Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
724 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 724 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, complemented |
| 2 | #11721874 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C9×#953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#63515 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11720332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11720330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11720329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10591725 | — | 3 | 1 | no | maximal |
| 9 | #10588712 | — | 3 | 1 | no | maximal |
| 10 | C24×C3×C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#6233 | — | 2 | 1 | no | — |
| 12 | C2×#6233 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C9×#67 | — | 2 | 1 | no | — |
| 14 | C2×C9×#67 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#611 | — | 2 | 1 | no | — |
| 16 | C2×C3×#611 | C22 | 1 | 1 | yes | characteristic |
| 17 | #88668 | — | 2 | 1 | no | — |
| 18 | D9×#67 | — | 2 | 1 | no | — |
| 19 | D3×#611 | — | 2 | 1 | no | — |
| 20 | #88663 | — | 2 | 1 | no | — |
| 21 | #88662 | — | 2 | 1 | no | — |
| 22 | #88658 | — | 2 | 1 | no | — |
| 23 | #88551 | — | 2 | 1 | no | — |
| 24 | #88551 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C9×#217 | — | 2 | 1 | no | — |
| 26 | C9×#217 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×#3676 | — | 2 | 1 | no | — |
| 28 | C3×#3676 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #64330 | — | 3 | 1 | no | — |
| 30 | #64162 | — | 3 | 1 | no | — |
| 31 | C3×#953 | — | 3 | 1 | no | — |
| 32 | C3×#953 | D3 | 1 | 1 | yes | characteristic |
| 33 | #63710 | — | 3 | 1 | no | — |
| 34 | #63581 | — | 3 | 1 | no | — |
| 35 | #63580 | — | 3 | 1 | no | — |
| 36 | #63580 | — | 3 | 1 | no | — |
| 37 | C9×#120 | — | 3 | 1 | no | — |
| 38 | #63515 | — | 3 | 1 | no | — |
| 39 | #63515 | — | 6 | 1 | no | — |
| 40 | #63515 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | #63393 | — | 3 | 1 | no | — |
| 42 | #63365 | — | 3 | 1 | no | — |
| 43 | #63365 | — | 3 | 1 | no | — |
| 44 | C23×C3×C9 | — | 2 | 1 | no | — |
| 45 | C23×C3×C9 | — | 2 | 1 | no | — |
| 46 | C23×C3×C9 | — | 2 | 1 | no | — |
| 47 | C23×C3×C9 | — | 4 | 2 | no | — |
| 48 | C23×C3×C9 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×C3⋊D9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | C22×D3×C9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 51 | C22×C3×D9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×D3×D9 | — | 2 | 1 | no | — |
| 53 | #6233 | — | 2 | 1 | no | — |
| 54 | #6233 | — | 2 | 1 | no | — |
| 55 | #6233 | — | 4 | 2 | no | — |
| 56 | C2×C3⋊Dic9 | — | 2 | 1 | no | — |
| 57 | C2×C3⋊Dic9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 58 | C9×#67 | — | 2 | 1 | no | — |
| 59 | C9×#67 | — | 2 | 1 | no | — |
| 60 | C9×#67 | — | 4 | 2 | no | — |
| 61 | C3×#611 | — | 2 | 1 | no | — |
| 62 | C3×#611 | — | 2 | 1 | no | — |
| 63 | C3×#611 | — | 4 | 2 | no | — |
| 64 | C2×C9×Dic3 | — | 2 | 1 | no | — |
| 65 | C2×C9×Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C2×C3×Dic9 | — | 2 | 1 | no | — |
| 67 | C2×C3×Dic9 | D4 | 1 | 1 | yes | characteristic, complemented |
| 68 | #6195 | — | 2 | 1 | no | — |
| 69 | #6194 | — | 2 | 1 | no | — |
| 70 | D3×Dic9 | — | 2 | 1 | no | — |
