Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
461 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #10594685 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#4909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590858 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589380 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589123 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71522 | — | 3 | 1 | no | maximal |
| 9 | #69253 | — | 3 | 1 | no | maximal |
| 10 | #64306 | — | 2 | 1 | no | — |
| 11 | C2×#3743 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×Dic12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×#904 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#904 | C22 | 1 | 1 | yes | characteristic |
| 15 | #63871 | — | 2 | 1 | no | — |
| 16 | #63822 | — | 2 | 1 | no | — |
| 17 | #63811 | — | 2 | 1 | no | — |
| 18 | #63811 | — | 2 | 1 | no | — |
| 19 | #63798 | — | 2 | 1 | no | — |
| 20 | #63798 | — | 2 | 1 | no | — |
| 21 | C32×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #63639 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#817 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×Dic24 | — | 2 | 1 | no | — |
| 25 | C3×#800 | — | 2 | 1 | no | — |
| 26 | #63565 | — | 2 | 1 | no | — |
| 27 | #63550 | — | 2 | 1 | no | — |
| 28 | #63547 | — | 2 | 1 | no | — |
| 29 | #5768 | — | 3 | 1 | no | — |
| 30 | #5768 | — | 3 | 1 | no | — |
| 31 | C3×#510 | — | 3 | 1 | no | — |
| 32 | #5195 | — | 3 | 1 | no | — |
| 33 | #5189 | — | 3 | 1 | no | — |
| 34 | #5179 | — | 3 | 1 | no | — |
| 35 | #4909 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | #4867 | — | 3 | 1 | no | — |
| 37 | C3×#360 | — | 3 | 1 | no | — |
| 38 | #4566 | — | 3 | 1 | no | — |
| 39 | #4518 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #4514 | — | 3 | 1 | no | — |
| 41 | #4514 | — | 3 | 1 | no | — |
| 42 | #4514 | — | 6 | 1 | no | — |
| 43 | #4488 | — | 3 | 1 | no | — |
| 44 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 45 | C3×#235 | — | 2 | 1 | no | — |
| 46 | C3×#235 | — | 2 | 1 | no | — |
| 47 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 48 | #3811 | — | 4 | 1 | no | — |
| 49 | #3805 | — | 4 | 1 | no | — |
| 50 | #3802 | — | 2 | 1 | no | — |
| 51 | C4×D32 | — | 4 | 1 | no | — |
| 52 | #3798 | — | 4 | 1 | no | — |
| 53 | #3797 | — | 2 | 1 | no | — |
| 54 | #3796 | — | 2 | 1 | no | — |
| 55 | #3796 | — | 2 | 1 | no | — |
| 56 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 58 | #3743 | — | 2 | 1 | no | — |
| 59 | #3743 | — | 2 | 1 | no | — |
| 60 | C3×C4⋊Dic3 | — | 2 | 1 | no | — |
| 61 | C3×Dic12 | — | 2 | 1 | no | — |
| 62 | C3×Dic12 | — | 2 | 1 | no | — |
| 63 | C3×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 64 | C3×Dic12 | D4 | 1 | 1 | yes | characteristic |
