Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
844 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 135 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 | D3×H(5,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×AGL(1,ℤ/8) | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | D3×#127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#453 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #5241 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #5198 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #5077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #4822 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#104 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #4747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | D3×#100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#453 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #1009 | — | 2 | 2 | no | — |
| 15 | #1009 | C22 | 1 | 2 | yes | complemented |
| 16 | D3×#41 | — | 2 | 2 | no | — |
| 17 | D3×#41 | C22 | 1 | 2 | yes | — |
| 18 | #1004 | — | 2 | 2 | no | — |
| 19 | #1004 | — | 2 | 2 | no | — |
| 20 | #1004 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×D3×D4 | — | 2 | 2 | no | — |
| 22 | C2×D3×D4 | — | 2 | 2 | no | — |
| 23 | C2×D3×D4 | — | 2 | 2 | no | — |
| 24 | C2×D3×D4 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×D3×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×AGL(1,ℤ/8) | C22 | 1 | 2 | yes | complemented |
| 27 | C3×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #949 | C22 | 1 | 2 | yes | complemented |
| 29 | #940 | — | 2 | 2 | no | — |
| 30 | #940 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #940 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #932 | C22 | 1 | 2 | yes | complemented |
| 33 | #914 | — | 2 | 2 | no | — |
| 34 | D3×SD16 | — | 2 | 2 | no | — |
| 35 | #911 | — | 2 | 2 | no | — |
| 36 | D3×D8 | — | 2 | 2 | no | — |
| 37 | #908 | C22 | 1 | 2 | yes | complemented |
| 38 | D3×M16 | C22 | 1 | 2 | yes | complemented |
| 39 | #874 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C42×D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#104 | C22 | 1 | 2 | yes | complemented |
| 42 | C3×#100 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #837 | C22 | 1 | 2 | yes | complemented |
| 44 | #833 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #825 | C22 | 1 | 2 | yes | complemented |
| 46 | #823 | C22 | 1 | 2 | yes | complemented |
| 47 | #805 | C22 | 1 | 2 | yes | complemented |
| 48 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 49 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 50 | C2×#127 | — | 3 | 1 | no | — |
| 51 | #453 | — | 3 | 1 | no | — |
| 52 | #453 | — | 3 | 2 | no | — |
| 53 | #453 | — | 3 | 1 | no | — |
| 54 | #453 | — | 3 | 2 | no | — |
