Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2793 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 2793 conjugacy classes of subgroups — too many to draw. Only its 340 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 | C2×#64149 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C3×#940 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#63979 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | C2×#63914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#63911 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C4×Dic32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #83185 | — | 3 | 2 | no | maximal |
| 8 | C22×C32×D4 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#638 | C22 | 1 | 4 | yes | — |
| 10 | C22×C4⋊(C3⋊D3) | C22 | 1 | 1 | yes | characteristic |
| 11 | C22×C3×#67 | C22 | 1 | 8 | yes | — |
| 12 | C22×C3×D12 | C22 | 1 | 2 | yes | — |
| 13 | C22×#626 | C22 | 1 | 8 | yes | — |
| 14 | C22×#625 | C22 | 1 | 4 | yes | — |
| 15 | #64149 | — | 2 | 4 | no | — |
| 16 | C2×C4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#940 | — | 2 | 8 | no | — |
| 18 | C2×C3×C4×Dic3 | C22 | 1 | 2 | yes | — |
| 19 | #63979 | — | 2 | 32 | no | — |
| 20 | C2×Dic32 | C22 | 1 | 4 | yes | — |
| 21 | #63914 | — | 2 | 4 | no | — |
| 22 | #63911 | — | 2 | 8 | no | — |
| 23 | C2×C3×#127 | — | 3 | 2 | no | — |
| 24 | C2×#940 | — | 3 | 2 | no | — |
| 25 | C2×#940 | — | 3 | 16 | no | — |
| 26 | C2×#940 | — | 3 | 2 | no | — |
| 27 | C2×#940 | — | 3 | 2 | no | — |
| 28 | C2×#940 | — | 6 | 1 | no | — |
| 29 | C2×#940 | D3 | 1 | 2 | yes | complemented |
| 30 | C2×#874 | — | 3 | 2 | no | — |
| 31 | C42×Dic3 | — | 3 | 2 | no | — |
| 32 | C24×C32 | C23 | 1 | 2 | yes | — |
| 33 | C23×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 34 | C23×C3×D3 | C23 | 1 | 4 | yes | — |
| 35 | C2×C32×D4 | — | 2 | 2 | no | — |
| 36 | C2×C32×D4 | — | 2 | 4 | no | — |
| 37 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×#638 | — | 2 | 8 | no | — |
| 39 | C2×#638 | — | 2 | 16 | no | — |
| 40 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 41 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 42 | C2×C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 43 | C2×C3×#67 | — | 2 | 16 | no | — |
| 44 | C2×C3×#67 | — | 2 | 32 | no | — |
| 45 | C22×C3×Dic3 | C23 | 1 | 4 | yes | — |
| 46 | C2×C3×D12 | — | 2 | 4 | no | — |
| 47 | C2×C3×D12 | — | 2 | 4 | no | — |
| 48 | C2×C3×D12 | — | 2 | 4 | no | — |
| 49 | C2×#626 | — | 2 | 16 | no | — |
| 50 | C2×#626 | — | 2 | 32 | no | — |
| 51 | C2×#625 | — | 2 | 8 | no | — |
| 52 | C2×#625 | — | 2 | 16 | no | — |
| 53 | C4×C3⋊Dic3 | D4 | 1 | 4 | yes | complemented |
| 54 | C3×C4×Dic3 | D4 | 1 | 8 | yes | complemented |
