← #72314478
Subgroups — #72314478
Order 2048.
At least 6153 conjugacy classes of subgroups; only the 1528 normal subgroups are shown.
The subgroup lattice has 336 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72314465 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C2×#147569 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×#146479 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C22×#12707 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#392109 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#7630939 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C26×D4 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×#3484 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C22×#3484 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C22×#3484 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#36614 | C4 | 1 | 2 | yes | complemented |
| 12 | C2×#35222 | C4 | 1 | 2 | yes | complemented |
| 13 | C2×#35222 | C22 | 1 | 2 | yes | — |
| 14 | C2×#35222 | C22 | 1 | 2 | yes | — |
| 15 | C2×#34171 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#34171 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#34171 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×#2127 | C22 | 1 | 8 | yes | complemented |
| 19 | C22×#1781 | C22 | 1 | 4 | yes | — |
| 20 | C22×#1781 | C22 | 1 | 4 | yes | complemented |
| 21 | C22×#1781 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#12582 | C22 | 1 | 8 | yes | complemented |
| 23 | C28 | D4 | 1 | 2 | yes | — |
| 24 | C23×H(5,𝔽2) | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C25×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C25×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C25×D4 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C25×D4 | D4 | 1 | 2 | yes | — |
| 29 | C25×D4 | D4 | 1 | 2 | yes | — |
| 30 | C25×D4 | D4 | 1 | 2 | yes | — |
| 31 | C25×D4 | C23 | 1 | 1 | yes | characteristic |
| 32 | C25×D4 | C23 | 1 | 1 | yes | characteristic |
| 33 | C25×D4 | C23 | 1 | 1 | yes | characteristic |
| 34 | C26×C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#3484 | D4 | 1 | 8 | yes | — |
| 36 | C22×#535 | C2×C4 | 1 | 2 | yes | — |
| 37 | C22×#535 | C2×C4 | 1 | 2 | yes | — |
| 38 | C22×#535 | C23 | 1 | 2 | yes | — |
| 39 | C22×#525 | C2×C4 | 1 | 2 | yes | — |
| 40 | C22×#525 | C2×C4 | 1 | 2 | yes | — |
| 41 | C22×#525 | C2×C4 | 1 | 2 | yes | — |
| 42 | C22×#518 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C22×#518 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C22×#518 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C23×#99 | C23 | 1 | 8 | yes | — |
| 46 | #35222 | D4 | 1 | 16 | yes | — |
| 47 | C2×#2435 | D4 | 1 | 8 | yes | — |
| 48 | C2×#2433 | D4 | 1 | 8 | yes | — |
| 49 | #34171 | D4 | 1 | 8 | yes | — |
| 50 | C2×#2309 | C2×C4 | 1 | 2 | yes | — |
| 51 | C2×#2309 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×#2309 | C23 | 1 | 2 | yes | — |
| 53 | C2×#2280 | C2×C4 | 1 | 2 | yes | — |
| 54 | C2×#2280 | C2×C4 | 1 | 2 | yes | — |
| 55 | C2×#2280 | C2×C4 | 1 | 2 | yes | — |
| 56 | C2×#1781 | D4 | 1 | 16 | yes | complemented |
| 57 | C27 | C22⋊C4 | 1 | 2 | yes | — |
| 58 | C27 | C22⋊C4 | 1 | 2 | yes | — |
| 59 | C27 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 60 | C27 | C22⋊C4 | 1 | 2 | yes | — |
