Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
708 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 81 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 | D3×Q8×A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | A4×#237 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×A4×SD16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | A4×#216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | A4×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | A4×ΓL(1,𝔽25) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#915 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | A4×#137 | — | 3 | 1 | no | maximal |
| 10 | C3×Q8×A4 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×D4×A4 | C22 | 1 | 1 | yes | characteristic |
| 12 | A4×#67 | — | 2 | 1 | no | — |
| 13 | C2×Dic3×A4 | — | 2 | 1 | no | — |
| 14 | C4×D3×A4 | — | 2 | 1 | no | — |
| 15 | C4×D3×A4 | C22 | 1 | 1 | yes | characteristic |
| 16 | A4×Dic6 | — | 2 | 1 | no | — |
| 17 | A4×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 18 | A4×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#915 | — | 4 | 1 | no | maximal |
| 20 | C3×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 21 | A4×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×D3×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×#237 | C2×C3 | 1 | 1 | yes | characteristic |
| 24 | A4×#41 | — | 3 | 1 | no | — |
| 25 | C2×Q8×A4 | — | 3 | 1 | no | — |
| 26 | C22×C3×SD16 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C22×#216 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C22×#214 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#915 | — | 3 | 1 | no | — |
| 30 | C2×#915 | — | 3 | 1 | no | — |
| 31 | C2×#915 | — | 3 | 1 | no | — |
| 32 | C2×#915 | — | 3 | 1 | no | — |
| 33 | C2×#915 | — | 3 | 1 | no | — |
| 34 | C2×#915 | — | 3 | 1 | no | — |
| 35 | C2×#915 | — | 3 | 1 | no | — |
| 36 | C2×#915 | — | 3 | 1 | no | — |
| 37 | C22×Dic12 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C22×ΓL(1,𝔽25) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 39 | A4×Q16 | — | 3 | 1 | no | — |
| 40 | A4×Q16 | — | 3 | 1 | no | — |
| 41 | A4×SD16 | — | 2 | 1 | no | — |
| 42 | A4×SD16 | — | 3 | 1 | no | — |
| 43 | A4×SD16 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | A4×M16 | — | 3 | 1 | no | — |
| 45 | C22×C3×A4 | — | 2 | 1 | no | — |
| 46 | C2×D3×A4 | D4 | 1 | 1 | yes | characteristic |
| 47 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 48 | C3×#237 | — | 4 | 1 | no | — |
| 49 | C3×C4×A4 | — | 2 | 1 | no | — |
| 50 | C3×C4×A4 | C23 | 1 | 1 | yes | characteristic |
| 51 | Dic3×A4 | — | 2 | 1 | no | — |
| 52 | Dic3×A4 | — | 2 | 1 | no | — |
| 53 | Dic3×A4 | D4 | 1 | 1 | yes | characteristic |
| 54 | C32×SD16 | — | 4 | 1 | no | — |
| 55 | C3×#216 | — | 4 | 1 | no | — |
| 56 | C3×#214 | — | 4 | 1 | no | — |
| 57 | C3×Dic12 | — | 4 | 1 | no | — |
| 58 | C3×ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 59 | C22×#137 | — | 3 | 1 | no | Sylow |
| 60 | C22×C3×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 61 | C22×C3×D4 | C22×C3 | 1 | 1 | yes | characteristic |
| 62 | C22×#67 | — | 2 | 1 | no | — |
| 63 | C23×Dic3 | — | 2 | 1 | no | — |
| 64 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 65 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 66 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 67 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 68 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 69 | C2×D3×Q8 | — | 6 | 1 | no | — |
| 70 | C2×#237 | — | 3 | 1 | no | — |
