Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
572 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #11722476 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11721833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#940 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#63495 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720296 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11720261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720260 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591523 | — | 3 | 1 | no | maximal |
| 9 | #10588757 | — | 3 | 1 | no | maximal |
| 10 | C2×C3×D4×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #88736 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C9×#67 | — | 2 | 2 | no | — |
| 13 | C2×C9×D12 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#3697 | C22 | 1 | 1 | yes | characteristic |
| 15 | D3×#611 | — | 2 | 2 | no | — |
| 16 | #88646 | — | 2 | 1 | no | — |
| 17 | D9×D12 | — | 2 | 1 | no | — |
| 18 | #88639 | — | 2 | 1 | no | — |
| 19 | #88638 | — | 2 | 1 | no | — |
| 20 | #88544 | — | 2 | 1 | no | — |
| 21 | #88543 | — | 2 | 1 | no | — |
| 22 | #88532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#3673 | — | 2 | 1 | no | — |
| 24 | C3×#3672 | — | 2 | 1 | no | — |
| 25 | C4×C9×Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#3667 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #64307 | — | 3 | 1 | no | — |
| 28 | #64141 | — | 3 | 1 | no | — |
| 29 | C3×#940 | D3 | 1 | 1 | yes | characteristic |
| 30 | C3×#932 | — | 3 | 1 | no | — |
| 31 | #63710 | — | 3 | 1 | no | — |
| 32 | #63570 | — | 3 | 1 | no | — |
| 33 | #63569 | — | 3 | 1 | no | — |
| 34 | #63558 | — | 3 | 1 | no | — |
| 35 | C9×#127 | — | 3 | 1 | no | — |
| 36 | #63495 | — | 3 | 1 | no | — |
| 37 | #63495 | — | 6 | 1 | no | — |
| 38 | #63495 | D3 | 1 | 1 | yes | characteristic, complemented |
| 39 | #63391 | — | 3 | 1 | no | — |
| 40 | #63364 | — | 3 | 1 | no | — |
| 41 | #63364 | — | 3 | 1 | no | — |
| 42 | C23×C3×C9 | — | 2 | 1 | no | — |
| 43 | C22×D3×C9 | D4 | 1 | 2 | yes | — |
| 44 | C2×D3×D9 | — | 2 | 2 | no | — |
| 45 | C3×D4×C9 | — | 2 | 1 | no | — |
| 46 | C3×D4×C9 | — | 2 | 1 | no | — |
| 47 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 48 | #6233 | — | 2 | 1 | no | — |
| 49 | C4⋊(C3⋊D9) | D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | C4×C3⋊D9 | — | 2 | 1 | no | — |
| 51 | #6226 | D4 | 1 | 1 | yes | characteristic, complemented |
| 52 | C9×#67 | — | 4 | 4 | no | — |
| 53 | C3×#611 | — | 2 | 1 | no | — |
| 54 | C2×C9×Dic3 | — | 2 | 1 | no | — |
| 55 | C9×D12 | — | 2 | 1 | no | — |
| 56 | C9×D12 | — | 2 | 1 | no | — |
| 57 | C3×D36 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C3×C4×D9 | — | 2 | 1 | no | — |
| 59 | C3×Dic18 | D4 | 1 | 1 | yes | characteristic, complemented |
| 60 | #6195 | — | 2 | 2 | no | — |
