Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
569 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 128 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 | #64364 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #64297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×#216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #63951 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #63950 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #63945 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #63944 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #63833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #63829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #63817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #5779 | — | 3 | 1 | no | maximal |
| 13 | #5766 | — | 3 | 1 | no | maximal |
| 14 | C2×C32×Q8 | C22 | 1 | 1 | yes | characteristic |
| 15 | #3832 | — | 2 | 1 | no | — |
| 16 | #3832 | C22 | 1 | 2 | yes | — |
| 17 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 18 | Q8×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 19 | #3828 | — | 2 | 2 | no | — |
| 20 | #3828 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3828 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#235 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3804 | — | 2 | 2 | no | — |
| 25 | #3799 | — | 2 | 1 | no | — |
| 26 | #3797 | C22 | 1 | 2 | yes | — |
| 27 | #3796 | C22 | 1 | 2 | yes | — |
| 28 | D3×Dic6 | — | 2 | 1 | no | — |
| 29 | C3×#216 | C22 | 1 | 2 | yes | — |
| 30 | C3×#216 | C22 | 1 | 2 | yes | — |
| 31 | C3×#216 | C22 | 1 | 2 | yes | — |
| 32 | C3×#215 | C22 | 1 | 2 | yes | — |
| 33 | C3×#208 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×C3×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 35 | #3719 | C22 | 1 | 1 | yes | characteristic |
| 36 | #3719 | C22 | 1 | 2 | yes | — |
| 37 | #3717 | C22 | 1 | 1 | yes | characteristic |
| 38 | #3717 | C22 | 1 | 2 | yes | — |
| 39 | #3716 | C22 | 1 | 1 | yes | characteristic |
| 40 | #3714 | C22 | 1 | 1 | yes | characteristic |
| 41 | #3712 | C22 | 1 | 2 | yes | — |
| 42 | #3710 | C22 | 1 | 2 | yes | — |
| 43 | #1010 | — | 3 | 1 | no | — |
| 44 | #1007 | — | 3 | 1 | no | — |
| 45 | #1007 | — | 3 | 1 | no | — |
| 46 | #1007 | — | 3 | 1 | no | — |
| 47 | #1007 | — | 6 | 1 | no | — |
| 48 | C3×#137 | — | 3 | 1 | no | — |
| 49 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 50 | #950 | — | 3 | 1 | no | — |
| 51 | C2×#216 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | #942 | — | 3 | 1 | no | — |
| 53 | #942 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #919 | — | 3 | 2 | no | — |
| 55 | #918 | — | 3 | 2 | no | — |
| 56 | #918 | — | 3 | 2 | no | — |
| 57 | #918 | — | 3 | 2 | no | — |
| 58 | D3×Q16 | — | 3 | 2 | no | — |
| 59 | D3×Q16 | — | 3 | 2 | no | — |
| 60 | #916 | — | 3 | 2 | no | — |
| 61 | #915 | — | 3 | 2 | no | — |
| 62 | #909 | — | 3 | 1 | no | — |
| 63 | #907 | — | 3 | 1 | no | — |
| 64 | #904 | — | 3 | 1 | no | — |
| 65 | #901 | — | 3 | 1 | no | — |
| 66 | C32×Q8 | — | 2 | 1 | no | — |
| 67 | C32×Q8 | C23 | 1 | 2 | yes | — |
| 68 | C2×C32×C4 | — | 2 | 1 | no | — |
| 69 | C2×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 70 | #638 | — | 2 | 1 | no | — |
| 71 | #638 | D4 | 1 | 2 | yes | — |
