Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 532 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 | #11722535 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#63448 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11721265 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11721255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C9×#806 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10590408 | — | 3 | 1 | no | maximal |
| 9 | #10588422 | — | 3 | 1 | no | maximal |
| 10 | C2×#6233 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C9×#67 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#611 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×C3×Dic9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #88668 | — | 2 | 1 | no | — |
| 15 | D9×#67 | — | 2 | 1 | no | — |
| 16 | D3×#611 | — | 2 | 1 | no | — |
| 17 | #88663 | — | 2 | 1 | no | — |
| 18 | #88662 | — | 2 | 1 | no | — |
| 19 | #88658 | — | 2 | 1 | no | — |
| 20 | C3×C9×C22⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #88551 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C9×#217 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×(C2×D9)⋊C4 | — | 2 | 1 | no | — |
| 24 | C3×C4⋊Dic9 | — | 2 | 1 | no | — |
| 25 | (C2×D3)⋊Dic9 | — | 2 | 1 | no | — |
| 26 | #88445 | — | 2 | 1 | no | — |
| 27 | Dic3⋊Dic9 | — | 2 | 1 | no | — |
| 28 | #88442 | — | 2 | 1 | no | — |
| 29 | #64330 | — | 3 | 1 | no | — |
| 30 | C3×#886 | — | 3 | 1 | no | — |
| 31 | #63966 | — | 3 | 1 | no | — |
| 32 | #63961 | — | 3 | 1 | no | — |
| 33 | #63710 | — | 3 | 1 | no | — |
| 34 | #63633 | — | 3 | 1 | no | — |
| 35 | C3×#806 | D3 | 1 | 1 | yes | characteristic |
| 36 | #63580 | — | 3 | 1 | no | — |
| 37 | #63497 | — | 3 | 1 | no | — |
| 38 | #63448 | — | 3 | 1 | no | — |
| 39 | #63448 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | C9×#99 | — | 3 | 1 | no | — |
| 41 | #63365 | — | 3 | 1 | no | — |
| 42 | #63365 | — | 3 | 1 | no | — |
| 43 | #63365 | — | 6 | 1 | no | — |
| 44 | C23×C3×C9 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×C3⋊D9 | D4 | 1 | 1 | yes | characteristic |
| 46 | C22×D3×C9 | D4 | 1 | 1 | yes | characteristic |
| 47 | C22×C3×D9 | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×D3×D9 | — | 2 | 1 | no | — |
| 49 | C2×C3×C4×C9 | — | 2 | 1 | no | — |
| 50 | #6233 | — | 2 | 1 | no | — |
| 51 | #6233 | — | 2 | 1 | no | — |
| 52 | C2×C3⋊Dic9 | — | 2 | 1 | no | — |
| 53 | C2×C3⋊Dic9 | D4 | 1 | 1 | yes | characteristic |
| 54 | C9×#67 | — | 2 | 1 | no | — |
| 55 | C9×#67 | — | 2 | 1 | no | — |
| 56 | C3×#611 | — | 2 | 1 | no | — |
| 57 | C3×#611 | — | 2 | 1 | no | — |
| 58 | C2×C9×Dic3 | — | 2 | 1 | no | — |
| 59 | C2×C9×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C3×Dic9 | — | 2 | 1 | no | — |
| 61 | C2×C3×Dic9 | — | 2 | 1 | no | — |
| 62 | C2×C3×Dic9 | — | 2 | 1 | no | — |
