Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2136 conjugacy classes of subgroups.
The subgroup lattice has 759 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10593143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#577 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10589940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589881 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10589879 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10589876 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #10589875 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #10589872 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | D9×#135 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10589864 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | C2×#63478 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #10589853 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | D9×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #87206 | — | 3 | 1 | no | maximal |
| 17 | C9×2−1+4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C9×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #63716 | — | 2 | 1 | no | — |
| 20 | #63716 | C22 | 1 | 3 | yes | complemented |
| 21 | #63716 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #63715 | — | 2 | 3 | no | — |
| 23 | #63715 | C22 | 1 | 3 | yes | complemented |
| 24 | #63715 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #41×D9 | — | 2 | 1 | no | — |
| 26 | #41×D9 | — | 2 | 3 | no | — |
| 27 | #41×D9 | C22 | 1 | 1 | yes | characteristic |
| 28 | #41×D9 | C22 | 1 | 3 | yes | complemented |
| 29 | #41×D9 | C22 | 1 | 3 | yes | complemented |
| 30 | #63713 | — | 2 | 1 | no | — |
| 31 | #63713 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×#3701 | — | 2 | 1 | no | — |
| 33 | C2×#3701 | C22 | 1 | 3 | yes | complemented |
| 34 | #63710 | — | 2 | 3 | no | — |
| 35 | #63710 | C22 | 1 | 3 | yes | complemented |
| 36 | C2×#3699 | — | 2 | 3 | no | — |
| 37 | C2×#3699 | C22 | 1 | 3 | yes | complemented |
| 38 | C9×#137 | C22 | 1 | 3 | yes | complemented |
| 39 | C9×AGL(1,ℤ/8) | C22 | 1 | 3 | yes | complemented |
| 40 | C9×#135 | C22 | 1 | 3 | yes | complemented |
| 41 | C2×C9×SD16 | C22 | 1 | 3 | yes | complemented |
| 42 | C9×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #63513 | C22 | 1 | 3 | yes | complemented |
| 44 | #63513 | C22 | 1 | 3 | yes | complemented |
| 45 | #63512 | C22 | 1 | 3 | yes | complemented |
| 46 | #63511 | C22 | 1 | 3 | yes | complemented |
| 47 | #63510 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #63505 | C22 | 1 | 3 | yes | complemented |
| 49 | C2×#3674 | C22 | 1 | 3 | yes | complemented |
| 50 | #63495 | C22 | 1 | 3 | yes | complemented |
| 51 | C2×#3673 | C22 | 1 | 3 | yes | complemented |
| 52 | #63481 | C22 | 1 | 3 | yes | complemented |
| 53 | #63480 | C22 | 1 | 6 | yes | complemented |
| 54 | Q16×D9 | C22 | 1 | 3 | yes | complemented |
| 55 | #63478 | C22 | 1 | 3 | yes | complemented |
| 56 | #63478 | C22 | 1 | 6 | yes | complemented |
| 57 | #63478 | C22 | 1 | 6 | yes | complemented |
| 58 | #63478 | C22 | 1 | 6 | yes | complemented |
| 59 | #63478 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #63477 | C22 | 1 | 6 | yes | complemented |
| 61 | #63476 | C22 | 1 | 6 | yes | complemented |
| 62 | SD16×D9 | C22 | 1 | 3 | yes | complemented |
| 63 | SD16×D9 | C22 | 1 | 3 | yes | complemented |
| 64 | #63474 | C22 | 1 | 3 | yes | complemented |
| 65 | #63473 | C22 | 1 | 6 | yes | complemented |
| 66 | D8×D9 | C22 | 1 | 3 | yes | complemented |
| 67 | #63471 | C22 | 1 | 3 | yes | complemented |
| 68 | #63470 | C22 | 1 | 3 | yes | complemented |
| 69 | #63469 | C22 | 1 | 3 | yes | complemented |
| 70 | M16×D9 | C22 | 1 | 3 | yes | complemented |
| 71 | #63467 | C22 | 1 | 3 | yes | complemented |
| 72 | C2×#3664 | C22 | 1 | 3 | yes | complemented |
| 73 | #63464 | C22 | 1 | 3 | yes | complemented |
| 74 | C2×C8×D9 | C22 | 1 | 3 | yes | complemented |
| 75 | #5968 | — | 3 | 1 | no | — |
| 76 | #5966 | — | 3 | 1 | no | — |
| 77 | C3×#577 | D3 | 1 | 1 | yes | characteristic |
| 78 | #5838 | — | 3 | 1 | no | — |
| 79 | #5835 | — | 3 | 1 | no | — |
| 80 | #5779 | — | 3 | 3 | no | — |
| 81 | #5777 | — | 3 | 3 | no | — |
| 82 | #5774 | — | 3 | 3 | no | — |
