Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
481 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 481 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #10594676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#4908 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590633 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589124 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71516 | — | 3 | 1 | no | maximal |
| 9 | #69120 | — | 3 | 1 | no | maximal |
| 10 | D3×#235 | — | 2 | 1 | no | — |
| 11 | #64113 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#904 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C3×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic |
| 15 | #63908 | — | 2 | 1 | no | — |
| 16 | #63829 | — | 2 | 1 | no | — |
| 17 | #63801 | — | 2 | 1 | no | — |
| 18 | #63800 | — | 2 | 1 | no | — |
| 19 | #63795 | — | 2 | 1 | no | — |
| 20 | #63794 | — | 2 | 1 | no | — |
| 21 | C32×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #63644 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#812 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×#800 | — | 2 | 1 | no | — |
| 25 | C3×D48 | — | 2 | 1 | no | — |
| 26 | #63563 | — | 2 | 1 | no | — |
| 27 | #63548 | — | 2 | 1 | no | — |
| 28 | #63546 | — | 2 | 1 | no | — |
| 29 | #5768 | — | 3 | 1 | no | — |
| 30 | #5748 | — | 3 | 1 | no | — |
| 31 | C3×#509 | — | 3 | 1 | no | — |
| 32 | #5159 | — | 3 | 1 | no | — |
| 33 | #5147 | — | 3 | 1 | no | — |
| 34 | #5135 | — | 3 | 1 | no | — |
| 35 | #4908 | — | 3 | 1 | no | — |
| 36 | #4908 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#349 | — | 3 | 1 | no | — |
| 38 | #4566 | — | 3 | 1 | no | — |
| 39 | #4518 | — | 3 | 1 | no | — |
| 40 | #4518 | — | 3 | 1 | no | — |
| 41 | #4518 | — | 3 | 1 | no | — |
| 42 | #4518 | — | 6 | 1 | no | — |
| 43 | #4514 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | #3828 | — | 2 | 1 | no | — |
| 45 | C3×#235 | — | 2 | 1 | no | — |
| 46 | C2×C3×D12 | — | 2 | 1 | no | — |
| 47 | C2×C3×C4×D3 | D4 | 1 | 1 | yes | characteristic |
| 48 | D3×#67 | — | 4 | 1 | no | — |
| 49 | C2×#625 | — | 4 | 1 | no | — |
| 50 | #3804 | — | 4 | 1 | no | — |
| 51 | D3×D12 | — | 2 | 1 | no | — |
| 52 | C4×D32 | — | 4 | 1 | no | — |
| 53 | #3799 | — | 2 | 1 | no | — |
| 54 | #3798 | — | 4 | 1 | no | — |
| 55 | #3795 | — | 2 | 1 | no | — |
| 56 | D3×Dic6 | — | 2 | 1 | no | — |
| 57 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 58 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 59 | #3746 | D4 | 1 | 1 | yes | characteristic, complemented |
| 60 | #3745 | D4 | 1 | 1 | yes | characteristic, complemented |
| 61 | #3744 | — | 2 | 1 | no | — |
| 62 | C2×C3×C3⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 63 | C3×Dic12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C3×D24 | — | 2 | 1 | no | — |
| 65 | C3×D24 | — | 2 | 1 | no | — |
