← #72303023
Subgroups — #72303023
Order 1024.
Only the 38403 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 338 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#63103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10586020 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10574884 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | C2×#60398 | C2 | 1 | 24 | yes | maximal, complemented |
| 5 | #10574876 | C2 | 1 | 16 | yes | maximal, complemented |
| 6 | #10574875 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | #10574874 | C2 | 1 | 32 | yes | maximal, complemented |
| 8 | #10574873 | C2 | 1 | 24 | yes | maximal, complemented |
| 9 | C2×#60070 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #63103 | C22 | 1 | 16 | yes | complemented |
| 11 | #63103 | C22 | 1 | 16 | yes | complemented |
| 12 | C2×2−1+6 | C22 | 1 | 4 | yes | complemented |
| 13 | C2×H(7,𝔽2) | C22 | 1 | 12 | yes | complemented |
| 14 | C22×#585 | C22 | 1 | 3 | yes | — |
| 15 | C22×#585 | C22 | 1 | 12 | yes | complemented |
| 16 | C22×#585 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #62859 | C22 | 1 | 24 | yes | complemented |
| 18 | #62852 | C22 | 1 | 24 | yes | complemented |
| 19 | #62848 | C22 | 1 | 12 | yes | complemented |
| 20 | #62842 | C22 | 1 | 36 | yes | complemented |
| 21 | #62811 | C22 | 1 | 48 | yes | complemented |
| 22 | C2×#3449 | C22 | 1 | 36 | yes | complemented |
| 23 | C2×#3428 | C22 | 1 | 3 | yes | complemented |
| 24 | #60402 | C22 | 1 | 128 | yes | complemented |
| 25 | #60401 | C22 | 1 | 384 | yes | complemented |
| 26 | #60400 | C22 | 1 | 128 | yes | complemented |
| 27 | #60399 | C22 | 1 | 384 | yes | complemented |
| 28 | #60398 | C22 | 1 | 192 | yes | complemented |
| 29 | #60398 | C22 | 1 | 192 | yes | complemented |
| 30 | #60398 | C22 | 1 | 192 | yes | complemented |
| 31 | #60398 | C22 | 1 | 64 | yes | complemented |
| 32 | C2×#3028 | C22 | 1 | 96 | yes | complemented |
| 33 | C2×#3027 | C22 | 1 | 96 | yes | complemented |
| 34 | C2×#3026 | C22 | 1 | 192 | yes | complemented |
| 35 | C2×#3025 | C22 | 1 | 192 | yes | complemented |
| 36 | #60070 | C22 | 1 | 48 | yes | complemented |
| 37 | #60070 | C22 | 1 | 48 | yes | complemented |
| 38 | C2×#2884 | C22 | 1 | 12 | yes | complemented |
| 39 | C2×#2883 | C22 | 1 | 36 | yes | complemented |
| 40 | C22×#410 | C22 | 1 | 36 | yes | complemented |
| 41 | 2−1+6 | C23 | 1 | 64 | yes | — |
| 42 | H(7,𝔽2) | C23 | 1 | 192 | yes | — |
| 43 | C2×#585 | D4 | 1 | 24 | yes | complemented |
| 44 | C2×#585 | D4 | 1 | 24 | yes | complemented |
| 45 | C2×#585 | C23 | 1 | 24 | yes | — |
| 46 | C2×#585 | C23 | 1 | 24 | yes | — |
| 47 | C2×#585 | C23 | 1 | 16 | yes | — |
| 48 | C2×#585 | C23 | 1 | 48 | yes | — |
| 49 | C2×#585 | C23 | 1 | 96 | yes | — |
| 50 | C2×#585 | C23 | 1 | 96 | yes | — |
| 51 | C22×2−1+4 | D4 | 1 | 12 | yes | complemented |
| 52 | C22×2−1+4 | C23 | 1 | 6 | yes | — |
| 53 | C22×2−1+4 | C23 | 1 | 2 | yes | complemented |
| 54 | C22×2−1+4 | C23 | 1 | 4 | yes | complemented |
| 55 | C22×H(5,𝔽2) | D4 | 1 | 12 | yes | complemented |
| 56 | C22×H(5,𝔽2) | C23 | 1 | 18 | yes | — |
| 57 | C22×H(5,𝔽2) | C23 | 1 | 48 | yes | — |
| 58 | C22×H(5,𝔽2) | C23 | 1 | 6 | yes | complemented |
| 59 | C22×H(5,𝔽2) | C23 | 1 | 4 | yes | complemented |
| 60 | C23×#41 | D4 | 1 | 24 | yes | complemented |
| 61 | C23×#41 | C23 | 1 | 18 | yes | — |
| 62 | C23×#41 | C23 | 1 | 1 | yes | characteristic |
| 63 | C23×#41 | C23 | 1 | 6 | yes | complemented |
| 64 | C23×#41 | C23 | 1 | 8 | yes | complemented |
| 65 | #3487 | C23 | 1 | 96 | yes | complemented |
| 66 | #3486 | C23 | 1 | 96 | yes | complemented |
| 67 | #3485 | C23 | 1 | 288 | yes | complemented |
| 68 | #3484 | C23 | 1 | 288 | yes | complemented |
| 69 | #3449 | C23 | 1 | 144 | yes | complemented |
| 70 | #3449 | C23 | 1 | 48 | yes | complemented |
| 71 | #3449 | C23 | 1 | 144 | yes | complemented |
| 72 | #3449 | C23 | 1 | 144 | yes | complemented |
| 73 | C2×#536 | C23 | 1 | 72 | yes | complemented |
| 74 | C2×#535 | C23 | 1 | 72 | yes | complemented |
| 75 | C2×#534 | C23 | 1 | 144 | yes | complemented |
| 76 | C2×#525 | C23 | 1 | 144 | yes | complemented |
| 77 | #3428 | C23 | 1 | 24 | yes | complemented |
| 78 | #3428 | C23 | 1 | 24 | yes | complemented |
| 79 | C2×#519 | C23 | 1 | 6 | yes | complemented |
| 80 | C2×#518 | C23 | 1 | 18 | yes | complemented |
| 81 | C22×#117 | C23 | 1 | 18 | yes | complemented |
| 82 | #3028 | C23 | 1 | 256 | yes | complemented |
| 83 | #3028 | C23 | 1 | 768 | yes | complemented |
| 84 | #3027 | C23 | 1 | 256 | yes | complemented |
| 85 | #3027 | C23 | 1 | 768 | yes | complemented |
| 86 | #3026 | C23 | 1 | 512 | yes | complemented |
| 87 | #3026 | C23 | 1 | 1536 | yes | complemented |
| 88 | #3025 | C23 | 1 | 512 | yes | complemented |
| 89 | #3025 | C23 | 1 | 1536 | yes | complemented |
| 90 | C2×#458 | C23 | 1 | 768 | yes | complemented |
| 91 | C2×B(4,𝔽2) | C23 | 1 | 768 | yes | complemented |
| 92 | #2884 | C23 | 1 | 192 | yes | complemented |
| 93 | #2883 | C23 | 1 | 576 | yes | complemented |
| 94 | C2×#410 | C23 | 1 | 48 | yes | complemented |
| 95 | C2×#410 | C23 | 1 | 144 | yes | complemented |
| 96 | C2×#410 | C23 | 1 | 288 | yes | complemented |
| 97 | C2×#410 | C23 | 1 | 288 | yes | complemented |
| 98 | C22×#99 | C23 | 1 | 144 | yes | complemented |
| 99 | #585 | C24 | 1 | 64 | yes | — |
| 100 | #585 | C24 | 1 | 64 | yes | — |
| 101 | #585 | C24 | 1 | 384 | yes | — |
| 102 | C2×2−1+4 | C2×D4 | 1 | 96 | yes | complemented |
| 103 | C2×2−1+4 | C2×D4 | 1 | 96 | yes | complemented |
| 104 | C2×2−1+4 | C2×D4 | 1 | 48 | yes | complemented |
| 105 | C2×2−1+4 | C24 | 1 | 48 | yes | — |
| 106 | C2×H(5,𝔽2) | C2×D4 | 1 | 96 | yes | complemented |
| 107 | C2×H(5,𝔽2) | C2×D4 | 1 | 96 | yes | complemented |
| 108 | C2×H(5,𝔽2) | C2×D4 | 1 | 144 | yes | complemented |
| 109 | C2×H(5,𝔽2) | C24 | 1 | 144 | yes | — |
| 110 | C2×H(5,𝔽2) | C24 | 1 | 64 | yes | — |
| 111 | C2×H(5,𝔽2) | C24 | 1 | 384 | yes | — |
| 112 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 113 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 114 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 115 | C22×#41 | C2×D4 | 1 | 12 | yes | — |
| 116 | C22×#41 | C2×D4 | 1 | 36 | yes | complemented |
| 117 | C22×#41 | C2×D4 | 1 | 24 | yes | complemented |
| 118 | C22×#41 | C2×D4 | 1 | 72 | yes | complemented |
| 119 | C22×#41 | C2×D4 | 1 | 192 | yes | complemented |
| 120 | C22×#41 | C2×D4 | 1 | 192 | yes | complemented |
| 121 | C22×#41 | C2×D4 | 1 | 36 | yes | complemented |
| 122 | C22×#41 | C2×D4 | 1 | 72 | yes | complemented |
| 123 | C22×#41 | C2×D4 | 1 | 72 | yes | complemented |
| 124 | C22×#41 | C24 | 1 | 12 | yes | — |
| 125 | C22×#41 | C24 | 1 | 36 | yes | — |
| 126 | C22×#41 | C24 | 1 | 72 | yes | — |
| 127 | C22×#41 | C24 | 1 | 72 | yes | — |
| 128 | C22×#41 | C24 | 1 | 4 | yes | — |
| 129 | C22×#41 | C24 | 1 | 12 | yes | — |
| 130 | C22×#41 | C24 | 1 | 4 | yes | — |
| 131 | C22×#41 | C24 | 1 | 4 | yes | — |
| 132 | C22×#41 | C24 | 1 | 12 | yes | complemented |
| 133 | C22×#41 | C24 | 1 | 12 | yes | complemented |
| 134 | C22×#41 | C24 | 1 | 24 | yes | complemented |
| 135 | C22×#41 | C24 | 1 | 8 | yes | complemented |
| 136 | C23×Q8 | C2×D4 | 1 | 24 | yes | complemented |
| 137 | C23×Q8 | C2×D4 | 1 | 18 | yes | complemented |
| 138 | C23×Q8 | C24 | 1 | 1 | yes | characteristic |
| 139 | C23×Q8 | C24 | 1 | 6 | yes | complemented |
| 140 | C23×Q8 | C24 | 1 | 8 | yes | complemented |
| 141 | C23×D4 | C2×D4 | 1 | 72 | yes | complemented |
| 142 | C23×D4 | C2×D4 | 1 | 18 | yes | complemented |
| 143 | C23×D4 | C24 | 1 | 36 | yes | — |
| 144 | C23×D4 | C24 | 1 | 3 | yes | — |
| 145 | C23×D4 | C24 | 1 | 12 | yes | — |
| 146 | C23×D4 | C24 | 1 | 6 | yes | complemented |
| 147 | C23×D4 | C24 | 1 | 24 | yes | complemented |
| 148 | C24×C4 | C2×D4 | 1 | 36 | yes | complemented |
| 149 | C24×C4 | C24 | 1 | 3 | yes | — |
| 150 | C24×C4 | C24 | 1 | 12 | yes | complemented |
| 151 | #536 | C24 | 1 | 96 | yes | complemented |
| 152 | #536 | C24 | 1 | 288 | yes | complemented |
| 153 | #535 | C24 | 1 | 96 | yes | complemented |
| 154 | #535 | C24 | 1 | 288 | yes | complemented |
| 155 | #534 | C24 | 1 | 192 | yes | — |
| 156 | #534 | C24 | 1 | 576 | yes | complemented |
| 157 | #525 | C24 | 1 | 192 | yes | complemented |
| 158 | #525 | C24 | 1 | 576 | yes | complemented |
| 159 | C2×#123 | C24 | 1 | 288 | yes | complemented |
| 160 | C2×#120 | C24 | 1 | 288 | yes | complemented |
| 161 | #519 | C24 | 1 | 48 | yes | complemented |
| 162 | #518 | C24 | 1 | 144 | yes | complemented |
| 163 | C2×#117 | C24 | 1 | 12 | yes | — |
| 164 | C2×#117 | C24 | 1 | 36 | yes | — |
| 165 | C2×#117 | C24 | 1 | 72 | yes | complemented |
| 166 | C2×#117 | C24 | 1 | 72 | yes | complemented |
| 167 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 168 | #458 | C24 | 1 | 2048 | yes | complemented |
| 169 | B(4,𝔽2) | C24 | 1 | 2048 | yes | complemented |
| 170 | #410 | C24 | 1 | 192 | yes | complemented |
| 171 | #410 | C24 | 1 | 192 | yes | complemented |
| 172 | #410 | C24 | 1 | 1152 | yes | complemented |
| 173 | C2×#99 | C24 | 1 | 192 | yes | — |
| 174 | C2×#99 | C24 | 1 | 1152 | yes | complemented |
| 175 | C25 | C22×D4 | 1 | 36 | yes | — |
| 176 | C25 | C25 | 1 | 3 | yes | — |
| 177 | C25 | C25 | 1 | 12 | yes | — |
| 178 | H(5,𝔽2) | C25 | 1 | 256 | yes | — |
| 179 | C2×#41 | #120 | 1 | 16 | yes | — |
| 180 | C2×#41 | #120 | 1 | 48 | yes | — |
| 181 | C2×#41 | #120 | 1 | 48 | yes | — |
| 182 | C2×#41 | #120 | 1 | 48 | yes | — |
| 183 | C2×#41 | #120 | 1 | 96 | yes | — |
| 184 | C2×#41 | C22×D4 | 1 | 144 | yes | — |
| 185 | C2×#41 | C22×D4 | 1 | 144 | yes | — |
| 186 | C2×#41 | C22×D4 | 1 | 24 | yes | — |
| 187 | C2×#41 | C22×D4 | 1 | 24 | yes | — |
| 188 | C2×#41 | C22×D4 | 1 | 192 | yes | — |
| 189 | C2×#41 | C22×D4 | 1 | 576 | yes | — |
| 190 | C2×#41 | C22×D4 | 1 | 144 | yes | — |
| 191 | C2×#41 | C22×D4 | 1 | 144 | yes | — |
| 192 | C2×#41 | C22×D4 | 1 | 144 | yes | — |
| 193 | C2×#41 | C22×D4 | 1 | 48 | yes | — |
| 194 | C2×#41 | C22×D4 | 1 | 48 | yes | — |
| 195 | C2×#41 | C22×D4 | 1 | 48 | yes | — |
| 196 | C2×#41 | C22×D4 | 1 | 48 | yes | — |
| 197 | C2×#41 | C25 | 1 | 24 | yes | — |
| 198 | C2×#41 | C25 | 1 | 144 | yes | — |
| 199 | C2×#41 | C25 | 1 | 24 | yes | — |
| 200 | C22×Q8 | C22×D4 | 1 | 12 | yes | — |
| 201 | C22×Q8 | C22×D4 | 1 | 12 | yes | — |
| 202 | C22×Q8 | C22×D4 | 1 | 36 | yes | — |
| 203 | C22×Q8 | C22×D4 | 1 | 12 | yes | — |
| 204 | C22×Q8 | C22×D4 | 1 | 192 | yes | — |
| 205 | C22×Q8 | C22×D4 | 1 | 72 | yes | — |
| 206 | C22×Q8 | C22×D4 | 1 | 72 | yes | — |
| 207 | C22×Q8 | C25 | 1 | 4 | yes | — |
| 208 | C22×Q8 | C25 | 1 | 12 | yes | — |
| 209 | C22×Q8 | C25 | 1 | 4 | yes | — |
| 210 | C22×D4 | C22×D4 | 1 | 36 | yes | — |
| 211 | C22×D4 | C22×D4 | 1 | 36 | yes | — |
| 212 | C22×D4 | C22×D4 | 1 | 36 | yes | — |
| 213 | C22×D4 | C22×D4 | 1 | 12 | yes | — |
| 214 | C22×D4 | C22×D4 | 1 | 72 | yes | — |
| 215 | C22×D4 | C22×D4 | 1 | 576 | yes | — |
| 216 | C22×D4 | C22×D4 | 1 | 72 | yes | — |
| 217 | C22×D4 | C22×D4 | 1 | 72 | yes | — |
| 218 | C22×D4 | C22×D4 | 1 | 144 | yes | — |
| 219 | C22×D4 | C25 | 1 | 144 | yes | — |
| 220 | C22×D4 | C25 | 1 | 24 | yes | — |
| 221 | C22×D4 | C25 | 1 | 12 | yes | — |
| 222 | C22×D4 | C25 | 1 | 8 | yes | — |
| 223 | C22×D4 | C25 | 1 | 24 | yes | — |
| 224 | C22×D4 | C25 | 1 | 4 | yes | — |
| 225 | C22×D4 | C25 | 1 | 12 | yes | — |
| 226 | C23×C4 | C22×D4 | 1 | 18 | yes | — |
| 227 | C23×C4 | C22×D4 | 1 | 18 | yes | — |
| 228 | C23×C4 | C22×D4 | 1 | 18 | yes | — |
| 229 | C23×C4 | C22×D4 | 1 | 18 | yes | — |
| 230 | C23×C4 | C22×D4 | 1 | 24 | yes | — |
| 231 | C23×C4 | C22×D4 | 1 | 72 | yes | — |
| 232 | C23×C4 | C22×D4 | 1 | 36 | yes | — |
| 233 | C23×C4 | C22×D4 | 1 | 144 | yes | — |
| 234 | C23×C4 | C22×D4 | 1 | 144 | yes | — |
| 235 | C23×C4 | C25 | 1 | 1 | yes | characteristic |
| 236 | C23×C4 | C25 | 1 | 3 | yes | — |
| 237 | C23×C4 | C25 | 1 | 6 | yes | — |
| 238 | C23×C4 | C25 | 1 | 6 | yes | — |
| 239 | C23×C4 | C25 | 1 | 12 | yes | — |
| 240 | C23×C4 | C25 | 1 | 8 | yes | — |
| 241 | C23×C4 | C25 | 1 | 24 | yes | — |
| 242 | #123 | C25 | 1 | 384 | yes | — |
| 243 | #120 | C25 | 1 | 384 | yes | — |
| 244 | #117 | C25 | 1 | 24 | yes | — |
| 245 | #117 | C25 | 1 | 24 | yes | — |
| 246 | #117 | C25 | 1 | 144 | yes | — |
| 247 | C2×C22⋊C4 | C25 | 1 | 24 | yes | — |
| 248 | C2×C22⋊C4 | C25 | 1 | 144 | yes | — |
| 249 | #99 | C25 | 1 | 768 | yes | — |
| 250 | C24 | C23×D4 | 1 | 24 | yes | — |
| 251 | C24 | C23×D4 | 1 | 144 | yes | — |
| 252 | C24 | C23×D4 | 1 | 18 | yes | — |
| 253 | C24 | C23×D4 | 1 | 18 | yes | — |
| 254 | C24 | C26 | 1 | 1 | yes | characteristic |
| 255 | C24 | C26 | 1 | 6 | yes | — |
| 256 | C24 | C26 | 1 | 8 | yes | — |
| 257 | #41 | C2×#120 | 1 | 64 | yes | — |
| 258 | #41 | C2×#120 | 1 | 192 | yes | — |
| 259 | #41 | C2×#120 | 1 | 192 | yes | — |
| 260 | #41 | C2×#120 | 1 | 64 | yes | — |
| 261 | C2×Q8 | C2×#120 | 1 | 16 | yes | — |
| 262 | C2×Q8 | C2×#120 | 1 | 48 | yes | — |
| 263 | C2×Q8 | C23×D4 | 1 | 144 | yes | — |
| 264 | C2×Q8 | C23×D4 | 1 | 24 | yes | — |
| 265 | C2×Q8 | C23×D4 | 1 | 24 | yes | — |
| 266 | C2×Q8 | C23×D4 | 1 | 48 | yes | — |
| 267 | C2×D4 | C2×#120 | 1 | 48 | yes | — |
| 268 | C2×D4 | C2×#120 | 1 | 144 | yes | — |
| 269 | C2×D4 | C23×D4 | 1 | 144 | yes | — |
| 270 | C2×D4 | C23×D4 | 1 | 144 | yes | — |
| 271 | C2×D4 | C23×D4 | 1 | 24 | yes | — |
| 272 | C2×D4 | C23×D4 | 1 | 24 | yes | — |
| 273 | C2×D4 | C23×D4 | 1 | 288 | yes | — |
| 274 | C2×D4 | C23×D4 | 1 | 48 | yes | — |
| 275 | C2×D4 | C26 | 1 | 48 | yes | — |
| 276 | C22×C4 | C2×#120 | 1 | 36 | yes | — |
| 277 | C22×C4 | C2×#120 | 1 | 36 | yes | — |
| 278 | C22×C4 | C2×#120 | 1 | 72 | yes | — |
| 279 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 280 | C22×C4 | C2×#120 | 1 | 36 | yes | — |
| 281 | C22×C4 | C23×D4 | 1 | 3 | yes | — |
| 282 | C22×C4 | C23×D4 | 1 | 3 | yes | — |
| 283 | C22×C4 | C23×D4 | 1 | 18 | yes | — |
| 284 | C22×C4 | C23×D4 | 1 | 3 | yes | — |
| 285 | C22×C4 | C23×D4 | 1 | 36 | yes | — |
| 286 | C22×C4 | C23×D4 | 1 | 3 | yes | — |
| 287 | C22×C4 | C23×D4 | 1 | 36 | yes | — |
| 288 | C22×C4 | C23×D4 | 1 | 18 | yes | — |
| 289 | C22×C4 | C23×D4 | 1 | 36 | yes | — |
| 290 | C22×C4 | C23×D4 | 1 | 36 | yes | — |
| 291 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 292 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 293 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 294 | C22×C4 | C23×D4 | 1 | 288 | yes | — |
| 295 | C22×C4 | C23×D4 | 1 | 144 | yes | — |
| 296 | C22×C4 | C26 | 1 | 1 | yes | characteristic |
| 297 | C22×C4 | C26 | 1 | 1 | yes | characteristic |
| 298 | C22×C4 | C26 | 1 | 6 | yes | — |
| 299 | C22×C4 | C26 | 1 | 8 | yes | — |
| 300 | C22⋊C4 | C26 | 1 | 48 | yes | — |
| 301 | C23 | C22×#120 | 1 | 12 | yes | — |
| 302 | C23 | C22×#120 | 1 | 36 | yes | — |
| 303 | C23 | C24×D4 | 1 | 48 | yes | — |
| 304 | C23 | C24×D4 | 1 | 3 | yes | — |
| 305 | C23 | C24×D4 | 1 | 3 | yes | — |
| 306 | C23 | C24×D4 | 1 | 36 | yes | — |
| 307 | C23 | C27 | 1 | 1 | yes | characteristic |
| 308 | Q8 | C22×#120 | 1 | 64 | yes | — |
| 309 | D4 | C22×#120 | 1 | 192 | yes | — |
| 310 | C2×C4 | C22×#120 | 1 | 3 | yes | — |
| 311 | C2×C4 | C22×#120 | 1 | 3 | yes | — |
| 312 | C2×C4 | C22×#120 | 1 | 6 | yes | — |
| 313 | C2×C4 | C22×#120 | 1 | 12 | yes | — |
| 314 | C2×C4 | C22×#120 | 1 | 36 | yes | — |
| 315 | C2×C4 | C22×#120 | 1 | 24 | yes | — |
| 316 | C2×C4 | C22×#120 | 1 | 72 | yes | — |
| 317 | C2×C4 | C22×#120 | 1 | 72 | yes | — |
| 318 | C2×C4 | C22×#120 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | C22×#120 | 1 | 3 | yes | — |
| 320 | C2×C4 | C22×#120 | 1 | 24 | yes | — |
| 321 | C2×C4 | C24×D4 | 1 | 3 | yes | — |
| 322 | C2×C4 | C24×D4 | 1 | 3 | yes | — |
| 323 | C2×C4 | C24×D4 | 1 | 3 | yes | — |
| 324 | C2×C4 | C24×D4 | 1 | 36 | yes | — |
| 325 | C2×C4 | C24×D4 | 1 | 3 | yes | — |
| 326 | C2×C4 | C24×D4 | 1 | 48 | yes | — |
| 327 | C22 | C23×#120 | 1 | 1 | yes | characteristic |
| 328 | C22 | C23×#120 | 1 | 3 | yes | — |
| 329 | C22 | C23×#120 | 1 | 24 | yes | — |
| 330 | C22 | C25×D4 | 1 | 3 | yes | — |
| 331 | C4 | C23×#120 | 1 | 1 | yes | characteristic |
| 332 | C4 | C23×#120 | 1 | 3 | yes | — |
| 333 | C4 | C23×#120 | 1 | 3 | yes | — |
| 334 | C4 | C23×#120 | 1 | 24 | yes | — |
| 335 | C4 | C23×#120 | 1 | 1 | yes | characteristic |
| 336 | C2 | C24×#120 | 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