| 61 | #6194 | — | 2 | 2 | no | — |
| 62 | D3×Dic9 | — | 2 | 2 | no | — |
| 63 | C3⋊(C9⋊C8) | — | 2 | 1 | no | — |
| 64 | C3×C9⋊C8 | — | 2 | 1 | no | — |
| 65 | #5198 | — | 9 | 1 | no | — |
| 66 | #5077 | — | 9 | 1 | no | — |
| 67 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 68 | #3828 | — | 3 | 1 | no | — |
| 69 | C2×C3×#67 | — | 2 | 2 | no | — |
| 70 | C3×#235 | — | 3 | 1 | no | — |
| 71 | C2×C3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | D3×#67 | — | 6 | 2 | no | — |
| 73 | #3802 | — | 6 | 1 | no | — |
| 74 | D3×D12 | — | 6 | 1 | no | — |
| 75 | #3796 | — | 6 | 1 | no | — |
| 76 | #3795 | — | 6 | 1 | no | — |
| 77 | #3754 | — | 6 | 1 | no | — |
| 78 | #3753 | — | 6 | 1 | no | — |
| 79 | #3748 | — | 3 | 1 | no | — |
| 80 | C3×#214 | — | 6 | 1 | no | — |
| 81 | C3×#213 | — | 6 | 1 | no | — |
| 82 | C3×C4×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 83 | C3×#208 | — | 3 | 1 | no | — |
| 84 | C2×D4×C9 | — | 2 | 1 | no | — |
| 85 | C2×D4×C9 | — | 3 | 1 | no | — |
| 86 | C2×D4×C9 | — | 6 | 2 | no | — |
| 87 | C2×D4×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 88 | C2×#611 | — | 6 | 2 | no | — |
| 89 | #3699 | — | 6 | 1 | no | — |
| 90 | #3699 | — | 6 | 1 | no | — |
| 91 | D4×D9 | — | 6 | 1 | no | — |
| 92 | D4×D9 | — | 6 | 1 | no | — |
| 93 | #3697 | — | 3 | 1 | no | — |
| 94 | #3697 | — | 6 | 1 | no | — |
| 95 | #3697 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | C42×C9 | — | 3 | 1 | no | — |
| 97 | #3673 | — | 2 | 1 | no | — |
| 98 | #3673 | — | 6 | 1 | no | — |
| 99 | #3673 | — | 6 | 2 | no | — |
| 100 | #3672 | — | 2 | 1 | no | — |
| 101 | #3672 | — | 6 | 1 | no | — |
| 102 | #3672 | — | 6 | 2 | no | — |
| 103 | #3667 | — | 3 | 1 | no | — |
| 104 | #3667 | — | 6 | 1 | no | — |
| 105 | #3667 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C22×C3×C9 | — | 4 | 2 | no | — |
| 107 | C22×C3×C9 | — | 4 | 1 | no | — |
| 108 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C3⋊D9 | — | 2 | 1 | no | — |
| 110 | C2×D3×C9 | — | 2 | 2 | no | — |
| 111 | C2×D3×C9 | — | 4 | 2 | no | — |
| 112 | C2×C3×D9 | — | 2 | 1 | no | — |
| 113 | D3×D9 | — | 8 | 2 | no | — |
| 114 | C3×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C3×C4×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 117 | C9×Dic3 | — | 2 | 2 | no | — |
| 118 | C3×Dic9 | — | 2 | 1 | no | — |
| 119 | #1009 | — | 9 | 1 | no | — |
| 120 | #1004 | — | 9 | 1 | no | — |
| 121 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 122 | C3×#127 | — | 3 | 1 | no | — |
| 123 | #940 | D9 | 1 | 1 | yes | characteristic, complemented |
| 124 | #932 | — | 3 | 1 | no | — |
| 125 | #932 | — | 9 | 1 | no | — |
| 126 | #932 | — | 9 | 1 | no | — |
| 127 | #932 | — | 18 | 1 | no | — |
| 128 | #837 | — | 9 | 1 | no | — |
| 129 | #833 | — | 9 | 1 | no | — |
| 130 | #825 | — | 9 | 1 | no | — |
| 131 | #823 | — | 9 | 1 | no | — |
| 132 | #805 | — | 9 | 1 | no | — |
