Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2234 conjugacy classes of subgroups.
The subgroup lattice has 389 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596679 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#64287 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10596532 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#64237 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10596516 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10596515 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #10596514 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10596502 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10596500 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#3830 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#1004 | — | 2 | 2 | no | — |
| 12 | #64330 | — | 2 | 4 | no | — |
| 13 | C2×#3805 | C22 | 1 | 8 | yes | complemented |
| 14 | #64313 | C22 | 1 | 8 | yes | complemented |
| 15 | D3×#237 | — | 2 | 8 | no | — |
| 16 | #64309 | C22 | 1 | 8 | yes | complemented |
| 17 | #64306 | C22 | 1 | 4 | yes | complemented |
| 18 | #64298 | — | 2 | 2 | no | — |
| 19 | C2×#3792 | C22 | 1 | 2 | yes | complemented |
| 20 | C22×#622 | C22 | 1 | 2 | yes | complemented |
| 21 | #64287 | C22 | 1 | 4 | yes | complemented |
| 22 | #64287 | C22 | 1 | 4 | yes | complemented |
| 23 | C2×#3788 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#3787 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#3776 | C22 | 1 | 4 | yes | complemented |
| 26 | #64239 | C22 | 1 | 16 | yes | complemented |
| 27 | C2×#3775 | C22 | 1 | 8 | yes | complemented |
| 28 | #64237 | C22 | 1 | 4 | yes | complemented |
| 29 | #64237 | C22 | 1 | 4 | yes | complemented |
| 30 | #64237 | C22 | 1 | 8 | yes | complemented |
| 31 | #64237 | C22 | 1 | 8 | yes | complemented |
| 32 | #64237 | C22 | 1 | 8 | yes | complemented |
| 33 | #64236 | C22 | 1 | 16 | yes | complemented |
| 34 | C2×#3774 | C22 | 1 | 4 | yes | complemented |
| 35 | #64228 | C22 | 1 | 2 | yes | complemented |
| 36 | #64227 | C22 | 1 | 4 | yes | complemented |
| 37 | #64226 | C22 | 1 | 8 | yes | complemented |
| 38 | #64225 | C22 | 1 | 2 | yes | complemented |
| 39 | #64224 | C22 | 1 | 8 | yes | complemented |
| 40 | #64223 | C22 | 1 | 4 | yes | complemented |
| 41 | #64223 | C22 | 1 | 4 | yes | complemented |
| 42 | #5966 | — | 6 | 2 | no | — |
| 43 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×#638 | D4 | 1 | 2 | yes | — |
| 45 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 46 | #3830 | D4 | 1 | 4 | yes | — |
| 47 | #3830 | C23 | 1 | 4 | yes | — |
| 48 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×C3×#67 | — | 2 | 8 | no | — |
| 51 | C3×#237 | — | 2 | 8 | no | — |
| 52 | C3×D3×D4 | — | 2 | 8 | no | — |
| 53 | C3×#235 | — | 2 | 4 | no | — |
| 54 | #3811 | — | 2 | 4 | no | — |
| 55 | D3×#67 | — | 2 | 16 | no | — |
| 56 | C2×#627 | C23 | 1 | 8 | yes | — |
