Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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 | #87163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4908 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#2115 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71450 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #69120 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #33531 | — | 3 | 1 | no | maximal, Sylow |
| 8 | #5964 | — | 2 | 1 | no | — |
| 9 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5830 | — | 2 | 1 | no | — |
| 11 | #5753 | — | 2 | 2 | no | — |
| 12 | #5752 | — | 2 | 2 | no | — |
| 13 | #5751 | — | 2 | 4 | no | — |
| 14 | #5748 | — | 2 | 1 | no | — |
| 15 | #5748 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×#904 | — | 2 | 2 | no | — |
| 17 | C2×#904 | C22 | 1 | 2 | yes | — |
| 18 | C22×D24 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×C3×M32 | C22 | 1 | 2 | yes | complemented |
| 20 | #5135 | C22 | 1 | 4 | yes | complemented |
| 21 | #5131 | — | 2 | 1 | no | — |
| 22 | #5115 | — | 2 | 2 | no | — |
| 23 | #5106 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #4908 | — | 2 | 4 | no | — |
| 25 | #4908 | C22 | 1 | 8 | yes | complemented |
| 26 | C2×#800 | — | 2 | 2 | no | — |
| 27 | C2×D48 | — | 2 | 2 | no | — |
| 28 | C3×#349 | C22 | 1 | 4 | yes | complemented |
| 29 | #4518 | C22 | 1 | 8 | yes | complemented |
| 30 | #3584 | — | 3 | 1 | no | — |
| 31 | C2×#509 | — | 3 | 2 | no | — |
| 32 | #3058 | — | 3 | 1 | no | — |
| 33 | #2190 | — | 3 | 8 | no | — |
| 34 | #2145 | — | 3 | 2 | no | — |
| 35 | #2115 | D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×C3×#41 | D4 | 1 | 1 | yes | characteristic |
| 37 | #1010 | — | 2 | 4 | no | — |
| 38 | #1009 | — | 2 | 4 | no | — |
| 39 | D3×#41 | — | 4 | 4 | no | — |
| 40 | #1007 | — | 4 | 1 | no | — |
| 41 | #1004 | — | 4 | 2 | no | — |
| 42 | #1004 | — | 4 | 1 | no | — |
| 43 | C2×#235 | — | 2 | 4 | no | — |
| 44 | C2×#235 | — | 2 | 2 | no | — |
| 45 | C22×D12 | — | 2 | 1 | no | — |
| 46 | C3×#131 | — | 2 | 2 | no | — |
| 47 | C3×#131 | — | 2 | 2 | no | — |
| 48 | C2×C3×M16 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 50 | C22×C3×C8 | D4 | 1 | 2 | yes | — |
| 51 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 52 | #947 | — | 4 | 1 | no | — |
| 53 | #940 | — | 4 | 1 | no | — |
| 54 | #937 | — | 4 | 2 | no | — |
| 55 | #930 | — | 2 | 4 | no | — |
| 56 | #926 | — | 2 | 1 | no | — |
| 57 | #909 | — | 2 | 4 | no | — |
| 58 | #909 | — | 2 | 8 | no | — |
| 59 | #908 | — | 2 | 4 | no | — |
| 60 | #908 | — | 2 | 8 | no | — |
| 61 | C2×Dic12 | — | 2 | 2 | no | — |
| 62 | C2×Dic12 | D4 | 1 | 2 | yes | complemented |
| 63 | #904 | — | 2 | 4 | no | — |
| 64 | #904 | — | 2 | 4 | no | — |
| 65 | #904 | — | 2 | 2 | no | — |
| 66 | #904 | — | 2 | 4 | no | — |
| 67 | #904 | — | 2 | 2 | no | — |
