← #72310822
Subgroups — #72310822
Order 2048.
At least 6545 conjugacy classes of subgroups; only the 830 normal subgroups are shown.
The subgroup lattice has 382 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72310819 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72310789 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72310753 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72310731 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72280972 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72265929 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #72262954 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#63103 | C22 | 1 | 1 | yes | characteristic |
| 9 | #7629120 | C4 | 1 | 2 | yes | complemented |
| 10 | #7629120 | C22 | 1 | 1 | yes | characteristic |
| 11 | #6628897 | C4 | 1 | 2 | yes | complemented |
| 12 | #6628897 | C22 | 1 | 2 | yes | — |
| 13 | #6628896 | C4 | 1 | 2 | yes | complemented |
| 14 | #6628896 | C22 | 1 | 2 | yes | — |
| 15 | #6370703 | C22 | 1 | 2 | yes | — |
| 16 | #6370692 | C4 | 1 | 2 | yes | complemented |
| 17 | #6370692 | C22 | 1 | 2 | yes | — |
| 18 | #6370692 | C22 | 1 | 1 | yes | characteristic |
| 19 | #392138 | C22 | 1 | 8 | yes | — |
| 20 | #213891 | C22 | 1 | 2 | yes | complemented |
| 21 | #213890 | C22 | 1 | 2 | yes | complemented |
| 22 | #213831 | C22 | 1 | 2 | yes | complemented |
| 23 | #213829 | C22 | 1 | 2 | yes | complemented |
| 24 | #128067 | C22 | 1 | 8 | yes | complemented |
| 25 | C2×2−1+6 | D4 | 1 | 4 | yes | — |
| 26 | C2×H(7,𝔽2) | C2×C4 | 1 | 2 | yes | — |
| 27 | C2×H(7,𝔽2) | C23 | 1 | 2 | yes | — |
| 28 | C22×#585 | C2×C4 | 1 | 2 | yes | — |
| 29 | C22×#585 | D4 | 1 | 4 | yes | — |
| 30 | C22×#585 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×#525 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C22×#525 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×#525 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×#2879 | D4 | 1 | 4 | yes | complemented |
| 35 | #35446 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | #35446 | C2×C4 | 1 | 4 | yes | complemented |
| 37 | #35446 | D4 | 1 | 1 | yes | characteristic |
| 38 | #35446 | D4 | 1 | 1 | yes | characteristic |
| 39 | #35446 | C23 | 1 | 1 | yes | characteristic |
| 40 | #35346 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #35346 | C2×C4 | 1 | 4 | yes | complemented |
| 42 | #35346 | D4 | 1 | 1 | yes | characteristic |
| 43 | #35346 | D4 | 1 | 1 | yes | characteristic |
| 44 | #35346 | C23 | 1 | 1 | yes | characteristic |
| 45 | #34044 | C2×C4 | 1 | 2 | yes | — |
| 46 | #34044 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #34044 | D4 | 1 | 1 | yes | characteristic |
| 48 | #34044 | D4 | 1 | 1 | yes | characteristic |
| 49 | #34044 | D4 | 1 | 4 | yes | complemented |
| 50 | #20593 | D4 | 1 | 4 | yes | complemented |
| 51 | #20592 | C23 | 1 | 4 | yes | — |
| 52 | #20586 | D4 | 1 | 4 | yes | — |
| 53 | #20586 | D4 | 1 | 4 | yes | complemented |
| 54 | #20586 | C23 | 1 | 4 | yes | — |
| 55 | #20585 | C2×C4 | 1 | 2 | yes | — |
| 56 | #20585 | C2×C4 | 1 | 4 | yes | complemented |