| 133 | #805 | — | 9 | 1 | no | — |
| 134 | C23×C32 | — | 2 | 1 | no | — |
| 135 | C22×C3×D3 | #67 | 1 | 2 | yes | — |
| 136 | C2×D32 | — | 6 | 2 | no | — |
| 137 | C32×D4 | — | 2 | 1 | no | — |
| 138 | C32×D4 | — | 2 | 1 | no | — |
| 139 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | #638 | — | 6 | 1 | no | — |
| 141 | C4⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 142 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 143 | #634 | — | 3 | 1 | no | — |
| 144 | C3×#67 | — | 4 | 4 | no | — |
| 145 | C3×#67 | — | 6 | 1 | no | — |
| 146 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 147 | C3×D12 | — | 2 | 1 | no | — |
| 148 | C3×D12 | — | 2 | 1 | no | — |
| 149 | C3×D12 | — | 3 | 1 | no | — |
| 150 | C3×C4×D3 | — | 6 | 1 | no | — |
| 151 | C3×Dic6 | — | 3 | 1 | no | — |
| 152 | #626 | — | 6 | 2 | no | — |
| 153 | #625 | — | 6 | 2 | no | — |
| 154 | D3×Dic3 | — | 6 | 2 | no | — |
| 155 | C23×C9 | — | 2 | 1 | no | — |
| 156 | C23×C9 | — | 3 | 2 | no | — |
| 157 | C23×C9 | — | 4 | 1 | no | — |
| 158 | C22×D9 | — | 6 | 2 | no | — |
| 159 | C3⋊(C3⋊C8) | — | 6 | 1 | no | — |
| 160 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 161 | D4×C9 | — | 2 | 2 | no | — |
| 162 | D4×C9 | — | 2 | 1 | no | — |
| 163 | D4×C9 | — | 2 | 1 | no | — |
| 164 | D4×C9 | — | 4 | 1 | no | — |
| 165 | D4×C9 | — | 6 | 1 | no | — |
| 166 | D4×C9 | — | 6 | 1 | no | — |
| 167 | D4×C9 | — | 12 | 4 | no | — |
| 168 | C2×C4×C9 | — | 2 | 1 | no | — |
| 169 | C2×C4×C9 | — | 6 | 1 | no | — |
| 170 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 171 | #611 | — | 2 | 1 | no | — |
| 172 | #611 | — | 6 | 2 | no | — |
| 173 | #611 | — | 6 | 2 | no | — |
| 174 | #611 | — | 6 | 1 | no | — |
| 175 | #611 | — | 12 | 1 | no | — |
| 176 | C2×Dic9 | — | 6 | 2 | no | — |
| 177 | D36 | — | 3 | 1 | no | — |
| 178 | D36 | — | 6 | 1 | no | — |
| 179 | D36 | #67 | 1 | 1 | yes | characteristic, complemented |
| 180 | C4×D9 | — | 2 | 1 | no | — |
| 181 | C4×D9 | — | 6 | 1 | no | — |
| 182 | C4×D9 | — | 12 | 1 | no | — |
| 183 | Dic18 | — | 3 | 1 | no | — |
| 184 | Dic18 | — | 6 | 1 | no | — |
| 185 | Dic18 | #67 | 1 | 1 | yes | characteristic, complemented |
| 186 | C9⋊C8 | — | 2 | 1 | no | — |
| 187 | C9⋊C8 | — | 6 | 2 | no | — |
| 188 | C9⋊C8 | — | 6 | 1 | no | — |
| 189 | #453 | — | 27 | 1 | no | Sylow |
| 190 | C2×C3×C9 | — | 2 | 1 | no | — |
| 191 | C2×C3×C9 | — | 8 | 1 | no | — |
| 192 | C2×C3×C9 | #120 | 1 | 1 | yes | characteristic |
| 193 | C3⋊D9 | — | 4 | 1 | no | — |
| 194 | D3×C9 | — | 4 | 2 | no | — |
| 195 | C3×D9 | — | 4 | 1 | no | — |
| 196 | C3×#41 | — | 9 | 1 | no | — |
| 197 | C2×C3×D4 | — | 2 | 1 | no | — |
| 198 | C2×C3×D4 | — | 3 | 1 | no | — |
| 199 | C2×C3×D4 | — | 6 | 2 | no | — |
| 200 | C2×C3×D4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 201 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 202 | C2×#67 | — | 2 | 2 | no | — |