| 61 | C27 | C2×D4 | 1 | 2 | yes | — |
| 62 | C27 | C2×D4 | 1 | 2 | yes | — |
| 63 | C27 | C2×D4 | 1 | 2 | yes | — |
| 64 | C22×H(5,𝔽2) | C22⋊C4 | 1 | 4 | yes | complemented |
| 65 | C23×#41 | C22×C4 | 1 | 2 | yes | — |
| 66 | C24×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 67 | C24×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 68 | C24×D4 | C22⋊C4 | 1 | 2 | yes | — |
| 69 | C24×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C24×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 71 | C24×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C24×D4 | C2×D4 | 1 | 2 | yes | — |
| 73 | C24×D4 | C2×D4 | 1 | 2 | yes | — |
| 74 | C24×D4 | C2×D4 | 1 | 2 | yes | — |
| 75 | C24×D4 | C2×D4 | 1 | 8 | yes | — |
| 76 | C24×D4 | C2×D4 | 1 | 8 | yes | — |
| 77 | C24×D4 | C2×D4 | 1 | 4 | yes | — |
| 78 | C24×D4 | C2×D4 | 1 | 4 | yes | — |
| 79 | C24×D4 | C2×D4 | 1 | 8 | yes | — |
| 80 | C24×D4 | #41 | 1 | 8 | yes | — |
| 81 | C24×D4 | C24 | 1 | 1 | yes | characteristic |
| 82 | C25×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 83 | C25×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 84 | C25×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 85 | C25×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C25×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 87 | C25×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 88 | C2×#535 | C22⋊C4 | 1 | 8 | yes | complemented |
| 89 | C2×#535 | C2×D4 | 1 | 8 | yes | — |
| 90 | C2×#535 | C2×D4 | 1 | 8 | yes | — |
| 91 | C22×#127 | C22⋊C4 | 1 | 4 | yes | complemented |
| 92 | C22×#127 | C2×D4 | 1 | 4 | yes | — |
| 93 | C22×#124 | C22⋊C4 | 1 | 4 | yes | complemented |
| 94 | C22×#124 | C2×D4 | 1 | 4 | yes | — |
| 95 | C2×#525 | C22⋊C4 | 1 | 8 | yes | complemented |
| 96 | C2×#525 | C22⋊C4 | 1 | 8 | yes | complemented |
| 97 | C22×C22⋊Q8 | C22⋊C4 | 1 | 4 | yes | complemented |
| 98 | C22×#121 | C22⋊C4 | 1 | 4 | yes | complemented |
| 99 | C2×#518 | C22⋊C4 | 1 | 4 | yes | complemented |
| 100 | C2×#518 | C22⋊C4 | 1 | 4 | yes | complemented |
| 101 | C2×#518 | C22⋊C4 | 1 | 4 | yes | complemented |
| 102 | C22×#117 | C22×C4 | 1 | 2 | yes | — |
| 103 | C22×#117 | C22×C4 | 1 | 2 | yes | — |
| 104 | C22×#117 | C22×C4 | 1 | 2 | yes | — |
| 105 | C22×#99 | C2×D4 | 1 | 16 | yes | complemented |
| 106 | #2309 | C22⋊C4 | 1 | 8 | yes | complemented |
| 107 | #2309 | C2×D4 | 1 | 8 | yes | — |
| 108 | #2309 | C2×D4 | 1 | 8 | yes | — |
| 109 | C2×#390 | C22⋊C4 | 1 | 8 | yes | complemented |
| 110 | C2×#390 | C2×D4 | 1 | 8 | yes | — |
| 111 | #2280 | C22⋊C4 | 1 | 8 | yes | complemented |
| 112 | #2280 | C22⋊C4 | 1 | 8 | yes | complemented |
| 113 | C2×C4×C22⋊C4 | C22⋊C4 | 1 | 8 | yes | complemented |
| 114 | C26 | #99 | 1 | 8 | yes | — |
| 115 | C26 | #99 | 1 | 8 | yes | — |
| 116 | C26 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C26 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C26 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 119 | C26 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 120 | C26 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 121 | C26 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 122 | C26 | #120 | 1 | 8 | yes | — |
| 123 | C26 | #120 | 1 | 8 | yes | — |
| 124 | C26 | #120 | 1 | 8 | yes | — |