| 71 | C2×#237 | — | 3 | 1 | no | — |
| 72 | C2×#237 | — | 3 | 1 | no | — |
| 73 | C2×#237 | — | 3 | 1 | no | — |
| 74 | C2×#237 | — | 6 | 1 | no | — |
| 75 | C2×#237 | — | 6 | 1 | no | — |
| 76 | C22×C4×D3 | — | 2 | 1 | no | — |
| 77 | C22×C4×D3 | C22×C3 | 1 | 1 | yes | characteristic |
| 78 | C22×Dic6 | — | 2 | 1 | no | — |
| 79 | C22×Dic6 | C22×C3 | 1 | 1 | yes | characteristic |
| 80 | C22×Dic6 | C22×C3 | 1 | 1 | yes | characteristic |
| 81 | Q8×A4 | — | 2 | 1 | no | — |
| 82 | Q8×A4 | — | 3 | 1 | no | — |
| 83 | Q8×A4 | — | 3 | 1 | no | — |
| 84 | Q8×A4 | — | 6 | 1 | no | — |
| 85 | Q8×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 86 | D4×A4 | — | 2 | 1 | no | — |
| 87 | D4×A4 | — | 6 | 1 | no | — |
| 88 | D4×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C2×C4×A4 | — | 3 | 1 | no | — |
| 90 | C2×C4×A4 | — | 6 | 1 | no | — |
| 91 | C2×C4×A4 | — | 6 | 1 | no | — |
| 92 | C3×#137 | — | 12 | 1 | no | — |
| 93 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 94 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 95 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 96 | C2×C3×SD16 | — | 3 | 1 | no | — |
| 97 | C22×C3×C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 98 | C2×#216 | — | 3 | 1 | no | — |
| 99 | C2×#216 | — | 3 | 1 | no | — |
| 100 | C2×#216 | — | 3 | 1 | no | — |
| 101 | C2×#216 | — | 3 | 1 | no | — |
| 102 | C2×#214 | — | 3 | 1 | no | — |
| 103 | C2×#214 | — | 3 | 1 | no | — |
| 104 | C2×#214 | — | 3 | 1 | no | — |
| 105 | C2×#214 | — | 3 | 1 | no | — |
| 106 | C22×C3⋊C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 107 | #915 | — | 3 | 2 | no | — |
| 108 | #915 | — | 3 | 2 | no | — |
| 109 | #915 | — | 3 | 2 | no | — |
| 110 | #915 | — | 3 | 2 | no | — |
| 111 | #915 | — | 3 | 2 | no | — |
| 112 | #915 | — | 3 | 2 | no | — |
| 113 | #915 | — | 3 | 2 | no | — |
| 114 | #915 | — | 3 | 1 | no | — |
| 115 | #915 | — | 3 | 1 | no | — |
| 116 | #915 | — | 3 | 1 | no | — |
| 117 | #915 | — | 3 | 1 | no | — |
| 118 | #915 | — | 3 | 1 | no | — |
| 119 | #915 | — | 3 | 1 | no | — |
| 120 | #915 | — | 3 | 1 | no | — |
| 121 | #915 | A4 | 1 | 1 | yes | characteristic, direct product factor |
| 122 | C2×Dic12 | — | 3 | 1 | no | — |
| 123 | C2×Dic12 | — | 3 | 1 | no | — |
| 124 | C2×Dic12 | — | 3 | 1 | no | — |
| 125 | C2×Dic12 | — | 3 | 1 | no | — |
| 126 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 127 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 128 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 129 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 130 | C8×A4 | — | 2 | 1 | no | — |
| 131 | C8×A4 | — | 3 | 1 | no | — |
| 132 | C8×A4 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | C2×C3×A4 | — | 4 | 1 | no | — |
| 134 | C2×C3×A4 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | D3×A4 | — | 2 | 1 | no | — |
| 136 | C32×Q8 | — | 4 | 1 | no | — |
| 137 | C32×D4 | — | 4 | 1 | no | — |
| 138 | C3×#67 | — | 8 | 1 | no | — |
| 139 | C2×C3×Dic3 | — | 8 | 1 | no | — |
| 140 | C3×C4×D3 | — | 4 | 1 | no | — |
| 141 | C3×C4×D3 | — | 8 | 1 | no | — |
| 142 | C3×Dic6 | — | 4 | 1 | no | — |
| 143 | C3×Dic6 | — | 4 | 1 | no | — |
| 144 | C3×Dic6 | — | 8 | 1 | no | — |
| 145 | C32×C8 | — | 4 | 1 | no | — |
| 146 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 147 | C22×#41 | — | 3 | 1 | no | — |
| 148 | C23×Q8 | — | 3 | 1 | no | — |
| 149 | C2×#137 | — | 9 | 1 | no | — |
| 150 | C2×#137 | — | 9 | 1 | no | — |
| 151 | C2×#137 | — | 9 | 1 | no | — |
| 152 | C2×#137 | — | 9 | 1 | no | — |
| 153 | C2×#137 | — | 9 | 1 | no | — |
