no | — |
| 423 | #121 | — | 3 | 576 | no | — |
| 424 | #121 | — | 3 | 576 | no | — |
| 425 | #121 | — | 3 | 144 | no | — |
| 426 | #121 | — | 3 | 144 | no | — |
| 427 | #121 | — | 3 | 48 | no | — |
| 428 | #120 | — | 3 | 144 | no | — |
| 429 | #120 | — | 3 | 144 | no | — |
| 430 | #120 | — | 3 | 576 | no | — |
| 431 | #120 | — | 3 | 576 | no | — |
| 432 | #120 | — | 3 | 16 | no | — |
| 433 | #120 | — | 3 | 144 | no | — |
| 434 | C4×Q8 | — | 3 | 32 | no | — |
| 435 | C4×Q8 | — | 3 | 32 | no | — |
| 436 | C4×D4 | — | 3 | 96 | no | — |
| 437 | C4×D4 | — | 3 | 288 | no | — |
| 438 | C4×D4 | — | 3 | 288 | no | — |
| 439 | C4×D4 | — | 3 | 288 | no | — |
| 440 | C4×D4 | — | 3 | 288 | no | — |
| 441 | C4×D4 | — | 3 | 96 | no | — |
| 442 | #117 | — | 3 | 48 | no | — |
| 443 | #117 | — | 3 | 144 | no | — |
| 444 | C2×C4⋊C4 | — | 3 | 36 | no | — |
| 445 | C2×C4⋊C4 | — | 3 | 36 | no | — |
| 446 | C2×C4⋊C4 | — | 3 | 72 | no | — |
| 447 | C2×C4⋊C4 | — | 3 | 72 | no | — |
| 448 | C2×C22⋊C4 | — | 3 | 72 | no | — |
| 449 | C2×C22⋊C4 | — | 3 | 72 | no | — |
| 450 | C2×C22⋊C4 | — | 3 | 144 | no | — |
| 451 | C2×C22⋊C4 | — | 3 | 144 | no | — |
| 452 | C2×C22⋊C4 | — | 3 | 144 | no | — |
| 453 | C2×C22⋊C4 | — | 3 | 72 | no | — |
| 454 | C2×C22⋊C4 | — | 3 | 72 | no | — |
| 455 | C2×C22⋊C4 | — | 3 | 72 | no | — |
| 456 | C2×C42 | — | 3 | 72 | no | — |
| 457 | C23×C3 | — | 4 | 24 | no | — |
| 458 | C23×C3 | — | 4 | 9 | no | — |
| 459 | C23×C3 | — | 32 | 6 | no | — |
| 460 | C22×D3 | — | 4 | 72 | no | — |
| 461 | C22×D3 | — | 32 | 24 | no | — |
| 462 | C2×A4 | — | 2 | 18 | no | — |
| 463 | C2×A4 | — | 2 | 1 | no | — |
| 464 | C2×A4 | C26 | 1 | 1 | yes | characteristic |
| 465 | S4 | — | 2 | 16 | no | — |
| 466 | C3×Q8 | — | 4 | 8 | no | — |
| 467 | C3×D4 | — | 4 | 72 | no | — |
| 468 | C2×C3×C4 | — | 4 | 36 | no | — |
| 469 | C2×C3×C4 | — | 4 | 6 | no | — |
| 470 | #67 | — | 4 | 16 | no | — |
| 471 | #67 | — | 4 | 144 | no | — |
| 472 | C2×Dic3 | — | 4 | 72 | no | — |
| 473 | D12 | — | 4 | 48 | no | — |
| 474 | C4×D3 | — | 4 | 96 | no | — |
| 475 | Dic6 | — | 4 | 48 | no | — |
| 476 | C24 | — | 3 | 9 | no | — |
| 477 | C24 | — | 3 | 24 | no | — |
| 478 | C24 | — | 3 | 24 | no | — |
| 479 | C24 | — | 3 | 18 | no | — |
| 480 | C24 | — | 3 | 18 | no | — |
| 481 | C24 | — | 3 | 72 | no | — |
| 482 | C24 | — | 3 | 9 | no | — |
| 483 | C24 | — | 3 | 72 | no | — |
| 484 | C24 | — | 4 | 24 | no | — |
| 485 | C24 | — | 4 | 9 | no | — |
| 486 | C24 | — | 6 | 6 | no | — |
| 487 | C24 | — | 6 | 36 | no | — |