| 125 | C26 | #120 | 1 | 4 | yes | — |
| 126 | C26 | #121 | 1 | 8 | yes | — |
| 127 | C26 | #123 | 1 | 4 | yes | — |
| 128 | C26 | C22×D4 | 1 | 2 | yes | — |
| 129 | C22×#41 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 130 | C22×#41 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 131 | C23×Q8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 132 | C23×D4 | #99 | 1 | 8 | yes | — |
| 133 | C23×D4 | #99 | 1 | 8 | yes | — |
| 134 | C23×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 135 | C23×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 136 | C23×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 137 | C23×D4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 138 | C23×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 139 | C23×D4 | C4×D4 | 1 | 8 | yes | — |
| 140 | C23×D4 | #120 | 1 | 8 | yes | — |
| 141 | C23×D4 | #120 | 1 | 8 | yes | — |
| 142 | C23×D4 | #120 | 1 | 8 | yes | — |
| 143 | C23×D4 | #120 | 1 | 4 | yes | — |
| 144 | C23×D4 | #120 | 1 | 8 | yes | — |
| 145 | C23×D4 | #121 | 1 | 8 | yes | — |
| 146 | C23×D4 | #121 | 1 | 16 | yes | — |
| 147 | C23×D4 | #121 | 1 | 16 | yes | — |
| 148 | C23×D4 | #123 | 1 | 4 | yes | — |
| 149 | C23×D4 | #123 | 1 | 8 | yes | — |
| 150 | C23×D4 | #124 | 1 | 8 | yes | — |
| 151 | C23×D4 | #127 | 1 | 8 | yes | — |
| 152 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 153 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 154 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 155 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 156 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 157 | C23×D4 | C2×#41 | 1 | 4 | yes | — |
| 158 | C23×D4 | H(5,𝔽2) | 1 | 8 | yes | — |
| 159 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 160 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 161 | C24×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 162 | C24×C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 163 | C24×C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 164 | C24×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 165 | C24×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 166 | C24×C4 | C4×D4 | 1 | 8 | yes | — |
| 167 | C24×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 168 | C2×#127 | #120 | 1 | 16 | yes | — |
| 169 | C2×#124 | #120 | 1 | 16 | yes | — |
| 170 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 171 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 172 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 173 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 174 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 175 | C2×#117 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 176 | C22×C4⋊C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 177 | C22×C42 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 178 | C22×C42 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 179 | #390 | #120 | 1 | 32 | yes | — |
| 180 | C25 | #379 | 1 | 2 | yes | — |
| 181 | C25 | #379 | 1 | 2 | yes | — |
| 182 | C25 | #379 | 1 | 4 | yes | — |
| 183 | C25 | #379 | 1 | 2 | yes | — |
| 184 | C25 | #379 | 1 | 4 | yes | — |
| 185 | C25 | #379 | 1 | 4 | yes | — |
| 186 | C25 | #386 | 1 | 4 | yes | — |
| 187 | C25 | #386 | 1 | 4 | yes | — |
| 188 | C25 | #386 | 1 | 4 | yes | — |