| 203 | C2×#67 | — | 18 | 2 | no | — |
| 204 | #239 | — | 18 | 1 | no | — |
| 205 | #237 | — | 18 | 1 | no | — |
| 206 | #237 | — | 18 | 1 | no | — |
| 207 | D3×D4 | — | 18 | 1 | no | — |
| 208 | D3×D4 | — | 18 | 1 | no | — |
| 209 | D3×D4 | — | 18 | 1 | no | — |
| 210 | D3×D4 | — | 18 | 2 | no | — |
| 211 | #235 | — | 3 | 1 | no | — |
| 212 | #235 | — | 9 | 1 | no | — |
| 213 | #235 | — | 9 | 1 | no | — |
| 214 | #235 | — | 18 | 1 | no | — |
| 215 | #235 | — | 18 | 1 | no | — |
| 216 | C2×D12 | — | 18 | 1 | no | — |
| 217 | C2×D12 | C2×D9 | 1 | 1 | yes | characteristic |
| 218 | C3×SD16 | — | 18 | 1 | no | — |
| 219 | C3×D8 | — | 18 | 1 | no | — |
| 220 | C3×M16 | — | 9 | 1 | no | — |
| 221 | C3×C42 | — | 3 | 1 | no | — |
| 222 | #214 | — | 6 | 1 | no | — |
| 223 | #214 | — | 18 | 1 | no | — |
| 224 | #214 | — | 18 | 1 | no | — |
| 225 | #214 | — | 18 | 2 | no | — |
| 226 | #213 | — | 6 | 1 | no | — |
| 227 | #213 | — | 18 | 1 | no | — |
| 228 | #213 | — | 18 | 1 | no | — |
| 229 | #213 | — | 18 | 2 | no | — |
| 230 | C4×Dic3 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 231 | #208 | — | 3 | 1 | no | — |
| 232 | #208 | — | 9 | 1 | no | — |
| 233 | #208 | — | 9 | 1 | no | — |
| 234 | #208 | — | 18 | 1 | no | — |
| 235 | C22×C32 | — | 4 | 1 | no | — |
| 236 | C22×C32 | — | 4 | 2 | no | — |
| 237 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 238 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 239 | C2×C3×D3 | — | 2 | 2 | no | — |
| 240 | C2×C3×D3 | — | 4 | 2 | no | — |
| 241 | C2×C3×D3 | — | 6 | 1 | no | — |
| 242 | D32 | — | 24 | 2 | no | — |
| 243 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 244 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 245 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 246 | C3×Dic3 | — | 2 | 2 | no | — |
| 247 | C3×Dic3 | — | 6 | 1 | no | — |
| 248 | C22×C9 | — | 2 | 1 | no | — |
| 249 | C22×C9 | — | 4 | 2 | no | — |
| 250 | C22×C9 | — | 4 | 2 | no | — |
| 251 | C22×C9 | — | 4 | 1 | no | — |
| 252 | C22×C9 | — | 6 | 2 | no | — |
| 253 | C22×C9 | — | 8 | 2 | no | — |
| 254 | C22×C9 | — | 12 | 2 | no | — |
| 255 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×D9 | — | 2 | 1 | no | — |
| 257 | C2×D9 | — | 6 | 1 | no | — |
| 258 | C2×D9 | — | 12 | 1 | no | — |
| 259 | C2×D9 | — | 24 | 2 | no | — |
| 260 | C4×C9 | — | 2 | 1 | no | — |
| 261 | C4×C9 | — | 2 | 1 | no | — |
| 262 | C4×C9 | — | 6 | 2 | no | — |
| 263 | C4×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 264 | C4×C9 | C2×#67 | 1 | 1 | yes | characteristic |
| 265 | Dic9 | — | 2 | 1 | no | — |
| 266 | Dic9 | — | 6 | 1 | no | — |
| 267 | Dic9 | — | 12 | 1 | no | — |
| 268 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 269 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 270 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 271 | #127 | — | 3 | 1 | no | — |
