← C24×C4×H(5,𝔽2) #72339118
Subgroups — C24×C4×H(5,𝔽2) #72339118
Order 2048.
17322440 conjugacy classes of subgroups.
The subgroup lattice has 310 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C24×C4×#41 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | C24×#520 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C23×C4×H(5,𝔽2) | C2 | 1 | 480 | yes | maximal, direct product factor |
| 4 | C24×#518 | C2 | 1 | 9 | yes | maximal, complemented |
| 5 | C25×C4×D4 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C25×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C24×H(5,𝔽2) | C4 | 1 | 256 | yes | direct product factor |
| 8 | C24×H(5,𝔽2) | C22 | 1 | 240 | yes | — |
| 9 | C25×#41 | C22 | 1 | 6 | yes | — |
| 10 | C26×D4 | C22 | 1 | 9 | yes | — |
| 11 | C27×C4 | C22 | 1 | 6 | yes | complemented |
| 12 | C22×C4×H(5,𝔽2) | C22 | 1 | 35840 | yes | direct product factor |
| 13 | C23×#520 | C22 | 1 | 1440 | yes | complemented |
| 14 | C23×#518 | C22 | 1 | 2160 | yes | complemented |
| 15 | C23×C4×#41 | C22 | 1 | 1440 | yes | complemented |
| 16 | C24×C4×Q8 | C22 | 1 | 6 | yes | complemented |
| 17 | C24×C4×Q8 | C22 | 1 | 2 | yes | complemented |
| 18 | C24×C4×D4 | C22 | 1 | 18 | yes | complemented |
| 19 | C24×C4×D4 | C22 | 1 | 36 | yes | complemented |
| 20 | C24×C4×D4 | C22 | 1 | 18 | yes | complemented |
| 21 | C24×C4×D4 | C22 | 1 | 2160 | yes | complemented |
| 22 | C24×#117 | C22 | 1 | 18 | yes | complemented |
| 23 | C25×C4⋊C4 | C22 | 1 | 9 | yes | complemented |
| 24 | C25×C22⋊C4 | C22 | 1 | 18 | yes | complemented |
| 25 | C25×C42 | C22 | 1 | 9 | yes | complemented |
| 26 | C28 | C23 | 1 | 6 | yes | — |
| 27 | C23×H(5,𝔽2) | C2×C4 | 1 | 30720 | yes | direct product factor |
| 28 | C23×H(5,𝔽2) | C23 | 1 | 8960 | yes | — |
| 29 | C24×#41 | C2×C4 | 1 | 768 | yes | complemented |
| 30 | C24×#41 | C23 | 1 | 720 | yes | — |
| 31 | C25×Q8 | C23 | 1 | 2 | yes | — |
| 32 | C25×D4 | C2×C4 | 1 | 1152 | yes | complemented |
| 33 | C25×D4 | C23 | 1 | 18 | yes | — |
| 34 | C25×D4 | C23 | 1 | 1080 | yes | — |
| 35 | C26×C4 | — | 4 | 192 | no | — |
| 36 | C26×C4 | C23 | 1 | 9 | yes | — |
| 37 | C26×C4 | C23 | 1 | 9 | yes | — |
| 38 | C26×C4 | C23 | 1 | 18 | yes | — |
| 39 | C26×C4 | C23 | 1 | 9 | yes | — |
| 40 | C26×C4 | C23 | 1 | 720 | yes | complemented |
| 41 | C2×C4×H(5,𝔽2) | C23 | 1 | 491520 | yes | direct product factor |
| 42 | C22×#520 | C23 | 1 | 53760 | yes | complemented |
| 43 | C22×#518 | C23 | 1 | 80640 | yes | complemented |