| 83 | #5773 | — | 3 | 3 | no | — |
| 84 | #5770 | — | 3 | 3 | no | — |
| 85 | D3×#135 | — | 3 | 3 | no | — |
| 86 | #5762 | — | 3 | 3 | no | — |
| 87 | C2×#916 | — | 3 | 3 | no | — |
| 88 | #5751 | — | 3 | 1 | no | — |
| 89 | D3×#131 | — | 3 | 1 | no | — |
| 90 | C9×#41 | — | 2 | 1 | no | — |
| 91 | C9×#41 | — | 2 | 3 | no | — |
| 92 | C9×#41 | C23 | 1 | 3 | yes | — |
| 93 | C9×#41 | C23 | 1 | 3 | yes | — |
| 94 | C9×#41 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×Q8×C9 | — | 2 | 1 | no | — |
| 96 | C2×Q8×C9 | C23 | 1 | 3 | yes | — |
| 97 | C2×D4×C9 | — | 2 | 3 | no | — |
| 98 | C2×D4×C9 | C23 | 1 | 3 | yes | — |
| 99 | C2×#611 | — | 2 | 3 | no | — |
| 100 | C2×#611 | — | 2 | 6 | no | — |
| 101 | C22×Dic9 | — | 2 | 3 | no | — |
| 102 | #3701 | — | 2 | 1 | no | — |
| 103 | #3701 | — | 2 | 3 | no | — |
| 104 | #3701 | — | 2 | 3 | no | — |
| 105 | #3701 | — | 2 | 3 | no | — |
| 106 | #3701 | D4 | 1 | 1 | yes | characteristic |
| 107 | #3701 | C23 | 1 | 3 | yes | — |
| 108 | #3701 | C23 | 1 | 6 | yes | — |
| 109 | #3701 | C23 | 1 | 1 | yes | characteristic |
| 110 | Q8×D9 | — | 2 | 1 | no | — |
| 111 | Q8×D9 | — | 2 | 3 | no | — |
| 112 | Q8×D9 | D4 | 1 | 1 | yes | characteristic |
| 113 | Q8×D9 | C23 | 1 | 3 | yes | — |
| 114 | Q8×D9 | C23 | 1 | 3 | yes | — |
| 115 | #3699 | — | 2 | 3 | no | — |
| 116 | #3699 | — | 2 | 6 | no | — |
| 117 | #3699 | — | 2 | 3 | no | — |
| 118 | #3699 | — | 2 | 3 | no | — |
| 119 | #3699 | — | 2 | 3 | no | — |
| 120 | #3699 | — | 2 | 3 | no | — |
| 121 | #3699 | — | 2 | 3 | no | — |
| 122 | #3699 | D4 | 1 | 3 | yes | — |
| 123 | #3699 | C23 | 1 | 3 | yes | — |
| 124 | #3699 | C23 | 1 | 6 | yes | — |
| 125 | #3699 | C23 | 1 | 1 | yes | characteristic |
| 126 | D4×D9 | — | 2 | 3 | no | — |
| 127 | D4×D9 | — | 2 | 3 | no | — |
| 128 | D4×D9 | — | 2 | 3 | no | — |
| 129 | D4×D9 | — | 2 | 6 | no | — |
| 130 | D4×D9 | — | 2 | 3 | no | — |
| 131 | D4×D9 | D4 | 1 | 3 | yes | — |
| 132 | D4×D9 | C23 | 1 | 3 | yes | — |
| 133 | D4×D9 | C23 | 1 | 3 | yes | — |
| 134 | #3697 | — | 2 | 6 | no | — |
| 135 | #3697 | — | 2 | 3 | no | — |
| 136 | #3697 | — | 2 | 3 | no | — |
| 137 | #3697 | — | 2 | 3 | no | — |
| 138 | #3697 | — | 2 | 3 | no | — |
| 139 | #3697 | C23 | 1 | 3 | yes | — |
| 140 | #3697 | C23 | 1 | 3 | yes | — |
| 141 | #3697 | C23 | 1 | 3 | yes | — |
| 142 | C2×D36 | — | 2 | 3 | no | — |
| 143 | C2×D36 | — | 2 | 3 | no | — |
| 144 | C2×D36 | C23 | 1 | 3 | yes | — |
| 145 | C2×C4×D9 | — | 2 | 3 | no | — |
| 146 | C2×C4×D9 | — | 2 | 3 | no | — |
| 147 | C2×C4×D9 | — | 2 | 3 | no | — |
| 148 | C2×C4×D9 | C23 | 1 | 3 | yes | — |
| 149 | C2×Dic18 | — | 2 | 3 | no | — |
| 150 | C2×Dic18 | C23 | 1 | 3 | yes | — |
| 151 | C9×Q16 | C23 | 1 | 3 | yes | — |
| 152 | C9×SD16 | C23 | 1 | 3 | yes | — |
| 153 | C9×SD16 | C23 | 1 | 6 | yes | — |
| 154 | C9×SD16 | C23 | 1 | 1 | yes | characteristic |
| 155 | C9×D8 | C23 | 1 | 3 | yes | — |
| 156 | C9×M16 | C23 | 1 | 3 | yes | — |
| 157 | C2×C8×C9 | C23 | 1 | 3 | yes | — |
| 158 | #3675 | C23 | 1 | 3 | yes | — |
| 159 | #3675 | C23 | 1 | 3 | yes | — |
| 160 | #3674 | C23 | 1 | 3 | yes | — |
| 161 | #3674 | C23 | 1 | 6 | yes | — |
| 162 | #3674 | C23 | 1 | 1 | yes | characteristic |
| 163 | #3673 | C23 | 1 | 3 | yes | — |
| 164 | #3673 | C23 | 1 | 6 | yes | — |
| 165 | #3673 | C23 | 1 | 1 | yes | characteristic |
| 166 | #3672 | C23 | 1 | 3 | yes | — |
| 167 | #3672 | C23 | 1 | 3 | yes | — |
| 168 | #3667 | C23 | 1 | 3 | yes | — |
| 169 | C2×C9⋊C8 | C23 | 1 | 3 | yes | — |
| 170 | D72 | C23 | 1 | 3 | yes | — |
| 171 | #3664 | C23 | 1 | 3 | yes | — |
| 172 | #3664 | C23 | 1 | 6 | yes | — |
| 173 | #3664 | C23 | 1 | 1 | yes | characteristic |
| 174 | #3663 | C23 | 1 | 6 | yes | — |
| 175 | C8×D9 | C23 | 1 | 1 | yes | characteristic |
| 176 | C8×D9 | C23 | 1 | 3 | yes | — |
| 177 | C8×D9 | C23 | 1 | 3 | yes | — |
| 178 | C8×D9 | C23 | 1 | 3 | yes | — |
| 179 | Dic36 | C23 | 1 | 3 | yes | — |
| 180 | #3584 | — | 9 | 1 | no | Sylow |
| 181 | C3×2−1+4 | C2×D3 | 1 | 1 | yes | characteristic |
| 182 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 183 | #1010 | — | 3 | 1 | no | — |
| 184 | #1010 | — | 3 | 3 | no | — |
| 185 | #1010 | — | 6 | 1 | no | — |
| 186 | #1009 | — | 3 | 1 | no | — |