| 272 | #104 | — | 27 | 1 | no | — |
| 273 | #104 | — | 27 | 1 | no | — |
| 274 | #100 | — | 27 | 1 | no | — |
| 275 | C3×C9 | #453 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 276 | C23×C3 | — | 2 | 1 | no | — |
| 277 | C23×C3 | — | 2 | 1 | no | — |
| 278 | C23×C3 | — | 3 | 2 | no | — |
| 279 | C23×C3 | — | 4 | 1 | no | — |
| 280 | C22×D3 | — | 18 | 2 | no | — |
| 281 | C22×D3 | — | 18 | 2 | no | — |
| 282 | C22×D3 | #611 | 1 | 2 | yes | — |
| 283 | C3×Q8 | — | 9 | 1 | no | — |
| 284 | C3×D4 | — | 2 | 2 | no | — |
| 285 | C3×D4 | — | 2 | 1 | no | — |
| 286 | C3×D4 | — | 2 | 1 | no | — |
| 287 | C3×D4 | — | 2 | 1 | no | — |
| 288 | C3×D4 | — | 2 | 1 | no | — |
| 289 | C3×D4 | — | 4 | 1 | no | — |
| 290 | C3×D4 | — | 6 | 1 | no | — |
| 291 | C3×D4 | — | 6 | 1 | no | — |
| 292 | C3×D4 | — | 9 | 1 | no | — |
| 293 | C3×D4 | — | 12 | 4 | no | — |
| 294 | C3×D4 | — | 18 | 1 | no | — |
| 295 | C2×C3×C4 | — | 2 | 1 | no | — |
| 296 | C2×C3×C4 | — | 6 | 1 | no | — |
| 297 | C2×C3×C4 | — | 18 | 1 | no | — |
| 298 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 299 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 300 | #67 | — | 4 | 4 | no | — |
| 301 | #67 | — | 6 | 1 | no | — |
| 302 | #67 | — | 18 | 2 | no | — |
| 303 | #67 | — | 18 | 2 | no | — |
| 304 | #67 | — | 18 | 2 | no | — |
| 305 | #67 | — | 18 | 1 | no | — |
| 306 | #67 | — | 18 | 1 | no | — |
| 307 | #67 | — | 36 | 1 | no | — |
| 308 | C2×Dic3 | — | 2 | 1 | no | — |
| 309 | C2×Dic3 | — | 18 | 2 | no | — |
| 310 | D12 | — | 2 | 1 | no | — |
| 311 | D12 | — | 2 | 1 | no | — |
| 312 | D12 | — | 3 | 1 | no | — |
| 313 | D12 | — | 9 | 1 | no | — |
| 314 | D12 | — | 9 | 1 | no | — |
| 315 | D12 | — | 18 | 1 | no | — |
| 316 | D12 | — | 18 | 2 | no | — |
| 317 | C4×D3 | — | 6 | 1 | no | — |
| 318 | C4×D3 | — | 18 | 2 | no | — |
| 319 | C4×D3 | — | 18 | 1 | no | — |
| 320 | C4×D3 | — | 18 | 1 | no | — |
| 321 | C4×D3 | — | 36 | 1 | no | — |
| 322 | Dic6 | — | 3 | 1 | no | — |
| 323 | Dic6 | — | 9 | 1 | no | — |
| 324 | Dic6 | — | 9 | 1 | no | — |
| 325 | Dic6 | — | 18 | 1 | no | — |
| 326 | C3×C8 | — | 18 | 1 | no | — |
| 327 | C3⋊C8 | — | 6 | 1 | no | — |
| 328 | C3⋊C8 | — | 18 | 2 | no | — |
| 329 | C3⋊C8 | — | 18 | 1 | no | — |
| 330 | C3⋊C8 | — | 18 | 1 | no | — |
| 331 | C2×C32 | — | 2 | 1 | no | — |
| 332 | C2×C32 | — | 8 | 1 | no | — |
| 333 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 334 | C3⋊D3 | — | 12 | 1 | no | — |
| 335 | C3×D3 | — | 4 | 2 | no | — |
| 336 | C3×D3 | — | 12 | 1 | no | — |
| 337 | C2×C9 | — | 2 | 1 | no | — |
| 338 | C2×C9 | — | 2 | 1 | no | — |
| 339 | C2×C9 | — | 4 | 1 | no | — |
| 340 | C2×C9 | — | 8 | 2 | no | — |
| 341 | C2×C9 | — | 8 | 1 | no | — |
| 342 | C2×C9 | — | 12 | 2 | no | — |
| 343 | C2×C9 | #937 | 1 | 1 | yes | characteristic |
| 344 | D9 | — | 4 | 1 | no | — |
| 345 | D9 | — | 12 | 1 | no | — |