| 57 | C2×#625 | C23 | 1 | 8 | yes | — |
| 58 | #3805 | — | 2 | 8 | no | — |
| 59 | #3805 | — | 2 | 8 | no | — |
| 60 | #3805 | C23 | 1 | 8 | yes | — |
| 61 | #3805 | C23 | 1 | 16 | yes | — |
| 62 | #3804 | — | 2 | 16 | no | — |
| 63 | C2×D3×Dic3 | — | 2 | 8 | no | — |
| 64 | #3802 | C23 | 1 | 4 | yes | — |
| 65 | C4×D32 | — | 2 | 4 | no | — |
| 66 | #3798 | C23 | 1 | 8 | yes | — |
| 67 | #3797 | C23 | 1 | 4 | yes | — |
| 68 | #3796 | — | 2 | 4 | no | — |
| 69 | #3795 | — | 2 | 8 | no | — |
| 70 | D3×Dic6 | — | 2 | 8 | no | — |
| 71 | #3792 | C23 | 1 | 8 | yes | — |
| 72 | C2×#622 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#622 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#622 | C23 | 1 | 2 | yes | — |
| 75 | C2×#622 | C23 | 1 | 4 | yes | — |
| 76 | C2×#622 | C23 | 1 | 4 | yes | — |
| 77 | #3788 | C23 | 1 | 4 | yes | — |
| 78 | #3787 | C23 | 1 | 2 | yes | — |
| 79 | #3787 | C23 | 1 | 2 | yes | — |
| 80 | #3776 | C23 | 1 | 4 | yes | — |
| 81 | #3776 | C23 | 1 | 4 | yes | — |
| 82 | #3776 | C23 | 1 | 8 | yes | — |
| 83 | #3775 | C23 | 1 | 8 | yes | — |
| 84 | #3775 | C23 | 1 | 8 | yes | — |
| 85 | #3775 | C23 | 1 | 16 | yes | — |
| 86 | #3774 | C23 | 1 | 4 | yes | — |
| 87 | #3774 | C23 | 1 | 4 | yes | — |
| 88 | #3774 | C23 | 1 | 8 | yes | — |
| 89 | #3584 | — | 9 | 1 | no | maximal, Sylow |
| 90 | C3×H(5,𝔽2) | — | 6 | 2 | no | — |
| 91 | #1010 | — | 6 | 8 | no | — |
| 92 | #1010 | — | 6 | 4 | no | — |
| 93 | D3×#41 | — | 6 | 4 | no | — |
| 94 | D3×#41 | — | 6 | 8 | no | — |
| 95 | #1004 | — | 2 | 2 | no | — |
| 96 | #1004 | — | 6 | 8 | no | — |
| 97 | #1004 | — | 6 | 8 | no | — |
| 98 | C2×#237 | — | 6 | 8 | no | — |
| 99 | C2×#237 | — | 6 | 2 | no | — |
| 100 | C2×#237 | — | 6 | 8 | no | — |
| 101 | C23×C32 | C2×D4 | 1 | 2 | yes | — |
| 102 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C22×C3×D3 | — | 2 | 8 | no | — |
| 104 | C2×D32 | — | 2 | 4 | no | — |
| 105 | C32×D4 | C2×D4 | 1 | 4 | yes | — |
| 106 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | #638 | C2×D4 | 1 | 8 | yes | — |
| 108 | C2×C3⋊Dic3 | C2×D4 | 1 | 4 | yes | — |
| 109 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 110 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 111 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 112 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 113 | C4×C3⋊D3 | C24 | 1 | 2 | yes | — |
| 114 | #634 | C2×D4 | 1 | 4 | yes | — |
| 115 | C3×#67 | — | 2 | 16 | no | — |
| 116 | C3×#67 | — | 2 | 8 | no | — |
| 117 | C2×C3×Dic3 | — | 2 | 8 | no | — |
| 118 | C3×D12 | — | 2 | 4 | no | — |
| 119 | C3×C4×D3 | — | 2 | 8 | no | — |
| 120 | C3×Dic6 | — | 2 | 4 | no | — |
| 121 | #627 | — | 2 | 8 | no | — |
| 122 | #627 | C24 | 1 | 8 | yes | — |
| 123 | #626 | — | 2 | 8 | no | — |
| 124 | #625 | — | 2 | 8 | no | — |
| 125 | #625 | C24 | 1 | 8 | yes | — |
| 126 | #624 | — | 2 | 4 | no | — |
| 127 | D3×Dic3 | — | 2 | 16 | no | — |