| 65 | C3×D24 | D4 | 1 | 1 | yes | characteristic |
| 66 | C3×D24 | D4 | 1 | 1 | yes | characteristic |
| 67 | C3×#204 | — | 2 | 1 | no | — |
| 68 | C3×#204 | — | 2 | 1 | no | — |
| 69 | Dic3⋊Dic3 | — | 4 | 1 | no | — |
| 70 | #3722 | — | 4 | 1 | no | — |
| 71 | #3718 | — | 2 | 1 | no | — |
| 72 | #3715 | — | 2 | 1 | no | — |
| 73 | #3715 | — | 2 | 1 | no | — |
| 74 | #3713 | — | 2 | 1 | no | — |
| 75 | C32×C16 | — | 2 | 1 | no | — |
| 76 | C3⋊(C3⋊C16) | — | 2 | 1 | no | — |
| 77 | #2191 | — | 9 | 1 | no | Sylow |
| 78 | D3×#41 | — | 6 | 1 | no | — |
| 79 | D3×#41 | — | 6 | 1 | no | — |
| 80 | C3×#135 | — | 3 | 1 | no | — |
| 81 | C3×#135 | — | 3 | 1 | no | — |
| 82 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 83 | #950 | — | 6 | 1 | no | — |
| 84 | #950 | — | 6 | 1 | no | — |
| 85 | #946 | — | 6 | 1 | no | — |
| 86 | #918 | — | 6 | 1 | no | — |
| 87 | #918 | — | 6 | 1 | no | — |
| 88 | #915 | — | 6 | 1 | no | — |
| 89 | #915 | — | 6 | 1 | no | — |
| 90 | #914 | — | 6 | 1 | no | — |
| 91 | #914 | — | 6 | 1 | no | — |
| 92 | #911 | — | 6 | 1 | no | — |
| 93 | #911 | — | 6 | 1 | no | — |
| 94 | C2×Dic12 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 95 | #904 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #904 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 98 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 99 | C2×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 100 | #897 | — | 6 | 1 | no | — |
| 101 | C3×Q32 | — | 6 | 1 | no | — |
| 102 | C3×SD32 | — | 6 | 1 | no | — |
| 103 | C3×M32 | — | 2 | 1 | no | — |
| 104 | C3×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 105 | C3×M32 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | C3×#106 | — | 3 | 1 | no | — |
| 107 | #835 | — | 6 | 1 | no | — |
| 108 | #829 | — | 6 | 1 | no | — |
| 109 | #829 | — | 6 | 1 | no | — |
| 110 | #828 | — | 6 | 1 | no | — |
| 111 | #827 | — | 6 | 1 | no | — |
| 112 | #817 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 113 | #812 | — | 3 | 1 | no | — |
| 114 | #812 | — | 3 | 1 | no | — |
| 115 | #812 | — | 6 | 1 | no | — |
| 116 | #810 | — | 6 | 1 | no | — |
| 117 | Dic24 | — | 2 | 1 | no | — |
| 118 | #800 | — | 2 | 1 | no | — |
| 119 | C22×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 120 | C2×D32 | — | 4 | 1 | no | — |
| 121 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 123 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 124 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 125 | C3×#67 | — | 4 | 1 | no | — |
| 126 | C3×#67 | — | 4 | 1 | no | — |
| 127 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 128 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 129 | C3×D12 | — | 2 | 1 | no | — |
| 130 | C3×D12 | — | 2 | 1 | no | — |
