Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5056 conjugacy classes of subgroups.
The subgroup lattice has 319 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #59655 | C2 | 1 | 9 | yes | maximal, complemented |
| 2 | #50705 | C2 | 1 | 18 | yes | maximal, complemented |
| 3 | #46432 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #43025 | C2 | 1 | 18 | yes | maximal, complemented |
| 5 | #39702 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | #34529 | C2 | 1 | 3 | yes | maximal |
| 7 | C2×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×Q82 | C22 | 1 | 3 | yes | complemented |
| 9 | C2×#554 | C22 | 1 | 9 | yes | — |
| 10 | C2×#543 | C22 | 1 | 6 | yes | complemented |
| 11 | #2863 | C22 | 1 | 3 | yes | complemented |
| 12 | #2840 | C22 | 1 | 2 | yes | complemented |
| 13 | #2811 | C22 | 1 | 6 | yes | complemented |
| 14 | #2811 | C22 | 1 | 3 | yes | complemented |
| 15 | #2806 | C22 | 1 | 9 | yes | complemented |
| 16 | #2804 | C22 | 1 | 9 | yes | — |
| 17 | #2788 | C22 | 1 | 18 | yes | complemented |
| 18 | #2732 | C22 | 1 | 9 | yes | — |
| 19 | #2729 | C22 | 1 | 18 | yes | complemented |
| 20 | #2729 | C22 | 1 | 18 | yes | complemented |
| 21 | #2720 | C22 | 1 | 18 | yes | complemented |
| 22 | #2704 | C22 | 1 | 18 | yes | complemented |
| 23 | #2704 | C22 | 1 | 18 | yes | complemented |
| 24 | #2692 | C22 | 1 | 18 | yes | — |
| 25 | #2683 | C22 | 1 | 18 | yes | — |
| 26 | #2666 | C22 | 1 | 18 | yes | complemented |
| 27 | #2589 | C22 | 1 | 18 | yes | complemented |
| 28 | #2583 | C22 | 1 | 18 | yes | complemented |
| 29 | #2582 | C22 | 1 | 9 | yes | complemented |
| 30 | #2556 | C22 | 1 | 18 | yes | complemented |
| 31 | #2550 | C22 | 1 | 18 | yes | complemented |
| 32 | #2549 | C22 | 1 | 18 | yes | complemented |
| 33 | #2538 | C22 | 1 | 9 | yes | — |
| 34 | #2492 | C22 | 1 | 18 | yes | complemented |
| 35 | #2465 | C22 | 1 | 18 | yes | complemented |
| 36 | #2453 | C22 | 1 | 18 | yes | complemented |
| 37 | #2452 | C22 | 1 | 18 | yes | — |
| 38 | #2450 | C22 | 1 | 18 | yes | — |
| 39 | #2449 | C22 | 1 | 18 | yes | — |
| 40 | #2440 | C22 | 1 | 18 | yes | complemented |
| 41 | #2437 | C22 | 1 | 18 | yes | complemented |
| 42 | #2429 | C22 | 1 | 18 | yes | complemented |
| 43 | #2429 | C22 | 1 | 18 | yes | complemented |
| 44 | #2417 | C22 | 1 | 18 | yes | — |
| 45 | C2×#396 | C22 | 1 | 6 | yes | complemented |
| 46 | #2379 | C22 | 1 | 9 | yes | — |
| 47 | #2367 | C22 | 1 | 18 | yes | — |
| 48 | #2360 | C22 | 1 | 18 | yes | complemented |
| 49 | #2358 | C22 | 1 | 18 | yes | — |
| 50 | #2337 | C22 | 1 | 18 | yes | — |
| 51 | #2321 | C22 | 1 | 18 | yes | — |
| 52 | C4×C4⋊Q8 | C22 | 1 | 9 | yes | complemented |
| 53 | C4×#124 | C22 | 1 | 9 | yes | — |
| 54 | H(3,𝔽4) | Q8 | 1 | 16 | yes | complemented |
| 55 | Q82 | — | 4 | 12 | no | — |
| 56 | #554 | — | 4 | 36 | no | — |
| 57 | #543 | — | 4 | 24 | no | — |
| 58 | C2×C4⋊Q8 | C23 | 1 | 9 | yes | — |
| 59 | C2×C4⋊Q8 | C23 | 1 | 18 | yes | — |
| 60 | C2×#125 | C23 | 1 | 18 | yes | — |
| 61 | C2×#124 | C23 | 1 | 9 | yes | — |