| 187 | #1009 | — | 3 | 3 | no | — |
| 188 | #1009 | — | 6 | 3 | no | — |
| 189 | D3×#41 | — | 3 | 1 | no | — |
| 190 | D3×#41 | — | 3 | 3 | no | — |
| 191 | D3×#41 | — | 3 | 3 | no | — |
| 192 | D3×#41 | — | 6 | 3 | no | — |
| 193 | D3×#41 | — | 6 | 1 | no | — |
| 194 | #1007 | — | 3 | 3 | no | — |
| 195 | #1007 | — | 6 | 1 | no | — |
| 196 | C2×#239 | — | 3 | 3 | no | — |
| 197 | C2×#239 | — | 6 | 1 | no | — |
| 198 | #1004 | — | 3 | 3 | no | — |
| 199 | #1004 | — | 6 | 3 | no | — |
| 200 | C2×#237 | — | 3 | 3 | no | — |
| 201 | C2×#237 | — | 6 | 3 | no | — |
| 202 | C3×#137 | C2×D3 | 1 | 3 | yes | — |
| 203 | C3×AGL(1,ℤ/8) | C2×D3 | 1 | 3 | yes | — |
| 204 | C3×#135 | C2×D3 | 1 | 3 | yes | — |
| 205 | C2×C3×SD16 | C2×D3 | 1 | 3 | yes | — |
| 206 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 207 | #951 | — | 3 | 3 | no | — |
| 208 | #950 | — | 3 | 3 | no | — |
| 209 | #950 | — | 3 | 3 | no | — |
| 210 | #949 | — | 3 | 3 | no | — |
| 211 | #948 | — | 3 | 1 | no | — |
| 212 | C2×#216 | — | 3 | 3 | no | — |
| 213 | #942 | — | 3 | 3 | no | — |
| 214 | #932 | — | 3 | 3 | no | — |
| 215 | C2×#213 | — | 3 | 3 | no | — |
| 216 | #919 | — | 3 | 3 | no | — |
| 217 | #918 | — | 3 | 6 | no | — |
| 218 | D3×Q16 | — | 3 | 3 | no | — |
| 219 | #916 | — | 3 | 3 | no | — |
| 220 | #916 | — | 3 | 6 | no | — |
| 221 | #916 | — | 3 | 6 | no | — |
| 222 | #916 | — | 3 | 6 | no | — |
| 223 | #916 | — | 3 | 1 | no | — |
| 224 | #915 | — | 3 | 6 | no | — |
| 225 | #914 | — | 3 | 6 | no | — |
| 226 | D3×SD16 | — | 3 | 3 | no | — |
| 227 | D3×SD16 | — | 3 | 3 | no | — |
| 228 | #912 | — | 3 | 3 | no | — |
| 229 | #911 | — | 3 | 6 | no | — |
| 230 | D3×D8 | — | 3 | 3 | no | — |
| 231 | #909 | — | 3 | 3 | no | — |
| 232 | #908 | — | 3 | 3 | no | — |
| 233 | #907 | — | 3 | 3 | no | — |
| 234 | D3×M16 | — | 3 | 3 | no | — |
| 235 | #904 | — | 3 | 3 | no | — |
| 236 | C2×#204 | — | 3 | 3 | no | — |
| 237 | #901 | — | 3 | 3 | no | — |
| 238 | C2×D3×C8 | — | 3 | 3 | no | — |
| 239 | C23×C9 | — | 2 | 3 | no | — |
| 240 | C22×D9 | — | 2 | 3 | no | — |
| 241 | C22×D9 | — | 2 | 3 | no | — |
| 242 | C22×D9 | — | 2 | 3 | no | — |
| 243 | C22×D9 | C2×D4 | 1 | 3 | yes | — |
| 244 | Q8×C9 | — | 2 | 3 | no | — |
| 245 | Q8×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 246 | Q8×C9 | C24 | 1 | 3 | yes | — |
| 247 | Q8×C9 | C24 | 1 | 1 | yes | characteristic |
| 248 | D4×C9 | — | 2 | 3 | no | — |
| 249 | D4×C9 | — | 2 | 3 | no | — |
| 250 | D4×C9 | — | 2 | 3 | no | — |
| 251 | D4×C9 | C2×D4 | 1 | 3 | yes | — |
| 252 | D4×C9 | C24 | 1 | 1 | yes | characteristic |
| 253 | D4×C9 | C24 | 1 | 3 | yes | — |
| 254 | C2×C4×C9 | — | 2 | 3 | no | — |
| 255 | C2×C4×C9 | — | 2 | 3 | no | — |
| 256 | C2×C4×C9 | — | 2 | 3 | no | — |
| 257 | C2×C4×C9 | C24 | 1 | 3 | yes | — |
| 258 | #611 | — | 2 | 3 | no | — |
| 259 | #611 | — | 2 | 3 | no | — |
| 260 | #611 | — | 2 | 1 | no | — |
| 261 | #611 | — | 2 | 6 | no | — |
| 262 | #611 | — | 2 | 3 | no | — |
| 263 | #611 | — | 2 | 3 | no | — |
| 264 | #611 | — | 2 | 3 | no | — |
| 265 | #611 | C2×D4 | 1 | 6 | yes | — |
| 266 | C2×Dic9 | — | 2 | 3 | no | — |
| 267 | C2×Dic9 | — | 2 | 6 | no | — |
| 268 | C2×Dic9 | — | 2 | 1 | no | — |
| 269 | C2×Dic9 | — | 2 | 3 | no | — |
| 270 | C2×Dic9 | C2×D4 | 1 | 3 | yes | — |
| 271 | D36 | — | 2 | 6 | no | — |
| 272 | D36 | — | 2 | 3 | no | — |
| 273 | D36 | — | 2 | 1 | no | — |
| 274 | D36 | — | 2 | 3 | no | — |
| 275 | D36 | C2×D4 | 1 | 3 | yes | — |
| 276 | D36 | C24 | 1 | 3 | yes | — |
| 277 | D36 | C24 | 1 | 1 | yes | characteristic |
| 278 | C4×D9 | — | 2 | 3 | no | — |
| 279 | C4×D9 | — | 2 | 3 | no | — |
| 280 | C4×D9 | — | 2 | 3 | no | — |
| 281 | C4×D9 | — | 2 | 3 | no | — |
| 282 | C4×D9 | — | 2 | 1 | no | — |
| 283 | C4×D9 | — | 2 | 3 | no | — |
| 284 | C4×D9 | — | 2 | 6 | no | — |
| 285 | C4×D9 | C2×D4 | 1 | 3 | yes | — |
| 286 | C4×D9 | C2×D4 | 1 | 3 | yes | — |
| 287 | C4×D9 | C24 | 1 | 1 | yes | characteristic |
| 288 | C4×D9 | C24 | 1 | 3 | yes | — |
| 289 | Dic18 | — | 2 | 3 | no | — |
| 290 | Dic18 | — | 2 | 3 | no | — |
| 291 | Dic18 | — | 2 | 3 | no | — |
| 292 | Dic18 | C2×D4 | 1 | 3 | yes | — |
| 293 | Dic18 | C24 | 1 | 1 | yes | characteristic |
| 294 | Dic18 | C24 | 1 | 3 | yes | — |