| 55 | Dic32 | D4 | 1 | 16 | yes | complemented |
| 56 | #2867 | — | 9 | 1 | no | Sylow |
| 57 | C22×C3×D4 | — | 2 | 1 | no | — |
| 58 | C22×C3×D4 | — | 3 | 8 | no | — |
| 59 | C22×C3×D4 | — | 3 | 2 | no | — |
| 60 | C22×C3×D4 | C2×D3 | 1 | 2 | yes | — |
| 61 | C22×#67 | — | 3 | 8 | no | — |
| 62 | C22×#67 | — | 3 | 8 | no | — |
| 63 | C22×#67 | — | 3 | 8 | no | — |
| 64 | C22×#67 | — | 6 | 4 | no | — |
| 65 | C22×#67 | C2×D3 | 1 | 8 | yes | — |
| 66 | C22×D12 | — | 3 | 8 | no | — |
| 67 | C22×D12 | — | 3 | 2 | no | — |
| 68 | C22×D12 | — | 6 | 1 | no | — |
| 69 | C22×D12 | C2×D3 | 1 | 2 | yes | — |
| 70 | C3×#127 | — | 6 | 8 | no | — |
| 71 | C2×C3×C42 | — | 3 | 2 | no | — |
| 72 | #940 | — | 2 | 8 | no | — |
| 73 | #940 | — | 6 | 8 | no | — |
| 74 | #940 | — | 6 | 64 | no | — |
| 75 | #940 | — | 6 | 8 | no | — |
| 76 | #940 | — | 6 | 8 | no | — |
| 77 | #940 | — | 6 | 8 | no | — |
| 78 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 79 | C2×C4×Dic3 | — | 3 | 8 | no | — |
| 80 | C2×C4×Dic3 | — | 6 | 1 | no | — |
| 81 | C2×C4×Dic3 | C2×D3 | 1 | 2 | yes | — |
| 82 | #874 | — | 6 | 8 | no | — |
| 83 | C23×C32 | — | 2 | 2 | no | — |
| 84 | C23×C32 | — | 2 | 8 | no | — |
| 85 | C23×C32 | — | 2 | 4 | no | — |
| 86 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 87 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 88 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 89 | C22×C3⋊D3 | — | 2 | 8 | no | — |
| 90 | C22×C3×D3 | — | 2 | 4 | no | — |
| 91 | C22×C3×D3 | — | 2 | 16 | no | — |
| 92 | C22×C3×D3 | — | 2 | 4 | no | — |
| 93 | C22×C3×D3 | — | 2 | 4 | no | — |
| 94 | C32×D4 | — | 4 | 4 | no | — |
| 95 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C32×C4 | C2×D4 | 1 | 4 | yes | — |
| 97 | #638 | — | 4 | 16 | no | — |
| 98 | C2×C3⋊Dic3 | C2×D4 | 1 | 8 | yes | — |
| 99 | C2×C3⋊Dic3 | C2×D4 | 1 | 4 | yes | — |
| 100 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 101 | C3×#67 | — | 4 | 32 | no | — |
| 102 | C2×C3×Dic3 | C2×D4 | 1 | 16 | yes | — |
| 103 | C2×C3×Dic3 | C2×D4 | 1 | 8 | yes | — |
| 104 | C3×D12 | — | 4 | 8 | no | — |
| 105 | #626 | — | 4 | 32 | no | — |
| 106 | #625 | — | 4 | 16 | no | — |
| 107 | C2×#127 | — | 3 | 2 | no | — |
| 108 | C2×#127 | — | 9 | 2 | no | — |
| 109 | C2×#127 | — | 9 | 8 | no | — |
| 110 | C2×#127 | — | 9 | 1 | no | — |
| 111 | C2×#127 | — | 9 | 1 | no | — |
| 112 | C43 | — | 9 | 1 | no | — |
| 113 | C24×C3 | — | 2 | 2 | no | — |
| 114 | C24×C3 | — | 3 | 4 | no | — |
| 115 | C24×C3 | C22×D3 | 1 | 4 | yes | — |
| 116 | C23×D3 | — | 3 | 4 | no | — |
| 117 | C23×D3 | — | 6 | 2 | no | — |
| 118 | C23×D3 | C22×D3 | 1 | 4 | yes | — |
| 119 | C2×C3×D4 | — | 2 | 4 | no | — |
| 120 | C2×C3×D4 | — | 2 | 4 | no | — |