| 62 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 63 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 64 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 65 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 66 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 67 | C2×C22⋊Q8 | C23 | 1 | 18 | yes | — |
| 68 | C2×#120 | C23 | 1 | 6 | yes | — |
| 69 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 70 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 71 | C2×C4×Q8 | C23 | 1 | 9 | yes | — |
| 72 | C2×C4×D4 | C23 | 1 | 18 | yes | — |
| 73 | C2×C4×D4 | C23 | 1 | 9 | yes | — |
| 74 | C22×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 75 | C22×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 76 | #400 | C23 | 1 | 18 | yes | — |
| 77 | #400 | C23 | 1 | 18 | yes | — |
| 78 | #399 | C23 | 1 | 18 | yes | — |
| 79 | #398 | C23 | 1 | 18 | yes | — |
| 80 | #398 | C23 | 1 | 18 | yes | — |
| 81 | #398 | C23 | 1 | 18 | yes | — |
| 82 | #398 | C23 | 1 | 18 | yes | — |
| 83 | #398 | C23 | 1 | 18 | yes | — |
| 84 | #398 | C23 | 1 | 18 | yes | — |
| 85 | #396 | C23 | 1 | 18 | yes | — |
| 86 | #396 | C23 | 1 | 18 | yes | — |
| 87 | #396 | C23 | 1 | 6 | yes | — |
| 88 | #396 | C23 | 1 | 6 | yes | — |
| 89 | #396 | C23 | 1 | 18 | yes | — |
| 90 | #396 | C23 | 1 | 18 | yes | — |
| 91 | #395 | C23 | 1 | 18 | yes | — |
| 92 | #395 | C23 | 1 | 18 | yes | — |
| 93 | #395 | C23 | 1 | 18 | yes | — |
| 94 | #395 | C23 | 1 | 18 | yes | — |
| 95 | #393 | C23 | 1 | 6 | yes | — |
| 96 | #393 | C23 | 1 | 18 | yes | — |
| 97 | #393 | C23 | 1 | 18 | yes | — |
| 98 | #391 | C23 | 1 | 9 | yes | — |
| 99 | #391 | C23 | 1 | 9 | yes | — |
| 100 | #391 | C23 | 1 | 18 | yes | — |
| 101 | #391 | C23 | 1 | 18 | yes | — |
| 102 | #391 | C23 | 1 | 9 | yes | — |
| 103 | #391 | C23 | 1 | 9 | yes | — |
| 104 | #391 | C23 | 1 | 18 | yes | — |
| 105 | #391 | C23 | 1 | 18 | yes | — |
| 106 | #390 | C23 | 1 | 9 | yes | — |
| 107 | #390 | C23 | 1 | 18 | yes | — |
| 108 | #389 | C23 | 1 | 18 | yes | — |
| 109 | #389 | C23 | 1 | 18 | yes | — |
| 110 | #389 | C23 | 1 | 18 | yes | — |
| 111 | #389 | C23 | 1 | 18 | yes | — |
| 112 | #389 | C23 | 1 | 9 | yes | — |
| 113 | #389 | C23 | 1 | 18 | yes | — |
| 114 | #389 | C23 | 1 | 18 | yes | — |
| 115 | #389 | C23 | 1 | 18 | yes | — |
| 116 | #388 | C23 | 1 | 18 | yes | — |
| 117 | #388 | C23 | 1 | 18 | yes | — |
| 118 | #388 | C23 | 1 | 18 | yes | — |
| 119 | #388 | C23 | 1 | 18 | yes | — |
| 120 | #388 | C23 | 1 | 18 | yes | — |
| 121 | #388 | C23 | 1 | 18 | yes | — |
| 122 | #387 | C23 | 1 | 18 | yes | — |
| 123 | #387 | C23 | 1 | 18 | yes | — |
| 124 | #387 | C23 | 1 | 18 | yes | — |
| 125 | #386 | C23 | 1 | 18 | yes | — |
| 126 | #386 | C23 | 1 | 18 | yes | — |
| 127 | #386 | C23 | 1 | 18 | yes | — |
| 128 | #385 | C23 | 1 | 18 | yes | — |
| 129 | #385 | C23 | 1 | 18 | yes | — |
| 130 | #385 | C23 | 1 | 18 | yes | — |
| 131 | #385 | C23 | 1 | 18 | yes | — |
| 132 | #385 | C23 | 1 | 18 | yes | — |
| 133 | #385 | C23 | 1 | 18 | yes | — |
