Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
152887 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 152887 conjugacy classes of subgroups — too many to draw. Only its 247 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×C22⋊#997 | C2 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C24×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 3 | C23×C22⋊A4 | — | 4 | 3 | no | maximal |
| 4 | C22⋊#997 | C22 | 1 | 1 | yes | characteristic, direct product factor |
| 5 | C22×#997 | — | 4 | 16 | no | maximal |
| 6 | C22×C22⋊SL(2,𝔽3) | — | 4 | 2 | no | maximal |
| 7 | C23×H(5,𝔽2) | — | 3 | 48 | no | — |
| 8 | C23×H(5,𝔽2) | — | 3 | 16 | no | — |
| 9 | C23×H(5,𝔽2) | — | 3 | 6 | no | — |
| 10 | C23×H(5,𝔽2) | — | 3 | 9 | no | — |
| 11 | C23×H(5,𝔽2) | C2×C3 | 1 | 3 | yes | complemented |
| 12 | C24×#41 | — | 3 | 2 | no | — |
| 13 | C25×D4 | — | 3 | 3 | no | — |
| 14 | C22×C22⋊A4 | — | 4 | 12 | no | — |
| 15 | C22×C22⋊A4 | — | 4 | 9 | no | — |
| 16 | C2×#997 | — | 4 | 48 | no | — |
| 17 | C2×C22⋊SL(2,𝔽3) | — | 4 | 6 | no | — |
| 18 | C27 | — | 3 | 1 | no | — |
| 19 | C27 | A4 | 1 | 3 | yes | complemented |
| 20 | C22×H(5,𝔽2) | — | 3 | 48 | no | — |
| 21 | C22×H(5,𝔽2) | — | 3 | 192 | no | — |
| 22 | C22×H(5,𝔽2) | — | 3 | 288 | no | — |
| 23 | C22×H(5,𝔽2) | — | 3 | 288 | no | — |
| 24 | C22×H(5,𝔽2) | — | 3 | 432 | no | — |
| 25 | C22×H(5,𝔽2) | — | 3 | 18 | no | — |
| 26 | C22×H(5,𝔽2) | — | 3 | 36 | no | — |
| 27 | C22×H(5,𝔽2) | — | 3 | 6 | no | — |
| 28 | C22×H(5,𝔽2) | — | 3 | 288 | no | — |
| 29 | C22×H(5,𝔽2) | — | 3 | 288 | no | — |
| 30 | C22×H(5,𝔽2) | — | 3 | 432 | no | — |
| 31 | C22×H(5,𝔽2) | — | 3 | 432 | no | — |
| 32 | C22×H(5,𝔽2) | — | 3 | 32 | no | — |
| 33 | C22×H(5,𝔽2) | — | 3 | 4 | no | — |
| 34 | C22×H(5,𝔽2) | — | 3 | 32 | no | — |
| 35 | C22×H(5,𝔽2) | — | 3 | 6 | no | — |
| 36 | C22×H(5,𝔽2) | — | 3 | 48 | no | — |
| 37 | C22×H(5,𝔽2) | — | 3 | 48 | no | — |
| 38 | C22×H(5,𝔽2) | — | 3 | 48 | no | — |
| 39 | C22×H(5,𝔽2) | — | 3 | 6 | no | — |
| 40 | C22×H(5,𝔽2) | — | 3 | 9 | no | — |
| 41 | C22×H(5,𝔽2) | A4 | 1 | 16 | yes | complemented |
| 42 | C22×H(5,𝔽2) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 43 | C23×#41 | — | 3 | 144 | no | — |
| 44 | C23×#41 | — | 3 | 48 | no | — |
| 45 | C23×#41 | — | 3 | 18 | no | — |
| 46 | C23×#41 | — | 3 | 18 | no | — |
| 47 | C23×#41 | — | 3 | 6 | no | — |
| 48 | C23×#41 | — | 3 | 6 | no | — |
| 49 | C24×Q8 | A4 | 1 | 2 | yes | complemented |
| 50 | C24×D4 | — | 3 | 6 | no | — |
| 51 | C24×D4 | — | 3 | 216 | no | — |
| 52 | C24×D4 | — | 3 | 9 | no | — |
| 53 | C24×D4 | — | 3 | 36 | no | — |
| 54 | C24×D4 | — | 3 | 9 | no | — |
| 55 | C24×D4 | — | 3 | 72 | no | — |
| 56 | C24×D4 | — | 3 | 9 | no | — |
| 57 | C24×D4 | — | 3 | 9 | no | — |
| 58 | C25×C4 | — | 3 | 3 | no | — |
| 59 | C2×C22⋊A4 | — | 4 | 18 | no | — |
| 60 | C2×C22⋊A4 | — | 4 | 3 | no | — |
| 61 | C23×A4 | — | 16 | 1 | no | — |
| 62 | C23×A4 | — | 16 | 12 | no | — |
| 63 | #997 | — | 4 | 16 | no | — |
| 64 | C22⋊SL(2,𝔽3) | — | 4 | 2 | no | — |
| 65 | C22×SL(2,𝔽3) | — | 16 | 8 | no | — |
| 66 | C26 | — | 3 | 36 | no | — |
| 67 | C26 | — | 3 | 12 | no | — |
| 68 | C26 | — | 3 | 9 | no | — |
| 69 | C26 | — | 3 | 3 | no | — |
| 70 | C26 | — | 3 | 3 | no | — |
| 71 | C26 | — | 3 | 36 | no | — |
| 72 | C26 | — | 3 | 9 | no | — |
| 73 | C26 | — | 3 | 12 | no | — |
| 74 | C26 | — | 4 | 12 | no | — |
| 75 | C26 | — | 12 | 12 | no | — |
| 76 | C26 | — | 12 | 12 | no | — |
| 77 | C26 | — | 12 | 4 | no | — |
| 78 | C26 | C2×A4 | 1 | 9 | yes | complemented |
| 79 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 80 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 81 | C2×H(5,𝔽2) | — | 3 | 576 | no | — |
| 82 | C2×H(5,𝔽2) | — | 3 | 1728 | no | — |
| 83 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 84 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 85 | C2×H(5,𝔽2) | — | 3 | 1728 | no | — |
| 86 | C2×H(5,𝔽2) | — | 3 | 3456 | no | — |
| 87 | C2×H(5,𝔽2) | — | 3 | 1728 | no | — |
| 88 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 89 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 90 | C2×H(5,𝔽2) | — | 3 | 192 | no | — |
| 91 | C2×H(5,𝔽2) | — | 3 | 576 | no | — |
| 92 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 93 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 94 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 95 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 96 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 97 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 98 | C2×H(5,𝔽2) | — | 3 | 432 | no | — |
| 99 | C2×H(5,𝔽2) | — | 3 | 432 | no | — |
| 100 | C2×H(5,𝔽2) | — | 3 | 864 | no | — |
| 101 | C2×H(5,𝔽2) | — | 3 | 288 | no | — |
| 102 | C2×H(5,𝔽2) | — | 3 | 96 | no | — |
| 103 | C2×H(5,𝔽2) | — | 3 | 432 | no | — |
| 104 | C2×H(5,𝔽2) | — | 3 | 144 | no | — |
| 105 | C2×H(5,𝔽2) | — | 3 | 48 | no | — |
| 106 | C2×H(5,𝔽2) | — | 3 | 16 | no | — |
| 107 | C2×H(5,𝔽2) | — | 3 | 96 | no | — |
| 108 | C2×H(5,𝔽2) | — | 3 | 144 | no | — |
| 109 | C2×H(5,𝔽2) | C2×A4 | 1 | 48 | yes | complemented |
| 110 | C22×#41 | — | 3 | 144 | no | — |
| 111 | C22×#41 | — | 3 | 144 | no | — |
| 112 | C22×#41 | — | 3 | 576 | no | — |
| 113 | C22×#41 | — | 3 | 432 | no | — |
| 114 | C22×#41 | — | 3 | 432 | no | — |
| 115 | C22×#41 | — | 3 | 864 | no | — |
| 116 | C22×#41 | — | 3 | 432 | no | — |
| 117 | C22×#41 | — | 3 | 432 | no | — |
| 118 | C22×#41 | — | 3 | 192 | no | — |
| 119 | C22×#41 | — | 3 | 36 | no | — |
| 120 | C22×#41 | — | 3 | 12 | no | — |
| 121 | C22×#41 | — | 3 | 96 | no | — |
| 122 | C22×#41 | — | 3 | 144 | no | — |
| 123 | C22×#41 | — | 3 | 144 | no | — |
| 124 | C22×#41 | — | 3 | 288 | no | — |
| 125 | C22×#41 | — | 3 | 36 | no | — |
| 126 | C22×#41 | — | 3 | 18 | no | — |
| 127 | C22×#41 | — | 3 | 18 | no | — |
| 128 | C22×#41 | — | 3 | 6 | no | — |
| 129 | C22×#41 | — | 3 | 2 | no | — |
| 130 | C22×#41 | — | 3 | 32 | no | — |
| 131 | C23×Q8 | — | 3 | 24 | no | — |
| 132 | C23×Q8 | — | 3 | 8 | no | — |
| 133 | C23×Q8 | — | 3 | 6 | no | — |
| 134 | C23×Q8 | C2×A4 | 1 | 6 | yes | complemented |
| 135 | C23×D4 | — | 3 | 216 | no | — |
| 136 | C23×D4 | — | 3 | 72 | no | — |
| 137 | C23×D4 | — | 3 | 36 | no | — |
| 138 | C23×D4 | — | 3 | 18 | no | — |
| 139 | C23×D4 | — | 3 | 18 | no | — |
| 140 | C23×D4 | — | 3 | 864 | no | — |
| 141 | C23×D4 | — | 3 | 216 | no | — |
| 142 | C23×D4 | — | 3 | 864 | no | — |
| 143 | C23×D4 | — | 3 | 216 | no | — |
| 144 | C23×D4 | — | 3 | 216 | no | — |
| 145 | C23×D4 | — | 3 | 432 | no | — |
| 146 | C23×D4 | — | 3 | 864 | no | — |
| 147 | C23×D4 | — | 3 | 864 | no | — |
| 148 | C23×D4 | — | 3 | 216 | no | — |
| 149 | C23×D4 | — | 3 | 288 | no | — |
| 150 | C23×D4 | — | 3 | 36 | no | — |
| 151 | C23×D4 | — | 3 | 36 | no | — |
| 152 | C23×D4 | — | 3 | 144 | no | — |
| 153 | C23×D4 | — | 3 | 216 | no | — |
| 154 | C23×D4 | — | 3 | 36 | no | — |
| 155 | C23×D4 | — | 3 | 18 | no | — |
| 156 | C23×D4 | — | 3 | 216 | no | — |
| 157 | C23×D4 | — | 3 | 9 | no | — |
| 158 | C23×D4 | — | 3 | 36 | no | — |
| 159 | C23×D4 | — | 3 | 9 | no | — |
| 160 | C23×D4 | — | 3 | 216 | no | — |
| 161 | C23×D4 | — | 3 | 432 | no | — |
| 162 | C23×D4 | — | 3 | 216 | no | — |
| 163 | C23×D4 | — | 3 | 9 | no | — |
| 164 | C23×D4 | — | 3 | 3 | no | — |
| 165 | C23×D4 | — | 3 | 48 | no | — |
| 166 | C24×C4 | — | 3 | 108 | no | — |
| 167 | C24×C4 | — | 3 | 36 | no | — |
| 168 | C24×C4 | — | 3 | 9 | no | — |
| 169 | C24×C4 | — | 3 | 18 | no | — |
| 170 | C24×C4 | — | 3 | 9 | no | — |
| 171 | C24×C4 | — | 3 | 2 | no | — |
| 172 | C22⋊A4 | — | 4 | 3 | no | — |
| 173 | C22×A4 | — | 16 | 48 | no | — |
| 174 | C22×A4 | — | 16 | 4 | no | — |
| 175 | C22×A4 | — | 16 | 3 | no | — |
| 176 | C22×A4 | — | 16 | 36 | no | — |
| 177 | C2×SL(2,𝔽3) | — | 16 | 24 | no | — |
| 178 | C25 | — | 3 | 54 | no | — |
| 179 | C25 | — | 3 | 18 | no | — |
| 180 | C25 | — | 3 | 108 | no | — |
| 181 | C25 | — | 3 | 36 | no | — |
| 182 | C25 | — | 3 | 96 | no | — |
| 183 | C25 | — | 3 | 144 | no | — |
| 184 | C25 | — | 3 | 108 | no | — |
| 185 | C25 | — | 3 | 36 | no | — |
| 186 | C25 | — | 3 | 108 | no | — |
| 187 | C25 | — | 3 | 72 | no | — |
| 188 | C25 | — | 3 | 108 | no | — |
| 189 | C25 | — | 3 | 108 | no | — |
| 190 | C25 | — | 3 | 24 | no | — |
| 191 | C25 | — | 3 | 6 | no | — |
| 192 | C25 | — | 3 | 6 | no | — |
| 193 | C25 | — | 3 | 9 | no | — |
| 194 | C25 | — | 3 | 1 | no | — |
| 195 | C25 | — | 3 | 12 | no | — |
| 196 | C25 | — | 3 | 16 | no | — |
| 197 | C25 | — | 3 | 9 | no | — |
| 198 | C25 | — | 3 | 9 | no | — |
| 199 | C25 | — | 3 | 36 | no | — |
| 200 | C25 | — | 3 | 9 | no | — |
| 201 | C25 | — | 3 | 36 | no | — |
| 202 | C25 | — | 3 | 36 | no | — |
| 203 | C25 | — | 4 | 18 | no | — |
| 204 | C25 | — | 6 | 36 | no | — |
| 205 | C25 | — | 6 | 12 | no | — |
| 206 | C25 | — | 12 | 48 | no | — |
| 207 | C25 | — | 12 | 48 | no | — |
| 208 | C25 | — | 12 | 18 | no | — |
| 209 | C25 | — | 12 | 144 | no | — |
| 210 | C25 | — | 12 | 144 | no | — |
| 211 | C25 | — | 12 | 144 | no | — |
| 212 | C25 | — | 12 | 54 | no | — |
| 213 | C25 | — | 12 | 18 | no | — |
| 214 | C25 | — | 12 | 144 | no | — |
| 215 | C25 | — | 12 | 48 | no | — |
| 216 | C25 | — | 12 | 48 | no | — |
| 217 | C25 | — | 12 | 54 | no | — |
| 218 | C25 | — | 12 | 6 | no | — |
| 219 | C25 | — | 12 | 18 | no | — |
| 220 | C25 | — | 12 | 18 | no | — |
| 221 | C25 | C22×A4 | 1 | 3 | yes | complemented |
| 222 | C25 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 223 | C25 | C22⋊A4 | 1 | 12 | yes | complemented |
| 224 | H(5,𝔽2) | — | 3 | 96 | no | — |
| 225 | H(5,𝔽2) | — | 3 | 1728 | no | — |
| 226 | H(5,𝔽2) | — | 3 | 1728 | no | — |
| 227 | H(5,𝔽2) | — | 3 | 288 | no | — |
| 228 | H(5,𝔽2) | — | 3 | 864 | no | — |
| 229 | H(5,𝔽2) | — | 3 | 576 | no | — |
| 230 | H(5,𝔽2) | — | 3 | 1728 | no | — |
| 231 | H(5,𝔽2) | — | 3 | 1728 | no | — |
| 232 | H(5,𝔽2) | — | 3 | 1728 | no | — |
| 233 | H(5,𝔽2) | — | 3 | 576 | no | — |
| 234 | H(5,𝔽2) | — | 3 | 576 | no | — |
| 235 | H(5,𝔽2) | — | 3 | 192 | no | — |
| 236 | H(5,𝔽2) | — | 3 | 576 | no | — |
| 237 | H(5,𝔽2) | — | 3 | 864 | no | — |
| 238 | H(5,𝔽2) | — | 3 | 3456 | no | — |
| 239 | H(5,𝔽2) | — | 3 | 864 | no | — |
| 240 | H(5,𝔽2) | — | 3 | 864 | no | — |
| 241 | H(5,𝔽2) | — | 3 | 864 | no | — |
| 242 | H(5,𝔽2) | — | 3 | 288 | no | — |
| 243 | H(5,𝔽2) | — | 3 | 576 | no | — |
| 244 | H(5,𝔽2) | — | 3 | 96 | no | — |
| 245 | H(5,𝔽2) | — | 3 | 192 | no | — |
| 246 | H(5,𝔽2) | — | 3 | 64 | no | — |
| 247 | H(5,𝔽2) | — | 3 | 288 | no | — |
| 248 | H(5,𝔽2) | — | 3 | 32 | no | — |
| 249 | H(5,𝔽2) | — | 3 | 288 | no | — |
| 250 | H(5,𝔽2) | — | 3 | 96 | no | — |
| 251 | H(5,𝔽2) | — | 3 | 432 | no | — |
| 252 | H(5,𝔽2) | — | 3 | 48 | no | — |
| 253 | H(5,𝔽2) | — | 3 | 144 | no | — |
| 254 | H(5,𝔽2) | C22×A4 | 1 | 16 | yes | complemented |
| 255 | C2×#41 | — | 3 | 864 | no | — |
| 256 | C2×#41 | — | 3 | 864 | no | — |
| 257 | C2×#41 | — | 3 | 864 | no | — |
| 258 | C2×#41 | — | 3 | 432 | no | — |
| 259 | C2×#41 | — | 3 | 432 | no | — |
| 260 | C2×#41 | — | 3 | 1728 | no | — |
| 261 | C2×#41 | — | 3 | 1728 | no | — |
| 262 | C2×#41 | — | 3 | 1728 | no | — |
| 263 | C2×#41 | — | 3 | 1728 | no | — |
| 264 | C2×#41 | — | 3 | 864 | no | — |
| 265 | C2×#41 | — | 3 | 288 | no | — |
| 266 | C2×#41 | — | 3 | 864 | no | — |
| 267 | C2×#41 | — | 3 | 288 | no | — |
| 268 | C2×#41 | — | 3 | 864 | no | — |
| 269 | C2×#41 | — | 3 | 288 | no | — |
| 270 | C2×#41 | — | 3 | 144 | no | — |
| 271 | C2×#41 | — | 3 | 48 | no | — |
| 272 | C2×#41 | — | 3 | 288 | no | — |
| 273 | C2×#41 | — | 3 | 288 | no | — |
| 274 | C2×#41 | — | 3 | 288 | no | — |
| 275 | C2×#41 | — | 3 | 288 | no | — |
| 276 | C2×#41 | — | 3 | 96 | no | — |
| 277 | C2×#41 | — | 3 | 96 | no | — |
| 278 | C22×Q8 | — | 3 | 24 | no | — |
| 279 | C22×Q8 | — | 3 | 48 | no | — |
| 280 | C22×Q8 | — | 3 | 72 | no | — |
| 281 | C22×Q8 | — | 3 | 72 | no | — |
| 282 | C22×Q8 | — | 3 | 72 | no | — |
| 283 | C22×Q8 | — | 3 | 16 | no | — |
| 284 | C22×Q8 | — | 3 | 4 | no | — |
| 285 | C22×Q8 | — | 3 | 8 | no | — |
| 286 | C22×Q8 | — | 3 | 24 | no | — |
| 287 | C22×Q8 | — | 3 | 24 | no | — |
| 288 | C22×Q8 | — | 3 | 6 | no | — |
| 289 | C22×Q8 | C22×A4 | 1 | 2 | yes | complemented |
| 290 | C22×Q8 | C22⋊A4 | 1 | 8 | yes | complemented |
| 291 | C22×D4 | — | 3 | 432 | no | — |
| 292 | C22×D4 | — | 3 | 216 | no | — |
| 293 | C22×D4 | — | 3 | 216 | no | — |
| 294 | C22×D4 | — | 3 | 576 | no | — |
| 295 | C22×D4 | — | 3 | 432 | no | — |
| 296 | C22×D4 | — | 3 | 864 | no | — |
| 297 | C22×D4 | — | 3 | 216 | no | — |
| 298 | C22×D4 | — | 3 | 216 | no | — |
| 299 | C22×D4 | — | 3 | 36 | no | — |
| 300 | C22×D4 | — | 3 | 36 | no | — |
| 301 | C22×D4 | — | 3 | 18 | no | — |
| 302 | C22×D4 | — | 3 | 6 | no | — |
| 303 | C22×D4 | — | 3 | 96 | no | — |
| 304 | C22×D4 | — | 3 | 864 | no | — |
| 305 | C22×D4 | — | 3 | 3456 | no | — |
| 306 | C22×D4 | — | 3 | 864 | no | — |
| 307 | C22×D4 | — | 3 | 864 | no | — |
| 308 | C22×D4 | — | 3 | 864 | no | — |
| 309 | C22×D4 | — | 3 | 432 | no | — |
| 310 | C22×D4 | — | 3 | 864 | no | — |
| 311 | C22×D4 | — | 3 | 864 | no | — |
| 312 | C22×D4 | — | 3 | 432 | no | — |
| 313 | C22×D4 | — | 3 | 864 | no | — |
| 314 | C22×D4 | — | 3 | 3456 | no | — |
| 315 | C22×D4 | — | 3 | 864 | no | — |
| 316 | C22×D4 | — | 3 | 216 | no | — |
| 317 | C22×D4 | — | 3 | 432 | no | — |
| 318 | C22×D4 | — | 3 | 864 | no | — |
| 319 | C22×D4 | — | 3 | 864 | no | — |
| 320 | C22×D4 | — | 3 | 216 | no | — |
| 321 | C22×D4 | — | 3 | 432 | no | — |
| 322 | C22×D4 | — | 3 | 432 | no | — |
| 323 | C22×D4 | — | 3 | 1728 | no | — |
| 324 | C22×D4 | — | 3 | 432 | no | — |
| 325 | C22×D4 | — | 3 | 432 | no | — |
| 326 | C22×D4 | — | 3 | 144 | no | — |
| 327 | C22×D4 | — | 3 | 576 | no | — |
| 328 | C22×D4 | — | 3 | 144 | no | — |
| 329 | C22×D4 | — | 3 | 432 | no | — |
| 330 | C22×D4 | — | 3 | 216 | no | — |
| 331 | C22×D4 | — | 3 | 432 | no | — |
| 332 | C22×D4 | — | 3 | 72 | no | — |
| 333 | C22×D4 | — | 3 | 144 | no | — |
| 334 | C22×D4 | — | 3 | 144 | no | — |
| 335 | C23×C4 | — | 3 | 36 | no | — |
| 336 | C23×C4 | — | 3 | 12 | no | — |
| 337 | C23×C4 | — | 3 | 108 | no | — |
| 338 | C23×C4 | — | 3 | 216 | no | — |
| 339 | C23×C4 | — | 3 | 108 | no | — |
| 340 | C23×C4 | — | 3 | 288 | no | — |
| 341 | C23×C4 | — | 3 | 108 | no | — |
| 342 | C23×C4 | — | 3 | 216 | no | — |
| 343 | C23×C4 | — | 3 | 432 | no | — |
| 344 | C23×C4 | — | 3 | 108 | no | — |
| 345 | C23×C4 | — | 3 | 18 | no | — |
| 346 | C23×C4 | — | 3 | 9 | no | — |
| 347 | C23×C4 | — | 3 | 18 | no | — |
| 348 | C23×C4 | — | 3 | 3 | no | — |
| 349 | C23×C4 | — | 3 | 48 | no | — |
| 350 | C23×C4 | — | 3 | 6 | no | — |
| 351 | C23×C4 | — | 3 | 6 | no | — |
| 352 | C23×C3 | — | 64 | 1 | no | — |
| 353 | C2×A4 | — | 16 | 72 | no | — |
| 354 | C2×A4 | — | 16 | 6 | no | — |
| 355 | C2×A4 | — | 16 | 1 | no | — |
| 356 | C2×A4 | — | 16 | 12 | no | — |
| 357 | SL(2,𝔽3) | — | 16 | 8 | no | — |
| 358 | C24 | — | 3 | 3 | no | — |
| 359 | C24 | — | 3 | 4 | no | — |
| 360 | C24 | — | 3 | 1 | no | — |
| 361 | C24 | — | 3 | 54 | no | — |
| 362 | C24 | — | 3 | 54 | no | — |
| 363 | C24 | — | 3 | 72 | no | — |
| 364 | C24 | — | 3 | 108 | no | — |
| 365 | C24 | — | 3 | 54 | no | — |
| 366 | C24 | — | 3 | 54 | no | — |
| 367 | C24 | — | 3 | 432 | no | — |
| 368 | C24 | — | 3 | 216 | no | — |
| 369 | C24 | — | 3 | 144 | no | — |
| 370 | C24 | — | 3 | 72 | no | — |
| 371 | C24 | — | 3 | 72 | no | — |
| 372 | C24 | — | 3 | 108 | no | — |
| 373 | C24 | — | 3 | 12 | no | — |
| 374 | C24 | — | 3 | 216 | no | — |
| 375 | C24 | — | 3 | 108 | no | — |
| 376 | C24 | — | 3 | 108 | no | — |
| 377 | C24 | — | 3 | 108 | no | — |
| 378 | C24 | — | 3 | 144 | no | — |
| 379 | C24 | — | 3 | 36 | no | — |
| 380 | C24 | — | 3 | 48 | no | — |
| 381 | C24 | — | 3 | 9 | no | — |
| 382 | C24 | — | 3 | 3 | no | — |
| 383 | C24 | — | 3 | 12 | no | — |
| 384 | C24 | — | 3 | 36 | no | — |
| 385 | C24 | — | 3 | 36 | no | — |
| 386 | C24 | — | 3 | 12 | no | — |
| 387 | C24 | — | 4 | 48 | no | — |
| 388 | C24 | — | 4 | 3 | no | — |
| 389 | C24 | — | 6 | 216 | no | — |
| 390 | C24 | — | 6 | 54 | no | — |
| 391 | C24 | — | 6 | 54 | no | — |
| 392 | C24 | — | 6 | 216 | no | — |
| 393 | C24 | — | 6 | 72 | no | — |
| 394 | C24 | — | 6 | 72 | no | — |
| 395 | C24 | — | 6 | 18 | no | — |
| 396 | C24 | — | 6 | 18 | no | — |
| 397 | C24 | — | 12 | 72 | no | — |
| 398 | C24 | — | 12 | 144 | no | — |
| 399 | C24 | — | 12 | 72 | no | — |
| 400 | C24 | — | 12 | 3 | no | — |
| 401 | C24 | — | 12 | 72 | no | — |
| 402 | C24 | — | 12 | 96 | no | — |
| 403 | C24 | — | 12 | 72 | no | — |
| 404 | C24 | — | 12 | 216 | no | — |
| 405 | C24 | — | 12 | 288 | no | — |
| 406 | C24 | — | 12 | 72 | no | — |
| 407 | C24 | — | 12 | 216 | no | — |
| 408 | C24 | — | 12 | 18 | no | — |
| 409 | C24 | — | 12 | 18 | no | — |
| 410 | C24 | — | 12 | 27 | no | — |
| 411 | C24 | — | 12 | 3 | no | — |
| 412 | C24 | — | 12 | 216 | no | — |
| 413 | C24 | — | 12 | 72 | no | — |
| 414 | C24 | — | 12 | 216 | no | — |
| 415 | C24 | — | 12 | 384 | no | — |
| 416 | C24 | — | 12 | 72 | no | — |
| 417 | C24 | — | 12 | 216 | no | — |
| 418 | C24 | — | 12 | 576 | no | — |
| 419 | C24 | — | 12 | 72 | no | — |
| 420 | C24 | — | 12 | 216 | no | — |
| 421 | C24 | — | 12 | 27 | no | — |
| 422 | C24 | — | 12 | 216 | no | — |
| 423 | C24 | — | 12 | 432 | no | — |
| 424 | C24 | — | 12 | 216 | no | — |
| 425 | C24 | — | 12 | 1 | no | — |
| 426 | C24 | — | 12 | 9 | no | — |
| 427 | C24 | — | 12 | 6 | no | — |
| 428 | C24 | — | 12 | 6 | no | — |
| 429 | C24 | — | 12 | 48 | no | — |
| 430 | C24 | — | 12 | 64 | no | — |
| 431 | C24 | — | 12 | 9 | no | — |
| 432 | C24 | #997 | 1 | 4 | yes | complemented |
| 433 | C24 | C2×C22⋊A4 | 1 | 3 | yes | — |
| 434 | C24 | C2×C22⋊A4 | 1 | 36 | yes | complemented |
| 435 | #41 | — | 3 | 576 | no | — |
| 436 | #41 | — | 3 | 288 | no | — |
| 437 | #41 | — | 3 | 288 | no | — |
| 438 | #41 | — | 3 | 1728 | no | — |
| 439 | #41 | — | 3 | 576 | no | — |
| 440 | #41 | — | 3 | 1728 | no | — |
| 441 | #41 | — | 3 | 864 | no | — |
| 442 | #41 | — | 3 | 576 | no | — |
| 443 | #41 | — | 3 | 192 | no | — |
| 444 | #41 | — | 3 | 288 | no | — |
| 445 | #41 | — | 3 | 864 | no | — |
| 446 | #41 | — | 3 | 96 | no | — |
| 447 | #41 | — | 3 | 96 | no | — |
| 448 | #41 | — | 3 | 32 | no | — |
| 449 | C2×Q8 | — | 3 | 72 | no | — |
| 450 | C2×Q8 | — | 3 | 72 | no | — |
| 451 | C2×Q8 | — | 3 | 144 | no | — |
| 452 | C2×Q8 | — | 3 | 144 | no | — |
| 453 | C2×Q8 | — | 3 | 48 | no | — |
| 454 | C2×Q8 | — | 3 | 72 | no | — |
| 455 | C2×Q8 | — | 3 | 24 | no | — |
| 456 | C2×Q8 | — | 3 | 8 | no | — |
| 457 | C2×Q8 | — | 3 | 24 | no | — |
| 458 | C2×Q8 | — | 3 | 24 | no | — |
| 459 | C2×Q8 | C2×C22⋊A4 | 1 | 24 | yes | complemented |
| 460 | C2×D4 | — | 3 | 1728 | no | — |
| 461 | C2×D4 | — | 3 | 432 | no | — |
| 462 | C2×D4 | — | 3 | 432 | no | — |
| 463 | C2×D4 | — | 3 | 864 | no | — |
| 464 | C2×D4 | — | 3 | 864 | no | — |
| 465 | C2×D4 | — | 3 | 216 | no | — |
| 466 | C2×D4 | — | 3 | 72 | no | — |
| 467 | C2×D4 | — | 3 | 576 | no | — |
| 468 | C2×D4 | — | 3 | 288 | no | — |
| 469 | C2×D4 | — | 3 | 288 | no | — |
| 470 | C2×D4 | — | 3 | 1728 | no | — |
| 471 | C2×D4 | — | 3 | 1728 | no | — |
| 472 | C2×D4 | — | 3 | 576 | no | — |
| 473 | C2×D4 | — | 3 | 864 | no | — |
| 474 | C2×D4 | — | 3 | 432 | no | — |
| 475 | C2×D4 | — | 3 | 432 | no | — |
| 476 | C2×D4 | — | 3 | 1728 | no | — |
| 477 | C2×D4 | — | 3 | 576 | no | — |
| 478 | C2×D4 | — | 3 | 1728 | no | — |
| 479 | C2×D4 | — | 3 | 432 | no | — |
| 480 | C2×D4 | — | 3 | 144 | no | — |
| 481 | C2×D4 | — | 3 | 576 | no | — |
| 482 | C2×D4 | — | 3 | 288 | no | — |
| 483 | C2×D4 | — | 3 | 144 | no | — |
| 484 | C2×D4 | — | 3 | 576 | no | — |
| 485 | C2×D4 | — | 3 | 144 | no | — |
| 486 | C2×D4 | — | 3 | 144 | no | — |
| 487 | C2×D4 | — | 3 | 48 | no | — |
| 488 | C22×C4 | — | 3 | 36 | no | — |
| 489 | C22×C4 | — | 3 | 36 | no | — |
| 490 | C22×C4 | — | 3 | 48 | no | — |
| 491 | C22×C4 | — | 3 | 36 | no | — |
| 492 | C22×C4 | — | 3 | 72 | no | — |
| 493 | C22×C4 | — | 3 | 36 | no | — |
| 494 | C22×C4 | — | 3 | 432 | no | — |
| 495 | C22×C4 | — | 3 | 864 | no | — |
| 496 | C22×C4 | — | 3 | 216 | no | — |
| 497 | C22×C4 | — | 3 | 108 | no | — |
| 498 | C22×C4 | — | 3 | 216 | no | — |
| 499 | C22×C4 | — | 3 | 432 | no | — |
| 500 | C22×C4 | — | 3 | 36 | no | — |
| 501 | C22×C4 | — | 3 | 144 | no | — |
| 502 | C22×C4 | — | 3 | 288 | no | — |
| 503 | C22×C4 | — | 3 | 144 | no | — |
| 504 | C22×C4 | — | 3 | 6 | no | — |
| 505 | C22×C4 | — | 3 | 2 | no | — |
| 506 | C22×C4 | — | 3 | 8 | no | — |
| 507 | C22×C3 | — | 64 | 3 | no | — |
| 508 | C22×C3 | — | 64 | 4 | no | — |
| 509 | A4 | — | 16 | 12 | no | — |
| 510 | A4 | — | 16 | 1 | no | — |
| 511 | C23 | — | 3 | 3 | no | — |
| 512 | C23 | — | 3 | 12 | no | — |
| 513 | C23 | — | 3 | 6 | no | — |
| 514 | C23 | — | 3 | 2 | no | — |
| 515 | C23 | — | 3 | 12 | no | — |
| 516 | C23 | — | 3 | 3 | no | — |
| 517 | C23 | — | 3 | 3 | no | — |
| 518 | C23 | — | 3 | 4 | no | — |
| 519 | C23 | — | 3 | 4 | no | — |
| 520 | C23 | — | 3 | 108 | no | — |
| 521 | C23 | — | 3 | 108 | no | — |
| 522 | C23 | — | 3 | 54 | no | — |
| 523 | C23 | — | 3 | 18 | no | — |
| 524 | C23 | — | 3 | 72 | no | — |
| 525 | C23 | — | 3 | 96 | no | — |
| 526 | C23 | — | 3 | 24 | no | — |
| 527 | C23 | — | 3 | 108 | no | — |
| 528 | C23 | — | 3 | 144 | no | — |
| 529 | C23 | — | 3 | 12 | no | — |
| 530 | C23 | — | 3 | 16 | no | — |
| 531 | C23 | — | 3 | 36 | no | — |
| 532 | C23 | — | 3 | 36 | no | — |
| 533 | C23 | — | 3 | 36 | no | — |
| 534 | C23 | — | 4 | 72 | no | — |
| 535 | C23 | — | 6 | 108 | no | — |
| 536 | C23 | — | 6 | 108 | no | — |
| 537 | C23 | — | 6 | 27 | no | — |
| 538 | C23 | — | 6 | 9 | no | — |
| 539 | C23 | — | 6 | 108 | no | — |
| 540 | C23 | — | 6 | 108 | no | — |
| 541 | C23 | — | 6 | 288 | no | — |
| 542 | C23 | — | 6 | 108 | no | — |
| 543 | C23 | — | 6 | 432 | no | — |
| 544 | C23 | — | 6 | 108 | no | — |
| 545 | C23 | — | 6 | 108 | no | — |
| 546 | C23 | — | 6 | 108 | no | — |
| 547 | C23 | — | 6 | 3 | no | — |
| 548 | C23 | — | 6 | 9 | no | — |
| 549 | C23 | — | 6 | 48 | no | — |
| 550 | C23 | — | 12 | 12 | no | — |
| 551 | C23 | — | 12 | 72 | no | — |
| 552 | C23 | — | 12 | 12 | no | — |
| 553 | C23 | — | 12 | 108 | no | — |
| 554 | C23 | — | 12 | 216 | no | — |
| 555 | C23 | — | 12 | 108 | no | — |
| 556 | C23 | — | 12 | 432 | no | — |
| 557 | C23 | — | 12 | 12 | no | — |
| 558 | C23 | — | 12 | 108 | no | — |
| 559 | C23 | — | 12 | 288 | no | — |
| 560 | C23 | — | 12 | 432 | no | — |
| 561 | C23 | — | 12 | 864 | no | — |
| 562 | C23 | — | 12 | 72 | no | — |
| 563 | C23 | — | 12 | 72 | no | — |
| 564 | C23 | — | 12 | 12 | no | — |
| 565 | C23 | — | 12 | 108 | no | — |
| 566 | C23 | — | 12 | 72 | no | — |
| 567 | C23 | — | 12 | 72 | no | — |
| 568 | C23 | — | 12 | 72 | no | — |
| 569 | C23 | — | 12 | 96 | no | — |
| 570 | C23 | — | 12 | 216 | no | — |
| 571 | C23 | — | 12 | 288 | no | — |
| 572 | C23 | — | 12 | 72 | no | — |
| 573 | C23 | C2×#997 | 1 | 6 | yes | complemented |
| 574 | C23 | C22×C22⋊A4 | 1 | 1 | yes | characteristic |
| 575 | C23 | C22×C22⋊A4 | 1 | 12 | yes | complemented |
| 576 | C23 | C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 577 | Q8 | — | 3 | 24 | no | — |
| 578 | Q8 | — | 3 | 48 | no | — |
| 579 | Q8 | — | 3 | 16 | no | — |
| 580 | Q8 | — | 3 | 72 | no | — |
| 581 | Q8 | — | 3 | 8 | no | — |
| 582 | Q8 | C22×C22⋊A4 | 1 | 8 | yes | complemented |
| 583 | D4 | — | 3 | 576 | no | — |
| 584 | D4 | — | 3 | 576 | no | — |
| 585 | D4 | — | 3 | 288 | no | — |
| 586 | D4 | — | 3 | 96 | no | — |
| 587 | C2×C4 | — | 3 | 72 | no | — |
| 588 | C2×C4 | — | 3 | 36 | no | — |
| 589 | C2×C4 | — | 3 | 72 | no | — |
| 590 | C2×C4 | — | 3 | 12 | no | — |
| 591 | C2×C4 | — | 3 | 288 | no | — |
| 592 | C2×C4 | — | 3 | 144 | no | — |
| 593 | C2×C4 | — | 3 | 288 | no | — |
| 594 | C2×C4 | — | 3 | 48 | no | — |
| 595 | C2×C4 | — | 3 | 24 | no | — |
| 596 | C2×C4 | — | 3 | 24 | no | — |
| 597 | C2×C3 | — | 64 | 6 | no | — |
| 598 | C2×C3 | — | 64 | 1 | no | — |
| 599 | C22 | — | 3 | 6 | no | — |
| 600 | C22 | — | 3 | 1 | no | — |
| 601 | C22 | — | 3 | 6 | no | — |
| 602 | C22 | — | 3 | 8 | no | — |
| 603 | C22 | — | 3 | 12 | no | — |
| 604 | C22 | — | 3 | 6 | no | — |
| 605 | C22 | — | 3 | 6 | no | — |
| 606 | C22 | — | 3 | 3 | no | — |
| 607 | C22 | — | 3 | 1 | no | — |
| 608 | C22 | — | 3 | 36 | no | — |
| 609 | C22 | — | 3 | 12 | no | — |
| 610 | C22 | — | 4 | 12 | no | — |
| 611 | C22 | — | 6 | 18 | no | — |
| 612 | C22 | — | 6 | 216 | no | — |
| 613 | C22 | — | 6 | 216 | no | — |
| 614 | C22 | — | 6 | 54 | no | — |
| 615 | C22 | — | 6 | 18 | no | — |
| 616 | C22 | — | 6 | 54 | no | — |
| 617 | C22 | — | 6 | 72 | no | — |
| 618 | C22 | — | 6 | 72 | no | — |
| 619 | C22 | — | 12 | 36 | no | — |
| 620 | C22 | — | 12 | 12 | no | — |
| 621 | C22 | — | 12 | 16 | no | — |
| 622 | C22 | — | 12 | 108 | no | — |
| 623 | C22 | — | 12 | 144 | no | — |
| 624 | C22 | — | 12 | 72 | no | — |
| 625 | C22 | — | 12 | 96 | no | — |
| 626 | C22 | — | 12 | 24 | no | — |
| 627 | C22 | C22×#997 | 1 | 1 | yes | characteristic, complemented |
| 628 | C22 | C22⋊#997 | 1 | 4 | yes | direct product factor |
| 629 | C22 | C2×C22⋊(C22⋊A4) | 1 | 3 | yes | — |
| 630 | C4 | — | 3 | 24 | no | — |
| 631 | C4 | — | 3 | 8 | no | — |
| 632 | C3 | — | 64 | 1 | no | Sylow |
| 633 | C2 | — | 3 | 6 | no | — |
| 634 | C2 | — | 3 | 1 | no | — |
| 635 | C2 | — | 3 | 1 | no | — |
| 636 | C2 | — | 6 | 12 | no | — |
| 637 | C2 | — | 6 | 36 | no | — |
| 638 | C2 | C2×C22⋊#997 | 1 | 6 | yes | direct product factor |
| 639 | C2 | C22×C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C22×C3 |
| Frattini | C2 | C22×C22⋊(C22⋊A4) |
| Fitting | C24×H(5,𝔽2) | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊#997 | C2 | direct (N × H) |
| 2. C24×H(5,𝔽2) | C3 | semidirect |
| 4. C22⋊#997 | C22 | direct (N × H) |
| 11. C23×H(5,𝔽2) | C2×C3 | semidirect |
| 19. C27 | A4 | semidirect |
| 41. C22×H(5,𝔽2) | A4 | semidirect |
| 42. C22×H(5,𝔽2) | C22×C3 | semidirect |
| 49. C24×Q8 | A4 | semidirect |
| 78. C26 | C2×A4 | semidirect |
| 109. C2×H(5,𝔽2) | C2×A4 | semidirect |
| 134. C23×Q8 | C2×A4 | semidirect |
| 221. C25 | C22×A4 | semidirect |
| 223. C25 | C22⋊A4 | semidirect |
| 254. H(5,𝔽2) | C22×A4 | semidirect |
| 289. C22×Q8 | C22×A4 | semidirect |
| 290. C22×Q8 | C22⋊A4 | semidirect |
| 432. C24 | #997 | semidirect |
| 434. C24 | C2×C22⋊A4 | semidirect |
| 459. C2×Q8 | C2×C22⋊A4 | semidirect |
| 573. C23 | C2×#997 | semidirect |
| 575. C23 | C22×C22⋊A4 | semidirect |
| 582. Q8 | C22×C22⋊A4 | semidirect |
| 627. C22 | C22×#997 | semidirect |
| 628. C22 | C22⋊#997 | direct (N × H) |
| 638. C2 | C2×C22⋊#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#997 | 2 |
| C24×H(5,𝔽2) | 3 |
| C23×C22⋊A4 | 4 |
| C22×#997 | 4 |
| C22×C22⋊SL(2,𝔽3) | 4 |