| 55 | #453 | — | 3 | 1 | no | — |
| 56 | #453 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 57 | C2×#104 | — | 3 | 2 | no | — |
| 58 | C2×#100 | — | 3 | 1 | no | — |
| 59 | C23×D3 | — | 2 | 2 | no | — |
| 60 | C23×D3 | — | 2 | 1 | no | — |
| 61 | C23×D3 | D4 | 1 | 2 | yes | — |
| 62 | C3×#41 | — | 2 | 2 | no | — |
| 63 | C3×#41 | C23 | 1 | 2 | yes | — |
| 64 | C2×C3×D4 | — | 2 | 2 | no | — |
| 65 | C2×C3×D4 | — | 2 | 2 | no | — |
| 66 | C2×C3×D4 | — | 2 | 2 | no | — |
| 67 | C2×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C3×D4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×#67 | — | 2 | 2 | no | — |
| 70 | C2×#67 | — | 2 | 4 | no | — |
| 71 | C2×#67 | — | 2 | 2 | no | — |
| 72 | C2×#67 | — | 2 | 2 | no | — |
| 73 | C2×#67 | — | 2 | 2 | no | — |
| 74 | C2×#67 | — | 2 | 1 | no | — |
| 75 | C2×#67 | D4 | 1 | 2 | yes | — |
| 76 | #239 | — | 2 | 2 | no | — |
| 77 | #239 | D4 | 1 | 2 | yes | complemented |
| 78 | D3×Q8 | D4 | 1 | 2 | yes | complemented |
| 79 | #237 | — | 2 | 4 | no | — |
| 80 | #237 | — | 2 | 2 | no | — |
| 81 | #237 | — | 2 | 2 | no | — |
| 82 | #237 | D4 | 1 | 2 | yes | complemented |
| 83 | D3×D4 | — | 2 | 4 | no | — |
| 84 | D3×D4 | — | 2 | 4 | no | — |
| 85 | D3×D4 | — | 2 | 4 | no | — |
| 86 | D3×D4 | — | 2 | 2 | no | — |
| 87 | D3×D4 | — | 2 | 4 | no | — |
| 88 | D3×D4 | — | 2 | 2 | no | — |
| 89 | D3×D4 | — | 2 | 2 | no | — |
| 90 | D3×D4 | — | 2 | 2 | no | — |
| 91 | D3×D4 | — | 2 | 2 | no | — |
| 92 | D3×D4 | — | 2 | 2 | no | — |
| 93 | D3×D4 | — | 2 | 2 | no | — |
| 94 | D3×D4 | — | 4 | 8 | no | — |
| 95 | D3×D4 | D4 | 1 | 2 | yes | complemented |
| 96 | #235 | — | 2 | 4 | no | — |
| 97 | #235 | — | 2 | 2 | no | — |
| 98 | #235 | — | 2 | 2 | no | — |
| 99 | #235 | C23 | 1 | 2 | yes | — |
| 100 | C2×D12 | — | 2 | 2 | no | — |
| 101 | C2×D12 | — | 2 | 2 | no | — |
| 102 | C2×D12 | — | 2 | 2 | no | — |
| 103 | C2×D12 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×D12 | C23 | 1 | 1 | yes | characteristic, complemented |
| 105 | C2×C4×D3 | — | 2 | 2 | no | — |
| 106 | C2×C4×D3 | — | 2 | 1 | no | — |
| 107 | C2×C4×D3 | — | 2 | 2 | no | — |
| 108 | C2×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 109 | C3×SD16 | — | 2 | 2 | no | — |
| 110 | C3×D8 | — | 2 | 2 | no | — |
| 111 | C3×M16 | C23 | 1 | 2 | yes | complemented |
| 112 | C3×C42 | C23 | 1 | 1 | yes | characteristic, complemented |
| 113 | #215 | — | 2 | 2 | no | — |
| 114 | #214 | — | 2 | 2 | no | — |
| 115 | #213 | — | 2 | 2 | no | — |
| 116 | #213 | — | 2 | 2 | no | — |
| 117 | C4×Dic3 | — | 2 | 1 | no | — |
| 118 | C4×Dic3 | C23 | 1 | 1 | yes | characteristic, complemented |
| 119 | #208 | C23 | 1 | 2 | yes | complemented |
| 120 | D24 | — | 2 | 2 | no | — |
| 121 | #204 | — | 2 | 2 | no | — |
| 122 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 123 | D3×C8 | — | 2 | 2 | no | — |