| 63 | C2×C3×Dic9 | D4 | 1 | 1 | yes | characteristic |
| 64 | #6195 | — | 2 | 1 | no | — |
| 65 | #6194 | — | 2 | 1 | no | — |
| 66 | D3×Dic9 | — | 2 | 1 | no | — |
| 67 | #6192 | — | 2 | 1 | no | — |
| 68 | (C3⋊D9)⋊C4 | — | 2 | 1 | no | — |
| 69 | Dic3×D9 | — | 2 | 1 | no | — |
| 70 | #6189 | — | 2 | 1 | no | — |
| 71 | #5053 | — | 9 | 1 | no | — |
| 72 | #4742 | — | 9 | 1 | no | — |
| 73 | C2×#638 | — | 3 | 1 | no | — |
| 74 | C2×C3×#67 | — | 3 | 1 | no | — |
| 75 | C2×C3×#67 | C2×D3 | 1 | 1 | yes | characteristic |
| 76 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 77 | #3811 | — | 6 | 1 | no | — |
| 78 | D3×#67 | — | 6 | 1 | no | — |
| 79 | D3×#67 | — | 6 | 1 | no | — |
| 80 | #3805 | — | 6 | 1 | no | — |
| 81 | #3804 | — | 6 | 1 | no | — |
| 82 | #3804 | — | 6 | 1 | no | — |
| 83 | C32×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #3757 | — | 3 | 1 | no | — |
| 85 | C3×#217 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | C3×(C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 87 | C3×C4⋊Dic3 | — | 6 | 1 | no | — |
| 88 | #3724 | — | 6 | 1 | no | — |
| 89 | Dic3⋊Dic3 | — | 6 | 1 | no | — |
| 90 | #3722 | — | 6 | 1 | no | — |
| 91 | (C2×D3)⋊Dic3 | — | 6 | 1 | no | — |
| 92 | C2×D4×C9 | — | 3 | 1 | no | — |
| 93 | C2×#611 | — | 3 | 1 | no | — |
| 94 | C2×#611 | — | 6 | 1 | no | — |
| 95 | C2×#611 | — | 6 | 1 | no | — |
| 96 | C2×#611 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | C22×Dic9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 98 | #3699 | — | 6 | 1 | no | — |
| 99 | #3699 | — | 6 | 1 | no | — |
| 100 | D4×D9 | — | 6 | 1 | no | — |
| 101 | D4×D9 | — | 6 | 1 | no | — |
| 102 | #3697 | — | 6 | 1 | no | — |
| 103 | C9×C22⋊C4 | — | 2 | 1 | no | — |
| 104 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 105 | C9×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | #3676 | — | 3 | 1 | no | — |
| 107 | #3676 | — | 6 | 1 | no | — |
| 108 | #3676 | — | 6 | 1 | no | — |
| 109 | (C2×D9)⋊C4 | — | 2 | 1 | no | — |
| 110 | (C2×D9)⋊C4 | — | 6 | 1 | no | — |
| 111 | C4⋊Dic9 | — | 2 | 1 | no | — |
| 112 | C4⋊Dic9 | — | 6 | 1 | no | — |
| 113 | Dic9⋊C4 | — | 6 | 1 | no | — |
| 114 | C22×C3×C9 | — | 4 | 1 | no | — |
| 115 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C2×C3⋊D9 | — | 2 | 1 | no | — |
| 119 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 120 | C2×D3×C9 | — | 2 | 1 | no | — |
| 121 | C2×D3×C9 | — | 4 | 1 | no | — |
| 122 | C2×C3×D9 | — | 2 | 1 | no | — |
| 123 | C2×C3×D9 | — | 4 | 1 | no | — |
| 124 | D3×D9 | — | 8 | 1 | no | — |
| 125 | C3×C4×C9 | — | 4 | 1 | no | — |
| 126 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 127 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 128 | C9×Dic3 | — | 2 | 1 | no | — |
| 129 | C9×Dic3 | — | 4 | 1 | no | — |
| 130 | C3×Dic9 | — | 2 | 1 | no | — |
| 131 | C3×Dic9 | — | 4 | 1 | no | — |