| 128 | D3×Dic3 | — | 2 | 8 | no | — |
| 129 | #622 | C24 | 1 | 1 | yes | characteristic |
| 130 | #622 | C24 | 1 | 2 | yes | — |
| 131 | #622 | C24 | 1 | 4 | yes | — |
| 132 | #622 | C24 | 1 | 1 | yes | characteristic |
| 133 | #585 | — | 9 | 2 | no | — |
| 134 | #578 | — | 9 | 4 | no | — |
| 135 | #577 | — | 9 | 8 | no | — |
| 136 | #576 | — | 9 | 4 | no | — |
| 137 | #575 | — | 9 | 2 | no | — |
| 138 | #575 | — | 9 | 4 | no | — |
| 139 | C2×#135 | — | 9 | 2 | no | — |
| 140 | C2×#135 | — | 9 | 4 | no | — |
| 141 | C2×#131 | — | 9 | 1 | no | — |
| 142 | C3×#41 | — | 6 | 4 | no | — |
| 143 | C3×#41 | — | 6 | 8 | no | — |
| 144 | C2×C3×D4 | — | 2 | 2 | no | — |
| 145 | C2×C3×D4 | — | 6 | 8 | no | — |
| 146 | C2×C3×D4 | — | 6 | 8 | no | — |
| 147 | C2×#67 | — | 2 | 8 | no | — |
| 148 | C2×#67 | — | 6 | 8 | no | — |
| 149 | C2×#67 | — | 6 | 4 | no | — |
| 150 | C2×#67 | — | 6 | 16 | no | — |
| 151 | C22×Dic3 | — | 6 | 4 | no | — |
| 152 | C22×Dic3 | — | 6 | 8 | no | — |
| 153 | #239 | — | 6 | 4 | no | — |
| 154 | D3×Q8 | — | 6 | 4 | no | — |
| 155 | D3×Q8 | — | 6 | 8 | no | — |
| 156 | #237 | — | 2 | 8 | no | — |
| 157 | #237 | — | 6 | 8 | no | — |
| 158 | #237 | — | 6 | 16 | no | — |
| 159 | #237 | — | 6 | 8 | no | — |
| 160 | #237 | — | 6 | 8 | no | — |
| 161 | #237 | — | 6 | 4 | no | — |
| 162 | #237 | — | 6 | 8 | no | — |
| 163 | #237 | — | 6 | 16 | no | — |
| 164 | #237 | — | 6 | 16 | no | — |
| 165 | #237 | — | 6 | 16 | no | — |
| 166 | D3×D4 | — | 2 | 8 | no | — |
| 167 | D3×D4 | — | 6 | 4 | no | — |
| 168 | D3×D4 | — | 6 | 8 | no | — |
| 169 | D3×D4 | — | 6 | 16 | no | — |
| 170 | #235 | — | 2 | 4 | no | — |
| 171 | #235 | — | 6 | 8 | no | — |
| 172 | #235 | — | 6 | 8 | no | — |
| 173 | #235 | — | 6 | 16 | no | — |
| 174 | C2×C4×D3 | — | 6 | 2 | no | — |
| 175 | C2×C4×D3 | — | 6 | 8 | no | — |
| 176 | C2×C4×D3 | — | 6 | 8 | no | — |
| 177 | C2×Dic6 | — | 6 | 8 | no | — |
| 178 | C2×Dic6 | — | 6 | 2 | no | — |
| 179 | C2×Dic6 | — | 6 | 8 | no | — |
| 180 | C22×C32 | — | 4 | 2 | no | — |
| 181 | C22×C32 | C22×D4 | 1 | 4 | yes | — |
| 182 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 184 | C2×C3⋊D3 | C22×D4 | 1 | 2 | yes | — |
| 185 | C2×C3×D3 | — | 2 | 8 | no | — |
| 186 | C2×C3×D3 | — | 8 | 8 | no | — |
| 187 | D32 | — | 8 | 4 | no | — |
| 188 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 189 | C3⋊Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 190 | C3⋊Dic3 | C22×D4 | 1 | 4 | yes | — |
| 191 | C3⋊Dic3 | C25 | 1 | 1 | yes | characteristic |
| 192 | C3×Dic3 | — | 2 | 8 | no | — |
| 193 | 2−1+4 | — | 9 | 8 | no | — |
| 194 | 2−1+4 | — | 18 | 2 | no | — |
| 195 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 196 | H(5,𝔽2) | — | 9 | 8 | no | — |
| 197 | H(5,𝔽2) | — | 18 | 4 | no | — |
| 198 | C2×#41 | — | 9 | 1 | no | — |
| 199 | C2×#41 | — | 9 | 8 | no | — |
| 200 | C2×#41 | — | 9 | 4 | no | — |
| 201 | C2×#41 | — | 18 | 8 | no | — |