| 44 | C22×C4×#41 | C23 | 1 | 53760 | yes | complemented |
| 45 | C23×C4×Q8 | C23 | 1 | 240 | yes | complemented |
| 46 | C23×C4×Q8 | C23 | 1 | 720 | yes | complemented |
| 47 | C23×C4×D4 | C23 | 1 | 2160 | yes | complemented |
| 48 | C23×C4×D4 | C23 | 1 | 4320 | yes | complemented |
| 49 | C23×C4×D4 | C23 | 1 | 2160 | yes | complemented |
| 50 | C23×C4×D4 | C23 | 1 | 80640 | yes | complemented |
| 51 | C23×#117 | C23 | 1 | 2160 | yes | complemented |
| 52 | C24×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 53 | C24×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 54 | C24×C4⋊C4 | C23 | 1 | 1080 | yes | complemented |
| 55 | C24×C22⋊C4 | C23 | 1 | 36 | yes | — |
| 56 | C24×C22⋊C4 | C23 | 1 | 2160 | yes | complemented |
| 57 | C24×C42 | C23 | 1 | 18 | yes | — |
| 58 | C24×C42 | C23 | 1 | 6 | yes | — |
| 59 | C24×C42 | C23 | 1 | 1080 | yes | complemented |
| 60 | C27 | — | 4 | 96 | no | — |
| 61 | C27 | — | 4 | 96 | no | — |
| 62 | C27 | C22×C4 | 1 | 384 | yes | complemented |
| 63 | C27 | C24 | 1 | 9 | yes | — |
| 64 | C27 | C24 | 1 | 360 | yes | — |
| 65 | C22×H(5,𝔽2) | C22×C4 | 1 | 573440 | yes | direct product factor |
| 66 | C22×H(5,𝔽2) | C24 | 1 | 61440 | yes | — |
| 67 | C23×#41 | C22×C4 | 1 | 46080 | yes | complemented |
| 68 | C23×#41 | C24 | 1 | 13440 | yes | — |
| 69 | C24×Q8 | C22×C4 | 1 | 128 | yes | complemented |
| 70 | C24×Q8 | C24 | 1 | 120 | yes | — |
| 71 | C24×D4 | C22×C4 | 1 | 1152 | yes | complemented |
| 72 | C24×D4 | C22×C4 | 1 | 69120 | yes | complemented |
| 73 | C24×D4 | C24 | 1 | 1080 | yes | — |
| 74 | C24×D4 | C24 | 1 | 20160 | yes | — |
| 75 | C25×C4 | — | 2 | 288 | no | — |
| 76 | C25×C4 | — | 4 | 11520 | no | — |
| 77 | C25×C4 | — | 4 | 288 | no | — |
| 78 | C25×C4 | — | 4 | 144 | no | — |
| 79 | C25×C4 | C22×C4 | 1 | 576 | yes | complemented |
| 80 | C25×C4 | C24 | 1 | 9 | yes | — |
| 81 | C25×C4 | C24 | 1 | 6 | yes | — |
| 82 | C25×C4 | C24 | 1 | 540 | yes | — |
| 83 | C25×C4 | C24 | 1 | 1080 | yes | — |
| 84 | C25×C4 | C24 | 1 | 540 | yes | — |
| 85 | C25×C4 | C24 | 1 | 6 | yes | — |
| 86 | C25×C4 | C24 | 1 | 540 | yes | — |
| 87 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 88 | C25×C4 | C24 | 1 | 13440 | yes | complemented |
| 89 | C4×H(5,𝔽2) | C24 | 1 | 1048576 | yes | direct product factor |
| 90 | C2×#520 | C24 | 1 | 368640 | yes | complemented |
| 91 | C2×#518 | C24 | 1 | 552960 | yes | complemented |
| 92 | C2×C4×#41 | C24 | 1 | 368640 | yes | complemented |