| 154 | C2×#137 | — | 9 | 1 | no | — |
| 155 | C2×#137 | — | 9 | 1 | no | — |
| 156 | C2×#137 | — | 9 | 1 | no | — |
| 157 | C22×Q16 | — | 3 | 1 | no | — |
| 158 | C22×Q16 | — | 3 | 1 | no | — |
| 159 | C22×SD16 | — | 3 | 1 | no | — |
| 160 | C22×SD16 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 161 | C22×M16 | — | 3 | 1 | no | — |
| 162 | C24×C3 | — | 2 | 1 | no | — |
| 163 | C23×D3 | C3×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×A4 | — | 2 | 1 | no | — |
| 165 | C22×A4 | — | 3 | 1 | no | — |
| 166 | C22×A4 | — | 4 | 1 | no | — |
| 167 | C3×#41 | — | 12 | 1 | no | — |
| 168 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 169 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 170 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 171 | C2×C3×Q8 | — | 12 | 1 | no | — |
| 172 | C2×C3×D4 | — | 3 | 1 | no | — |
| 173 | C2×C3×D4 | — | 3 | 1 | no | — |
| 174 | C2×C3×D4 | — | 6 | 1 | no | — |
| 175 | C22×C3×C4 | — | 2 | 1 | no | — |
| 176 | C22×C3×C4 | C23×C3 | 1 | 1 | yes | characteristic |
| 177 | C2×#67 | — | 6 | 1 | no | — |
| 178 | C2×#67 | — | 6 | 1 | no | — |
| 179 | C2×#67 | — | 6 | 1 | no | — |
| 180 | C2×#67 | — | 6 | 1 | no | — |
| 181 | C22×Dic3 | — | 2 | 1 | no | — |
| 182 | C22×Dic3 | — | 2 | 1 | no | — |
| 183 | C22×Dic3 | — | 6 | 1 | no | — |
| 184 | C22×Dic3 | — | 6 | 1 | no | — |
| 185 | C22×Dic3 | — | 6 | 1 | no | — |
| 186 | C22×Dic3 | — | 6 | 1 | no | — |
| 187 | C22×Dic3 | C3×D4 | 1 | 1 | yes | characteristic |
| 188 | D3×Q8 | — | 3 | 2 | no | — |
| 189 | D3×Q8 | — | 3 | 1 | no | — |
| 190 | D3×Q8 | — | 3 | 1 | no | — |
| 191 | D3×Q8 | — | 3 | 1 | no | — |
| 192 | D3×Q8 | — | 6 | 1 | no | — |
| 193 | D3×Q8 | — | 6 | 1 | no | — |
| 194 | D3×Q8 | — | 6 | 2 | no | — |
| 195 | D3×Q8 | — | 6 | 2 | no | — |
| 196 | D3×Q8 | — | 6 | 1 | no | — |
| 197 | D3×Q8 | — | 6 | 1 | no | — |
| 198 | D3×Q8 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 199 | #237 | — | 3 | 2 | no | — |
| 200 | #237 | — | 3 | 1 | no | — |
| 201 | #237 | — | 3 | 1 | no | — |
| 202 | #237 | — | 3 | 1 | no | — |
| 203 | #237 | — | 6 | 1 | no | — |
| 204 | #237 | — | 6 | 1 | no | — |
| 205 | #237 | — | 6 | 2 | no | — |
| 206 | #237 | — | 6 | 2 | no | — |
| 207 | #237 | — | 6 | 1 | no | — |
| 208 | #237 | — | 6 | 1 | no | — |
| 209 | #237 | C2×A4 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×D3 | — | 3 | 1 | no | — |
| 211 | C2×C4×D3 | — | 3 | 1 | no | — |
| 212 | C2×C4×D3 | — | 3 | 1 | no | — |
| 213 | C2×C4×D3 | — | 3 | 1 | no | — |
| 214 | C2×C4×D3 | — | 6 | 1 | no | — |
| 215 | C2×C4×D3 | — | 6 | 1 | no | — |
| 216 | C2×C4×D3 | — | 6 | 1 | no | — |
| 217 | C2×C4×D3 | — | 6 | 1 | no | — |
| 218 | C2×Dic6 | — | 3 | 1 | no | — |
| 219 | C2×Dic6 | — | 3 | 1 | no | — |
| 220 | C2×Dic6 | — | 3 | 1 | no | — |
| 221 | C2×Dic6 | — | 3 | 1 | no | — |
| 222 | C2×Dic6 | — | 6 | 1 | no | — |
| 223 | C2×Dic6 | — | 6 | 1 | no | — |
| 224 | C2×Dic6 | — | 6 | 1 | no | — |
| 225 | C2×Dic6 | — | 6 | 1 | no | — |
| 226 | C2×Dic6 | — | 6 | 1 | no | — |
| 227 | C2×Dic6 | — | 6 | 1 | no | — |
| 228 | C4×A4 | — | 2 | 1 | no | — |
| 229 | C4×A4 | — | 2 | 1 | no | — |
| 230 | C4×A4 | — | 3 | 1 | no | — |
| 231 | C4×A4 | — | 4 | 1 | no | — |
| 232 | C4×A4 | — | 6 | 1 | no | — |
| 233 | C4×A4 | — | 6 | 1 | no | — |
| 234 | C4×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 235 | C3×Q16 | — | 12 | 1 | no | — |
| 236 | C3×Q16 | — | 12 | 1 | no | — |
| 237 | C3×SD16 | — | 3 | 2 | no | — |
| 238 | C3×SD16 | — | 3 | 1 | no | — |
| 239 | C3×SD16 | — | 3 | 1 | no | — |
| 240 | C3×SD16 | — | 3 | 1 | no | — |
| 241 | C3×SD16 | — | 4 | 1 | no | — |
| 242 | C3×SD16 | — | 8 | 1 | no | — |
| 243 | C3×SD16 | — | 12 | 1 | no | — |
| 244 | C3×SD16 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 245 | C3×M16 | — | 12 | 1 | no | — |
| 246 | C2×C3×C8 | — | 3 | 1 | no | — |
| 247 | C2×C3×C8 | — | 3 | 1 | no | — |
| 248 | #216 | — | 3 | 2 | no | — |
| 249 | #216 | — | 3 | 1 | no | — |
| 250 | #216 | — | 3 | 1 | no | — |
| 251 | #216 | — | 3 | 1 | no | — |
| 252 | #216 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 253 | #214 | — | 3 | 2 | no | — |
| 254 | #214 | — | 3 | 1 | no | — |
| 255 | #214 | — | 3 | 1 | no | — |
| 256 | #214 | — | 3 | 1 | no | — |
| 257 | #214 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 258 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 259 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 260 | Dic12 | — | 3 | 2 | no | — |
| 261 | Dic12 | — | 3 | 1 | no | — |
| 262 | Dic12 | — | 3 | 1 | no | — |
| 263 | Dic12 | — | 3 | 1 | no | — |
| 264 | Dic12 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 265 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 266 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 267 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 268 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 269 | ΓL(1,𝔽25) | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 270 | C22×C32 | — | 8 | 1 | no | — |
| 271 | C2×C3×D3 | — | 4 | 1 | no | — |
| 272 | C3×A4 | #137 | 1 | 1 | yes | characteristic, complemented |
| 273 | C32×C4 | — | 4 | 1 | no | — |
| 274 | C32×C4 | — | 8 | 1 | no | — |
| 275 | C3×Dic3 | — | 4 | 1 | no | — |
| 276 | C3×Dic3 | — | 8 | 1 | no | — |
| 277 | C3×Dic3 | — | 8 | 1 | no | — |
| 278 | C2×#41 | — | 9 | 1 | no | — |
| 279 | C2×#41 | — | 9 | 1 | no | — |
| 280 | C2×#41 | — | 9 | 1 | no | — |
| 281 | C2×#41 | — | 9 | 1 | no | — |
| 282 | C2×#41 | — | 18 | 1 | no | — |
| 283 | C2×#41 | — | 18 | 1 | no | — |
| 284 | C22×Q8 | — | 3 | 1 | no | — |
| 285 | C22×Q8 | — | 3 | 1 | no | — |
| 286 | C22×Q8 | — | 6 | 1 | no | — |
| 287 | C22×Q8 | — | 9 | 1 | no | — |
| 288 | C22×Q8 | — | 9 | 1 | no | — |
| 289 | C22×Q8 | — | 9 | 1 | no | — |
| 290 | C22×Q8 | — | 9 | 1 | no | — |
| 291 | C22×Q8 | — | 18 | 1 | no | — |
| 292 | C22×Q8 | — | 18 | 1 | no | — |
| 293 | C22×Q8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 294 | C22×D4 | — | 6 | 1 | no | — |
| 295 | C22×D4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 296 | C23×C4 | — | 3 | 1 | no | — |
| 297 | C23×C4 | — | 6 | 1 | no | — |
| 298 | C23×C4 | — | 6 | 1 | no | — |
| 299 | #137 | — | 3 | 1 | no | — |
| 300 | #137 | — | 9 | 1 | no | — |
| 301 | #137 | — | 9 | 1 | no | — |
| 302 | #137 | — | 9 | 1 | no | — |
| 303 | #137 | — | 9 | 1 | no | — |
| 304 | #137 | — | 9 | 1 | no | — |
| 305 | #137 | — | 9 | 1 | no | — |
| 306 | #137 | — | 9 | 2 | no | — |
| 307 | #137 | — | 9 | 2 | no | — |
| 308 | #137 | — | 9 | 2 | no | — |
| 309 | #137 | — | 9 | 2 | no | — |
| 310 | #137 | — | 9 | 2 | no | — |
| 311 | #137 | — | 9 | 2 | no | — |
| 312 | #137 | — | 9 | 2 | no | — |
| 313 | #137 | — | 9 | 1 | no | — |
| 314 | C2×Q16 | — | 9 | 1 | no | — |
| 315 | C2×Q16 | — | 9 | 1 | no | — |
| 316 | C2×Q16 | — | 9 | 1 | no | — |
| 317 | C2×Q16 | — | 9 | 1 | no | — |
| 318 | C2×Q16 | — | 9 | 1 | no | — |
| 319 | C2×Q16 | — | 9 | 1 | no | — |
| 320 | C2×Q16 | — | 9 | 1 | no | — |
| 321 | C2×Q16 | — | 9 | 1 | no | — |
| 322 | C2×SD16 | — | 3 | 1 | no | — |
| 323 | C2×SD16 | — | 3 | 1 | no | — |
| 324 | C2×SD16 | — | 3 | 1 | no | — |
| 325 | C2×SD16 | — | 3 | 1 | no | — |
| 326 | C2×SD16 | — | 9 | 1 | no | — |
| 327 | C2×SD16 | — | 9 | 1 | no | — |
| 328 | C2×SD16 | — | 9 | 1 | no | — |
| 329 | C2×SD16 | — | 9 | 1 | no | — |
| 330 | C2×M16 | — | 9 | 1 | no | — |
| 331 | C2×M16 | — | 9 | 1 | no | — |
| 332 | C2×M16 | — | 9 | 1 | no | — |
| 333 | C2×M16 | — | 9 | 1 | no | — |
| 334 | C22×C8 | — | 3 | 1 | no | — |
| 335 | C22×C8 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 336 | C23×C3 | — | 4 | 1 | no | — |
| 337 | C23×C3 | — | 6 | 1 | no | — |
| 338 | C23×C3 | — | 6 | 1 | no | — |
| 339 | C23×C3 | — | 12 | 1 | no | — |
| 340 | C23×C3 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 341 | C22×D3 | — | 2 | 1 | no | — |
| 342 | C22×D3 | — | 3 | 1 | no | — |
| 343 | C22×D3 | — | 3 | 1 | no | — |
| 344 | C22×D3 | — | 6 | 1 | no | — |
| 345 | C2×A4 | — | 2 | 1 | no | — |
| 346 | C2×A4 | — | 4 | 1 | no | — |
| 347 | C2×A4 | — | 6 | 1 | no | — |
| 348 | C2×A4 | — | 8 | 1 | no | — |
| 349 | C2×A4 | D3×D4 | 1 | 1 | yes | characteristic |
| 350 | C3×Q8 | — | 3 | 1 | no | — |
| 351 | C3×Q8 | — | 4 | 1 | no | — |
| 352 | C3×Q8 | — | 6 | 1 | no | — |
| 353 | C3×Q8 | — | 6 | 1 | no | — |
| 354 | C3×Q8 | — | 8 | 1 | no | — |
| 355 | C3×Q8 | — | 12 | 1 | no | — |
| 356 | C3×Q8 | — | 12 | 1 | no | — |
| 357 | C3×Q8 | — | 24 | 1 | no | — |
| 358 | C3×Q8 | C22×A4 | 1 | 1 | yes | characteristic |
| 359 | C3×D4 | — | 3 | 1 | no | — |
| 360 | C3×D4 | — | 4 | 1 | no | — |
| 361 | C3×D4 | — | 6 | 1 | no | — |
| 362 | C3×D4 | — | 6 | 1 | no | — |
| 363 | C3×D4 | — | 8 | 1 | no | — |
| 364 | C3×D4 | — | 24 | 1 | no | — |
| 365 | C3×D4 | C22×A4 | 1 | 1 | yes | characteristic |
| 366 | C2×C3×C4 | — | 3 | 1 | no | — |
| 367 | C2×C3×C4 | — | 3 | 1 | no | — |
| 368 | C2×C3×C4 | — | 6 | 1 | no | — |
| 369 | C2×C3×C4 | — | 6 | 1 | no | — |
| 370 | C2×C3×C4 | — | 12 | 1 | no | — |
| 371 | C2×C3×C4 | — | 24 | 1 | no | — |
| 372 | C2×C3×C4 | — | 24 | 1 | no | — |
| 373 | #67 | — | 2 | 1 | no | — |
| 374 | #67 | — | 6 | 1 | no | — |
| 375 | #67 | — | 6 | 1 | no | — |
| 376 | #67 | — | 6 | 2 | no | — |
| 377 | #67 | — | 6 | 1 | no | — |
| 378 | C2×Dic3 | — | 2 | 1 | no | — |
| 379 | C2×Dic3 | — | 3 | 1 | no | — |
| 380 | C2×Dic3 | — | 3 | 1 | no | — |
| 381 | C2×Dic3 | — | 6 | 1 | no | — |
| 382 | C2×Dic3 | — | 6 | 1 | no | — |
| 383 | C2×Dic3 | — | 6 | 1 | no | — |
| 384 | C2×Dic3 | — | 6 | 1 | no | — |
| 385 | C2×Dic3 | — | 6 | 2 | no | — |
| 386 | C2×Dic3 | — | 6 | 1 | no | — |
| 387 | C2×Dic3 | — | 6 | 1 | no | — |
| 388 | C2×Dic3 | — | 6 | 1 | no | — |
| 389 | C4×D3 | — | 2 | 1 | no | — |
| 390 | C4×D3 | — | 3 | 2 | no | — |
| 391 | C4×D3 | — | 3 | 1 | no | — |
| 392 | C4×D3 | — | 3 | 1 | no | — |
| 393 | C4×D3 | — | 3 | 1 | no | — |
| 394 | C4×D3 | — | 6 | 1 | no | — |
| 395 | C4×D3 | — | 6 | 1 | no | — |
| 396 | C4×D3 | — | 6 | 2 | no | — |
| 397 | C4×D3 | — | 6 | 1 | no | — |
| 398 | C4×D3 | C22×A4 | 1 | 1 | yes | characteristic |
| 399 | Dic6 | — | 2 | 1 | no | — |
| 400 | Dic6 | — | 3 | 1 | no | — |
| 401 | Dic6 | — | 3 | 1 | no | — |
| 402 | Dic6 | — | 6 | 1 | no | — |
| 403 | Dic6 | — | 6 | 1 | no | — |
| 404 | Dic6 | — | 6 | 1 | no | — |
| 405 | Dic6 | — | 6 | 1 | no | — |
| 406 | Dic6 | — | 6 | 2 | no | — |
| 407 | Dic6 | — | 6 | 1 | no | — |
| 408 | Dic6 | — | 6 | 1 | no | — |
| 409 | Dic6 | — | 6 | 1 | no | — |
| 410 | Dic6 | C22×A4 | 1 | 1 | yes | characteristic |
| 411 | Dic6 | C22×A4 | 1 | 1 | yes | characteristic |
| 412 | C3×C8 | — | 3 | 1 | no | — |
| 413 | C3×C8 | — | 4 | 1 | no | — |
| 414 | C3×C8 | — | 8 | 1 | no | — |
| 415 | C3×C8 | — | 12 | 1 | no | — |
| 416 | C3×C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 417 | C3⋊C8 | — | 3 | 1 | no | — |
| 418 | C3⋊C8 | C22×A4 | 1 | 1 | yes | characteristic |
| 419 | C2×C32 | — | 4 | 1 | no | — |
| 420 | C2×C32 | — | 16 | 1 | no | — |
| 421 | C3×D3 | — | 8 | 1 | no | — |
| 422 | C24 | — | 2 | 1 | no | — |
| 423 | C24 | — | 3 | 1 | no | — |
| 424 | #41 | — | 3 | 1 | no | — |
| 425 | #41 | — | 9 | 1 | no | — |
| 426 | #41 | — | 9 | 1 | no | — |
| 427 | #41 | — | 9 | 2 | no | — |
| 428 | #41 | — | 9 | 1 | no | — |
| 429 | #41 | — | 18 | 1 | no | — |
| 430 | #41 | — | 18 | 1 | no | — |
| 431 | #41 | — | 18 | 2 | no | — |
| 432 | #41 | — | 18 | 2 | no | — |
| 433 | #41 | — | 18 | 1 | no | — |
| 434 | #41 | — | 18 | 1 | no | — |
| 435 | C2×Q8 | — | 3 | 1 | no | — |
| 436 | C2×Q8 | — | 3 | 1 | no | — |
| 437 | C2×Q8 | — | 3 | 1 | no | — |
| 438 | C2×Q8 | — | 6 | 1 | no | — |
| 439 | C2×Q8 | — | 9 | 1 | no | — |
| 440 | C2×Q8 | — | 9 | 1 | no | — |
| 441 | C2×Q8 | — | 9 | 1 | no | — |
| 442 | C2×Q8 | — | 9 | 1 | no | — |
| 443 | C2×Q8 | — | 9 | 1 | no | — |
| 444 | C2×Q8 | — | 9 | 1 | no | — |
| 445 | C2×Q8 | — | 9 | 2 | no | — |
| 446 | C2×Q8 | — | 9 | 1 | no | — |
| 447 | C2×Q8 | — | 18 | 1 | no | — |
| 448 | C2×Q8 | — | 18 | 1 | no | — |
| 449 | C2×Q8 | — | 18 | 1 | no | — |
| 450 | C2×Q8 | — | 18 | 1 | no | — |
| 451 | C2×Q8 | — | 18 | 1 | no | — |
| 452 | C2×Q8 | — | 18 | 1 | no | — |
| 453 | C2×Q8 | — | 18 | 1 | no | — |
| 454 | C2×Q8 | — | 18 | 1 | no | — |
| 455 | C2×Q8 | — | 18 | 1 | no | — |
| 456 | C2×Q8 | — | 18 | 2 | no | — |
| 457 | C2×Q8 | — | 18 | 2 | no | — |
| 458 | C2×Q8 | — | 18 | 1 | no | — |
| 459 | C2×D4 | — | 3 | 1 | no | — |
| 460 | C2×D4 | — | 3 | 1 | no | — |
| 461 | C2×D4 | — | 6 | 1 | no | — |
| 462 | C2×D4 | — | 18 | 1 | no | — |
| 463 | C2×D4 | — | 18 | 1 | no | — |
| 464 | C2×D4 | — | 18 | 1 | no | — |
| 465 | C2×D4 | — | 18 | 1 | no | — |
| 466 | C22×C4 | — | 2 | 1 | no | — |
| 467 | C22×C4 | — | 3 | 1 | no | — |
| 468 | C22×C4 | — | 6 | 1 | no | — |
| 469 | C22×C4 | — | 6 | 1 | no | — |
| 470 | C22×C4 | — | 9 | 1 | no | — |
| 471 | C22×C4 | — | 9 | 1 | no | — |
| 472 | C22×C4 | — | 9 | 1 | no | — |
| 473 | C22×C4 | — | 9 | 1 | no | — |
| 474 | C22×C4 | — | 18 | 1 | no | — |
| 475 | C22×C4 | — | 18 | 1 | no | — |
| 476 | C22×C4 | — | 18 | 1 | no | — |
| 477 | C22×C4 | — | 18 | 1 | no | — |
| 478 | C22×C4 | — | 18 | 1 | no | — |
| 479 | C22×C4 | — | 18 | 1 | no | — |
| 480 | C22×C4 | — | 18 | 1 | no | — |
| 481 | C22×C4 | — | 18 | 1 | no | — |
| 482 | C22×C4 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 483 | Q16 | — | 3 | 1 | no | — |
| 484 | Q16 | — | 3 | 1 | no | — |
| 485 | Q16 | — | 9 | 1 | no | — |
| 486 | Q16 | — | 9 | 1 | no | — |
| 487 | Q16 | — | 9 | 1 | no | — |
| 488 | Q16 | — | 9 | 2 | no | — |
| 489 | Q16 | — | 9 | 1 | no | — |
| 490 | Q16 | — | 9 | 2 | no | — |
| 491 | Q16 | — | 9 | 1 | no | — |
| 492 | Q16 | — | 9 | 1 | no | — |
| 493 | SD16 | — | 3 | 2 | no | — |
| 494 | SD16 | — | 3 | 1 | no | — |
| 495 | SD16 | — | 3 | 1 | no | — |
| 496 | SD16 | — | 3 | 1 | no | — |
| 497 | SD16 | — | 3 | 1 | no | — |
| 498 | SD16 | — | 9 | 1 | no | — |
| 499 | SD16 | — | 9 | 1 | no | — |
| 500 | SD16 | — | 9 | 2 | no | — |
| 501 | SD16 | — | 9 | 1 | no | — |
| 502 | SD16 | D3×A4 | 1 | 1 | yes | characteristic, complemented |
| 503 | M16 | — | 3 | 1 | no | — |
| 504 | M16 | — | 9 | 1 | no | — |
| 505 | M16 | — | 9 | 1 | no | — |
| 506 | M16 | — | 9 | 2 | no | — |
| 507 | M16 | — | 9 | 1 | no | — |