| 71 | #6192 | — | 2 | 1 | no | — |
| 72 | (C3⋊D9)⋊C4 | — | 2 | 1 | no | — |
| 73 | Dic3×D9 | — | 2 | 1 | no | — |
| 74 | #6189 | — | 2 | 1 | no | — |
| 75 | #5032 | — | 9 | 1 | no | — |
| 76 | #5032 | — | 9 | 1 | no | — |
| 77 | C24×C32 | C2×D3 | 1 | 1 | yes | characteristic |
| 78 | C2×#638 | — | 3 | 1 | no | — |
| 79 | C2×#638 | — | 6 | 1 | no | — |
| 80 | C2×C3×#67 | — | 2 | 1 | no | — |
| 81 | C2×C3×#67 | — | 3 | 1 | no | — |
| 82 | C2×C3×#67 | — | 6 | 1 | no | — |
| 83 | C2×C3×#67 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #3811 | — | 6 | 1 | no | — |
| 85 | D3×#67 | — | 6 | 1 | no | — |
| 86 | D3×#67 | — | 6 | 1 | no | — |
| 87 | #3805 | — | 6 | 1 | no | — |
| 88 | #3804 | — | 6 | 1 | no | — |
| 89 | #3804 | — | 6 | 1 | no | — |
| 90 | C24×C9 | — | 2 | 1 | no | — |
| 91 | C24×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | #3757 | — | 3 | 1 | no | — |
| 93 | #3757 | — | 6 | 1 | no | — |
| 94 | C3×#217 | — | 2 | 1 | no | — |
| 95 | C3×#217 | — | 3 | 1 | no | — |
| 96 | C3×#217 | — | 6 | 1 | no | — |
| 97 | C3×#217 | C2×D3 | 1 | 1 | yes | characteristic |
| 98 | C2×D4×C9 | — | 3 | 1 | no | — |
| 99 | C2×D4×C9 | — | 6 | 1 | no | — |
| 100 | C2×#611 | — | 2 | 1 | no | — |
| 101 | C2×#611 | — | 3 | 1 | no | — |
| 102 | C2×#611 | — | 6 | 1 | no | — |
| 103 | C2×#611 | — | 6 | 1 | no | — |
| 104 | C2×#611 | — | 6 | 1 | no | — |
| 105 | C2×#611 | — | 6 | 2 | no | — |
| 106 | C2×#611 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | #3699 | — | 6 | 1 | no | — |
| 108 | #3699 | — | 6 | 1 | no | — |
| 109 | D4×D9 | — | 6 | 1 | no | — |
| 110 | D4×D9 | — | 6 | 1 | no | — |
| 111 | #3697 | — | 6 | 1 | no | — |
| 112 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 113 | C9×C22⋊C4 | — | 6 | 1 | no | — |
| 114 | #3676 | — | 2 | 1 | no | — |
| 115 | #3676 | — | 3 | 1 | no | — |
| 116 | #3676 | — | 6 | 1 | no | — |
| 117 | #3676 | — | 6 | 1 | no | — |
| 118 | #3676 | — | 6 | 2 | no | — |
| 119 | #3676 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 120 | C22×C3×C9 | — | 2 | 2 | no | — |
| 121 | C22×C3×C9 | — | 2 | 2 | no | — |
| 122 | C22×C3×C9 | — | 2 | 2 | no | — |
| 123 | C22×C3×C9 | — | 4 | 1 | no | — |
| 124 | C22×C3×C9 | — | 4 | 1 | no | — |
| 125 | C22×C3×C9 | — | 4 | 1 | no | — |
| 126 | C22×C3×C9 | — | 4 | 1 | no | — |
| 127 | C22×C3×C9 | — | 4 | 1 | no | — |
| 128 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C3×C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C3⋊D9 | — | 2 | 1 | no | — |
| 132 | C2×C3⋊D9 | — | 4 | 1 | no | — |
| 133 | C2×D3×C9 | — | 2 | 1 | no | — |
| 134 | C2×D3×C9 | — | 4 | 1 | no | — |
| 135 | C2×C3×D9 | — | 2 | 1 | no | — |
| 136 | C2×C3×D9 | — | 4 | 1 | no | — |
| 137 | D3×D9 | — | 8 | 1 | no | — |
| 138 | C3⋊Dic9 | — | 2 | 1 | no | — |
| 139 | C3⋊Dic9 | — | 4 | 1 | no | — |
| 140 | C9×Dic3 | — | 2 | 1 | no | — |
| 141 | C9×Dic3 | — | 4 | 1 | no | — |
| 142 | C3×Dic9 | — | 2 | 1 | no | — |
| 143 | C3×Dic9 | — | 4 | 1 | no | — |
| 144 | #1004 | — | 9 | 1 | no | — |
| 145 | #1004 | — | 9 | 1 | no | — |
| 146 | C3×#120 | — | 3 | 1 | no | — |
| 147 | C3×#120 | — | 9 | 1 | no | — |
| 148 | #953 | — | 3 | 1 | no | — |
| 149 | #953 | — | 9 | 1 | no | — |
| 150 | #953 | — | 9 | 1 | no | — |
| 151 | #953 | — | 18 | 1 | no | — |
| 152 | #953 | D9 | 1 | 1 | yes | characteristic, complemented |
| 153 | #834 | — | 9 | 1 | no | — |