| 93 | C22×C4×Q8 | C24 | 1 | 4480 | yes | complemented |
| 94 | C22×C4×Q8 | C24 | 1 | 13440 | yes | complemented |
| 95 | C22×C4×D4 | C24 | 1 | 40320 | yes | complemented |
| 96 | C22×C4×D4 | C24 | 1 | 80640 | yes | complemented |
| 97 | C22×C4×D4 | C24 | 1 | 40320 | yes | complemented |
| 98 | C22×C4×D4 | C24 | 1 | 552960 | yes | complemented |
| 99 | C22×#117 | C24 | 1 | 40320 | yes | complemented |
| 100 | C23×C4⋊C4 | C24 | 1 | 1080 | yes | — |
| 101 | C23×C4⋊C4 | C24 | 1 | 360 | yes | — |
| 102 | C23×C4⋊C4 | C24 | 1 | 20160 | yes | complemented |
| 103 | C23×C22⋊C4 | C24 | 1 | 2160 | yes | — |
| 104 | C23×C22⋊C4 | C24 | 1 | 40320 | yes | complemented |
| 105 | C23×C42 | C24 | 1 | 360 | yes | — |
| 106 | C23×C42 | C24 | 1 | 1080 | yes | — |
| 107 | C23×C42 | C24 | 1 | 20160 | yes | complemented |
| 108 | C26 | — | 2 | 144 | no | — |
| 109 | C26 | — | 2 | 144 | no | — |
| 110 | C26 | — | 4 | 2880 | no | — |
| 111 | C26 | — | 4 | 6144 | no | — |
| 112 | C26 | — | 4 | 2880 | no | — |
| 113 | C26 | C23×C4 | 1 | 288 | yes | — |
| 114 | C26 | C23×C4 | 1 | 11520 | yes | complemented |
| 115 | C26 | C25 | 1 | 270 | yes | — |
| 116 | C26 | C25 | 1 | 3360 | yes | — |
| 117 | C26 | C25 | 1 | 1 | yes | characteristic |
| 118 | C2×H(5,𝔽2) | C23×C4 | 1 | 1966080 | yes | direct product factor |
| 119 | C2×H(5,𝔽2) | C25 | 1 | 65536 | yes | — |
| 120 | C22×#41 | C23×C4 | 1 | 430080 | yes | complemented |
| 121 | C22×#41 | C25 | 1 | 46080 | yes | — |
| 122 | C23×Q8 | C23×C4 | 1 | 3840 | yes | complemented |
| 123 | C23×Q8 | C25 | 1 | 1120 | yes | — |
| 124 | C23×D4 | C23×C4 | 1 | 34560 | yes | complemented |
| 125 | C23×D4 | C23×C4 | 1 | 645120 | yes | complemented |
| 126 | C23×D4 | C25 | 1 | 10080 | yes | — |
| 127 | C23×D4 | C25 | 1 | 69120 | yes | — |
| 128 | C24×C4 | — | 2 | 144 | no | — |
| 129 | C24×C4 | — | 2 | 96 | no | — |
| 130 | C24×C4 | — | 2 | 8640 | no | — |
| 131 | C24×C4 | — | 4 | 107520 | no | — |
| 132 | C24×C4 | — | 4 | 8640 | no | — |
| 133 | C24×C4 | — | 4 | 4320 | no | — |
| 134 | C24×C4 | C23×C4 | 1 | 192 | yes | — |
| 135 | C24×C4 | C23×C4 | 1 | 17280 | yes | complemented |
| 136 | C24×C4 | H(5,𝔽2) | 1 | 32 | yes | direct product factor |
| 137 | C24×C4 | C25 | 1 | 270 | yes | — |
| 138 | C24×C4 | C25 | 1 | 180 | yes | — |
| 139 | C24×C4 | C25 | 1 | 5040 | yes | — |
| 140 | C24×C4 | C25 | 1 | 10080 | yes | — |
| 141 | C24×C4 | C25 | 1 | 5040 | yes | — |
| 142 | C24×C4 | C25 | 1 | 180 | yes | — |
| 143 | C24×C4 | C25 | 1 | 5040 | yes | — |