| 189 | C25 | #392 | 1 | 16 | yes | — |
| 190 | C25 | #394 | 1 | 16 | yes | — |
| 191 | C25 | C2×#99 | 1 | 4 | yes | — |
| 192 | C25 | C2×#99 | 1 | 4 | yes | — |
| 193 | C25 | C2×#99 | 1 | 4 | yes | — |
| 194 | C25 | C2×#99 | 1 | 4 | yes | — |
| 195 | C25 | C2×#99 | 1 | 4 | yes | — |
| 196 | C25 | C2×#99 | 1 | 4 | yes | — |
| 197 | C25 | C2×#99 | 1 | 4 | yes | — |
| 198 | C25 | C2×#99 | 1 | 4 | yes | — |
| 199 | C25 | C2×#99 | 1 | 4 | yes | — |
| 200 | C25 | C2×#99 | 1 | 4 | yes | — |
| 201 | C25 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C25 | C2×#120 | 1 | 4 | yes | — |
| 203 | C25 | C2×#120 | 1 | 4 | yes | — |
| 204 | C25 | C2×#120 | 1 | 4 | yes | — |
| 205 | C25 | C2×#120 | 1 | 2 | yes | — |
| 206 | C25 | C2×#121 | 1 | 4 | yes | — |
| 207 | C25 | C2×#123 | 1 | 2 | yes | — |
| 208 | C25 | #534 | 1 | 4 | yes | — |
| 209 | C25 | #534 | 1 | 4 | yes | — |
| 210 | C22×Q8 | #379 | 1 | 4 | yes | complemented |
| 211 | C22×D4 | #379 | 1 | 4 | yes | complemented |
| 212 | C22×D4 | #386 | 1 | 8 | yes | — |
| 213 | C22×D4 | #390 | 1 | 8 | yes | — |
| 214 | C22×D4 | #392 | 1 | 16 | yes | — |
| 215 | C22×D4 | #394 | 1 | 16 | yes | — |
| 216 | C22×D4 | C2×#120 | 1 | 8 | yes | — |
| 217 | C22×D4 | C2×#120 | 1 | 8 | yes | — |
| 218 | C22×D4 | C2×#120 | 1 | 2 | yes | — |
| 219 | C22×D4 | C2×#121 | 1 | 4 | yes | — |
| 220 | C22×D4 | C2×#121 | 1 | 4 | yes | — |
| 221 | C22×D4 | C2×#123 | 1 | 2 | yes | — |
| 222 | C22×D4 | C2×#124 | 1 | 2 | yes | — |
| 223 | C22×D4 | C2×#127 | 1 | 2 | yes | — |
| 224 | C22×D4 | #534 | 1 | 8 | yes | — |
| 225 | C22×D4 | #535 | 1 | 8 | yes | — |
| 226 | C22×D4 | D42 | 1 | 16 | yes | — |
| 227 | C22×D4 | D42 | 1 | 16 | yes | — |
| 228 | C22×D4 | #546 | 1 | 16 | yes | — |
| 229 | C22×D4 | #546 | 1 | 16 | yes | — |
| 230 | C23×C4 | #379 | 1 | 2 | yes | — |
| 231 | C23×C4 | #379 | 1 | 2 | yes | — |
| 232 | C23×C4 | #379 | 1 | 2 | yes | — |
| 233 | C23×C4 | #386 | 1 | 4 | yes | — |
| 234 | C23×C4 | #386 | 1 | 8 | yes | — |
| 235 | C23×C4 | #390 | 1 | 8 | yes | — |
| 236 | C23×C4 | C2×#99 | 1 | 4 | yes | — |
| 237 | C23×C4 | C2×#99 | 1 | 4 | yes | — |
| 238 | C23×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 239 | C23×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 240 | C23×C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 241 | C23×C4 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 242 | C23×C4 | C2×C4×D4 | 1 | 4 | yes | — |
| 243 | C23×C4 | #518 | 1 | 4 | yes | — |
| 244 | C2×C4⋊C4 | #379 | 1 | 8 | yes | complemented |
| 245 | C2×C42 | #379 | 1 | 8 | yes | complemented |
| 246 | C2×C42 | #379 | 1 | 8 | yes | complemented |
| 247 | C24 | #1438 | 1 | 4 | yes | — |
| 248 | C24 | #1438 | 1 | 8 | yes | — |
| 249 | C24 | #1781 | 1 | 4 | yes | — |
| 250 | C24 | #1781 | 1 | 8 | yes | — |
| 251 | C24 | #1781 | 1 | 4 | yes | — |
| 252 | C24 | #1781 | 1 | 8 | yes | — |
| 253 | C24 | #1781 | 1 | 8 | yes | — |
| 254 | C24 | #1781 | 1 | 8 | yes | — |
| 255 | C24 | #1898 | 1 | 8 | yes | — |
| 256 | C24 | #1898 | 1 | 8 | yes | — |
| 257 | C24 | #1898 | 1 | 8 | yes | — |
| 258 | C24 | #1898 | 1 | 8 | yes | — |
| 259 | C24 | C2×#379 | 1 | 1 | yes | characteristic |
| 260 | C24 | C2×#379 | 1 | 1 | yes | characteristic |
| 261 | C24 | C2×#379 | 1 | 1 | yes | characteristic |