| 132 | #1004 | — | 9 | 1 | no | — |
| 133 | #1004 | — | 9 | 1 | no | — |
| 134 | C3×#123 | — | 9 | 1 | no | — |
| 135 | #935 | — | 9 | 1 | no | — |
| 136 | #929 | — | 9 | 1 | no | — |
| 137 | #929 | — | 9 | 1 | no | — |
| 138 | #886 | — | 3 | 1 | no | — |
| 139 | #886 | — | 9 | 1 | no | — |
| 140 | C3×#99 | — | 3 | 1 | no | — |
| 141 | #834 | — | 9 | 1 | no | — |
| 142 | #806 | — | 9 | 1 | no | — |
| 143 | #806 | — | 9 | 1 | no | — |
| 144 | #806 | — | 9 | 1 | no | — |
| 145 | #806 | — | 18 | 1 | no | — |
| 146 | #806 | D9 | 1 | 1 | yes | characteristic, complemented |
| 147 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 149 | C22×C3×D3 | — | 3 | 1 | no | — |
| 150 | C22×C3×D3 | D12 | 1 | 1 | yes | characteristic |
| 151 | C2×D32 | — | 6 | 1 | no | — |
| 152 | C2×C32×C4 | — | 2 | 1 | no | — |
| 153 | #638 | — | 6 | 1 | no | — |
| 154 | #638 | — | 6 | 1 | no | — |
| 155 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 156 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 157 | C3×#67 | — | 2 | 1 | no | — |
| 158 | C3×#67 | — | 2 | 1 | no | — |
| 159 | C3×#67 | — | 6 | 1 | no | — |
| 160 | C3×#67 | — | 6 | 1 | no | — |
| 161 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 162 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 163 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 164 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 165 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 166 | C2×C3×Dic3 | D12 | 1 | 1 | yes | characteristic |
| 167 | #627 | — | 6 | 1 | no | — |
| 168 | #626 | — | 6 | 1 | no | — |
| 169 | #626 | — | 6 | 1 | no | — |
| 170 | #625 | — | 6 | 1 | no | — |
| 171 | #624 | — | 6 | 1 | no | — |
| 172 | D3×Dic3 | — | 6 | 1 | no | — |
| 173 | D3×Dic3 | — | 6 | 1 | no | — |
| 174 | C23×C9 | — | 2 | 1 | no | — |
| 175 | C23×C9 | — | 3 | 1 | no | — |
| 176 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 177 | C22×D9 | — | 3 | 1 | no | — |
| 178 | C22×D9 | — | 6 | 1 | no | — |
| 179 | C22×D9 | — | 6 | 1 | no | — |
| 180 | C22×D9 | #67 | 1 | 1 | yes | characteristic |
| 181 | D4×C9 | — | 6 | 1 | no | — |
| 182 | D4×C9 | — | 6 | 1 | no | — |
| 183 | C2×C4×C9 | — | 2 | 1 | no | — |
| 184 | C2×C4×C9 | — | 3 | 1 | no | — |
| 185 | C2×C4×C9 | — | 4 | 1 | no | — |
| 186 | C2×C4×C9 | — | 6 | 1 | no | — |
| 187 | #611 | — | 2 | 1 | no | — |
| 188 | #611 | — | 2 | 1 | no | — |
| 189 | #611 | — | 6 | 1 | no | — |
| 190 | #611 | — | 6 | 1 | no | — |
| 191 | #611 | — | 6 | 1 | no | — |
| 192 | #611 | — | 6 | 1 | no | — |
| 193 | #611 | — | 12 | 1 | no | — |
| 194 | #611 | — | 12 | 1 | no | — |
| 195 | C2×Dic9 | — | 2 | 1 | no | — |
| 196 | C2×Dic9 | — | 2 | 1 | no | — |
| 197 | C2×Dic9 | — | 2 | 1 | no | — |
| 198 | C2×Dic9 | — | 3 | 1 | no | — |
| 199 | C2×Dic9 | — | 6 | 1 | no | — |
| 200 | C2×Dic9 | — | 6 | 1 | no | — |
| 201 | C2×Dic9 | — | 6 | 1 | no | — |