| 144 | C24×C4 | C25 | 1 | 30 | yes | — |
| 145 | C24×C4 | C25 | 1 | 46080 | yes | complemented |
| 146 | #520 | C25 | 1 | 393216 | yes | complemented |
| 147 | #518 | C25 | 1 | 589824 | yes | complemented |
| 148 | C4×#41 | C25 | 1 | 393216 | yes | complemented |
| 149 | C2×C4×Q8 | C25 | 1 | 15360 | yes | complemented |
| 150 | C2×C4×Q8 | C25 | 1 | 46080 | yes | complemented |
| 151 | C2×C4×D4 | C25 | 1 | 138240 | yes | complemented |
| 152 | C2×C4×D4 | C25 | 1 | 276480 | yes | complemented |
| 153 | C2×C4×D4 | C25 | 1 | 138240 | yes | complemented |
| 154 | C2×C4×D4 | C25 | 1 | 589824 | yes | complemented |
| 155 | C2×#117 | C25 | 1 | 138240 | yes | complemented |
| 156 | C22×C4⋊C4 | C25 | 1 | 10080 | yes | — |
| 157 | C22×C4⋊C4 | C25 | 1 | 3360 | yes | — |
| 158 | C22×C4⋊C4 | C25 | 1 | 69120 | yes | complemented |
| 159 | C22×C22⋊C4 | C25 | 1 | 20160 | yes | — |
| 160 | C22×C22⋊C4 | C25 | 1 | 138240 | yes | complemented |
| 161 | C22×C42 | C25 | 1 | 3360 | yes | — |
| 162 | C22×C42 | C25 | 1 | 10080 | yes | — |
| 163 | C22×C42 | C25 | 1 | 69120 | yes | complemented |
| 164 | C25 | — | 2 | 2160 | no | — |
| 165 | C25 | — | 2 | 2160 | no | — |
| 166 | C25 | — | 2 | 4608 | no | — |
| 167 | C25 | — | 4 | 13440 | no | — |
| 168 | C25 | — | 4 | 92160 | no | — |
| 169 | C25 | — | 4 | 13440 | no | — |
| 170 | C25 | C24×C4 | 1 | 4320 | yes | — |
| 171 | C25 | C24×C4 | 1 | 16 | yes | — |
| 172 | C25 | C24×C4 | 1 | 53760 | yes | complemented |
| 173 | C25 | C2×H(5,𝔽2) | 1 | 16 | yes | — |
| 174 | C25 | #585 | 1 | 16 | yes | — |
| 175 | C25 | C26 | 1 | 1260 | yes | — |
| 176 | C25 | C26 | 1 | 5760 | yes | — |
| 177 | C25 | C26 | 1 | 15 | yes | — |
| 178 | H(5,𝔽2) | C24×C4 | 1 | 1048576 | yes | direct product factor |
| 179 | C2×#41 | C24×C4 | 1 | 737280 | yes | complemented |
| 180 | C2×#41 | C26 | 1 | 24576 | yes | — |
| 181 | C22×Q8 | C24×C4 | 1 | 17920 | yes | complemented |
| 182 | C22×Q8 | C26 | 1 | 1920 | yes | — |
| 183 | C22×D4 | C24×C4 | 1 | 161280 | yes | complemented |
| 184 | C22×D4 | C24×C4 | 1 | 1105920 | yes | complemented |
| 185 | C22×D4 | C26 | 1 | 17280 | yes | — |
| 186 | C22×D4 | C26 | 1 | 36864 | yes | — |
| 187 | C23×C4 | — | 2 | 2160 | no | — |
| 188 | C23×C4 | — | 2 | 1440 | no | — |
| 189 | C23×C4 | — | 2 | 40320 | no | — |
| 190 | C23×C4 | — | 4 | 184320 | no | — |
| 191 | C23×C4 | — | 4 | 40320 | no | — |
| 192 | C23×C4 | — | 4 | 20160 | no | — |
| 193 | C23×C4 | C24×C4 | 1 | 2880 | yes | — |
