Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2275 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4×#3832 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5570 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | Q8×#627 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595353 | C2 | 1 | 2 | yes | maximal |
| 5 | #10594508 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10594484 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #10593909 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10593903 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #10593882 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #87018 | — | 3 | 2 | no | maximal |
| 11 | C2×#3832 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#3797 | C22 | 1 | 6 | yes | — |
| 13 | C32×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 14 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | #64102 | C22 | 1 | 3 | yes | — |
| 16 | #64101 | C22 | 1 | 3 | yes | — |
| 17 | C4×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | — |
| 18 | C42×C3⋊D3 | C22 | 1 | 3 | yes | — |
| 19 | C3×Q8×Dic3 | C22 | 1 | 4 | yes | — |
| 20 | C3×#890 | C22 | 1 | 12 | yes | — |
| 21 | C3×#869 | C22 | 1 | 6 | yes | — |
| 22 | C3×C4×Dic6 | C22 | 1 | 6 | yes | — |
| 23 | #63919 | C22 | 1 | 1 | yes | characteristic |
| 24 | #63919 | C22 | 1 | 6 | yes | — |
| 25 | #63919 | C22 | 1 | 6 | yes | — |
| 26 | #63918 | C22 | 1 | 12 | yes | — |
| 27 | C4×#627 | C22 | 1 | 6 | yes | — |
| 28 | #63900 | C22 | 1 | 6 | yes | — |
| 29 | #63900 | C22 | 1 | 6 | yes | — |
| 30 | #63895 | C22 | 1 | 24 | yes | — |
| 31 | #63894 | C22 | 1 | 12 | yes | — |
| 32 | #63874 | C22 | 1 | 6 | yes | — |
| 33 | #63873 | C22 | 1 | 3 | yes | — |
| 34 | #63871 | C22 | 1 | 6 | yes | — |
| 35 | #63870 | C22 | 1 | 6 | yes | — |
| 36 | #63865 | C22 | 1 | 6 | yes | — |
| 37 | C3×#557 | — | 3 | 2 | no | — |
| 38 | #5727 | — | 3 | 6 | no | — |
| 39 | D3×C4⋊Q8 | — | 3 | 6 | no | — |
| 40 | #5690 | — | 3 | 12 | no | — |
| 41 | #5689 | — | 3 | 12 | no | — |
| 42 | #5578 | — | 3 | 6 | no | — |
| 43 | Q8×D12 | — | 3 | 6 | no | — |
| 44 | #5574 | — | 3 | 4 | no | — |
| 45 | C4×#239 | — | 3 | 2 | no | — |
| 46 | C4×#239 | — | 6 | 1 | no | — |
| 47 | #5570 | D3 | 1 | 2 | yes | complemented |
| 48 | Q8×Dic6 | — | 3 | 4 | no | — |
| 49 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 50 | #3832 | Q8 | 1 | 8 | yes | complemented |
| 51 | C2×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 52 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 53 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 54 | C2×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 55 | C2×C3×Dic6 | C23 | 1 | 6 | yes | — |
| 56 | C2×#627 | C23 | 1 | 2 | yes | — |
| 57 | C2×#627 | C23 | 1 | 12 | yes | — |
| 58 | C2×#624 | C23 | 1 | 12 | yes | — |
| 59 | #3797 | — | 4 | 12 | no | — |
| 60 | C32×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 61 | C32×C42 | C23 | 1 | 3 | yes | — |
| 62 | #3752 | C23 | 1 | 6 | yes | — |
| 63 | C4⋊(C3⋊Dic3) | C23 | 1 | 3 | yes | — |
| 64 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 66 | C4×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 67 | C3×C4⋊Dic3 | C23 | 1 | 12 | yes | — |
| 68 | C3×C4⋊Dic3 | C23 | 1 | 12 | yes | — |
| 69 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 70 | C3×Dic3⋊C4 | C23 | 1 | 12 | yes | — |
| 71 | C3×C4×Dic3 | C23 | 1 | 12 | yes | — |
| 72 | #3724 | C23 | 1 | 6 | yes | — |
| 73 | #3724 | C23 | 1 | 2 | yes | — |
| 74 | #3724 | C23 | 1 | 6 | yes | — |
| 75 | Dic3⋊Dic3 | C23 | 1 | 12 | yes | — |
| 76 | #3722 | C23 | 1 | 12 | yes | — |
| 77 | #3503 | — | 9 | 1 | no | Sylow |
| 78 | C2×#239 | — | 3 | 2 | no | — |
| 79 | C2×#239 | — | 6 | 1 | no | — |
| 80 | C2×D3×Q8 | — | 3 | 12 | no | — |
| 81 | C3×C4⋊Q8 | — | 3 | 6 | no | — |
| 82 | C3×#125 | — | 3 | 12 | no | — |
| 83 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 84 | C3×C4×Q8 | — | 3 | 4 | no | — |
| 85 | C3×C4×Q8 | — | 3 | 6 | no | — |
| 86 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 87 | #946 | — | 3 | 6 | no | — |
| 88 | Q8×Dic3 | — | 3 | 2 | no | — |
| 89 | Q8×Dic3 | — | 6 | 1 | no | — |
| 90 | Q8×Dic3 | C2×D3 | 1 | 4 | yes | — |
| 91 | #944 | — | 3 | 6 | no | — |
| 92 | #897 | — | 3 | 6 | no | — |
| 93 | #897 | — | 3 | 24 | no | — |
| 94 | #896 | — | 3 | 24 | no | — |
| 95 | #896 | — | 3 | 12 | no | — |
| 96 | #893 | — | 3 | 6 | no | — |
| 97 | #893 | — | 3 | 12 | no | — |
| 98 | #893 | — | 6 | 3 | no | — |
| 99 | #892 | — | 3 | 6 | no | — |
| 100 | #892 | — | 6 | 3 | no | — |
| 101 | D3×C4⋊C4 | — | 3 | 12 | no | — |
| 102 | D3×C4⋊C4 | — | 3 | 12 | no | — |
| 103 | #890 | C2×D3 | 1 | 12 | yes | — |
| 104 | #889 | — | 3 | 12 | no | — |
| 105 | #888 | — | 3 | 12 | no | — |
| 106 | #888 | — | 3 | 12 | no | — |
| 107 | #888 | — | 3 | 2 | no | — |
| 108 | #888 | — | 3 | 12 | no | — |
| 109 | C4×D12 | — | 3 | 6 | no | — |
| 110 | C4×D12 | — | 3 | 12 | no | — |
| 111 | C4×D12 | — | 6 | 3 | no | — |
| 112 | #872 | — | 3 | 12 | no | — |
| 113 | C42×D3 | — | 3 | 6 | no | — |
| 114 | C42×D3 | — | 6 | 3 | no | — |
| 115 | #869 | — | 3 | 12 | no | — |
| 116 | #869 | C2×D3 | 1 | 6 | yes | — |
| 117 | C4×Dic6 | — | 3 | 12 | no | — |
| 118 | C4×Dic6 | C2×D3 | 1 | 6 | yes | — |
| 119 | C22×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 120 | C32×Q8 | C2×Q8 | 1 | 4 | yes | complemented |
| 121 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 122 | C2×C32×C4 | C24 | 1 | 3 | yes | — |