| 202 | C2×Dic9 | — | 12 | 1 | no | — |
| 203 | C2×Dic9 | #67 | 1 | 1 | yes | characteristic |
| 204 | D36 | — | 6 | 1 | no | — |
| 205 | C4×D9 | — | 6 | 1 | no | — |
| 206 | C4×D9 | — | 6 | 1 | no | — |
| 207 | Dic18 | — | 6 | 1 | no | — |
| 208 | #458 | — | 27 | 1 | no | Sylow |
| 209 | C2×C3×C9 | — | 2 | 1 | no | — |
| 210 | C2×C3×C9 | — | 2 | 1 | no | — |
| 211 | C2×C3×C9 | — | 2 | 1 | no | — |
| 212 | C2×C3×C9 | #120 | 1 | 1 | yes | characteristic |
| 213 | C3⋊D9 | — | 4 | 1 | no | — |
| 214 | D3×C9 | — | 4 | 1 | no | — |
| 215 | C3×D9 | — | 4 | 1 | no | — |
| 216 | C2×C3×D4 | — | 3 | 1 | no | — |
| 217 | C2×C3×D4 | — | 9 | 1 | no | — |
| 218 | C22×C3×C4 | — | 9 | 1 | no | — |
| 219 | C2×#67 | — | 3 | 1 | no | — |
| 220 | C2×#67 | — | 9 | 1 | no | — |
| 221 | C2×#67 | — | 9 | 1 | no | — |
| 222 | C2×#67 | — | 18 | 1 | no | — |
| 223 | C2×#67 | — | 18 | 1 | no | — |
| 224 | C2×#67 | — | 18 | 1 | no | — |
| 225 | C2×#67 | C2×D9 | 1 | 1 | yes | characteristic |
| 226 | C22×Dic3 | — | 3 | 1 | no | — |
| 227 | #237 | — | 18 | 1 | no | — |
| 228 | #237 | — | 18 | 1 | no | — |
| 229 | #237 | — | 18 | 1 | no | — |
| 230 | #237 | — | 18 | 1 | no | — |
| 231 | D3×D4 | — | 18 | 1 | no | — |
| 232 | D3×D4 | — | 18 | 1 | no | — |
| 233 | D3×D4 | — | 18 | 1 | no | — |
| 234 | D3×D4 | — | 18 | 1 | no | — |
| 235 | #235 | — | 18 | 1 | no | — |
| 236 | #235 | — | 18 | 1 | no | — |
| 237 | C3×C4⋊C4 | — | 18 | 1 | no | — |
| 238 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 239 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 240 | C3×C22⋊C4 | — | 18 | 1 | no | — |
| 241 | C3×C22⋊C4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 242 | C3×C22⋊C4 | D32 | 1 | 1 | yes | characteristic |
| 243 | #217 | — | 9 | 1 | no | — |
| 244 | #217 | — | 9 | 1 | no | — |
| 245 | #217 | — | 18 | 1 | no | — |
| 246 | #217 | — | 18 | 1 | no | — |
| 247 | #217 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 248 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 249 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 250 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 251 | (C2×D3)⋊C4 | — | 18 | 1 | no | — |
| 252 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 253 | C4⋊Dic3 | — | 18 | 1 | no | — |
| 254 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 255 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 256 | Dic3⋊C4 | — | 18 | 1 | no | — |
| 257 | C22×C32 | — | 4 | 1 | no | — |
| 258 | C22×C32 | C2×D12 | 1 | 1 | yes | characteristic |
| 259 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 260 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 262 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 263 | C2×C3×D3 | — | 2 | 1 | no | — |
| 264 | C2×C3×D3 | — | 4 | 1 | no | — |
| 265 | C2×C3×D3 | — | 6 | 1 | no | — |
| 266 | C2×C3×D3 | — | 12 | 1 | no | — |