| 295 | C8×C9 | C24 | 1 | 3 | yes | — |
| 296 | C8×C9 | C24 | 1 | 1 | yes | characteristic |
| 297 | C9⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 298 | C9⋊C8 | C24 | 1 | 3 | yes | — |
| 299 | #585 | — | 9 | 1 | no | — |
| 300 | #585 | — | 9 | 1 | no | — |
| 301 | #578 | — | 9 | 1 | no | — |
| 302 | #578 | — | 9 | 3 | no | — |
| 303 | #577 | — | 9 | 3 | no | — |
| 304 | #577 | — | 9 | 3 | no | — |
| 305 | #577 | — | 9 | 1 | no | — |
| 306 | #577 | D9 | 1 | 1 | yes | characteristic, complemented |
| 307 | #576 | — | 9 | 1 | no | — |
| 308 | #576 | — | 9 | 3 | no | — |
| 309 | #575 | — | 9 | 3 | no | — |
| 310 | #575 | — | 9 | 3 | no | — |
| 311 | C2×#135 | — | 9 | 3 | no | — |
| 312 | C2×#135 | — | 9 | 3 | no | — |
| 313 | C2×#131 | — | 9 | 1 | no | — |
| 314 | C3×#41 | — | 2 | 1 | no | — |
| 315 | C3×#41 | — | 2 | 3 | no | — |
| 316 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 317 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 318 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 319 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 320 | C2×C3×Q8 | C22×D3 | 1 | 3 | yes | — |
| 321 | C2×C3×D4 | — | 2 | 3 | no | — |
| 322 | C2×C3×D4 | C22×D3 | 1 | 3 | yes | — |
| 323 | C2×#67 | — | 6 | 6 | no | — |
| 324 | C2×#67 | — | 6 | 3 | no | — |
| 325 | C22×Dic3 | — | 6 | 3 | no | — |
| 326 | #239 | — | 3 | 1 | no | — |
| 327 | #239 | — | 3 | 6 | no | — |
| 328 | #239 | — | 3 | 3 | no | — |
| 329 | #239 | — | 3 | 1 | no | — |
| 330 | #239 | — | 6 | 3 | no | — |
| 331 | #239 | — | 6 | 3 | no | — |
| 332 | #239 | — | 6 | 3 | no | — |
| 333 | #239 | — | 6 | 1 | no | — |
| 334 | D3×Q8 | — | 3 | 1 | no | — |
| 335 | D3×Q8 | — | 3 | 3 | no | — |
| 336 | D3×Q8 | — | 3 | 3 | no | — |
| 337 | D3×Q8 | — | 6 | 3 | no | — |
| 338 | D3×Q8 | — | 6 | 1 | no | — |
| 339 | #237 | — | 3 | 3 | no | — |
| 340 | #237 | — | 3 | 6 | no | — |
| 341 | #237 | — | 3 | 1 | no | — |
| 342 | #237 | — | 3 | 3 | no | — |
| 343 | #237 | — | 6 | 3 | no | — |
| 344 | #237 | — | 6 | 3 | no | — |
| 345 | #237 | — | 6 | 3 | no | — |
| 346 | #237 | — | 6 | 3 | no | — |
| 347 | #237 | — | 6 | 3 | no | — |
| 348 | #237 | — | 6 | 6 | no | — |
| 349 | #237 | — | 6 | 3 | no | — |
| 350 | D3×D4 | — | 3 | 3 | no | — |
| 351 | D3×D4 | — | 3 | 3 | no | — |
| 352 | D3×D4 | — | 3 | 3 | no | — |
| 353 | D3×D4 | — | 6 | 3 | no | — |
| 354 | D3×D4 | — | 6 | 6 | no | — |
| 355 | D3×D4 | — | 6 | 3 | no | — |
| 356 | D3×D4 | — | 6 | 3 | no | — |
| 357 | D3×D4 | — | 6 | 3 | no | — |
| 358 | #235 | — | 3 | 3 | no | — |
| 359 | #235 | — | 3 | 3 | no | — |
| 360 | #235 | — | 3 | 3 | no | — |
| 361 | #235 | — | 6 | 3 | no | — |
| 362 | #235 | — | 6 | 3 | no | — |
| 363 | #235 | — | 6 | 3 | no | — |
| 364 | #235 | — | 6 | 3 | no | — |
| 365 | #235 | — | 6 | 6 | no | — |
| 366 | C2×D12 | — | 3 | 3 | no | — |
| 367 | C2×D12 | — | 6 | 3 | no | — |
| 368 | C2×D12 | — | 6 | 3 | no | — |
| 369 | C2×C4×D3 | — | 3 | 3 | no | — |
| 370 | C2×C4×D3 | — | 6 | 3 | no | — |
| 371 | C2×C4×D3 | — | 6 | 3 | no | — |
| 372 | C2×C4×D3 | — | 6 | 3 | no | — |
| 373 | C2×Dic6 | — | 3 | 3 | no | — |
| 374 | C2×Dic6 | — | 6 | 3 | no | — |
| 375 | C3×Q16 | C22×D3 | 1 | 3 | yes | — |
| 376 | C3×SD16 | C22×D3 | 1 | 1 | yes | characteristic |
| 377 | C3×SD16 | C22×D3 | 1 | 3 | yes | — |
| 378 | C3×SD16 | C22×D3 | 1 | 6 | yes | — |
| 379 | C3×D8 | C22×D3 | 1 | 3 | yes | — |
| 380 | C3×M16 | C22×D3 | 1 | 3 | yes | — |
| 381 | C2×C3×C8 | C22×D3 | 1 | 3 | yes | — |
| 382 | #216 | — | 3 | 6 | no | — |
| 383 | #216 | — | 3 | 3 | no | — |
| 384 | #216 | — | 3 | 1 | no | — |
| 385 | #215 | — | 3 | 3 | no | — |
| 386 | #215 | — | 3 | 3 | no | — |
| 387 | #214 | — | 3 | 3 | no | — |
| 388 | #214 | — | 3 | 3 | no | — |
| 389 | #213 | — | 3 | 1 | no | — |
| 390 | #213 | — | 3 | 3 | no | — |
| 391 | #213 | — | 3 | 6 | no | — |
| 392 | #208 | — | 3 | 3 | no | — |
| 393 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 394 | Dic12 | — | 3 | 3 | no | — |
| 395 | D24 | — | 3 | 3 | no | — |
| 396 | #204 | — | 3 | 3 | no | — |
| 397 | #204 | — | 3 | 6 | no | — |
| 398 | #204 | — | 3 | 1 | no | — |
| 399 | ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 400 | D3×C8 | — | 3 | 1 | no | — |
| 401 | D3×C8 | — | 3 | 3 | no | — |
| 402 | D3×C8 | — | 3 | 3 | no | — |