| 194 | C23×C4 | C24×C4 | 1 | 80640 | yes | complemented |
| 195 | C23×C4 | C2×H(5,𝔽2) | 1 | 480 | yes | direct product factor |
| 196 | C23×C4 | C26 | 1 | 840 | yes | — |
| 197 | C23×C4 | C26 | 1 | 1260 | yes | — |
| 198 | C23×C4 | C26 | 1 | 8640 | yes | — |
| 199 | C23×C4 | C26 | 1 | 8640 | yes | — |
| 200 | C23×C4 | C26 | 1 | 17280 | yes | — |
| 201 | C23×C4 | C26 | 1 | 840 | yes | — |
| 202 | C23×C4 | C26 | 1 | 8640 | yes | — |
| 203 | C23×C4 | C26 | 1 | 140 | yes | — |
| 204 | C23×C4 | C26 | 1 | 24576 | yes | complemented |
| 205 | C4×Q8 | C26 | 1 | 8192 | yes | complemented |
| 206 | C4×Q8 | C26 | 1 | 24576 | yes | complemented |
| 207 | C4×D4 | C26 | 1 | 73728 | yes | complemented |
| 208 | C4×D4 | C26 | 1 | 147456 | yes | complemented |
| 209 | C4×D4 | C26 | 1 | 73728 | yes | complemented |
| 210 | #117 | C26 | 1 | 73728 | yes | complemented |
| 211 | C2×C4⋊C4 | C26 | 1 | 17280 | yes | — |
| 212 | C2×C4⋊C4 | C26 | 1 | 5760 | yes | — |
| 213 | C2×C4⋊C4 | C26 | 1 | 36864 | yes | complemented |
| 214 | C2×C22⋊C4 | C26 | 1 | 34560 | yes | — |
| 215 | C2×C22⋊C4 | C26 | 1 | 73728 | yes | complemented |
| 216 | C2×C42 | C26 | 1 | 17280 | yes | — |
| 217 | C2×C42 | C26 | 1 | 5760 | yes | — |
| 218 | C2×C42 | C26 | 1 | 36864 | yes | complemented |
| 219 | C24 | — | 2 | 5040 | no | — |
| 220 | C24 | — | 2 | 5040 | no | — |
| 221 | C24 | — | 2 | 34560 | no | — |
| 222 | C24 | — | 4 | 11520 | no | — |
| 223 | C24 | — | 4 | 215040 | no | — |
| 224 | C24 | — | 4 | 11520 | no | — |
| 225 | C24 | C4×H(5,𝔽2) | 1 | 256 | yes | direct product factor |
| 226 | C24 | C25×C4 | 1 | 10080 | yes | — |
| 227 | C24 | C25×C4 | 1 | 120 | yes | — |
| 228 | C24 | C25×C4 | 1 | 46080 | yes | complemented |
| 229 | C24 | C22×H(5,𝔽2) | 1 | 120 | yes | — |
| 230 | C24 | C2×#585 | 1 | 120 | yes | — |
| 231 | C24 | C27 | 1 | 1080 | yes | — |
| 232 | C24 | C27 | 1 | 1536 | yes | — |
| 233 | C24 | C27 | 1 | 35 | yes | — |
| 234 | #41 | C25×C4 | 1 | 196608 | yes | complemented |
| 235 | C2×Q8 | C25×C4 | 1 | 15360 | yes | complemented |
| 236 | C2×Q8 | C27 | 1 | 512 | yes | — |
| 237 | C2×D4 | C25×C4 | 1 | 138240 | yes | complemented |
| 238 | C2×D4 | C25×C4 | 1 | 294912 | yes | complemented |
| 239 | C2×D4 | C27 | 1 | 4608 | yes | — |
| 240 | C22×C4 | — | 2 | 5040 | no | — |
| 241 | C22×C4 | — | 2 | 3360 | no | — |
| 242 | C22×C4 | — | 2 | 34560 | no | — |
| 243 | C22×C4 | — | 4 | 49152 | no | — |
| 244 | C22×C4 | — | 4 | 34560 | no | — |
| 245 | C22×C4 | — | 4 | 17280 | no | — |