| 68 | #904 | D4 | 1 | 4 | yes | complemented |
| 69 | #904 | C23 | 1 | 4 | yes | — |
| 70 | C2×D24 | — | 2 | 2 | no | — |
| 71 | C2×D24 | — | 2 | 2 | no | — |
| 72 | C2×D24 | — | 2 | 2 | no | — |
| 73 | C2×D24 | — | 2 | 1 | no | — |
| 74 | C2×D24 | D4 | 1 | 2 | yes | complemented |
| 75 | C2×D24 | C23 | 1 | 2 | yes | — |
| 76 | C2×#204 | — | 2 | 4 | no | — |
| 77 | C2×#204 | — | 2 | 2 | no | — |
| 78 | C3×M32 | — | 2 | 2 | no | — |
| 79 | C3×M32 | C23 | 1 | 4 | yes | — |
| 80 | C2×C3×C16 | — | 2 | 2 | no | — |
| 81 | #821 | — | 2 | 4 | no | — |
| 82 | #818 | — | 2 | 1 | no | — |
| 83 | #817 | C23 | 1 | 2 | yes | — |
| 84 | #800 | — | 2 | 8 | no | — |
| 85 | D48 | — | 2 | 8 | no | — |
| 86 | #585 | — | 6 | 1 | no | — |
| 87 | #578 | — | 6 | 2 | no | — |
| 88 | #577 | — | 6 | 4 | no | — |
| 89 | #576 | — | 6 | 2 | no | — |
| 90 | #575 | — | 3 | 4 | no | — |
| 91 | #575 | — | 6 | 1 | no | — |
| 92 | C2×#135 | — | 3 | 2 | no | — |
| 93 | C2×#135 | — | 6 | 2 | no | — |
| 94 | C22×D8 | — | 3 | 1 | no | — |
| 95 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #535 | — | 6 | 1 | no | — |
| 97 | #509 | — | 3 | 8 | no | — |
| 98 | #509 | — | 6 | 4 | no | — |
| 99 | C2×SD32 | — | 6 | 2 | no | — |
| 100 | C2×D16 | — | 6 | 2 | no | — |
| 101 | C2×M32 | C2×D3 | 1 | 2 | yes | complemented |
| 102 | #469 | — | 3 | 4 | no | — |
| 103 | #466 | — | 6 | 2 | no | — |
| 104 | #427 | — | 3 | 1 | no | — |
| 105 | #418 | — | 6 | 1 | no | — |
| 106 | #360 | — | 3 | 8 | no | — |
| 107 | #349 | C2×D3 | 1 | 4 | yes | complemented |
| 108 | C23×D3 | — | 4 | 1 | no | — |
| 109 | C3×#41 | — | 2 | 2 | no | — |
| 110 | C3×#41 | — | 2 | 2 | no | — |
| 111 | C2×C3×Q8 | D8 | 1 | 1 | yes | characteristic |
| 112 | C2×C3×D4 | D8 | 1 | 2 | yes | — |
| 113 | C2×C3×D4 | D8 | 1 | 1 | yes | characteristic |
| 114 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 115 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×#67 | — | 4 | 4 | no | — |
| 117 | C2×#67 | — | 4 | 2 | no | — |
| 118 | C2×#67 | — | 4 | 4 | no | — |
| 119 | #239 | — | 4 | 4 | no | — |
| 120 | D3×Q8 | — | 4 | 4 | no | — |
| 121 | #237 | — | 4 | 8 | no | — |
| 122 | #237 | — | 4 | 4 | no | — |
| 123 | D3×D4 | — | 4 | 8 | no | — |
| 124 | D3×D4 | — | 4 | 4 | no | — |
| 125 | #235 | — | 2 | 8 | no | — |
| 126 | #235 | — | 2 | 4 | no | — |
| 127 | #235 | — | 2 | 4 | no | — |
| 128 | #235 | — | 4 | 4 | no | — |
| 129 | #235 | — | 4 | 4 | no | — |
| 130 | #235 | — | 4 | 2 | no | — |
| 131 | #235 | — | 4 | 2 | no | — |
| 132 | C2×D12 | — | 2 | 4 | no | — |
| 133 | C2×D12 | — | 2 | 2 | no | — |
| 134 | C2×D12 | — | 2 | 2 | no | — |
| 135 | C2×D12 | — | 4 | 2 | no | — |
| 136 | C2×D12 | — | 4 | 2 | no | — |
| 137 | C2×D12 | — | 4 | 1 | no | — |
| 138 | C2×C4×D3 | — | 4 | 4 | no | — |
| 139 | C2×C4×D3 | — | 4 | 2 | no | — |
| 140 | C2×Dic6 | — | 2 | 4 | no | — |