| 57 | #20585 | C2×C4 | 1 | 4 | yes | complemented |
| 58 | #20585 | C23 | 1 | 2 | yes | — |
| 59 | #20584 | D4 | 1 | 4 | yes | — |
| 60 | C2×#585 | C22⋊C4 | 1 | 8 | yes | — |
| 61 | C2×#585 | C2×D4 | 1 | 8 | yes | — |
| 62 | C22×2−1+4 | C22⋊C4 | 1 | 4 | yes | — |
| 63 | C22×2−1+4 | C2×D4 | 1 | 2 | yes | — |
| 64 | C22×2−1+4 | C2×D4 | 1 | 2 | yes | — |
| 65 | C22×2−1+4 | #41 | 1 | 2 | yes | — |
| 66 | C22×H(5,𝔽2) | C22×C4 | 1 | 4 | yes | — |
| 67 | C22×H(5,𝔽2) | C22×C4 | 1 | 1 | yes | characteristic |
| 68 | C22×H(5,𝔽2) | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C22×H(5,𝔽2) | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C22×H(5,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 71 | C22×H(5,𝔽2) | C2×D4 | 1 | 2 | yes | — |
| 72 | C22×H(5,𝔽2) | #41 | 1 | 2 | yes | — |
| 73 | C22×H(5,𝔽2) | C24 | 1 | 1 | yes | characteristic |
| 74 | C23×#41 | C22⋊C4 | 1 | 4 | yes | — |
| 75 | C23×#41 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | C23×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C23×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C23×#41 | C2×D4 | 1 | 2 | yes | — |
| 79 | C23×#41 | C2×D4 | 1 | 2 | yes | — |
| 80 | C23×#41 | C2×D4 | 1 | 2 | yes | — |
| 81 | C23×#41 | C2×D4 | 1 | 2 | yes | — |
| 82 | C23×#41 | #41 | 1 | 2 | yes | — |
| 83 | C23×#41 | #41 | 1 | 2 | yes | — |
| 84 | C25×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 85 | C22×#123 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 86 | C22×#123 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C22×#123 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 88 | C22×#123 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C22×#123 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×#123 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C22×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 93 | C22×#120 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C22×#120 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C22×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×#120 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×#117 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C22×#117 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 99 | C22×#117 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 100 | #2879 | C2×D4 | 1 | 8 | yes | — |
| 101 | #2309 | C22⋊C4 | 1 | 4 | yes | — |
| 102 | #2309 | C2×D4 | 1 | 8 | yes | — |
| 103 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 104 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 106 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 107 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | #2308 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 109 | #2308 | C22×C4 | 1 | 4 | yes | — |
| 110 | #2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 111 | #2308 | C22×C4 | 1 | 1 | yes | characteristic |
| 112 | #2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | #2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | #2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | #2308 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | #2280 | C22⋊C4 | 1 | 4 | yes | — |