| 72 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 73 | C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 74 | C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 75 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 76 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 77 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 78 | C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 79 | #634 | — | 2 | 2 | no | — |
| 80 | #634 | D4 | 1 | 1 | yes | characteristic |
| 81 | #634 | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×#67 | — | 2 | 1 | no | — |
| 83 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 84 | C3×D12 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×C4×D3 | — | 2 | 1 | no | — |
| 86 | C3×Dic6 | — | 2 | 1 | no | — |
| 87 | C3×Dic6 | C23 | 1 | 2 | yes | — |
| 88 | C3×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 89 | #627 | — | 2 | 2 | no | — |
| 90 | #626 | — | 2 | 2 | no | — |
| 91 | #624 | — | 2 | 2 | no | — |
| 92 | D3×Dic3 | — | 2 | 2 | no | — |
| 93 | C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 95 | C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 96 | #578 | — | 9 | 1 | no | Sylow |
| 97 | C3×#41 | — | 3 | 1 | no | — |
| 98 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 99 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 100 | C2×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | C2×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 102 | #239 | — | 3 | 2 | no | — |
| 103 | #239 | — | 3 | 2 | no | — |
| 104 | #239 | — | 3 | 2 | no | — |
| 105 | #239 | — | 6 | 2 | no | — |
| 106 | #239 | — | 6 | 1 | no | — |
| 107 | #239 | — | 6 | 1 | no | — |
| 108 | #239 | — | 6 | 1 | no | — |
| 109 | #239 | — | 6 | 2 | no | — |
| 110 | D3×Q8 | — | 3 | 2 | no | — |
| 111 | D3×Q8 | — | 3 | 2 | no | — |
| 112 | D3×Q8 | — | 3 | 2 | no | — |
| 113 | D3×Q8 | — | 3 | 2 | no | — |
| 114 | D3×Q8 | — | 6 | 2 | no | — |
| 115 | D3×Q8 | — | 6 | 1 | no | — |
| 116 | D3×Q8 | — | 6 | 1 | no | — |
| 117 | D3×Q8 | — | 6 | 1 | no | — |
| 118 | D3×Q8 | — | 6 | 2 | no | — |
| 119 | #237 | — | 3 | 2 | no | — |
| 120 | #237 | — | 6 | 2 | no | — |
| 121 | #235 | — | 3 | 1 | no | — |
| 122 | #235 | — | 3 | 1 | no | — |
| 123 | #235 | — | 3 | 1 | no | — |
| 124 | #235 | — | 3 | 1 | no | — |
| 125 | #235 | — | 6 | 1 | no | — |
| 126 | #235 | — | 6 | 1 | no | — |
| 127 | #235 | — | 6 | 1 | no | — |
| 128 | #235 | — | 6 | 2 | no | — |
| 129 | #235 | — | 6 | 2 | no | — |
| 130 | #235 | — | 6 | 2 | no | — |
| 131 | #235 | — | 6 | 4 | no | — |
| 132 | #235 | C2×D3 | 1 | 1 | yes | characteristic |
| 133 | C2×Dic6 | — | 6 | 1 | no | — |
| 134 | C2×Dic6 | C2×D3 | 1 | 1 | yes | characteristic |
| 135 | C3×Q16 | — | 3 | 2 | no | — |
| 136 | C3×Q16 | — | 3 | 2 | no | — |
| 137 | C3×Q16 | — | 3 | 2 | no | — |
| 138 | C3×SD16 | — | 3 | 2 | no | — |
| 139 | C3×M16 | — | 3 | 1 | no | — |
| 140 | C2×C3×C8 | — | 3 | 1 | no | — |
| 141 | #216 | — | 3 | 1 | no | — |
| 142 | #216 | — | 3 | 2 | no | — |
| 143 | #216 | C2×D3 | 1 | 2 | yes | — |
| 144 | #216 | C2×D3 | 1 | 2 | yes | — |
| 145 | #216 | C2×D3 | 1 | 2 | yes | — |
| 146 | #215 | — | 3 | 1 | no | — |
| 147 | #215 | — | 3 | 2 | no | — |
| 148 | #215 | C2×D3 | 1 | 2 | yes | — |
| 149 | #214 | — | 3 | 1 | no | — |
| 150 | #213 | — | 3 | 1 | no | — |
| 151 | #208 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | C2×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 153 | Dic12 | — | 3 | 1 | no | — |
| 154 | Dic12 | — | 3 | 2 | no | — |
| 155 | D24 | — | 3 | 1 | no | — |
| 156 | #204 | — | 3 | 1 | no | — |
| 157 | #204 | — | 3 | 1 | no | — |
| 158 | #204 | — | 3 | 2 | no | — |
| 159 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 160 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 161 | D3×C8 | — | 3 | 2 | no | — |
| 162 | D3×C8 | — | 3 | 2 | no | — |
| 163 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 165 | C2×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×C3×D3 | — | 2 | 1 | no | — |
| 167 | C32×C4 | — | 2 | 2 | no | — |
| 168 | C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 170 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 171 | C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 172 | C3×Dic3 | — | 2 | 2 | no | — |
| 173 | C3×Dic3 | — | 2 | 1 | no | — |
| 174 | 2−1+4 | — | 9 | 1 | no | — |
| 175 | 2−1+4 | — | 9 | 1 | no | — |
| 176 | #137 | — | 3 | 1 | no | — |
| 177 | #137 | — | 9 | 1 | no | — |
| 178 | #137 | — | 9 | 2 | no | — |
| 179 | #137 | — | 9 | 2 | no | — |
| 180 | #135 | — | 9 | 1 | no | — |
| 181 | #135 | — | 9 | 2 | no | — |
| 182 | C2×Q16 | — | 3 | 1 | no | — |
| 183 | C2×Q16 | — | 9 | 2 | no | — |
| 184 | #131 | — | 9 | 1 | no | — |
| 185 | C3×Q8 | — | 2 | 2 | no | — |
| 186 | C3×Q8 | — | 2 | 1 | no | — |
| 187 | C3×Q8 | — | 2 | 1 | no | — |
| 188 | C3×Q8 | — | 2 | 2 | no | — |
| 189 | C3×Q8 | — | 3 | 1 | no | — |
| 190 | C3×Q8 | — | 3 | 2 | no | — |
| 191 | C3×Q8 | — | 6 | 1 | no | — |
| 192 | C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 193 | C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 194 | C3×D4 | — | 3 | 1 | no | — |
| 195 | C3×D4 | — | 6 | 1 | no | — |
| 196 | C2×C3×C4 | — | 2 | 2 | no | — |
| 197 | C2×C3×C4 | — | 2 | 1 | no | — |
| 198 | C2×C3×C4 | — | 2 | 1 | no | — |
| 199 | C2×C3×C4 | — | 2 | 1 | no | — |
| 200 | C2×C3×C4 | — | 6 | 1 | no | — |
| 201 | C2×C3×C4 | — | 6 | 1 | no | — |
| 202 | C2×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 204 | #67 | — | 2 | 1 | no | — |
| 205 | #67 | — | 3 | 2 | no | — |
| 206 | #67 | — | 3 | 2 | no | — |
| 207 | #67 | — | 6 | 2 | no | — |
| 208 | #67 | — | 6 | 2 | no | — |
| 209 | #67 | — | 6 | 2 | no | — |
| 210 | #67 | — | 6 | 1 | no | — |
| 211 | #67 | — | 6 | 1 | no | — |
| 212 | C2×Dic3 | — | 2 | 1 | no | — |
| 213 | C2×Dic3 | — | 6 | 2 | no | — |
| 214 | D12 | — | 3 | 1 | no | — |
| 215 | D12 | — | 3 | 1 | no | — |
| 216 | D12 | — | 3 | 1 | no | — |
| 217 | D12 | — | 3 | 1 | no | — |
| 218 | D12 | — | 6 | 1 | no | — |
| 219 | D12 | — | 6 | 1 | no | — |
| 220 | D12 | — | 6 | 2 | no | — |
| 221 | D12 | — | 6 | 2 | no | — |
| 222 | D12 | — | 6 | 4 | no | — |
| 223 | D12 | — | 6 | 2 | no | — |
| 224 | D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 225 | C4×D3 | — | 2 | 1 | no | — |
| 226 | C4×D3 | — | 3 | 2 | no | — |
| 227 | C4×D3 | — | 3 | 2 | no | — |
| 228 | C4×D3 | — | 6 | 2 | no | — |
| 229 | C4×D3 | — | 6 | 2 | no | — |
| 230 | C4×D3 | — | 6 | 2 | no | — |
| 231 | C4×D3 | — | 6 | 2 | no | — |
| 232 | C4×D3 | — | 6 | 2 | no | — |
| 233 | C4×D3 | — | 6 | 2 | no | — |
| 234 | C4×D3 | — | 6 | 2 | no | — |
| 235 | C4×D3 | — | 6 | 2 | no | — |
| 236 | C4×D3 | — | 6 | 4 | no | — |
| 237 | C4×D3 | — | 6 | 4 | no | — |
| 238 | C4×D3 | — | 6 | 2 | no | — |
| 239 | C4×D3 | — | 6 | 1 | no | — |
| 240 | C4×D3 | — | 6 | 1 | no | — |
| 241 | Dic6 | — | 2 | 1 | no | — |
| 242 | Dic6 | — | 3 | 1 | no | — |
| 243 | Dic6 | — | 3 | 1 | no | — |
| 244 | Dic6 | — | 3 | 1 | no | — |
| 245 | Dic6 | — | 3 | 1 | no | — |
| 246 | Dic6 | — | 6 | 1 | no | — |
| 247 | Dic6 | — | 6 | 1 | no | — |
| 248 | Dic6 | — | 6 | 2 | no | — |
| 249 | Dic6 | — | 6 | 2 | no | — |
| 250 | Dic6 | — | 6 | 2 | no | — |
| 251 | Dic6 | — | 6 | 2 | no | — |
| 252 | Dic6 | — | 6 | 4 | no | — |
| 253 | Dic6 | C22×D3 | 1 | 2 | yes | — |
| 254 | Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 255 | C3×C8 | — | 3 | 1 | no | — |
| 256 | C3×C8 | — | 3 | 2 | no | — |
| 257 | C3×C8 | — | 3 | 1 | no | — |
| 258 | C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 259 | C3⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 260 | C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 261 | C2×C32 | — | 2 | 1 | no | — |
| 262 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 263 | C3⋊D3 | — | 2 | 2 | no | — |
| 264 | C3⋊D3 | — | 4 | 1 | no | — |
| 265 | C3×D3 | — | 4 | 1 | no | — |
| 266 | #41 | — | 3 | 1 | no | — |
| 267 | #41 | — | 9 | 1 | no | — |
| 268 | #41 | — | 9 | 2 | no | — |
| 269 | #41 | — | 9 | 2 | no | — |
| 270 | #41 | — | 9 | 1 | no | — |
| 271 | #41 | — | 18 | 2 | no | — |
| 272 | #41 | — | 18 | 2 | no | — |
| 273 | #41 | — | 18 | 1 | no | — |
| 274 | #41 | — | 18 | 1 | no | — |
| 275 | C2×Q8 | — | 3 | 1 | no | — |
| 276 | C2×Q8 | — | 9 | 2 | no | — |
| 277 | C2×Q8 | — | 9 | 2 | no | — |
| 278 | C2×Q8 | — | 18 | 1 | no | — |
| 279 | C2×Q8 | — | 18 | 1 | no | — |
| 280 | C2×Q8 | D32 | 1 | 1 | yes | characteristic |
| 281 | Q16 | — | 3 | 2 | no | — |
| 282 | Q16 | — | 3 | 2 | no | — |
| 283 | Q16 | — | 3 | 2 | no | — |
| 284 | Q16 | — | 9 | 1 | no | — |
| 285 | Q16 | — | 9 | 2 | no | — |
| 286 | SD16 | — | 3 | 2 | no | — |
| 287 | SD16 | — | 9 | 1 | no | — |
| 288 | SD16 | — | 9 | 1 | no | — |
| 289 | SD16 | — | 9 | 2 | no | — |
| 290 | D8 | — | 9 | 1 | no | — |
| 291 | M16 | — | 3 | 1 | no | — |
| 292 | M16 | — | 9 | 2 | no | — |
| 293 | C2×C8 | — | 3 | 1 | no | — |
| 294 | C2×C8 | — | 9 | 2 | no | — |
| 295 | C22×C3 | — | 2 | 1 | no | — |
| 296 | C22×C3 | — | 6 | 1 | no | — |
| 297 | C22×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 298 | C22×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×D3 | — | 2 | 1 | no | — |
| 300 | C2×D3 | — | 3 | 2 | no | — |
| 301 | C2×D3 | — | 3 | 2 | no | — |
| 302 | C2×D3 | — | 6 | 2 | no | — |
| 303 | C2×D3 | — | 6 | 2 | no | — |
| 304 | C2×D3 | — | 6 | 1 | no | — |
| 305 | C2×D3 | — | 6 | 1 | no | — |
| 306 | C3×C4 | — | 2 | 4 | no | — |
| 307 | C3×C4 | — | 2 | 2 | no | — |
| 308 | C3×C4 | — | 2 | 2 | no | — |
| 309 | C3×C4 | — | 2 | 1 | no | — |
| 310 | C3×C4 | — | 2 | 1 | no | — |
| 311 | C3×C4 | — | 6 | 1 | no | — |
| 312 | C3×C4 | — | 6 | 2 | no | — |
| 313 | C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 314 | C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 315 | C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 316 | C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 317 | Dic3 | — | 2 | 2 | no | — |
| 318 | Dic3 | — | 2 | 1 | no | — |
| 319 | Dic3 | — | 3 | 2 | no | — |
| 320 | Dic3 | — | 3 | 2 | no | — |
| 321 | Dic3 | — | 6 | 2 | no | — |
| 322 | Dic3 | — | 6 | 2 | no | — |
| 323 | Dic3 | — | 6 | 1 | no | — |
| 324 | Dic3 | — | 6 | 1 | no | — |
| 325 | C32 | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 326 | Q8 | — | 2 | 1 | no | — |
| 327 | Q8 | — | 3 | 2 | no | — |