| 131 | C3×C4×D3 | — | 4 | 1 | no | — |
| 132 | C3×C4×D3 | — | 4 | 1 | no | — |
| 133 | C3×Dic6 | — | 2 | 1 | no | — |
| 134 | C3×Dic6 | — | 2 | 1 | no | — |
| 135 | C3×Dic6 | — | 4 | 1 | no | — |
| 136 | C3×Dic6 | — | 4 | 1 | no | — |
| 137 | #627 | — | 4 | 1 | no | — |
| 138 | #626 | — | 4 | 1 | no | — |
| 139 | #626 | — | 4 | 1 | no | — |
| 140 | #625 | — | 4 | 1 | no | — |
| 141 | #624 | — | 4 | 1 | no | — |
| 142 | D3×Dic3 | — | 4 | 1 | no | — |
| 143 | D3×Dic3 | — | 4 | 1 | no | — |
| 144 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 147 | #575 | — | 9 | 1 | no | — |
| 148 | #510 | — | 3 | 1 | no | — |
| 149 | #510 | — | 9 | 1 | no | — |
| 150 | #470 | — | 9 | 1 | no | — |
| 151 | #360 | — | 3 | 1 | no | — |
| 152 | #360 | — | 9 | 1 | no | — |
| 153 | #349 | — | 9 | 1 | no | — |
| 154 | C3×#41 | — | 6 | 1 | no | — |
| 155 | C3×#41 | — | 6 | 1 | no | — |
| 156 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 157 | #239 | — | 6 | 1 | no | — |
| 158 | #239 | — | 6 | 1 | no | — |
| 159 | D3×Q8 | — | 6 | 1 | no | — |
| 160 | D3×Q8 | — | 6 | 1 | no | — |
| 161 | #237 | — | 6 | 1 | no | — |
| 162 | #237 | — | 6 | 1 | no | — |
| 163 | #237 | — | 12 | 1 | no | — |
| 164 | #237 | — | 12 | 1 | no | — |
| 165 | D3×D4 | — | 6 | 1 | no | — |
| 166 | D3×D4 | — | 6 | 1 | no | — |
| 167 | D3×D4 | — | 12 | 1 | no | — |
| 168 | D3×D4 | — | 12 | 1 | no | — |
| 169 | #235 | — | 2 | 1 | no | — |
| 170 | #235 | — | 2 | 1 | no | — |
| 171 | #235 | — | 12 | 1 | no | — |
| 172 | #235 | — | 12 | 1 | no | — |
| 173 | C2×C4×D3 | — | 3 | 1 | no | — |
| 174 | C2×C4×D3 | — | 3 | 1 | no | — |
| 175 | C2×C4×D3 | — | 6 | 1 | no | — |
| 176 | C2×C4×D3 | — | 12 | 1 | no | — |
| 177 | C2×C4×D3 | — | 12 | 1 | no | — |
| 178 | C2×Dic6 | — | 2 | 1 | no | — |
| 179 | C3×Q16 | — | 3 | 1 | no | — |
| 180 | C3×Q16 | — | 3 | 1 | no | — |
| 181 | C3×Q16 | — | 6 | 1 | no | — |
| 182 | C3×Q16 | — | 6 | 1 | no | — |
| 183 | C3×SD16 | — | 6 | 1 | no | — |
| 184 | C3×SD16 | — | 6 | 1 | no | — |
| 185 | C3×D8 | — | 3 | 1 | no | — |
| 186 | C3×D8 | — | 3 | 1 | no | — |
| 187 | C2×C3×C8 | — | 2 | 1 | no | — |
| 188 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 189 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 190 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 191 | #216 | — | 6 | 1 | no | — |
| 192 | #216 | — | 6 | 1 | no | — |
| 193 | #215 | — | 6 | 1 | no | — |
| 194 | #215 | — | 6 | 1 | no | — |
| 195 | #214 | — | 6 | 1 | no | — |
| 196 | #214 | — | 6 | 1 | no | — |
| 197 | #213 | — | 6 | 1 | no | — |
| 198 | #213 | — | 6 | 1 | no | — |