| 154 | #834 | — | 9 | 1 | no | — |
| 155 | #806 | — | 9 | 1 | no | — |
| 156 | #806 | — | 9 | 1 | no | — |
| 157 | #806 | — | 9 | 1 | no | — |
| 158 | #806 | — | 9 | 1 | no | — |
| 159 | C23×C32 | — | 2 | 1 | no | — |
| 160 | C23×C32 | — | 2 | 1 | no | — |
| 161 | C23×C32 | — | 2 | 1 | no | — |
| 162 | C23×C32 | — | 4 | 2 | no | — |
| 163 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 164 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 165 | C22×C3×D3 | — | 3 | 1 | no | — |
| 166 | C22×C3×D3 | #67 | 1 | 1 | yes | characteristic |
| 167 | C2×D32 | — | 6 | 1 | no | — |
| 168 | #638 | — | 6 | 1 | no | — |
| 169 | #638 | — | 6 | 1 | no | — |
| 170 | #638 | — | 12 | 2 | no | — |
| 171 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 172 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 173 | C3×#67 | — | 2 | 1 | no | — |
| 174 | C3×#67 | — | 2 | 1 | no | — |
| 175 | C3×#67 | — | 4 | 2 | no | — |
| 176 | C3×#67 | — | 6 | 1 | no | — |
| 177 | C3×#67 | — | 6 | 1 | no | — |
| 178 | C3×#67 | — | 12 | 2 | no | — |
| 179 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 180 | C2×C3×Dic3 | — | 3 | 1 | no | — |
| 181 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 182 | C2×C3×Dic3 | #67 | 1 | 1 | yes | characteristic |
| 183 | #627 | — | 6 | 1 | no | — |
| 184 | #626 | — | 6 | 1 | no | — |
| 185 | #626 | — | 6 | 1 | no | — |
| 186 | #625 | — | 6 | 1 | no | — |
| 187 | #624 | — | 6 | 1 | no | — |
| 188 | D3×Dic3 | — | 6 | 1 | no | — |
| 189 | D3×Dic3 | — | 6 | 1 | no | — |
| 190 | C23×C9 | — | 2 | 2 | no | — |
| 191 | C23×C9 | — | 2 | 1 | no | — |
| 192 | C23×C9 | — | 2 | 1 | no | — |
| 193 | C23×C9 | — | 2 | 1 | no | — |
| 194 | C23×C9 | — | 2 | 1 | no | — |
| 195 | C23×C9 | — | 3 | 1 | no | — |
| 196 | C23×C9 | — | 4 | 1 | no | — |
| 197 | C23×C9 | — | 4 | 1 | no | — |
| 198 | C23×C9 | — | 4 | 2 | no | — |
| 199 | C23×C9 | — | 4 | 4 | no | — |
| 200 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | C22×D9 | — | 3 | 1 | no | — |
| 202 | C22×D9 | — | 6 | 1 | no | — |
| 203 | C22×D9 | — | 6 | 1 | no | — |
| 204 | C22×D9 | #67 | 1 | 1 | yes | characteristic, complemented |
| 205 | D4×C9 | — | 6 | 1 | no | — |
| 206 | D4×C9 | — | 6 | 1 | no | — |
| 207 | D4×C9 | — | 12 | 2 | no | — |
| 208 | C2×C4×C9 | — | 3 | 1 | no | — |
| 209 | C2×C4×C9 | — | 6 | 1 | no | — |
| 210 | #611 | — | 2 | 1 | no | — |
| 211 | #611 | — | 2 | 1 | no | — |
| 212 | #611 | — | 4 | 2 | no | — |
| 213 | #611 | — | 6 | 1 | no | — |
| 214 | #611 | — | 6 | 1 | no | — |
| 215 | #611 | — | 6 | 1 | no | — |
| 216 | #611 | — | 6 | 1 | no | — |
| 217 | #611 | — | 12 | 1 | no | — |
| 218 | #611 | — | 12 | 1 | no | — |
| 219 | #611 | — | 12 | 2 | no | — |
| 220 | #611 | — | 12 | 4 | no | — |
| 221 | C2×Dic9 | — | 2 | 1 | no | — |
| 222 | C2×Dic9 | — | 3 | 1 | no | — |
| 223 | C2×Dic9 | — | 6 | 1 | no | — |
| 224 | C2×Dic9 | — | 6 | 1 | no | — |
| 225 | C2×Dic9 | — | 6 | 2 | no | — |
| 226 | C2×Dic9 | — | 6 | 1 | no | — |
| 227 | C2×Dic9 | #67 | 1 | 1 | yes | characteristic, complemented |
| 228 | D36 | — | 6 | 1 | no | — |
| 229 | C4×D9 | — | 6 | 1 | no | — |
| 230 | C4×D9 | — | 6 | 1 | no | — |
| 231 | Dic18 | — | 6 | 1 | no | — |
| 232 | B(4,𝔽2) | — | 27 | 1 | no | Sylow |
| 233 | C2×C3×C9 | — | 2 | 1 | no | — |
| 234 | C2×C3×C9 | — | 2 | 1 | no | — |
| 235 | C2×C3×C9 | — | 2 | 1 | no | — |