| 262 | C24 | C2×#386 | 1 | 2 | yes | — |
| 263 | C24 | #2308 | 1 | 2 | yes | — |
| 264 | C24 | C2×#392 | 1 | 4 | yes | — |
| 265 | C24 | C2×#394 | 1 | 4 | yes | — |
| 266 | C24 | #2403 | 1 | 4 | yes | — |
| 267 | C24 | #2403 | 1 | 4 | yes | — |
| 268 | C24 | #2405 | 1 | 4 | yes | — |
| 269 | C24 | #2405 | 1 | 4 | yes | — |
| 270 | C24 | #2410 | 1 | 8 | yes | — |
| 271 | C24 | #2410 | 1 | 8 | yes | — |
| 272 | C24 | #2613 | 1 | 8 | yes | — |
| 273 | C24 | #2846 | 1 | 8 | yes | — |
| 274 | C24 | C22×#99 | 1 | 2 | yes | — |
| 275 | C24 | C22×#99 | 1 | 2 | yes | — |
| 276 | C24 | C22×#99 | 1 | 2 | yes | — |
| 277 | C24 | C22×#99 | 1 | 2 | yes | — |
| 278 | C2×D4 | #2403 | 1 | 8 | yes | — |
| 279 | C2×D4 | #2405 | 1 | 8 | yes | — |
| 280 | C2×D4 | #2408 | 1 | 16 | yes | — |
| 281 | C2×D4 | #2410 | 1 | 16 | yes | — |
| 282 | C2×D4 | #2433 | 1 | 8 | yes | — |
| 283 | C2×D4 | #2435 | 1 | 8 | yes | — |
| 284 | C22×C4 | #1438 | 1 | 4 | yes | — |
| 285 | C22×C4 | #1781 | 1 | 4 | yes | — |
| 286 | C22×C4 | #1781 | 1 | 4 | yes | — |
| 287 | C22×C4 | C2×#379 | 1 | 2 | yes | — |
| 288 | C22×C4 | C2×#379 | 1 | 2 | yes | — |
| 289 | C22×C4 | C2×#386 | 1 | 2 | yes | — |
| 290 | C22×C4 | C2×#390 | 1 | 2 | yes | — |
| 291 | C22×C4 | #2308 | 1 | 2 | yes | — |
| 292 | C22×C4 | #2309 | 1 | 2 | yes | — |
| 293 | C22×C4 | D4×C22⋊C4 | 1 | 8 | yes | — |
| 294 | C22×C4 | D4×C22⋊C4 | 1 | 8 | yes | — |
| 295 | C23 | #10965 | 1 | 16 | yes | — |
| 296 | C23 | #12707 | 1 | 8 | yes | complemented |
| 297 | C23 | C2×#1438 | 1 | 1 | yes | characteristic |
| 298 | C23 | #13867 | 1 | 2 | yes | — |
| 299 | C23 | #13867 | 1 | 2 | yes | — |
| 300 | C23 | #14335 | 1 | 1 | yes | characteristic |
| 301 | C23 | #14679 | 1 | 1 | yes | characteristic |
| 302 | C23 | #14715 | 1 | 8 | yes | — |
| 303 | C23 | #14724 | 1 | 8 | yes | — |
| 304 | C23 | C2×#1781 | 1 | 2 | yes | — |
| 305 | C23 | C2×#1781 | 1 | 2 | yes | — |
| 306 | C23 | C2×#1781 | 1 | 1 | yes | characteristic |
| 307 | C23 | C2×#1781 | 1 | 2 | yes | — |
| 308 | C23 | C2×#1781 | 1 | 1 | yes | characteristic |
| 309 | C23 | C2×#1781 | 1 | 1 | yes | characteristic |
| 310 | C23 | C2×#1781 | 1 | 2 | yes | — |
| 311 | C23 | C2×#1781 | 1 | 1 | yes | characteristic |
| 312 | C23 | C2×#1898 | 1 | 2 | yes | — |
| 313 | C23 | C2×#1898 | 1 | 2 | yes | — |
| 314 | C23 | C2×#1898 | 1 | 2 | yes | — |
| 315 | C23 | C2×#1898 | 1 | 2 | yes | — |
| 316 | C23 | #21746 | 1 | 2 | yes | — |
| 317 | C23 | #21746 | 1 | 2 | yes | — |
| 318 | C23 | #21746 | 1 | 2 | yes | — |
| 319 | C23 | #21746 | 1 | 2 | yes | — |
| 320 | C2×C4 | #13867 | 1 | 4 | yes | — |
| 321 | C2×C4 | #13902 | 1 | 4 | yes | — |
| 322 | C22 | #154094 | 1 | 1 | yes | characteristic |
| 323 | C22 | C2×#10965 | 1 | 2 | yes | — |
| 324 | C22 | #359428 | 1 | 2 | yes | — |
| 325 | C22 | #359428 | 1 | 2 | yes | — |
| 326 | C22 | #359428 | 1 | 2 | yes | — |
| 327 | C22 | #359428 | 1 | 2 | yes | — |
| 328 | C22 | #382422 | 1 | 2 | yes | — |
| 329 | C22 | #392109 | 1 | 1 | yes | characteristic |
| 330 | C22 | #392109 | 1 | 1 | yes | characteristic |
| 331 | C22 | C2×#12707 | 1 | 4 | yes | — |
| 332 | C2 | #72210555 | 1 | 2 | yes | — |
| 333 | C2 | #72218057 | 1 | 4 | yes | — |
| 334 | C2 | #72218375 | 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