| 199 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 200 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 201 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 202 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 203 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 204 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 205 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 206 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 207 | Dic12 | — | 2 | 1 | no | — |
| 208 | Dic12 | — | 2 | 1 | no | — |
| 209 | Dic12 | D12 | 1 | 1 | yes | characteristic |
| 210 | Dic12 | #67 | 1 | 1 | yes | characteristic |
| 211 | D24 | D12 | 1 | 1 | yes | characteristic |
| 212 | D24 | #67 | 1 | 1 | yes | characteristic |
| 213 | #204 | — | 2 | 1 | no | — |
| 214 | #204 | — | 2 | 1 | no | — |
| 215 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 216 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 217 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 218 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 219 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 220 | ΓL(1,𝔽25) | — | 12 | 1 | no | — |
| 221 | C3×C16 | — | 2 | 1 | no | — |
| 222 | C3×C16 | — | 2 | 1 | no | — |
| 223 | C3×C16 | — | 4 | 1 | no | — |
| 224 | C3⋊C16 | — | 6 | 1 | no | — |
| 225 | C3⋊C16 | — | 6 | 1 | no | — |
| 226 | C3⋊C16 | — | 12 | 1 | no | — |
| 227 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 228 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 229 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 230 | C2×C3×D3 | — | 4 | 1 | no | — |
| 231 | C2×C3×D3 | — | 4 | 1 | no | — |
| 232 | D32 | — | 8 | 2 | no | — |
| 233 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 234 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 235 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 236 | C3×Dic3 | — | 4 | 1 | no | — |
| 237 | C3×Dic3 | — | 4 | 1 | no | — |
| 238 | C3×Dic3 | — | 8 | 1 | no | — |
| 239 | C3×Dic3 | — | 8 | 1 | no | — |
| 240 | C2×#41 | — | 18 | 1 | no | — |
| 241 | #137 | — | 18 | 1 | no | — |
| 242 | #137 | — | 18 | 1 | no | — |
| 243 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 244 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 245 | #135 | — | 3 | 1 | no | — |
| 246 | #135 | — | 3 | 1 | no | — |
| 247 | #135 | — | 18 | 1 | no | — |
| 248 | C2×Q16 | — | 3 | 1 | no | — |
| 249 | C2×M16 | — | 9 | 1 | no | — |
| 250 | C22⋊Q8 | — | 18 | 1 | no | — |
| 251 | Q32 | — | 6 | 1 | no | — |
| 252 | Q32 | — | 18 | 1 | no | — |
| 253 | SD32 | — | 6 | 1 | no | — |
| 254 | SD32 | — | 18 | 1 | no | — |
| 255 | M32 | — | 9 | 1 | no | — |
| 256 | M32 | D32 | 1 | 1 | yes | characteristic, complemented |
| 257 | #106 | — | 3 | 1 | no | — |
| 258 | #103 | — | 18 | 1 | no | — |
| 259 | C22×D3 | — | 3 | 1 | no | — |
| 260 | C22×D3 | — | 3 | 1 | no | — |
| 261 | C22×D3 | — | 6 | 1 | no | — |
| 262 | C22×D3 | — | 12 | 1 | no | — |
| 263 | C22×D3 | — | 12 | 1 | no | — |