| 236 | C2×C3×C9 | — | 4 | 2 | no | — |
| 237 | C2×C3×C9 | #120 | 1 | 1 | yes | characteristic |
| 238 | C3⋊D9 | — | 4 | 1 | no | — |
| 239 | D3×C9 | — | 4 | 1 | no | — |
| 240 | C3×D9 | — | 4 | 1 | no | — |
| 241 | C24×C3 | — | 2 | 1 | no | — |
| 242 | C24×C3 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 243 | C24×C3 | D32 | 1 | 1 | yes | characteristic |
| 244 | C2×C3×D4 | — | 3 | 1 | no | — |
| 245 | C2×C3×D4 | — | 6 | 1 | no | — |
| 246 | C2×C3×D4 | — | 9 | 1 | no | — |
| 247 | C2×C3×D4 | — | 18 | 1 | no | — |
| 248 | C2×#67 | — | 2 | 1 | no | — |
| 249 | C2×#67 | — | 3 | 1 | no | — |
| 250 | C2×#67 | — | 6 | 1 | no | — |
| 251 | C2×#67 | — | 9 | 1 | no | — |
| 252 | C2×#67 | — | 9 | 1 | no | — |
| 253 | C2×#67 | — | 18 | 1 | no | — |
| 254 | C2×#67 | — | 18 | 1 | no | — |
| 255 | C2×#67 | — | 18 | 1 | no | — |
| 256 | C2×#67 | — | 18 | 1 | no | — |
| 257 | C2×#67 | — | 18 | 1 | no | — |
| 258 | C2×#67 | — | 18 | 2 | no | — |
| 259 | C2×#67 | C2×D9 | 1 | 1 | yes | characteristic |
| 260 | #237 | — | 18 | 1 | no | — |
| 261 | #237 | — | 18 | 1 | no | — |
| 262 | #237 | — | 18 | 1 | no | — |
| 263 | #237 | — | 18 | 1 | no | — |
| 264 | D3×D4 | — | 18 | 1 | no | — |
| 265 | D3×D4 | — | 18 | 1 | no | — |
| 266 | D3×D4 | — | 18 | 1 | no | — |
| 267 | D3×D4 | — | 18 | 1 | no | — |
| 268 | #235 | — | 18 | 1 | no | — |
| 269 | #235 | — | 18 | 1 | no | — |
| 270 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 271 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 272 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 273 | C3×C22⋊C4 | — | 18 | 1 | no | — |
| 274 | #217 | — | 2 | 1 | no | — |
| 275 | #217 | — | 3 | 1 | no | — |
| 276 | #217 | — | 6 | 1 | no | — |
| 277 | #217 | — | 9 | 1 | no | — |
| 278 | #217 | — | 9 | 1 | no | — |
| 279 | #217 | — | 18 | 1 | no | — |
| 280 | #217 | — | 18 | 1 | no | — |
| 281 | #217 | — | 18 | 1 | no | — |
| 282 | #217 | — | 18 | 2 | no | — |
| 283 | #217 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 284 | C22×C32 | — | 2 | 2 | no | — |
| 285 | C22×C32 | — | 2 | 2 | no | — |
| 286 | C22×C32 | — | 2 | 2 | no | — |
| 287 | C22×C32 | — | 4 | 1 | no | — |
| 288 | C22×C32 | — | 4 | 1 | no | — |
| 289 | C22×C32 | — | 4 | 1 | no | — |
| 290 | C22×C32 | — | 4 | 1 | no | — |
| 291 | C22×C32 | — | 4 | 1 | no | — |
| 292 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 293 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 294 | C22×C32 | C2×#67 | 1 | 1 | yes | characteristic |
| 295 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 296 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 297 | C2×C3×D3 | — | 2 | 1 | no | — |
| 298 | C2×C3×D3 | — | 4 | 1 | no | — |
| 299 | C2×C3×D3 | — | 6 | 1 | no | — |
| 300 | C2×C3×D3 | — | 12 | 1 | no | — |
| 301 | D32 | — | 24 | 1 | no | — |
| 302 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 303 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 304 | C3×Dic3 | — | 2 | 1 | no | — |
| 305 | C3×Dic3 | — | 4 | 1 | no | — |
| 306 | C3×Dic3 | — | 6 | 1 | no | — |
| 307 | C3×Dic3 | — | 12 | 1 | no | — |
| 308 | C22×C9 | — | 2 | 2 | no | — |
| 309 | C22×C9 | — | 2 | 4 | no | — |
| 310 | C22×C9 | — | 2 | 2 | no | — |
| 311 | C22×C9 | — | 2 | 2 | no | — |
| 312 | C22×C9 | — | 2 | 1 | no | — |
| 313 | C22×C9 | — | 2 | 1 | no | — |
| 314 | C22×C9 | — | 2 | 1 | no | — |