| 121 | C2×C3×D4 | — | 2 | 4 | no | — |
| 122 | C2×C3×D4 | — | 2 | 4 | no | — |
| 123 | C2×C3×D4 | — | 4 | 4 | no | — |
| 124 | C2×C3×D4 | — | 6 | 32 | no | — |
| 125 | C2×C3×D4 | — | 6 | 16 | no | — |
| 126 | C2×C3×D4 | — | 6 | 4 | no | — |
| 127 | C2×C3×D4 | — | 6 | 4 | no | — |
| 128 | C2×C3×D4 | — | 6 | 4 | no | — |
| 129 | C22×C3×C4 | — | 2 | 1 | no | — |
| 130 | C22×C3×C4 | — | 3 | 4 | no | — |
| 131 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 132 | C2×#67 | — | 2 | 32 | no | — |
| 133 | C2×#67 | — | 2 | 16 | no | — |
| 134 | C2×#67 | — | 6 | 16 | no | — |
| 135 | C2×#67 | — | 6 | 32 | no | — |
| 136 | C2×#67 | — | 6 | 16 | no | — |
| 137 | C2×#67 | — | 6 | 32 | no | — |
| 138 | C2×#67 | — | 6 | 16 | no | — |
| 139 | C2×#67 | — | 6 | 32 | no | — |
| 140 | C2×#67 | — | 6 | 16 | no | — |
| 141 | C2×#67 | — | 12 | 16 | no | — |
| 142 | C22×Dic3 | — | 3 | 4 | no | — |
| 143 | C22×Dic3 | — | 6 | 2 | no | — |
| 144 | C22×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 145 | C2×D12 | — | 2 | 4 | no | — |
| 146 | C2×D12 | — | 2 | 4 | no | — |
| 147 | C2×D12 | — | 2 | 4 | no | — |
| 148 | C2×D12 | — | 6 | 4 | no | — |
| 149 | C2×D12 | — | 6 | 16 | no | — |
| 150 | C2×D12 | — | 6 | 32 | no | — |
| 151 | C2×D12 | — | 6 | 4 | no | — |
| 152 | C2×D12 | — | 6 | 4 | no | — |
| 153 | C2×D12 | — | 6 | 4 | no | — |
| 154 | C2×D12 | — | 12 | 4 | no | — |
| 155 | C3×C42 | — | 3 | 8 | no | — |
| 156 | C4×Dic3 | — | 3 | 8 | no | — |
| 157 | C4×Dic3 | — | 3 | 32 | no | — |
| 158 | C4×Dic3 | — | 6 | 4 | no | — |
| 159 | C4×Dic3 | #67 | 1 | 8 | yes | complemented |
| 160 | C22×C32 | — | 4 | 4 | no | — |
| 161 | C22×C32 | — | 4 | 2 | no | — |
| 162 | C22×C32 | — | 4 | 8 | no | — |
| 163 | C22×C32 | C22×D4 | 1 | 4 | yes | — |
| 164 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 165 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 166 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 167 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 168 | C2×C3⋊D3 | — | 4 | 8 | no | — |
| 169 | C2×C3×D3 | — | 4 | 8 | no | — |
| 170 | C2×C3×D3 | — | 4 | 8 | no | — |
| 171 | C2×C3×D3 | — | 4 | 4 | no | — |
| 172 | C2×C3×D3 | — | 4 | 8 | no | — |
| 173 | C32×C4 | #127 | 1 | 4 | yes | complemented |
| 174 | C3⋊Dic3 | #127 | 1 | 8 | yes | complemented |
| 175 | C3×Dic3 | #127 | 1 | 16 | yes | complemented |
| 176 | C22×D4 | — | 3 | 8 | no | — |
| 177 | C22×D4 | — | 3 | 2 | no | — |
| 178 | C22×D4 | — | 9 | 8 | no | — |
| 179 | C22×D4 | — | 9 | 4 | no | — |
| 180 | C22×D4 | — | 9 | 4 | no | — |
| 181 | C22×D4 | — | 9 | 1 | no | — |
| 182 | C22×D4 | D32 | 1 | 1 | yes | characteristic |
| 183 | #127 | — | 6 | 8 | no | — |
| 184 | #127 | — | 18 | 8 | no | — |
| 185 | #127 | — | 18 | 4 | no | — |