| 346 | D9 | — | 24 | 1 | no | — |
| 347 | #41 | — | 9 | 1 | no | — |
| 348 | #41 | — | 27 | 1 | no | — |
| 349 | #41 | — | 54 | 1 | no | — |
| 350 | #41 | — | 54 | 1 | no | — |
| 351 | C2×D4 | — | 3 | 1 | no | — |
| 352 | C2×D4 | — | 6 | 2 | no | — |
| 353 | C2×D4 | — | 54 | 1 | no | — |
| 354 | C2×D4 | — | 54 | 1 | no | — |
| 355 | C2×D4 | — | 54 | 2 | no | — |
| 356 | C2×D4 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 357 | SD16 | — | 18 | 1 | no | — |
| 358 | SD16 | — | 54 | 1 | no | — |
| 359 | D8 | — | 18 | 1 | no | — |
| 360 | D8 | — | 54 | 1 | no | — |
| 361 | M16 | — | 9 | 1 | no | — |
| 362 | M16 | — | 27 | 1 | no | — |
| 363 | C42 | — | 3 | 1 | no | — |
| 364 | C22×C3 | — | 2 | 1 | no | — |
| 365 | C22×C3 | — | 4 | 2 | no | — |
| 366 | C22×C3 | — | 4 | 2 | no | — |
| 367 | C22×C3 | — | 4 | 2 | no | — |
| 368 | C22×C3 | — | 4 | 1 | no | — |
| 369 | C22×C3 | — | 4 | 1 | no | — |
| 370 | C22×C3 | — | 6 | 2 | no | — |
| 371 | C22×C3 | — | 8 | 2 | no | — |
| 372 | C22×C3 | — | 12 | 2 | no | — |
| 373 | C22×C3 | — | 18 | 1 | no | — |
| 374 | C22×C3 | C2×#611 | 1 | 1 | yes | characteristic |
| 375 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 376 | C2×D3 | — | 2 | 2 | no | — |
| 377 | C2×D3 | — | 4 | 2 | no | — |
| 378 | C2×D3 | — | 6 | 1 | no | — |
| 379 | C2×D3 | — | 18 | 1 | no | — |
| 380 | C2×D3 | — | 18 | 1 | no | — |
| 381 | C2×D3 | — | 36 | 1 | no | — |
| 382 | C2×D3 | — | 72 | 2 | no | — |
| 383 | C2×D3 | — | 72 | 2 | no | — |
| 384 | C3×C4 | — | 2 | 1 | no | — |
| 385 | C3×C4 | — | 2 | 1 | no | — |
| 386 | C3×C4 | — | 6 | 2 | no | — |
| 387 | C3×C4 | — | 18 | 1 | no | — |
| 388 | C3×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 389 | C3×C4 | D4×D9 | 1 | 1 | yes | characteristic |
| 390 | C3×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 391 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 392 | Dic3 | — | 2 | 2 | no | — |
| 393 | Dic3 | — | 6 | 1 | no | — |
| 394 | Dic3 | — | 18 | 1 | no | — |
| 395 | Dic3 | — | 18 | 1 | no | — |
| 396 | Dic3 | — | 36 | 1 | no | — |
| 397 | C32 | #5077 | 1 | 1 | yes | characteristic |
| 398 | C9 | — | 2 | 1 | no | — |
| 399 | C9 | #5198 | 1 | 1 | yes | characteristic, complemented |
| 400 | C23 | — | 2 | 1 | no | — |
| 401 | C23 | — | 3 | 2 | no | — |
| 402 | C23 | — | 54 | 2 | no | — |
| 403 | Q8 | — | 9 | 1 | no | — |
| 404 | Q8 | — | 27 | 1 | no | — |
| 405 | D4 | — | 2 | 1 | no | — |
| 406 | D4 | — | 2 | 1 | no | — |
| 407 | D4 | — | 6 | 1 | no | — |
| 408 | D4 | — | 6 | 1 | no | — |
| 409 | D4 | — | 9 | 1 | no | — |
| 410 | D4 | — | 12 | 4 | no | — |
| 411 | D4 | — | 18 | 1 | no | — |
| 412 | D4 | — | 27 | 1 | no | — |
| 413 | D4 | — | 54 | 2 | no | — |
| 414 | D4 | — | 54 | 2 | no | — |
| 415 | D4 | — | 54 | 1 | no | — |
| 416 | C2×C4 | — | 6 | 1 | no | — |
| 417 | C2×C4 | — | 18 | 1 | no | — |
| 418 | C2×C4 | — | 54 | 2 | no | — |