| 315 | C22×C9 | — | 4 | 2 | no | — |
| 316 | C22×C9 | — | 4 | 2 | no | — |
| 317 | C22×C9 | — | 4 | 1 | no | — |
| 318 | C22×C9 | — | 4 | 2 | no | — |
| 319 | C22×C9 | — | 4 | 2 | no | — |
| 320 | C22×C9 | — | 4 | 1 | no | — |
| 321 | C22×C9 | — | 4 | 1 | no | — |
| 322 | C22×C9 | — | 4 | 1 | no | — |
| 323 | C22×C9 | — | 4 | 2 | no | — |
| 324 | C22×C9 | — | 4 | 2 | no | — |
| 325 | C22×C9 | — | 4 | 2 | no | — |
| 326 | C22×C9 | — | 4 | 1 | no | — |
| 327 | C22×C9 | — | 6 | 1 | no | — |
| 328 | C22×C9 | — | 12 | 1 | no | — |
| 329 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 330 | C22×C9 | D3×D4 | 1 | 1 | yes | characteristic |
| 331 | C22×C9 | C2×#67 | 1 | 1 | yes | characteristic |
| 332 | C2×D9 | — | 2 | 1 | no | — |
| 333 | C2×D9 | — | 4 | 1 | no | — |
| 334 | C2×D9 | — | 6 | 1 | no | — |
| 335 | C2×D9 | — | 12 | 1 | no | — |
| 336 | C2×D9 | — | 12 | 1 | no | — |
| 337 | C2×D9 | — | 12 | 2 | no | — |
| 338 | C2×D9 | — | 24 | 1 | no | — |
| 339 | C4×C9 | — | 6 | 1 | no | — |
| 340 | C4×C9 | — | 12 | 1 | no | — |
| 341 | Dic9 | — | 2 | 1 | no | — |
| 342 | Dic9 | — | 4 | 1 | no | — |
| 343 | Dic9 | — | 6 | 1 | no | — |
| 344 | Dic9 | — | 12 | 1 | no | — |
| 345 | Dic9 | — | 12 | 2 | no | — |
| 346 | Dic9 | — | 12 | 1 | no | — |
| 347 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 348 | #120 | — | 3 | 1 | no | — |
| 349 | #120 | — | 9 | 1 | no | — |
| 350 | #120 | — | 27 | 1 | no | — |
| 351 | #99 | — | 27 | 1 | no | — |
| 352 | #99 | — | 27 | 1 | no | — |
| 353 | #99 | — | 27 | 1 | no | — |
| 354 | C3×C9 | B(4,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | C23×C3 | — | 2 | 2 | no | — |
| 356 | C23×C3 | — | 2 | 1 | no | — |
| 357 | C23×C3 | — | 2 | 1 | no | — |
| 358 | C23×C3 | — | 2 | 1 | no | — |
| 359 | C23×C3 | — | 2 | 1 | no | — |
| 360 | C23×C3 | — | 2 | 1 | no | — |
| 361 | C23×C3 | — | 2 | 1 | no | — |
| 362 | C23×C3 | — | 2 | 1 | no | — |
| 363 | C23×C3 | — | 3 | 1 | no | — |
| 364 | C23×C3 | — | 4 | 1 | no | — |
| 365 | C23×C3 | — | 4 | 1 | no | — |
| 366 | C23×C3 | — | 4 | 2 | no | — |
| 367 | C23×C3 | — | 4 | 2 | no | — |
| 368 | C23×C3 | — | 4 | 4 | no | — |
| 369 | C23×C3 | — | 9 | 1 | no | — |
| 370 | C23×C3 | C22×D9 | 1 | 1 | yes | characteristic |
| 371 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 372 | C22×D3 | — | 3 | 1 | no | — |
| 373 | C22×D3 | — | 9 | 1 | no | — |
| 374 | C22×D3 | — | 9 | 1 | no | — |
| 375 | C22×D3 | — | 18 | 1 | no | — |
| 376 | C22×D3 | — | 18 | 1 | no | — |
| 377 | C22×D3 | — | 18 | 1 | no | — |
| 378 | C22×D3 | #611 | 1 | 1 | yes | characteristic, complemented |
| 379 | C3×D4 | — | 6 | 1 | no | — |
| 380 | C3×D4 | — | 6 | 1 | no | — |
| 381 | C3×D4 | — | 12 | 2 | no | — |
| 382 | C3×D4 | — | 18 | 1 | no | — |
| 383 | C3×D4 | — | 18 | 1 | no | — |
| 384 | C3×D4 | — | 36 | 2 | no | — |
| 385 | C2×C3×C4 | — | 3 | 1 | no | — |
| 386 | C2×C3×C4 | — | 6 | 1 | no | — |
| 387 | C2×C3×C4 | — | 9 | 1 | no | — |
| 388 | C2×C3×C4 | — | 18 | 1 | no | — |
| 389 | #67 | — | 2 | 1 | no | — |
| 390 | #67 | — | 2 | 1 | no | — |
| 391 | #67 | — | 4 | 2 | no | — |
| 392 | #67 | — | 6 | 1 | no | — |
| 393 | #67 | — | 6 | 1 | no | — |
| 394 | #67 | — | 12 | 2 | no | — |
| 395 | #67 | — | 18 | 1 | no | — |
| 396 | #67 | — | 18 | 1 | no | — |
| 397 | #67 | — | 18 | 1 | no | — |
| 398 | #67 | — | 18 | 1 | no | — |
| 399 | #67 | — | 18 | 1 | no | — |
| 400 | #67 | — | 18 | 1 | no | — |
| 401 | #67 | — | 18 | 1 | no | — |
| 402 | #67 | — | 18 | 1 | no | — |
| 403 | #67 | — | 36 | 1 | no | — |
| 404 | #67 | — | 36 | 1 | no | — |
| 405 | #67 | — | 36 | 2 | no | — |
| 406 | #67 | — | 36 | 2 | no | — |
| 407 | #67 | — | 36 | 4 | no | — |
| 408 | C2×Dic3 | — | 2 | 1 | no | — |
| 409 | C2×Dic3 | — | 3 | 1 | no | — |
| 410 | C2×Dic3 | — | 6 | 1 | no | — |
| 411 | C2×Dic3 | — | 9 | 1 | no | — |
| 412 | C2×Dic3 | — | 9 | 1 | no | — |
| 413 | C2×Dic3 | — | 18 | 1 | no | — |
| 414 | C2×Dic3 | — | 18 | 1 | no | — |
| 415 | C2×Dic3 | — | 18 | 1 | no | — |
| 416 | C2×Dic3 | — | 18 | 2 | no | — |
| 417 | C2×Dic3 | — | 18 | 1 | no | — |
| 418 | C2×Dic3 | — | 18 | 1 | no | — |
| 419 | C2×Dic3 | #611 | 1 | 1 | yes | characteristic, complemented |
| 420 | D12 | — | 18 | 1 | no | — |
| 421 | D12 | — | 18 | 1 | no | — |
| 422 | C4×D3 | — | 18 | 1 | no | — |
| 423 | C4×D3 | — | 18 | 1 | no | — |
| 424 | C4×D3 | — | 18 | 1 | no | — |
| 425 | C4×D3 | — | 18 | 1 | no | — |
| 426 | Dic6 | — | 18 | 1 | no | — |
| 427 | Dic6 | — | 18 | 1 | no | — |
| 428 | C2×C32 | — | 2 | 1 | no | — |
| 429 | C2×C32 | — | 2 | 1 | no | — |
| 430 | C2×C32 | — | 2 | 1 | no | — |
| 431 | C2×C32 | — | 4 | 2 | no | — |
| 432 | C2×C32 | #937 | 1 | 1 | yes | characteristic |
| 433 | C3⋊D3 | — | 12 | 1 | no | — |
| 434 | C3×D3 | — | 4 | 1 | no | — |
| 435 | C3×D3 | — | 12 | 1 | no | — |
| 436 | C2×C9 | — | 2 | 2 | no | — |
| 437 | C2×C9 | — | 2 | 1 | no | — |
| 438 | C2×C9 | — | 2 | 1 | no | — |
| 439 | C2×C9 | — | 2 | 1 | no | — |
| 440 | C2×C9 | — | 2 | 1 | no | — |
| 441 | C2×C9 | — | 4 | 1 | no | — |
| 442 | C2×C9 | — | 4 | 1 | no | — |
| 443 | C2×C9 | — | 4 | 4 | no | — |
| 444 | C2×C9 | — | 4 | 2 | no | — |
| 445 | C2×C9 | — | 12 | 1 | no | — |
| 446 | C2×C9 | #937 | 1 | 1 | yes | characteristic |
| 447 | D9 | — | 4 | 1 | no | — |
| 448 | D9 | — | 12 | 1 | no | — |
| 449 | D9 | — | 24 | 1 | no | — |
| 450 | C24 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 451 | #41 | — | 54 | 1 | no | — |
| 452 | #41 | — | 54 | 1 | no | — |
| 453 | #41 | — | 54 | 1 | no | — |
| 454 | C2×D4 | — | 3 | 1 | no | — |
| 455 | C2×D4 | — | 6 | 1 | no | — |
| 456 | C2×D4 | — | 9 | 1 | no | — |
| 457 | C2×D4 | — | 18 | 1 | no | — |
| 458 | C2×D4 | — | 27 | 1 | no | — |
| 459 | C2×D4 | — | 54 | 1 | no | — |
| 460 | C2×D4 | — | 54 | 1 | no | — |
| 461 | C2×D4 | — | 54 | 1 | no | — |
| 462 | C2×D4 | — | 54 | 1 | no | — |
| 463 | C22⋊C4 | — | 3 | 1 | no | — |
| 464 | C22⋊C4 | — | 6 | 1 | no | — |
| 465 | C22⋊C4 | — | 9 | 1 | no | — |
| 466 | C22⋊C4 | — | 18 | 1 | no | — |
| 467 | C22⋊C4 | — | 27 | 1 | no | — |
| 468 | C22⋊C4 | — | 54 | 1 | no | — |
| 469 | C22×C3 | — | 2 | 2 | no | — |
| 470 | C22×C3 | — | 2 | 2 | no | — |
| 471 | C22×C3 | — | 2 | 2 | no | — |
| 472 | C22×C3 | — | 2 | 4 | no | — |
| 473 | C22×C3 | — | 2 | 2 | no | — |
| 474 | C22×C3 | — | 2 | 2 | no | — |
| 475 | C22×C3 | — | 2 | 2 | no | — |
| 476 | C22×C3 | — | 2 | 1 | no | — |
| 477 | C22×C3 | — | 2 | 1 | no | — |
| 478 | C22×C3 | — | 2 | 1 | no | — |
| 479 | C22×C3 | — | 4 | 2 | no | — |
| 480 | C22×C3 | — | 4 | 2 | no | — |
| 481 | C22×C3 | — | 4 | 1 | no | — |
| 482 | C22×C3 | — | 4 | 1 | no | — |
| 483 | C22×C3 | — | 4 | 1 | no | — |
| 484 | C22×C3 | — | 4 | 1 | no | — |