| 508 | C2×C8 | — | 3 | 1 | no | — |
| 509 | C2×C8 | — | 3 | 1 | no | — |
| 510 | C2×C8 | — | 9 | 1 | no | — |
| 511 | C2×C8 | — | 9 | 1 | no | — |
| 512 | C22×C3 | — | 2 | 1 | no | — |
| 513 | C22×C3 | — | 3 | 1 | no | — |
| 514 | C22×C3 | — | 3 | 1 | no | — |
| 515 | C22×C3 | — | 6 | 1 | no | — |
| 516 | C22×C3 | — | 8 | 1 | no | — |
| 517 | C22×C3 | — | 12 | 1 | no | — |
| 518 | C22×C3 | — | 12 | 1 | no | — |
| 519 | C22×C3 | — | 12 | 1 | no | — |
| 520 | C22×C3 | — | 12 | 1 | no | — |
| 521 | C22×C3 | — | 12 | 1 | no | — |
| 522 | C22×C3 | — | 16 | 1 | no | — |
| 523 | C22×C3 | C3×#137 | 1 | 1 | yes | characteristic, complemented |
| 524 | C2×D3 | — | 3 | 1 | no | — |
| 525 | C2×D3 | — | 6 | 1 | no | — |
| 526 | C2×D3 | — | 6 | 1 | no | — |
| 527 | C2×D3 | — | 6 | 1 | no | — |
| 528 | C2×D3 | — | 6 | 1 | no | — |
| 529 | C2×D3 | D4×A4 | 1 | 1 | yes | characteristic |
| 530 | A4 | — | 2 | 1 | no | — |
| 531 | A4 | #915 | 1 | 1 | yes | characteristic, direct product factor |
| 532 | C3×C4 | — | 2 | 1 | no | — |
| 533 | C3×C4 | — | 3 | 1 | no | — |
| 534 | C3×C4 | — | 4 | 1 | no | — |
| 535 | C3×C4 | — | 6 | 1 | no | — |
| 536 | C3×C4 | — | 8 | 1 | no | — |
| 537 | C3×C4 | — | 8 | 1 | no | — |
| 538 | C3×C4 | — | 12 | 1 | no | — |
| 539 | C3×C4 | — | 16 | 1 | no | — |
| 540 | C3×C4 | — | 24 | 1 | no | — |
| 541 | C3×C4 | — | 24 | 1 | no | — |
| 542 | C3×C4 | C23×A4 | 1 | 1 | yes | characteristic |
| 543 | Dic3 | — | 2 | 1 | no | — |
| 544 | Dic3 | — | 2 | 1 | no | — |
| 545 | Dic3 | — | 3 | 1 | no | — |
| 546 | Dic3 | — | 6 | 1 | no | — |
| 547 | Dic3 | — | 6 | 1 | no | — |
| 548 | Dic3 | D4×A4 | 1 | 1 | yes | characteristic |
| 549 | C32 | — | 4 | 1 | no | Sylow |
| 550 | C23 | — | 4 | 1 | no | — |
| 551 | C23 | — | 6 | 1 | no | — |
| 552 | C23 | — | 6 | 1 | no | — |
| 553 | C23 | — | 6 | 1 | no | — |
| 554 | C23 | — | 9 | 1 | no | — |
| 555 | C23 | — | 9 | 1 | no | — |
| 556 | C23 | — | 12 | 1 | no | — |
| 557 | C23 | — | 18 | 1 | no | — |
| 558 | C23 | C3×D3×D4 | 1 | 1 | yes | characteristic |
| 559 | Q8 | — | 3 | 1 | no | — |
| 560 | Q8 | — | 3 | 1 | no | — |
| 561 | Q8 | — | 3 | 1 | no | — |
| 562 | Q8 | — | 6 | 1 | no | — |
| 563 | Q8 | — | 6 | 1 | no | — |
| 564 | Q8 | — | 6 | 1 | no | — |
| 565 | Q8 | — | 9 | 1 | no | — |
| 566 | Q8 | — | 9 | 1 | no | — |
| 567 | Q8 | — | 18 | 1 | no | — |
| 568 | Q8 | — | 18 | 1 | no | — |
| 569 | Q8 | — | 18 | 1 | no | — |
| 570 | Q8 | — | 18 | 1 | no | — |
| 571 | Q8 | — | 18 | 1 | no | — |
| 572 | Q8 | — | 18 | 1 | no | — |
| 573 | Q8 | — | 18 | 1 | no | — |
| 574 | Q8 | — | 18 | 2 | no | — |
| 575 | Q8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 576 | D4 | — | 3 | 1 | no | — |
| 577 | D4 | — | 6 | 1 | no | — |
| 578 | D4 | — | 6 | 1 | no | — |
| 579 | D4 | — | 6 | 1 | no | — |
| 580 | D4 | — | 18 | 1 | no | — |
| 581 | D4 | — | 18 | 1 | no | — |
| 582 | D4 | — | 18 | 1 | no | — |
| 583 | D4 | — | 18 | 2 | no | — |
| 584 | D4 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 585 | C2×C4 | — | 3 | 1 | no | — |
| 586 | C2×C4 | — | 3 | 1 | no | — |
| 587 | C2×C4 | — | 3 | 1 | no | — |
| 588 | C2×C4 | — | 6 | 1 | no | — |
| 589 | C2×C4 | — | 6 | 1 | no | — |
| 590 | C2×C4 | — | 6 | 1 | no | — |
| 591 | C2×C4 | — | 6 | 1 | no | — |
| 592 | C2×C4 | — | 9 | 1 | no | — |
| 593 | C2×C4 | — | 9 | 1 | no | — |
| 594 | C2×C4 | — | 9 | 1 | no | — |
| 595 | C2×C4 | — | 9 | 2 | no | — |
| 596 | C2×C4 | — | 9 | 1 | no | — |
| 597 | C2×C4 | — | 9 | 1 | no | — |
| 598 | C2×C4 | — | 18 | 1 | no | — |
| 599 | C2×C4 | — | 18 | 1 | no | — |
| 600 | C2×C4 | — | 18 | 1 | no | — |