| 419 | C2×C4 | — | 54 | 1 | no | — |
| 420 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 421 | C8 | — | 18 | 1 | no | — |
| 422 | C8 | — | 54 | 1 | no | — |
| 423 | C2×C3 | — | 2 | 1 | no | — |
| 424 | C2×C3 | — | 2 | 1 | no | — |
| 425 | C2×C3 | — | 2 | 1 | no | — |
| 426 | C2×C3 | — | 4 | 1 | no | — |
| 427 | C2×C3 | — | 8 | 2 | no | — |
| 428 | C2×C3 | — | 8 | 1 | no | — |
| 429 | C2×C3 | — | 8 | 1 | no | — |
| 430 | C2×C3 | — | 12 | 2 | no | — |
| 431 | C2×C3 | — | 36 | 1 | no | — |
| 432 | C2×C3 | #63499 | 1 | 1 | yes | characteristic |
| 433 | C2×C3 | #63983 | 1 | 1 | yes | characteristic |
| 434 | D3 | — | 4 | 2 | no | — |
| 435 | D3 | — | 12 | 1 | no | — |
| 436 | D3 | — | 36 | 1 | no | — |
| 437 | D3 | — | 36 | 1 | no | — |
| 438 | D3 | — | 72 | 1 | no | — |
| 439 | C22 | — | 4 | 2 | no | — |
| 440 | C22 | — | 4 | 1 | no | — |
| 441 | C22 | — | 6 | 2 | no | — |
| 442 | C22 | — | 12 | 2 | no | — |
| 443 | C22 | — | 18 | 1 | no | — |
| 444 | C22 | — | 54 | 1 | no | — |
| 445 | C22 | — | 216 | 2 | no | — |
| 446 | C22 | D3×#611 | 1 | 1 | yes | characteristic |
| 447 | C4 | — | 6 | 2 | no | — |
| 448 | C4 | — | 18 | 1 | no | — |
| 449 | C4 | — | 54 | 1 | no | — |
| 450 | C4 | D9×#67 | 1 | 1 | yes | characteristic |
| 451 | C4 | #88668 | 1 | 1 | yes | characteristic |
| 452 | C3 | — | 2 | 1 | no | — |
| 453 | C3 | #10588757 | 1 | 1 | yes | characteristic, complemented |
| 454 | C3 | #10591523 | 1 | 1 | yes | characteristic |
| 455 | C2 | — | 2 | 1 | no | — |
| 456 | C2 | — | 8 | 1 | no | — |
| 457 | C2 | — | 12 | 2 | no | — |
| 458 | C2 | — | 36 | 1 | no | — |
| 459 | C2 | — | 108 | 1 | no | — |
| 460 | C2 | #11721292 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722476 | C2 | semidirect |
| 2. #11721833 | C2 | semidirect |
| 3. C9×#940 | C2 | semidirect |
| 4. C3×#63495 | C2 | semidirect |
| 5. #11720296 | C2 | semidirect |
| 6. #11720261 | C2 | semidirect |
| 7. #11720260 | C2 | semidirect |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 22. #88532 | C22 | semidirect |
| 25. C4×C9×Dic3 | C22 | semidirect |
| 26. C3×#3667 | C22 | semidirect |
| 38. #63495 | D3 | semidirect |
| 49. C4⋊(C3⋊D9) | D4 | semidirect |
| 51. #6226 | D4 | semidirect |
| 57. C3×D36 | D4 | semidirect |
| 59. C3×Dic18 | D4 | semidirect |
| 87. C2×D4×C9 | C2×D3 | semidirect |
| 105. #3667 | C2×D3 | semidirect |
| 123. #940 | D9 | semidirect |
| 179. D36 | #67 | semidirect |
| 185. Dic18 | #67 | semidirect |
| 200. C2×C3×D4 | C2×D9 | semidirect |
| 230. C4×Dic3 | C2×D9 | semidirect |
| 275. C3×C9 | #453 | semidirect |
| 356. C2×D4 | D3×D9 | semidirect |
| 399. C9 | #5198 | semidirect |
| 453. C3 | #10588757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722476 | 2 |
| #11721833 | 2 |
| C9×#940 | 2 |
| C3×#63495 | 2 |
| #11720296 | 2 |
| #11720261 | 2 |
| #11720260 | 2 |
| #10591523 | 3 |
| #10588757 | 3 |