| 264 | C3×Q8 | — | 6 | 1 | no | — |
| 265 | C3×Q8 | — | 6 | 1 | no | — |
| 266 | C3×Q8 | — | 12 | 1 | no | — |
| 267 | C3×Q8 | — | 12 | 1 | no | — |
| 268 | C3×D4 | — | 6 | 1 | no | — |
| 269 | C3×D4 | — | 6 | 1 | no | — |
| 270 | C3×D4 | — | 12 | 1 | no | — |
| 271 | C3×D4 | — | 12 | 1 | no | — |
| 272 | C2×C3×C4 | — | 2 | 1 | no | — |
| 273 | C2×C3×C4 | — | 12 | 1 | no | — |
| 274 | C2×C3×C4 | — | 12 | 1 | no | — |
| 275 | C2×C3×C4 | — | 12 | 1 | no | — |
| 276 | C2×C3×C4 | — | 12 | 1 | no | — |
| 277 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 279 | #67 | — | 4 | 1 | no | — |
| 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 | C2×Dic3 | — | 3 | 1 | no | — |
| 286 | C2×Dic3 | — | 3 | 1 | no | — |
| 287 | C2×Dic3 | — | 4 | 1 | no | — |
| 288 | C2×Dic3 | — | 4 | 1 | no | — |
| 289 | C2×Dic3 | — | 6 | 1 | no | — |
| 290 | C2×Dic3 | — | 12 | 1 | no | — |
| 291 | C2×Dic3 | — | 12 | 1 | no | — |
| 292 | D12 | — | 2 | 1 | no | — |
| 293 | D12 | — | 2 | 1 | no | — |
| 294 | D12 | — | 12 | 1 | no | — |
| 295 | D12 | — | 12 | 1 | no | — |
| 296 | C4×D3 | — | 4 | 1 | no | — |
| 297 | C4×D3 | — | 4 | 1 | no | — |
| 298 | C4×D3 | — | 6 | 1 | no | — |
| 299 | C4×D3 | — | 6 | 1 | no | — |
| 300 | C4×D3 | — | 6 | 1 | no | — |
| 301 | C4×D3 | — | 6 | 1 | no | — |
| 302 | C4×D3 | — | 12 | 1 | no | — |
| 303 | C4×D3 | — | 12 | 1 | no | — |
| 304 | C4×D3 | — | 12 | 1 | no | — |
| 305 | C4×D3 | — | 12 | 1 | no | — |
| 306 | C4×D3 | — | 12 | 1 | no | — |
| 307 | C4×D3 | — | 12 | 1 | no | — |
| 308 | Dic6 | — | 2 | 1 | no | — |
| 309 | Dic6 | — | 2 | 1 | no | — |
| 310 | Dic6 | — | 4 | 1 | no | — |
| 311 | Dic6 | — | 4 | 1 | no | — |
| 312 | Dic6 | — | 12 | 1 | no | — |
| 313 | Dic6 | — | 12 | 1 | no | — |
| 314 | C3×C8 | — | 2 | 1 | no | — |
| 315 | C3×C8 | — | 2 | 1 | no | — |
| 316 | C3×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 317 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 318 | C3×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 319 | C3×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 320 | C3⋊C8 | — | 6 | 1 | no | — |
| 321 | C3⋊C8 | — | 6 | 1 | no | — |
| 322 | C3⋊C8 | — | 12 | 1 | no | — |
| 323 | C2×C32 | — | 2 | 1 | no | — |
| 324 | C2×C32 | #447 | 1 | 1 | yes | characteristic |
| 325 | C3⋊D3 | — | 4 | 1 | no | — |
| 326 | C3×D3 | — | 8 | 1 | no | — |
| 327 | C3×D3 | — | 8 | 1 | no | — |
| 328 | #41 | — | 6 | 1 | no | — |
| 329 | #41 | — | 6 | 1 | no | — |
| 330 | #41 | — | 18 | 1 | no | — |
| 331 | #41 | — | 18 | 1 | no | — |
| 332 | #41 | — | 36 | 1 | no | — |
| 333 | #41 | — | 36 | 1 | no | — |
| 334 | C2×Q8 | — | 6 | 1 | no | — |
| 335 | C2×Q8 | — | 18 | 1 | no | — |
| 336 | C2×D4 | — | 18 | 1 | no | — |
| 337 | C2×D4 | — | 36 | 1 | no | — |
| 338 | C22×C4 | — | 9 | 1 | no | — |