| 403 | D3×C8 | — | 3 | 3 | no | — |
| 404 | C22×C9 | — | 2 | 3 | no | — |
| 405 | C22×C9 | — | 2 | 1 | no | — |
| 406 | C22×C9 | — | 8 | 3 | no | — |
| 407 | C22×C9 | C22×D4 | 1 | 3 | yes | — |
| 408 | C2×D9 | — | 2 | 3 | no | — |
| 409 | C2×D9 | — | 2 | 1 | no | — |
| 410 | C2×D9 | — | 4 | 3 | no | — |
| 411 | C2×D9 | — | 8 | 3 | no | — |
| 412 | C2×D9 | — | 8 | 3 | no | — |
| 413 | C2×D9 | — | 8 | 3 | no | — |
| 414 | C2×D9 | C22×D4 | 1 | 3 | yes | — |
| 415 | C2×D9 | C22×D4 | 1 | 1 | yes | characteristic |
| 416 | C4×C9 | — | 2 | 1 | no | — |
| 417 | C4×C9 | — | 2 | 3 | no | — |
| 418 | C4×C9 | C22×D4 | 1 | 3 | yes | — |
| 419 | C4×C9 | C25 | 1 | 1 | yes | characteristic |
| 420 | Dic9 | — | 2 | 1 | no | — |
| 421 | Dic9 | — | 2 | 3 | no | — |
| 422 | Dic9 | C22×D4 | 1 | 3 | yes | — |
| 423 | Dic9 | C22×D4 | 1 | 1 | yes | characteristic |
| 424 | 2−1+4 | — | 9 | 3 | no | — |
| 425 | 2−1+4 | — | 9 | 1 | no | — |
| 426 | 2−1+4 | — | 9 | 3 | no | — |
| 427 | 2−1+4 | — | 18 | 1 | no | — |
| 428 | 2−1+4 | — | 18 | 1 | no | — |
| 429 | 2−1+4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 430 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 431 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 432 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 433 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 434 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 435 | H(5,𝔽2) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 436 | C2×#41 | — | 9 | 1 | no | — |
| 437 | C2×#41 | — | 9 | 3 | no | — |
| 438 | C2×#41 | — | 9 | 3 | no | — |
| 439 | C2×#41 | — | 9 | 3 | no | — |
| 440 | C2×#41 | — | 9 | 3 | no | — |
| 441 | C2×#41 | — | 18 | 3 | no | — |
| 442 | C2×#41 | — | 18 | 1 | no | — |
| 443 | C2×#41 | — | 18 | 1 | no | — |
| 444 | C2×#41 | — | 18 | 3 | no | — |
| 445 | #137 | — | 9 | 3 | no | — |
| 446 | #137 | — | 9 | 3 | no | — |
| 447 | #137 | — | 9 | 6 | no | — |
| 448 | #137 | — | 9 | 6 | no | — |
| 449 | #137 | — | 9 | 3 | no | — |
| 450 | #137 | C2×D9 | 1 | 3 | yes | complemented |
| 451 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 452 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 453 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 454 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 455 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 456 | AGL(1,ℤ/8) | C2×D9 | 1 | 3 | yes | complemented |
| 457 | #135 | — | 9 | 3 | no | — |
| 458 | #135 | — | 9 | 3 | no | — |
| 459 | #135 | — | 9 | 3 | no | — |
| 460 | #135 | — | 9 | 1 | no | — |
| 461 | #135 | — | 9 | 3 | no | — |
| 462 | #135 | — | 9 | 6 | no | — |
| 463 | #135 | — | 9 | 6 | no | — |
| 464 | #135 | — | 9 | 6 | no | — |
| 465 | #135 | — | 9 | 3 | no | — |
| 466 | #135 | — | 9 | 3 | no | — |
| 467 | #135 | C2×D9 | 1 | 3 | yes | complemented |
| 468 | C2×Q16 | — | 9 | 3 | no | — |
| 469 | C2×Q16 | — | 9 | 3 | no | — |
| 470 | C2×SD16 | — | 9 | 3 | no | — |
| 471 | C2×SD16 | — | 9 | 3 | no | — |
| 472 | C2×SD16 | — | 9 | 3 | no | — |
| 473 | C2×SD16 | C2×D9 | 1 | 3 | yes | complemented |
| 474 | C2×D8 | — | 9 | 3 | no | — |
| 475 | C2×D8 | — | 9 | 3 | no | — |
| 476 | #131 | — | 9 | 1 | no | — |
| 477 | #131 | — | 9 | 3 | no | — |
| 478 | #131 | — | 9 | 3 | no | — |
| 479 | #131 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 480 | C2×M16 | — | 9 | 3 | no | — |
| 481 | C22×C8 | — | 9 | 3 | no | — |
| 482 | C23×C3 | — | 2 | 3 | no | — |
| 483 | C22×D3 | — | 3 | 3 | no | — |
| 484 | C22×D3 | — | 6 | 3 | no | — |
| 485 | C22×D3 | — | 6 | 3 | no | — |
| 486 | C22×D3 | — | 6 | 3 | no | — |
| 487 | C3×Q8 | — | 2 | 3 | no | — |
| 488 | C3×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 489 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 490 | C3×Q8 | C23×D3 | 1 | 3 | yes | — |
| 491 | C3×D4 | — | 2 | 3 | no | — |
| 492 | C3×D4 | — | 2 | 3 | no | — |
| 493 | C3×D4 | — | 2 | 3 | no | — |
| 494 | C3×D4 | D3×D4 | 1 | 3 | yes | — |
| 495 | C3×D4 | C23×D3 | 1 | 3 | yes | — |
| 496 | C3×D4 | C23×D3 | 1 | 1 | yes | characteristic |
| 497 | C2×C3×C4 | — | 2 | 3 | no | — |
| 498 | C2×C3×C4 | — | 2 | 3 | no | — |
| 499 | C2×C3×C4 | — | 2 | 3 | no | — |
| 500 | C2×C3×C4 | C23×D3 | 1 | 3 | yes | — |
| 501 | #67 | — | 3 | 6 | no | — |
| 502 | #67 | — | 6 | 3 | no | — |
| 503 | #67 | — | 6 | 3 | no | — |
| 504 | #67 | — | 6 | 1 | no | — |
| 505 | #67 | — | 6 | 3 | no | — |
| 506 | #67 | — | 6 | 6 | no | — |
| 507 | #67 | — | 6 | 3 | no | — |
| 508 | #67 | — | 6 | 3 | no | — |
| 509 | C2×Dic3 | — | 3 | 3 | no | — |
| 510 | C2×Dic3 | — | 6 | 6 | no | — |
| 511 | C2×Dic3 | — | 6 | 1 | no | — |
| 512 | C2×Dic3 | — | 6 | 3 | no | — |
| 513 | C2×Dic3 | — | 6 | 3 | no | — |
| 514 | D12 | — | 3 | 3 | no | — |
| 515 | D12 | — | 3 | 3 | no | — |
| 516 | D12 | — | 3 | 1 | no | — |
| 517 | D12 | — | 6 | 3 | no | — |
| 518 | D12 | — | 6 | 6 | no | — |
| 519 | D12 | — | 6 | 1 | no | — |
| 520 | D12 | — | 6 | 3 | no | — |
| 521 | C4×D3 | — | 3 | 3 | no | — |
| 522 | C4×D3 | — | 3 | 3 | no | — |
| 523 | C4×D3 | — | 3 | 1 | no | — |
| 524 | C4×D3 | — | 3 | 3 | no | — |
| 525 | C4×D3 | — | 6 | 1 | no | — |
| 526 | C4×D3 | — | 6 | 3 | no | — |
| 527 | C4×D3 | — | 6 | 6 | no | — |
| 528 | C4×D3 | — | 6 | 3 | no | — |
| 529 | C4×D3 | — | 6 | 3 | no | — |
| 530 | C4×D3 | — | 6 | 3 | no | — |
| 531 | C4×D3 | — | 6 | 3 | no | — |
| 532 | Dic6 | — | 3 | 3 | no | — |
| 533 | Dic6 | — | 3 | 3 | no | — |
| 534 | Dic6 | — | 3 | 1 | no | — |
| 535 | Dic6 | — | 6 | 3 | no | — |
| 536 | Dic6 | — | 6 | 3 | no | — |
| 537 | Dic6 | — | 6 | 3 | no | — |
| 538 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 539 | C3×C8 | C23×D3 | 1 | 3 | yes | — |
| 540 | C3⋊C8 | — | 3 | 1 | no | — |
| 541 | C3⋊C8 | — | 3 | 3 | no | — |
| 542 | C2×C9 | — | 2 | 3 | no | — |
| 543 | C2×C9 | — | 4 | 1 | no | — |
| 544 | C2×C9 | — | 4 | 3 | no | — |
| 545 | C2×C9 | C23×D4 | 1 | 1 | yes | characteristic |
| 546 | D9 | — | 2 | 1 | no | — |
| 547 | D9 | — | 2 | 3 | no | — |
| 548 | D9 | — | 4 | 3 | no | — |
| 549 | D9 | — | 4 | 1 | no | — |
| 550 | #41 | — | 2 | 1 | no | — |
| 551 | #41 | — | 2 | 3 | no | — |
| 552 | #41 | — | 9 | 1 | no | — |
| 553 | #41 | — | 9 | 3 | no | — |
| 554 | #41 | — | 9 | 3 | no | — |
| 555 | #41 | — | 9 | 1 | no | — |
| 556 | #41 | — | 9 | 3 | no | — |
| 557 | #41 | — | 9 | 6 | no | — |
| 558 | #41 | — | 9 | 3 | no | — |
| 559 | #41 | — | 9 | 1 | no | — |
| 560 | #41 | — | 9 | 6 | no | — |
| 561 | #41 | — | 9 | 3 | no | — |
| 562 | #41 | — | 9 | 3 | no | — |
| 563 | #41 | — | 18 | 3 | no | — |
| 564 | #41 | — | 18 | 3 | no | — |
| 565 | #41 | — | 18 | 6 | no | — |
| 566 | #41 | — | 18 | 3 | no | — |
| 567 | #41 | — | 18 | 3 | no | — |
| 568 | #41 | — | 18 | 3 | no | — |
| 569 | #41 | — | 18 | 3 | no | — |
| 570 | #41 | — | 18 | 3 | no | — |
| 571 | #41 | — | 18 | 3 | no | — |
| 572 | #41 | — | 18 | 3 | no | — |
| 573 | #41 | — | 18 | 3 | no | — |
| 574 | #41 | — | 18 | 6 | no | — |
| 575 | #41 | — | 18 | 3 | no | — |
| 576 | #41 | — | 18 | 3 | no | — |
| 577 | #41 | — | 18 | 1 | no | — |
| 578 | #41 | — | 18 | 3 | no | — |
| 579 | #41 | C22×D9 | 1 | 3 | yes | — |
| 580 | #41 | C22×D9 | 1 | 3 | yes | — |
| 581 | #41 | C22×D9 | 1 | 1 | yes | characteristic |
| 582 | C2×Q8 | — | 2 | 1 | no | — |
| 583 | C2×Q8 | — | 9 | 1 | no | — |
| 584 | C2×Q8 | — | 9 | 3 | no | — |
| 585 | C2×Q8 | — | 9 | 3 | no | — |
| 586 | C2×Q8 | — | 9 | 3 | no | — |
| 587 | C2×Q8 | — | 18 | 3 | no | — |
| 588 | C2×Q8 | — | 18 | 3 | no | — |
| 589 | C2×Q8 | — | 18 | 1 | no | — |
| 590 | C2×Q8 | C22×D9 | 1 | 3 | yes | — |
| 591 | C2×D4 | — | 2 | 3 | no | — |
| 592 | C2×D4 | — | 9 | 3 | no | — |
| 593 | C2×D4 | — | 9 | 3 | no | — |
| 594 | C2×D4 | — | 9 | 3 | no | — |
| 595 | C2×D4 | — | 9 | 3 | no | — |
| 596 | C2×D4 | — | 18 | 3 | no | — |
| 597 | C2×D4 | — | 18 | 3 | no | — |
| 598 | C2×D4 | — | 18 | 6 | no | — |
| 599 | C2×D4 | — | 18 | 3 | no | — |
| 600 | C2×D4 | — | 18 | 3 | no | — |
| 601 | C2×D4 | — | 18 | 3 | no | — |
| 602 | C2×D4 | — | 18 | 6 | no | — |
| 603 | C2×D4 | — | 18 | 3 | no | — |
| 604 | C2×D4 | — | 18 | 3 | no | — |
| 605 | C2×D4 | C22×D9 | 1 | 3 | yes | — |
| 606 | C22×C4 | — | 9 | 3 | no | — |
| 607 | C22×C4 | — | 18 | 3 | no | — |
| 608 | C22×C4 | — | 18 | 3 | no | — |
| 609 | C22×C4 | — | 18 | 3 | no | — |
| 610 | C22×C4 | — | 18 | 3 | no | — |
| 611 | Q16 | — | 9 | 1 | no | — |
| 612 | Q16 | — | 9 | 3 | no | — |
| 613 | Q16 | — | 9 | 6 | no | — |
| 614 | Q16 | — | 9 | 3 | no | — |
| 615 | Q16 | C22×D9 | 1 | 3 | yes | — |
| 616 | SD16 | — | 9 | 3 | no | — |
| 617 | SD16 | — | 9 | 3 | no | — |
| 618 | SD16 | — | 9 | 3 | no | — |
| 619 | SD16 | — | 9 | 3 | no | — |
| 620 | SD16 | — | 9 | 1 | no | — |
| 621 | SD16 | — | 9 | 3 | no | — |
| 622 | SD16 | — | 9 | 6 | no | — |
| 623 | SD16 | C22×D9 | 1 | 1 | yes | characteristic |
| 624 | SD16 | C22×D9 | 1 | 3 | yes | — |
| 625 | SD16 | C22×D9 | 1 | 6 | yes | — |
| 626 | D8 | — | 9 | 3 | no | — |
| 627 | D8 | — | 9 | 1 | no | — |
| 628 | D8 | — | 9 | 6 | no | — |
| 629 | D8 | — | 9 | 3 | no | — |
| 630 | D8 | C22×D9 | 1 | 3 | yes | — |
| 631 | M16 | — | 9 | 3 | no | — |
| 632 | M16 | — | 9 | 6 | no | — |
| 633 | M16 | C22×D9 | 1 | 3 | yes | — |
| 634 | C2×C8 | — | 9 | 3 | no | — |
| 635 | C2×C8 | — | 9 | 1 | no | — |
| 636 | C2×C8 | — | 9 | 3 | no | — |
| 637 | C2×C8 | — | 9 | 3 | no | — |
| 638 | C2×C8 | — | 9 | 3 | no | — |
| 639 | C2×C8 | C22×D9 | 1 | 3 | yes | — |
| 640 | C22×C3 | — | 2 | 3 | no | — |
| 641 | C22×C3 | — | 2 | 1 | no | — |
| 642 | C22×C3 | — | 8 | 3 | no | — |
| 643 | C22×C3 | C2×D3×D4 | 1 | 3 | yes | — |
| 644 | C2×D3 | — | 3 | 1 | no | — |
| 645 | C2×D3 | — | 3 | 3 | no | — |
| 646 | C2×D3 | — | 6 | 3 | no | — |
| 647 | C2×D3 | — | 6 | 1 | no | — |
| 648 | C2×D3 | — | 12 | 3 | no | — |
| 649 | C2×D3 | — | 24 | 3 | no | — |
| 650 | C2×D3 | — | 24 | 3 | no | — |
| 651 | C2×D3 | — | 24 | 3 | no | — |
| 652 | C3×C4 | — | 2 | 1 | no | — |
| 653 | C3×C4 | — | 2 | 3 | no | — |
| 654 | C3×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 655 | C3×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 656 | Dic3 | — | 3 | 3 | no | — |
| 657 | Dic3 | — | 3 | 1 | no | — |
| 658 | Dic3 | — | 6 | 1 | no | — |
| 659 | Dic3 | — | 6 | 3 | no | — |
| 660 | C9 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 661 | C23 | — | 2 | 3 | no | — |
| 662 | C23 | — | 9 | 3 | no | — |
| 663 | C23 | — | 18 | 3 | no | — |
| 664 | C23 | — | 18 | 3 | no | — |
| 665 | C23 | — | 18 | 3 | no | — |
| 666 | Q8 | — | 2 | 3 | no | — |
| 667 | Q8 | — | 9 | 3 | no | — |
| 668 | Q8 | — | 9 | 1 | no | — |
| 669 | Q8 | — | 9 | 3 | no | — |
| 670 | Q8 | — | 18 | 3 | no | — |
| 671 | Q8 | — | 18 | 3 | no | — |
| 672 | Q8 | — | 18 | 3 | no | — |
| 673 | Q8 | D4×D9 | 1 | 1 | yes | characteristic |
| 674 | Q8 | C23×D9 | 1 | 1 | yes | characteristic |
| 675 | Q8 | C23×D9 | 1 | 3 | yes | — |
| 676 | D4 | — | 2 | 3 | no | — |
| 677 | D4 | — | 2 | 3 | no | — |
| 678 | D4 | — | 2 | 3 | no | — |
| 679 | D4 | — | 9 | 6 | no | — |
| 680 | D4 | — | 9 | 3 | no | — |
| 681 | D4 | — | 9 | 1 | no | — |
| 682 | D4 | — | 9 | 3 | no | — |
| 683 | D4 | — | 18 | 1 | no | — |
| 684 | D4 | — | 18 | 3 | no | — |
| 685 | D4 | — | 18 | 6 | no | — |
| 686 | D4 | — | 18 | 3 | no | — |
| 687 | D4 | — | 18 | 3 | no | — |
| 688 | D4 | — | 18 | 1 | no | — |
| 689 | D4 | — | 18 | 3 | no | — |
| 690 | D4 | — | 18 | 6 | no | — |
| 691 | D4 | — | 18 | 3 | no | — |
| 692 | D4 | — | 18 | 3 | no | — |
| 693 | D4 | — | 18 | 3 | no | — |
| 694 | D4 | D4×D9 | 1 | 3 | yes | — |
| 695 | D4 | C23×D9 | 1 | 3 | yes | — |
| 696 | D4 | C23×D9 | 1 | 1 | yes | characteristic |
| 697 | C2×C4 | — | 2 | 3 | no | — |
| 698 | C2×C4 | — | 2 | 3 | no | — |
| 699 | C2×C4 | — | 2 | 3 | no | — |
| 700 | C2×C4 | — | 9 | 3 | no | — |
| 701 | C2×C4 | — | 9 | 1 | no | — |
| 702 | C2×C4 | — | 9 | 3 | no | — |
| 703 | C2×C4 | — | 9 | 3 | no | — |
| 704 | C2×C4 | — | 9 | 3 | no | — |
| 705 | C2×C4 | — | 18 | 1 | no | — |
| 706 | C2×C4 | — | 18 | 3 | no | — |
| 707 | C2×C4 | — | 18 | 6 | no | — |
| 708 | C2×C4 | — | 18 | 3 | no | — |
| 709 | C2×C4 | — | 18 | 3 | no | — |
| 710 | C2×C4 | — | 18 | 1 | no | — |
| 711 | C2×C4 | — | 18 | 3 | no | — |
| 712 | C2×C4 | — | 18 | 6 | no | — |
| 713 | C2×C4 | — | 18 | 3 | no | — |
| 714 | C2×C4 | — | 18 | 3 | no | — |
| 715 | C2×C4 | — | 18 | 3 | no | — |
| 716 | C2×C4 | C23×D9 | 1 | 3 | yes | — |
| 717 | C8 | — | 9 | 1 | no | — |
| 718 | C8 | — | 9 | 3 | no | — |
| 719 | C8 | C23×D9 | 1 | 1 | yes | characteristic |
| 720 | C8 | C23×D9 | 1 | 3 | yes | — |
| 721 | C2×C3 | — | 2 | 3 | no | — |
| 722 | C2×C3 | — | 4 | 1 | no | — |
| 723 | C2×C3 | — | 4 | 3 | no | — |
| 724 | C2×C3 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 725 | D3 | — | 6 | 1 | no | — |
| 726 | D3 | — | 6 | 3 | no | — |