| 488 | C24 | — | 6 | 72 | no | — |
| 489 | C24 | — | 6 | 24 | no | — |
| 490 | C24 | — | 12 | 9 | no | — |
| 491 | C24 | — | 12 | 24 | no | — |
| 492 | C24 | — | 12 | 48 | no | — |
| 493 | C24 | — | 24 | 6 | no | — |
| 494 | C24 | — | 24 | 6 | no | — |
| 495 | C24 | — | 24 | 24 | no | — |
| 496 | C24 | — | 24 | 18 | no | — |
| 497 | C24 | — | 24 | 18 | no | — |
| 498 | C24 | — | 24 | 24 | no | — |
| 499 | C24 | — | 24 | 24 | no | — |
| 500 | C24 | C22×S4 | 1 | 6 | yes | complemented |
| 501 | C24 | C24×D3 | 1 | 18 | yes | — |
| 502 | C24 | C24×D3 | 1 | 1 | yes | characteristic |
| 503 | #41 | — | 3 | 48 | no | — |
| 504 | #41 | — | 3 | 144 | no | — |
| 505 | #41 | — | 3 | 144 | no | — |
| 506 | #41 | — | 6 | 48 | no | — |
| 507 | #41 | — | 6 | 144 | no | — |
| 508 | #41 | — | 6 | 144 | no | — |
| 509 | #41 | — | 6 | 48 | no | — |
| 510 | #41 | — | 6 | 144 | no | — |
| 511 | #41 | — | 6 | 48 | no | — |
| 512 | #41 | — | 6 | 48 | no | — |
| 513 | #41 | — | 6 | 144 | no | — |
| 514 | #41 | — | 6 | 144 | no | — |
| 515 | #41 | — | 6 | 576 | no | — |
| 516 | #41 | — | 6 | 288 | no | — |
| 517 | #41 | — | 6 | 96 | no | — |
| 518 | #41 | — | 6 | 32 | no | — |
| 519 | #41 | — | 6 | 288 | no | — |
| 520 | #41 | — | 6 | 48 | no | — |
| 521 | #41 | — | 6 | 144 | no | — |
| 522 | #41 | C22×S4 | 1 | 48 | yes | complemented |
| 523 | C2×Q8 | — | 3 | 8 | no | — |
| 524 | C2×Q8 | — | 3 | 8 | no | — |
| 525 | C2×Q8 | — | 3 | 24 | no | — |
| 526 | C2×Q8 | — | 3 | 48 | no | — |
| 527 | C2×Q8 | — | 3 | 6 | no | — |
| 528 | C2×Q8 | — | 6 | 2 | no | — |
| 529 | C2×Q8 | — | 6 | 12 | no | — |
| 530 | C2×Q8 | — | 6 | 36 | no | — |
| 531 | C2×Q8 | — | 6 | 72 | no | — |
| 532 | C2×Q8 | — | 6 | 96 | no | — |
| 533 | C2×Q8 | — | 6 | 32 | no | — |
| 534 | C2×Q8 | — | 6 | 36 | no | — |
| 535 | C2×Q8 | C22×S4 | 1 | 2 | yes | complemented |
| 536 | C2×D4 | — | 3 | 36 | no | — |
| 537 | C2×D4 | — | 3 | 144 | no | — |
| 538 | C2×D4 | — | 3 | 72 | no | — |
| 539 | C2×D4 | — | 3 | 72 | no | — |
| 540 | C2×D4 | — | 3 | 288 | no | — |
| 541 | C2×D4 | — | 3 | 144 | no | — |
| 542 | C2×D4 | — | 3 | 72 | no | — |
| 543 | C2×D4 | — | 3 | 16 | no | — |
| 544 | C2×D4 | — | 3 | 16 | no | — |
| 545 | C2×D4 | — | 3 | 144 | no | — |
| 546 | C2×D4 | — | 3 | 48 | no | — |
| 547 | C2×D4 | — | 3 | 16 | no | — |
| 548 | C2×D4 | — | 3 | 144 | no | — |
| 549 | C2×D4 | — | 3 | 144 | no | — |
| 550 | C2×D4 | — | 3 | 18 | no | — |
| 551 | C2×D4 | — | 3 | 72 | no | — |
| 552 | C2×D4 | — | 6 | 36 | no | — |
| 553 | C2×D4 | — | 6 | 144 | no | — |
| 554 | C2×D4 | — | 6 | 18 | no | — |
| 555 | C2×D4 | — | 6 | 72 | no | — |
| 556 | C2×D4 | — | 6 | 36 | no | — |
| 557 | C2×D4 | — | 6 | 72 | no | — |
| 558 | C2×D4 | — | 6 | 72 | no | — |
| 559 | C2×D4 | — | 6 | 288 | no | — |
| 560 | C2×D4 | — | 6 | 576 | no | — |
| 561 | C2×D4 | — | 6 | 288 | no | — |
| 562 | C2×D4 | — | 6 | 72 | no | — |
| 563 | C2×D4 | — | 6 | 72 | no | — |
| 564 | C2×D4 | — | 6 | 288 | no | — |
| 565 | C2×D4 | — | 6 | 72 | no | — |
| 566 | C2×D4 | — | 6 | 144 | no | — |
| 567 | C2×D4 | — | 6 | 72 | no | — |
| 568 | C2×D4 | — | 6 | 144 | no | — |
| 569 | C2×D4 | — | 6 | 288 | no | — |
| 570 | C2×D4 | — | 6 | 36 | no | — |
| 571 | C2×D4 | — | 12 | 72 | no | — |
| 572 | C2×D4 | — | 12 | 72 | no | — |
| 573 | C2×D4 | — | 12 | 144 | no | — |
| 574 | C2×D4 | — | 24 | 144 | no | — |
| 575 | C2×D4 | — | 24 | 144 | no | — |
| 576 | C2×D4 | C22×S4 | 1 | 18 | yes | complemented |
| 577 | C2×D4 | C22×S4 | 1 | 72 | yes | complemented |
| 578 | C22×C4 | — | 3 | 9 | no | — |
| 579 | C22×C4 | — | 3 | 36 | no | — |
| 580 | C22×C4 | — | 3 | 6 | no | — |
| 581 | C22×C4 | — | 3 | 18 | no | — |
| 582 | C22×C4 | — | 3 | 36 | no | — |
| 583 | C22×C4 | — | 3 | 36 | no | — |
| 584 | C22×C4 | — | 3 | 12 | no | — |
| 585 | C22×C4 | — | 3 | 72 | no | — |
| 586 | C22×C4 | — | 3 | 6 | no | — |
| 587 | C22×C4 | — | 3 | 72 | no | — |
| 588 | C22×C4 | — | 3 | 96 | no | — |
| 589 | C22×C4 | — | 3 | 72 | no | — |
| 590 | C22×C4 | — | 3 | 72 | no | — |
| 591 | C22×C4 | — | 6 | 36 | no | — |
| 592 | C22×C4 | — | 6 | 9 | no | — |
| 593 | C22×C4 | — | 6 | 18 | no | — |
| 594 | C22×C4 | — | 6 | 72 | no | — |
| 595 | C22×C4 | — | 6 | 144 | no | — |
| 596 | C22×C4 | — | 6 | 72 | no | — |
| 597 | C22×C4 | — | 6 | 24 | no | — |
| 598 | C22×C4 | — | 6 | 72 | no | — |
| 599 | C22×C4 | — | 24 | 24 | no | — |
| 600 | C22×C4 | — | 24 | 24 | no | — |
| 601 | C22×C4 | C22×S4 | 1 | 9 | yes | complemented |
| 602 | C22×C4 | C24×D3 | 1 | 12 | yes | — |
| 603 | C4⋊C4 | — | 3 | 48 | no | — |
| 604 | C4⋊C4 | — | 3 | 48 | no | — |
| 605 | C4⋊C4 | — | 3 | 96 | no | — |
| 606 | C4⋊C4 | — | 3 | 96 | no | — |
| 607 | C22⋊C4 | — | 3 | 16 | no | — |
| 608 | C22⋊C4 | — | 3 | 16 | no | — |
| 609 | C22⋊C4 | — | 3 | 144 | no | — |
| 610 | C22⋊C4 | — | 3 | 144 | no | — |
| 611 | C22⋊C4 | — | 3 | 144 | no | — |
| 612 | C22⋊C4 | — | 3 | 96 | no | — |
| 613 | C22⋊C4 | — | 3 | 96 | no | — |
| 614 | C22⋊C4 | — | 3 | 16 | no | — |
| 615 | C42 | — | 3 | 96 | no | — |
| 616 | C22×C3 | — | 4 | 18 | no | — |
| 617 | C22×C3 | — | 4 | 1 | no | — |
| 618 | C22×C3 | — | 16 | 24 | no | — |
| 619 | C22×C3 | — | 16 | 9 | no | — |
| 620 | C2×D3 | — | 4 | 16 | no | — |
| 621 | C2×D3 | — | 16 | 72 | no | — |
| 622 | A4 | H(7,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 623 | C3×C4 | — | 4 | 12 | no | — |
| 624 | Dic3 | — | 4 | 16 | no | — |
| 625 | C23 | — | 2 | 18 | no | — |
| 626 | C23 | — | 2 | 1 | no | — |
| 627 | C23 | — | 3 | 1 | no | — |
| 628 | C23 | — | 3 | 18 | no | — |
| 629 | C23 | — | 3 | 1 | no | — |
| 630 | C23 | — | 3 | 18 | no | — |
| 631 | C23 | — | 3 | 18 | no | — |
| 632 | C23 | — | 3 | 9 | no | — |
| 633 | C23 | — | 3 | 72 | no | — |
| 634 | C23 | — | 3 | 16 | no | — |
| 635 | C23 | — | 6 | 1 | no | — |
| 636 | C23 | — | 6 | 9 | no | — |
| 637 | C23 | — | 6 | 24 | no | — |
| 638 | C23 | — | 6 | 18 | no | — |
| 639 | C23 | — | 6 | 36 | no | — |
| 640 | C23 | — | 6 | 72 | no | — |
| 641 | C23 | — | 6 | 72 | no | — |
| 642 | C23 | — | 8 | 6 | no | — |
| 643 | C23 | — | 12 | 24 | no | — |
| 644 | C23 | — | 12 | 24 | no | — |
| 645 | C23 | — | 12 | 9 | no | — |
| 646 | C23 | — | 12 | 9 | no | — |
| 647 | C23 | — | 12 | 18 | no | — |
| 648 | C23 | — | 12 | 9 | no | — |
| 649 | C23 | — | 12 | 9 | no | — |
| 650 | C23 | — | 12 | 72 | no | — |
| 651 | C23 | — | 12 | 72 | no | — |
| 652 | C23 | — | 12 | 72 | no | — |
| 653 | C23 | — | 12 | 72 | no | — |
| 654 | C23 | — | 24 | 24 | no | — |
| 655 | C23 | — | 24 | 18 | no | — |
| 656 | C23 | — | 24 | 72 | no | — |
| 657 | C23 | — | 24 | 12 | no | — |
| 658 | C23 | — | 48 | 24 | no | — |
| 659 | C23 | — | 48 | 72 | no | — |
| 660 | C23 | C23×S4 | 1 | 9 | yes | — |
| 661 | C23 | C23×S4 | 1 | 24 | yes | — |
| 662 | C23 | C25×D3 | 1 | 1 | yes | characteristic |
| 663 | Q8 | — | 3 | 24 | no | — |
| 664 | Q8 | — | 6 | 8 | no | — |
| 665 | Q8 | — | 6 | 48 | no | — |
| 666 | Q8 | — | 6 | 48 | no | — |
| 667 | Q8 | C23×S4 | 1 | 8 | yes | — |
| 668 | D4 | — | 3 | 144 | no | — |
| 669 | D4 | — | 3 | 72 | no | — |
| 670 | D4 | — | 6 | 72 | no | — |
| 671 | D4 | — | 6 | 48 | no | — |
| 672 | D4 | — | 6 | 16 | no | — |
| 673 | D4 | — | 6 | 144 | no | — |
| 674 | D4 | — | 6 | 16 | no | — |
| 675 | D4 | — | 6 | 32 | no | — |
| 676 | D4 | — | 6 | 16 | no | — |
| 677 | D4 | — | 6 | 16 | no | — |
| 678 | D4 | — | 6 | 144 | no | — |
| 679 | D4 | — | 6 | 48 | no | — |
| 680 | D4 | — | 12 | 144 | no | — |
| 681 | D4 | — | 12 | 144 | no | — |
| 682 | D4 | C23×S4 | 1 | 72 | yes | — |
| 683 | C2×C4 | — | 3 | 6 | no | — |
| 684 | C2×C4 | — | 3 | 36 | no | — |
| 685 | C2×C4 | — | 3 | 12 | no | — |
| 686 | C2×C4 | — | 3 | 12 | no | — |
| 687 | C2×C4 | — | 3 | 72 | no | — |
| 688 | C2×C4 | — | 3 | 12 | no | — |
| 689 | C2×C4 | — | 3 | 16 | no | — |
| 690 | C2×C4 | — | 3 | 16 | no | — |
| 691 | C2×C4 | — | 3 | 16 | no | — |
| 692 | C2×C4 | — | 6 | 6 | no | — |
| 693 | C2×C4 | — | 6 | 36 | no | — |
| 694 | C2×C4 | — | 6 | 96 | no | — |
| 695 | C2×C4 | — | 6 | 72 | no | — |
| 696 | C2×C4 | — | 6 | 72 | no | — |
| 697 | C2×C4 | — | 6 | 96 | no | — |
| 698 | C2×C4 | — | 12 | 72 | no | — |
| 699 | C2×C4 | — | 12 | 72 | no | — |
| 700 | C2×C4 | C23×S4 | 1 | 6 | yes | — |
| 701 | C2×C4 | C23×S4 | 1 | 36 | yes | — |
| 702 | C2×C3 | — | 4 | 1 | no | — |
| 703 | C2×C3 | — | 8 | 18 | no | — |
| 704 | C2×C3 | — | 8 | 1 | no | — |
| 705 | D3 | — | 8 | 16 | no | — |
| 706 | C22 | — | 3 | 1 | no | — |
| 707 | C22 | — | 3 | 1 | no | — |
| 708 | C22 | — | 3 | 2 | no | — |
| 709 | C22 | — | 3 | 1 | no | — |
| 710 | C22 | — | 3 | 18 | no | — |
| 711 | C22 | — | 4 | 9 | no | — |
| 712 | C22 | — | 4 | 24 | no | — |
| 713 | C22 | — | 6 | 18 | no | — |
| 714 | C22 | — | 6 | 18 | no | — |
| 715 | C22 | — | 6 | 1 | no | — |
| 716 | C22 | — | 6 | 1 | no | — |
| 717 | C22 | — | 6 | 18 | no | — |
| 718 | C22 | — | 6 | 18 | no | — |
| 719 | C22 | — | 6 | 1 | no | — |
| 720 | C22 | — | 6 | 16 | no | — |
| 721 | C22 | — | 6 | 16 | no | — |
| 722 | C22 | — | 6 | 16 | no | — |
| 723 | C22 | — | 12 | 18 | no | — |
| 724 | C22 | — | 12 | 9 | no | — |
| 725 | C22 | — | 12 | 72 | no | — |
| 726 | C22 | — | 12 | 18 | no | — |
| 727 | C22 | — | 24 | 72 | no | — |
| 728 | C22 | — | 24 | 24 | no | — |
| 729 | C22 | — | 24 | 72 | no | — |
| 730 | C22 | #87568 | 1 | 1 | yes | characteristic, complemented |
| 731 | C22 | C24×S4 | 1 | 1 | yes | characteristic |
| 732 | C22 | C24×S4 | 1 | 18 | yes | — |
| 733 | C4 | — | 3 | 12 | no | — |
| 734 | C4 | — | 6 | 16 | no | — |
| 735 | C4 | — | 6 | 16 | no | — |
| 736 | C4 | — | 6 | 16 | no | — |
| 737 | C4 | C24×S4 | 1 | 12 | yes | — |
| 738 | C3 | — | 4 | 1 | no | Sylow |
| 739 | C2 | — | 2 | 1 | no | — |
| 740 | C2 | — | 2 | 18 | no | — |
| 741 | C2 | — | 3 | 1 | no | — |
| 742 | C2 | — | 3 | 1 | no | — |
| 743 | C2 | — | 6 | 1 | no | — |
| 744 | C2 | — | 6 | 18 | no | — |
| 745 | C2 | — | 12 | 16 | no | — |
| 746 | C2 | C25×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×S4 |
| commutator, cosocle | C2×A4 | C26 |
| Fitting | C23×H(5,𝔽2) | D3 |