| 66 | C3×D24 | D4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#204 | — | 2 | 1 | no | — |
| 68 | C3×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 69 | C3×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 70 | (C2×D3)⋊Dic3 | — | 4 | 1 | no | — |
| 71 | #3719 | — | 2 | 1 | no | — |
| 72 | #3717 | — | 2 | 1 | no | — |
| 73 | #3716 | — | 2 | 1 | no | — |
| 74 | #3714 | — | 2 | 1 | no | — |
| 75 | C32×C16 | — | 2 | 1 | no | — |
| 76 | C3×C3⋊C16 | — | 2 | 1 | no | — |
| 77 | #2190 | — | 9 | 1 | no | Sylow |
| 78 | D3×#41 | — | 6 | 1 | no | — |
| 79 | C2×#235 | — | 6 | 1 | no | — |
| 80 | C3×#135 | — | 3 | 1 | no | — |
| 81 | C2×C3×D8 | — | 3 | 1 | no | — |
| 82 | C2×C3×M16 | — | 3 | 1 | no | — |
| 83 | #950 | — | 6 | 1 | no | — |
| 84 | #938 | — | 6 | 1 | no | — |
| 85 | #930 | — | 6 | 1 | no | — |
| 86 | #918 | — | 6 | 1 | no | — |
| 87 | #915 | — | 6 | 1 | no | — |
| 88 | #914 | — | 6 | 1 | no | — |
| 89 | #911 | — | 6 | 1 | no | — |
| 90 | #909 | — | 6 | 1 | no | — |
| 91 | #909 | — | 6 | 1 | no | — |
| 92 | #908 | — | 6 | 1 | no | — |
| 93 | #908 | — | 6 | 1 | no | — |
| 94 | #904 | — | 3 | 1 | no | — |
| 95 | #904 | — | 3 | 1 | no | — |
| 96 | #904 | — | 6 | 1 | no | — |
| 97 | #904 | — | 6 | 1 | no | — |
| 98 | #904 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C2×D24 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 100 | C2×ΓL(1,𝔽25) | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | C3×SD32 | — | 6 | 1 | no | — |
| 102 | C3×D16 | — | 6 | 1 | no | — |
| 103 | C3×M32 | — | 2 | 1 | no | — |
| 104 | C3×M32 | — | 3 | 1 | no | — |
| 105 | C3×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C3×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 107 | #832 | — | 6 | 1 | no | — |
| 108 | #827 | — | 6 | 1 | no | — |
| 109 | #826 | — | 6 | 1 | no | — |
| 110 | #821 | — | 6 | 1 | no | — |
| 111 | #817 | — | 3 | 1 | no | — |
| 112 | #817 | — | 3 | 1 | no | — |
| 113 | #817 | — | 6 | 1 | no | — |
| 114 | #812 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 115 | #800 | — | 2 | 1 | no | — |
| 116 | #800 | — | 6 | 1 | no | — |
| 117 | D48 | — | 2 | 1 | no | — |
| 118 | D48 | — | 6 | 1 | no | — |
| 119 | C22×C3×D3 | — | 4 | 1 | no | — |
| 120 | C22×C3×D3 | D8 | 1 | 1 | yes | characteristic |
| 121 | C2×D32 | — | 4 | 1 | no | — |
| 122 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | #638 | — | 4 | 1 | no | — |
| 124 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 125 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 126 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 127 | #634 | — | 2 | 1 | no | — |
| 128 | C3×#67 | — | 4 | 1 | no | — |
| 129 | C2×C3×Dic3 | D8 | 1 | 1 | yes | characteristic |
| 130 | C3×D12 | — | 2 | 1 | no | — |
| 131 | C3×D12 | — | 4 | 1 | no | — |
| 132 | C3×D12 | — | 4 | 1 | no | — |
| 133 | C3×C4×D3 | — | 2 | 1 | no | — |
| 134 | C3×C4×D3 | — | 2 | 1 | no | — |
| 135 | C3×C4×D3 | — | 4 | 1 | no | — |