| 124 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 125 | H(5,𝔽2) | — | 3 | 1 | no | — |
| 126 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 127 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 128 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 129 | H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 130 | C2×#41 | — | 3 | 2 | no | — |
| 131 | C2×#41 | — | 6 | 2 | no | — |
| 132 | C22×D4 | — | 3 | 1 | no | — |
| 133 | C22×D4 | — | 3 | 1 | no | — |
| 134 | C22×D4 | — | 6 | 2 | no | — |
| 135 | C22×D4 | — | 6 | 2 | no | — |
| 136 | C22×D4 | — | 6 | 2 | no | — |
| 137 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 138 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 139 | AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 140 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 141 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 142 | AGL(1,ℤ/8) | C2×D3 | 1 | 2 | yes | complemented |
| 143 | C2×SD16 | — | 6 | 2 | no | — |
| 144 | C2×D8 | — | 6 | 2 | no | — |
| 145 | C2×M16 | — | 3 | 2 | no | — |
| 146 | #127 | — | 3 | 1 | no | — |
| 147 | #127 | — | 3 | 1 | no | — |
| 148 | #127 | — | 3 | 1 | no | — |
| 149 | #127 | — | 6 | 2 | no | — |
| 150 | #127 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 151 | C2×C42 | — | 3 | 1 | no | — |
| 152 | #104 | — | 3 | 2 | no | — |
| 153 | #104 | — | 3 | 2 | no | — |
| 154 | #104 | — | 3 | 2 | no | — |
| 155 | #104 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | #100 | — | 3 | 1 | no | — |
| 157 | #100 | — | 3 | 2 | no | — |
| 158 | #100 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 159 | C23×C3 | — | 2 | 2 | no | — |
| 160 | C23×C3 | — | 2 | 1 | no | — |
| 161 | C23×C3 | C2×D4 | 1 | 2 | yes | — |
| 162 | C22×D3 | — | 2 | 4 | no | — |
| 163 | C22×D3 | — | 2 | 2 | no | — |
| 164 | C22×D3 | — | 2 | 2 | no | — |
| 165 | C22×D3 | — | 2 | 2 | no | — |
| 166 | C22×D3 | — | 2 | 2 | no | — |
| 167 | C22×D3 | — | 2 | 1 | no | — |
| 168 | C22×D3 | — | 4 | 4 | no | — |
| 169 | C22×D3 | — | 4 | 4 | no | — |
| 170 | C22×D3 | — | 4 | 1 | no | — |
| 171 | C22×D3 | — | 4 | 1 | no | — |
| 172 | C22×D3 | — | 8 | 4 | no | — |
| 173 | C22×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C22×D3 | C2×D4 | 1 | 2 | yes | — |
| 175 | C3×Q8 | C2×D4 | 1 | 2 | yes | complemented |
| 176 | C3×D4 | — | 2 | 4 | no | — |
| 177 | C3×D4 | — | 2 | 2 | no | — |
| 178 | C3×D4 | — | 2 | 2 | no | — |
| 179 | C3×D4 | — | 2 | 2 | no | — |
| 180 | C3×D4 | — | 4 | 4 | no | — |
| 181 | C3×D4 | C2×D4 | 1 | 2 | yes | complemented |
| 182 | C2×C3×C4 | — | 2 | 2 | no | — |
| 183 | C2×C3×C4 | — | 2 | 1 | no | — |
| 184 | C2×C3×C4 | — | 2 | 2 | no | — |
| 185 | C2×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 186 | #67 | — | 2 | 4 | no | — |