| 727 | D3 | — | 12 | 3 | no | — |
| 728 | D3 | — | 12 | 1 | no | — |
| 729 | C22 | — | 2 | 1 | no | — |
| 730 | C22 | — | 2 | 3 | no | — |
| 731 | C22 | — | 8 | 3 | no | — |
| 732 | C22 | — | 9 | 1 | no | — |
| 733 | C22 | — | 9 | 3 | no | — |
| 734 | C22 | — | 18 | 3 | no | — |
| 735 | C22 | — | 18 | 1 | no | — |
| 736 | C22 | — | 36 | 3 | no | — |
| 737 | C22 | — | 72 | 3 | no | — |
| 738 | C22 | — | 72 | 3 | no | — |
| 739 | C22 | — | 72 | 3 | no | — |
| 740 | C22 | C2×D4×D9 | 1 | 3 | yes | — |
| 741 | C4 | — | 2 | 1 | no | — |
| 742 | C4 | — | 2 | 3 | no | — |
| 743 | C4 | — | 9 | 1 | no | — |
| 744 | C4 | — | 9 | 3 | no | — |
| 745 | C4 | — | 18 | 1 | no | — |
| 746 | C4 | — | 18 | 3 | no | — |
| 747 | C4 | C2×D4×D9 | 1 | 3 | yes | — |
| 748 | C4 | C24×D9 | 1 | 1 | yes | characteristic |
| 749 | C3 | #87206 | 1 | 1 | yes | characteristic |
| 750 | C2 | — | 2 | 3 | no | — |
| 751 | C2 | — | 4 | 3 | no | — |
| 752 | C2 | — | 4 | 1 | no | — |
| 753 | C2 | — | 18 | 1 | no | — |
| 754 | C2 | — | 18 | 3 | no | — |
| 755 | C2 | — | 36 | 3 | no | — |
| 756 | C2 | — | 36 | 1 | no | — |
| 757 | C2 | C22×D4×D9 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C9×#577 | C2 |
| socle | C2×C3 | C22×D3×D4 |
| hypercenter | #577 | D9 |
| hypocenter | C9 | #3584 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #577 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593143 | C2 | semidirect |
| 2. #10593141 | C2 | semidirect |
| 3. C9×#577 | C2 | semidirect |
| 4. #10589940 | C2 | semidirect |
| 5. #10589937 | C2 | semidirect |
| 6. #10589881 | C2 | semidirect |
| 7. #10589879 | C2 | semidirect |
| 8. #10589876 | C2 | semidirect |
| 9. #10589875 | C2 | semidirect |
| 10. #10589872 | C2 | semidirect |
| 11. D9×#135 | C2 | semidirect |
| 12. #10589864 | C2 | semidirect |
| 13. C2×#63478 | C2 | semidirect |
| 14. #10589853 | C2 | semidirect |
| 15. D9×#131 | C2 | semidirect |
| 17. C9×2−1+4 | C22 | semidirect |
| 18. C9×H(5,𝔽2) | C22 | semidirect |
| 20. #63716 | C22 | semidirect |
| 21. #63716 | C22 | semidirect |
| 23. #63715 | C22 | semidirect |
| 24. #63715 | C22 | semidirect |
| 28. #41×D9 | C22 | semidirect |
| 29. #41×D9 | C22 | semidirect |
| 31. #63713 | C22 | semidirect |
| 33. C2×#3701 | C22 | semidirect |
| 35. #63710 | C22 | semidirect |
| 37. C2×#3699 | C22 | semidirect |
| 38. C9×#137 | C22 | semidirect |
| 39. C9×AGL(1,ℤ/8) | C22 | semidirect |
| 40. C9×#135 | C22 | semidirect |
| 41. C2×C9×SD16 | C22 | semidirect |
| 42. C9×#131 | C22 | semidirect |
| 43. #63513 | C22 | semidirect |
| 44. #63513 | C22 | semidirect |
| 45. #63512 | C22 | semidirect |
| 46. #63511 | C22 | semidirect |
| 47. #63510 | C22 | semidirect |
| 48. #63505 | C22 | semidirect |
| 49. C2×#3674 | C22 | semidirect |
| 50. #63495 | C22 | semidirect |
| 51. C2×#3673 | C22 | semidirect |
| 52. #63481 | C22 | semidirect |
| 53. #63480 | C22 | semidirect |
| 54. Q16×D9 | C22 | semidirect |
| 55. #63478 | C22 | semidirect |
| 56. #63478 | C22 | semidirect |
| 57. #63478 | C22 | semidirect |
| 58. #63478 | C22 | semidirect |
| 59. #63478 | C22 | semidirect |
| 60. #63477 | C22 | semidirect |
| 61. #63476 | C22 | semidirect |
| 62. SD16×D9 | C22 | semidirect |
| 63. SD16×D9 | C22 | semidirect |
| 64. #63474 | C22 | semidirect |
| 65. #63473 | C22 | semidirect |
| 66. D8×D9 | C22 | semidirect |
| 67. #63471 | C22 | semidirect |
| 68. #63470 | C22 | semidirect |
| 69. #63469 | C22 | semidirect |
| 70. M16×D9 | C22 | semidirect |
| 71. #63467 | C22 | semidirect |
| 72. C2×#3664 | C22 | semidirect |
| 73. #63464 | C22 | semidirect |
| 74. C2×C8×D9 | C22 | semidirect |
| 306. #577 | D9 | semidirect |
| 429. 2−1+4 | C2×D9 | semidirect |
| 435. H(5,𝔽2) | C2×D9 | semidirect |
| 450. #137 | C2×D9 | semidirect |
| 456. AGL(1,ℤ/8) | C2×D9 | semidirect |
| 467. #135 | C2×D9 | semidirect |
| 473. C2×SD16 | C2×D9 | semidirect |
| 479. #131 | C2×D9 | semidirect |
| 660. C9 | #3584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593143 | 2 |
| #10593141 | 2 |
| C9×#577 | 2 |
| #10589940 | 2 |
| #10589937 | 2 |
| #10589881 | 2 |
| #10589879 | 2 |
| #10589876 | 2 |
| #10589875 | 2 |
| #10589872 | 2 |
| D9×#135 | 2 |
| #10589864 | 2 |
| C2×#63478 | 2 |
| #10589853 | 2 |
| D9×#131 | 2 |
| #87206 | 3 |