| 339 | C22×C4 | — | 36 | 1 | no | — |
| 340 | Q16 | — | 3 | 1 | no | — |
| 341 | Q16 | — | 3 | 1 | no | — |
| 342 | Q16 | — | 6 | 1 | no | — |
| 343 | Q16 | — | 6 | 1 | no | — |
| 344 | Q16 | — | 18 | 1 | no | — |
| 345 | SD16 | — | 6 | 1 | no | — |
| 346 | SD16 | — | 6 | 1 | no | — |
| 347 | SD16 | — | 18 | 1 | no | — |
| 348 | SD16 | — | 18 | 1 | no | — |
| 349 | D8 | — | 3 | 1 | no | — |
| 350 | D8 | — | 3 | 1 | no | — |
| 351 | D8 | — | 18 | 1 | no | — |
| 352 | M16 | — | 18 | 1 | no | — |
| 353 | M16 | — | 18 | 1 | no | — |
| 354 | C2×C8 | — | 9 | 1 | no | — |
| 355 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 356 | C4⋊C4 | — | 6 | 1 | no | — |
| 357 | C4⋊C4 | — | 36 | 1 | no | — |
| 358 | C22⋊C4 | — | 36 | 1 | no | — |
| 359 | C16 | — | 2 | 1 | no | — |
| 360 | C16 | — | 18 | 1 | no | — |
| 361 | C22×C3 | — | 2 | 1 | no | — |
| 362 | C22×C3 | — | 12 | 1 | no | — |
| 363 | C22×C3 | — | 12 | 1 | no | — |
| 364 | C22×C3 | D3×D8 | 1 | 1 | yes | characteristic |
| 365 | C22×C3 | D3×D8 | 1 | 1 | yes | characteristic |
| 366 | C2×D3 | — | 4 | 1 | no | — |
| 367 | C2×D3 | — | 4 | 1 | no | — |
| 368 | C2×D3 | — | 6 | 1 | no | — |
| 369 | C2×D3 | — | 6 | 1 | no | — |
| 370 | C2×D3 | — | 12 | 1 | no | — |
| 371 | C2×D3 | — | 12 | 1 | no | — |
| 372 | C2×D3 | — | 12 | 1 | no | — |
| 373 | C2×D3 | — | 24 | 1 | no | — |
| 374 | C2×D3 | — | 24 | 2 | no | — |
| 375 | C2×D3 | — | 24 | 2 | no | — |
| 376 | C3×C4 | — | 2 | 1 | no | — |
| 377 | C3×C4 | — | 2 | 1 | no | — |
| 378 | C3×C4 | — | 12 | 1 | no | — |
| 379 | C3×C4 | — | 12 | 1 | no | — |
| 380 | C3×C4 | — | 24 | 1 | no | — |
| 381 | C3×C4 | — | 24 | 1 | no | — |
| 382 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 383 | C3×C4 | #911 | 1 | 1 | yes | characteristic |
| 384 | C3×C4 | #914 | 1 | 1 | yes | characteristic |
| 385 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 386 | Dic3 | — | 4 | 1 | no | — |
| 387 | Dic3 | — | 4 | 1 | no | — |
| 388 | Dic3 | — | 6 | 1 | no | — |
| 389 | Dic3 | — | 6 | 1 | no | — |
| 390 | Dic3 | — | 8 | 1 | no | — |
| 391 | Dic3 | — | 8 | 1 | no | — |
| 392 | Dic3 | — | 12 | 1 | no | — |
| 393 | C32 | #2191 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 394 | C23 | — | 9 | 1 | no | — |
| 395 | C23 | — | 36 | 1 | no | — |
| 396 | Q8 | — | 6 | 1 | no | — |
| 397 | Q8 | — | 6 | 1 | no | — |
| 398 | Q8 | — | 12 | 1 | no | — |
| 399 | Q8 | — | 12 | 1 | no | — |
| 400 | Q8 | — | 36 | 1 | no | — |
| 401 | D4 | — | 6 | 1 | no | — |
| 402 | D4 | — | 6 | 1 | no | — |
| 403 | D4 | — | 12 | 1 | no | — |
| 404 | D4 | — | 12 | 1 | no | — |
| 405 | D4 | — | 36 | 1 | no | — |
| 406 | D4 | — | 36 | 1 | no | — |
| 407 | D4 | — | 36 | 1 | no | — |
| 408 | C2×C4 | — | 9 | 1 | no | — |
| 409 | C2×C4 | — | 12 | 1 | no | — |