| 485 | C22×C3 | — | 4 | 1 | no | — |
| 486 | C22×C3 | — | 4 | 2 | no | — |
| 487 | C22×C3 | — | 4 | 2 | no | — |
| 488 | C22×C3 | — | 4 | 1 | no | — |
| 489 | C22×C3 | — | 4 | 1 | no | — |
| 490 | C22×C3 | — | 4 | 1 | no | — |
| 491 | C22×C3 | — | 4 | 2 | no | — |
| 492 | C22×C3 | — | 4 | 2 | no | — |
| 493 | C22×C3 | — | 4 | 2 | no | — |
| 494 | C22×C3 | — | 4 | 1 | no | — |
| 495 | C22×C3 | — | 4 | 1 | no | — |
| 496 | C22×C3 | — | 6 | 1 | no | — |
| 497 | C22×C3 | — | 12 | 1 | no | — |
| 498 | C22×C3 | — | 18 | 1 | no | — |
| 499 | C22×C3 | — | 36 | 1 | no | — |
| 500 | C22×C3 | D4×D9 | 1 | 1 | yes | characteristic |
| 501 | C22×C3 | D4×D9 | 1 | 1 | yes | characteristic |
| 502 | C22×C3 | C2×#611 | 1 | 1 | yes | characteristic |
| 503 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 504 | C22×C3 | D3×#67 | 1 | 1 | yes | characteristic |
| 505 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 506 | C2×D3 | — | 2 | 1 | no | — |
| 507 | C2×D3 | — | 4 | 1 | no | — |
| 508 | C2×D3 | — | 6 | 1 | no | — |
| 509 | C2×D3 | — | 12 | 1 | no | — |
| 510 | C2×D3 | — | 18 | 1 | no | — |
| 511 | C2×D3 | — | 18 | 1 | no | — |
| 512 | C2×D3 | — | 36 | 1 | no | — |
| 513 | C2×D3 | — | 36 | 1 | no | — |
| 514 | C2×D3 | — | 36 | 1 | no | — |
| 515 | C2×D3 | — | 36 | 2 | no | — |
| 516 | C2×D3 | — | 72 | 1 | no | — |
| 517 | C2×D3 | — | 72 | 1 | no | — |
| 518 | C3×C4 | — | 6 | 1 | no | — |
| 519 | C3×C4 | — | 12 | 1 | no | — |
| 520 | C3×C4 | — | 18 | 1 | no | — |
| 521 | C3×C4 | — | 36 | 1 | no | — |
| 522 | Dic3 | — | 2 | 1 | no | — |
| 523 | Dic3 | — | 4 | 1 | no | — |
| 524 | Dic3 | — | 6 | 1 | no | — |
| 525 | Dic3 | — | 12 | 1 | no | — |
| 526 | Dic3 | — | 18 | 1 | no | — |
| 527 | Dic3 | — | 18 | 1 | no | — |
| 528 | Dic3 | — | 36 | 1 | no | — |
| 529 | Dic3 | — | 36 | 1 | no | — |
| 530 | Dic3 | — | 36 | 2 | no | — |
| 531 | Dic3 | — | 36 | 1 | no | — |
| 532 | C32 | #5032 | 1 | 1 | yes | characteristic |
| 533 | C9 | — | 2 | 1 | no | — |
| 534 | C9 | #5032 | 1 | 1 | yes | characteristic, complemented |
| 535 | C23 | — | 2 | 1 | no | — |
| 536 | C23 | — | 2 | 1 | no | — |
| 537 | C23 | — | 2 | 1 | no | — |
| 538 | C23 | — | 3 | 1 | no | — |
| 539 | C23 | — | 4 | 2 | no | — |
| 540 | C23 | — | 9 | 1 | no | — |
| 541 | C23 | — | 27 | 1 | no | — |
| 542 | C23 | — | 54 | 1 | no | — |
| 543 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 544 | Q8 | — | 54 | 1 | no | — |
| 545 | D4 | — | 6 | 1 | no | — |
| 546 | D4 | — | 6 | 1 | no | — |
| 547 | D4 | — | 12 | 2 | no | — |
| 548 | D4 | — | 18 | 1 | no | — |
| 549 | D4 | — | 18 | 1 | no | — |
| 550 | D4 | — | 36 | 2 | no | — |
| 551 | D4 | — | 54 | 1 | no | — |
| 552 | D4 | — | 54 | 1 | no | — |
| 553 | D4 | — | 54 | 1 | no | — |
| 554 | D4 | — | 54 | 1 | no | — |
| 555 | D4 | — | 54 | 1 | no | — |
| 556 | D4 | — | 108 | 2 | no | — |
| 557 | C2×C4 | — | 3 | 1 | no | — |
| 558 | C2×C4 | — | 6 | 1 | no | — |
| 559 | C2×C4 | — | 9 | 1 | no | — |
| 560 | C2×C4 | — | 18 | 1 | no | — |
| 561 | C2×C4 | — | 27 | 1 | no | — |
| 562 | C2×C4 | — | 54 | 1 | no | — |
| 563 | C2×C4 | — | 54 | 1 | no | — |
| 564 | C2×C4 | — | 54 | 1 | no | — |
| 565 | C2×C4 | — | 54 | 1 | no | — |
| 566 | C2×C3 | — | 2 | 2 | no | — |
| 567 | C2×C3 | — | 2 | 1 | no | — |
| 568 | C2×C3 | — | 2 | 1 | no | — |
| 569 | C2×C3 | — | 2 | 1 | no | — |