| 134 | #385 | C23 | 1 | 18 | yes | — |
| 135 | #384 | C23 | 1 | 9 | yes | — |
| 136 | #383 | C23 | 1 | 6 | yes | — |
| 137 | #382 | C23 | 1 | 9 | yes | — |
| 138 | #380 | C23 | 1 | 18 | yes | — |
| 139 | #380 | C23 | 1 | 18 | yes | — |
| 140 | #379 | C23 | 1 | 6 | yes | — |
| 141 | C4×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 142 | C4×C4⋊C4 | C23 | 1 | 18 | yes | — |
| 143 | C4×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 144 | C4×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 145 | C4×C22⋊C4 | C23 | 1 | 18 | yes | — |
| 146 | C2×#95 | C23 | 1 | 6 | yes | — |
| 147 | C43 | C23 | 1 | 3 | yes | — |
| 148 | C25 | C24 | 1 | 2 | yes | — |
| 149 | C22×Q8 | C24 | 1 | 9 | yes | — |
| 150 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 151 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 152 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 153 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 154 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 155 | C22×D4 | C24 | 1 | 9 | yes | — |
| 156 | C23×C4 | C24 | 1 | 18 | yes | — |
| 157 | C23×C4 | C24 | 1 | 18 | yes | — |
| 158 | C4⋊Q8 | — | 2 | 36 | no | — |
| 159 | C4⋊Q8 | — | 4 | 36 | no | — |
| 160 | #125 | — | 4 | 36 | no | — |
| 161 | #124 | C2×Q8 | 1 | 72 | yes | — |
| 162 | C22⋊Q8 | — | 2 | 72 | no | — |
| 163 | C22⋊Q8 | — | 4 | 36 | no | — |
| 164 | C22⋊Q8 | — | 4 | 36 | no | — |
| 165 | C22⋊Q8 | — | 4 | 36 | no | — |
| 166 | C22⋊Q8 | — | 4 | 36 | no | — |
| 167 | C22⋊Q8 | — | 4 | 36 | no | — |
| 168 | #120 | C2×Q8 | 1 | 48 | yes | — |
| 169 | C4×Q8 | — | 4 | 18 | no | — |
| 170 | C4×Q8 | — | 4 | 18 | no | — |
| 171 | C4×Q8 | — | 4 | 18 | no | — |
| 172 | C4×D4 | — | 4 | 18 | no | — |
| 173 | C4×D4 | — | 4 | 36 | no | — |
| 174 | C2×C4⋊C4 | — | 4 | 36 | no | — |
| 175 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 176 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 177 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 178 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 179 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 180 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 181 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 182 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 183 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 184 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 185 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 186 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 187 | C2×C4⋊C4 | C24 | 1 | 18 | yes | — |
| 188 | C2×C4⋊C4 | C24 | 1 | 9 | yes | — |
| 189 | C2×C22⋊C4 | — | 4 | 36 | no | — |
| 190 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 191 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 192 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 193 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 194 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 195 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 196 | C2×C22⋊C4 | C24 | 1 | 18 | yes | — |
| 197 | C2×C42 | C24 | 1 | 9 | yes | — |
| 198 | C2×C42 | C24 | 1 | 18 | yes | — |
| 199 | C2×C42 | C24 | 1 | 18 | yes | — |
| 200 | C2×C42 | C24 | 1 | 9 | yes | — |
| 201 | C2×C42 | C24 | 1 | 3 | yes | — |
| 202 | #95 | C24 | 1 | 18 | yes | — |
| 203 | #95 | C24 | 1 | 6 | yes | — |
| 204 | #95 | C24 | 1 | 18 | yes | — |
| 205 | #95 | C24 | 1 | 18 | yes | — |
| 206 | #95 | C24 | 1 | 18 | yes | — |
| 207 | #95 | C24 | 1 | 18 | yes | — |
| 208 | #95 | C24 | 1 | 18 | yes | — |
| 209 | #95 | C24 | 1 | 18 | yes | — |
| 210 | #95 | C24 | 1 | 18 | yes | — |
| 211 | #95 | C24 | 1 | 18 | yes | — |
| 212 | #95 | C24 | 1 | 18 | yes | — |
| 213 | C24 | — | 4 | 6 | no | — |
| 214 | C24 | — | 4 | 6 | no | — |
| 215 | C24 | C22×Q8 | 1 | 8 | yes | — |
| 216 | C24 | C25 | 1 | 6 | yes | — |
| 217 | C2×Q8 | — | 2 | 18 | no | — |
| 218 | C2×Q8 | — | 4 | 3 | no | — |
| 219 | C2×Q8 | — | 4 | 3 | no | — |
| 220 | C2×Q8 | — | 4 | 3 | no | — |
| 221 | C2×Q8 | — | 4 | 3 | no | — |
| 222 | C2×Q8 | — | 4 | 9 | no | — |
| 223 | C2×Q8 | — | 4 | 9 | no | — |
| 224 | C2×Q8 | — | 4 | 6 | no | — |
| 225 | C2×Q8 | — | 4 | 6 | no | — |
| 226 | C2×Q8 | — | 4 | 6 | no | — |
| 227 | C2×Q8 | — | 4 | 6 | no | — |
| 228 | C2×Q8 | — | 4 | 3 | no | — |
| 229 | C2×Q8 | — | 4 | 6 | no | — |
| 230 | C2×Q8 | — | 4 | 6 | no | — |
| 231 | C2×Q8 | C22×Q8 | 1 | 12 | yes | — |
| 232 | C2×Q8 | H(5,𝔽2) | 1 | 12 | yes | — |
| 233 | C2×D4 | — | 4 | 9 | no | — |
| 234 | C2×D4 | — | 4 | 9 | no | — |
| 235 | C2×D4 | C22×Q8 | 1 | 36 | yes | — |
| 236 | C22×C4 | — | 2 | 36 | no | — |
| 237 | C22×C4 | — | 4 | 18 | no | — |
| 238 | C22×C4 | — | 4 | 18 | no | — |
| 239 | C22×C4 | — | 4 | 18 | no | — |
| 240 | C22×C4 | — | 4 | 18 | no | — |
| 241 | C22×C4 | — | 4 | 18 | no | — |
| 242 | C22×C4 | C25 | 1 | 3 | yes | — |
| 243 | C22×C4 | C25 | 1 | 18 | yes | — |
| 244 | C22×C4 | C25 | 1 | 18 | yes | — |
| 245 | C22×C4 | C25 | 1 | 9 | yes | — |
| 246 | C22×C4 | C25 | 1 | 9 | yes | — |
| 247 | C4⋊C4 | — | 2 | 36 | no | — |
| 248 | C4⋊C4 | — | 2 | 36 | no | — |
| 249 | C4⋊C4 | — | 2 | 36 | no | — |
| 250 | C4⋊C4 | — | 2 | 36 | no | — |
| 251 | C4⋊C4 | — | 2 | 36 | no | — |
| 252 | C4⋊C4 | — | 4 | 9 | no | — |
| 253 | C4⋊C4 | — | 4 | 18 | no | — |
| 254 | C4⋊C4 | — | 4 | 18 | no | — |
| 255 | C4⋊C4 | — | 4 | 9 | no | — |
| 256 | C4⋊C4 | — | 4 | 9 | no | — |
| 257 | C4⋊C4 | — | 4 | 9 | no | — |
| 258 | C4⋊C4 | — | 4 | 9 | no | — |
| 259 | C4⋊C4 | — | 4 | 18 | no | — |
| 260 | C4⋊C4 | — | 4 | 18 | no | — |
| 261 | C22⋊C4 | — | 2 | 36 | no | — |
| 262 | C22⋊C4 | — | 2 | 36 | no | — |
| 263 | C22⋊C4 | — | 4 | 18 | no | — |
| 264 | C22⋊C4 | — | 4 | 18 | no | — |
| 265 | C22⋊C4 | — | 4 | 18 | no | — |
| 266 | C22⋊C4 | — | 4 | 18 | no | — |
| 267 | C22⋊C4 | C22×Q8 | 1 | 72 | yes | — |
| 268 | C42 | — | 2 | 18 | no | — |
| 269 | C42 | — | 4 | 9 | no | — |
| 270 | C42 | — | 4 | 18 | no | — |
| 271 | C42 | — | 4 | 18 | no | — |
| 272 | C42 | C22×Q8 | 1 | 12 | yes | — |
| 273 | C23 | — | 2 | 18 | no | — |
| 274 | C23 | — | 2 | 18 | no | — |
| 275 | C23 | — | 4 | 24 | no | — |
| 276 | C23 | — | 16 | 2 | no | — |
| 277 | C23 | — | 16 | 6 | no | — |
| 278 | C23 | C23×Q8 | 1 | 12 | yes | — |
| 279 | C23 | C26 | 1 | 1 | yes | characteristic |
| 280 | Q8 | — | 4 | 12 | no | — |
| 281 | Q8 | — | 4 | 12 | no | — |
| 282 | Q8 | — | 8 | 18 | no | — |
| 283 | Q8 | — | 16 | 1 | no | — |
| 284 | Q8 | — | 16 | 6 | no | — |
| 285 | Q8 | — | 16 | 6 | no | — |
| 286 | D4 | — | 4 | 36 | no | — |
| 287 | C2×C4 | — | 2 | 9 | no | — |
| 288 | C2×C4 | — | 2 | 9 | no | — |
| 289 | C2×C4 | — | 2 | 9 | no | — |
| 290 | C2×C4 | — | 2 | 9 | no | — |
| 291 | C2×C4 | — | 2 | 18 | no | — |
| 292 | C2×C4 | — | 2 | 18 | no | — |
| 293 | C2×C4 | — | 2 | 18 | no | — |
| 294 | C2×C4 | — | 2 | 18 | no | — |
| 295 | C2×C4 | — | 2 | 9 | no | — |
| 296 | C2×C4 | — | 2 | 18 | no | — |
| 297 | C2×C4 | — | 2 | 18 | no | — |
| 298 | C2×C4 | — | 8 | 36 | no | — |
| 299 | C2×C4 | — | 16 | 18 | no | — |
| 300 | C2×C4 | C23×Q8 | 1 | 18 | yes | — |
| 301 | C2×C4 | C2×H(5,𝔽2) | 1 | 18 | yes | — |
| 302 | C22 | — | 2 | 36 | no | — |
| 303 | C22 | — | 4 | 6 | no | — |
| 304 | C22 | — | 4 | 18 | no | — |
| 305 | C22 | — | 16 | 8 | no | — |
| 306 | C22 | C24×Q8 | 1 | 1 | yes | characteristic |
| 307 | C22 | C22×H(5,𝔽2) | 1 | 3 | yes | — |
| 308 | C22 | 2−1+6 | 1 | 3 | yes | — |
| 309 | C4 | — | 2 | 18 | no | — |
| 310 | C4 | — | 2 | 18 | no | — |
| 311 | C4 | — | 4 | 3 | no | — |
| 312 | C4 | — | 4 | 18 | no | — |
| 313 | C4 | — | 4 | 18 | no | — |
| 314 | C2 | — | 4 | 12 | no | — |
| 315 | C2 | #62895 | 1 | 3 | yes | — |
| 316 | C2 | #62980 | 1 | 1 | yes | characteristic |
| 317 | C2 | Q8×H(5,𝔽2) | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| prime radical | C2×H(3,𝔽4) | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #59655 | C2 | semidirect |
| 2. #50705 | C2 | semidirect |
| 3. #46432 | C2 | semidirect |
| 4. #43025 | C2 | semidirect |
| 5. #39702 | C2 | semidirect |
| 8. C2×Q82 | C22 | semidirect |
| 10. C2×#543 | C22 | semidirect |
| 11. #2863 | C22 | semidirect |
| 12. #2840 | C22 | semidirect |
| 13. #2811 | C22 | semidirect |
| 14. #2811 | C22 | semidirect |
| 15. #2806 | C22 | semidirect |
| 17. #2788 | C22 | semidirect |
| 19. #2729 | C22 | semidirect |
| 20. #2729 | C22 | semidirect |
| 21. #2720 | C22 | semidirect |
| 22. #2704 | C22 | semidirect |
| 23. #2704 | C22 | semidirect |
| 26. #2666 | C22 | semidirect |
| 27. #2589 | C22 | semidirect |
| 28. #2583 | C22 | semidirect |
| 29. #2582 | C22 | semidirect |
| 30. #2556 | C22 | semidirect |
| 31. #2550 | C22 | semidirect |
| 32. #2549 | C22 | semidirect |
| 34. #2492 | C22 | semidirect |
| 35. #2465 | C22 | semidirect |
| 36. #2453 | C22 | semidirect |
| 40. #2440 | C22 | semidirect |
| 41. #2437 | C22 | semidirect |
| 42. #2429 | C22 | semidirect |
| 43. #2429 | C22 | semidirect |
| 45. C2×#396 | C22 | semidirect |
| 48. #2360 | C22 | semidirect |
| 52. C4×C4⋊Q8 | C22 | semidirect |
| 54. H(3,𝔽4) | Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #59655 | 2 |
| #50705 | 2 |
| #46432 | 2 |
| #43025 | 2 |
| #39702 | 2 |
| #34529 | 2 |