| 141 | C2×Dic6 | — | 2 | 2 | no | — |
| 142 | C3×M16 | — | 2 | 2 | no | — |
| 143 | C3×M16 | — | 2 | 4 | no | — |
| 144 | C2×C3×C8 | — | 2 | 2 | no | — |
| 145 | C2×C3×C8 | — | 2 | 2 | no | — |
| 146 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 147 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 150 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 151 | #217 | — | 4 | 1 | no | — |
| 152 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 153 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 154 | C4×Dic3 | — | 4 | 1 | no | — |
| 155 | Dic12 | — | 2 | 4 | no | — |
| 156 | Dic12 | — | 2 | 2 | no | — |
| 157 | Dic12 | C2×D4 | 1 | 4 | yes | — |
| 158 | D24 | — | 2 | 4 | no | — |
| 159 | D24 | — | 2 | 2 | no | — |
| 160 | D24 | — | 2 | 4 | no | — |
| 161 | D24 | — | 4 | 1 | no | — |
| 162 | D24 | — | 4 | 1 | no | — |
| 163 | D24 | C2×D4 | 1 | 4 | yes | — |
| 164 | #204 | — | 2 | 8 | no | — |
| 165 | #204 | — | 2 | 4 | no | — |
| 166 | #204 | — | 2 | 4 | no | — |
| 167 | C3×C16 | — | 2 | 4 | no | — |
| 168 | 2−1+4 | — | 6 | 4 | no | — |
| 169 | 2−1+4 | — | 12 | 1 | no | — |
| 170 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 171 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 172 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 173 | C2×#41 | — | 6 | 4 | no | — |
| 174 | C2×#41 | — | 6 | 2 | no | — |
| 175 | C2×#41 | — | 12 | 4 | no | — |
| 176 | C2×#41 | D12 | 1 | 1 | yes | characteristic |
| 177 | C22×D4 | — | 6 | 1 | no | — |
| 178 | #137 | — | 6 | 8 | no | — |
| 179 | #137 | — | 6 | 4 | no | — |
| 180 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 181 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 182 | #135 | — | 3 | 4 | no | — |
| 183 | #135 | — | 3 | 4 | no | — |
| 184 | #135 | — | 6 | 4 | no | — |
| 185 | #135 | — | 6 | 4 | no | — |
| 186 | #135 | — | 6 | 2 | no | — |
| 187 | #135 | — | 6 | 4 | no | — |
| 188 | #135 | — | 6 | 2 | no | — |
| 189 | C2×Q16 | — | 3 | 2 | no | — |
| 190 | C2×Q16 | — | 6 | 2 | no | — |
| 191 | C2×SD16 | — | 6 | 4 | no | — |
| 192 | C2×SD16 | — | 6 | 2 | no | — |
| 193 | C2×D8 | — | 3 | 2 | no | — |
| 194 | C2×D8 | — | 3 | 2 | no | — |
| 195 | C2×D8 | — | 6 | 2 | no | — |
| 196 | C2×D8 | — | 6 | 1 | no | — |
| 197 | C2×D8 | — | 6 | 2 | no | — |
| 198 | C2×D8 | — | 6 | 2 | no | — |
| 199 | #131 | — | 2 | 2 | no | — |
| 200 | #131 | — | 2 | 2 | no | — |
| 201 | C2×M16 | D12 | 1 | 1 | yes | characteristic |
| 202 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 203 | C22×C8 | D12 | 1 | 2 | yes | — |
| 204 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 205 | #127 | — | 12 | 1 | no | — |
| 206 | #124 | — | 12 | 1 | no | — |
| 207 | #121 | — | 6 | 4 | no | — |
| 208 | #120 | — | 12 | 2 | no | — |
| 209 | #117 | — | 6 | 1 | no | — |
| 210 | SD32 | — | 6 | 8 | no | — |
| 211 | D16 | — | 6 | 8 | no | — |