| 202 | #137 | — | 9 | 8 | no | — |
| 203 | #137 | — | 9 | 16 | no | — |
| 204 | AGL(1,ℤ/8) | — | 9 | 8 | no | — |
| 205 | AGL(1,ℤ/8) | — | 9 | 16 | no | — |
| 206 | #135 | — | 9 | 4 | no | — |
| 207 | #135 | — | 9 | 4 | no | — |
| 208 | #135 | — | 9 | 8 | no | — |
| 209 | #135 | — | 9 | 4 | no | — |
| 210 | #135 | — | 9 | 8 | no | — |
| 211 | #135 | — | 9 | 4 | no | — |
| 212 | #135 | — | 9 | 8 | no | — |
| 213 | C2×Q16 | — | 9 | 2 | no | — |
| 214 | C2×Q16 | — | 9 | 4 | no | — |
| 215 | C2×SD16 | — | 9 | 4 | no | — |
| 216 | C2×SD16 | — | 9 | 8 | no | — |
| 217 | C2×D8 | — | 9 | 2 | no | — |
| 218 | C2×D8 | — | 9 | 4 | no | — |
| 219 | #131 | — | 9 | 4 | no | — |
| 220 | #131 | — | 9 | 4 | no | — |
| 221 | C2×M16 | — | 9 | 1 | no | — |
| 222 | C2×M16 | — | 9 | 2 | no | — |
| 223 | C22×C8 | — | 9 | 1 | no | — |
| 224 | C22×C8 | — | 9 | 2 | no | — |
| 225 | C23×C3 | — | 2 | 4 | no | — |
| 226 | C23×C3 | — | 6 | 8 | no | — |
| 227 | C22×D3 | — | 2 | 8 | no | — |
| 228 | C22×D3 | — | 6 | 2 | no | — |
| 229 | C22×D3 | — | 6 | 8 | no | — |
| 230 | C3×Q8 | — | 6 | 4 | no | — |
| 231 | C3×D4 | — | 2 | 8 | no | — |
| 232 | C3×D4 | — | 6 | 4 | no | — |
| 233 | C3×D4 | — | 6 | 16 | no | — |
| 234 | C3×D4 | — | 6 | 8 | no | — |
| 235 | C2×C3×C4 | — | 2 | 2 | no | — |
| 236 | C2×C3×C4 | — | 6 | 8 | no | — |
| 237 | C2×C3×C4 | — | 6 | 8 | no | — |
| 238 | #67 | — | 2 | 8 | no | — |
| 239 | #67 | — | 2 | 16 | no | — |
| 240 | #67 | — | 6 | 8 | no | — |
| 241 | #67 | — | 6 | 16 | no | — |
| 242 | #67 | — | 6 | 8 | no | — |
| 243 | #67 | — | 6 | 16 | no | — |
| 244 | C2×Dic3 | — | 2 | 8 | no | — |
| 245 | C2×Dic3 | — | 6 | 4 | no | — |
| 246 | C2×Dic3 | — | 6 | 8 | no | — |
| 247 | C2×Dic3 | — | 6 | 8 | no | — |
| 248 | C2×Dic3 | — | 6 | 2 | no | — |
| 249 | C2×Dic3 | — | 6 | 16 | no | — |
| 250 | C2×Dic3 | — | 6 | 8 | no | — |
| 251 | D12 | — | 2 | 4 | no | — |
| 252 | D12 | — | 6 | 8 | no | — |
| 253 | C4×D3 | — | 2 | 8 | no | — |
| 254 | C4×D3 | — | 6 | 4 | no | — |
| 255 | C4×D3 | — | 6 | 4 | no | — |
| 256 | C4×D3 | — | 6 | 8 | no | — |
| 257 | C4×D3 | — | 6 | 8 | no | — |
| 258 | C4×D3 | — | 6 | 16 | no | — |
| 259 | Dic6 | — | 2 | 4 | no | — |
| 260 | Dic6 | — | 6 | 8 | no | — |
| 261 | Dic6 | — | 6 | 8 | no | — |
| 262 | Dic6 | — | 6 | 16 | no | — |
| 263 | C2×C32 | — | 2 | 4 | no | — |
| 264 | C2×C32 | — | 2 | 1 | no | — |
| 265 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 266 | C3⋊D3 | — | 2 | 2 | no | — |
| 267 | C3×D3 | — | 4 | 8 | no | — |
| 268 | #41 | — | 6 | 8 | no | — |
| 269 | #41 | — | 6 | 4 | no | — |
| 270 | #41 | — | 9 | 8 | no | — |
| 271 | #41 | — | 9 | 4 | no | — |
| 272 | #41 | — | 9 | 4 | no | — |
| 273 | #41 | — | 9 | 8 | no | — |
| 274 | #41 | — | 9 | 16 | no | — |
| 275 | #41 | — | 18 | 16 | no | — |
| 276 | #41 | — | 18 | 8 | no | — |
| 277 | #41 | — | 18 | 8 | no | — |
| 278 | #41 | — | 18 | 8 | no | — |
| 279 | #41 | — | 18 | 4 | no | — |
| 280 | C2×Q8 | — | 9 | 8 | no | — |
| 281 | C2×Q8 | — | 9 | 1 | no | — |
| 282 | C2×Q8 | — | 9 | 4 | no | — |
| 283 | C2×Q8 | — | 18 | 8 | no | — |
| 284 | C2×D4 | — | 6 | 8 | no | — |
| 285 | C2×D4 | — | 6 | 8 | no | — |
| 286 | C2×D4 | — | 9 | 4 | no | — |
| 287 | C2×D4 | — | 9 | 2 | no | — |
| 288 | C2×D4 | — | 9 | 8 | no | — |
| 289 | C2×D4 | — | 18 | 4 | no | — |
| 290 | C2×D4 | — | 18 | 16 | no | — |
| 291 | C2×D4 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 292 | C22×C4 | — | 9 | 2 | no | — |
| 293 | C22×C4 | — | 9 | 1 | no | — |
| 294 | C22×C4 | — | 18 | 4 | no | — |
| 295 | C22×C4 | — | 18 | 8 | no | — |
| 296 | Q16 | — | 9 | 4 | no | — |
| 297 | Q16 | — | 9 | 4 | no | — |
| 298 | Q16 | — | 9 | 8 | no | — |
| 299 | SD16 | — | 9 | 8 | no | — |
| 300 | SD16 | — | 9 | 8 | no | — |
| 301 | SD16 | — | 9 | 16 | no | — |
| 302 | D8 | — | 9 | 4 | no | — |
| 303 | D8 | — | 9 | 4 | no | — |
| 304 | D8 | — | 9 | 8 | no | — |
| 305 | M16 | — | 9 | 4 | no | — |
| 306 | M16 | — | 9 | 8 | no | — |
| 307 | C2×C8 | — | 9 | 1 | no | — |
| 308 | C2×C8 | — | 9 | 1 | no | — |
| 309 | C2×C8 | — | 9 | 2 | no | — |
| 310 | C2×C8 | — | 9 | 2 | no | — |
| 311 | C2×C8 | — | 9 | 4 | no | — |
| 312 | C2×C8 | — | 9 | 2 | no | — |
| 313 | C2×C8 | — | 9 | 4 | no | — |
| 314 | C22×C3 | — | 2 | 8 | no | — |
| 315 | C22×C3 | — | 2 | 2 | no | — |
| 316 | C22×C3 | — | 6 | 8 | no | — |
| 317 | C22×C3 | — | 8 | 4 | no | — |
| 318 | C22×C3 | — | 24 | 8 | no | — |
| 319 | C2×D3 | — | 2 | 8 | no | — |
| 320 | C2×D3 | — | 6 | 4 | no | — |
| 321 | C2×D3 | — | 8 | 8 | no | — |
| 322 | C2×D3 | — | 24 | 2 | no | — |
| 323 | C2×D3 | — | 24 | 8 | no | — |
| 324 | C3×C4 | — | 2 | 4 | no | — |
| 325 | C3×C4 | — | 6 | 8 | no | — |
| 326 | Dic3 | — | 2 | 8 | no | — |
| 327 | Dic3 | — | 6 | 8 | no | — |
| 328 | Dic3 | — | 6 | 2 | no | — |
| 329 | Dic3 | — | 6 | 2 | no | — |
| 330 | C32 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 331 | C23 | — | 6 | 8 | no | — |
| 332 | C23 | — | 9 | 1 | no | — |
| 333 | C23 | — | 18 | 4 | no | — |
| 334 | C23 | C2×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 335 | Q8 | — | 6 | 4 | no | — |
| 336 | Q8 | — | 9 | 8 | no | — |
| 337 | Q8 | — | 9 | 4 | no | — |
| 338 | Q8 | — | 18 | 8 | no | — |
| 339 | D4 | — | 6 | 16 | no | — |
| 340 | D4 | — | 6 | 8 | no | — |
| 341 | D4 | — | 6 | 4 | no | — |
| 342 | D4 | — | 9 | 8 | no | — |
| 343 | D4 | — | 9 | 8 | no | — |
| 344 | D4 | — | 18 | 8 | no | — |
| 345 | D4 | — | 18 | 8 | no | — |
| 346 | D4 | C2×GO+(4,𝔽2) | 1 | 4 | yes | — |
| 347 | C2×C4 | — | 6 | 8 | no | — |
| 348 | C2×C4 | — | 6 | 8 | no | — |
| 349 | C2×C4 | — | 9 | 1 | no | — |
| 350 | C2×C4 | — | 9 | 4 | no | — |
| 351 | C2×C4 | — | 9 | 4 | no | — |
| 352 | C2×C4 | — | 9 | 2 | no | — |
| 353 | C2×C4 | — | 9 | 2 | no | — |
| 354 | C2×C4 | — | 9 | 2 | no | — |
| 355 | C2×C4 | — | 18 | 4 | no | — |
| 356 | C2×C4 | — | 18 | 8 | no | — |
| 357 | C2×C4 | — | 18 | 16 | no | — |
| 358 | C2×C4 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 359 | C8 | — | 9 | 1 | no | — |
| 360 | C8 | — | 9 | 1 | no | — |
| 361 | C8 | — | 9 | 2 | no | — |
| 362 | C8 | — | 9 | 4 | no | — |
| 363 | C2×C3 | — | 2 | 2 | no | — |
| 364 | C2×C3 | — | 4 | 8 | no | — |
| 365 | C2×C3 | — | 4 | 2 | no | — |
| 366 | C2×C3 | — | 12 | 8 | no | — |
| 367 | D3 | — | 4 | 8 | no | — |
| 368 | D3 | — | 12 | 4 | no | — |
| 369 | C22 | — | 4 | 2 | no | — |
| 370 | C22 | — | 6 | 8 | no | — |
| 371 | C22 | — | 9 | 2 | no | — |
| 372 | C22 | — | 24 | 8 | no | — |
| 373 | C22 | — | 36 | 1 | no | — |
| 374 | C22 | — | 72 | 4 | no | — |
| 375 | C22 | C22×GO+(4,𝔽2) | 1 | 4 | yes | — |
| 376 | C22 | C22×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 6 | 8 | no | — |
| 378 | C4 | — | 9 | 1 | no | — |
| 379 | C4 | — | 9 | 1 | no | — |
| 380 | C4 | — | 9 | 4 | no | — |
| 381 | C4 | C22×GO+(4,𝔽2) | 1 | 2 | yes | — |
| 382 | C3 | — | 2 | 2 | no | — |
| 383 | C2 | — | 2 | 1 | no | — |
| 384 | C2 | — | 2 | 4 | no | — |
| 385 | C2 | — | 12 | 8 | no | — |
| 386 | C2 | — | 18 | 2 | no | — |
| 387 | C2 | C23×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×GO+(4,𝔽2) |
| commutator, cosocle | C3⋊Dic3 | C25 |
| Fitting | C2×C32×D4 | D4 |
| socle | C2×C32 | C23×D4 |
| hypercenter | C2×D4 | GO+(4,𝔽2) |
| hypocenter | C32 | #3584 |
| LCS | G ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596679 | C2 | semidirect |
| 2. C2×#64287 | C2 | semidirect |
| 3. #10596532 | C2 | semidirect |
| 4. C2×#64237 | C2 | semidirect |
| 5. #10596516 | C2 | semidirect |
| 6. #10596515 | C2 | semidirect |
| 7. #10596514 | C2 | semidirect |
| 8. #10596502 | C2 | semidirect |
| 9. #10596500 | C2 | semidirect |
| 13. C2×#3805 | C22 | semidirect |
| 14. #64313 | C22 | semidirect |
| 16. #64309 | C22 | semidirect |
| 17. #64306 | C22 | semidirect |
| 19. C2×#3792 | C22 | semidirect |
| 20. C22×#622 | C22 | semidirect |
| 21. #64287 | C22 | semidirect |
| 22. #64287 | C22 | semidirect |
| 23. C2×#3788 | C22 | semidirect |
| 24. C2×#3787 | C22 | semidirect |
| 25. C2×#3776 | C22 | semidirect |
| 26. #64239 | C22 | semidirect |
| 27. C2×#3775 | C22 | semidirect |
| 28. #64237 | C22 | semidirect |
| 29. #64237 | C22 | semidirect |
| 30. #64237 | C22 | semidirect |
| 31. #64237 | C22 | semidirect |
| 32. #64237 | C22 | semidirect |
| 33. #64236 | C22 | semidirect |
| 34. C2×#3774 | C22 | semidirect |
| 35. #64228 | C22 | semidirect |
| 36. #64227 | C22 | semidirect |
| 37. #64226 | C22 | semidirect |
| 38. #64225 | C22 | semidirect |
| 39. #64224 | C22 | semidirect |
| 40. #64223 | C22 | semidirect |
| 41. #64223 | C22 | semidirect |
| 330. C32 | #3584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596679 | 2 |
| C2×#64287 | 2 |
| #10596532 | 2 |
| C2×#64237 | 2 |
| #10596516 | 2 |
| #10596515 | 2 |
| #10596514 | 2 |
| #10596502 | 2 |
| #10596500 | 2 |
| #3584 | 9 |