| 187 | #67 | — | 2 | 4 | no | — |
| 188 | #67 | — | 2 | 2 | no | — |
| 189 | #67 | — | 2 | 2 | no | — |
| 190 | #67 | — | 2 | 4 | no | — |
| 191 | #67 | — | 2 | 2 | no | — |
| 192 | #67 | — | 4 | 4 | no | — |
| 193 | #67 | — | 4 | 4 | no | — |
| 194 | #67 | — | 4 | 2 | no | — |
| 195 | C2×Dic3 | — | 2 | 2 | no | — |
| 196 | C2×Dic3 | — | 2 | 1 | no | — |
| 197 | C2×Dic3 | — | 2 | 2 | no | — |
| 198 | C2×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | D12 | — | 2 | 4 | no | — |
| 200 | D12 | — | 2 | 2 | no | — |
| 201 | D12 | — | 2 | 2 | no | — |
| 202 | D12 | — | 2 | 2 | no | — |
| 203 | D12 | — | 4 | 4 | no | — |
| 204 | D12 | C2×D4 | 1 | 2 | yes | complemented |
| 205 | C4×D3 | — | 2 | 4 | no | — |
| 206 | C4×D3 | — | 2 | 4 | no | — |
| 207 | C4×D3 | — | 2 | 2 | no | — |
| 208 | C4×D3 | — | 2 | 2 | no | — |
| 209 | C4×D3 | — | 2 | 2 | no | — |
| 210 | C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 211 | C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 212 | Dic6 | — | 2 | 2 | no | — |
| 213 | Dic6 | C2×D4 | 1 | 2 | yes | complemented |
| 214 | C3×C8 | — | 2 | 2 | no | — |
| 215 | C3⋊C8 | — | 2 | 2 | no | — |
| 216 | C24 | — | 3 | 2 | no | — |
| 217 | C24 | — | 6 | 1 | no | — |
| 218 | C24 | — | 6 | 2 | no | — |
| 219 | #41 | — | 2 | 2 | no | — |
| 220 | #41 | — | 3 | 2 | no | — |
| 221 | #41 | — | 3 | 2 | no | — |
| 222 | #41 | — | 3 | 2 | no | — |
| 223 | #41 | — | 6 | 2 | no | — |
| 224 | #41 | — | 6 | 2 | no | — |
| 225 | #41 | — | 6 | 4 | no | — |
| 226 | #41 | — | 6 | 2 | no | — |
| 227 | #41 | — | 6 | 2 | no | — |
| 228 | #41 | — | 6 | 4 | no | — |
| 229 | #41 | — | 6 | 2 | no | — |
| 230 | #41 | C22×D3 | 1 | 2 | yes | — |
| 231 | C2×Q8 | — | 3 | 2 | no | — |
| 232 | C2×D4 | — | 2 | 2 | no | — |
| 233 | C2×D4 | — | 2 | 2 | no | — |
| 234 | C2×D4 | — | 2 | 2 | no | — |
| 235 | C2×D4 | — | 3 | 2 | no | — |
| 236 | C2×D4 | — | 3 | 2 | no | — |
| 237 | C2×D4 | — | 3 | 1 | no | — |
| 238 | C2×D4 | — | 3 | 1 | no | — |
| 239 | C2×D4 | — | 6 | 2 | no | — |
| 240 | C2×D4 | — | 6 | 2 | no | — |
| 241 | C2×D4 | — | 6 | 2 | no | — |
| 242 | C2×D4 | — | 6 | 2 | no | — |
| 243 | C2×D4 | — | 6 | 2 | no | — |
| 244 | C2×D4 | — | 6 | 2 | no | — |
| 245 | C2×D4 | — | 6 | 2 | no | — |
| 246 | C2×D4 | — | 6 | 1 | no | — |
| 247 | C2×D4 | — | 6 | 2 | no | — |
| 248 | C2×D4 | — | 6 | 2 | no | — |
| 249 | C2×D4 | — | 6 | 4 | no | — |
| 250 | C2×D4 | — | 6 | 4 | no | — |
| 251 | C2×D4 | — | 6 | 4 | no | — |
| 252 | C2×D4 | — | 6 | 4 | no | — |
| 253 | C2×D4 | — | 6 | 4 | no | — |
| 254 | C2×D4 | — | 6 | 2 | no | — |
| 255 | C2×D4 | — | 6 | 2 | no | — |
| 256 | C2×D4 | — | 6 | 2 | no | — |
| 257 | C2×D4 | — | 6 | 2 | no | — |
| 258 | C2×D4 | — | 6 | 2 | no | — |
| 259 | C2×D4 | — | 12 | 8 | no | — |
| 260 | C2×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 261 | C2×D4 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 262 | C22×C4 | — | 3 | 1 | no | — |
| 263 | C22×C4 | — | 6 | 2 | no | — |
| 264 | C22×C4 | — | 6 | 1 | no | — |
| 265 | C22×C4 | — | 6 | 2 | no | — |
| 266 | SD16 | — | 2 | 2 | no | — |
| 267 | SD16 | — | 6 | 2 | no | — |
| 268 | SD16 | — | 6 | 2 | no | — |
| 269 | SD16 | — | 6 | 2 | no | — |
| 270 | D8 | — | 2 | 2 | no | — |
| 271 | D8 | — | 6 | 2 | no | — |
| 272 | D8 | — | 6 | 2 | no | — |
| 273 | D8 | — | 6 | 2 | no | — |
| 274 | M16 | — | 3 | 2 | no | — |
| 275 | M16 | — | 6 | 2 | no | — |
| 276 | M16 | C22×D3 | 1 | 2 | yes | complemented |
| 277 | C2×C8 | — | 6 | 2 | no | — |
| 278 | C42 | — | 3 | 1 | no | — |
| 279 | C42 | — | 6 | 1 | no | — |
| 280 | C42 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 281 | C22×C3 | — | 2 | 2 | no | — |
| 282 | C22×C3 | — | 2 | 2 | no | — |
| 283 | C22×C3 | — | 4 | 2 | no | — |
| 284 | C22×C3 | — | 4 | 2 | no | — |
| 285 | C22×C3 | — | 4 | 1 | no | — |
| 286 | C22×C3 | — | 8 | 2 | no | — |
| 287 | C22×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×D3 | — | 2 | 2 | no | — |
| 289 | C2×D3 | — | 2 | 2 | no | — |
| 290 | C2×D3 | — | 2 | 2 | no | — |
| 291 | C2×D3 | — | 4 | 4 | no | — |
| 292 | C2×D3 | — | 4 | 4 | no | — |
| 293 | C2×D3 | — | 4 | 2 | no | — |
| 294 | C2×D3 | — | 4 | 2 | no | — |
| 295 | C2×D3 | — | 4 | 1 | no | — |
| 296 | C2×D3 | — | 8 | 2 | no | — |
| 297 | C2×D3 | — | 8 | 2 | no | — |
| 298 | C2×D3 | — | 8 | 4 | no | — |
| 299 | C2×D3 | — | 8 | 2 | no | — |
| 300 | C2×D3 | — | 8 | 2 | no | — |
| 301 | C2×D3 | #120 | 1 | 1 | yes | characteristic |
| 302 | C2×D3 | #120 | 1 | 1 | yes | characteristic |
| 303 | C3×C4 | — | 2 | 2 | no | — |
| 304 | C3×C4 | — | 2 | 2 | no | — |
| 305 | C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 306 | Dic3 | — | 2 | 2 | no | — |
| 307 | Dic3 | — | 2 | 2 | no | — |
| 308 | Dic3 | #120 | 1 | 2 | yes | — |
| 309 | C23 | — | 2 | 2 | no | — |
| 310 | C23 | — | 2 | 1 | no | — |
| 311 | C23 | — | 3 | 1 | no | — |
| 312 | C23 | — | 3 | 2 | no | — |
| 313 | C23 | — | 6 | 2 | no | — |
| 314 | C23 | — | 6 | 2 | no | — |
| 315 | C23 | — | 6 | 2 | no | — |
| 316 | C23 | — | 6 | 2 | no | — |
| 317 | C23 | — | 6 | 4 | no | — |
| 318 | C23 | — | 6 | 1 | no | — |
| 319 | C23 | — | 12 | 1 | no | — |
| 320 | C23 | — | 12 | 1 | no | — |
| 321 | C23 | — | 12 | 4 | no | — |
| 322 | C23 | — | 12 | 4 | no | — |
| 323 | C23 | — | 24 | 4 | no | — |
| 324 | C23 | D3×D4 | 1 | 2 | yes | — |
| 325 | Q8 | — | 3 | 2 | no | — |
| 326 | Q8 | — | 6 | 2 | no | — |
| 327 | Q8 | D3×D4 | 1 | 2 | yes | complemented |
| 328 | D4 | — | 2 | 4 | no | — |
| 329 | D4 | — | 2 | 2 | no | — |
| 330 | D4 | — | 2 | 2 | no | — |
| 331 | D4 | — | 2 | 2 | no | — |
| 332 | D4 | — | 3 | 2 | no | — |
| 333 | D4 | — | 4 | 4 | no | — |
| 334 | D4 | — | 6 | 2 | no | — |
| 335 | D4 | — | 6 | 4 | no | — |
| 336 | D4 | — | 6 | 4 | no | — |
| 337 | D4 | — | 6 | 2 | no | — |
| 338 | D4 | — | 6 | 2 | no | — |
| 339 | D4 | — | 6 | 4 | no | — |
| 340 | D4 | — | 6 | 4 | no | — |
| 341 | D4 | — | 6 | 2 | no | — |
| 342 | D4 | — | 6 | 2 | no | — |
| 343 | D4 | — | 6 | 2 | no | — |
| 344 | D4 | — | 12 | 4 | no | — |
| 345 | D4 | — | 12 | 2 | no | — |
| 346 | D4 | — | 12 | 4 | no | — |
| 347 | D4 | — | 12 | 4 | no | — |
| 348 | D4 | D3×D4 | 1 | 2 | yes | complemented |
| 349 | C2×C4 | — | 2 | 2 | no | — |
| 350 | C2×C4 | — | 2 | 1 | no | — |
| 351 | C2×C4 | — | 2 | 2 | no | — |
| 352 | C2×C4 | — | 3 | 1 | no | — |
| 353 | C2×C4 | — | 3 | 2 | no | — |
| 354 | C2×C4 | — | 3 | 2 | no | — |
| 355 | C2×C4 | — | 6 | 2 | no | — |
| 356 | C2×C4 | — | 6 | 2 | no | — |
| 357 | C2×C4 | — | 6 | 4 | no | — |
| 358 | C2×C4 | — | 6 | 4 | no | — |
| 359 | C2×C4 | — | 6 | 2 | no | — |
| 360 | C2×C4 | — | 6 | 2 | no | — |
| 361 | C2×C4 | — | 6 | 1 | no | — |
| 362 | C2×C4 | — | 6 | 2 | no | — |
| 363 | C2×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 2 | 2 | no | — |
| 365 | C8 | — | 6 | 2 | no | — |
| 366 | C2×C3 | — | 2 | 1 | no | — |
| 367 | C2×C3 | — | 4 | 2 | no | — |
| 368 | C2×C3 | — | 4 | 2 | no | — |
| 369 | C2×C3 | — | 8 | 1 | no | — |
| 370 | C2×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 371 | D3 | — | 2 | 1 | no | — |
| 372 | D3 | — | 4 | 2 | no | — |
| 373 | D3 | — | 4 | 2 | no | — |
| 374 | D3 | — | 8 | 1 | no | — |
| 375 | D3 | #453 | 1 | 2 | yes | direct product factor |
| 376 | C22 | — | 2 | 2 | no | — |
| 377 | C22 | — | 2 | 2 | no | — |
| 378 | C22 | — | 3 | 1 | no | — |
| 379 | C22 | — | 3 | 1 | no | — |
| 380 | C22 | — | 4 | 2 | no | — |
| 381 | C22 | — | 4 | 2 | no | — |
| 382 | C22 | — | 4 | 1 | no | — |
| 383 | C22 | — | 6 | 2 | no | — |
| 384 | C22 | — | 6 | 2 | no | — |
| 385 | C22 | — | 6 | 2 | no | — |
| 386 | C22 | — | 8 | 2 | no | — |
| 387 | C22 | — | 12 | 2 | no | — |
| 388 | C22 | — | 12 | 2 | no | — |
| 389 | C22 | — | 12 | 4 | no | — |
| 390 | C22 | — | 12 | 4 | no | — |
| 391 | C22 | — | 12 | 1 | no | — |
| 392 | C22 | — | 24 | 2 | no | — |
| 393 | C22 | — | 24 | 2 | no | — |
| 394 | C22 | — | 24 | 2 | no | — |
| 395 | C22 | — | 24 | 4 | no | — |
| 396 | C22 | — | 24 | 2 | no | — |
| 397 | C22 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 398 | C4 | — | 2 | 2 | no | — |
| 399 | C4 | — | 2 | 2 | no | — |
| 400 | C4 | — | 3 | 2 | no | — |
| 401 | C4 | — | 6 | 2 | no | — |
| 402 | C4 | — | 6 | 2 | no | — |
| 403 | C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 404 | C3 | C2×#453 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C2 | — | 2 | 1 | no | — |
| 406 | C2 | — | 3 | 2 | no | — |
| 407 | C2 | — | 4 | 2 | no | — |
| 408 | C2 | — | 4 | 2 | no | — |
| 409 | C2 | — | 6 | 1 | no | — |
| 410 | C2 | — | 8 | 1 | no | — |
| 411 | C2 | — | 12 | 2 | no | — |
| 412 | C2 | — | 12 | 2 | no | — |
| 413 | C2 | — | 24 | 1 | no | — |
| 414 | C2 | D3×#120 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×#120 |
| commutator, cosocle | C2×C3×C4 | C24 |
| Frattini | C2×C4 | C23×D3 |
| Fitting | C3×#453 | C2 |
| socle | C2×C3 | C2×#120 |
| hypercenter | #453 | D3 |
| hypocenter | C3 | C2×#453 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #453 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×H(5,𝔽2) | C2 | semidirect |
| 2. D3×AGL(1,ℤ/8) | C2 | semidirect |
| 3. D3×#127 | C2 | semidirect |
| 4. C3×#453 | C2 | semidirect |
| 5. #5241 | C2 | semidirect |
| 6. #5198 | C2 | semidirect |
| 7. #5077 | C2 | semidirect |
| 8. #4822 | C2 | semidirect |
| 9. D3×#104 | C2 | semidirect |
| 10. #4747 | C2 | semidirect |
| 11. D3×#100 | C2 | semidirect |
| 13. C3×H(5,𝔽2) | C22 | semidirect |
| 15. #1009 | C22 | semidirect |
| 20. #1004 | C22 | semidirect |
| 25. C2×D3×D4 | C22 | semidirect |
| 26. C3×AGL(1,ℤ/8) | C22 | semidirect |
| 27. C3×#127 | C22 | semidirect |
| 28. #949 | C22 | semidirect |
| 30. #940 | C22 | semidirect |
| 31. #940 | C22 | semidirect |
| 32. #932 | C22 | semidirect |
| 37. #908 | C22 | semidirect |
| 38. D3×M16 | C22 | semidirect |
| 39. #874 | C22 | semidirect |
| 40. C42×D3 | C22 | semidirect |
| 41. C3×#104 | C22 | semidirect |
| 42. C3×#100 | C22 | semidirect |
| 43. #837 | C22 | semidirect |
| 44. #833 | C22 | semidirect |
| 45. #825 | C22 | semidirect |
| 46. #823 | C22 | semidirect |
| 47. #805 | C22 | semidirect |
| 56. #453 | D3 | direct (N × H) |
| 68. C2×C3×D4 | C23 | semidirect |
| 77. #239 | D4 | semidirect |
| 78. D3×Q8 | D4 | semidirect |
| 82. #237 | D4 | semidirect |
| 95. D3×D4 | D4 | semidirect |
| 104. C2×D12 | C23 | semidirect |
| 111. C3×M16 | C23 | semidirect |
| 112. C3×C42 | C23 | semidirect |
| 118. C4×Dic3 | C23 | semidirect |
| 119. #208 | C23 | semidirect |
| 129. H(5,𝔽2) | C2×D3 | semidirect |
| 142. AGL(1,ℤ/8) | C2×D3 | semidirect |
| 150. #127 | C2×D3 | semidirect |
| 155. #104 | C2×D3 | semidirect |
| 158. #100 | C2×D3 | semidirect |
| 175. C3×Q8 | C2×D4 | semidirect |
| 181. C3×D4 | C2×D4 | semidirect |
| 204. D12 | C2×D4 | semidirect |
| 213. Dic6 | C2×D4 | semidirect |
| 261. C2×D4 | C22×D3 | semidirect |
| 276. M16 | C22×D3 | semidirect |
| 280. C42 | C22×D3 | semidirect |
| 327. Q8 | D3×D4 | semidirect |
| 348. D4 | D3×D4 | semidirect |
| 375. D3 | #453 | direct (N × H) |
| 404. C3 | C2×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×H(5,𝔽2) | 2 |
| D3×AGL(1,ℤ/8) | 2 |
| D3×#127 | 2 |
| C3×#453 | 2 |
| #5241 | 2 |
| #5198 | 2 |
| #5077 | 2 |
| #4822 | 2 |
| D3×#104 | 2 |
| #4747 | 2 |
| D3×#100 | 2 |
| C2×#453 | 3 |