| 186 | #127 | — | 18 | 32 | no | — |
| 187 | #127 | — | 18 | 4 | no | — |
| 188 | C2×C42 | — | 3 | 2 | no | — |
| 189 | C2×C42 | — | 9 | 4 | no | — |
| 190 | C2×C42 | — | 9 | 1 | no | — |
| 191 | C23×C3 | — | 2 | 4 | no | — |
| 192 | C23×C3 | — | 2 | 16 | no | — |
| 193 | C23×C3 | — | 2 | 4 | no | — |
| 194 | C23×C3 | — | 2 | 4 | no | — |
| 195 | C23×C3 | — | 2 | 4 | no | — |
| 196 | C23×C3 | — | 2 | 1 | no | — |
| 197 | C23×C3 | — | 4 | 8 | no | — |
| 198 | C23×C3 | — | 4 | 4 | no | — |
| 199 | C23×C3 | — | 6 | 16 | no | — |
| 200 | C23×C3 | — | 6 | 4 | no | — |
| 201 | C23×C3 | — | 6 | 4 | no | — |
| 202 | C23×C3 | — | 6 | 4 | no | — |
| 203 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 204 | C22×D3 | — | 2 | 4 | no | — |
| 205 | C22×D3 | — | 2 | 4 | no | — |
| 206 | C22×D3 | — | 2 | 16 | no | — |
| 207 | C22×D3 | — | 2 | 4 | no | — |
| 208 | C22×D3 | — | 6 | 4 | no | — |
| 209 | C22×D3 | — | 6 | 4 | no | — |
| 210 | C22×D3 | — | 6 | 16 | no | — |
| 211 | C22×D3 | — | 6 | 4 | no | — |
| 212 | C22×D3 | — | 6 | 4 | no | — |
| 213 | C22×D3 | — | 12 | 4 | no | — |
| 214 | C22×D3 | — | 12 | 8 | no | — |
| 215 | C3×D4 | — | 4 | 8 | no | — |
| 216 | C3×D4 | — | 4 | 8 | no | — |
| 217 | C3×D4 | — | 12 | 32 | no | — |
| 218 | C3×D4 | — | 12 | 8 | no | — |
| 219 | C2×C3×C4 | — | 2 | 4 | no | — |
| 220 | C2×C3×C4 | — | 2 | 2 | no | — |
| 221 | C2×C3×C4 | — | 3 | 16 | no | — |
| 222 | C2×C3×C4 | — | 3 | 8 | no | — |
| 223 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 224 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 225 | C2×C3×C4 | C2×#67 | 1 | 4 | yes | — |
| 226 | #67 | — | 4 | 32 | no | — |
| 227 | #67 | — | 12 | 32 | no | — |
| 228 | #67 | — | 12 | 32 | no | — |
| 229 | #67 | — | 12 | 32 | no | — |
| 230 | #67 | — | 12 | 32 | no | — |
| 231 | C2×Dic3 | — | 3 | 16 | no | — |
| 232 | C2×Dic3 | — | 3 | 8 | no | — |
| 233 | C2×Dic3 | — | 6 | 4 | no | — |
| 234 | C2×Dic3 | — | 6 | 8 | no | — |
| 235 | C2×Dic3 | D3×D4 | 1 | 16 | yes | — |
| 236 | C2×Dic3 | C2×#67 | 1 | 8 | yes | — |
| 237 | D12 | — | 4 | 8 | no | — |
| 238 | D12 | — | 12 | 8 | no | — |
| 239 | D12 | — | 12 | 32 | no | — |
| 240 | D12 | — | 12 | 8 | no | — |
| 241 | C2×C32 | — | 8 | 2 | no | — |
| 242 | C2×C32 | C2×#127 | 1 | 2 | yes | — |
| 243 | C2×C32 | C2×#127 | 1 | 4 | yes | — |
| 244 | C2×C32 | C2×#127 | 1 | 1 | yes | characteristic |
| 245 | C3⋊D3 | — | 8 | 2 | no | — |
| 246 | C3×D3 | — | 8 | 4 | no | — |
| 247 | C24 | — | 3 | 4 | no | — |
| 248 | C24 | — | 9 | 2 | no | — |
| 249 | C24 | C2×D32 | 1 | 2 | yes | — |
| 250 | C2×D4 | — | 2 | 4 | no | — |
| 251 | C2×D4 | — | 2 | 2 | no | — |
| 252 | C2×D4 | — | 6 | 16 | no | — |
| 253 | C2×D4 | — | 6 | 32 | no | — |