| 123 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 124 | C2×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 125 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 126 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 127 | C4⋊(C3⋊D3) | C2×Q8 | 1 | 12 | yes | complemented |
| 128 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 129 | C4×C3⋊D3 | — | 2 | 6 | no | — |
| 130 | C4×C3⋊D3 | C2×Q8 | 1 | 12 | yes | complemented |
| 131 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 132 | C2×C3×Dic3 | C24 | 1 | 12 | yes | — |
| 133 | C3×Dic6 | — | 2 | 12 | no | — |
| 134 | #627 | — | 2 | 4 | no | — |
| 135 | #627 | — | 4 | 12 | no | — |
| 136 | #624 | — | 4 | 12 | no | — |
| 137 | Q82 | — | 9 | 2 | no | — |
| 138 | #557 | — | 3 | 2 | no | — |
| 139 | #554 | — | 9 | 6 | no | — |
| 140 | D4×Q8 | — | 9 | 6 | no | — |
| 141 | #544 | — | 9 | 6 | no | — |
| 142 | #533 | — | 9 | 3 | no | — |
| 143 | C2×C4⋊Q8 | — | 9 | 3 | no | — |
| 144 | #520 | — | 9 | 2 | no | — |
| 145 | C4×#41 | — | 9 | 1 | no | — |
| 146 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 147 | C2×C3×Q8 | — | 3 | 6 | no | — |
| 148 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 149 | #239 | — | 3 | 16 | no | — |
| 150 | #239 | — | 6 | 8 | no | — |
| 151 | D3×Q8 | — | 12 | 24 | no | — |
| 152 | C2×D12 | — | 3 | 6 | no | — |
| 153 | C2×D12 | — | 6 | 3 | no | — |
| 154 | C2×C4×D3 | — | 3 | 6 | no | — |
| 155 | C2×C4×D3 | — | 3 | 6 | no | — |
| 156 | C2×C4×D3 | — | 3 | 6 | no | — |
| 157 | C2×C4×D3 | — | 3 | 24 | no | — |
| 158 | C2×C4×D3 | — | 6 | 3 | no | — |
| 159 | C2×C4×D3 | — | 6 | 3 | no | — |
| 160 | C2×C4×D3 | — | 6 | 3 | no | — |
| 161 | C2×Dic6 | — | 3 | 4 | no | — |
| 162 | C2×Dic6 | — | 3 | 24 | no | — |
| 163 | C2×Dic6 | C22×D3 | 1 | 6 | yes | — |
| 164 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 165 | C3×C4⋊C4 | — | 3 | 12 | no | — |
| 166 | C3×C4⋊C4 | — | 3 | 12 | no | — |
| 167 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 168 | C3×C4⋊C4 | — | 3 | 12 | no | — |
| 169 | C3×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 170 | C3×C42 | — | 2 | 3 | no | — |
| 171 | C3×C42 | — | 3 | 12 | no | — |
| 172 | C3×C42 | C22×D3 | 1 | 6 | yes | — |
| 173 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 174 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 175 | (C2×D3)⋊C4 | — | 3 | 12 | no | — |
| 176 | (C2×D3)⋊C4 | — | 6 | 6 | no | — |
| 177 | C4⋊Dic3 | — | 3 | 6 | no | — |
| 178 | C4⋊Dic3 | — | 3 | 12 | no | — |
| 179 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 180 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 181 | C4⋊Dic3 | C22×D3 | 1 | 12 | yes | — |
| 182 | C4⋊Dic3 | C22×D3 | 1 | 12 | yes | — |
| 183 | Dic3⋊C4 | — | 3 | 12 | no | — |
| 184 | Dic3⋊C4 | — | 3 | 12 | no | — |
| 185 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 186 | Dic3⋊C4 | — | 3 | 12 | no | — |
| 187 | Dic3⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 188 | C4×Dic3 | — | 3 | 6 | no | — |
| 189 | C4×Dic3 | — | 3 | 2 | no | — |
| 190 | C4×Dic3 | — | 3 | 6 | no | — |
| 191 | C4×Dic3 | — | 6 | 1 | no | — |
| 192 | C4×Dic3 | — | 6 | 3 | no | — |
| 193 | C4×Dic3 | — | 6 | 3 | no | — |
| 194 | C4×Dic3 | C22×D3 | 1 | 12 | yes | — |
| 195 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 196 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 197 | C2×C3⋊D3 | — | 2 | 3 | no | — |
| 198 | C2×C3⋊D3 | C22×Q8 | 1 | 6 | yes | — |
| 199 | C32×C4 | — | 2 | 3 | no | — |
| 200 | C32×C4 | C22×Q8 | 1 | 6 | yes | — |
| 201 | C32×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 202 | C3⋊Dic3 | — | 2 | 3 | no | — |
| 203 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 204 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | — |
| 205 | C3×Dic3 | — | 2 | 12 | no | — |
| 206 | C3×Dic3 | — | 2 | 4 | no | — |
| 207 | C2×#41 | — | 9 | 1 | no | — |
| 208 | C22×Q8 | — | 9 | 6 | no | — |
| 209 | C4⋊Q8 | — | 3 | 6 | no | — |
| 210 | C4⋊Q8 | — | 9 | 12 | no | — |
| 211 | C4⋊Q8 | — | 9 | 6 | no | — |
| 212 | C4⋊Q8 | — | 9 | 6 | no | — |
| 213 | C4⋊Q8 | — | 9 | 1 | no | — |
| 214 | C4⋊Q8 | — | 9 | 3 | no | — |
| 215 | #125 | — | 3 | 12 | no | — |
| 216 | #125 | — | 9 | 6 | no | — |
| 217 | C22⋊Q8 | — | 9 | 6 | no | — |
| 218 | C22⋊Q8 | — | 9 | 24 | no | — |
| 219 | C22⋊Q8 | — | 9 | 6 | no | — |
| 220 | C4×Q8 | — | 3 | 4 | no | — |
| 221 | C4×Q8 | — | 3 | 6 | no | — |
| 222 | C4×Q8 | — | 9 | 6 | no | — |
| 223 | C4×Q8 | — | 9 | 1 | no | — |
| 224 | C4×Q8 | D32 | 1 | 1 | yes | characteristic |
| 225 | C4×D4 | — | 9 | 12 | no | — |
| 226 | C4×D4 | — | 9 | 3 | no | — |
| 227 | C4×D4 | — | 9 | 3 | no | — |
| 228 | #117 | — | 9 | 6 | no | — |
| 229 | #117 | — | 9 | 3 | no | — |
| 230 | C2×C4⋊C4 | — | 9 | 6 | no | — |
| 231 | C2×C4⋊C4 | — | 9 | 6 | no | — |
| 232 | C2×C42 | — | 9 | 3 | no | — |
| 233 | C22×D3 | — | 3 | 6 | no | — |
| 234 | C22×D3 | — | 6 | 3 | no | — |
| 235 | C3×Q8 | — | 2 | 4 | no | — |
| 236 | C3×Q8 | — | 6 | 12 | no | — |
| 237 | C3×Q8 | D3×Q8 | 1 | 8 | yes | complemented |
| 238 | C2×C3×C4 | — | 2 | 3 | no | — |
| 239 | C2×C3×C4 | — | 2 | 1 | no | — |
| 240 | C2×C3×C4 | — | 2 | 3 | no | — |
| 241 | C2×C3×C4 | — | 3 | 12 | no | — |
| 242 | C2×C3×C4 | — | 3 | 4 | no | — |
| 243 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 244 | C2×C3×C4 | C23×D3 | 1 | 6 | yes | — |
| 245 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 246 | C2×Dic3 | — | 3 | 2 | no | — |
| 247 | C2×Dic3 | — | 3 | 2 | no | — |
| 248 | C2×Dic3 | — | 3 | 6 | no | — |
| 249 | C2×Dic3 | — | 6 | 1 | no | — |
| 250 | C2×Dic3 | — | 6 | 1 | no | — |
| 251 | C2×Dic3 | — | 6 | 3 | no | — |