| 136 | C3×Dic6 | — | 2 | 1 | no | — |
| 137 | #627 | — | 4 | 1 | no | — |
| 138 | #626 | — | 4 | 1 | no | — |
| 139 | #626 | — | 4 | 1 | no | — |
| 140 | #625 | — | 4 | 1 | no | — |
| 141 | #625 | — | 8 | 2 | no | — |
| 142 | #624 | — | 4 | 1 | no | — |
| 143 | D3×Dic3 | — | 4 | 1 | no | — |
| 144 | D3×Dic3 | — | 4 | 1 | no | — |
| 145 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 148 | #575 | — | 9 | 1 | no | — |
| 149 | #509 | — | 3 | 1 | no | — |
| 150 | #509 | — | 9 | 1 | no | — |
| 151 | #469 | — | 9 | 1 | no | — |
| 152 | #360 | — | 9 | 1 | no | — |
| 153 | #360 | — | 9 | 1 | no | — |
| 154 | #349 | — | 3 | 1 | no | — |
| 155 | C3×#41 | — | 6 | 1 | no | — |
| 156 | C2×C3×D4 | — | 6 | 1 | no | — |
| 157 | C22×C3×C4 | — | 3 | 1 | no | — |
| 158 | C2×#67 | — | 12 | 1 | no | — |
| 159 | C2×#67 | — | 12 | 1 | no | — |
| 160 | C2×#67 | — | 12 | 1 | no | — |
| 161 | #239 | — | 6 | 1 | no | — |
| 162 | D3×Q8 | — | 6 | 1 | no | — |
| 163 | #237 | — | 6 | 1 | no | — |
| 164 | #237 | — | 12 | 1 | no | — |
| 165 | D3×D4 | — | 6 | 1 | no | — |
| 166 | D3×D4 | — | 12 | 1 | no | — |
| 167 | #235 | — | 2 | 1 | no | — |
| 168 | #235 | — | 6 | 1 | no | — |
| 169 | #235 | — | 6 | 1 | no | — |
| 170 | #235 | — | 6 | 1 | no | — |
| 171 | #235 | — | 6 | 1 | no | — |
| 172 | #235 | — | 12 | 1 | no | — |
| 173 | #235 | — | 12 | 1 | no | — |
| 174 | #235 | — | 12 | 1 | no | — |
| 175 | #235 | — | 12 | 1 | no | — |
| 176 | C2×D12 | — | 2 | 1 | no | — |
| 177 | C2×D12 | — | 6 | 1 | no | — |
| 178 | C2×C4×D3 | — | 12 | 1 | no | — |
| 179 | C2×C4×D3 | — | 12 | 1 | no | — |
| 180 | C2×C4×D3 | D12 | 1 | 1 | yes | characteristic |
| 181 | C2×Dic6 | — | 6 | 1 | no | — |
| 182 | C3×Q16 | — | 3 | 1 | no | — |
| 183 | C3×SD16 | — | 6 | 1 | no | — |
| 184 | C3×D8 | — | 3 | 1 | no | — |
| 185 | C3×D8 | — | 6 | 1 | no | — |
| 186 | C3×D8 | — | 6 | 1 | no | — |
| 187 | C3×M16 | — | 6 | 1 | no | — |
| 188 | C3×M16 | — | 6 | 1 | no | — |
| 189 | C2×C3×C8 | — | 2 | 1 | no | — |
| 190 | C2×C3×C8 | — | 3 | 1 | no | — |
| 191 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 192 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | #217 | — | 12 | 1 | no | — |
| 194 | #216 | — | 6 | 1 | no | — |
| 195 | #215 | — | 6 | 1 | no | — |
| 196 | #214 | — | 6 | 1 | no | — |
| 197 | #213 | — | 6 | 1 | no | — |
| 198 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 199 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 200 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 201 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 202 | C2×C3⋊C8 | D12 | 1 | 1 | yes | characteristic |
| 203 | Dic12 | — | 3 | 1 | no | — |
| 204 | Dic12 | — | 3 | 1 | no | — |
| 205 | Dic12 | — | 6 | 1 | no | — |
| 206 | Dic12 | — | 6 | 1 | no | — |
| 207 | Dic12 | #67 | 1 | 1 | yes | characteristic, complemented |
| 208 | D24 | — | 2 | 1 | no | — |
| 209 | D24 | — | 2 | 1 | no | — |