| 254 | C2×D4 | — | 6 | 4 | no | — |
| 255 | C2×D4 | — | 6 | 4 | no | — |
| 256 | C2×D4 | — | 6 | 4 | no | — |
| 257 | C2×D4 | — | 18 | 32 | no | — |
| 258 | C2×D4 | — | 18 | 16 | no | — |
| 259 | C2×D4 | — | 18 | 8 | no | — |
| 260 | C2×D4 | — | 18 | 16 | no | — |
| 261 | C2×D4 | — | 18 | 16 | no | — |
| 262 | C2×D4 | — | 18 | 8 | no | — |
| 263 | C2×D4 | — | 18 | 4 | no | — |
| 264 | C2×D4 | — | 18 | 2 | no | — |
| 265 | C22×C4 | — | 3 | 4 | no | — |
| 266 | C22×C4 | — | 9 | 2 | no | — |
| 267 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 268 | C42 | — | 3 | 8 | no | — |
| 269 | C42 | — | 9 | 16 | no | — |
| 270 | C42 | — | 9 | 4 | no | — |
| 271 | C22×C3 | — | 2 | 4 | no | — |
| 272 | C22×C3 | — | 2 | 2 | no | — |
| 273 | C22×C3 | — | 2 | 1 | no | — |
| 274 | C22×C3 | — | 4 | 8 | no | — |
| 275 | C22×C3 | — | 4 | 4 | no | — |
| 276 | C22×C3 | — | 4 | 8 | no | — |
| 277 | C22×C3 | — | 4 | 8 | no | — |
| 278 | C22×C3 | — | 4 | 8 | no | — |
| 279 | C22×C3 | — | 4 | 4 | no | — |
| 280 | C22×C3 | — | 8 | 8 | no | — |
| 281 | C22×C3 | — | 12 | 8 | no | — |
| 282 | C22×C3 | — | 12 | 8 | no | — |
| 283 | C22×C3 | — | 12 | 8 | no | — |
| 284 | C22×C3 | — | 12 | 4 | no | — |
| 285 | C22×C3 | C2×D3×D4 | 1 | 8 | yes | — |
| 286 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 287 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 288 | C22×C3 | C22×#67 | 1 | 2 | yes | — |
| 289 | C2×D3 | — | 4 | 8 | no | — |
| 290 | C2×D3 | — | 4 | 8 | no | — |
| 291 | C2×D3 | — | 4 | 4 | no | — |
| 292 | C2×D3 | — | 4 | 8 | no | — |
| 293 | C2×D3 | — | 12 | 4 | no | — |
| 294 | C2×D3 | — | 12 | 8 | no | — |
| 295 | C2×D3 | — | 12 | 8 | no | — |
| 296 | C2×D3 | — | 12 | 8 | no | — |
| 297 | C2×D3 | — | 12 | 4 | no | — |
| 298 | C2×D3 | — | 12 | 8 | no | — |
| 299 | C2×D3 | — | 24 | 8 | no | — |
| 300 | C3×C4 | — | 2 | 4 | no | — |
| 301 | C3×C4 | — | 3 | 16 | no | — |
| 302 | C3×C4 | #940 | 1 | 8 | yes | complemented |
| 303 | Dic3 | — | 3 | 16 | no | — |
| 304 | Dic3 | — | 6 | 8 | no | — |
| 305 | Dic3 | #940 | 1 | 16 | yes | complemented |
| 306 | C32 | #2867 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 307 | C23 | — | 2 | 8 | no | — |
| 308 | C23 | — | 2 | 4 | no | — |
| 309 | C23 | — | 2 | 2 | no | — |
| 310 | C23 | — | 6 | 16 | no | — |
| 311 | C23 | — | 6 | 4 | no | — |
| 312 | C23 | — | 6 | 4 | no | — |
| 313 | C23 | — | 6 | 4 | no | — |
| 314 | C23 | — | 18 | 8 | no | — |
| 315 | C23 | — | 18 | 4 | no | — |
| 316 | C23 | — | 18 | 2 | no | — |
| 317 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 318 | D4 | — | 4 | 4 | no | — |
| 319 | D4 | — | 12 | 32 | no | — |
| 320 | D4 | — | 12 | 8 | no | — |
| 321 | D4 | — | 36 | 32 | no | — |
| 322 | D4 | — | 36 | 16 | no | — |
