Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
872 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 114 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 | C2×C3⋊D3×D16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11800468 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11797257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11772984 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#67825 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D3×#1419 | — | 3 | 2 | no | maximal |
| 7 | C2×D8×C3⋊D3 | — | 2 | 1 | no | — |
| 8 | C2×C32×D16 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#63653 | — | 2 | 1 | no | — |
| 10 | C3⋊D3×D16 | — | 2 | 1 | no | — |
| 11 | C3⋊D3×D16 | — | 2 | 1 | no | — |
| 12 | C3⋊D3×D16 | C4 | 1 | 2 | yes | — |
| 13 | C3⋊D3×D16 | C4 | 1 | 2 | yes | — |
| 14 | C2×#63626 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C16×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 16 | #10590913 | — | 2 | 1 | no | — |
| 17 | C3×#4506 | C22 | 1 | 2 | yes | complemented |
| 18 | C3×#4499 | C22 | 1 | 2 | yes | complemented |
| 19 | #10589144 | — | 2 | 1 | no | — |
| 20 | #10589069 | — | 2 | 1 | no | — |
| 21 | #10589067 | — | 2 | 1 | no | — |
| 22 | C2×D3×D16 | — | 3 | 2 | no | — |
| 23 | C2×D3×D16 | — | 6 | 1 | no | — |
| 24 | D3×M64 | — | 3 | 2 | no | — |
| 25 | D3×#368 | — | 3 | 2 | no | — |
| 26 | C3×#1419 | — | 3 | 2 | no | — |
| 27 | #67825 | D3 | 1 | 2 | yes | complemented |
| 28 | #67604 | — | 3 | 2 | no | — |
| 29 | #67583 | — | 3 | 2 | no | — |
| 30 | C2×D4×C3⋊D3 | — | 4 | 1 | no | — |
| 31 | C2×C32×D8 | — | 2 | 1 | no | — |
| 32 | C2×#3753 | — | 4 | 1 | no | — |
| 33 | D8×C3⋊D3 | — | 2 | 2 | no | — |
| 34 | D8×C3⋊D3 | — | 2 | 2 | no | — |
| 35 | D8×C3⋊D3 | — | 4 | 1 | no | — |
| 36 | D8×C3⋊D3 | — | 4 | 1 | no | — |
| 37 | C2×#3745 | — | 2 | 1 | no | — |
| 38 | C2×C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 39 | #63818 | — | 4 | 1 | no | — |
| 40 | C32×D16 | — | 2 | 1 | no | — |
| 41 | C32×D16 | C2×C4 | 1 | 2 | yes | — |
| 42 | C2×C32×C16 | C23 | 1 | 1 | yes | characteristic |
| 43 | #63653 | — | 2 | 2 | no | — |
| 44 | #63653 | — | 2 | 2 | no | — |
| 45 | C2×C3⋊(C3⋊C16) | D4 | 1 | 1 | yes | characteristic |
| 46 | #63626 | — | 2 | 1 | no | — |
| 47 | #63626 | C2×C4 | 1 | 2 | yes | — |
| 48 | C16×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C16×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C16×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 51 | C16×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 52 | C3×#819 | — | 2 | 2 | no | — |
| 53 | #63578 | — | 4 | 1 | no | — |
| 54 | C3×C3⋊C32 | — | 2 | 2 | no | — |
| 55 | C2×#1419 | — | 9 | 1 | no | Sylow |
| 56 | C2×D3×D8 | — | 6 | 2 | no | — |
| 57 | C2×D3×D8 | — | 6 | 2 | no | — |
| 58 | C2×C3×D16 | — | 2 | 1 | no | — |
| 59 | C2×C3×D16 | C2×D3 | 1 | 2 | yes | — |
| 60 | C2×#826 | — | 6 | 2 | no | — |
| 61 | C2×#826 | — | 6 | 2 | no | — |
| 62 | D3×D16 | — | 3 | 4 | no | — |
| 63 | D3×D16 | — | 3 | 4 | no | — |
| 64 | D3×D16 | — | 6 | 2 | no | — |
| 65 | D3×D16 | — | 6 | 2 | no | — |
| 66 | D3×D16 | — | 6 | 2 | no | — |
| 67 | D3×D16 | — | 6 | 2 | no | — |
| 68 | D3×D16 | — | 6 | 2 | no | — |
| 69 | D3×D16 | — | 6 | 2 | no | — |
| 70 | C2×D48 | — | 3 | 2 | no | — |
| 71 | C2×D48 | — | 6 | 1 | no | — |
| 72 | C2×D3×C16 | — | 3 | 2 | no | — |
| 73 | C2×D3×C16 | — | 6 | 1 | no | — |
| 74 | D3×#108 | — | 6 | 2 | no | — |
| 75 | C3×M64 | — | 3 | 2 | no | — |
| 76 | C3×#368 | — | 3 | 2 | no | — |
| 77 | #4506 | C2×D3 | 1 | 2 | yes | complemented |
| 78 | #4499 | C2×D3 | 1 | 2 | yes | complemented |
| 79 | #4493 | — | 6 | 2 | no | — |
| 80 | #4447 | — | 6 | 2 | no | — |
| 81 | D3×C32 | — | 6 | 2 | no | — |
| 82 | C23×C3⋊D3 | — | 8 | 1 | no | — |
| 83 | C2×C32×D4 | — | 4 | 1 | no | — |
| 84 | C2×#638 | — | 8 | 1 | no | — |
| 85 | D4×C3⋊D3 | — | 4 | 2 | no | — |
| 86 | D4×C3⋊D3 | — | 4 | 2 | no | — |
| 87 | D4×C3⋊D3 | — | 8 | 1 | no | — |
| 88 | D4×C3⋊D3 | — | 8 | 1 | no | — |
| 89 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 90 | C2×C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 91 | C32×D8 | — | 2 | 2 | no | — |
| 92 | C32×D8 | — | 4 | 1 | no | — |
| 93 | C2×C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | #3753 | — | 4 | 2 | no | — |
| 95 | #3753 | — | 4 | 2 | no | — |
| 96 | C2×C3⋊(C3⋊C8) | D8 | 1 | 1 | yes | characteristic |
| 97 | #3745 | — | 2 | 2 | no | — |
| 98 | #3745 | — | 4 | 1 | no | — |
| 99 | C8×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | C8×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 101 | C8×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 102 | C8×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic |
| 103 | C3×#208 | — | 4 | 2 | no | — |
| 104 | #3712 | — | 8 | 1 | no | — |
| 105 | #3710 | — | 8 | 1 | no | — |
| 106 | C32×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C32×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C3⋊(C3⋊C16) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | C3⋊(C3⋊C16) | C22⋊C4 | 1 | 1 | yes | characteristic |
| 110 | C22×D16 | — | 9 | 1 | no | — |
| 111 | C2×M64 | — | 9 | 1 | no | — |
| 112 | C2×#368 | — | 9 | 1 | no | — |
| 113 | #1419 | — | 3 | 2 | no | — |
| 114 | #1419 | — | 9 | 2 | no | — |
| 115 | C2×D3×D4 | — | 12 | 2 | no | — |
| 116 | C2×D3×D4 | — | 12 | 2 | no | — |
| 117 | C2×C3×D8 | — | 2 | 2 | no | — |
| 118 | C2×C3×D8 | — | 2 | 2 | no | — |
| 119 | C2×#213 | — | 12 | 2 | no | — |
| 120 | C2×#213 | — | 12 | 2 | no | — |
| 121 | D3×D8 | — | 6 | 4 | no | — |
| 122 | D3×D8 | — | 6 | 4 | no | — |
| 123 | D3×D8 | — | 6 | 4 | no | — |
| 124 | D3×D8 | — | 6 | 4 | no | — |
| 125 | D3×D8 | — | 12 | 2 | no | — |
| 126 | D3×D8 | — | 12 | 2 | no | — |
| 127 | D3×D8 | — | 12 | 2 | no | — |
| 128 | D3×D8 | — | 12 | 2 | no | — |
| 129 | D3×M16 | — | 12 | 2 | no | — |
| 130 | C2×D24 | — | 6 | 2 | no | — |
| 131 | C2×D24 | — | 6 | 2 | no | — |
| 132 | C2×D3×C8 | — | 3 | 2 | no | — |
| 133 | C2×D3×C8 | — | 6 | 1 | no | — |
| 134 | C3×D16 | — | 2 | 2 | no | — |
| 135 | C3×D16 | — | 2 | 2 | no | — |
| 136 | C3×D16 | — | 2 | 2 | no | — |
| 137 | C3×D16 | C4×D3 | 1 | 4 | yes | — |
| 138 | C2×C3×C16 | — | 2 | 1 | no | — |
| 139 | C2×C3×C16 | C22×D3 | 1 | 2 | yes | — |
| 140 | C3×#108 | — | 6 | 2 | no | — |
| 141 | #826 | — | 6 | 4 | no | — |
| 142 | #826 | — | 6 | 4 | no | — |
| 143 | #826 | — | 6 | 4 | no | — |
| 144 | #826 | — | 6 | 4 | no | — |
| 145 | #822 | — | 12 | 2 | no | — |
| 146 | #819 | — | 2 | 2 | no | — |
| 147 | C2×C3⋊C16 | — | 3 | 2 | no | — |
| 148 | C2×C3⋊C16 | — | 6 | 1 | no | — |
| 149 | D48 | — | 3 | 4 | no | — |
| 150 | D48 | — | 6 | 2 | no | — |
| 151 | D48 | — | 6 | 2 | no | — |
| 152 | D48 | — | 6 | 2 | no | — |
| 153 | D3×C16 | — | 3 | 2 | no | — |
| 154 | D3×C16 | — | 3 | 2 | no | — |
| 155 | D3×C16 | — | 3 | 2 | no | — |
| 156 | D3×C16 | — | 3 | 2 | no | — |
| 157 | D3×C16 | — | 6 | 1 | no | — |
| 158 | D3×C16 | — | 6 | 1 | no | — |
| 159 | D3×C16 | — | 6 | 1 | no | — |
| 160 | D3×C16 | — | 6 | 1 | no | — |
| 161 | C3×C32 | — | 6 | 2 | no | — |
| 162 | C3⋊C32 | — | 2 | 2 | no | — |
| 163 | C23×C32 | — | 8 | 1 | no | — |
| 164 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 165 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 166 | C22×C3⋊D3 | — | 8 | 2 | no | — |
| 167 | C22×C3⋊D3 | — | 16 | 4 | no | — |
| 168 | C22×C3⋊D3 | SD32 | 1 | 1 | yes | characteristic |
| 169 | C32×D4 | — | 4 | 2 | no | — |
| 170 | C32×D4 | — | 8 | 1 | no | — |
| 171 | C2×C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 172 | #638 | — | 8 | 2 | no | — |
| 173 | #638 | — | 8 | 2 | no | — |
| 174 | C2×C3⋊Dic3 | SD32 | 1 | 1 | yes | characteristic |
| 175 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 176 | C4⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 177 | C4×C3⋊D3 | #102 | 1 | 1 | yes | characteristic |
| 178 | C4×C3⋊D3 | #102 | 1 | 1 | yes | characteristic |
| 179 | C4×C3⋊D3 | D16 | 1 | 1 | yes | characteristic |
| 180 | C4×C3⋊D3 | D16 | 1 | 1 | yes | characteristic |
| 181 | C32×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C32×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 183 | C3⋊(C3⋊C8) | #102 | 1 | 1 | yes | characteristic |
| 184 | C3⋊(C3⋊C8) | #102 | 1 | 1 | yes | characteristic |
| 185 | C3×C3⋊C8 | — | 8 | 2 | no | — |
| 186 | C22×D8 | — | 18 | 1 | no | — |
| 187 | C2×D16 | — | 9 | 2 | no | — |
| 188 | C2×D16 | — | 9 | 2 | no | — |
| 189 | C2×D16 | — | 9 | 1 | no | — |
| 190 | C2×D16 | — | 18 | 1 | no | — |
| 191 | C2×D16 | — | 18 | 1 | no | — |
| 192 | C2×D16 | — | 18 | 1 | no | — |
| 193 | C2×D16 | D32 | 1 | 1 | yes | characteristic |
| 194 | C22×C16 | — | 9 | 1 | no | — |
| 195 | C2×#108 | — | 18 | 1 | no | — |
| 196 | M64 | — | 3 | 2 | no | — |
| 197 | M64 | — | 18 | 1 | no | — |
| 198 | C2×C32 | — | 18 | 1 | no | — |
| 199 | #368 | — | 3 | 2 | no | — |
| 200 | #368 | — | 18 | 1 | no | — |
| 201 | C23×D3 | — | 24 | 2 | no | — |
| 202 | C23×D3 | — | 24 | 2 | no | — |
| 203 | C2×C3×D4 | — | 4 | 2 | no | — |
| 204 | C2×C3×D4 | — | 4 | 2 | no | — |
| 205 | C2×#67 | — | 24 | 2 | no | — |
| 206 | C2×#67 | — | 24 | 2 | no | — |
| 207 | D3×D4 | — | 12 | 4 | no | — |
| 208 | D3×D4 | — | 12 | 4 | no | — |
| 209 | D3×D4 | — | 12 | 4 | no | — |
| 210 | D3×D4 | — | 12 | 4 | no | — |
| 211 | D3×D4 | — | 24 | 2 | no | — |
| 212 | D3×D4 | — | 24 | 2 | no | — |
| 213 | D3×D4 | — | 24 | 2 | no | — |
| 214 | D3×D4 | — | 24 | 2 | no | — |
| 215 | C2×D12 | — | 12 | 2 | no | — |
| 216 | C2×D12 | — | 12 | 2 | no | — |
| 217 | C2×C4×D3 | — | 3 | 2 | no | — |
| 218 | C2×C4×D3 | — | 6 | 1 | no | — |
| 219 | C3×D8 | — | 2 | 4 | no | — |
| 220 | C3×D8 | — | 2 | 4 | no | — |
| 221 | C3×D8 | — | 4 | 2 | no | — |
| 222 | C3×D8 | — | 4 | 2 | no | — |
| 223 | C3×M16 | — | 12 | 2 | no | — |
| 224 | C2×C3×C8 | — | 2 | 1 | no | — |
| 225 | C2×C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 226 | #213 | — | 12 | 4 | no | — |
| 227 | #213 | — | 12 | 4 | no | — |
| 228 | #213 | — | 12 | 4 | no | — |
| 229 | #213 | — | 12 | 4 | no | — |
| 230 | #208 | — | 4 | 2 | no | — |
| 231 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 232 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 233 | D24 | — | 6 | 4 | no | — |
| 234 | D24 | — | 6 | 4 | no | — |
| 235 | D24 | — | 12 | 2 | no | — |
| 236 | D24 | — | 12 | 2 | no | — |
| 237 | ΓL(1,𝔽25) | — | 24 | 2 | no | — |
| 238 | D3×C8 | — | 3 | 2 | no | — |
| 239 | D3×C8 | — | 3 | 2 | no | — |
| 240 | D3×C8 | — | 3 | 2 | no | — |
| 241 | D3×C8 | — | 3 | 2 | no | — |
| 242 | D3×C8 | — | 6 | 1 | no | — |
| 243 | D3×C8 | — | 6 | 1 | no | — |
| 244 | D3×C8 | — | 6 | 1 | no | — |
| 245 | D3×C8 | — | 6 | 1 | no | — |
| 246 | D3×C8 | — | 24 | 2 | no | — |
| 247 | C3×C16 | — | 2 | 1 | no | — |
| 248 | C3×C16 | — | 2 | 1 | no | — |
| 249 | C3×C16 | C2×C4×D3 | 1 | 2 | yes | — |
| 250 | C3×C16 | D3×D4 | 1 | 2 | yes | — |
| 251 | C3⋊C16 | — | 3 | 2 | no | — |
| 252 | C3⋊C16 | — | 3 | 2 | no | — |
| 253 | C3⋊C16 | — | 6 | 1 | no | — |
| 254 | C3⋊C16 | — | 6 | 1 | no | — |
| 255 | C22×C32 | — | 8 | 2 | no | — |
| 256 | C22×C32 | — | 16 | 2 | no | — |
| 257 | C22×C32 | C2×SD32 | 1 | 1 | yes | characteristic |
| 258 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 259 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 260 | C2×C3⋊D3 | — | 16 | 4 | no | — |
| 261 | C2×C3⋊D3 | — | 16 | 2 | no | — |
| 262 | C2×C3⋊D3 | — | 16 | 4 | no | — |
| 263 | C2×C3⋊D3 | #357 | 1 | 1 | yes | characteristic |
| 264 | C2×C3⋊D3 | #357 | 1 | 1 | yes | characteristic |
| 265 | C32×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 266 | C32×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 267 | C3⋊Dic3 | #357 | 1 | 1 | yes | characteristic |
| 268 | C3⋊Dic3 | #357 | 1 | 1 | yes | characteristic |
| 269 | C22×D4 | — | 36 | 1 | no | — |
| 270 | C2×D8 | — | 2 | 1 | no | — |
| 271 | C2×D8 | — | 18 | 2 | no | — |
| 272 | C2×D8 | — | 18 | 2 | no | — |
| 273 | C2×D8 | — | 18 | 1 | no | — |
| 274 | C2×D8 | — | 36 | 1 | no | — |
| 275 | C2×D8 | — | 36 | 1 | no | — |
| 276 | C2×D8 | — | 36 | 1 | no | — |
| 277 | C2×M16 | — | 36 | 1 | no | — |
| 278 | C22×C8 | — | 9 | 1 | no | — |
| 279 | D16 | — | 2 | 1 | no | — |
| 280 | D16 | — | 9 | 2 | no | — |
| 281 | D16 | — | 18 | 2 | no | — |
| 282 | D16 | — | 18 | 2 | no | — |
| 283 | D16 | — | 18 | 1 | no | — |
| 284 | D16 | #624 | 1 | 2 | yes | — |
| 285 | C2×C16 | — | 9 | 1 | no | — |
| 286 | C2×C16 | — | 9 | 1 | no | — |
| 287 | C2×C16 | — | 9 | 1 | no | — |
| 288 | C2×C16 | — | 9 | 1 | no | — |
| 289 | C2×C16 | — | 9 | 1 | no | — |
| 290 | C2×C16 | C2×D32 | 1 | 1 | yes | characteristic |
| 291 | #108 | — | 6 | 2 | no | — |
| 292 | #108 | — | 36 | 1 | no | — |
| 293 | C32 | — | 6 | 2 | no | — |
| 294 | C23×C3 | — | 8 | 2 | no | — |
| 295 | C23×C3 | — | 8 | 2 | no | — |
| 296 | C22×D3 | — | 3 | 2 | no | — |
| 297 | C22×D3 | — | 6 | 1 | no | — |
| 298 | C22×D3 | — | 24 | 4 | no | — |
| 299 | C22×D3 | — | 24 | 4 | no | — |
| 300 | C22×D3 | — | 24 | 4 | no | — |
| 301 | C22×D3 | — | 24 | 4 | no | — |
| 302 | C22×D3 | — | 24 | 2 | no | — |
| 303 | C22×D3 | — | 24 | 2 | no | — |
| 304 | C22×D3 | — | 48 | 8 | no | — |
| 305 | C22×D3 | — | 48 | 8 | no | — |
| 306 | C3×D4 | — | 4 | 4 | no | — |
| 307 | C3×D4 | — | 4 | 4 | no | — |
| 308 | C3×D4 | — | 8 | 2 | no | — |
| 309 | C3×D4 | — | 8 | 2 | no | — |
| 310 | C2×C3×C4 | — | 2 | 1 | no | — |
| 311 | C2×C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 312 | #67 | — | 24 | 4 | no | — |
| 313 | #67 | — | 24 | 4 | no | — |
| 314 | #67 | — | 24 | 4 | no | — |
| 315 | #67 | — | 24 | 4 | no | — |
| 316 | C2×Dic3 | — | 3 | 2 | no | — |
| 317 | C2×Dic3 | — | 6 | 1 | no | — |
| 318 | D12 | — | 12 | 4 | no | — |
| 319 | D12 | — | 12 | 4 | no | — |
| 320 | D12 | — | 24 | 2 | no | — |
| 321 | D12 | — | 24 | 2 | no | — |
| 322 | C4×D3 | — | 3 | 2 | no | — |
| 323 | C4×D3 | — | 3 | 2 | no | — |
| 324 | C4×D3 | — | 3 | 2 | no | — |
| 325 | C4×D3 | — | 3 | 2 | no | — |
| 326 | C4×D3 | — | 6 | 1 | no | — |
| 327 | C4×D3 | — | 6 | 1 | no | — |
| 328 | C4×D3 | — | 6 | 1 | no | — |
| 329 | C4×D3 | — | 6 | 1 | no | — |
| 330 | C3×C8 | — | 2 | 1 | no | — |
| 331 | C3×C8 | — | 2 | 1 | no | — |
| 332 | C3×C8 | — | 24 | 2 | no | — |
| 333 | C3×C8 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 334 | C3×C8 | D3×SD16 | 1 | 2 | yes | — |
| 335 | C3⋊C8 | — | 3 | 2 | no | — |
| 336 | C3⋊C8 | — | 3 | 2 | no | — |
| 337 | C3⋊C8 | — | 6 | 1 | no | — |
| 338 | C3⋊C8 | — | 6 | 1 | no | — |
| 339 | C3⋊C8 | — | 8 | 2 | no | — |
| 340 | C2×C32 | — | 2 | 1 | no | — |
| 341 | C2×C32 | — | 16 | 2 | no | — |
| 342 | C2×C32 | C2×#357 | 1 | 1 | yes | characteristic |
| 343 | C3⋊D3 | — | 2 | 1 | no | — |
| 344 | C3⋊D3 | — | 16 | 2 | no | — |
| 345 | C3⋊D3 | #1419 | 1 | 2 | yes | complemented |
| 346 | C24 | — | 72 | 1 | no | — |
| 347 | C2×D4 | — | 4 | 1 | no | — |
| 348 | C2×D4 | — | 36 | 2 | no | — |
| 349 | C2×D4 | — | 36 | 2 | no | — |
| 350 | C2×D4 | — | 36 | 1 | no | — |
| 351 | C2×D4 | — | 72 | 1 | no | — |
| 352 | C2×D4 | — | 72 | 1 | no | — |
| 353 | C2×D4 | — | 72 | 1 | no | — |
| 354 | C22×C4 | — | 9 | 1 | no | — |
| 355 | D8 | — | 2 | 2 | no | — |
| 356 | D8 | — | 4 | 1 | no | — |
| 357 | D8 | — | 18 | 2 | no | — |
| 358 | D8 | — | 36 | 2 | no | — |
| 359 | D8 | — | 36 | 2 | no | — |
| 360 | D8 | — | 36 | 1 | no | — |
| 361 | M16 | — | 12 | 2 | no | — |
| 362 | M16 | — | 72 | 1 | no | — |
| 363 | C2×C8 | — | 9 | 1 | no | — |
| 364 | C2×C8 | — | 9 | 1 | no | — |
| 365 | C2×C8 | — | 9 | 1 | no | — |
| 366 | C2×C8 | — | 9 | 1 | no | — |
| 367 | C2×C8 | — | 9 | 1 | no | — |
| 368 | C2×C8 | — | 72 | 1 | no | — |
| 369 | C2×C8 | #3811 | 1 | 1 | yes | characteristic |
| 370 | C16 | — | 9 | 1 | no | — |
| 371 | C16 | — | 9 | 1 | no | — |
| 372 | C16 | C2×#624 | 1 | 1 | yes | characteristic |
| 373 | C16 | #3811 | 1 | 1 | yes | characteristic |
| 374 | C22×C3 | — | 2 | 1 | no | — |
| 375 | C22×C3 | — | 8 | 4 | no | — |
| 376 | C22×C3 | — | 8 | 4 | no | — |
| 377 | C22×C3 | — | 16 | 4 | no | — |
| 378 | C22×C3 | — | 16 | 4 | no | — |
| 379 | C22×C3 | D3×SD32 | 1 | 2 | yes | — |
| 380 | C2×D3 | — | 3 | 2 | no | — |
| 381 | C2×D3 | — | 3 | 2 | no | — |
| 382 | C2×D3 | — | 6 | 1 | no | — |
| 383 | C2×D3 | — | 6 | 1 | no | — |
| 384 | C2×D3 | — | 6 | 4 | no | — |
| 385 | C2×D3 | — | 6 | 4 | no | — |
| 386 | C2×D3 | — | 24 | 4 | no | — |
| 387 | C2×D3 | — | 24 | 4 | no | — |
| 388 | C2×D3 | — | 48 | 8 | no | — |
| 389 | C2×D3 | — | 48 | 8 | no | — |
| 390 | C2×D3 | — | 48 | 8 | no | — |
| 391 | C2×D3 | — | 48 | 8 | no | — |
| 392 | C2×D3 | — | 48 | 4 | no | — |
| 393 | C2×D3 | — | 48 | 4 | no | — |
| 394 | C3×C4 | — | 2 | 1 | no | — |
| 395 | C3×C4 | — | 2 | 1 | no | — |
| 396 | C3×C4 | D3×#102 | 1 | 2 | yes | — |
| 397 | C3×C4 | D3×D16 | 1 | 2 | yes | — |
| 398 | Dic3 | — | 3 | 2 | no | — |
| 399 | Dic3 | — | 3 | 2 | no | — |
| 400 | Dic3 | — | 6 | 1 | no | — |
| 401 | Dic3 | — | 6 | 1 | no | — |
| 402 | C32 | C2×#1419 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 403 | C23 | — | 8 | 1 | no | — |
| 404 | C23 | — | 9 | 1 | no | — |
| 405 | C23 | — | 72 | 2 | no | — |
| 406 | C23 | — | 72 | 2 | no | — |
| 407 | C23 | — | 72 | 1 | no | — |
| 408 | C23 | — | 144 | 4 | no | — |
| 409 | D4 | — | 4 | 2 | no | — |
| 410 | D4 | — | 8 | 1 | no | — |
| 411 | D4 | — | 36 | 2 | no | — |
| 412 | D4 | — | 72 | 2 | no | — |
| 413 | D4 | — | 72 | 2 | no | — |
| 414 | D4 | — | 72 | 1 | no | — |
| 415 | C2×C4 | — | 9 | 1 | no | — |
| 416 | C2×C4 | — | 9 | 1 | no | — |
| 417 | C2×C4 | — | 9 | 1 | no | — |
| 418 | C2×C4 | — | 9 | 1 | no | — |
| 419 | C2×C4 | — | 9 | 1 | no | — |
| 420 | C2×C4 | #63926 | 1 | 1 | yes | characteristic |
| 421 | C8 | — | 9 | 1 | no | — |
| 422 | C8 | — | 9 | 1 | no | — |
| 423 | C8 | — | 24 | 2 | no | — |
| 424 | C8 | #63930 | 1 | 1 | yes | characteristic |
| 425 | C8 | #63974 | 1 | 1 | yes | characteristic |
| 426 | C2×C3 | — | 2 | 2 | no | — |
| 427 | C2×C3 | — | 2 | 2 | no | — |
| 428 | C2×C3 | — | 2 | 1 | no | — |
| 429 | C2×C3 | — | 16 | 4 | no | — |
| 430 | C2×C3 | — | 16 | 4 | no | — |
| 431 | C2×C3 | D3×#357 | 1 | 2 | yes | — |
| 432 | D3 | — | 3 | 4 | no | — |
| 433 | D3 | — | 6 | 2 | no | — |
| 434 | D3 | — | 6 | 2 | no | — |
| 435 | D3 | — | 6 | 2 | no | — |
| 436 | D3 | — | 48 | 4 | no | — |
| 437 | D3 | — | 48 | 4 | no | — |
| 438 | C22 | — | 8 | 2 | no | — |
| 439 | C22 | — | 9 | 1 | no | — |
| 440 | C22 | — | 9 | 1 | no | — |
| 441 | C22 | — | 16 | 2 | no | — |
| 442 | C22 | — | 18 | 2 | no | — |
| 443 | C22 | — | 72 | 2 | no | — |
| 444 | C22 | — | 144 | 2 | no | — |
| 445 | C22 | — | 144 | 4 | no | — |
| 446 | C22 | — | 144 | 4 | no | — |
| 447 | C22 | #10591029 | 1 | 1 | yes | characteristic |
| 448 | C4 | — | 9 | 1 | no | — |
| 449 | C4 | — | 9 | 1 | no | — |
| 450 | C4 | #10591025 | 1 | 1 | yes | characteristic |
| 451 | C4 | #10591416 | 1 | 1 | yes | characteristic |
| 452 | C3 | — | 2 | 1 | no | — |
| 453 | C3 | D3×#1419 | 1 | 2 | yes | complemented |
| 454 | C2 | — | 2 | 1 | no | — |
| 455 | C2 | — | 9 | 2 | no | — |
| 456 | C2 | — | 16 | 2 | no | — |
| 457 | C2 | — | 18 | 1 | no | — |
| 458 | C2 | — | 144 | 2 | no | — |
| 459 | C2 | #11796597 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11800468 | C2 | semidirect |
| 3. #11797257 | C2 | semidirect |
| 4. #11772984 | C2 | semidirect |
| 5. C3×#67825 | C2 | semidirect |
| 17. C3×#4506 | C22 | semidirect |
| 18. C3×#4499 | C22 | semidirect |
| 27. #67825 | D3 | semidirect |
| 77. #4506 | C2×D3 | semidirect |
| 78. #4499 | C2×D3 | semidirect |
| 345. C3⋊D3 | #1419 | semidirect |
| 402. C32 | C2×#1419 | semidirect |
| 453. C3 | D3×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊D3×D16 | 2 |
| #11800468 | 2 |
| #11797257 | 2 |
| #11772984 | 2 |
| C3×#67825 | 2 |
| D3×#1419 | 3 |