| 210 | D24 | — | 3 | 1 | no | — |
| 211 | D24 | — | 3 | 1 | no | — |
| 212 | D24 | — | 6 | 1 | no | — |
| 213 | D24 | — | 6 | 1 | no | — |
| 214 | D24 | #67 | 1 | 1 | yes | characteristic, complemented |
| 215 | #204 | — | 2 | 1 | no | — |
| 216 | #204 | — | 6 | 1 | no | — |
| 217 | #204 | — | 6 | 1 | no | — |
| 218 | #204 | — | 6 | 1 | no | — |
| 219 | #204 | — | 6 | 1 | no | — |
| 220 | #204 | — | 12 | 1 | no | — |
| 221 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 222 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 223 | C3×C16 | — | 2 | 1 | no | — |
| 224 | C3×C16 | — | 2 | 1 | no | — |
| 225 | C3×C16 | — | 4 | 1 | no | — |
| 226 | C3×C16 | — | 6 | 1 | no | — |
| 227 | C3⋊C16 | — | 2 | 1 | no | — |
| 228 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 229 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 230 | C2×C3×D3 | — | 2 | 1 | no | — |
| 231 | C2×C3×D3 | — | 4 | 1 | no | — |
| 232 | C2×C3×D3 | — | 4 | 1 | no | — |
| 233 | C2×C3×D3 | — | 8 | 1 | no | — |
| 234 | C2×C3×D3 | — | 8 | 1 | no | — |
| 235 | C2×C3×D3 | — | 8 | 1 | no | — |
| 236 | D32 | — | 8 | 2 | no | — |
| 237 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 238 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 239 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 240 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 241 | C3×Dic3 | — | 2 | 1 | no | — |
| 242 | C3×Dic3 | — | 4 | 1 | no | — |
| 243 | C2×#41 | — | 18 | 1 | no | — |
| 244 | #137 | — | 18 | 1 | no | — |
| 245 | #137 | — | 18 | 1 | no | — |
| 246 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 247 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 248 | #135 | — | 3 | 1 | no | — |
| 249 | #135 | — | 9 | 1 | no | — |
| 250 | #135 | — | 18 | 1 | no | — |
| 251 | C2×D8 | — | 3 | 1 | no | — |
| 252 | C2×M16 | — | 3 | 1 | no | — |
| 253 | #121 | — | 18 | 1 | no | — |
| 254 | SD32 | — | 6 | 1 | no | — |
| 255 | SD32 | — | 18 | 1 | no | — |
| 256 | D16 | — | 6 | 1 | no | — |
| 257 | D16 | — | 18 | 1 | no | — |
| 258 | M32 | — | 3 | 1 | no | — |
| 259 | M32 | D32 | 1 | 1 | yes | characteristic, complemented |
| 260 | #106 | — | 9 | 1 | no | — |
| 261 | #102 | — | 18 | 1 | no | — |
| 262 | C23×C3 | — | 3 | 1 | no | — |
| 263 | C23×C3 | — | 12 | 1 | no | — |
| 264 | C22×D3 | — | 4 | 1 | no | — |
| 265 | C22×D3 | — | 12 | 1 | no | — |
| 266 | C22×D3 | — | 12 | 1 | no | — |
| 267 | C22×D3 | D24 | 1 | 1 | yes | characteristic |
| 268 | C3×Q8 | — | 6 | 1 | no | — |
| 269 | C3×D4 | — | 6 | 1 | no | — |
| 270 | C3×D4 | — | 12 | 1 | no | — |
| 271 | C3×D4 | — | 12 | 1 | no | — |
| 272 | C3×D4 | — | 12 | 1 | no | — |
| 273 | C2×C3×C4 | — | 2 | 1 | no | — |
| 274 | C2×C3×C4 | — | 3 | 1 | no | — |
| 275 | C2×C3×C4 | — | 6 | 1 | no | — |
| 276 | C2×C3×C4 | — | 6 | 1 | no | — |
| 277 | C2×C3×C4 | — | 12 | 1 | no | — |
| 278 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 279 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 280 | #67 | — | 4 | 1 | no | — |