| 601 | C2×C4 | — | 18 | 1 | no | — |
| 602 | C2×C4 | — | 18 | 1 | no | — |
| 603 | C2×C4 | — | 18 | 1 | no | — |
| 604 | C2×C4 | — | 18 | 1 | no | — |
| 605 | C2×C4 | — | 18 | 2 | no | — |
| 606 | C2×C4 | — | 18 | 1 | no | — |
| 607 | C2×C4 | — | 18 | 2 | no | — |
| 608 | C2×C4 | — | 18 | 1 | no | — |
| 609 | C2×C4 | — | 18 | 1 | no | — |
| 610 | C8 | — | 3 | 1 | no | — |
| 611 | C8 | — | 3 | 1 | no | — |
| 612 | C8 | — | 9 | 1 | no | — |
| 613 | C8 | C2×D3×A4 | 1 | 1 | yes | characteristic |
| 614 | C2×C3 | — | 3 | 1 | no | — |
| 615 | C2×C3 | — | 3 | 1 | no | — |
| 616 | C2×C3 | — | 4 | 1 | no | — |
| 617 | C2×C3 | — | 4 | 1 | no | — |
| 618 | C2×C3 | — | 8 | 1 | no | — |
| 619 | C2×C3 | — | 12 | 1 | no | — |
| 620 | C2×C3 | — | 16 | 1 | no | — |
| 621 | C2×C3 | — | 24 | 1 | no | — |
| 622 | C2×C3 | — | 32 | 1 | no | — |
| 623 | C2×C3 | C2×D4×A4 | 1 | 1 | yes | characteristic |
| 624 | D3 | — | 2 | 1 | no | — |
| 625 | D3 | — | 6 | 1 | no | — |
| 626 | C22 | — | 2 | 1 | no | — |
| 627 | C22 | — | 3 | 1 | no | — |
| 628 | C22 | — | 3 | 1 | no | — |
| 629 | C22 | — | 3 | 1 | no | — |
| 630 | C22 | — | 6 | 1 | no | — |
| 631 | C22 | — | 9 | 1 | no | — |
| 632 | C22 | — | 12 | 1 | no | — |
| 633 | C22 | — | 12 | 1 | no | — |
| 634 | C22 | — | 12 | 1 | no | — |
| 635 | C22 | — | 12 | 1 | no | — |
| 636 | C22 | — | 18 | 1 | no | — |
| 637 | C22 | — | 18 | 1 | no | — |
| 638 | C22 | — | 18 | 1 | no | — |
| 639 | C22 | — | 18 | 1 | no | — |
| 640 | C22 | C3×#915 | 1 | 1 | yes | characteristic, complemented |
| 641 | C4 | — | 2 | 1 | no | — |
| 642 | C4 | — | 3 | 1 | no | — |
| 643 | C4 | — | 3 | 1 | no | — |
| 644 | C4 | — | 6 | 1 | no | — |
| 645 | C4 | — | 6 | 1 | no | — |
| 646 | C4 | — | 6 | 1 | no | — |
| 647 | C4 | — | 9 | 1 | no | — |
| 648 | C4 | — | 18 | 1 | no | — |
| 649 | C4 | — | 18 | 1 | no | — |
| 650 | C4 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 651 | C3 | — | 4 | 1 | no | — |
| 652 | C3 | — | 8 | 1 | no | — |
| 653 | C3 | A4×#137 | 1 | 1 | yes | characteristic, complemented |
| 654 | C2 | — | 3 | 1 | no | — |
| 655 | C2 | — | 3 | 1 | no | — |
| 656 | C2 | — | 4 | 1 | no | — |
| 657 | C2 | — | 6 | 1 | no | — |
| 658 | C2 | — | 12 | 1 | no | — |
| 659 | C2 | — | 18 | 1 | no | — |
| 660 | C2 | D3×D4×A4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×Q8×A4 | C2 | semidirect |
| 3. C3×A4×SD16 | C2 | semidirect |
| 4. A4×#216 | C2 | semidirect |
| 5. A4×#214 | C2 | semidirect |
| 6. A4×Dic12 | C2 | semidirect |
| 7. A4×ΓL(1,𝔽25) | C2 | semidirect |
| 8. C22×#915 | C3 | semidirect |
| 22. C22×D3×Q8 | C2×C3 | semidirect |
| 26. C22×C3×SD16 | C2×C3 | semidirect |
| 27. C22×#216 | C2×C3 | semidirect |
| 28. C22×#214 | C2×C3 | semidirect |
| 37. C22×Dic12 | C2×C3 | semidirect |
| 38. C22×ΓL(1,𝔽25) | C2×C3 | semidirect |
| 43. A4×SD16 | D3 | semidirect |
| 121. #915 | A4 | direct (N × H) |
| 160. C22×SD16 | C3×D3 | semidirect |
| 198. D3×Q8 | C2×A4 | semidirect |
| 244. C3×SD16 | C2×A4 | semidirect |
| 252. #216 | C2×A4 | semidirect |
| 257. #214 | C2×A4 | semidirect |
| 264. Dic12 | C2×A4 | semidirect |
| 269. ΓL(1,𝔽25) | C2×A4 | semidirect |
| 272. C3×A4 | #137 | semidirect |
| 502. SD16 | D3×A4 | semidirect |
| 523. C22×C3 | C3×#137 | semidirect |
| 531. A4 | #915 | direct (N × H) |
| 640. C22 | C3×#915 | semidirect |
| 653. C3 | A4×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Q8×A4 | 2 |
| A4×#237 | 2 |
| C3×A4×SD16 | 2 |
| A4×#216 | 2 |
| A4×#214 | 2 |
| A4×Dic12 | 2 |
| A4×ΓL(1,𝔽25) | 2 |
| C22×#915 | 3 |
| A4×#137 | 3 |
| C3×#915 | 4 |