Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
12640 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 12640 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11715842 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 2 | C2×#87521 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C2×#87519 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#87548 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#60402 | — | 3 | 1 | no | maximal, Sylow |
| 6 | #87548 | C22 | 1 | 4 | yes | complemented |
| 7 | C2×#5950 | C22 | 1 | 3 | yes | — |
| 8 | #87521 | C22 | 1 | 12 | yes | complemented |
| 9 | #87519 | C22 | 1 | 12 | yes | complemented |
| 10 | C2×#5934 | C22 | 1 | 3 | yes | complemented |
| 11 | C2×#5932 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#5919 | — | 4 | 3 | no | maximal |
| 13 | C2×2−1+6 | D3 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×#3487 | — | 3 | 3 | no | — |
| 15 | #60402 | — | 3 | 24 | no | — |
| 16 | #60402 | — | 3 | 8 | no | — |
| 17 | C2×#3027 | — | 3 | 9 | no | — |
| 18 | C2×#3027 | — | 3 | 3 | no | — |
| 19 | C2×#3025 | — | 3 | 9 | no | — |
| 20 | C2×#3025 | — | 3 | 3 | no | — |
| 21 | C2×#2884 | — | 3 | 3 | no | — |
| 22 | #5950 | C23 | 1 | 6 | yes | — |
| 23 | C2×#997 | C23 | 1 | 1 | yes | characteristic |
| 24 | C2×#994 | — | 8 | 1 | no | — |
| 25 | C2×Q8×A4 | — | 4 | 3 | no | — |
| 26 | #5934 | C23 | 1 | 6 | yes | complemented |
| 27 | #5932 | C23 | 1 | 2 | yes | complemented |
| 28 | #5919 | — | 4 | 24 | no | — |
| 29 | C2×C4⋊S4 | — | 4 | 9 | no | — |
| 30 | C2×C4×S4 | — | 4 | 9 | no | — |
| 31 | 2−1+6 | — | 3 | 12 | no | — |
| 32 | 2−1+6 | — | 6 | 4 | no | — |
| 33 | 2−1+6 | C2×D3 | 1 | 4 | yes | complemented |
| 34 | C2×#585 | — | 3 | 9 | no | — |
| 35 | C2×#585 | — | 6 | 1 | no | — |
| 36 | C2×#585 | C2×D3 | 1 | 3 | yes | — |
| 37 | C22×2−1+4 | — | 3 | 3 | no | — |
| 38 | C22×2−1+4 | — | 6 | 3 | no | — |
| 39 | C23×#41 | — | 3 | 1 | no | — |
| 40 | #3487 | — | 3 | 24 | no | — |
| 41 | #3487 | — | 3 | 24 | no | — |
| 42 | #3487 | — | 6 | 12 | no | — |
| 43 | #3487 | — | 6 | 12 | no | — |
| 44 | C2×#550 | — | 6 | 3 | no | — |
| 45 | C2×#550 | — | 6 | 9 | no | — |
| 46 | C2×#548 | — | 6 | 9 | no | — |
| 47 | C2×#548 | — | 6 | 3 | no | — |
| 48 | C2×#535 | — | 3 | 9 | no | — |
| 49 | C2×#535 | — | 3 | 9 | no | — |
| 50 | C2×#525 | — | 3 | 9 | no | — |
| 51 | C2×#525 | — | 3 | 9 | no | — |
| 52 | C2×#519 | — | 3 | 3 | no | — |
| 53 | #3027 | — | 3 | 72 | no | — |
| 54 | #3027 | — | 3 | 36 | no | — |
| 55 | #3027 | — | 3 | 72 | no | — |
| 56 | #3027 | — | 3 | 12 | no | — |
| 57 | #3025 | — | 3 | 72 | no | — |
| 58 | #3025 | — | 3 | 36 | no | — |
| 59 | #3025 | — | 3 | 72 | no | — |
| 60 | #3025 | — | 3 | 12 | no | — |
| 61 | C2×#458 | — | 3 | 9 | no | — |
| 62 | C2×#458 | — | 3 | 6 | no | — |
| 63 | C2×#458 | — | 3 | 1 | no | — |
| 64 | C2×B(4,𝔽2) | — | 3 | 18 | no | — |
| 65 | C2×B(4,𝔽2) | — | 3 | 9 | no | — |
| 66 | C2×B(4,𝔽2) | — | 3 | 18 | no | — |
| 67 | C2×B(4,𝔽2) | — | 3 | 3 | no | — |
| 68 | #2884 | — | 3 | 24 | no | — |
| 69 | #2884 | — | 3 | 24 | no | — |
| 70 | C2×#410 | — | 3 | 18 | no | — |
| 71 | C2×#410 | — | 3 | 9 | no | — |
| 72 | C2×#410 | — | 3 | 9 | no | — |
| 73 | C22×S4 | — | 4 | 9 | no | — |
| 74 | C2×#239 | — | 16 | 1 | no | — |
| 75 | #997 | C24 | 1 | 1 | yes | characteristic |
| 76 | #994 | — | 8 | 4 | no | — |
| 77 | C2×#41⋊C3 | — | 8 | 3 | no | — |
| 78 | Q8×A4 | — | 4 | 12 | no | — |
| 79 | C2×C4×A4 | — | 4 | 9 | no | — |
| 80 | C2×SL(2,ℤ/4) | — | 4 | 3 | no | — |
| 81 | C4⋊S4 | — | 4 | 36 | no | — |
| 82 | C4×S4 | — | 4 | 36 | no | — |
| 83 | #585 | — | 3 | 36 | no | — |
| 84 | #585 | — | 3 | 18 | no | — |
| 85 | #585 | — | 3 | 36 | no | — |
| 86 | #585 | — | 6 | 4 | no | — |
| 87 | #585 | — | 6 | 18 | no | — |
| 88 | #585 | — | 6 | 6 | no | — |
| 89 | #585 | — | 6 | 72 | no | — |
| 90 | #585 | — | 6 | 12 | no | — |
| 91 | #585 | — | 6 | 18 | no | — |
| 92 | #585 | — | 6 | 12 | no | — |
| 93 | #585 | — | 6 | 4 | no | — |
| 94 | #585 | C22×D3 | 1 | 6 | yes | — |
| 95 | C2×2−1+4 | — | 3 | 12 | no | — |
| 96 | C2×2−1+4 | — | 3 | 12 | no | — |
| 97 | C2×2−1+4 | — | 3 | 12 | no | — |
| 98 | C2×2−1+4 | — | 3 | 12 | no | — |
| 99 | C2×2−1+4 | — | 6 | 12 | no | — |
| 100 | C2×2−1+4 | — | 6 | 3 | no | — |
| 101 | C2×2−1+4 | — | 6 | 3 | no | — |
| 102 | C2×2−1+4 | — | 6 | 18 | no | — |
| 103 | C2×2−1+4 | — | 6 | 24 | no | — |
| 104 | C2×2−1+4 | — | 6 | 36 | no | — |
| 105 | C2×2−1+4 | — | 6 | 9 | no | — |
| 106 | C2×2−1+4 | — | 6 | 36 | no | — |
| 107 | C2×2−1+4 | — | 6 | 3 | no | — |
| 108 | C2×2−1+4 | — | 6 | 12 | no | — |
| 109 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 110 | C2×H(5,𝔽2) | — | 3 | 9 | no | — |
| 111 | C2×H(5,𝔽2) | — | 3 | 6 | no | — |
| 112 | C2×H(5,𝔽2) | — | 6 | 3 | no | — |
| 113 | C2×H(5,𝔽2) | — | 6 | 9 | no | — |
| 114 | C2×H(5,𝔽2) | C22×D3 | 1 | 1 | yes | characteristic |
| 115 | C22×#41 | — | 3 | 9 | no | — |
| 116 | C22×#41 | — | 3 | 3 | no | — |
| 117 | C22×#41 | — | 3 | 8 | no | — |
| 118 | C22×#41 | — | 3 | 9 | no | — |
| 119 | C22×#41 | — | 3 | 9 | no | — |
| 120 | C22×#41 | — | 6 | 3 | no | — |
| 121 | C22×#41 | — | 6 | 18 | no | — |
| 122 | C22×#41 | — | 6 | 9 | no | — |
| 123 | C22×#41 | — | 6 | 9 | no | — |
| 124 | C22×#41 | — | 6 | 3 | no | — |
| 125 | C22×#41 | — | 6 | 12 | no | — |
| 126 | C23×Q8 | — | 3 | 1 | no | — |
| 127 | C23×Q8 | — | 3 | 9 | no | — |
| 128 | C23×Q8 | — | 6 | 2 | no | — |
| 129 | C23×Q8 | S4 | 1 | 3 | yes | complemented |
| 130 | C23×D4 | — | 3 | 3 | no | — |
| 131 | C24×C4 | — | 3 | 3 | no | — |
| 132 | #550 | — | 6 | 72 | no | — |
| 133 | #550 | — | 6 | 24 | no | — |
| 134 | #550 | — | 6 | 24 | no | — |
| 135 | #550 | — | 6 | 72 | no | — |
| 136 | #548 | — | 6 | 24 | no | — |
| 137 | #548 | — | 6 | 72 | no | — |
| 138 | #548 | — | 6 | 72 | no | — |
| 139 | #548 | — | 6 | 24 | no | — |
| 140 | #535 | — | 3 | 36 | no | — |
| 141 | #535 | — | 3 | 72 | no | — |
| 142 | #535 | — | 3 | 36 | no | — |
| 143 | #535 | — | 6 | 18 | no | — |
| 144 | #535 | — | 6 | 36 | no | — |
| 145 | #535 | — | 6 | 18 | no | — |
| 146 | C2×#127 | — | 6 | 9 | no | — |
| 147 | C2×#127 | — | 6 | 9 | no | — |
| 148 | C2×#124 | — | 6 | 9 | no | — |
| 149 | C2×#124 | — | 6 | 9 | no | — |
| 150 | #525 | — | 3 | 36 | no | — |
| 151 | #525 | — | 3 | 72 | no | — |
| 152 | #525 | — | 3 | 36 | no | — |
| 153 | #525 | — | 6 | 18 | no | — |
| 154 | #525 | — | 6 | 36 | no | — |
| 155 | #525 | — | 6 | 18 | no | — |
| 156 | C2×#123 | — | 3 | 9 | no | — |
| 157 | C2×#123 | — | 3 | 3 | no | — |
| 158 | C2×C22⋊Q8 | — | 6 | 9 | no | — |
| 159 | C2×C22⋊Q8 | — | 6 | 9 | no | — |
| 160 | C2×#121 | — | 6 | 18 | no | — |
| 161 | C2×#121 | — | 6 | 9 | no | — |
| 162 | C2×#121 | — | 6 | 9 | no | — |
| 163 | C2×#121 | — | 6 | 9 | no | — |
| 164 | C2×#121 | — | 6 | 9 | no | — |
| 165 | C2×#120 | — | 3 | 18 | no | — |
| 166 | C2×#120 | — | 3 | 9 | no | — |
| 167 | C2×#120 | — | 3 | 9 | no | — |
| 168 | #519 | — | 3 | 24 | no | — |
| 169 | #519 | — | 6 | 12 | no | — |
| 170 | C2×C4×Q8 | — | 6 | 9 | no | — |
| 171 | C2×C4×Q8 | — | 6 | 3 | no | — |
| 172 | C2×C4×D4 | — | 6 | 18 | no | — |
| 173 | C2×C4×D4 | — | 6 | 9 | no | — |
| 174 | C2×C4×D4 | — | 6 | 9 | no | — |
| 175 | C2×#117 | — | 3 | 9 | no | — |
| 176 | C2×#117 | — | 3 | 9 | no | — |
| 177 | #458 | — | 3 | 36 | no | — |
| 178 | #458 | — | 3 | 6 | no | — |
| 179 | #458 | — | 3 | 36 | no | — |
| 180 | #458 | — | 3 | 48 | no | — |
| 181 | #458 | — | 3 | 2 | no | — |
| 182 | B(4,𝔽2) | — | 3 | 72 | no | — |
| 183 | B(4,𝔽2) | — | 3 | 36 | no | — |
| 184 | B(4,𝔽2) | — | 3 | 18 | no | — |
| 185 | B(4,𝔽2) | — | 3 | 72 | no | — |
| 186 | B(4,𝔽2) | — | 3 | 36 | no | — |
| 187 | B(4,𝔽2) | — | 3 | 144 | no | — |
| 188 | B(4,𝔽2) | — | 3 | 6 | no | — |
| 189 | #410 | — | 3 | 36 | no | — |
| 190 | #410 | — | 3 | 36 | no | — |
| 191 | #410 | — | 3 | 144 | no | — |
| 192 | #410 | — | 3 | 36 | no | — |
| 193 | #410 | — | 3 | 36 | no | — |
| 194 | C2×#99 | — | 3 | 18 | no | — |
| 195 | C2×#99 | — | 3 | 18 | no | — |
| 196 | C2×#99 | — | 3 | 3 | no | — |
| 197 | C2×#99 | — | 3 | 9 | no | — |
| 198 | C22×A4 | — | 4 | 3 | no | — |
| 199 | C2×S4 | — | 4 | 18 | no | — |
| 200 | C2×S4 | — | 8 | 18 | no | — |
| 201 | C2×C3×Q8 | — | 16 | 1 | no | — |
| 202 | #239 | — | 16 | 8 | no | — |
| 203 | C2×D12 | — | 16 | 3 | no | — |
| 204 | C2×C4×D3 | — | 16 | 3 | no | — |
| 205 | #41⋊C3 | — | 8 | 6 | no | — |
| 206 | C2×SL(2,𝔽3) | — | 8 | 1 | no | — |
| 207 | C4×A4 | — | 4 | 18 | no | — |
| 208 | SL(2,ℤ/4) | — | 4 | 6 | no | — |
| 209 | C25 | — | 3 | 3 | no | — |
| 210 | 2−1+4 | — | 6 | 6 | no | — |
| 211 | 2−1+4 | — | 6 | 12 | no | — |
| 212 | 2−1+4 | — | 6 | 24 | no | — |
| 213 | 2−1+4 | — | 6 | 12 | no | — |
| 214 | 2−1+4 | — | 6 | 72 | no | — |
| 215 | 2−1+4 | — | 6 | 72 | no | — |
| 216 | 2−1+4 | — | 6 | 18 | no | — |
| 217 | 2−1+4 | — | 6 | 72 | no | — |
| 218 | 2−1+4 | — | 6 | 72 | no | — |
| 219 | 2−1+4 | — | 6 | 18 | no | — |
| 220 | 2−1+4 | — | 6 | 36 | no | — |
| 221 | 2−1+4 | — | 6 | 36 | no | — |
| 222 | 2−1+4 | — | 6 | 12 | no | — |
| 223 | 2−1+4 | — | 6 | 6 | no | — |
| 224 | 2−1+4 | — | 6 | 72 | no | — |
| 225 | 2−1+4 | — | 6 | 36 | no | — |
| 226 | H(5,𝔽2) | — | 2 | 4 | no | — |
| 227 | H(5,𝔽2) | — | 3 | 18 | no | — |
| 228 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 229 | H(5,𝔽2) | — | 3 | 18 | no | — |
| 230 | H(5,𝔽2) | — | 3 | 24 | no | — |
| 231 | H(5,𝔽2) | — | 6 | 1 | no | — |
| 232 | H(5,𝔽2) | — | 6 | 9 | no | — |
| 233 | H(5,𝔽2) | — | 6 | 12 | no | — |
| 234 | H(5,𝔽2) | — | 6 | 36 | no | — |
| 235 | H(5,𝔽2) | — | 6 | 36 | no | — |
| 236 | H(5,𝔽2) | — | 6 | 9 | no | — |
| 237 | H(5,𝔽2) | — | 6 | 36 | no | — |
| 238 | H(5,𝔽2) | — | 6 | 36 | no | — |
| 239 | H(5,𝔽2) | — | 6 | 72 | no | — |
| 240 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 241 | H(5,𝔽2) | — | 6 | 36 | no | — |
| 242 | H(5,𝔽2) | C23×D3 | 1 | 1 | yes | characteristic |
| 243 | C2×#41 | — | 2 | 3 | no | — |
| 244 | C2×#41 | — | 3 | 18 | no | — |
| 245 | C2×#41 | — | 3 | 36 | no | — |
| 246 | C2×#41 | — | 3 | 18 | no | — |
| 247 | C2×#41 | — | 3 | 36 | no | — |
| 248 | C2×#41 | — | 3 | 36 | no | — |
| 249 | C2×#41 | — | 3 | 12 | no | — |
| 250 | C2×#41 | — | 3 | 12 | no | — |
| 251 | C2×#41 | — | 3 | 18 | no | — |
| 252 | C2×#41 | — | 3 | 18 | no | — |
| 253 | C2×#41 | — | 3 | 36 | no | — |
| 254 | C2×#41 | — | 6 | 1 | no | — |
| 255 | C2×#41 | — | 6 | 6 | no | — |
| 256 | C2×#41 | — | 6 | 9 | no | — |
| 257 | C2×#41 | — | 6 | 18 | no | — |
| 258 | C2×#41 | — | 6 | 36 | no | — |
| 259 | C2×#41 | — | 6 | 18 | no | — |
| 260 | C2×#41 | — | 6 | 72 | no | — |
| 261 | C2×#41 | — | 6 | 18 | no | — |
| 262 | C2×#41 | — | 6 | 18 | no | — |
| 263 | C2×#41 | — | 6 | 36 | no | — |
| 264 | C2×#41 | — | 6 | 18 | no | — |
| 265 | C2×#41 | — | 6 | 36 | no | — |
| 266 | C2×#41 | — | 6 | 9 | no | — |
| 267 | C2×#41 | — | 6 | 18 | no | — |
| 268 | C2×#41 | — | 6 | 144 | no | — |
| 269 | C2×#41 | — | 6 | 36 | no | — |
| 270 | C2×#41 | — | 6 | 36 | no | — |
| 271 | C2×#41 | — | 6 | 9 | no | — |
| 272 | C2×#41 | — | 6 | 12 | no | — |
| 273 | C2×#41 | — | 6 | 72 | no | — |
| 274 | C2×#41 | — | 6 | 24 | no | — |
| 275 | C2×#41 | — | 6 | 6 | no | — |
| 276 | C2×#41 | — | 6 | 18 | no | — |
| 277 | C2×#41 | — | 6 | 72 | no | — |
| 278 | C2×#41 | — | 6 | 36 | no | — |
| 279 | C2×#41 | — | 6 | 36 | no | — |
| 280 | C2×#41 | — | 6 | 1 | no | — |
| 281 | C2×#41 | — | 12 | 6 | no | — |
| 282 | C2×#41 | — | 12 | 36 | no | — |
| 283 | C2×#41 | — | 12 | 12 | no | — |
| 284 | C2×#41 | — | 12 | 9 | no | — |
| 285 | C2×#41 | — | 12 | 1 | no | — |
| 286 | C22×Q8 | — | 3 | 9 | no | — |
| 287 | C22×Q8 | — | 3 | 4 | no | — |
| 288 | C22×Q8 | — | 3 | 12 | no | — |
| 289 | C22×Q8 | — | 3 | 3 | no | — |
| 290 | C22×Q8 | — | 3 | 9 | no | — |
| 291 | C22×Q8 | — | 3 | 12 | no | — |
| 292 | C22×Q8 | — | 3 | 9 | no | — |
| 293 | C22×Q8 | — | 3 | 36 | no | — |
| 294 | C22×Q8 | — | 3 | 36 | no | — |
| 295 | C22×Q8 | — | 6 | 3 | no | — |
| 296 | C22×Q8 | — | 6 | 9 | no | — |
| 297 | C22×Q8 | — | 6 | 18 | no | — |
| 298 | C22×Q8 | — | 6 | 36 | no | — |
| 299 | C22×Q8 | — | 6 | 8 | no | — |
| 300 | C22×Q8 | — | 6 | 24 | no | — |
| 301 | C22×Q8 | C2×S4 | 1 | 12 | yes | complemented |
| 302 | C22×D4 | — | 3 | 9 | no | — |
| 303 | C22×D4 | — | 3 | 9 | no | — |
| 304 | C22×D4 | — | 3 | 3 | no | — |
| 305 | C22×D4 | — | 3 | 9 | no | — |
| 306 | C22×D4 | — | 3 | 12 | no | — |
| 307 | C22×D4 | — | 6 | 9 | no | — |
| 308 | C22×D4 | — | 6 | 9 | no | — |
| 309 | C22×D4 | — | 6 | 18 | no | — |
| 310 | C22×D4 | — | 6 | 9 | no | — |
| 311 | C22×D4 | — | 6 | 18 | no | — |
| 312 | C22×D4 | — | 6 | 3 | no | — |
| 313 | C22×D4 | — | 6 | 18 | no | — |
| 314 | C22×D4 | — | 6 | 9 | no | — |
| 315 | C22×D4 | — | 6 | 9 | no | — |
| 316 | C23×C4 | — | 3 | 3 | no | — |
| 317 | C23×C4 | — | 3 | 18 | no | — |
| 318 | C23×C4 | — | 3 | 9 | no | — |
| 319 | C23×C4 | — | 3 | 1 | no | — |
| 320 | C23×C4 | — | 3 | 12 | no | — |
| 321 | C23×C4 | — | 6 | 9 | no | — |
| 322 | C23×C4 | — | 6 | 9 | no | — |
| 323 | C23×C4 | — | 6 | 18 | no | — |
| 324 | C23×C4 | — | 6 | 6 | no | — |
| 325 | C23×C4 | C2×S4 | 1 | 9 | yes | — |
| 326 | #127 | — | 6 | 36 | no | — |
| 327 | #127 | — | 6 | 72 | no | — |
| 328 | #127 | — | 6 | 36 | no | — |
| 329 | #124 | — | 6 | 72 | no | — |
| 330 | #124 | — | 6 | 36 | no | — |
| 331 | #124 | — | 6 | 36 | no | — |
| 332 | #123 | — | 3 | 6 | no | — |
| 333 | #123 | — | 3 | 36 | no | — |
| 334 | #123 | — | 3 | 6 | no | — |
| 335 | #123 | — | 6 | 3 | no | — |
| 336 | #123 | — | 6 | 18 | no | — |
| 337 | #123 | — | 6 | 3 | no | — |
| 338 | C22⋊Q8 | — | 6 | 72 | no | — |
| 339 | C22⋊Q8 | — | 6 | 36 | no | — |
| 340 | C22⋊Q8 | — | 6 | 36 | no | — |
| 341 | #121 | — | 6 | 36 | no | — |
| 342 | #121 | — | 6 | 144 | no | — |
| 343 | #121 | — | 6 | 36 | no | — |
| 344 | #121 | — | 6 | 36 | no | — |
| 345 | #121 | — | 6 | 36 | no | — |
| 346 | #121 | — | 6 | 72 | no | — |
| 347 | #121 | — | 6 | 36 | no | — |
| 348 | #121 | — | 6 | 36 | no | — |
| 349 | #120 | — | 3 | 72 | no | — |
| 350 | #120 | — | 3 | 36 | no | — |
| 351 | #120 | — | 3 | 18 | no | — |
| 352 | #120 | — | 3 | 18 | no | — |
| 353 | #120 | — | 6 | 36 | no | — |
| 354 | #120 | — | 6 | 18 | no | — |
| 355 | #120 | — | 6 | 9 | no | — |
| 356 | #120 | — | 6 | 9 | no | — |
| 357 | C4×Q8 | — | 6 | 72 | no | — |
| 358 | C4×Q8 | — | 6 | 24 | no | — |
| 359 | C4×D4 | — | 6 | 36 | no | — |
| 360 | C4×D4 | — | 6 | 144 | no | — |
| 361 | C4×D4 | — | 6 | 36 | no | — |
| 362 | C4×D4 | — | 6 | 36 | no | — |
| 363 | C4×D4 | — | 6 | 36 | no | — |
| 364 | #117 | — | 3 | 36 | no | — |
| 365 | #117 | — | 3 | 36 | no | — |
| 366 | #117 | — | 6 | 18 | no | — |
| 367 | #117 | — | 6 | 18 | no | — |
| 368 | C2×C4⋊C4 | — | 6 | 9 | no | — |
| 369 | C2×C4⋊C4 | — | 6 | 9 | no | — |
| 370 | C2×C4⋊C4 | — | 6 | 9 | no | — |
| 371 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 372 | C2×C22⋊C4 | — | 3 | 9 | no | — |
| 373 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 374 | C2×C22⋊C4 | — | 6 | 18 | no | — |
| 375 | C2×C22⋊C4 | — | 6 | 9 | no | — |
| 376 | C2×C22⋊C4 | — | 6 | 9 | no | — |
| 377 | C2×C22⋊C4 | — | 6 | 9 | no | — |
| 378 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 379 | C2×C42 | — | 6 | 9 | no | — |
| 380 | C2×C42 | — | 6 | 9 | no | — |
| 381 | #99 | — | 3 | 72 | no | — |
| 382 | #99 | — | 3 | 72 | no | — |
| 383 | #99 | — | 3 | 6 | no | — |
| 384 | #99 | — | 3 | 18 | no | — |
| 385 | #99 | — | 3 | 6 | no | — |
| 386 | #99 | — | 3 | 18 | no | — |
| 387 | C22×D3 | — | 16 | 3 | no | — |
| 388 | C2×A4 | — | 4 | 6 | no | — |
| 389 | C2×A4 | — | 4 | 3 | no | — |
| 390 | S4 | — | 8 | 18 | no | — |
| 391 | C3×Q8 | — | 16 | 4 | no | — |
| 392 | C2×C3×C4 | — | 16 | 3 | no | — |
| 393 | C2×Dic3 | — | 16 | 1 | no | — |
| 394 | D12 | — | 16 | 12 | no | — |
| 395 | C4×D3 | — | 16 | 12 | no | — |
| 396 | SL(2,𝔽3) | — | 8 | 1 | no | — |
| 397 | C24 | — | 3 | 1 | no | — |
| 398 | C24 | — | 3 | 9 | no | — |
| 399 | C24 | — | 3 | 6 | no | — |
| 400 | C24 | — | 6 | 9 | no | — |
| 401 | C24 | — | 6 | 9 | no | — |
| 402 | C24 | — | 6 | 2 | no | — |
| 403 | C24 | — | 24 | 6 | no | — |
| 404 | C24 | C22×S4 | 1 | 3 | yes | — |
| 405 | #41 | — | 2 | 6 | no | — |
| 406 | #41 | — | 6 | 1 | no | — |
| 407 | #41 | — | 6 | 18 | no | — |
| 408 | #41 | — | 6 | 36 | no | — |
| 409 | #41 | — | 6 | 18 | no | — |
| 410 | #41 | — | 6 | 36 | no | — |
| 411 | #41 | — | 6 | 36 | no | — |
| 412 | #41 | — | 6 | 3 | no | — |
| 413 | #41 | — | 6 | 72 | no | — |
| 414 | #41 | — | 6 | 72 | no | — |
| 415 | #41 | — | 6 | 72 | no | — |
| 416 | #41 | — | 6 | 36 | no | — |
| 417 | #41 | — | 6 | 72 | no | — |
| 418 | #41 | — | 6 | 36 | no | — |
| 419 | #41 | — | 6 | 72 | no | — |
| 420 | #41 | — | 6 | 18 | no | — |
| 421 | #41 | — | 6 | 18 | no | — |
| 422 | #41 | — | 6 | 3 | no | — |
| 423 | #41 | — | 6 | 1 | no | — |
| 424 | #41 | — | 6 | 72 | no | — |
| 425 | #41 | — | 6 | 36 | no | — |
| 426 | #41 | — | 6 | 36 | no | — |
| 427 | #41 | — | 6 | 72 | no | — |
| 428 | #41 | — | 6 | 72 | no | — |
| 429 | #41 | — | 6 | 18 | no | — |
| 430 | #41 | — | 6 | 18 | no | — |
| 431 | #41 | — | 6 | 4 | no | — |
| 432 | #41 | — | 6 | 4 | no | — |
| 433 | #41 | — | 6 | 6 | no | — |
| 434 | #41 | — | 12 | 48 | no | — |
| 435 | #41 | — | 12 | 72 | no | — |
| 436 | #41 | — | 12 | 8 | no | — |
| 437 | C2×Q8 | — | 2 | 1 | no | — |
| 438 | C2×Q8 | — | 3 | 36 | no | — |
| 439 | C2×Q8 | — | 3 | 6 | no | — |
| 440 | C2×Q8 | — | 3 | 36 | no | — |
| 441 | C2×Q8 | — | 3 | 12 | no | — |
| 442 | C2×Q8 | — | 3 | 12 | no | — |
| 443 | C2×Q8 | — | 3 | 36 | no | — |
| 444 | C2×Q8 | — | 3 | 18 | no | — |
| 445 | C2×Q8 | — | 3 | 18 | no | — |
| 446 | C2×Q8 | — | 3 | 9 | no | — |
| 447 | C2×Q8 | — | 6 | 3 | no | — |
| 448 | C2×Q8 | — | 6 | 9 | no | — |
| 449 | C2×Q8 | — | 6 | 18 | no | — |
| 450 | C2×Q8 | — | 6 | 18 | no | — |
| 451 | C2×Q8 | — | 6 | 6 | no | — |
| 452 | C2×Q8 | — | 6 | 36 | no | — |
| 453 | C2×Q8 | — | 6 | 36 | no | — |
| 454 | C2×Q8 | — | 6 | 72 | no | — |
| 455 | C2×Q8 | — | 6 | 72 | no | — |
| 456 | C2×Q8 | — | 6 | 18 | no | — |
| 457 | C2×Q8 | #1020 | 1 | 1 | yes | characteristic |
| 458 | C2×D4 | — | 3 | 18 | no | — |
| 459 | C2×D4 | — | 3 | 3 | no | — |
| 460 | C2×D4 | — | 3 | 18 | no | — |
| 461 | C2×D4 | — | 3 | 3 | no | — |
| 462 | C2×D4 | — | 3 | 18 | no | — |
| 463 | C2×D4 | — | 3 | 36 | no | — |
| 464 | C2×D4 | — | 3 | 3 | no | — |
| 465 | C2×D4 | — | 3 | 3 | no | — |
| 466 | C2×D4 | — | 3 | 18 | no | — |
| 467 | C2×D4 | — | 6 | 18 | no | — |
| 468 | C2×D4 | — | 6 | 18 | no | — |
| 469 | C2×D4 | — | 6 | 9 | no | — |
| 470 | C2×D4 | — | 6 | 18 | no | — |
| 471 | C2×D4 | — | 6 | 36 | no | — |
| 472 | C2×D4 | — | 6 | 36 | no | — |
| 473 | C2×D4 | — | 6 | 3 | no | — |
| 474 | C2×D4 | — | 6 | 6 | no | — |
| 475 | C2×D4 | — | 6 | 18 | no | — |
| 476 | C2×D4 | — | 6 | 18 | no | — |
| 477 | C2×D4 | — | 6 | 72 | no | — |
| 478 | C2×D4 | — | 6 | 36 | no | — |
| 479 | C2×D4 | — | 6 | 3 | no | — |
| 480 | C2×D4 | — | 6 | 72 | no | — |
| 481 | C2×D4 | — | 6 | 18 | no | — |
| 482 | C2×D4 | — | 6 | 12 | no | — |
| 483 | C2×D4 | — | 6 | 12 | no | — |
| 484 | C2×D4 | — | 6 | 18 | no | — |
| 485 | C2×D4 | — | 6 | 72 | no | — |
| 486 | C2×D4 | — | 6 | 36 | no | — |
| 487 | C2×D4 | — | 6 | 18 | no | — |
| 488 | C2×D4 | — | 6 | 3 | no | — |
| 489 | C2×D4 | — | 12 | 18 | no | — |
| 490 | C2×D4 | — | 12 | 9 | no | — |
| 491 | C2×D4 | — | 12 | 18 | no | — |
| 492 | C2×D4 | — | 12 | 3 | no | — |
| 493 | C2×D4 | — | 24 | 18 | no | — |
| 494 | C2×D4 | — | 24 | 36 | no | — |
| 495 | C2×D4 | — | 24 | 18 | no | — |
| 496 | C22×C4 | — | 3 | 9 | no | — |
| 497 | C22×C4 | — | 3 | 6 | no | — |
| 498 | C22×C4 | — | 3 | 18 | no | — |
| 499 | C22×C4 | — | 3 | 9 | no | — |
| 500 | C22×C4 | — | 3 | 9 | no | — |
| 501 | C22×C4 | — | 3 | 18 | no | — |
| 502 | C22×C4 | — | 3 | 3 | no | — |
| 503 | C22×C4 | — | 3 | 72 | no | — |
| 504 | C22×C4 | — | 3 | 18 | no | — |
| 505 | C22×C4 | — | 3 | 18 | no | — |
| 506 | C22×C4 | — | 3 | 2 | no | — |
| 507 | C22×C4 | — | 6 | 18 | no | — |
| 508 | C22×C4 | — | 6 | 9 | no | — |
| 509 | C22×C4 | — | 6 | 36 | no | — |
| 510 | C22×C4 | — | 6 | 18 | no | — |
| 511 | C22×C4 | — | 6 | 36 | no | — |
| 512 | C22×C4 | — | 6 | 36 | no | — |
| 513 | C22×C4 | — | 6 | 24 | no | — |
| 514 | C22×C4 | — | 6 | 24 | no | — |
| 515 | C22×C4 | — | 6 | 3 | no | — |
| 516 | C22×C4 | — | 6 | 9 | no | — |
| 517 | C22×C4 | — | 6 | 3 | no | — |
| 518 | C22×C4 | — | 6 | 3 | no | — |
| 519 | C22×C4 | — | 6 | 3 | no | — |
| 520 | C22×C4 | — | 12 | 18 | no | — |
| 521 | C22×C4 | — | 12 | 9 | no | — |
| 522 | C22×C4 | — | 12 | 18 | no | — |
| 523 | C22×C4 | — | 12 | 3 | no | — |
| 524 | C22×C4 | C22×S4 | 1 | 18 | yes | — |
| 525 | C4⋊C4 | — | 6 | 36 | no | — |
| 526 | C4⋊C4 | — | 6 | 36 | no | — |
| 527 | C4⋊C4 | — | 6 | 36 | no | — |
| 528 | C4⋊C4 | — | 6 | 6 | no | — |
| 529 | C4⋊C4 | — | 6 | 6 | no | — |
| 530 | C22⋊C4 | — | 3 | 18 | no | — |
| 531 | C22⋊C4 | — | 3 | 6 | no | — |
| 532 | C22⋊C4 | — | 6 | 72 | no | — |
| 533 | C22⋊C4 | — | 6 | 36 | no | — |
| 534 | C22⋊C4 | — | 6 | 18 | no | — |
| 535 | C22⋊C4 | — | 6 | 18 | no | — |
| 536 | C22⋊C4 | — | 6 | 9 | no | — |
| 537 | C22⋊C4 | — | 6 | 3 | no | — |
| 538 | C22⋊C4 | — | 6 | 6 | no | — |
| 539 | C22⋊C4 | — | 6 | 36 | no | — |
| 540 | C22⋊C4 | — | 6 | 6 | no | — |
| 541 | C42 | — | 6 | 36 | no | — |
| 542 | C42 | — | 6 | 36 | no | — |
| 543 | C22×C3 | — | 16 | 1 | no | — |
| 544 | C2×D3 | — | 16 | 6 | no | — |
| 545 | C2×D3 | — | 32 | 6 | no | — |
| 546 | A4 | — | 4 | 3 | no | — |
| 547 | C3×C4 | — | 16 | 6 | no | — |
| 548 | Dic3 | — | 16 | 2 | no | — |
| 549 | C23 | — | 3 | 1 | no | — |
| 550 | C23 | — | 3 | 3 | no | — |
| 551 | C23 | — | 3 | 3 | no | — |
| 552 | C23 | — | 3 | 3 | no | — |
| 553 | C23 | — | 3 | 18 | no | — |
| 554 | C23 | — | 4 | 6 | no | — |
| 555 | C23 | — | 6 | 9 | no | — |
| 556 | C23 | — | 6 | 18 | no | — |
| 557 | C23 | — | 6 | 8 | no | — |
| 558 | C23 | — | 6 | 3 | no | — |
| 559 | C23 | — | 12 | 9 | no | — |
| 560 | C23 | — | 12 | 2 | no | — |
| 561 | C23 | — | 12 | 18 | no | — |
| 562 | C23 | — | 12 | 18 | no | — |
| 563 | C23 | — | 12 | 18 | no | — |
| 564 | C23 | — | 12 | 3 | no | — |
| 565 | C23 | — | 24 | 6 | no | — |
| 566 | C23 | — | 24 | 4 | no | — |
| 567 | C23 | — | 24 | 18 | no | — |
| 568 | C23 | C23×S4 | 1 | 3 | yes | — |
| 569 | Q8 | — | 2 | 1 | no | — |
| 570 | Q8 | — | 3 | 24 | no | — |
| 571 | Q8 | — | 3 | 36 | no | — |
| 572 | Q8 | — | 6 | 12 | no | — |
| 573 | Q8 | — | 6 | 18 | no | — |
| 574 | Q8 | — | 6 | 18 | no | — |
| 575 | Q8 | — | 6 | 1 | no | — |
| 576 | Q8 | C2×#1020 | 1 | 4 | yes | — |
| 577 | D4 | — | 6 | 36 | no | — |
| 578 | D4 | — | 6 | 36 | no | — |
| 579 | D4 | — | 6 | 36 | no | — |
| 580 | D4 | — | 6 | 3 | no | — |
| 581 | D4 | — | 6 | 3 | no | — |
| 582 | D4 | — | 6 | 6 | no | — |
| 583 | D4 | — | 6 | 6 | no | — |
| 584 | D4 | — | 6 | 6 | no | — |
| 585 | D4 | — | 6 | 12 | no | — |
| 586 | D4 | — | 12 | 36 | no | — |
| 587 | D4 | — | 12 | 12 | no | — |
| 588 | D4 | — | 24 | 18 | no | — |
| 589 | D4 | — | 24 | 18 | no | — |
| 590 | D4 | — | 24 | 72 | no | — |
| 591 | D4 | — | 24 | 36 | no | — |
| 592 | C2×C4 | — | 3 | 18 | no | — |
| 593 | C2×C4 | — | 3 | 18 | no | — |
| 594 | C2×C4 | — | 3 | 9 | no | — |
| 595 | C2×C4 | — | 3 | 18 | no | — |
| 596 | C2×C4 | — | 3 | 18 | no | — |
| 597 | C2×C4 | — | 3 | 18 | no | — |
| 598 | C2×C4 | — | 3 | 3 | no | — |
| 599 | C2×C4 | — | 3 | 3 | no | — |
| 600 | C2×C4 | — | 6 | 9 | no | — |
| 601 | C2×C4 | — | 6 | 72 | no | — |
| 602 | C2×C4 | — | 6 | 18 | no | — |
| 603 | C2×C4 | — | 6 | 18 | no | — |
| 604 | C2×C4 | — | 6 | 3 | no | — |
| 605 | C2×C4 | — | 6 | 1 | no | — |
| 606 | C2×C4 | — | 6 | 6 | no | — |
| 607 | C2×C4 | — | 6 | 6 | no | — |
| 608 | C2×C4 | — | 6 | 18 | no | — |
| 609 | C2×C4 | — | 6 | 6 | no | — |
| 610 | C2×C4 | — | 6 | 6 | no | — |
| 611 | C2×C4 | — | 12 | 36 | no | — |
| 612 | C2×C4 | — | 12 | 3 | no | — |
| 613 | C2×C4 | — | 12 | 18 | no | — |
| 614 | C2×C4 | — | 12 | 6 | no | — |
| 615 | C2×C4 | — | 12 | 1 | no | — |
| 616 | C2×C4 | — | 12 | 12 | no | — |
| 617 | C2×C4 | C2×#1020 | 1 | 3 | yes | — |
| 618 | C2×C3 | — | 16 | 2 | no | — |
| 619 | C2×C3 | — | 16 | 1 | no | — |
| 620 | D3 | — | 32 | 6 | no | — |
| 621 | C22 | — | 3 | 3 | no | — |
| 622 | C22 | — | 3 | 3 | no | — |
| 623 | C22 | — | 4 | 3 | no | — |
| 624 | C22 | — | 6 | 6 | no | — |
| 625 | C22 | — | 6 | 6 | no | — |
| 626 | C22 | — | 12 | 3 | no | — |
| 627 | C22 | — | 12 | 1 | no | — |
| 628 | C22 | — | 12 | 3 | no | — |
| 629 | C22 | — | 12 | 18 | no | — |
| 630 | C22 | — | 12 | 18 | no | — |
| 631 | C22 | — | 12 | 18 | no | — |
| 632 | C22 | — | 12 | 6 | no | — |
| 633 | C22 | — | 12 | 6 | no | — |
| 634 | C22 | — | 24 | 9 | no | — |
| 635 | C22 | — | 24 | 18 | no | — |
| 636 | C22 | — | 24 | 8 | no | — |
| 637 | C22 | — | 24 | 6 | no | — |
| 638 | C22 | C22×#1020 | 1 | 1 | yes | characteristic |
| 639 | C4 | — | 3 | 18 | no | — |
| 640 | C4 | — | 6 | 1 | no | — |
| 641 | C4 | — | 6 | 1 | no | — |
| 642 | C4 | — | 12 | 18 | no | — |
| 643 | C4 | — | 12 | 6 | no | — |
| 644 | C4 | — | 12 | 2 | no | — |
| 645 | C4 | C22×#1020 | 1 | 6 | yes | — |
| 646 | C3 | — | 16 | 1 | no | Sylow |
| 647 | C2 | — | 6 | 3 | no | — |
| 648 | C2 | — | 6 | 3 | no | — |
| 649 | C2 | — | 12 | 6 | no | — |
| 650 | C2 | — | 24 | 6 | no | — |
| 651 | C2 | #11715842 | 1 | 2 | yes | direct product factor |
| 652 | C2 | C23×#1020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#1020 |
| commutator, cosocle, hypocenter | #997 | C24 |
| Frattini | C2 | C23×#1020 |
| Fitting | C2×2−1+6 | D3 |
| hypercenter | C2×Q8 | #1020 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11715842 | C2 | direct (N × H) |
| 2. C2×#87521 | C2 | semidirect |
| 3. C2×#87519 | C2 | semidirect |
| 4. C2×#87548 | C2 | semidirect |
| 6. #87548 | C22 | semidirect |
| 8. #87521 | C22 | semidirect |
| 9. #87519 | C22 | semidirect |
| 10. C2×#5934 | C22 | semidirect |
| 11. C2×#5932 | C22 | semidirect |
| 13. C2×2−1+6 | D3 | semidirect |
| 26. #5934 | C23 | semidirect |
| 27. #5932 | C23 | semidirect |
| 33. 2−1+6 | C2×D3 | semidirect |
| 129. C23×Q8 | S4 | semidirect |
| 301. C22×Q8 | C2×S4 | semidirect |
| 651. C2 | #11715842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11715842 | 2 |
| C2×#87521 | 2 |
| C2×#87519 | 2 |
| C2×#87548 | 2 |
| C2×#60402 | 3 |
| C2×#5919 | 4 |