| 410 | C2×C4 | — | 12 | 1 | no | — |
| 411 | C2×C4 | — | 12 | 1 | no | — |
| 412 | C2×C4 | — | 12 | 1 | no | — |
| 413 | C2×C4 | — | 18 | 1 | no | — |
| 414 | C2×C4 | — | 18 | 1 | no | — |
| 415 | C2×C4 | — | 36 | 1 | no | — |
| 416 | C2×C4 | — | 36 | 1 | no | — |
| 417 | C2×C4 | — | 36 | 1 | no | — |
| 418 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 18 | 1 | no | — |
| 420 | C8 | D3×D12 | 1 | 1 | yes | characteristic |
| 421 | C8 | D3×#67 | 1 | 1 | yes | characteristic |
| 422 | C2×C3 | — | 2 | 1 | no | — |
| 423 | C2×C3 | — | 2 | 1 | no | — |
| 424 | C2×C3 | — | 2 | 1 | no | — |
| 425 | C2×C3 | — | 4 | 1 | no | — |
| 426 | C2×C3 | — | 24 | 1 | no | — |
| 427 | C2×C3 | — | 24 | 1 | no | — |
| 428 | C2×C3 | #4773 | 1 | 1 | yes | characteristic |
| 429 | C2×C3 | #5156 | 1 | 1 | yes | characteristic |
| 430 | D3 | — | 8 | 1 | no | — |
| 431 | D3 | — | 8 | 1 | no | — |
| 432 | D3 | — | 12 | 1 | no | — |
| 433 | D3 | — | 12 | 1 | no | — |
| 434 | D3 | — | 24 | 1 | no | — |
| 435 | C22 | — | 12 | 1 | no | — |
| 436 | C22 | — | 12 | 1 | no | — |
| 437 | C22 | — | 18 | 1 | no | — |
| 438 | C22 | — | 36 | 1 | no | — |
| 439 | C22 | — | 72 | 2 | no | — |
| 440 | C22 | #63797 | 1 | 1 | yes | characteristic |
| 441 | C4 | — | 12 | 1 | no | — |
| 442 | C4 | — | 12 | 1 | no | — |
| 443 | C4 | — | 18 | 1 | no | — |
| 444 | C4 | — | 24 | 1 | no | — |
| 445 | C4 | — | 24 | 1 | no | — |
| 446 | C4 | #63798 | 1 | 1 | yes | characteristic |
| 447 | C4 | #63922 | 1 | 1 | yes | characteristic |
| 448 | C3 | — | 2 | 1 | no | — |
| 449 | C3 | #69253 | 1 | 1 | yes | characteristic, complemented |
| 450 | C3 | #71522 | 1 | 1 | yes | characteristic, complemented |
| 451 | C2 | — | 2 | 1 | no | — |
| 452 | C2 | — | 24 | 1 | no | — |
| 453 | C2 | — | 24 | 1 | no | — |
| 454 | C2 | — | 36 | 1 | no | — |
| 455 | C2 | #10590945 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#4909 | C2 | semidirect |
| 3. #10590858 | C2 | semidirect |
| 4. #10590636 | C2 | semidirect |
| 5. #10589380 | C2 | semidirect |
| 6. C3×#4518 | C2 | semidirect |
| 7. #10589123 | C2 | semidirect |
| 12. C2×C3×Dic12 | C22 | semidirect |
| 21. C32×M32 | C22 | semidirect |
| 22. #63639 | C22 | semidirect |
| 23. C3×#817 | C22 | semidirect |
| 35. #4909 | D3 | semidirect |
| 39. #4518 | D3 | semidirect |
| 94. C2×Dic12 | C2×D3 | semidirect |
| 104. C3×M32 | C2×D3 | semidirect |
| 105. C3×M32 | C2×D3 | semidirect |
| 112. #817 | C2×D3 | semidirect |
| 256. M32 | D32 | semidirect |
| 393. C32 | #2191 | semidirect |
| 449. C3 | #69253 | semidirect |
| 450. C3 | #71522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594685 | 2 |
| C3×#4909 | 2 |
| #10590858 | 2 |
| #10590636 | 2 |
| #10589380 | 2 |
| C3×#4518 | 2 |
| #10589123 | 2 |
| #71522 | 3 |
| #69253 | 3 |