| 267 | D32 | — | 24 | 1 | no | — |
| 268 | C32×C4 | — | 4 | 1 | no | — |
| 269 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 270 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 271 | C3×Dic3 | — | 2 | 1 | no | — |
| 272 | C3×Dic3 | — | 4 | 1 | no | — |
| 273 | C3×Dic3 | — | 6 | 1 | no | — |
| 274 | C3×Dic3 | — | 12 | 1 | no | — |
| 275 | C22×C9 | — | 2 | 1 | no | — |
| 276 | C22×C9 | — | 2 | 1 | no | — |
| 277 | C22×C9 | — | 2 | 1 | no | — |
| 278 | C22×C9 | — | 4 | 1 | no | — |
| 279 | C22×C9 | — | 6 | 1 | no | — |
| 280 | C22×C9 | — | 8 | 1 | no | — |
| 281 | C22×C9 | — | 12 | 1 | no | — |
| 282 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 283 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 284 | C22×C9 | C2×#67 | 1 | 1 | yes | characteristic |
| 285 | C2×D9 | — | 2 | 1 | no | — |
| 286 | C2×D9 | — | 4 | 1 | no | — |
| 287 | C2×D9 | — | 6 | 1 | no | — |
| 288 | C2×D9 | — | 12 | 1 | no | — |
| 289 | C2×D9 | — | 12 | 1 | no | — |
| 290 | C2×D9 | — | 24 | 1 | no | — |
| 291 | C2×D9 | — | 24 | 1 | no | — |
| 292 | C4×C9 | — | 4 | 1 | no | — |
| 293 | C4×C9 | — | 6 | 1 | no | — |
| 294 | C4×C9 | — | 8 | 1 | no | — |
| 295 | C4×C9 | — | 12 | 1 | no | — |
| 296 | Dic9 | — | 2 | 1 | no | — |
| 297 | Dic9 | — | 4 | 1 | no | — |
| 298 | Dic9 | — | 6 | 1 | no | — |
| 299 | Dic9 | — | 12 | 1 | no | — |
| 300 | Dic9 | — | 12 | 1 | no | — |
| 301 | Dic9 | — | 24 | 1 | no | — |
| 302 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 303 | #123 | — | 9 | 1 | no | — |
| 304 | #123 | — | 27 | 1 | no | — |
| 305 | #123 | — | 27 | 1 | no | — |
| 306 | #99 | — | 3 | 1 | no | — |
| 307 | #99 | — | 27 | 1 | no | — |
| 308 | #99 | — | 27 | 1 | no | — |
| 309 | C3×C9 | #458 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 310 | C23×C3 | — | 2 | 1 | no | — |
| 311 | C23×C3 | — | 3 | 1 | no | — |
| 312 | C23×C3 | — | 9 | 1 | no | — |
| 313 | C23×C3 | C22×D9 | 1 | 1 | yes | characteristic |
| 314 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 315 | C22×D3 | — | 3 | 1 | no | — |
| 316 | C22×D3 | — | 9 | 1 | no | — |
| 317 | C22×D3 | — | 9 | 1 | no | — |
| 318 | C22×D3 | — | 18 | 1 | no | — |
| 319 | C22×D3 | — | 18 | 1 | no | — |
| 320 | C22×D3 | — | 18 | 1 | no | — |
| 321 | C22×D3 | D36 | 1 | 1 | yes | characteristic |
| 322 | C3×D4 | — | 6 | 1 | no | — |
| 323 | C3×D4 | — | 6 | 1 | no | — |
| 324 | C3×D4 | — | 18 | 1 | no | — |
| 325 | C3×D4 | — | 18 | 1 | no | — |
| 326 | C2×C3×C4 | — | 2 | 1 | no | — |
| 327 | C2×C3×C4 | — | 2 | 1 | no | — |
| 328 | C2×C3×C4 | — | 3 | 1 | no | — |
| 329 | C2×C3×C4 | — | 4 | 1 | no | — |
| 330 | C2×C3×C4 | — | 6 | 1 | no | — |
| 331 | C2×C3×C4 | — | 9 | 1 | no | — |
| 332 | C2×C3×C4 | — | 18 | 1 | no | — |
| 333 | C2×C3×C4 | — | 18 | 1 | no | — |
| 334 | C2×C3×C4 | — | 18 | 1 | no | — |
| 335 | #67 | — | 2 | 1 | no | — |