| 246 | C22×C4 | C25×C4 | 1 | 6720 | yes | — |
| 247 | C22×C4 | C25×C4 | 1 | 69120 | yes | complemented |
| 248 | C22×C4 | C22×H(5,𝔽2) | 1 | 1120 | yes | direct product factor |
| 249 | C22×C4 | C27 | 1 | 720 | yes | — |
| 250 | C22×C4 | C27 | 1 | 1080 | yes | — |
| 251 | C22×C4 | C27 | 1 | 2304 | yes | — |
| 252 | C22×C4 | C27 | 1 | 2304 | yes | — |
| 253 | C22×C4 | C27 | 1 | 4608 | yes | — |
| 254 | C22×C4 | C27 | 1 | 720 | yes | — |
| 255 | C22×C4 | C27 | 1 | 2304 | yes | — |
| 256 | C22×C4 | C27 | 1 | 120 | yes | — |
| 257 | C4⋊C4 | C27 | 1 | 4608 | yes | — |
| 258 | C4⋊C4 | C27 | 1 | 1536 | yes | — |
| 259 | C22⋊C4 | C27 | 1 | 9216 | yes | — |
| 260 | C42 | C27 | 1 | 1536 | yes | — |
| 261 | C42 | C27 | 1 | 4608 | yes | — |
| 262 | C23 | — | 2 | 40320 | no | — |
| 263 | C23 | — | 2 | 2160 | no | — |
| 264 | C23 | — | 2 | 2160 | no | — |
| 265 | C23 | — | 4 | 1536 | no | — |
| 266 | C23 | — | 4 | 92160 | no | — |
| 267 | C23 | — | 4 | 1536 | no | — |
| 268 | C23 | C2×C4×H(5,𝔽2) | 1 | 960 | yes | direct product factor |
| 269 | C23 | C26×C4 | 1 | 4320 | yes | — |
| 270 | C23 | C26×C4 | 1 | 140 | yes | — |
| 271 | C23 | C26×C4 | 1 | 6144 | yes | complemented |
| 272 | C23 | C23×H(5,𝔽2) | 1 | 140 | yes | — |
| 273 | C23 | C22×#585 | 1 | 140 | yes | — |
| 274 | C23 | C28 | 1 | 144 | yes | — |
| 275 | C23 | C28 | 1 | 15 | yes | — |
| 276 | Q8 | C26×C4 | 1 | 2048 | yes | complemented |
| 277 | D4 | C26×C4 | 1 | 18432 | yes | complemented |
| 278 | C2×C4 | — | 2 | 2160 | no | — |
| 279 | C2×C4 | — | 2 | 1440 | no | — |
| 280 | C2×C4 | — | 2 | 4608 | no | — |
| 281 | C2×C4 | — | 4 | 4608 | no | — |
| 282 | C2×C4 | — | 4 | 2304 | no | — |
| 283 | C2×C4 | C26×C4 | 1 | 2880 | yes | — |
| 284 | C2×C4 | C26×C4 | 1 | 9216 | yes | complemented |
| 285 | C2×C4 | C23×H(5,𝔽2) | 1 | 480 | yes | direct product factor |
| 286 | C2×C4 | C28 | 1 | 96 | yes | — |
| 287 | C2×C4 | C28 | 1 | 144 | yes | — |
| 288 | C2×C4 | C28 | 1 | 96 | yes | — |
| 289 | C2×C4 | C28 | 1 | 16 | yes | — |
| 290 | C22 | — | 2 | 144 | no | — |
| 291 | C22 | — | 2 | 144 | no | — |
| 292 | C22 | — | 2 | 8640 | no | — |
| 293 | C22 | — | 4 | 6144 | no | — |
| 294 | C22 | C22×C4×H(5,𝔽2) | 1 | 560 | yes | direct product factor |
| 295 | C22 | C27×C4 | 1 | 288 | yes | — |
| 296 | C22 | C27×C4 | 1 | 30 | yes | — |
| 297 | C22 | C24×H(5,𝔽2) | 1 | 30 | yes | — |
| 298 | C22 | C23×#585 | 1 | 30 | yes | — |
| 299 | C22 | C29 | 1 | 1 | yes | characteristic |
| 300 | C4 | — | 2 | 144 | no | — |