| 323 | D4 | — | 36 | 16 | no | — |
| 324 | D4 | — | 36 | 4 | no | — |
| 325 | C2×C4 | — | 3 | 16 | no | — |
| 326 | C2×C4 | — | 3 | 8 | no | — |
| 327 | C2×C4 | — | 9 | 8 | no | — |
| 328 | C2×C4 | — | 9 | 4 | no | — |
| 329 | C2×C4 | D3×#67 | 1 | 4 | yes | — |
| 330 | C2×C4 | #3811 | 1 | 2 | yes | — |
| 331 | C2×C3 | — | 2 | 1 | no | — |
| 332 | C2×C3 | — | 2 | 4 | no | — |
| 333 | C2×C3 | — | 2 | 2 | no | — |
| 334 | C2×C3 | — | 8 | 4 | no | — |
| 335 | C2×C3 | — | 8 | 4 | no | — |
| 336 | C2×C3 | — | 24 | 4 | no | — |
| 337 | C2×C3 | D3×#127 | 1 | 4 | yes | — |
| 338 | C2×C3 | D3×#127 | 1 | 4 | yes | — |
| 339 | C2×C3 | C2×#940 | 1 | 2 | yes | — |
| 340 | C2×C3 | C2×#940 | 1 | 4 | yes | — |
| 341 | D3 | — | 8 | 4 | no | — |
| 342 | D3 | — | 24 | 4 | no | — |
| 343 | D3 | — | 24 | 4 | no | — |
| 344 | C22 | — | 4 | 2 | no | — |
| 345 | C22 | — | 4 | 8 | no | — |
| 346 | C22 | — | 4 | 4 | no | — |
| 347 | C22 | — | 12 | 4 | no | — |
| 348 | C22 | — | 12 | 8 | no | — |
| 349 | C22 | — | 12 | 8 | no | — |
| 350 | C22 | — | 12 | 8 | no | — |
| 351 | C22 | — | 36 | 2 | no | — |
| 352 | C22 | — | 36 | 8 | no | — |
| 353 | C22 | — | 36 | 4 | no | — |
| 354 | C22 | D32×D4 | 1 | 4 | yes | — |
| 355 | C22 | C2×D3×#67 | 1 | 2 | yes | — |
| 356 | C22 | C2×#3811 | 1 | 1 | yes | characteristic |
| 357 | C4 | — | 3 | 16 | no | — |
| 358 | C4 | — | 9 | 8 | no | — |
| 359 | C4 | #63979 | 1 | 4 | yes | complemented |
| 360 | C3 | — | 2 | 1 | no | — |
| 361 | C3 | #83185 | 1 | 2 | yes | complemented |
| 362 | C2 | — | 8 | 2 | no | — |
| 363 | C2 | — | 24 | 4 | no | — |
| 364 | C2 | — | 72 | 2 | no | — |
| 365 | C2 | D3×#940 | 1 | 4 | yes | — |
| 366 | C2 | #10595300 | 1 | 2 | yes | — |
| 367 | C2 | C2×#63979 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C22×C32×D4 | C22 |
| hypercenter | C22×D4 | D32 |
| hypocenter | C32 | #2867 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64149 | C2 | semidirect |
| 2. C2×C3×#940 | C2 | semidirect |
| 3. C2×#63979 | C2 | semidirect |
| 4. C2×#63914 | C2 | semidirect |
| 5. C2×#63911 | C2 | semidirect |
| 6. C4×Dic32 | C2 | semidirect |
| 29. C2×#940 | D3 | semidirect |
| 53. C4×C3⋊Dic3 | D4 | semidirect |
| 54. C3×C4×Dic3 | D4 | semidirect |
| 55. Dic32 | D4 | semidirect |
| 159. C4×Dic3 | #67 | semidirect |
| 173. C32×C4 | #127 | semidirect |
| 174. C3⋊Dic3 | #127 | semidirect |
| 175. C3×Dic3 | #127 | semidirect |
| 302. C3×C4 | #940 | semidirect |
| 305. Dic3 | #940 | semidirect |
| 306. C32 | #2867 | semidirect |
| 359. C4 | #63979 | semidirect |
| 361. C3 | #83185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64149 | 2 |
| C2×C3×#940 | 2 |
| C2×#63979 | 2 |
| C2×#63914 | 2 |
| C2×#63911 | 2 |
| C4×Dic32 | 2 |
| #83185 | 3 |