| 336 | #67 | — | 2 | 1 | no | — |
| 337 | #67 | — | 6 | 1 | no | — |
| 338 | #67 | — | 6 | 1 | no | — |
| 339 | #67 | — | 18 | 1 | no | — |
| 340 | #67 | — | 18 | 1 | no | — |
| 341 | #67 | — | 18 | 1 | no | — |
| 342 | #67 | — | 18 | 1 | no | — |
| 343 | #67 | — | 18 | 1 | no | — |
| 344 | #67 | — | 18 | 1 | no | — |
| 345 | #67 | — | 18 | 1 | no | — |
| 346 | #67 | — | 18 | 1 | no | — |
| 347 | #67 | — | 36 | 1 | no | — |
| 348 | #67 | — | 36 | 1 | no | — |
| 349 | C2×Dic3 | — | 2 | 1 | no | — |
| 350 | C2×Dic3 | — | 3 | 1 | no | — |
| 351 | C2×Dic3 | — | 6 | 1 | no | — |
| 352 | C2×Dic3 | — | 6 | 1 | no | — |
| 353 | C2×Dic3 | — | 6 | 1 | no | — |
| 354 | C2×Dic3 | — | 9 | 1 | no | — |
| 355 | C2×Dic3 | — | 9 | 1 | no | — |
| 356 | C2×Dic3 | — | 18 | 1 | no | — |
| 357 | C2×Dic3 | — | 18 | 1 | no | — |
| 358 | C2×Dic3 | — | 18 | 1 | no | — |
| 359 | C2×Dic3 | — | 18 | 1 | no | — |
| 360 | C2×Dic3 | — | 18 | 1 | no | — |
| 361 | C2×Dic3 | — | 36 | 1 | no | — |
| 362 | C2×Dic3 | D36 | 1 | 1 | yes | characteristic |
| 363 | D12 | — | 18 | 1 | no | — |
| 364 | D12 | — | 18 | 1 | no | — |
| 365 | C4×D3 | — | 18 | 1 | no | — |
| 366 | C4×D3 | — | 18 | 1 | no | — |
| 367 | C4×D3 | — | 18 | 1 | no | — |
| 368 | C4×D3 | — | 18 | 1 | no | — |
| 369 | Dic6 | — | 18 | 1 | no | — |
| 370 | Dic6 | — | 18 | 1 | no | — |
| 371 | C2×C32 | — | 2 | 1 | no | — |
| 372 | C2×C32 | — | 2 | 1 | no | — |
| 373 | C2×C32 | — | 2 | 1 | no | — |
| 374 | C2×C32 | #882 | 1 | 1 | yes | characteristic |
| 375 | C3⋊D3 | — | 12 | 1 | no | — |
| 376 | C3×D3 | — | 4 | 1 | no | — |
| 377 | C3×D3 | — | 12 | 1 | no | — |
| 378 | C2×C9 | — | 2 | 1 | no | — |
| 379 | C2×C9 | — | 2 | 1 | no | — |
| 380 | C2×C9 | — | 2 | 1 | no | — |
| 381 | C2×C9 | — | 2 | 1 | no | — |
| 382 | C2×C9 | — | 4 | 1 | no | — |
| 383 | C2×C9 | — | 4 | 1 | no | — |
| 384 | C2×C9 | — | 4 | 1 | no | — |
| 385 | C2×C9 | — | 12 | 1 | no | — |
| 386 | C2×C9 | #937 | 1 | 1 | yes | characteristic |
| 387 | D9 | — | 4 | 1 | no | — |
| 388 | D9 | — | 12 | 1 | no | — |
| 389 | D9 | — | 24 | 1 | no | — |
| 390 | #41 | — | 54 | 1 | no | — |
| 391 | #41 | — | 54 | 1 | no | — |
| 392 | #41 | — | 54 | 1 | no | — |
| 393 | C2×D4 | — | 3 | 1 | no | — |
| 394 | C2×D4 | — | 9 | 1 | no | — |
| 395 | C2×D4 | — | 27 | 1 | no | — |
| 396 | C2×D4 | — | 54 | 1 | no | — |
| 397 | C2×D4 | — | 54 | 1 | no | — |
| 398 | C2×D4 | — | 54 | 1 | no | — |
| 399 | C22×C4 | — | 9 | 1 | no | — |
| 400 | C4⋊C4 | — | 18 | 1 | no | — |
| 401 | C4⋊C4 | — | 54 | 1 | no | — |
| 402 | C4⋊C4 | — | 54 | 1 | no | — |
| 403 | C22⋊C4 | — | 3 | 1 | no | — |
| 404 | C22⋊C4 | — | 18 | 1 | no | — |
| 405 | C22⋊C4 | — | 27 | 1 | no | — |
| 406 | C22⋊C4 | — | 54 | 1 | no | — |
| 407 | C22⋊C4 | — | 54 | 1 | no | — |
| 408 | C22⋊C4 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 409 | C22×C3 | — | 2 | 1 | no | — |