| 328 | Q8 | — | 3 | 1 | no | — |
| 329 | Q8 | — | 6 | 1 | no | — |
| 330 | Q8 | — | 9 | 1 | no | — |
| 331 | Q8 | — | 9 | 1 | no | — |
| 332 | Q8 | — | 18 | 2 | no | — |
| 333 | Q8 | — | 18 | 2 | no | — |
| 334 | Q8 | C2×D32 | 1 | 2 | yes | — |
| 335 | D4 | — | 3 | 1 | no | — |
| 336 | D4 | — | 6 | 1 | no | — |
| 337 | D4 | — | 9 | 2 | no | — |
| 338 | D4 | — | 9 | 1 | no | — |
| 339 | D4 | — | 9 | 1 | no | — |
| 340 | D4 | — | 18 | 2 | no | — |
| 341 | D4 | — | 18 | 2 | no | — |
| 342 | D4 | — | 18 | 1 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 6 | 1 | no | — |
| 345 | C2×C4 | — | 6 | 1 | no | — |
| 346 | C2×C4 | — | 9 | 2 | no | — |
| 347 | C2×C4 | — | 18 | 2 | no | — |
| 348 | C2×C4 | — | 18 | 2 | no | — |
| 349 | C2×C4 | — | 18 | 2 | no | — |
| 350 | C2×C4 | — | 18 | 2 | no | — |
| 351 | C2×C4 | — | 18 | 1 | no | — |
| 352 | C2×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 353 | C8 | — | 3 | 1 | no | — |
| 354 | C8 | — | 3 | 1 | no | — |
| 355 | C8 | — | 3 | 2 | no | — |
| 356 | C2×C3 | — | 2 | 1 | no | — |
| 357 | C2×C3 | — | 2 | 1 | no | — |
| 358 | C2×C3 | — | 2 | 1 | no | — |
| 359 | C2×C3 | — | 4 | 1 | no | — |
| 360 | C2×C3 | — | 12 | 1 | no | — |
| 361 | C2×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 362 | C2×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 363 | D3 | — | 4 | 1 | no | — |
| 364 | D3 | — | 6 | 2 | no | — |
| 365 | D3 | — | 6 | 2 | no | — |
| 366 | D3 | — | 12 | 2 | no | — |
| 367 | D3 | — | 12 | 2 | no | — |
| 368 | D3 | — | 12 | 1 | no | — |
| 369 | D3 | — | 12 | 1 | no | — |
| 370 | C22 | — | 6 | 1 | no | — |
| 371 | C22 | — | 9 | 2 | no | — |
| 372 | C22 | — | 18 | 1 | no | — |
| 373 | C22 | #3811 | 1 | 1 | yes | characteristic |
| 374 | C4 | — | 2 | 2 | no | — |
| 375 | C4 | — | 6 | 1 | no | — |
| 376 | C4 | — | 6 | 2 | no | — |
| 377 | C4 | — | 9 | 2 | no | — |
| 378 | C4 | — | 18 | 1 | no | — |
| 379 | C4 | #3811 | 1 | 1 | yes | characteristic |
| 380 | C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 381 | C3 | — | 2 | 1 | no | — |
| 382 | C3 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 383 | C3 | #5779 | 1 | 1 | yes | characteristic, complemented |
| 384 | C2 | — | 2 | 1 | no | — |
| 385 | C2 | — | 12 | 1 | no | — |
| 386 | C2 | — | 18 | 2 | no | — |
| 387 | C2 | — | 36 | 1 | no | — |
| 388 | C2 | C2×#3811 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#3811 |
| commutator, cosocle | C32×C4 | C24 |
| Frattini | C4 | C22×D32 |
| Fitting | C2×C32×Q8 | C22 |
| socle | C2×C32 | C22×D4 |
| hypercenter | C2×Q8 | D32 |
| hypocenter | C32 | #578 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #64364 | C2 | semidirect |
| 2. #64297 | C2 | semidirect |
| 3. C2×C3×#216 | C2 | semidirect |
| 4. C3×#942 | C2 | semidirect |
| 5. #63951 | C2 | semidirect |
| 6. #63950 | C2 | semidirect |
| 7. #63945 | C2 | semidirect |
| 8. #63944 | C2 | semidirect |
| 9. #63833 | C2 | semidirect |
| 10. #63829 | C2 | semidirect |
| 11. #63817 | C2 | semidirect |
| 51. C2×#216 | D3 | semidirect |
| 53. #942 | D3 | semidirect |
| 325. C32 | #578 | semidirect |
| 382. C3 | #5766 | semidirect |
| 383. C3 | #5779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64364 | 2 |
| #64297 | 2 |
| C2×C3×#216 | 2 |
| C3×#942 | 2 |
| #63951 | 2 |
| #63950 | 2 |
| #63945 | 2 |
| #63944 | 2 |
| #63833 | 2 |
| #63829 | 2 |
| #63817 | 2 |
| #5779 | 3 |
| #5766 | 3 |