| 252 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 253 | C2×Dic3 | C23×D3 | 1 | 12 | yes | — |
| 254 | D12 | — | 3 | 24 | no | — |
| 255 | D12 | — | 6 | 12 | no | — |
| 256 | C4×D3 | — | 3 | 24 | no | — |
| 257 | C4×D3 | — | 6 | 12 | no | — |
| 258 | C4×D3 | — | 6 | 12 | no | — |
| 259 | C4×D3 | — | 6 | 12 | no | — |
| 260 | C4×D3 | — | 12 | 6 | no | — |
| 261 | C4×D3 | — | 12 | 6 | no | — |
| 262 | C4×D3 | — | 12 | 24 | no | — |
| 263 | Dic6 | — | 2 | 12 | no | — |
| 264 | Dic6 | — | 6 | 8 | no | — |
| 265 | Dic6 | — | 12 | 24 | no | — |
| 266 | C2×C32 | C23×Q8 | 1 | 1 | yes | characteristic |
| 267 | C2×C32 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 268 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 269 | C3⋊D3 | — | 2 | 6 | no | — |
| 270 | #41 | — | 9 | 8 | no | — |
| 271 | C2×Q8 | — | 3 | 6 | no | — |
| 272 | C2×Q8 | — | 9 | 2 | no | — |
| 273 | C2×Q8 | — | 9 | 12 | no | — |
| 274 | C2×Q8 | — | 36 | 12 | no | — |
| 275 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 276 | C2×D4 | — | 9 | 3 | no | — |
| 277 | C22×C4 | — | 9 | 12 | no | — |
| 278 | C22×C4 | — | 9 | 3 | no | — |
| 279 | C22×C4 | — | 9 | 3 | no | — |
| 280 | C22×C4 | — | 9 | 3 | no | — |
| 281 | C4⋊C4 | — | 3 | 12 | no | — |
| 282 | C4⋊C4 | — | 3 | 12 | no | — |
| 283 | C4⋊C4 | — | 3 | 2 | no | — |
| 284 | C4⋊C4 | — | 3 | 12 | no | — |
| 285 | C4⋊C4 | — | 9 | 6 | no | — |
| 286 | C4⋊C4 | — | 9 | 6 | no | — |
| 287 | C4⋊C4 | — | 9 | 2 | no | — |
| 288 | C4⋊C4 | — | 9 | 12 | no | — |
| 289 | C4⋊C4 | — | 9 | 3 | no | — |
| 290 | C4⋊C4 | C2×D32 | 1 | 3 | yes | — |
| 291 | C22⋊C4 | — | 9 | 12 | no | — |
| 292 | C22⋊C4 | — | 9 | 6 | no | — |
| 293 | C42 | — | 3 | 12 | no | — |
| 294 | C42 | — | 9 | 1 | no | — |
| 295 | C42 | — | 9 | 3 | no | — |
| 296 | C42 | — | 9 | 3 | no | — |
| 297 | C42 | C2×D32 | 1 | 3 | yes | — |
| 298 | C22×C3 | — | 2 | 1 | no | — |
| 299 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 300 | C2×D3 | — | 3 | 12 | no | — |
| 301 | C2×D3 | — | 6 | 6 | no | — |
| 302 | C2×D3 | — | 6 | 6 | no | — |
| 303 | C2×D3 | — | 6 | 6 | no | — |
| 304 | C2×D3 | — | 12 | 3 | no | — |
| 305 | C2×D3 | — | 12 | 3 | no | — |
| 306 | C3×C4 | — | 2 | 6 | no | — |
| 307 | C3×C4 | — | 2 | 6 | no | — |
| 308 | C3×C4 | — | 2 | 2 | no | — |
| 309 | C3×C4 | — | 4 | 3 | no | — |
| 310 | C3×C4 | — | 6 | 12 | no | — |
| 311 | C3×C4 | — | 6 | 4 | no | — |
| 312 | C3×C4 | C2×D3×Q8 | 1 | 12 | yes | — |
| 313 | C3×C4 | #1009 | 1 | 4 | yes | — |
| 314 | Dic3 | — | 2 | 12 | no | — |
| 315 | Dic3 | — | 2 | 4 | no | — |
| 316 | Dic3 | — | 3 | 4 | no | — |
| 317 | Dic3 | — | 3 | 4 | no | — |
| 318 | Dic3 | — | 6 | 2 | no | — |
| 319 | Dic3 | — | 6 | 2 | no | — |
| 320 | Dic3 | — | 6 | 6 | no | — |
| 321 | Dic3 | — | 12 | 3 | no | — |
| 322 | C32 | #3503 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 323 | C23 | — | 9 | 3 | no | — |
| 324 | Q8 | — | 6 | 12 | no | — |
| 325 | Q8 | — | 18 | 4 | no | — |
| 326 | Q8 | — | 36 | 12 | no | — |
| 327 | Q8 | #3797 | 1 | 4 | yes | complemented |
| 328 | D4 | — | 9 | 12 | no | — |
| 329 | C2×C4 | — | 3 | 4 | no | — |
| 330 | C2×C4 | — | 3 | 12 | no | — |
| 331 | C2×C4 | — | 9 | 1 | no | — |
| 332 | C2×C4 | — | 9 | 1 | no | — |
| 333 | C2×C4 | — | 9 | 12 | no | — |
| 334 | C2×C4 | — | 9 | 3 | no | — |
| 335 | C2×C4 | — | 18 | 6 | no | — |
| 336 | C2×C4 | — | 18 | 6 | no | — |
| 337 | C2×C4 | — | 36 | 12 | no | — |
| 338 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 339 | C2×C4 | C22×D32 | 1 | 3 | yes | — |
| 340 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 341 | C2×C3 | — | 2 | 1 | no | — |
| 342 | C2×C3 | — | 2 | 1 | no | — |
| 343 | C2×C3 | — | 2 | 1 | no | — |
| 344 | C2×C3 | C22×D3×Q8 | 1 | 2 | yes | — |
| 345 | C2×C3 | C2×#1009 | 1 | 2 | yes | — |
| 346 | C2×C3 | D3×2−1+4 | 1 | 2 | yes | — |
| 347 | D3 | — | 6 | 12 | no | — |
| 348 | D3 | — | 12 | 6 | no | — |
| 349 | C22 | — | 9 | 6 | no | — |
| 350 | C22 | — | 18 | 3 | no | — |
| 351 | C22 | — | 18 | 3 | no | — |
| 352 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 3 | no | — |
| 354 | C4 | — | 6 | 12 | no | — |
| 355 | C4 | — | 6 | 4 | no | — |
| 356 | C4 | — | 9 | 2 | no | — |
| 357 | C4 | — | 9 | 2 | no | — |
| 358 | C4 | — | 18 | 3 | no | — |
| 359 | C4 | C2×#3797 | 1 | 6 | yes | — |
| 360 | C4 | #64320 | 1 | 2 | yes | — |
| 361 | C3 | — | 2 | 1 | no | — |
| 362 | C3 | #87018 | 1 | 2 | yes | complemented |
| 363 | C2 | — | 18 | 6 | no | — |
| 364 | C2 | C22×#3797 | 1 | 1 | yes | characteristic |
| 365 | C2 | C2×#64320 | 1 | 1 | yes | characteristic |
| 366 | C2 | #10596694 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C4×Q8 | C22 |
| prime radical | C2×#3832 | C22 |
| hypercenter | C4×Q8 | D32 |
| hypocenter | C32 | #3503 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5570 | C2 | semidirect |
| 3. Q8×#627 | C2 | semidirect |
| 5. #10594508 | C2 | semidirect |
| 6. #10594484 | C2 | semidirect |
| 7. #10593909 | C2 | semidirect |
| 8. #10593903 | C2 | semidirect |
| 9. #10593882 | C2 | semidirect |
| 47. #5570 | D3 | semidirect |
| 50. #3832 | Q8 | semidirect |
| 120. C32×Q8 | C2×Q8 | semidirect |
| 127. C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 130. C4×C3⋊D3 | C2×Q8 | semidirect |
| 237. C3×Q8 | D3×Q8 | semidirect |
| 322. C32 | #3503 | semidirect |
| 327. Q8 | #3797 | semidirect |
| 362. C3 | #87018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3832 | 2 |
| C3×#5570 | 2 |
| Q8×#627 | 2 |
| #10595353 | 2 |
| #10594508 | 2 |
| #10594484 | 2 |
| #10593909 | 2 |
| #10593903 | 2 |
| #10593882 | 2 |
| #87018 | 3 |