| 410 | C22×C3 | — | 2 | 1 | no | — |
| 411 | C22×C3 | — | 2 | 1 | no | — |
| 412 | C22×C3 | — | 4 | 1 | no | — |
| 413 | C22×C3 | — | 4 | 1 | no | — |
| 414 | C22×C3 | — | 6 | 1 | no | — |
| 415 | C22×C3 | — | 8 | 1 | no | — |
| 416 | C22×C3 | — | 12 | 1 | no | — |
| 417 | C22×C3 | — | 18 | 1 | no | — |
| 418 | C22×C3 | — | 36 | 1 | no | — |
| 419 | C22×C3 | C2×D36 | 1 | 1 | yes | characteristic |
| 420 | C22×C3 | D4×D9 | 1 | 1 | yes | characteristic |
| 421 | C22×C3 | D4×D9 | 1 | 1 | yes | characteristic |
| 422 | C22×C3 | D3×D12 | 1 | 1 | yes | characteristic |
| 423 | C22×C3 | #3802 | 1 | 1 | yes | characteristic |
| 424 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 425 | C2×D3 | — | 2 | 1 | no | — |
| 426 | C2×D3 | — | 4 | 1 | no | — |
| 427 | C2×D3 | — | 6 | 1 | no | — |
| 428 | C2×D3 | — | 12 | 1 | no | — |
| 429 | C2×D3 | — | 18 | 1 | no | — |
| 430 | C2×D3 | — | 18 | 1 | no | — |
| 431 | C2×D3 | — | 36 | 1 | no | — |
| 432 | C2×D3 | — | 36 | 1 | no | — |
| 433 | C2×D3 | — | 36 | 1 | no | — |
| 434 | C2×D3 | — | 72 | 1 | no | — |
| 435 | C2×D3 | — | 72 | 1 | no | — |
| 436 | C2×D3 | — | 72 | 1 | no | — |
| 437 | C3×C4 | — | 4 | 1 | no | — |
| 438 | C3×C4 | — | 4 | 1 | no | — |
| 439 | C3×C4 | — | 6 | 1 | no | — |
| 440 | C3×C4 | — | 8 | 1 | no | — |
| 441 | C3×C4 | — | 12 | 1 | no | — |
| 442 | C3×C4 | — | 18 | 1 | no | — |
| 443 | C3×C4 | — | 36 | 1 | no | — |
| 444 | Dic3 | — | 2 | 1 | no | — |
| 445 | Dic3 | — | 4 | 1 | no | — |
| 446 | Dic3 | — | 6 | 1 | no | — |
| 447 | Dic3 | — | 12 | 1 | no | — |
| 448 | Dic3 | — | 18 | 1 | no | — |
| 449 | Dic3 | — | 18 | 1 | no | — |
| 450 | Dic3 | — | 36 | 1 | no | — |
| 451 | Dic3 | — | 36 | 1 | no | — |
| 452 | Dic3 | — | 36 | 1 | no | — |
| 453 | Dic3 | — | 72 | 1 | no | — |
| 454 | C32 | #4742 | 1 | 1 | yes | characteristic |
| 455 | C9 | — | 2 | 1 | no | — |
| 456 | C9 | #5053 | 1 | 1 | yes | characteristic, complemented |
| 457 | C23 | — | 3 | 1 | no | — |
| 458 | C23 | — | 9 | 1 | no | — |
| 459 | C23 | — | 27 | 1 | no | — |
| 460 | C23 | — | 54 | 1 | no | — |
| 461 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 462 | Q8 | — | 54 | 1 | no | — |
| 463 | D4 | — | 6 | 1 | no | — |
| 464 | D4 | — | 6 | 1 | no | — |
| 465 | D4 | — | 18 | 1 | no | — |
| 466 | D4 | — | 18 | 1 | no | — |
| 467 | D4 | — | 54 | 1 | no | — |
| 468 | D4 | — | 54 | 1 | no | — |
| 469 | D4 | — | 54 | 1 | no | — |
| 470 | D4 | — | 54 | 1 | no | — |
| 471 | D4 | — | 54 | 1 | no | — |
| 472 | C2×C4 | — | 2 | 1 | no | — |
| 473 | C2×C4 | — | 3 | 1 | no | — |
| 474 | C2×C4 | — | 6 | 1 | no | — |
| 475 | C2×C4 | — | 9 | 1 | no | — |
| 476 | C2×C4 | — | 18 | 1 | no | — |
| 477 | C2×C4 | — | 18 | 1 | no | — |
| 478 | C2×C4 | — | 18 | 1 | no | — |
| 479 | C2×C4 | — | 27 | 1 | no | — |
| 480 | C2×C4 | — | 54 | 1 | no | — |
| 481 | C2×C4 | — | 54 | 1 | no | — |
| 482 | C2×C4 | — | 54 | 1 | no | — |
| 483 | C2×C4 | — | 54 | 1 | no | — |
| 484 | C2×C3 | — | 2 | 1 | no | — |
| 485 | C2×C3 | — | 2 | 1 | no | — |
| 486 | C2×C3 | — | 2 | 1 | no | — |
| 487 | C2×C3 | — | 2 | 1 | no | — |
| 488 | C2×C3 | — | 2 | 1 | no | — |
| 489 | C2×C3 | — | 2 | 1 | no | — |
| 490 | C2×C3 | — | 2 | 1 | no | — |
| 491 | C2×C3 | — | 4 | 1 | no | — |
| 492 | C2×C3 | — | 4 | 1 | no | — |
| 493 | C2×C3 | — | 4 | 1 | no | — |
| 494 | C2×C3 | — | 12 | 1 | no | — |
| 495 | C2×C3 | — | 36 | 1 | no | — |
| 496 | C2×C3 | #63444 | 1 | 1 | yes | characteristic |
| 497 | C2×C3 | #63922 | 1 | 1 | yes | characteristic |
| 498 | D3 | — | 4 | 1 | no | — |
| 499 | D3 | — | 12 | 1 | no | — |
| 500 | D3 | — | 36 | 1 | no | — |
| 501 | D3 | — | 36 | 1 | no | — |
| 502 | D3 | — | 72 | 1 | no | — |
| 503 | C22 | — | 4 | 1 | no | — |
| 504 | C22 | — | 6 | 1 | no | — |
| 505 | C22 | — | 12 | 1 | no | — |
| 506 | C22 | — | 18 | 1 | no | — |
| 507 | C22 | — | 36 | 1 | no | — |
| 508 | C22 | — | 54 | 1 | no | — |
| 509 | C22 | — | 108 | 1 | no | — |
| 510 | C22 | — | 216 | 1 | no | — |
| 511 | C22 | D3×D36 | 1 | 1 | yes | characteristic |
| 512 | C22 | #88646 | 1 | 1 | yes | characteristic |
| 513 | C22 | D9×#67 | 1 | 1 | yes | characteristic |
| 514 | C4 | — | 4 | 1 | no | — |
| 515 | C4 | — | 6 | 1 | no | — |
| 516 | C4 | — | 12 | 1 | no | — |
| 517 | C4 | — | 18 | 1 | no | — |
| 518 | C4 | — | 36 | 1 | no | — |
| 519 | C4 | — | 54 | 1 | no | — |
| 520 | C4 | — | 108 | 1 | no | — |
| 521 | C3 | — | 2 | 1 | no | — |
| 522 | C3 | #10588422 | 1 | 1 | yes | characteristic, complemented |
| 523 | C3 | #10590408 | 1 | 1 | yes | characteristic |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 2 | 1 | no | — |
| 526 | C2 | — | 2 | 1 | no | — |
| 527 | C2 | — | 12 | 1 | no | — |
| 528 | C2 | — | 36 | 1 | no | — |
| 529 | C2 | — | 108 | 1 | no | — |
| 530 | C2 | #11721049 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#63448 | C2 | semidirect |
| 3. #11721265 | C2 | semidirect |
| 4. #11721255 | C2 | semidirect |
| 5. #11720523 | C2 | semidirect |
| 6. C9×#806 | C2 | semidirect |
| 7. #11720329 | C2 | semidirect |
| 13. C22×C3×Dic9 | C22 | semidirect |
| 20. C3×C9×C22⋊C4 | C22 | semidirect |
| 21. #88551 | C22 | semidirect |
| 22. C9×#217 | C22 | semidirect |
| 39. #63448 | D3 | semidirect |
| 97. C22×Dic9 | C2×D3 | semidirect |
| 105. C9×C22⋊C4 | C2×D3 | semidirect |
| 146. #806 | D9 | semidirect |
| 241. C3×C22⋊C4 | C2×D9 | semidirect |
| 247. #217 | C2×D9 | semidirect |
| 309. C3×C9 | #458 | semidirect |
| 408. C22⋊C4 | D3×D9 | semidirect |
| 456. C9 | #5053 | semidirect |
| 522. C3 | #10588422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722535 | 2 |
| C3×#63448 | 2 |
| #11721265 | 2 |
| #11721255 | 2 |
| #11720523 | 2 |
| C9×#806 | 2 |
| #11720329 | 2 |
| #10590408 | 3 |
| #10588422 | 3 |