| 212 | M32 | — | 2 | 2 | no | — |
| 213 | M32 | C22×D3 | 1 | 4 | yes | — |
| 214 | C2×C16 | — | 2 | 2 | no | — |
| 215 | #107 | — | 6 | 1 | no | — |
| 216 | #106 | — | 3 | 2 | no | — |
| 217 | #102 | — | 6 | 4 | no | — |
| 218 | C23×C3 | C2×D8 | 1 | 2 | yes | — |
| 219 | C23×C3 | C2×D8 | 1 | 1 | yes | characteristic |
| 220 | C22×D3 | — | 4 | 4 | no | — |
| 221 | C22×D3 | — | 4 | 2 | no | — |
| 222 | C22×D3 | — | 4 | 2 | no | — |
| 223 | C22×D3 | — | 8 | 2 | no | — |
| 224 | C22×D3 | — | 16 | 2 | no | — |
| 225 | C3×Q8 | — | 2 | 2 | no | — |
| 226 | C3×D4 | — | 2 | 4 | no | — |
| 227 | C3×D4 | — | 2 | 2 | no | — |
| 228 | C2×C3×C4 | — | 2 | 2 | no | — |
| 229 | C2×C3×C4 | — | 2 | 2 | no | — |
| 230 | C2×C3×C4 | #120 | 1 | 2 | yes | — |
| 231 | C2×C3×C4 | C2×D8 | 1 | 2 | yes | — |
| 232 | C2×C3×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 233 | C2×C3×C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 234 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 235 | #67 | — | 4 | 8 | no | — |
| 236 | #67 | — | 4 | 4 | no | — |
| 237 | #67 | — | 4 | 4 | no | — |
| 238 | #67 | — | 16 | 4 | no | — |
| 239 | C2×Dic3 | — | 4 | 4 | no | — |
| 240 | C2×Dic3 | — | 4 | 2 | no | — |
| 241 | C2×Dic3 | — | 4 | 2 | no | — |
| 242 | D12 | — | 2 | 4 | no | — |
| 243 | D12 | — | 4 | 4 | no | — |
| 244 | D12 | — | 4 | 2 | no | — |
| 245 | D12 | — | 4 | 2 | no | — |
| 246 | D12 | — | 4 | 2 | no | — |
| 247 | D12 | — | 8 | 2 | no | — |
| 248 | C4×D3 | — | 4 | 8 | no | — |
| 249 | C4×D3 | — | 4 | 4 | no | — |
| 250 | C4×D3 | — | 4 | 4 | no | — |
| 251 | Dic6 | — | 2 | 4 | no | — |
| 252 | Dic6 | — | 4 | 4 | no | — |
| 253 | Dic6 | — | 4 | 2 | no | — |
| 254 | C3×C8 | — | 2 | 2 | no | — |
| 255 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 256 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 257 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 258 | C24 | — | 12 | 1 | no | — |
| 259 | #41 | — | 2 | 2 | no | — |
| 260 | #41 | — | 2 | 2 | no | — |
| 261 | #41 | — | 6 | 8 | no | — |
| 262 | #41 | — | 6 | 4 | no | — |
| 263 | #41 | — | 6 | 4 | no | — |
| 264 | #41 | — | 12 | 4 | no | — |
| 265 | #41 | — | 12 | 8 | no | — |
| 266 | #41 | — | 12 | 4 | no | — |
| 267 | #41 | — | 12 | 4 | no | — |
| 268 | #41 | — | 12 | 4 | no | — |
| 269 | #41 | — | 12 | 2 | no | — |
| 270 | #41 | — | 12 | 2 | no | — |
| 271 | C2×Q8 | — | 6 | 4 | no | — |
| 272 | C2×Q8 | — | 6 | 2 | no | — |
| 273 | C2×Q8 | — | 12 | 4 | no | — |
| 274 | C2×Q8 | D24 | 1 | 1 | yes | characteristic |
| 275 | C2×D4 | — | 6 | 4 | no | — |
| 276 | C2×D4 | — | 6 | 2 | no | — |
| 277 | C2×D4 | — | 6 | 2 | no | — |
| 278 | C2×D4 | — | 12 | 8 | no | — |
| 279 | C2×D4 | — | 12 | 4 | no | — |
| 280 | C2×D4 | — | 12 | 4 | no | — |
| 281 | C2×D4 | — | 12 | 2 | no | — |
| 282 | C2×D4 | — | 12 | 4 | no | — |
| 283 | C2×D4 | — | 12 | 2 | no | — |
| 284 | C2×D4 | — | 12 | 1 | no | — |
| 285 | C2×D4 | — | 12 | 2 | no | — |
| 286 | C2×D4 | D24 | 1 | 2 | yes | — |
| 287 | C2×D4 | D24 | 1 | 1 | yes | characteristic |
| 288 | C22×C4 | — | 12 | 4 | no | — |
| 289 | C22×C4 | — | 12 | 2 | no | — |
| 290 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 291 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 292 | Q16 | — | 3 | 4 | no | — |
| 293 | Q16 | — | 6 | 4 | no | — |
| 294 | Q16 | — | 6 | 2 | no | — |
| 295 | SD16 | — | 6 | 8 | no | — |
| 296 | SD16 | — | 6 | 4 | no | — |
| 297 | SD16 | — | 6 | 4 | no | — |
| 298 | D8 | — | 3 | 4 | no | — |
| 299 | D8 | — | 6 | 4 | no | — |
| 300 | D8 | — | 6 | 2 | no | — |
| 301 | D8 | — | 6 | 4 | no | — |
| 302 | D8 | — | 12 | 1 | no | — |
| 303 | D8 | — | 12 | 1 | no | — |
| 304 | M16 | — | 2 | 2 | no | — |
| 305 | M16 | — | 2 | 4 | no | — |
| 306 | C2×C8 | — | 2 | 2 | no | — |
| 307 | C2×C8 | — | 2 | 2 | no | — |
| 308 | C2×C8 | C2×D12 | 1 | 2 | yes | — |
| 309 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 310 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 311 | C2×C8 | D3×D4 | 1 | 2 | yes | — |
| 312 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 313 | C4⋊C4 | — | 6 | 2 | no | — |
| 314 | C22⋊C4 | — | 12 | 1 | no | — |
| 315 | C22⋊C4 | — | 12 | 4 | no | — |
| 316 | C42 | — | 12 | 1 | no | — |
| 317 | C16 | — | 2 | 4 | no | — |
| 318 | C22×C3 | — | 2 | 2 | no | — |
| 319 | C22×C3 | — | 4 | 1 | no | — |
| 320 | C22×C3 | — | 4 | 2 | no | — |
| 321 | C22×C3 | #447 | 1 | 2 | yes | — |
| 322 | C22×C3 | C22×D8 | 1 | 1 | yes | characteristic |
| 323 | C2×D3 | — | 4 | 4 | no | — |
| 324 | C2×D3 | — | 8 | 4 | no | — |
| 325 | C2×D3 | — | 8 | 2 | no | — |
| 326 | C2×D3 | — | 16 | 2 | no | — |
| 327 | C2×D3 | — | 16 | 4 | no | — |
| 328 | C2×D3 | — | 16 | 4 | no | — |
| 329 | C3×C4 | — | 2 | 2 | no | — |
| 330 | C3×C4 | #447 | 1 | 2 | yes | — |
| 331 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 332 | C3×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 333 | Dic3 | — | 4 | 4 | no | — |
| 334 | Dic3 | — | 8 | 2 | no | — |
| 335 | C23 | — | 12 | 4 | no | — |
| 336 | C23 | — | 12 | 2 | no | — |
| 337 | C23 | — | 12 | 2 | no | — |
| 338 | C23 | — | 24 | 2 | no | — |
| 339 | C23 | — | 48 | 2 | no | — |
| 340 | C23 | C2×D24 | 1 | 2 | yes | — |
| 341 | C23 | C2×D24 | 1 | 1 | yes | characteristic |
| 342 | Q8 | — | 2 | 2 | no | — |
| 343 | Q8 | — | 6 | 4 | no | — |
| 344 | Q8 | — | 12 | 4 | no | — |
| 345 | Q8 | — | 12 | 2 | no | — |
| 346 | D4 | — | 2 | 4 | no | — |
| 347 | D4 | — | 2 | 2 | no | — |
| 348 | D4 | — | 6 | 4 | no | — |
| 349 | D4 | — | 12 | 4 | no | — |
| 350 | D4 | — | 12 | 8 | no | — |
| 351 | D4 | — | 12 | 4 | no | — |
| 352 | D4 | — | 12 | 4 | no | — |
| 353 | D4 | — | 12 | 2 | no | — |
| 354 | D4 | — | 12 | 2 | no | — |
| 355 | D4 | — | 12 | 2 | no | — |
| 356 | D4 | — | 24 | 2 | no | — |
| 357 | D4 | — | 48 | 4 | no | — |
| 358 | C2×C4 | — | 2 | 2 | no | — |
| 359 | C2×C4 | — | 2 | 2 | no | — |
| 360 | C2×C4 | — | 12 | 8 | no | — |
| 361 | C2×C4 | — | 12 | 4 | no | — |
| 362 | C2×C4 | — | 12 | 2 | no | — |
| 363 | C2×C4 | — | 12 | 4 | no | — |
| 364 | C2×C4 | — | 12 | 4 | no | — |
| 365 | C2×C4 | — | 12 | 2 | no | — |
| 366 | C2×C4 | #882 | 1 | 2 | yes | — |
| 367 | C2×C4 | C2×D24 | 1 | 2 | yes | — |
| 368 | C2×C4 | C2×D24 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | #908 | 1 | 2 | yes | — |
| 370 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 371 | C8 | — | 2 | 2 | no | — |
| 372 | C8 | #882 | 1 | 1 | yes | characteristic |
| 373 | C8 | #882 | 1 | 1 | yes | characteristic |
| 374 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 375 | C2×C3 | — | 2 | 1 | no | — |
| 376 | C2×C3 | — | 2 | 2 | no | — |
| 377 | C2×C3 | — | 4 | 2 | no | — |
| 378 | C2×C3 | C2×#447 | 1 | 1 | yes | characteristic |
| 379 | D3 | — | 8 | 4 | no | — |
| 380 | D3 | — | 16 | 2 | no | — |
| 381 | C22 | — | 2 | 2 | no | — |
| 382 | C22 | — | 4 | 1 | no | — |
| 383 | C22 | — | 4 | 2 | no | — |
| 384 | C22 | — | 12 | 4 | no | — |
| 385 | C22 | — | 24 | 4 | no | — |
| 386 | C22 | — | 24 | 2 | no | — |
| 387 | C22 | — | 48 | 2 | no | — |
| 388 | C22 | — | 48 | 4 | no | — |
| 389 | C22 | — | 48 | 4 | no | — |
| 390 | C22 | #4732 | 1 | 2 | yes | — |
| 391 | C22 | C22×D24 | 1 | 1 | yes | characteristic |
| 392 | C4 | — | 2 | 2 | no | — |
| 393 | C4 | — | 12 | 4 | no | — |
| 394 | C4 | — | 24 | 2 | no | — |
| 395 | C4 | #4732 | 1 | 2 | yes | — |
| 396 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 397 | C4 | C2×#908 | 1 | 1 | yes | characteristic |
| 398 | C3 | #33531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | C2 | — | 2 | 1 | no | — |
| 400 | C2 | — | 2 | 2 | no | — |
| 401 | C2 | — | 4 | 2 | no | — |
| 402 | C2 | — | 24 | 4 | no | — |
| 403 | C2 | — | 48 | 2 | no | — |
| 404 | C2 | C2×#4732 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87163 | C2 | semidirect |
| 2. #83799 | C2 | semidirect |
| 3. C2×#4908 | C2 | semidirect |
| 4. C3×#2115 | C2 | semidirect |
| 5. #71450 | C2 | semidirect |
| 6. #69120 | C2 | semidirect |
| 15. #5748 | C22 | semidirect |
| 18. C22×D24 | C22 | semidirect |
| 19. C2×C3×M32 | C22 | semidirect |
| 20. #5135 | C22 | semidirect |
| 23. #5106 | C22 | semidirect |
| 25. #4908 | C22 | semidirect |
| 28. C3×#349 | C22 | semidirect |
| 29. #4518 | C22 | semidirect |
| 35. #2115 | D3 | semidirect |
| 62. C2×Dic12 | D4 | semidirect |
| 68. #904 | D4 | semidirect |
| 74. C2×D24 | D4 | semidirect |
| 101. C2×M32 | C2×D3 | semidirect |
| 107. #349 | C2×D3 | semidirect |
| 398. C3 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87163 | 2 |
| #83799 | 2 |
| C2×#4908 | 2 |
| C3×#2115 | 2 |
| #71450 | 2 |
| #69120 | 2 |
| #33531 | 3 |