| socle | C23 | C25×D3 |
| hypercenter | C2×H(5,𝔽2) | S4 |
| hypocenter | A4 | H(7,𝔽2) |
| LCS | G ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C2 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11715776 | C2 | semidirect |
| 2. S4×H(5,𝔽2) | C2 | semidirect |
| 3. #11715774 | C2 | semidirect |
| 4. C2×#87477 | C2 | semidirect |
| 5. C2×A4×H(5,𝔽2) | C2 | semidirect |
| 8. A4×H(5,𝔽2) | C22 | semidirect |
| 9. C2×A4×#41 | C22 | semidirect |
| 10. C22×D4×A4 | C22 | semidirect |
| 11. C22×GL(2,ℤ/4) | C22 | semidirect |
| 12. #87490 | C22 | semidirect |
| 13. #87489 | C22 | semidirect |
| 14. #41×S4 | C22 | semidirect |
| 15. #87483 | C22 | semidirect |
| 16. #87477 | C22 | semidirect |
| 17. #87477 | C22 | semidirect |
| 18. C2×#5914 | C22 | semidirect |
| 19. C2×D4×S4 | C22 | semidirect |
| 20. C2×#5912 | C22 | semidirect |
| 22. C23×H(5,𝔽2) | D3 | semidirect |
| 32. C24×A4 | C23 | semidirect |
| 33. C23×S4 | C23 | semidirect |
| 39. A4×#41 | C23 | semidirect |
| 40. C2×Q8×A4 | C23 | semidirect |
| 41. C2×D4×A4 | C23 | semidirect |
| 42. C2×D4×A4 | C23 | semidirect |
| 43. C22×C4×A4 | C23 | semidirect |
| 44. C2×GL(2,ℤ/4) | C23 | semidirect |
| 45. C2×GL(2,ℤ/4) | C23 | semidirect |
| 46. C22×SL(2,ℤ/4) | C23 | semidirect |
| 47. #5919 | C23 | semidirect |
| 48. Q8×S4 | C23 | semidirect |
| 49. #5914 | C23 | semidirect |
| 50. D4×S4 | C23 | semidirect |
| 51. #5912 | C23 | semidirect |
| 52. #5912 | C23 | semidirect |
| 53. C2×C4⋊S4 | C23 | semidirect |
| 54. C2×C4×S4 | C23 | semidirect |
| 55. C2×A4⋊Q8 | C23 | semidirect |
| 68. C22×H(5,𝔽2) | C2×D3 | semidirect |
| 69. C23×#41 | C2×D3 | semidirect |
| 70. C24×D4 | C2×D3 | semidirect |
| 133. C26 | C22×D3 | semidirect |
| 169. C2×H(5,𝔽2) | S4 | semidirect |
| 178. C22×#41 | C22×D3 | semidirect |
| 179. C23×Q8 | C22×D3 | semidirect |
| 189. C23×D4 | C22×D3 | semidirect |
| 190. C23×D4 | C22×D3 | semidirect |
| 191. C24×C4 | C22×D3 | semidirect |
| 318. H(5,𝔽2) | C2×S4 | semidirect |
| 351. C2×#41 | C2×S4 | semidirect |
| 395. C22×D4 | C2×S4 | semidirect |
| 500. C24 | C22×S4 | semidirect |
| 522. #41 | C22×S4 | semidirect |
| 535. C2×Q8 | C22×S4 | semidirect |
| 576. C2×D4 | C22×S4 | semidirect |
| 577. C2×D4 | C22×S4 | semidirect |
| 601. C22×C4 | C22×S4 | semidirect |
| 622. A4 | H(7,𝔽2) | semidirect |
| 730. C22 | #87568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11715776 | 2 |
| S4×H(5,𝔽2) | 2 |
| #11715774 | 2 |
| C2×#87477 | 2 |
| C2×A4×H(5,𝔽2) | 2 |
| #10586066 | 3 |
| #87568 | 4 |