| 570 | C2×C3 | — | 2 | 1 | no | — |
| 571 | C2×C3 | — | 2 | 1 | no | — |
| 572 | C2×C3 | — | 2 | 1 | no | — |
| 573 | C2×C3 | — | 2 | 1 | no | — |
| 574 | C2×C3 | — | 4 | 1 | no | — |
| 575 | C2×C3 | — | 4 | 1 | no | — |
| 576 | C2×C3 | — | 4 | 4 | no | — |
| 577 | C2×C3 | — | 4 | 2 | no | — |
| 578 | C2×C3 | — | 4 | 2 | no | — |
| 579 | C2×C3 | — | 12 | 1 | no | — |
| 580 | C2×C3 | — | 36 | 1 | no | — |
| 581 | C2×C3 | #63499 | 1 | 1 | yes | characteristic |
| 582 | C2×C3 | #63983 | 1 | 1 | yes | characteristic |
| 583 | D3 | — | 4 | 1 | no | — |
| 584 | D3 | — | 12 | 1 | no | — |
| 585 | D3 | — | 36 | 1 | no | — |
| 586 | D3 | — | 36 | 1 | no | — |
| 587 | D3 | — | 72 | 1 | no | — |
| 588 | C22 | — | 2 | 2 | no | — |
| 589 | C22 | — | 2 | 2 | no | — |
| 590 | C22 | — | 2 | 2 | no | — |
| 591 | C22 | — | 4 | 1 | no | — |
| 592 | C22 | — | 4 | 1 | no | — |
| 593 | C22 | — | 4 | 1 | no | — |
| 594 | C22 | — | 4 | 1 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 6 | 1 | no | — |
| 597 | C22 | — | 12 | 1 | no | — |
| 598 | C22 | — | 18 | 1 | no | — |
| 599 | C22 | — | 36 | 1 | no | — |
| 600 | C22 | — | 54 | 1 | no | — |
| 601 | C22 | — | 108 | 1 | no | — |
| 602 | C22 | — | 216 | 1 | no | — |
| 603 | C22 | D3×#611 | 1 | 1 | yes | characteristic |
| 604 | C22 | D9×#67 | 1 | 1 | yes | characteristic |
| 605 | C22 | #88668 | 1 | 1 | yes | characteristic |
| 606 | C4 | — | 6 | 1 | no | — |
| 607 | C4 | — | 12 | 1 | no | — |
| 608 | C4 | — | 18 | 1 | no | — |
| 609 | C4 | — | 36 | 1 | no | — |
| 610 | C4 | — | 54 | 1 | no | — |
| 611 | C4 | — | 108 | 1 | no | — |
| 612 | C3 | — | 2 | 1 | no | — |
| 613 | C3 | #10588712 | 1 | 1 | yes | characteristic, complemented |
| 614 | C3 | #10591725 | 1 | 1 | yes | characteristic |
| 615 | C2 | — | 2 | 1 | no | — |
| 616 | C2 | — | 2 | 1 | no | — |
| 617 | C2 | — | 2 | 1 | no | — |
| 618 | C2 | — | 4 | 2 | no | — |
| 619 | C2 | — | 12 | 1 | no | — |
| 620 | C2 | — | 36 | 1 | no | — |
| 621 | C2 | — | 108 | 1 | no | — |
| 622 | C2 | #11721292 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722535 | C2 | semidirect |
| 2. #11721874 | C2 | semidirect |
| 3. C9×#953 | C2 | semidirect |
| 4. C3×#63515 | C2 | semidirect |
| 5. #11720332 | C2 | semidirect |
| 6. #11720330 | C2 | semidirect |
| 7. #11720329 | C2 | semidirect |
| 10. C24×C3×C9 | C22 | semidirect |
| 24. #88551 | C22 | semidirect |
| 26. C9×#217 | C22 | semidirect |
| 28. C3×#3676 | C22 | semidirect |
| 40. #63515 | D3 | semidirect |
| 49. C22×C3⋊D9 | D4 | semidirect |
| 50. C22×D3×C9 | D4 | semidirect |
| 51. C22×C3×D9 | D4 | semidirect |
| 57. C2×C3⋊Dic9 | D4 | semidirect |
| 65. C2×C9×Dic3 | D4 | semidirect |
| 67. C2×C3×Dic9 | D4 | semidirect |
| 91. C24×C9 | C2×D3 | semidirect |
| 119. #3676 | C2×D3 | semidirect |
| 152. #953 | D9 | semidirect |
| 204. C22×D9 | #67 | semidirect |
| 227. C2×Dic9 | #67 | semidirect |
| 242. C24×C3 | C2×D9 | semidirect |
| 283. #217 | C2×D9 | semidirect |
| 354. C3×C9 | B(4,𝔽2) | semidirect |
| 378. C22×D3 | #611 | semidirect |
| 419. C2×Dic3 | #611 | semidirect |
| 450. C24 | D3×D9 | semidirect |
| 534. C9 | #5032 | semidirect |
| 613. C3 | #10588712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722535 | 2 |
| #11721874 | 2 |
| C9×#953 | 2 |
| C3×#63515 | 2 |
| #11720332 | 2 |
| #11720330 | 2 |
| #11720329 | 2 |
| #10591725 | 3 |
| #10588712 | 3 |