| 117 | #1781 | C22⋊C4 | 1 | 8 | yes | — |
| 118 | #1781 | C2×D4 | 1 | 8 | yes | — |
| 119 | C26 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C22×#41 | #99 | 1 | 8 | yes | complemented |
| 121 | C22×#41 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 122 | C22×#41 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 123 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 124 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 125 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 126 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 127 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 128 | C22×#41 | C4×D4 | 1 | 2 | yes | — |
| 129 | C22×#41 | #120 | 1 | 2 | yes | — |
| 130 | C22×#41 | #120 | 1 | 2 | yes | — |
| 131 | C22×#41 | #120 | 1 | 2 | yes | — |
| 132 | C22×#41 | #120 | 1 | 2 | yes | — |
| 133 | C22×#41 | #120 | 1 | 2 | yes | — |
| 134 | C22×#41 | #120 | 1 | 2 | yes | — |
| 135 | C22×#41 | #120 | 1 | 2 | yes | — |
| 136 | C22×#41 | #120 | 1 | 2 | yes | — |
| 137 | C22×#41 | #120 | 1 | 2 | yes | — |
| 138 | C22×#41 | #121 | 1 | 2 | yes | — |
| 139 | C22×#41 | #121 | 1 | 2 | yes | — |
| 140 | C22×#41 | #121 | 1 | 2 | yes | — |
| 141 | C22×#41 | #121 | 1 | 2 | yes | — |
| 142 | C22×#41 | #121 | 1 | 2 | yes | — |
| 143 | C22×#41 | #121 | 1 | 2 | yes | — |
| 144 | C22×#41 | #121 | 1 | 2 | yes | — |
| 145 | C22×#41 | #121 | 1 | 2 | yes | — |
| 146 | C22×#41 | #121 | 1 | 2 | yes | — |
| 147 | C22×#41 | #121 | 1 | 2 | yes | — |
| 148 | C22×#41 | #121 | 1 | 2 | yes | — |
| 149 | C22×#41 | #121 | 1 | 2 | yes | — |
| 150 | C22×#41 | #123 | 1 | 2 | yes | — |
| 151 | C22×#41 | #123 | 1 | 2 | yes | — |
| 152 | C22×#41 | #123 | 1 | 2 | yes | — |
| 153 | C22×#41 | #124 | 1 | 2 | yes | — |
| 154 | C22×#41 | #124 | 1 | 2 | yes | — |
| 155 | C22×#41 | #124 | 1 | 2 | yes | — |
| 156 | C22×#41 | #127 | 1 | 2 | yes | — |
| 157 | C22×#41 | #127 | 1 | 2 | yes | — |
| 158 | C22×#41 | #127 | 1 | 2 | yes | — |
| 159 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 160 | C22×#41 | C22×D4 | 1 | 2 | yes | — |
| 161 | C22×#41 | C2×#41 | 1 | 2 | yes | — |
| 162 | C23×Q8 | #99 | 1 | 4 | yes | complemented |
| 163 | C23×Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 164 | C23×Q8 | #120 | 1 | 1 | yes | characteristic |
| 165 | C23×Q8 | #120 | 1 | 2 | yes | — |
| 166 | C23×Q8 | #121 | 1 | 2 | yes | — |
| 167 | C23×Q8 | #121 | 1 | 2 | yes | — |
| 168 | C23×Q8 | #121 | 1 | 2 | yes | — |
| 169 | C23×Q8 | #121 | 1 | 2 | yes | — |
| 170 | C23×Q8 | #123 | 1 | 1 | yes | characteristic |
| 171 | C23×Q8 | #123 | 1 | 2 | yes | — |
| 172 | C23×D4 | #99 | 1 | 4 | yes | complemented |
| 173 | C23×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C23×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C23×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 176 | C23×D4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C23×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 178 | C23×D4 | C4×D4 | 1 | 2 | yes | — |
| 179 | C23×D4 | C4×D4 | 1 | 2 | yes | — |
| 180 | C23×D4 | #120 | 1 | 1 | yes | characteristic |
| 181 | C23×D4 | #120 | 1 | 2 | yes | — |
| 182 | C23×D4 | #120 | 1 | 2 | yes | — |
| 183 | C23×D4 | #120 | 1 | 2 | yes | — |
| 184 | C23×D4 | #121 | 1 | 2 | yes | — |
| 185 | C23×D4 | #121 | 1 | 2 | yes | — |
| 186 | C23×D4 | #121 | 1 | 2 | yes | — |
| 187 | C23×D4 | #121 | 1 | 2 | yes | — |
| 188 | C23×D4 | #121 | 1 | 2 | yes | — |
| 189 | C23×D4 | #121 | 1 | 2 | yes | — |
| 190 | C23×D4 | #123 | 1 | 1 | yes | characteristic |
| 191 | C23×D4 | #123 | 1 | 2 | yes | — |
| 192 | C23×D4 | #124 | 1 | 2 | yes | — |
| 193 | C23×D4 | #127 | 1 | 2 | yes | — |
| 194 | C23×D4 | C23×C4 | 1 | 1 | yes | characteristic |
| 195 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 196 | C23×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 197 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 198 | C23×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 199 | C23×D4 | C2×#41 | 1 | 2 | yes | — |
| 200 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C24×C4 | #120 | 1 | 2 | yes | — |
| 205 | C24×C4 | #120 | 1 | 1 | yes | characteristic |
| 206 | C24×C4 | #120 | 1 | 1 | yes | characteristic |
| 207 | C24×C4 | #121 | 1 | 2 | yes | — |
| 208 | C24×C4 | #121 | 1 | 2 | yes | — |
| 209 | C24×C4 | #123 | 1 | 2 | yes | — |
| 210 | C24×C4 | #123 | 1 | 1 | yes | characteristic |
| 211 | C24×C4 | #123 | 1 | 1 | yes | characteristic |
| 212 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 215 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 216 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C22×C22⋊C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 218 | #379 | C2×C22⋊C4 | 1 | 8 | yes | — |
| 219 | C25 | #379 | 1 | 1 | yes | characteristic |
| 220 | C25 | #386 | 1 | 1 | yes | characteristic |
| 221 | C25 | #386 | 1 | 1 | yes | characteristic |
| 222 | C25 | #390 | 1 | 2 | yes | — |
| 223 | C25 | #392 | 1 | 2 | yes | — |
| 224 | C25 | #394 | 1 | 2 | yes | — |
| 225 | C25 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 226 | C25 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 227 | C25 | C2×#120 | 1 | 1 | yes | characteristic |
| 228 | C25 | C2×#121 | 1 | 2 | yes | — |
| 229 | C25 | C2×#123 | 1 | 1 | yes | characteristic |
| 230 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 231 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 232 | C22×Q8 | #386 | 1 | 2 | yes | — |
| 233 | C22×Q8 | #392 | 1 | 2 | yes | — |
| 234 | C22×Q8 | #392 | 1 | 2 | yes | — |
| 235 | C22×Q8 | #392 | 1 | 2 | yes | — |
| 236 | C22×Q8 | #394 | 1 | 2 | yes | — |
| 237 | C22×Q8 | #394 | 1 | 2 | yes | — |
| 238 | C22×Q8 | #394 | 1 | 2 | yes | — |
| 239 | C22×Q8 | C2×#99 | 1 | 8 | yes | — |
| 240 | C22×Q8 | C2×#121 | 1 | 2 | yes | — |
| 241 | C22×D4 | #379 | 1 | 2 | yes | — |
| 242 | C22×D4 | #379 | 1 | 2 | yes | — |
| 243 | C22×D4 | #386 | 1 | 2 | yes | — |
| 244 | C22×D4 | #386 | 1 | 2 | yes | — |
| 245 | C22×D4 | #386 | 1 | 2 | yes | — |
| 246 | C22×D4 | #386 | 1 | 2 | yes | — |
| 247 | C22×D4 | #386 | 1 | 2 | yes | — |
| 248 | C22×D4 | #390 | 1 | 2 | yes | — |
| 249 | C22×D4 | #390 | 1 | 2 | yes | — |
| 250 | C22×D4 | #390 | 1 | 2 | yes | — |
| 251 | C22×D4 | #390 | 1 | 2 | yes | — |
| 252 | C22×D4 | #392 | 1 | 2 | yes | — |
| 253 | C22×D4 | #392 | 1 | 2 | yes | — |
| 254 | C22×D4 | #392 | 1 | 2 | yes | — |
| 255 | C22×D4 | #392 | 1 | 2 | yes | — |
| 256 | C22×D4 | #392 | 1 | 2 | yes | — |
| 257 | C22×D4 | #394 | 1 | 2 | yes | — |
| 258 | C22×D4 | #394 | 1 | 2 | yes | — |
| 259 | C22×D4 | #394 | 1 | 2 | yes | — |
| 260 | C22×D4 | #394 | 1 | 2 | yes | — |
| 261 | C22×D4 | #394 | 1 | 2 | yes | — |
| 262 | C22×D4 | C2×#99 | 1 | 8 | yes | — |
| 263 | C22×D4 | C2×C4×D4 | 1 | 2 | yes | — |
| 264 | C22×D4 | C2×C4×D4 | 1 | 2 | yes | — |
| 265 | C22×D4 | C2×#120 | 1 | 2 | yes | — |
| 266 | C22×D4 | C2×#120 | 1 | 2 | yes | — |
| 267 | C22×D4 | C2×#121 | 1 | 2 | yes | — |
| 268 | C22×D4 | C2×#121 | 1 | 2 | yes | — |
| 269 | C22×D4 | C2×#121 | 1 | 2 | yes | — |
| 270 | C22×D4 | C2×#124 | 1 | 2 | yes | — |
| 271 | C22×D4 | C2×#127 | 1 | 2 | yes | — |
| 272 | C23×C4 | #379 | 1 | 1 | yes | characteristic |
| 273 | C23×C4 | #379 | 1 | 1 | yes | characteristic |
| 274 | C23×C4 | #379 | 1 | 1 | yes | characteristic |
| 275 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 276 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 277 | C23×C4 | #386 | 1 | 2 | yes | — |
| 278 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 279 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 280 | C23×C4 | #386 | 1 | 2 | yes | — |
| 281 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 282 | C23×C4 | #386 | 1 | 2 | yes | — |
| 283 | C23×C4 | #386 | 1 | 1 | yes | characteristic |
| 284 | C23×C4 | #386 | 1 | 2 | yes | — |
| 285 | C23×C4 | #390 | 1 | 2 | yes | — |
| 286 | C23×C4 | #390 | 1 | 2 | yes | — |
| 287 | C23×C4 | #390 | 1 | 2 | yes | — |
| 288 | C23×C4 | #392 | 1 | 2 | yes | — |
| 289 | C23×C4 | #392 | 1 | 2 | yes | — |
| 290 | C23×C4 | #392 | 1 | 2 | yes | — |
| 291 | C23×C4 | #392 | 1 | 2 | yes | — |
| 292 | C23×C4 | #392 | 1 | 2 | yes | — |
| 293 | C23×C4 | #392 | 1 | 2 | yes | — |
| 294 | C23×C4 | #392 | 1 | 2 | yes | — |
| 295 | C23×C4 | #394 | 1 | 2 | yes | — |
| 296 | C23×C4 | #394 | 1 | 2 | yes | — |
| 297 | C23×C4 | #394 | 1 | 2 | yes | — |
| 298 | C23×C4 | #394 | 1 | 2 | yes | — |
| 299 | C23×C4 | #394 | 1 | 2 | yes | — |
| 300 | C23×C4 | #394 | 1 | 2 | yes | — |
| 301 | C23×C4 | #394 | 1 | 2 | yes | — |
| 302 | C23×C4 | C2×#99 | 1 | 4 | yes | — |
| 303 | C23×C4 | C2×#99 | 1 | 4 | yes | — |
| 304 | C23×C4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 305 | C23×C4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 306 | C23×C4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 307 | C23×C4 | B(4,𝔽2) | 1 | 4 | yes | — |
| 308 | C23×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 309 | C23×C4 | C2×#120 | 1 | 2 | yes | — |
| 310 | C23×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 311 | C23×C4 | C2×#121 | 1 | 2 | yes | — |
| 312 | C23×C4 | C2×#123 | 1 | 1 | yes | characteristic |
| 313 | C23×C4 | C2×#123 | 1 | 2 | yes | — |
| 314 | C24 | #1438 | 1 | 2 | yes | — |
| 315 | C24 | #1438 | 1 | 2 | yes | — |
| 316 | C24 | #1438 | 1 | 2 | yes | — |
| 317 | C24 | #1781 | 1 | 4 | yes | — |
| 318 | C24 | #1889 | 1 | 4 | yes | — |
| 319 | C24 | C2×#379 | 1 | 1 | yes | characteristic |
| 320 | C24 | C2×#386 | 1 | 1 | yes | characteristic |
| 321 | C24 | C2×#386 | 1 | 1 | yes | characteristic |
| 322 | C24 | C2×#390 | 1 | 2 | yes | — |
| 323 | C24 | C2×#392 | 1 | 2 | yes | — |
| 324 | C24 | C2×#394 | 1 | 2 | yes | — |
| 325 | C24 | C2×B(4,𝔽2) | 1 | 4 | yes | — |
| 326 | C22×C4 | #1438 | 1 | 2 | yes | — |
| 327 | C22×C4 | #1438 | 1 | 2 | yes | — |
| 328 | C22×C4 | #1438 | 1 | 1 | yes | characteristic |
| 329 | C22×C4 | #1438 | 1 | 2 | yes | — |
| 330 | C22×C4 | #1438 | 1 | 1 | yes | characteristic |
| 331 | C22×C4 | #1438 | 1 | 1 | yes | characteristic |
| 332 | C22×C4 | #1438 | 1 | 1 | yes | characteristic |
| 333 | C22×C4 | #1781 | 1 | 2 | yes | — |
| 334 | C22×C4 | #1781 | 1 | 2 | yes | — |
| 335 | C22×C4 | #1889 | 1 | 2 | yes | — |
| 336 | C22×C4 | #1889 | 1 | 2 | yes | — |
| 337 | C22×C4 | #1889 | 1 | 2 | yes | — |
| 338 | C22×C4 | #1889 | 1 | 2 | yes | — |
| 339 | C22×C4 | #1889 | 1 | 4 | yes | — |
| 340 | C22×C4 | #1898 | 1 | 4 | yes | — |
| 341 | C22×C4 | #1898 | 1 | 4 | yes | — |
| 342 | C22×C4 | #1898 | 1 | 8 | yes | — |
| 343 | C22×C4 | #2021 | 1 | 4 | yes | — |
| 344 | C22×C4 | #2021 | 1 | 4 | yes | — |
| 345 | C22×C4 | #2021 | 1 | 4 | yes | — |
| 346 | C22×C4 | #2021 | 1 | 4 | yes | — |
| 347 | C22×C4 | #2021 | 1 | 8 | yes | — |
| 348 | C22×C4 | #2021 | 1 | 8 | yes | — |
| 349 | C22×C4 | C2×#386 | 1 | 2 | yes | — |
| 350 | C22×C4 | C2×#392 | 1 | 2 | yes | — |
| 351 | C22×C4 | C2×#394 | 1 | 2 | yes | — |
| 352 | C22×C4 | C22×#99 | 1 | 4 | yes | — |
| 353 | C22×C4 | C2×B(4,𝔽2) | 1 | 4 | yes | — |
| 354 | C23 | #10965 | 1 | 4 | yes | — |
| 355 | C23 | #10991 | 1 | 4 | yes | — |
| 356 | C23 | C2×#1438 | 1 | 1 | yes | characteristic |
| 357 | C23 | C2×#1781 | 1 | 2 | yes | — |
| 358 | C23 | C2×#1889 | 1 | 2 | yes | — |
| 359 | C23 | C2×#1889 | 1 | 2 | yes | — |
| 360 | C23 | C2×#2021 | 1 | 4 | yes | — |
| 361 | C2×C4 | #10965 | 1 | 2 | yes | — |
| 362 | C2×C4 | #10965 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #10965 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | #10991 | 1 | 2 | yes | — |
| 365 | C2×C4 | #10991 | 1 | 2 | yes | — |
| 366 | C2×C4 | #10991 | 1 | 4 | yes | — |
| 367 | C2×C4 | #10991 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | #10991 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | #10991 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | #10991 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C2×#1898 | 1 | 4 | yes | — |
| 372 | C2×C4 | C2×#2021 | 1 | 4 | yes | — |
| 373 | C22 | C2×#10965 | 1 | 1 | yes | characteristic |
| 374 | C22 | C2×#10991 | 1 | 1 | yes | characteristic |
| 375 | C22 | C2×#10991 | 1 | 1 | yes | characteristic |
| 376 | C4 | #115690 | 1 | 1 | yes | characteristic |
| 377 | C4 | #115690 | 1 | 1 | yes | characteristic |
| 378 | C4 | #115690 | 1 | 1 | yes | characteristic |
| 379 | C4 | #115690 | 1 | 1 | yes | characteristic |
| 380 | C2 | C2×#115690 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta