← C2×#10574873 #72240588
Subgroups — C2×#10574873 #72240588
Order 1024.
Only the 38405 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 290 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×H(7,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#62842 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#60398 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #10574873 | C2 | 1 | 64 | yes | maximal, direct product factor |
| 5 | C2×#60401 | C2 | 1 | 16 | yes | maximal, complemented |
| 6 | C2×#60399 | C2 | 1 | 16 | yes | maximal, complemented |
| 7 | C22×#3026 | C2 | 1 | 16 | yes | maximal, complemented |
| 8 | C22×#2883 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×H(7,𝔽2) | C22 | 1 | 16 | yes | complemented |
| 10 | C2×H(7,𝔽2) | C22 | 1 | 32 | yes | complemented |
| 11 | C22×#585 | C22 | 1 | 4 | yes | complemented |
| 12 | C23×H(5,𝔽2) | C22 | 1 | 3 | yes | — |
| 13 | C23×H(5,𝔽2) | C22 | 1 | 8 | yes | complemented |
| 14 | C23×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #62842 | C22 | 1 | 96 | yes | complemented |
| 16 | C2×#3485 | C22 | 1 | 24 | yes | complemented |
| 17 | C2×#3484 | C22 | 1 | 24 | yes | complemented |
| 18 | C2×#3449 | C22 | 1 | 12 | yes | complemented |
| 19 | C22×#534 | C22 | 1 | 24 | yes | complemented |
| 20 | C22×#518 | C22 | 1 | 3 | yes | complemented |
| 21 | #60401 | C22 | 1 | 512 | yes | complemented |
| 22 | #60399 | C22 | 1 | 512 | yes | complemented |
| 23 | #60398 | C22 | 1 | 256 | yes | complemented |
| 24 | C2×#3028 | C22 | 1 | 32 | yes | complemented |
| 25 | C2×#3027 | C22 | 1 | 32 | yes | complemented |
| 26 | C2×#3026 | C22 | 1 | 64 | yes | complemented |
| 27 | C2×#3026 | C22 | 1 | 128 | yes | complemented |
| 28 | C2×#3026 | C22 | 1 | 512 | yes | complemented |
| 29 | C2×#3025 | C22 | 1 | 64 | yes | complemented |
| 30 | C22×#458 | C22 | 1 | 64 | yes | complemented |
| 31 | C22×B(4,𝔽2) | C22 | 1 | 64 | yes | complemented |
| 32 | C2×#2883 | C22 | 1 | 48 | yes | complemented |
| 33 | C2×#2883 | C22 | 1 | 96 | yes | complemented |
| 34 | C22×#410 | C22 | 1 | 12 | yes | complemented |
| 35 | C23×#99 | C22 | 1 | 24 | yes | complemented |
| 36 | H(7,𝔽2) | C23 | 1 | 256 | yes | complemented |
| 37 | C2×#585 | C23 | 1 | 32 | yes | — |
| 38 | C2×#585 | C23 | 1 | 64 | yes | complemented |
| 39 | C22×H(5,𝔽2) | D4 | 1 | 24 | yes | complemented |
| 40 | C22×H(5,𝔽2) | D4 | 1 | 48 | yes | complemented |
| 41 | C22×H(5,𝔽2) | C23 | 1 | 24 | yes | — |
| 42 | C22×H(5,𝔽2) | C23 | 1 | 48 | yes | — |
| 43 | C22×H(5,𝔽2) | C23 | 1 | 16 | yes | — |
| 44 | C22×H(5,𝔽2) | C23 | 1 | 64 | yes | — |
| 45 | C22×H(5,𝔽2) | C23 | 1 | 128 | yes | complemented |
| 46 | C22×H(5,𝔽2) | C23 | 1 | 16 | yes | complemented |
| 47 | C23×#41 | D4 | 1 | 12 | yes | complemented |
| 48 | C23×#41 | C23 | 1 | 6 | yes | — |
| 49 | C23×#41 | C23 | 1 | 2 | yes | complemented |
| 50 | C23×#41 | C23 | 1 | 4 | yes | complemented |
| 51 | C24×D4 | D4 | 1 | 12 | yes | complemented |
| 52 | C24×D4 | C23 | 1 | 12 | yes | — |
| 53 | C24×D4 | C23 | 1 | 1 | yes | characteristic |
| 54 | C24×D4 | C23 | 1 | 4 | yes | complemented |
| 55 | C24×D4 | C23 | 1 | 4 | yes | complemented |
| 56 | #3485 | C23 | 1 | 384 | yes | complemented |
| 57 | #3484 | C23 | 1 | 384 | yes | complemented |
| 58 | #3449 | C23 | 1 | 192 | yes | complemented |
| 59 | C2×#536 | C23 | 1 | 24 | yes | complemented |
| 60 | C2×#535 | C23 | 1 | 24 | yes | complemented |
| 61 | C2×#534 | C23 | 1 | 48 | yes | complemented |
| 62 | C2×#534 | C23 | 1 | 96 | yes | complemented |
| 63 | C2×#534 | C23 | 1 | 384 | yes | complemented |
| 64 | C2×#525 | C23 | 1 | 48 | yes | complemented |
| 65 | C22×#123 | C23 | 1 | 48 | yes | complemented |
| 66 | C22×#120 | C23 | 1 | 48 | yes | complemented |
| 67 | C2×#518 | C23 | 1 | 24 | yes | complemented |
| 68 | C2×#518 | C23 | 1 | 48 | yes | complemented |
| 69 | C22×#117 | C23 | 1 | 6 | yes | complemented |
| 70 | C23×C22⋊C4 | C23 | 1 | 12 | yes | complemented |
| 71 | #3028 | C23 | 1 | 512 | yes | complemented |
| 72 | #3027 | C23 | 1 | 512 | yes | complemented |
| 73 | #3026 | C23 | 1 | 1024 | yes | complemented |
| 74 | #3026 | C23 | 1 | 2048 | yes | complemented |
| 75 | #3025 | C23 | 1 | 1024 | yes | complemented |
| 76 | C2×#458 | C23 | 1 | 256 | yes | complemented |
| 77 | C2×#458 | C23 | 1 | 1024 | yes | complemented |
| 78 | C2×B(4,𝔽2) | C23 | 1 | 256 | yes | complemented |
| 79 | C2×B(4,𝔽2) | C23 | 1 | 1024 | yes | complemented |
| 80 | #2883 | C23 | 1 | 768 | yes | complemented |
| 81 | C2×#410 | C23 | 1 | 96 | yes | complemented |
| 82 | C2×#410 | C23 | 1 | 192 | yes | complemented |
| 83 | C22×#99 | C23 | 1 | 48 | yes | complemented |
| 84 | C22×#99 | C23 | 1 | 192 | yes | complemented |
| 85 | C22×#99 | C23 | 1 | 384 | yes | complemented |
| 86 | C26 | C2×D4 | 1 | 12 | yes | complemented |
| 87 | C26 | C24 | 1 | 2 | yes | — |
| 88 | C26 | C24 | 1 | 4 | yes | complemented |
| 89 | #585 | C24 | 1 | 256 | yes | — |
| 90 | C2×H(5,𝔽2) | C2×D4 | 1 | 192 | yes | complemented |
| 91 | C2×H(5,𝔽2) | C2×D4 | 1 | 384 | yes | complemented |
| 92 | C2×H(5,𝔽2) | C24 | 1 | 192 | yes | — |
| 93 | C2×H(5,𝔽2) | C24 | 1 | 64 | yes | — |
| 94 | C2×H(5,𝔽2) | C24 | 1 | 128 | yes | — |
| 95 | C2×H(5,𝔽2) | C24 | 1 | 512 | yes | — |
| 96 | C22×#41 | C2×D4 | 1 | 96 | yes | complemented |
| 97 | C22×#41 | C2×D4 | 1 | 24 | yes | complemented |
| 98 | C22×#41 | C2×D4 | 1 | 48 | yes | complemented |
| 99 | C22×#41 | C2×D4 | 1 | 192 | yes | complemented |
| 100 | C22×#41 | C24 | 1 | 24 | yes | — |
| 101 | C22×#41 | C24 | 1 | 48 | yes | — |
| 102 | C22×#41 | C24 | 1 | 16 | yes | complemented |
| 103 | C22×#41 | C24 | 1 | 32 | yes | complemented |
| 104 | C23×Q8 | C2×D4 | 1 | 6 | yes | complemented |
| 105 | C23×Q8 | C24 | 1 | 2 | yes | complemented |
| 106 | C23×D4 | C2×D4 | 1 | 12 | yes | — |
| 107 | C23×D4 | C2×D4 | 1 | 12 | yes | — |
| 108 | C23×D4 | C2×D4 | 1 | 24 | yes | — |
| 109 | C23×D4 | C2×D4 | 1 | 6 | yes | complemented |
| 110 | C23×D4 | C2×D4 | 1 | 24 | yes | complemented |
| 111 | C23×D4 | C2×D4 | 1 | 96 | yes | complemented |
| 112 | C23×D4 | C2×D4 | 1 | 48 | yes | complemented |
| 113 | C23×D4 | C2×D4 | 1 | 96 | yes | complemented |
| 114 | C23×D4 | C2×D4 | 1 | 192 | yes | complemented |
| 115 | C23×D4 | C24 | 1 | 12 | yes | — |
| 116 | C23×D4 | C24 | 1 | 48 | yes | — |
| 117 | C23×D4 | C24 | 1 | 96 | yes | — |
| 118 | C23×D4 | C24 | 1 | 4 | yes | — |
| 119 | C23×D4 | C24 | 1 | 8 | yes | — |
| 120 | C23×D4 | C24 | 1 | 4 | yes | — |
| 121 | C23×D4 | C24 | 1 | 8 | yes | complemented |
| 122 | C23×D4 | C24 | 1 | 2 | yes | complemented |
| 123 | C23×D4 | C24 | 1 | 32 | yes | complemented |
| 124 | C23×D4 | C24 | 1 | 32 | yes | complemented |
| 125 | C24×C4 | C2×D4 | 1 | 12 | yes | complemented |
| 126 | C24×C4 | C2×D4 | 1 | 12 | yes | complemented |
| 127 | C24×C4 | C24 | 1 | 1 | yes | characteristic |
| 128 | C24×C4 | C24 | 1 | 4 | yes | complemented |
| 129 | C24×C4 | C24 | 1 | 4 | yes | complemented |
| 130 | #536 | C24 | 1 | 192 | yes | complemented |
| 131 | #535 | C24 | 1 | 192 | yes | complemented |
| 132 | #534 | C24 | 1 | 384 | yes | complemented |
| 133 | #534 | C24 | 1 | 768 | yes | complemented |
| 134 | #525 | C24 | 1 | 384 | yes | complemented |
| 135 | C2×#123 | C24 | 1 | 96 | yes | complemented |
| 136 | C2×#123 | C24 | 1 | 384 | yes | complemented |
| 137 | C2×#120 | C24 | 1 | 96 | yes | complemented |
| 138 | C2×#120 | C24 | 1 | 384 | yes | complemented |
| 139 | #518 | C24 | 1 | 192 | yes | complemented |
| 140 | C2×#117 | C24 | 1 | 24 | yes | complemented |
| 141 | C2×#117 | C24 | 1 | 48 | yes | complemented |
| 142 | C22×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 143 | C22×C22⋊C4 | C24 | 1 | 48 | yes | complemented |
| 144 | C22×C22⋊C4 | C24 | 1 | 96 | yes | complemented |
| 145 | #458 | C24 | 1 | 2048 | yes | complemented |
| 146 | B(4,𝔽2) | C24 | 1 | 2048 | yes | complemented |
| 147 | #410 | C24 | 1 | 768 | yes | complemented |
| 148 | C2×#99 | C24 | 1 | 192 | yes | complemented |
| 149 | C2×#99 | C24 | 1 | 384 | yes | complemented |
| 150 | C2×#99 | C24 | 1 | 1536 | yes | complemented |
| 151 | C25 | C22×D4 | 1 | 12 | yes | — |
| 152 | C25 | C22×D4 | 1 | 12 | yes | — |
| 153 | C25 | C22×D4 | 1 | 24 | yes | — |
| 154 | C25 | C22×D4 | 1 | 12 | yes | — |
| 155 | C25 | C22×D4 | 1 | 48 | yes | — |
| 156 | C25 | C22×D4 | 1 | 96 | yes | complemented |
| 157 | C25 | C25 | 1 | 1 | yes | characteristic |
| 158 | C25 | C25 | 1 | 4 | yes | — |
| 159 | C25 | C25 | 1 | 8 | yes | — |
| 160 | C25 | C25 | 1 | 4 | yes | — |
| 161 | C25 | C25 | 1 | 16 | yes | complemented |
| 162 | H(5,𝔽2) | C25 | 1 | 256 | yes | — |
| 163 | C2×#41 | C22×D4 | 1 | 96 | yes | — |
| 164 | C2×#41 | C22×D4 | 1 | 768 | yes | complemented |
| 165 | C2×#41 | C22×D4 | 1 | 192 | yes | complemented |
| 166 | C2×#41 | C25 | 1 | 96 | yes | — |
| 167 | C22×Q8 | C22×D4 | 1 | 24 | yes | — |
| 168 | C22×Q8 | C22×D4 | 1 | 48 | yes | complemented |
| 169 | C22×Q8 | C25 | 1 | 8 | yes | complemented |
| 170 | C22×D4 | #120 | 1 | 16 | yes | — |
| 171 | C22×D4 | #120 | 1 | 96 | yes | — |
| 172 | C22×D4 | #120 | 1 | 48 | yes | — |
| 173 | C22×D4 | #120 | 1 | 96 | yes | — |
| 174 | C22×D4 | C22×D4 | 1 | 48 | yes | — |
| 175 | C22×D4 | C22×D4 | 1 | 96 | yes | — |
| 176 | C22×D4 | C22×D4 | 1 | 48 | yes | — |
| 177 | C22×D4 | C22×D4 | 1 | 96 | yes | — |
| 178 | C22×D4 | C22×D4 | 1 | 24 | yes | — |
| 179 | C22×D4 | C22×D4 | 1 | 96 | yes | — |
| 180 | C22×D4 | C22×D4 | 1 | 24 | yes | — |
| 181 | C22×D4 | C22×D4 | 1 | 48 | yes | — |
| 182 | C22×D4 | C22×D4 | 1 | 192 | yes | — |
| 183 | C22×D4 | C22×D4 | 1 | 48 | yes | complemented |
| 184 | C22×D4 | C22×D4 | 1 | 192 | yes | complemented |
| 185 | C22×D4 | C22×D4 | 1 | 768 | yes | complemented |
| 186 | C22×D4 | C22×D4 | 1 | 384 | yes | complemented |
| 187 | C22×D4 | C25 | 1 | 24 | yes | — |
| 188 | C22×D4 | C25 | 1 | 192 | yes | — |
| 189 | C22×D4 | C25 | 1 | 48 | yes | — |
| 190 | C22×D4 | C25 | 1 | 16 | yes | — |
| 191 | C22×D4 | C25 | 1 | 16 | yes | — |
| 192 | C22×D4 | C25 | 1 | 32 | yes | complemented |
| 193 | C22×D4 | C25 | 1 | 8 | yes | complemented |
| 194 | C23×C4 | C22×D4 | 1 | 6 | yes | — |
| 195 | C23×C4 | C22×D4 | 1 | 6 | yes | — |
| 196 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 197 | C23×C4 | C22×D4 | 1 | 12 | yes | — |
| 198 | C23×C4 | C22×D4 | 1 | 48 | yes | — |
| 199 | C23×C4 | C22×D4 | 1 | 48 | yes | — |
| 200 | C23×C4 | C22×D4 | 1 | 96 | yes | complemented |
| 201 | C23×C4 | C22×D4 | 1 | 96 | yes | complemented |
| 202 | C23×C4 | C25 | 1 | 2 | yes | — |
| 203 | C23×C4 | C25 | 1 | 4 | yes | — |
| 204 | C23×C4 | C25 | 1 | 4 | yes | — |
| 205 | C23×C4 | C25 | 1 | 16 | yes | complemented |
| 206 | C23×C4 | C25 | 1 | 16 | yes | complemented |
| 207 | #123 | C25 | 1 | 384 | yes | complemented |
| 208 | #120 | C25 | 1 | 384 | yes | complemented |
| 209 | #117 | C25 | 1 | 96 | yes | complemented |
| 210 | C2×C22⋊C4 | C25 | 1 | 24 | yes | — |
| 211 | C2×C22⋊C4 | C25 | 1 | 48 | yes | — |
| 212 | C2×C22⋊C4 | C25 | 1 | 192 | yes | complemented |
| 213 | #99 | C25 | 1 | 768 | yes | complemented |
| 214 | C24 | C2×#120 | 1 | 48 | yes | — |
| 215 | C24 | C2×#120 | 1 | 48 | yes | — |
| 216 | C24 | C2×#120 | 1 | 8 | yes | — |
| 217 | C24 | C2×#120 | 1 | 24 | yes | — |
| 218 | C24 | C23×D4 | 1 | 24 | yes | — |
| 219 | C24 | C23×D4 | 1 | 48 | yes | — |
| 220 | C24 | C23×D4 | 1 | 192 | yes | — |
| 221 | C24 | C23×D4 | 1 | 3 | yes | — |
| 222 | C24 | C23×D4 | 1 | 6 | yes | — |
| 223 | C24 | C23×D4 | 1 | 3 | yes | — |
| 224 | C24 | C23×D4 | 1 | 24 | yes | — |
| 225 | C24 | C23×D4 | 1 | 48 | yes | — |
| 226 | C24 | C23×D4 | 1 | 24 | yes | — |
| 227 | C24 | C23×D4 | 1 | 48 | yes | — |
| 228 | C24 | C26 | 1 | 1 | yes | characteristic |
| 229 | C24 | C26 | 1 | 2 | yes | — |
| 230 | C24 | C26 | 1 | 8 | yes | — |
| 231 | C24 | C26 | 1 | 8 | yes | — |
| 232 | C2×Q8 | C23×D4 | 1 | 96 | yes | — |
| 233 | C2×D4 | C2×#120 | 1 | 128 | yes | — |
| 234 | C2×D4 | C2×#120 | 1 | 192 | yes | — |
| 235 | C2×D4 | C2×#120 | 1 | 384 | yes | — |
| 236 | C2×D4 | C2×#120 | 1 | 64 | yes | — |
| 237 | C2×D4 | C23×D4 | 1 | 192 | yes | — |
| 238 | C2×D4 | C23×D4 | 1 | 48 | yes | — |
| 239 | C2×D4 | C23×D4 | 1 | 96 | yes | — |
| 240 | C2×D4 | C23×D4 | 1 | 384 | yes | — |
| 241 | C2×D4 | C23×D4 | 1 | 96 | yes | — |
| 242 | C2×D4 | C26 | 1 | 48 | yes | — |
| 243 | C22×C4 | C2×#120 | 1 | 24 | yes | — |
| 244 | C22×C4 | C2×#120 | 1 | 24 | yes | — |
| 245 | C22×C4 | C2×#120 | 1 | 4 | yes | — |
| 246 | C22×C4 | C2×#120 | 1 | 12 | yes | — |
| 247 | C22×C4 | C23×D4 | 1 | 12 | yes | — |
| 248 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 249 | C22×C4 | C23×D4 | 1 | 12 | yes | — |
| 250 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 251 | C22×C4 | C23×D4 | 1 | 24 | yes | — |
| 252 | C22×C4 | C23×D4 | 1 | 48 | yes | — |
| 253 | C22×C4 | C23×D4 | 1 | 192 | yes | — |
| 254 | C22×C4 | C23×D4 | 1 | 192 | yes | — |
| 255 | C22×C4 | C26 | 1 | 4 | yes | — |
| 256 | C22×C4 | C26 | 1 | 8 | yes | — |
| 257 | C22⋊C4 | C26 | 1 | 48 | yes | — |
| 258 | C23 | C22×#120 | 1 | 6 | yes | — |
| 259 | C23 | C22×#120 | 1 | 6 | yes | — |
| 260 | C23 | C22×#120 | 1 | 48 | yes | — |
| 261 | C23 | C22×#120 | 1 | 32 | yes | — |
| 262 | C23 | C22×#120 | 1 | 96 | yes | — |
| 263 | C23 | C22×#120 | 1 | 1 | yes | characteristic |
| 264 | C23 | C22×#120 | 1 | 3 | yes | — |
| 265 | C23 | C22×#120 | 1 | 16 | yes | — |
| 266 | C23 | C24×D4 | 1 | 48 | yes | — |
| 267 | C23 | C24×D4 | 1 | 6 | yes | — |
| 268 | C23 | C24×D4 | 1 | 3 | yes | — |
| 269 | C23 | C24×D4 | 1 | 6 | yes | — |
| 270 | C23 | C24×D4 | 1 | 48 | yes | — |
| 271 | C23 | C24×D4 | 1 | 3 | yes | — |
| 272 | C23 | C27 | 1 | 1 | yes | characteristic |
| 273 | D4 | C22×#120 | 1 | 256 | yes | — |
| 274 | C2×C4 | C22×#120 | 1 | 24 | yes | — |
| 275 | C2×C4 | C22×#120 | 1 | 16 | yes | — |
| 276 | C2×C4 | C22×#120 | 1 | 48 | yes | — |
| 277 | C2×C4 | C22×#120 | 1 | 8 | yes | — |
| 278 | C2×C4 | C24×D4 | 1 | 24 | yes | — |
| 279 | C2×C4 | C24×D4 | 1 | 48 | yes | — |
| 280 | C22 | C23×#120 | 1 | 2 | yes | — |
| 281 | C22 | C23×#120 | 1 | 6 | yes | — |
| 282 | C22 | C23×#120 | 1 | 3 | yes | — |
| 283 | C22 | C23×#120 | 1 | 32 | yes | — |
| 284 | C22 | C23×#120 | 1 | 1 | yes | characteristic |
| 285 | C22 | C25×D4 | 1 | 3 | yes | — |
| 286 | C4 | C23×#120 | 1 | 16 | yes | — |
| 287 | C2 | #10574873 | 1 | 2 | yes | direct product factor |
| 288 | C2 | C24×#120 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. C22×H(7,𝔽2) | C2 | semidirect |
| 2. C2×#62842 | C2 | semidirect |
| 3. C2×#60398 | C2 | semidirect |
| 4. #10574873 | C2 | direct (N × H) |
| 5. C2×#60401 | C2 | semidirect |
| 6. C2×#60399 | C2 | semidirect |
| 7. C22×#3026 | C2 | semidirect |
| 8. C22×#2883 | C2 | semidirect |
| 9. C2×H(7,𝔽2) | C22 | semidirect |
| 10. C2×H(7,𝔽2) | C22 | semidirect |
| 11. C22×#585 | C22 | semidirect |
| 13. C23×H(5,𝔽2) | C22 | semidirect |
| 14. C23×H(5,𝔽2) | C22 | semidirect |
| 15. #62842 | C22 | semidirect |
| 16. C2×#3485 | C22 | semidirect |
| 17. C2×#3484 | C22 | semidirect |
| 18. C2×#3449 | C22 | semidirect |
| 19. C22×#534 | C22 | semidirect |
| 20. C22×#518 | C22 | semidirect |
| 21. #60401 | C22 | semidirect |
| 22. #60399 | C22 | semidirect |
| 23. #60398 | C22 | semidirect |
| 24. C2×#3028 | C22 | semidirect |
| 25. C2×#3027 | C22 | semidirect |
| 26. C2×#3026 | C22 | semidirect |
| 27. C2×#3026 | C22 | semidirect |
| 28. C2×#3026 | C22 | semidirect |
| 29. C2×#3025 | C22 | semidirect |
| 30. C22×#458 | C22 | semidirect |
| 31. C22×B(4,𝔽2) | C22 | semidirect |
| 32. C2×#2883 | C22 | semidirect |
| 33. C2×#2883 | C22 | semidirect |
| 34. C22×#410 | C22 | semidirect |
| 35. C23×#99 | C22 | semidirect |
| 36. H(7,𝔽2) | C23 | semidirect |
| 38. C2×#585 | C23 | semidirect |
| 39. C22×H(5,𝔽2) | D4 | semidirect |
| 40. C22×H(5,𝔽2) | D4 | semidirect |
| 45. C22×H(5,𝔽2) | C23 | semidirect |
| 46. C22×H(5,𝔽2) | C23 | semidirect |
| 47. C23×#41 | D4 | semidirect |
| 49. C23×#41 | C23 | semidirect |
| 50. C23×#41 | C23 | semidirect |
| 51. C24×D4 | D4 | semidirect |
| 54. C24×D4 | C23 | semidirect |
| 55. C24×D4 | C23 | semidirect |
| 56. #3485 | C23 | semidirect |
| 57. #3484 | C23 | semidirect |
| 58. #3449 | C23 | semidirect |
| 59. C2×#536 | C23 | semidirect |
| 60. C2×#535 | C23 | semidirect |
| 61. C2×#534 | C23 | semidirect |
| 62. C2×#534 | C23 | semidirect |
| 63. C2×#534 | C23 | semidirect |
| 64. C2×#525 | C23 | semidirect |
| 65. C22×#123 | C23 | semidirect |
| 66. C22×#120 | C23 | semidirect |
| 67. C2×#518 | C23 | semidirect |
| 68. C2×#518 | C23 | semidirect |
| 69. C22×#117 | C23 | semidirect |
| 70. C23×C22⋊C4 | C23 | semidirect |
| 71. #3028 | C23 | semidirect |
| 72. #3027 | C23 | semidirect |
| 73. #3026 | C23 | semidirect |
| 74. #3026 | C23 | semidirect |
| 75. #3025 | C23 | semidirect |
| 76. C2×#458 | C23 | semidirect |
| 77. C2×#458 | C23 | semidirect |
| 78. C2×B(4,𝔽2) | C23 | semidirect |
| 79. C2×B(4,𝔽2) | C23 | semidirect |
| 80. #2883 | C23 | semidirect |
| 81. C2×#410 | C23 | semidirect |
| 82. C2×#410 | C23 | semidirect |
| 83. C22×#99 | C23 | semidirect |
| 84. C22×#99 | C23 | semidirect |
| 85. C22×#99 | C23 | semidirect |
| 86. C26 | C2×D4 | semidirect |
| 88. C26 | C24 | semidirect |
| 90. C2×H(5,𝔽2) | C2×D4 | semidirect |
| 91. C2×H(5,𝔽2) | C2×D4 | semidirect |
| 96. C22×#41 | C2×D4 | semidirect |
| 97. C22×#41 | C2×D4 | semidirect |
| 98. C22×#41 | C2×D4 | semidirect |
| 99. C22×#41 | C2×D4 | semidirect |
| 102. C22×#41 | C24 | semidirect |
| 103. C22×#41 | C24 | semidirect |
| 104. C23×Q8 | C2×D4 | semidirect |
| 105. C23×Q8 | C24 | semidirect |
| 109. C23×D4 | C2×D4 | semidirect |
| 110. C23×D4 | C2×D4 | semidirect |
| 111. C23×D4 | C2×D4 | semidirect |
| 112. C23×D4 | C2×D4 | semidirect |
| 113. C23×D4 | C2×D4 | semidirect |
| 114. C23×D4 | C2×D4 | semidirect |
| 121. C23×D4 | C24 | semidirect |
| 122. C23×D4 | C24 | semidirect |
| 123. C23×D4 | C24 | semidirect |
| 124. C23×D4 | C24 | semidirect |
| 125. C24×C4 | C2×D4 | semidirect |
| 126. C24×C4 | C2×D4 | semidirect |
| 128. C24×C4 | C24 | semidirect |
| 129. C24×C4 | C24 | semidirect |
| 130. #536 | C24 | semidirect |
| 131. #535 | C24 | semidirect |
| 132. #534 | C24 | semidirect |
| 133. #534 | C24 | semidirect |
| 134. #525 | C24 | semidirect |
| 135. C2×#123 | C24 | semidirect |
| 136. C2×#123 | C24 | semidirect |
| 137. C2×#120 | C24 | semidirect |
| 138. C2×#120 | C24 | semidirect |
| 139. #518 | C24 | semidirect |
| 140. C2×#117 | C24 | semidirect |
| 141. C2×#117 | C24 | semidirect |
| 143. C22×C22⋊C4 | C24 | semidirect |
| 144. C22×C22⋊C4 | C24 | semidirect |
| 145. #458 | C24 | semidirect |
| 146. B(4,𝔽2) | C24 | semidirect |
| 147. #410 | C24 | semidirect |
| 148. C2×#99 | C24 | semidirect |
| 149. C2×#99 | C24 | semidirect |
| 150. C2×#99 | C24 | semidirect |
| 156. C25 | C22×D4 | semidirect |
| 161. C25 | C25 | semidirect |
| 164. C2×#41 | C22×D4 | semidirect |
| 165. C2×#41 | C22×D4 | semidirect |
| 168. C22×Q8 | C22×D4 | semidirect |
| 169. C22×Q8 | C25 | semidirect |
| 183. C22×D4 | C22×D4 | semidirect |
| 184. C22×D4 | C22×D4 | semidirect |
| 185. C22×D4 | C22×D4 | semidirect |
| 186. C22×D4 | C22×D4 | semidirect |
| 192. C22×D4 | C25 | semidirect |
| 193. C22×D4 | C25 | semidirect |
| 200. C23×C4 | C22×D4 | semidirect |
| 201. C23×C4 | C22×D4 | semidirect |
| 205. C23×C4 | C25 | semidirect |
| 206. C23×C4 | C25 | semidirect |
| 207. #123 | C25 | semidirect |
| 208. #120 | C25 | semidirect |
| 209. #117 | C25 | semidirect |
| 212. C2×C22⋊C4 | C25 | semidirect |
| 213. #99 | C25 | semidirect |
| 287. C2 | #10574873 | 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