| 301 | C4 | — | 2 | 96 | no | — |
| 302 | C4 | C27×C4 | 1 | 192 | yes | — |
| 303 | C4 | C24×H(5,𝔽2) | 1 | 32 | yes | direct product factor |
| 304 | C2 | — | 2 | 288 | no | — |
| 305 | C2 | C28×C4 | 1 | 1 | yes | characteristic |
| 306 | C2 | C25×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 307 | C2 | C24×#585 | 1 | 1 | yes | characteristic |
| 308 | C2 | C23×C4×H(5,𝔽2) | 1 | 60 | yes | direct product factor |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C24×C4×#41 | C2 | semidirect |
| 2. C24×#520 | C2 | semidirect |
| 3. C23×C4×H(5,𝔽2) | C2 | direct (N × H) |
| 4. C24×#518 | C2 | semidirect |
| 5. C25×C4×D4 | C2 | semidirect |
| 7. C24×H(5,𝔽2) | C4 | direct (N × H) |
| 11. C27×C4 | C22 | semidirect |
| 12. C22×C4×H(5,𝔽2) | C22 | direct (N × H) |
| 13. C23×#520 | C22 | semidirect |
| 14. C23×#518 | C22 | semidirect |
| 15. C23×C4×#41 | C22 | semidirect |
| 16. C24×C4×Q8 | C22 | semidirect |
| 17. C24×C4×Q8 | C22 | semidirect |
| 18. C24×C4×D4 | C22 | semidirect |
| 19. C24×C4×D4 | C22 | semidirect |
| 20. C24×C4×D4 | C22 | semidirect |
| 21. C24×C4×D4 | C22 | semidirect |
| 22. C24×#117 | C22 | semidirect |
| 23. C25×C4⋊C4 | C22 | semidirect |
| 24. C25×C22⋊C4 | C22 | semidirect |
| 25. C25×C42 | C22 | semidirect |
| 27. C23×H(5,𝔽2) | C2×C4 | direct (N × H) |
| 29. C24×#41 | C2×C4 | semidirect |
| 32. C25×D4 | C2×C4 | semidirect |
| 40. C26×C4 | C23 | semidirect |
| 41. C2×C4×H(5,𝔽2) | C23 | direct (N × H) |
| 42. C22×#520 | C23 | semidirect |
| 43. C22×#518 | C23 | semidirect |
| 44. C22×C4×#41 | C23 | semidirect |
| 45. C23×C4×Q8 | C23 | semidirect |
| 46. C23×C4×Q8 | C23 | semidirect |
| 47. C23×C4×D4 | C23 | semidirect |
| 48. C23×C4×D4 | C23 | semidirect |
| 49. C23×C4×D4 | C23 | semidirect |
| 50. C23×C4×D4 | C23 | semidirect |
| 51. C23×#117 | C23 | semidirect |
| 54. C24×C4⋊C4 | C23 | semidirect |
| 56. C24×C22⋊C4 | C23 | semidirect |
| 59. C24×C42 | C23 | semidirect |
| 62. C27 | C22×C4 | semidirect |
| 65. C22×H(5,𝔽2) | C22×C4 | direct (N × H) |
| 67. C23×#41 | C22×C4 | semidirect |
| 69. C24×Q8 | C22×C4 | semidirect |
| 71. C24×D4 | C22×C4 | semidirect |
| 72. C24×D4 | C22×C4 | semidirect |
| 79. C25×C4 | C22×C4 | semidirect |
| 88. C25×C4 | C24 | semidirect |
| 89. C4×H(5,𝔽2) | C24 | direct (N × H) |
| 90. C2×#520 | C24 | semidirect |
| 91. C2×#518 | C24 | semidirect |
| 92. C2×C4×#41 | C24 | semidirect |
| 93. C22×C4×Q8 | C24 | semidirect |
| 94. C22×C4×Q8 | C24 | semidirect |
| 95. C22×C4×D4 | C24 | semidirect |