| 281 | #67 | — | 12 | 1 | no | — |
| 282 | #67 | — | 12 | 1 | no | — |
| 283 | #67 | — | 12 | 1 | no | — |
| 284 | #67 | — | 12 | 1 | no | — |
| 285 | #67 | — | 12 | 1 | no | — |
| 286 | #67 | — | 12 | 1 | no | — |
| 287 | #67 | — | 24 | 1 | no | — |
| 288 | #67 | — | 24 | 2 | no | — |
| 289 | #67 | — | 24 | 2 | no | — |
| 290 | C2×Dic3 | — | 12 | 1 | no | — |
| 291 | C2×Dic3 | — | 12 | 1 | no | — |
| 292 | C2×Dic3 | — | 12 | 1 | no | — |
| 293 | C2×Dic3 | — | 12 | 1 | no | — |
| 294 | C2×Dic3 | — | 24 | 1 | no | — |
| 295 | C2×Dic3 | D24 | 1 | 1 | yes | characteristic |
| 296 | D12 | — | 2 | 1 | no | — |
| 297 | D12 | — | 4 | 1 | no | — |
| 298 | D12 | — | 4 | 1 | no | — |
| 299 | D12 | — | 6 | 1 | no | — |
| 300 | D12 | — | 6 | 1 | no | — |
| 301 | D12 | — | 12 | 1 | no | — |
| 302 | D12 | — | 12 | 1 | no | — |
| 303 | D12 | — | 12 | 1 | no | — |
| 304 | C4×D3 | — | 2 | 1 | no | — |
| 305 | C4×D3 | — | 2 | 1 | no | — |
| 306 | C4×D3 | — | 4 | 1 | no | — |
| 307 | C4×D3 | — | 12 | 1 | no | — |
| 308 | C4×D3 | — | 12 | 1 | no | — |
| 309 | C4×D3 | — | 12 | 1 | no | — |
| 310 | C4×D3 | — | 12 | 1 | no | — |
| 311 | C4×D3 | — | 12 | 1 | no | — |
| 312 | C4×D3 | — | 12 | 1 | no | — |
| 313 | C4×D3 | — | 24 | 1 | no | — |
| 314 | Dic6 | — | 2 | 1 | no | — |
| 315 | Dic6 | — | 6 | 1 | no | — |
| 316 | Dic6 | — | 6 | 1 | no | — |
| 317 | Dic6 | — | 12 | 1 | no | — |
| 318 | Dic6 | — | 12 | 1 | no | — |
| 319 | Dic6 | — | 12 | 1 | no | — |
| 320 | C3×C8 | — | 2 | 1 | no | — |
| 321 | C3×C8 | — | 2 | 1 | no | — |
| 322 | C3×C8 | — | 6 | 1 | no | — |
| 323 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 324 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 325 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 326 | C3×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 327 | C3⋊C8 | — | 2 | 1 | no | — |
| 328 | C2×C32 | — | 2 | 1 | no | — |
| 329 | C2×C32 | #447 | 1 | 1 | yes | characteristic |
| 330 | C3⋊D3 | — | 8 | 1 | no | — |
| 331 | C3×D3 | — | 4 | 1 | no | — |
| 332 | C3×D3 | — | 8 | 1 | no | — |
| 333 | C3×D3 | — | 16 | 1 | no | — |
| 334 | #41 | — | 6 | 1 | no | — |
| 335 | #41 | — | 18 | 1 | no | — |
| 336 | #41 | — | 18 | 1 | no | — |
| 337 | #41 | — | 18 | 1 | no | — |
| 338 | #41 | — | 36 | 1 | no | — |
| 339 | #41 | — | 36 | 1 | no | — |
| 340 | C2×Q8 | — | 18 | 1 | no | — |
| 341 | C2×D4 | — | 6 | 1 | no | — |
| 342 | C2×D4 | — | 18 | 1 | no | — |
| 343 | C2×D4 | — | 36 | 1 | no | — |
| 344 | C2×D4 | — | 36 | 1 | no | — |
| 345 | C22×C4 | — | 3 | 1 | no | — |
| 346 | C22×C4 | — | 36 | 1 | no | — |
| 347 | Q16 | — | 3 | 1 | no | — |
| 348 | Q16 | — | 9 | 1 | no | — |
| 349 | Q16 | — | 18 | 1 | no | — |
| 350 | SD16 | — | 6 | 1 | no | — |
| 351 | SD16 | — | 18 | 1 | no | — |
| 352 | SD16 | — | 18 | 1 | no | — |
| 353 | SD16 | — | 18 | 1 | no | — |
| 354 | D8 | — | 3 | 1 | no | — |
| 355 | D8 | — | 6 | 1 | no | — |
| 356 | D8 | — | 6 | 1 | no | — |
| 357 | D8 | — | 9 | 1 | no | — |
| 358 | D8 | — | 18 | 1 | no | — |
| 359 | M16 | — | 6 | 1 | no | — |
| 360 | M16 | — | 6 | 1 | no | — |
| 361 | C2×C8 | — | 3 | 1 | no | — |
| 362 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 363 | C4⋊C4 | — | 18 | 1 | no | — |
| 364 | C22⋊C4 | — | 36 | 1 | no | — |
| 365 | C16 | — | 2 | 1 | no | — |
| 366 | C16 | — | 6 | 1 | no | — |
| 367 | C22×C3 | — | 2 | 1 | no | — |
| 368 | C22×C3 | — | 6 | 1 | no | — |
| 369 | C22×C3 | — | 12 | 1 | no | — |
| 370 | C22×C3 | — | 12 | 1 | no | — |
| 371 | C22×C3 | — | 24 | 1 | no | — |
| 372 | C22×C3 | — | 24 | 1 | no | — |
| 373 | C22×C3 | — | 24 | 1 | no | — |
| 374 | C22×C3 | C2×D24 | 1 | 1 | yes | characteristic |
| 375 | C22×C3 | D3×D8 | 1 | 1 | yes | characteristic |
| 376 | C2×D3 | — | 2 | 1 | no | — |
| 377 | C2×D3 | — | 4 | 1 | no | — |
| 378 | C2×D3 | — | 4 | 1 | no | — |
| 379 | C2×D3 | — | 8 | 1 | no | — |
| 380 | C2×D3 | — | 8 | 1 | no | — |
| 381 | C2×D3 | — | 8 | 1 | no | — |
| 382 | C2×D3 | — | 12 | 1 | no | — |
| 383 | C2×D3 | — | 12 | 1 | no | — |
| 384 | C2×D3 | — | 24 | 1 | no | — |
| 385 | C2×D3 | — | 24 | 2 | no | — |
| 386 | C2×D3 | — | 24 | 2 | no | — |
| 387 | C3×C4 | — | 2 | 1 | no | — |
| 388 | C3×C4 | — | 2 | 1 | no | — |
| 389 | C3×C4 | — | 6 | 1 | no | — |
| 390 | C3×C4 | — | 12 | 1 | no | — |
| 391 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 392 | C3×C4 | #908 | 1 | 1 | yes | characteristic |
| 393 | C3×C4 | #911 | 1 | 1 | yes | characteristic |
| 394 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 395 | Dic3 | — | 2 | 1 | no | — |
| 396 | Dic3 | — | 4 | 1 | no | — |
| 397 | Dic3 | — | 12 | 1 | no | — |
| 398 | Dic3 | — | 12 | 1 | no | — |
| 399 | Dic3 | — | 24 | 1 | no | — |
| 400 | Dic3 | — | 24 | 1 | no | — |
| 401 | Dic3 | — | 24 | 1 | no | — |
| 402 | Dic3 | — | 48 | 1 | no | — |
| 403 | C32 | #2190 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 404 | C23 | — | 3 | 1 | no | — |
| 405 | C23 | — | 12 | 1 | no | — |
| 406 | C23 | — | 36 | 1 | no | — |
| 407 | Q8 | — | 6 | 1 | no | — |
| 408 | Q8 | — | 18 | 1 | no | — |
| 409 | Q8 | — | 36 | 1 | no | — |
| 410 | D4 | — | 6 | 1 | no | — |
| 411 | D4 | — | 12 | 1 | no | — |
| 412 | D4 | — | 12 | 1 | no | — |
| 413 | D4 | — | 12 | 1 | no | — |
| 414 | D4 | — | 18 | 1 | no | — |
| 415 | D4 | — | 36 | 1 | no | — |
| 416 | D4 | — | 36 | 1 | no | — |
| 417 | D4 | — | 36 | 1 | no | — |
| 418 | D4 | — | 36 | 1 | no | — |
| 419 | D4 | — | 72 | 2 | no | — |
| 420 | C2×C4 | — | 3 | 1 | no | — |
| 421 | C2×C4 | — | 6 | 1 | no | — |
| 422 | C2×C4 | — | 6 | 1 | no | — |
| 423 | C2×C4 | — | 12 | 1 | no | — |
| 424 | C2×C4 | — | 36 | 1 | no | — |
| 425 | C2×C4 | — | 36 | 1 | no | — |
| 426 | C2×C4 | — | 36 | 1 | no | — |
| 427 | C2×C4 | — | 36 | 1 | no | — |
| 428 | C2×C4 | — | 36 | 1 | no | — |
| 429 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 430 | C8 | — | 6 | 1 | no | — |
| 431 | C8 | #3802 | 1 | 1 | yes | characteristic |
| 432 | C8 | D3×#67 | 1 | 1 | yes | characteristic |
| 433 | C2×C3 | — | 2 | 1 | no | — |
| 434 | C2×C3 | — | 2 | 1 | no | — |
| 435 | C2×C3 | — | 2 | 1 | no | — |
| 436 | C2×C3 | — | 4 | 1 | no | — |
| 437 | C2×C3 | — | 12 | 1 | no | — |
| 438 | C2×C3 | — | 24 | 1 | no | — |
| 439 | C2×C3 | — | 48 | 1 | no | — |
| 440 | C2×C3 | #4732 | 1 | 1 | yes | characteristic |
| 441 | C2×C3 | #5156 | 1 | 1 | yes | characteristic |
| 442 | D3 | — | 4 | 1 | no | — |
| 443 | D3 | — | 8 | 1 | no | — |
| 444 | D3 | — | 16 | 1 | no | — |
| 445 | D3 | — | 24 | 1 | no | — |
| 446 | D3 | — | 24 | 1 | no | — |
| 447 | D3 | — | 48 | 1 | no | — |
| 448 | C22 | — | 6 | 1 | no | — |
| 449 | C22 | — | 12 | 1 | no | — |
| 450 | C22 | — | 12 | 1 | no | — |
| 451 | C22 | — | 24 | 1 | no | — |
| 452 | C22 | — | 24 | 1 | no | — |
| 453 | C22 | — | 24 | 1 | no | — |
| 454 | C22 | — | 36 | 1 | no | — |
| 455 | C22 | — | 72 | 2 | no | — |
| 456 | C22 | D3×D24 | 1 | 1 | yes | characteristic |
| 457 | C4 | — | 6 | 1 | no | — |
| 458 | C4 | — | 12 | 1 | no | — |
| 459 | C4 | — | 36 | 1 | no | — |
| 460 | C4 | — | 72 | 1 | no | — |
| 461 | C4 | #63795 | 1 | 1 | yes | characteristic |
| 462 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 463 | C3 | — | 2 | 1 | no | — |
| 464 | C3 | #69120 | 1 | 1 | yes | characteristic, complemented |
| 465 | C3 | #71516 | 1 | 1 | yes | characteristic, complemented |
| 466 | C2 | — | 2 | 1 | no | — |
| 467 | C2 | — | 12 | 1 | no | — |
| 468 | C2 | — | 24 | 1 | no | — |
| 469 | C2 | — | 48 | 1 | no | — |
| 470 | C2 | — | 72 | 1 | no | — |
| 471 | C2 | #10590944 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10594676 | C2 | semidirect |
| 2. C3×#4908 | C2 | semidirect |
| 3. #10590836 | C2 | semidirect |
| 4. #10590633 | C2 | semidirect |
| 5. #10589384 | C2 | semidirect |
| 6. C3×#4514 | C2 | semidirect |
| 7. #10589124 | C2 | semidirect |
| 13. C2×C3×D24 | C22 | semidirect |
| 21. C32×M32 | C22 | semidirect |
| 22. #63644 | C22 | semidirect |
| 23. C3×#812 | C22 | semidirect |
| 36. #4908 | D3 | semidirect |
| 43. #4514 | D3 | semidirect |
| 59. #3746 | D4 | semidirect |
| 60. #3745 | D4 | semidirect |
| 63. C3×Dic12 | D4 | semidirect |
| 66. C3×D24 | D4 | semidirect |
| 99. C2×D24 | C2×D3 | semidirect |
| 105. C3×M32 | C2×D3 | semidirect |
| 106. C3×M32 | C2×D3 | semidirect |
| 114. #812 | C2×D3 | semidirect |
| 207. Dic12 | #67 | semidirect |
| 214. D24 | #67 | semidirect |
| 259. M32 | D32 | semidirect |
| 403. C32 | #2190 | semidirect |
| 464. C3 | #69120 | semidirect |
| 465. C3 | #71516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594676 | 2 |
| C3×#4908 | 2 |
| #10590836 | 2 |
| #10590633 | 2 |
| #10589384 | 2 |
| C3×#4514 | 2 |
| #10589124 | 2 |
| #71516 | 3 |
| #69120 | 3 |