Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
495 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #10593953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#4712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590371 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590279 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4465 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589086 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71327 | — | 3 | 1 | no | maximal |
| 9 | #68370 | — | 3 | 1 | no | maximal |
| 10 | #64084 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C3×D24 | — | 2 | 1 | no | — |
| 12 | C2×C3×#204 | — | 2 | 1 | no | — |
| 13 | C3×#875 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#874 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#870 | C22 | 1 | 1 | yes | characteristic |
| 16 | #63910 | — | 2 | 1 | no | — |
| 17 | #63896 | — | 2 | 1 | no | — |
| 18 | #63890 | — | 2 | 1 | no | — |
| 19 | #63888 | — | 2 | 1 | no | — |
| 20 | #63886 | — | 2 | 1 | no | — |
| 21 | #63854 | — | 2 | 1 | no | — |
| 22 | C2×#3716 | — | 2 | 1 | no | — |
| 23 | C2×#3714 | — | 2 | 1 | no | — |
| 24 | C32×#97 | C22 | 1 | 1 | yes | characteristic |
| 25 | #63630 | C22 | 1 | 1 | yes | characteristic |
| 26 | C3×#803 | C22 | 1 | 1 | yes | characteristic |
| 27 | #63562 | — | 2 | 1 | no | — |
| 28 | #63562 | — | 2 | 1 | no | — |
| 29 | #5700 | — | 3 | 1 | no | — |
| 30 | #5684 | — | 3 | 1 | no | — |
| 31 | C3×#496 | — | 3 | 1 | no | — |
| 32 | #5074 | — | 3 | 1 | no | — |
| 33 | #5071 | — | 3 | 1 | no | — |
| 34 | #5067 | — | 3 | 1 | no | — |
| 35 | #4712 | — | 3 | 1 | no | — |
| 36 | #4712 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#330 | — | 3 | 1 | no | — |
| 38 | #4540 | — | 3 | 1 | no | — |
| 39 | #4465 | D3 | 1 | 1 | yes | characteristic, complemented |
| 40 | #4464 | — | 3 | 1 | no | — |
| 41 | #4464 | — | 3 | 1 | no | — |
| 42 | #4464 | — | 3 | 1 | no | — |
| 43 | #4464 | — | 6 | 1 | no | — |
| 44 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×C3×D12 | — | 2 | 1 | no | — |
| 47 | C2×C3×D12 | — | 2 | 1 | no | — |
| 48 | C2×C3×D12 | — | 2 | 1 | no | — |
| 49 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×#626 | — | 2 | 1 | no | — |
| 52 | C2×#626 | — | 2 | 1 | no | — |
| 53 | C2×#624 | — | 2 | 1 | no | — |
| 54 | C2×D3×Dic3 | — | 2 | 1 | no | — |
| 55 | C2×C32×C8 | — | 2 | 1 | no | — |
| 56 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 57 | #3752 | — | 2 | 1 | no | — |
| 58 | #3752 | — | 2 | 1 | no | — |
| 59 | C2×C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 60 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 61 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 62 | C3×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 63 | C3×C4⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 64 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 65 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 66 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 67 | C3×D24 | — | 4 | 2 | no | — |
| 68 | C3×#204 | — | 4 | 2 | no | — |
| 69 | #3724 | — | 2 | 1 | no | — |
| 70 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 71 | #3722 | — | 2 | 1 | no | — |
| 72 | (C2×D3)⋊Dic3 | — | 2 | 1 | no | — |
| 73 | #3716 | — | 4 | 2 | no | — |
| 74 | #3714 | — | 4 | 2 | no | — |
| 75 | #1656 | — | 9 | 1 | no | Sylow |
| 76 | C2×C3×SD16 | — | 6 | 1 | no | — |
| 77 | C2×C3×D8 | — | 6 | 1 | no | — |
| 78 | C3×#127 | — | 3 | 1 | no | — |
| 79 | C3×#125 | — | 3 | 1 | no | — |
| 80 | C3×#124 | — | 3 | 1 | no | — |
| 81 | #946 | — | 6 | 1 | no | — |
| 82 | #939 | — | 6 | 1 | no | — |
| 83 | C2×#214 | — | 6 | 1 | no | — |
| 84 | C2×#213 | — | 6 | 1 | no | — |
| 85 | C2×D24 | — | 2 | 1 | no | — |
| 86 | C2×D24 | — | 6 | 1 | no | — |
| 87 | C2×#204 | — | 2 | 1 | no | — |
| 88 | C2×#204 | — | 6 | 1 | no | — |
| 89 | #896 | — | 6 | 1 | no | — |
| 90 | #896 | — | 6 | 1 | no | — |
| 91 | #895 | — | 6 | 1 | no | — |
| 92 | #895 | — | 6 | 1 | no | — |
| 93 | #894 | — | 6 | 1 | no | — |
| 94 | #894 | — | 6 | 1 | no | — |
| 95 | #886 | — | 6 | 1 | no | — |
| 96 | #884 | — | 6 | 1 | no | — |
| 97 | #883 | — | 6 | 1 | no | — |
| 98 | #878 | — | 6 | 1 | no | — |
| 99 | #875 | — | 3 | 1 | no | — |
| 100 | #875 | — | 3 | 1 | no | — |
| 101 | #875 | — | 6 | 1 | no | — |
| 102 | #875 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | #874 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | #870 | C2×D3 | 1 | 1 | yes | characteristic |
| 105 | C3×#97 | — | 2 | 1 | no | — |
| 106 | C3×#97 | — | 3 | 1 | no | — |
| 107 | C3×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 108 | C3×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | #832 | — | 6 | 1 | no | — |
| 110 | #832 | — | 6 | 1 | no | — |
| 111 | #809 | — | 6 | 1 | no | — |
| 112 | #809 | — | 6 | 1 | no | — |
| 113 | #803 | — | 3 | 1 | no | — |
| 114 | #803 | — | 3 | 1 | no | — |
| 115 | #803 | — | 6 | 1 | no | — |
| 116 | #803 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 118 | C22×C3×D3 | — | 2 | 1 | no | — |
| 119 | C22×C3×D3 | — | 4 | 1 | no | — |
| 120 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 124 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 125 | #634 | — | 4 | 1 | no | — |
| 126 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 127 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 128 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 129 | C3×D12 | — | 4 | 1 | no | — |
| 130 | C3×D12 | — | 4 | 1 | no | — |
| 131 | C3×D12 | — | 4 | 1 | no | — |
| 132 | C3×D12 | — | 4 | 1 | no | — |
| 133 | C3×D12 | — | 4 | 1 | no | — |
| 134 | C3×D12 | — | 4 | 2 | no | — |
| 135 | C3×Dic6 | — | 4 | 1 | no | — |
| 136 | #626 | — | 8 | 1 | no | — |
| 137 | #626 | — | 8 | 1 | no | — |
| 138 | #624 | — | 8 | 1 | no | — |
| 139 | D3×Dic3 | — | 8 | 1 | no | — |
| 140 | C32×C8 | — | 2 | 2 | no | — |
| 141 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 142 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 143 | #562 | — | 9 | 1 | no | — |
| 144 | #496 | — | 3 | 1 | no | — |
| 145 | #496 | — | 9 | 1 | no | — |
| 146 | #490 | — | 9 | 1 | no | — |
| 147 | #330 | — | 3 | 1 | no | — |
| 148 | #329 | — | 9 | 1 | no | — |
| 149 | #329 | — | 9 | 1 | no | — |
| 150 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 151 | C2×C3×D4 | — | 3 | 1 | no | — |
| 152 | C2×C3×D4 | — | 6 | 1 | no | — |
| 153 | C2×C3×D4 | — | 6 | 1 | no | — |
| 154 | C2×C3×D4 | — | 6 | 1 | no | — |
| 155 | C2×#67 | — | 6 | 1 | no | — |
| 156 | C2×#67 | — | 6 | 1 | no | — |
| 157 | C22×Dic3 | — | 6 | 1 | no | — |
| 158 | C2×D12 | — | 2 | 1 | no | — |
| 159 | C2×D12 | — | 2 | 1 | no | — |
| 160 | C2×D12 | — | 2 | 1 | no | — |
| 161 | C2×D12 | — | 3 | 1 | no | — |
| 162 | C2×D12 | — | 3 | 1 | no | — |
| 163 | C2×D12 | — | 6 | 1 | no | — |
| 164 | C2×D12 | — | 6 | 1 | no | — |
| 165 | C2×D12 | — | 6 | 1 | no | — |
| 166 | C2×D12 | #67 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×D3 | — | 6 | 1 | no | — |
| 168 | C2×C4×D3 | — | 6 | 1 | no | — |
| 169 | C2×C4×D3 | — | 6 | 1 | no | — |
| 170 | C2×Dic6 | — | 3 | 1 | no | — |
| 171 | C2×Dic6 | — | 3 | 1 | no | — |
| 172 | C2×Dic6 | — | 6 | 1 | no | — |
| 173 | C2×Dic6 | #67 | 1 | 1 | yes | characteristic |
| 174 | C3×SD16 | — | 12 | 2 | no | — |
| 175 | C3×D8 | — | 12 | 2 | no | — |
| 176 | C2×C3×C8 | — | 2 | 1 | no | — |
| 177 | C2×C3×C8 | — | 2 | 1 | no | — |
| 178 | C2×C3×C8 | — | 4 | 1 | no | — |
| 179 | C2×C3×C8 | — | 6 | 1 | no | — |
| 180 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 181 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 182 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 183 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 184 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 185 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 186 | C3×C42 | — | 2 | 1 | no | — |
| 187 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 188 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 189 | #217 | — | 6 | 1 | no | — |
| 190 | #214 | — | 12 | 2 | no | — |
| 191 | #213 | — | 12 | 2 | no | — |
| 192 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 193 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 194 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 195 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 196 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 197 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 198 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 199 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 200 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 201 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 202 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 203 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 204 | C4⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 205 | C4⋊Dic3 | D12 | 1 | 1 | yes | characteristic |
| 206 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 207 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 208 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 209 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 210 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 211 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 212 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 213 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 214 | C2×C3⋊C8 | — | 12 | 1 | no | — |
| 215 | D24 | — | 4 | 2 | no | — |
| 216 | D24 | — | 12 | 2 | no | — |
| 217 | #204 | — | 4 | 2 | no | — |
| 218 | #204 | — | 12 | 2 | no | — |
| 219 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 220 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 221 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 222 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 223 | C2×C3×D3 | — | 4 | 1 | no | — |
| 224 | C2×C3×D3 | — | 4 | 1 | no | — |
| 225 | C2×C3×D3 | — | 4 | 1 | no | — |
| 226 | C2×C3×D3 | — | 8 | 1 | no | — |
| 227 | C2×C3×D3 | — | 8 | 1 | no | — |
| 228 | C2×C3×D3 | — | 8 | 1 | no | — |
| 229 | C32×C4 | — | 2 | 1 | no | — |
| 230 | C32×C4 | — | 2 | 1 | no | — |
| 231 | C32×C4 | — | 2 | 1 | no | — |
| 232 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 233 | C3×Dic3 | — | 4 | 1 | no | — |
| 234 | C3×Dic3 | — | 4 | 1 | no | — |
| 235 | C3×Dic3 | — | 4 | 1 | no | — |
| 236 | C2×SD16 | — | 6 | 1 | no | — |
| 237 | C2×SD16 | — | 18 | 1 | no | — |
| 238 | C2×D8 | — | 6 | 1 | no | — |
| 239 | C2×D8 | — | 18 | 1 | no | — |
| 240 | #127 | — | 3 | 1 | no | — |
| 241 | #125 | — | 3 | 1 | no | — |
| 242 | #124 | — | 3 | 1 | no | — |
| 243 | #124 | — | 9 | 1 | no | — |
| 244 | #123 | — | 18 | 1 | no | — |
| 245 | #123 | — | 18 | 1 | no | — |
| 246 | C22⋊Q8 | — | 18 | 1 | no | — |
| 247 | C22⋊Q8 | — | 18 | 1 | no | — |
| 248 | #121 | — | 18 | 1 | no | — |
| 249 | #121 | — | 18 | 1 | no | — |
| 250 | #102 | — | 18 | 1 | no | — |
| 251 | #102 | — | 18 | 1 | no | — |
| 252 | #97 | — | 3 | 1 | no | — |
| 253 | #97 | — | 9 | 1 | no | — |
| 254 | #97 | D32 | 1 | 1 | yes | characteristic |
| 255 | C23×C3 | — | 6 | 1 | no | — |
| 256 | C23×C3 | — | 12 | 1 | no | — |
| 257 | C22×D3 | — | 2 | 1 | no | — |
| 258 | C22×D3 | — | 4 | 1 | no | — |
| 259 | C22×D3 | — | 6 | 1 | no | — |
| 260 | C22×D3 | — | 6 | 1 | no | — |
| 261 | C22×D3 | — | 12 | 1 | no | — |
| 262 | C3×Q8 | — | 12 | 1 | no | — |
| 263 | C3×D4 | — | 12 | 1 | no | — |
| 264 | C3×D4 | — | 12 | 1 | no | — |
| 265 | C3×D4 | — | 12 | 1 | no | — |
| 266 | C3×D4 | — | 12 | 1 | no | — |
| 267 | C3×D4 | — | 12 | 1 | no | — |
| 268 | C3×D4 | — | 12 | 2 | no | — |
| 269 | C2×C3×C4 | — | 2 | 1 | no | — |
| 270 | C2×C3×C4 | — | 2 | 1 | no | — |
| 271 | C2×C3×C4 | — | 2 | 1 | no | — |
| 272 | C2×C3×C4 | — | 6 | 1 | no | — |
| 273 | C2×C3×C4 | — | 6 | 1 | no | — |
| 274 | C2×C3×C4 | — | 6 | 1 | no | — |
| 275 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 276 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 280 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 281 | #67 | — | 24 | 1 | no | — |
| 282 | #67 | — | 24 | 1 | no | — |
| 283 | C2×Dic3 | — | 2 | 1 | no | — |
| 284 | C2×Dic3 | — | 2 | 1 | no | — |
| 285 | C2×Dic3 | — | 2 | 1 | no | — |
| 286 | C2×Dic3 | — | 6 | 1 | no | — |
| 287 | C2×Dic3 | — | 6 | 1 | no | — |
| 288 | C2×Dic3 | — | 12 | 1 | no | — |
| 289 | C2×Dic3 | — | 24 | 1 | no | — |
| 290 | D12 | — | 4 | 1 | no | — |
| 291 | D12 | — | 4 | 1 | no | — |
| 292 | D12 | — | 4 | 1 | no | — |
| 293 | D12 | — | 4 | 1 | no | — |
| 294 | D12 | — | 4 | 1 | no | — |
| 295 | D12 | — | 4 | 2 | no | — |
| 296 | D12 | — | 12 | 1 | no | — |
| 297 | D12 | — | 12 | 1 | no | — |
| 298 | D12 | — | 24 | 1 | no | — |
| 299 | D12 | — | 24 | 1 | no | — |
| 300 | D12 | — | 24 | 1 | no | — |
| 301 | C4×D3 | — | 24 | 1 | no | — |
| 302 | C4×D3 | — | 24 | 1 | no | — |
| 303 | C4×D3 | — | 24 | 1 | no | — |
| 304 | Dic6 | — | 4 | 1 | no | — |
| 305 | Dic6 | — | 12 | 1 | no | — |
| 306 | Dic6 | — | 12 | 1 | no | — |
| 307 | Dic6 | — | 24 | 1 | no | — |
| 308 | C3×C8 | — | 2 | 2 | no | — |
| 309 | C3×C8 | — | 2 | 2 | no | — |
| 310 | C3×C8 | — | 4 | 2 | no | — |
| 311 | C3×C8 | — | 6 | 2 | no | — |
| 312 | C3⋊C8 | — | 2 | 2 | no | — |
| 313 | C3⋊C8 | — | 12 | 1 | no | — |
| 314 | C3⋊C8 | — | 12 | 1 | no | — |
| 315 | C3⋊C8 | — | 12 | 2 | no | — |
| 316 | C2×C32 | #453 | 1 | 1 | yes | characteristic |
| 317 | C2×C32 | #453 | 1 | 1 | yes | characteristic |
| 318 | C2×C32 | #454 | 1 | 1 | yes | characteristic |
| 319 | C3⋊D3 | — | 8 | 1 | no | — |
| 320 | C3×D3 | — | 8 | 1 | no | — |
| 321 | C3×D3 | — | 16 | 1 | no | — |
| 322 | C2×Q8 | — | 3 | 1 | no | — |
| 323 | C2×Q8 | — | 9 | 1 | no | — |
| 324 | C2×D4 | — | 3 | 1 | no | — |
| 325 | C2×D4 | — | 6 | 1 | no | — |
| 326 | C2×D4 | — | 6 | 1 | no | — |
| 327 | C2×D4 | — | 6 | 1 | no | — |
| 328 | C2×D4 | — | 9 | 1 | no | — |
| 329 | C2×D4 | — | 18 | 1 | no | — |
| 330 | C2×D4 | — | 18 | 1 | no | — |
| 331 | C22×C4 | — | 18 | 1 | no | — |
| 332 | C22×C4 | — | 18 | 1 | no | — |
| 333 | SD16 | — | 12 | 2 | no | — |
| 334 | SD16 | — | 36 | 2 | no | — |
| 335 | D8 | — | 12 | 2 | no | — |
| 336 | D8 | — | 36 | 2 | no | — |
| 337 | C2×C8 | — | 2 | 1 | no | — |
| 338 | C2×C8 | — | 6 | 1 | no | — |
| 339 | C2×C8 | — | 18 | 1 | no | — |
| 340 | C4⋊C4 | — | 3 | 1 | no | — |
| 341 | C4⋊C4 | — | 3 | 1 | no | — |
| 342 | C4⋊C4 | — | 6 | 1 | no | — |
| 343 | C4⋊C4 | — | 6 | 1 | no | — |
| 344 | C4⋊C4 | — | 18 | 1 | no | — |
| 345 | C4⋊C4 | — | 18 | 1 | no | — |
| 346 | C22⋊C4 | — | 6 | 1 | no | — |
| 347 | C22⋊C4 | — | 6 | 1 | no | — |
| 348 | C22⋊C4 | — | 18 | 1 | no | — |
| 349 | C22⋊C4 | — | 18 | 1 | no | — |
| 350 | C22⋊C4 | — | 18 | 1 | no | — |
| 351 | C22⋊C4 | — | 18 | 1 | no | — |
| 352 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 353 | C22×C3 | — | 2 | 1 | no | — |
| 354 | C22×C3 | — | 12 | 1 | no | — |
| 355 | C22×C3 | — | 12 | 1 | no | — |
| 356 | C22×C3 | — | 12 | 1 | no | — |
| 357 | C22×C3 | — | 24 | 1 | no | — |
| 358 | C22×C3 | — | 24 | 1 | no | — |
| 359 | C22×C3 | — | 24 | 1 | no | — |
| 360 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 361 | C22×C3 | #937 | 1 | 1 | yes | characteristic |
| 362 | C2×D3 | — | 4 | 1 | no | — |
| 363 | C2×D3 | — | 4 | 1 | no | — |
| 364 | C2×D3 | — | 4 | 1 | no | — |
| 365 | C2×D3 | — | 8 | 1 | no | — |
| 366 | C2×D3 | — | 8 | 1 | no | — |
| 367 | C2×D3 | — | 8 | 1 | no | — |
| 368 | C2×D3 | — | 12 | 1 | no | — |
| 369 | C2×D3 | — | 12 | 1 | no | — |
| 370 | C2×D3 | — | 12 | 1 | no | — |
| 371 | C2×D3 | — | 12 | 1 | no | — |
| 372 | C2×D3 | — | 12 | 1 | no | — |
| 373 | C2×D3 | — | 12 | 1 | no | — |
| 374 | C2×D3 | — | 24 | 1 | no | — |
| 375 | C2×D3 | — | 24 | 1 | no | — |
| 376 | C2×D3 | — | 24 | 1 | no | — |
| 377 | C3×C4 | — | 2 | 1 | no | — |
| 378 | C3×C4 | — | 2 | 1 | no | — |
| 379 | C3×C4 | — | 2 | 1 | no | — |
| 380 | C3×C4 | — | 2 | 1 | no | — |
| 381 | C3×C4 | — | 2 | 1 | no | — |
| 382 | C3×C4 | — | 2 | 1 | no | — |
| 383 | C3×C4 | — | 4 | 1 | no | — |
| 384 | C3×C4 | — | 4 | 1 | no | — |
| 385 | C3×C4 | — | 4 | 1 | no | — |
| 386 | C3×C4 | — | 12 | 1 | no | — |
| 387 | C3×C4 | — | 12 | 1 | no | — |
| 388 | C3×C4 | — | 12 | 1 | no | — |
| 389 | Dic3 | — | 4 | 1 | no | — |
| 390 | Dic3 | — | 4 | 1 | no | — |
| 391 | Dic3 | — | 4 | 1 | no | — |
| 392 | Dic3 | — | 12 | 1 | no | — |
| 393 | Dic3 | — | 12 | 1 | no | — |
| 394 | Dic3 | — | 24 | 1 | no | — |
| 395 | C32 | #1656 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 396 | C23 | — | 6 | 1 | no | — |
| 397 | C23 | — | 12 | 1 | no | — |
| 398 | C23 | — | 18 | 1 | no | — |
| 399 | Q8 | — | 12 | 1 | no | — |
| 400 | Q8 | — | 36 | 1 | no | — |
| 401 | D4 | — | 12 | 1 | no | — |
| 402 | D4 | — | 12 | 1 | no | — |
| 403 | D4 | — | 12 | 1 | no | — |
| 404 | D4 | — | 12 | 1 | no | — |
| 405 | D4 | — | 12 | 1 | no | — |
| 406 | D4 | — | 12 | 2 | no | — |
| 407 | D4 | — | 36 | 1 | no | — |
| 408 | D4 | — | 72 | 1 | no | — |
| 409 | D4 | — | 72 | 1 | no | — |
| 410 | C2×C4 | — | 6 | 1 | no | — |
| 411 | C2×C4 | — | 6 | 1 | no | — |
| 412 | C2×C4 | — | 6 | 1 | no | — |
| 413 | C2×C4 | — | 18 | 1 | no | — |
| 414 | C2×C4 | — | 72 | 1 | no | — |
| 415 | C2×C4 | — | 72 | 1 | no | — |
| 416 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 417 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 418 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 419 | C8 | — | 2 | 2 | no | — |
| 420 | C8 | — | 6 | 2 | no | — |
| 421 | C8 | — | 36 | 1 | no | — |
| 422 | C2×C3 | — | 2 | 1 | no | — |
| 423 | C2×C3 | — | 2 | 1 | no | — |
| 424 | C2×C3 | — | 2 | 1 | no | — |
| 425 | C2×C3 | — | 24 | 1 | no | — |
| 426 | C2×C3 | — | 48 | 1 | no | — |
| 427 | C2×C3 | #4753 | 1 | 1 | yes | characteristic |
| 428 | C2×C3 | #4822 | 1 | 1 | yes | characteristic |
| 429 | C2×C3 | #4822 | 1 | 1 | yes | characteristic |
| 430 | C2×C3 | #5077 | 1 | 1 | yes | characteristic |
| 431 | C2×C3 | #5198 | 1 | 1 | yes | characteristic |
| 432 | C2×C3 | #5201 | 1 | 1 | yes | characteristic |
| 433 | D3 | — | 8 | 1 | no | — |
| 434 | D3 | — | 16 | 1 | no | — |
| 435 | D3 | — | 24 | 1 | no | — |
| 436 | D3 | — | 24 | 1 | no | — |
| 437 | D3 | — | 48 | 1 | no | — |
| 438 | C22 | — | 12 | 1 | no | — |
| 439 | C22 | — | 12 | 1 | no | — |
| 440 | C22 | — | 12 | 1 | no | — |
| 441 | C22 | — | 24 | 1 | no | — |
| 442 | C22 | — | 24 | 1 | no | — |
| 443 | C22 | — | 24 | 1 | no | — |
| 444 | C22 | — | 36 | 1 | no | — |
| 445 | C22 | — | 36 | 1 | no | — |
| 446 | C22 | — | 36 | 1 | no | — |
| 447 | C22 | #63922 | 1 | 1 | yes | characteristic |
| 448 | C4 | — | 2 | 1 | no | — |
| 449 | C4 | — | 2 | 1 | no | — |
| 450 | C4 | — | 2 | 1 | no | — |
| 451 | C4 | — | 12 | 1 | no | — |
| 452 | C4 | — | 12 | 1 | no | — |
| 453 | C4 | — | 12 | 1 | no | — |
| 454 | C4 | — | 36 | 1 | no | — |
| 455 | C3 | — | 2 | 1 | no | — |
| 456 | C3 | #68370 | 1 | 1 | yes | characteristic, complemented |
| 457 | C3 | #71327 | 1 | 1 | yes | characteristic, complemented |
| 458 | C2 | — | 24 | 1 | no | — |
| 459 | C2 | — | 48 | 1 | no | — |
| 460 | C2 | — | 72 | 1 | no | — |
| 461 | C2 | #10590395 | 1 | 1 | yes | characteristic |
| 462 | C2 | #10591013 | 1 | 1 | yes | characteristic |
| 463 | C2 | #10591020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63922 |
| commutator, cosocle | C32×C42 | C23 |
| Frattini | C42 | C2×D32 |
| Fitting | C32×#97 | C22 |
| socle | C22×C32 | #120 |
| hypercenter | #97 | D32 |
| hypocenter | C32 | #1656 |
| LCS | G ▷ C32×C42 ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593953 | C2 | semidirect |
| 2. C3×#4712 | C2 | semidirect |
| 3. #10590371 | C2 | semidirect |
| 4. #10590279 | C2 | semidirect |
| 5. #10589330 | C2 | semidirect |
| 6. C3×#4465 | C2 | semidirect |
| 7. #10589086 | C2 | semidirect |
| 36. #4712 | D3 | semidirect |
| 39. #4465 | D3 | semidirect |
| 395. C32 | #1656 | semidirect |
| 456. C3 | #68370 | semidirect |
| 457. C3 | #71327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593953 | 2 |
| C3×#4712 | 2 |
| #10590371 | 2 |
| #10590279 | 2 |
| #10589330 | 2 |
| C3×#4465 | 2 |
| #10589086 | 2 |
| #71327 | 3 |
| #68370 | 3 |