| 96. C22×C4×D4 | C24 | semidirect |
| 97. C22×C4×D4 | C24 | semidirect |
| 98. C22×C4×D4 | C24 | semidirect |
| 99. C22×#117 | C24 | semidirect |
| 102. C23×C4⋊C4 | C24 | semidirect |
| 104. C23×C22⋊C4 | C24 | semidirect |
| 107. C23×C42 | C24 | semidirect |
| 114. C26 | C23×C4 | semidirect |
| 118. C2×H(5,𝔽2) | C23×C4 | direct (N × H) |
| 120. C22×#41 | C23×C4 | semidirect |
| 122. C23×Q8 | C23×C4 | semidirect |
| 124. C23×D4 | C23×C4 | semidirect |
| 125. C23×D4 | C23×C4 | semidirect |
| 135. C24×C4 | C23×C4 | semidirect |
| 136. C24×C4 | H(5,𝔽2) | direct (N × H) |
| 145. C24×C4 | C25 | semidirect |
| 146. #520 | C25 | semidirect |
| 147. #518 | C25 | semidirect |
| 148. C4×#41 | C25 | semidirect |
| 149. C2×C4×Q8 | C25 | semidirect |
| 150. C2×C4×Q8 | C25 | semidirect |
| 151. C2×C4×D4 | C25 | semidirect |
| 152. C2×C4×D4 | C25 | semidirect |
| 153. C2×C4×D4 | C25 | semidirect |
| 154. C2×C4×D4 | C25 | semidirect |
| 155. C2×#117 | C25 | semidirect |
| 158. C22×C4⋊C4 | C25 | semidirect |
| 160. C22×C22⋊C4 | C25 | semidirect |
| 163. C22×C42 | C25 | semidirect |
| 172. C25 | C24×C4 | semidirect |
| 178. H(5,𝔽2) | C24×C4 | direct (N × H) |
| 179. C2×#41 | C24×C4 | semidirect |
| 181. C22×Q8 | C24×C4 | semidirect |
| 183. C22×D4 | C24×C4 | semidirect |
| 184. C22×D4 | C24×C4 | semidirect |
| 194. C23×C4 | C24×C4 | semidirect |
| 195. C23×C4 | C2×H(5,𝔽2) | direct (N × H) |
| 204. C23×C4 | C26 | semidirect |
| 205. C4×Q8 | C26 | semidirect |
| 206. C4×Q8 | C26 | semidirect |
| 207. C4×D4 | C26 | semidirect |
| 208. C4×D4 | C26 | semidirect |
| 209. C4×D4 | C26 | semidirect |
| 210. #117 | C26 | semidirect |
| 213. C2×C4⋊C4 | C26 | semidirect |
| 215. C2×C22⋊C4 | C26 | semidirect |
| 218. C2×C42 | C26 | semidirect |
| 225. C24 | C4×H(5,𝔽2) | direct (N × H) |
| 228. C24 | C25×C4 | semidirect |
| 234. #41 | C25×C4 | semidirect |
| 235. C2×Q8 | C25×C4 | semidirect |
| 237. C2×D4 | C25×C4 | semidirect |
| 238. C2×D4 | C25×C4 | semidirect |
| 247. C22×C4 | C25×C4 | semidirect |
| 248. C22×C4 | C22×H(5,𝔽2) | direct (N × H) |
| 268. C23 | C2×C4×H(5,𝔽2) | direct (N × H) |
| 271. C23 | C26×C4 | semidirect |
| 276. Q8 | C26×C4 | semidirect |
| 277. D4 | C26×C4 | semidirect |
| 284. C2×C4 | C26×C4 | semidirect |
| 285. C2×C4 | C23×H(5,𝔽2) | direct (N × H) |
| 294. C22 | C22×C4×H(5,𝔽2) | direct (N × H) |
| 303. C4 | C24×H(5,𝔽2) | direct (N × H) |
| 308. C2 | C23×C4×H(5,𝔽2) | direct (N × H) |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta