Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2153 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 2153 conjugacy classes of subgroups — too many to draw. Only its 190 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 | C22×#3802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10596077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63927 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#5036 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10591516 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10591172 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10591159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10590597 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10590594 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #80002 | — | 3 | 2 | no | maximal |
| 11 | C23×D32 | — | 2 | 1 | no | — |
| 12 | C2×#3830 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C22×C4×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C3×D12 | C22 | 1 | 2 | yes | — |
| 15 | C22×#625 | — | 2 | 1 | no | — |
| 16 | C2×#3802 | — | 2 | 1 | no | — |
| 17 | C2×#3802 | — | 2 | 1 | no | — |
| 18 | C2×#3802 | — | 2 | 8 | no | — |
| 19 | C2×#3802 | C22 | 1 | 2 | yes | — |
| 20 | C2×#3802 | C22 | 1 | 2 | yes | — |
| 21 | C32×#121 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #64147 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #64146 | — | 2 | 1 | no | — |
| 24 | D4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 25 | #64133 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #64106 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #64101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #64092 | — | 2 | 1 | no | — |
| 29 | #64090 | — | 2 | 1 | no | — |
| 30 | C2×C3×#213 | C22 | 1 | 4 | yes | complemented |
| 31 | #63927 | — | 2 | 8 | no | — |
| 32 | C2×#3716 | C22 | 1 | 4 | yes | complemented |
| 33 | C2×#3712 | C22 | 1 | 2 | yes | complemented |
| 34 | C3×#830 | C22 | 1 | 2 | yes | complemented |
| 35 | C3×#809 | C22 | 1 | 4 | yes | complemented |
| 36 | #63563 | C22 | 1 | 4 | yes | complemented |
| 37 | #63557 | C22 | 1 | 2 | yes | complemented |
| 38 | C22×D3×D4 | — | 3 | 2 | no | — |
| 39 | C2×#911 | — | 3 | 4 | no | — |
| 40 | #5606 | — | 3 | 2 | no | — |
| 41 | #5606 | — | 6 | 1 | no | — |
| 42 | C3×#447 | — | 3 | 2 | no | — |
| 43 | #5218 | — | 3 | 2 | no | — |
| 44 | #5156 | — | 3 | 4 | no | — |
| 45 | #5036 | D3 | 1 | 2 | yes | complemented |
| 46 | #4776 | — | 3 | 4 | no | — |
| 47 | #4770 | — | 3 | 4 | no | — |
| 48 | #4731 | — | 3 | 2 | no | — |
| 49 | #4726 | — | 3 | 2 | no | — |
| 50 | C23×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 51 | C23×C3×D3 | — | 2 | 2 | no | — |
| 52 | C22×D32 | — | 2 | 8 | no | — |
| 53 | C22×D32 | — | 2 | 2 | no | — |
| 54 | C22×D32 | — | 2 | 2 | no | — |
| 55 | C22×D32 | — | 4 | 4 | no | — |
| 56 | C22×D32 | — | 4 | 4 | no | — |
| 57 | C2×C32×D4 | — | 2 | 1 | no | — |
| 58 | C2×C32×D4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 59 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#638 | — | 2 | 1 | no | — |
| 61 | C2×#638 | — | 2 | 1 | no | — |
| 62 | C22×C3⋊Dic3 | — | 2 | 1 | no | — |
| 63 | C22×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 64 | #3830 | — | 2 | 4 | no | — |
| 65 | C2×C4×C3⋊D3 | — | 2 | 4 | no | — |
| 66 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 67 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×#634 | C23 | 1 | 1 | yes | characteristic, complemented |
| 71 | C2×C3×D12 | — | 2 | 2 | no | — |
| 72 | C2×C3×D12 | — | 2 | 8 | no | — |
| 73 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 74 | C2×#625 | — | 2 | 8 | no | — |
| 75 | C2×#625 | — | 2 | 2 | no | — |
| 76 | C2×#625 | — | 2 | 2 | no | — |
| 77 | #3802 | — | 2 | 8 | no | — |
| 78 | #3802 | — | 2 | 8 | no | — |
| 79 | #3802 | — | 2 | 4 | no | — |
| 80 | #3802 | — | 2 | 8 | no | — |
| 81 | #3802 | D4 | 1 | 8 | yes | complemented |
| 82 | C32×C4⋊C4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 83 | C32×C22⋊C4 | — | 2 | 1 | no | — |
| 84 | #3757 | — | 2 | 1 | no | — |
| 85 | #3757 | — | 2 | 1 | no | — |
| 86 | #3752 | — | 2 | 1 | no | — |
| 87 | #3752 | — | 2 | 1 | no | — |
| 88 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 89 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 90 | #3750 | — | 2 | 1 | no | — |
| 91 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 92 | C3×#213 | — | 2 | 8 | no | — |
| 93 | C2×C3×C3⋊C8 | C23 | 1 | 4 | yes | complemented |
| 94 | #3716 | — | 2 | 8 | no | — |
| 95 | #3712 | — | 2 | 4 | no | — |
| 96 | #3003 | — | 9 | 1 | no | Sylow |
| 97 | C24×D3 | — | 6 | 2 | no | — |
| 98 | C22×C3×D4 | — | 3 | 2 | no | — |
| 99 | C22×#67 | — | 6 | 2 | no | — |
| 100 | C2×#237 | — | 3 | 2 | no | — |
| 101 | C2×#237 | — | 6 | 1 | no | — |
| 102 | C2×D3×D4 | — | 3 | 4 | no | — |
| 103 | C2×D3×D4 | — | 3 | 4 | no | — |
| 104 | C2×D3×D4 | — | 6 | 2 | no | — |
| 105 | C2×D3×D4 | — | 6 | 2 | no | — |
| 106 | C2×D3×D4 | — | 6 | 16 | no | — |
| 107 | C22×D12 | C2×D3 | 1 | 2 | yes | — |
| 108 | C22×C4×D3 | — | 3 | 2 | no | — |
| 109 | C22×C4×D3 | — | 6 | 1 | no | — |
| 110 | C2×C3×D8 | — | 3 | 4 | no | — |
| 111 | C3×#121 | — | 2 | 1 | no | — |
| 112 | C3×#121 | C2×D3 | 1 | 2 | yes | complemented |
| 113 | #938 | — | 3 | 2 | no | — |
| 114 | #938 | — | 6 | 1 | no | — |
| 115 | #937 | — | 6 | 2 | no | — |
| 116 | #937 | — | 6 | 2 | no | — |
| 117 | D4×Dic3 | — | 6 | 2 | no | — |
| 118 | D4×Dic3 | — | 6 | 2 | no | — |
| 119 | C2×#214 | — | 3 | 4 | no | — |
| 120 | C2×#213 | C2×D3 | 1 | 4 | yes | complemented |
| 121 | #924 | — | 3 | 2 | no | — |
| 122 | #924 | — | 6 | 1 | no | — |
| 123 | #911 | — | 6 | 16 | no | — |
| 124 | C2×#204 | — | 3 | 4 | no | — |
| 125 | C2×ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 126 | #897 | — | 3 | 2 | no | — |
| 127 | #897 | — | 6 | 1 | no | — |
| 128 | #892 | — | 3 | 2 | no | — |
| 129 | #892 | — | 6 | 1 | no | — |
| 130 | #883 | — | 6 | 2 | no | — |
| 131 | #883 | — | 6 | 2 | no | — |
| 132 | #67⋊C4 | — | 6 | 2 | no | — |
| 133 | #67⋊C4 | — | 6 | 2 | no | — |
| 134 | C3×#102 | — | 3 | 4 | no | — |
| 135 | C3×C22⋊C8 | — | 3 | 2 | no | — |
| 136 | #832 | — | 3 | 4 | no | — |
| 137 | #830 | C2×D3 | 1 | 2 | yes | complemented |
| 138 | #821 | — | 3 | 4 | no | — |
| 139 | (C2×D3)⋊C8 | — | 3 | 4 | no | — |
| 140 | #809 | C2×D3 | 1 | 4 | yes | complemented |
| 141 | C23×C32 | — | 2 | 1 | no | — |
| 142 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 144 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 145 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 146 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C22×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C22×C3×D3 | — | 2 | 8 | no | — |
| 149 | C22×C3×D3 | — | 2 | 4 | no | — |
| 150 | C22×C3×D3 | — | 4 | 4 | no | — |
| 151 | C22×C3×D3 | — | 4 | 4 | no | — |
| 152 | C2×D32 | — | 2 | 8 | no | — |
| 153 | C2×D32 | — | 2 | 8 | no | — |
| 154 | C2×D32 | — | 4 | 32 | no | — |
| 155 | C2×D32 | — | 4 | 4 | no | — |
| 156 | C2×D32 | — | 4 | 4 | no | — |
| 157 | C2×D32 | — | 4 | 4 | no | — |
| 158 | C2×D32 | — | 4 | 4 | no | — |
| 159 | C32×D4 | — | 2 | 2 | no | — |
| 160 | C32×D4 | — | 4 | 2 | no | — |
| 161 | C2×C32×C4 | — | 2 | 1 | no | — |
| 162 | C2×C32×C4 | — | 2 | 2 | no | — |
| 163 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 165 | #638 | — | 4 | 2 | no | — |
| 166 | #638 | — | 4 | 2 | no | — |
| 167 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 168 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 169 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 170 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 171 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 174 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 175 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 176 | C4×C3⋊D3 | C2×D4 | 1 | 4 | yes | — |
| 177 | #634 | — | 2 | 2 | no | — |
| 178 | C3×D12 | — | 2 | 8 | no | — |
| 179 | C3×D12 | — | 2 | 4 | no | — |
| 180 | C3×D12 | C2×D4 | 1 | 8 | yes | — |
| 181 | #625 | — | 2 | 8 | no | — |
| 182 | #625 | — | 2 | 8 | no | — |
| 183 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 184 | C23×D4 | — | 9 | 1 | no | — |
| 185 | C2×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 186 | #525 | — | 9 | 1 | no | — |
| 187 | #450 | — | 9 | 2 | no | — |
| 188 | #450 | — | 9 | 2 | no | — |
| 189 | #447 | — | 3 | 2 | no | — |
| 190 | #447 | — | 9 | 2 | no | — |
| 191 | #418 | — | 9 | 2 | no | — |
| 192 | #407 | — | 9 | 1 | no | — |
| 193 | C24×C3 | — | 6 | 2 | no | — |
| 194 | C23×D3 | — | 2 | 2 | no | — |
| 195 | C23×D3 | — | 3 | 2 | no | — |
| 196 | C23×D3 | — | 6 | 1 | no | — |
| 197 | C23×D3 | — | 6 | 4 | no | — |
| 198 | C23×D3 | — | 6 | 4 | no | — |
| 199 | C23×D3 | — | 6 | 16 | no | — |
| 200 | C23×D3 | — | 12 | 8 | no | — |
| 201 | C23×D3 | — | 12 | 8 | no | — |
| 202 | C2×C3×D4 | — | 2 | 2 | no | — |
| 203 | C2×C3×D4 | — | 2 | 2 | no | — |
| 204 | C2×C3×D4 | — | 2 | 1 | no | — |
| 205 | C2×C3×D4 | — | 3 | 4 | no | — |
| 206 | C2×C3×D4 | — | 6 | 8 | no | — |
| 207 | C2×C3×D4 | — | 6 | 2 | no | — |
| 208 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | complemented |
| 209 | C22×C3×C4 | — | 2 | 1 | no | — |
| 210 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 211 | C2×#67 | — | 6 | 4 | no | — |
| 212 | C2×#67 | — | 6 | 4 | no | — |
| 213 | C2×#67 | — | 6 | 16 | no | — |
| 214 | C2×#67 | — | 6 | 2 | no | — |
| 215 | C2×#67 | — | 6 | 2 | no | — |
| 216 | C2×#67 | — | 6 | 2 | no | — |
| 217 | C2×#67 | — | 6 | 2 | no | — |
| 218 | C22×Dic3 | — | 3 | 2 | no | — |
| 219 | C22×Dic3 | — | 6 | 1 | no | — |
| 220 | C22×Dic3 | — | 6 | 2 | no | — |
| 221 | C22×Dic3 | — | 6 | 2 | no | — |
| 222 | #237 | — | 6 | 8 | no | — |
| 223 | #237 | — | 12 | 4 | no | — |
| 224 | D3×D4 | — | 3 | 16 | no | — |
| 225 | D3×D4 | — | 6 | 8 | no | — |
| 226 | D3×D4 | — | 6 | 8 | no | — |
| 227 | D3×D4 | — | 6 | 16 | no | — |
| 228 | D3×D4 | — | 6 | 16 | no | — |
| 229 | D3×D4 | — | 6 | 8 | no | — |
| 230 | C2×D12 | — | 2 | 2 | no | — |
| 231 | C2×D12 | — | 2 | 8 | no | — |
| 232 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 233 | C2×C4×D3 | — | 3 | 2 | no | — |
| 234 | C2×C4×D3 | — | 3 | 2 | no | — |
| 235 | C2×C4×D3 | — | 3 | 2 | no | — |
| 236 | C2×C4×D3 | — | 3 | 2 | no | — |
| 237 | C2×C4×D3 | — | 6 | 1 | no | — |
| 238 | C2×C4×D3 | — | 6 | 1 | no | — |
| 239 | C2×C4×D3 | — | 6 | 1 | no | — |
| 240 | C2×C4×D3 | — | 6 | 1 | no | — |
| 241 | C2×C4×D3 | — | 6 | 8 | no | — |
| 242 | C2×C4×D3 | — | 12 | 4 | no | — |
| 243 | C2×Dic6 | — | 3 | 2 | no | — |
| 244 | C2×Dic6 | — | 6 | 1 | no | — |
| 245 | C3×D8 | — | 6 | 8 | no | — |
| 246 | C2×C3×C8 | — | 3 | 4 | no | — |
| 247 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 248 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | complemented |
| 249 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 250 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 251 | #217 | — | 6 | 2 | no | — |
| 252 | #217 | — | 6 | 2 | no | — |
| 253 | #217 | — | 6 | 2 | no | — |
| 254 | #217 | — | 6 | 2 | no | — |
| 255 | #214 | — | 6 | 8 | no | — |
| 256 | #213 | — | 2 | 8 | no | — |
| 257 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 258 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 259 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 260 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 261 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 262 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 263 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 264 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 265 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 266 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 267 | C4×Dic3 | — | 6 | 2 | no | — |
| 268 | C4×Dic3 | — | 6 | 2 | no | — |
| 269 | C2×C3⋊C8 | C22×D3 | 1 | 4 | yes | complemented |
| 270 | #204 | — | 6 | 8 | no | — |
| 271 | ΓL(1,𝔽25) | — | 6 | 8 | no | — |
| 272 | C22×C32 | — | 2 | 1 | no | — |
| 273 | C22×C32 | — | 2 | 1 | no | — |
| 274 | C22×C32 | — | 4 | 1 | no | — |
| 275 | C22×C32 | — | 4 | 1 | no | — |
| 276 | C22×C32 | — | 4 | 1 | no | — |
| 277 | C22×C32 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 278 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×C3⋊D3 | — | 2 | 8 | no | — |
| 280 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 281 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 282 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 283 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 284 | C2×C3⋊D3 | #120 | 1 | 2 | yes | — |
| 285 | C2×C3⋊D3 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 286 | C2×C3×D3 | — | 2 | 8 | no | — |
| 287 | C2×C3×D3 | — | 4 | 16 | no | — |
| 288 | C2×C3×D3 | — | 4 | 4 | no | — |
| 289 | C2×C3×D3 | — | 4 | 4 | no | — |
| 290 | D32 | — | 4 | 16 | no | — |
| 291 | D32 | — | 4 | 16 | no | — |
| 292 | C32×C4 | — | 2 | 1 | no | — |
| 293 | C32×C4 | — | 4 | 1 | no | — |
| 294 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 295 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 296 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 297 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 298 | C3⋊Dic3 | #120 | 1 | 2 | yes | — |
| 299 | C25 | — | 18 | 1 | no | — |
| 300 | C2×#41 | — | 9 | 1 | no | — |
| 301 | C22×D4 | — | 3 | 2 | no | — |
| 302 | C22×D4 | — | 9 | 2 | no | — |
| 303 | C22×D4 | — | 9 | 2 | no | — |
| 304 | C22×D4 | — | 18 | 1 | no | — |
| 305 | C22×D4 | — | 18 | 1 | no | — |
| 306 | C22×D4 | — | 18 | 1 | no | — |
| 307 | C22×D4 | — | 18 | 8 | no | — |
| 308 | C23×C4 | — | 9 | 1 | no | — |
| 309 | AGL(1,ℤ/8) | — | 18 | 8 | no | — |
| 310 | C2×SD16 | — | 9 | 4 | no | — |
| 311 | C2×D8 | — | 3 | 4 | no | — |
| 312 | C2×M16 | — | 9 | 2 | no | — |
| 313 | #123 | — | 18 | 1 | no | — |
| 314 | C22⋊Q8 | — | 9 | 1 | no | — |
| 315 | C22⋊Q8 | — | 9 | 1 | no | — |
| 316 | #121 | — | 9 | 1 | no | — |
| 317 | #121 | D32 | 1 | 1 | yes | characteristic, complemented |
| 318 | #120 | — | 18 | 1 | no | — |
| 319 | C4×D4 | — | 18 | 1 | no | — |
| 320 | C4×D4 | — | 18 | 1 | no | — |
| 321 | #117 | — | 9 | 1 | no | — |
| 322 | #102 | — | 3 | 4 | no | — |
| 323 | #102 | — | 9 | 4 | no | — |
| 324 | C22⋊C8 | — | 3 | 2 | no | — |
| 325 | C22⋊C8 | — | 9 | 2 | no | — |
| 326 | C23×C3 | — | 2 | 2 | no | — |
| 327 | C23×C3 | — | 2 | 2 | no | — |
| 328 | C23×C3 | — | 2 | 1 | no | — |
| 329 | C23×C3 | — | 6 | 8 | no | — |
| 330 | C23×C3 | — | 6 | 4 | no | — |
| 331 | C23×C3 | — | 12 | 4 | no | — |
| 332 | C23×C3 | — | 12 | 4 | no | — |
| 333 | C23×C3 | D3×D4 | 1 | 2 | yes | — |
| 334 | C22×D3 | — | 2 | 8 | no | — |
| 335 | C22×D3 | — | 2 | 4 | no | — |
| 336 | C22×D3 | — | 3 | 2 | no | — |
| 337 | C22×D3 | — | 3 | 2 | no | — |
| 338 | C22×D3 | — | 4 | 4 | no | — |
| 339 | C22×D3 | — | 4 | 4 | no | — |
| 340 | C22×D3 | — | 6 | 1 | no | — |
| 341 | C22×D3 | — | 6 | 1 | no | — |
| 342 | C22×D3 | — | 6 | 16 | no | — |
| 343 | C22×D3 | — | 6 | 16 | no | — |
| 344 | C22×D3 | — | 6 | 4 | no | — |
| 345 | C22×D3 | — | 6 | 4 | no | — |
| 346 | C22×D3 | — | 6 | 4 | no | — |
| 347 | C22×D3 | — | 12 | 2 | no | — |
| 348 | C22×D3 | — | 12 | 2 | no | — |
| 349 | C22×D3 | — | 12 | 2 | no | — |
| 350 | C22×D3 | — | 12 | 8 | no | — |
| 351 | C22×D3 | — | 12 | 64 | no | — |
| 352 | C22×D3 | — | 12 | 8 | no | — |
| 353 | C22×D3 | — | 12 | 8 | no | — |
| 354 | C22×D3 | — | 12 | 8 | no | — |
| 355 | C3×D4 | — | 2 | 4 | no | — |
| 356 | C3×D4 | — | 3 | 8 | no | — |
| 357 | C3×D4 | — | 4 | 2 | no | — |
| 358 | C3×D4 | — | 4 | 4 | no | — |
| 359 | C3×D4 | — | 4 | 4 | no | — |
| 360 | C3×D4 | — | 6 | 8 | no | — |
| 361 | C3×D4 | — | 6 | 4 | no | — |
| 362 | C2×C3×C4 | — | 2 | 4 | no | — |
| 363 | C2×C3×C4 | — | 2 | 2 | no | — |
| 364 | C2×C3×C4 | — | 2 | 2 | no | — |
| 365 | C2×C3×C4 | — | 2 | 1 | no | — |
| 366 | C2×C3×C4 | — | 2 | 1 | no | — |
| 367 | C2×C3×C4 | — | 4 | 2 | no | — |
| 368 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 369 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 370 | #67 | — | 6 | 16 | no | — |
| 371 | #67 | — | 6 | 16 | no | — |
| 372 | #67 | — | 12 | 4 | no | — |
| 373 | #67 | — | 12 | 4 | no | — |
| 374 | #67 | — | 12 | 4 | no | — |
| 375 | #67 | — | 12 | 4 | no | — |
| 376 | C2×Dic3 | — | 3 | 2 | no | — |
| 377 | C2×Dic3 | — | 3 | 2 | no | — |
| 378 | C2×Dic3 | — | 6 | 1 | no | — |
| 379 | C2×Dic3 | — | 6 | 1 | no | — |
| 380 | C2×Dic3 | — | 6 | 4 | no | — |
| 381 | C2×Dic3 | — | 6 | 2 | no | — |
| 382 | C2×Dic3 | — | 6 | 2 | no | — |
| 383 | C2×Dic3 | — | 6 | 2 | no | — |
| 384 | C2×Dic3 | — | 6 | 2 | no | — |
| 385 | C2×Dic3 | — | 12 | 2 | no | — |
| 386 | C2×Dic3 | — | 12 | 4 | no | — |
| 387 | C2×Dic3 | — | 12 | 4 | no | — |
| 388 | D12 | — | 2 | 8 | no | — |
| 389 | D12 | — | 2 | 4 | no | — |
| 390 | D12 | D3×D4 | 1 | 8 | yes | — |
| 391 | C4×D3 | — | 3 | 8 | no | — |
| 392 | C4×D3 | — | 6 | 4 | no | — |
| 393 | C4×D3 | — | 6 | 4 | no | — |
| 394 | C4×D3 | — | 6 | 4 | no | — |
| 395 | C4×D3 | — | 6 | 4 | no | — |
| 396 | C4×D3 | — | 12 | 2 | no | — |
| 397 | C4×D3 | — | 12 | 2 | no | — |
| 398 | C4×D3 | — | 12 | 2 | no | — |
| 399 | Dic6 | — | 6 | 4 | no | — |
| 400 | Dic6 | — | 12 | 2 | no | — |
| 401 | C3×C8 | — | 6 | 4 | no | — |
| 402 | C3⋊C8 | — | 2 | 4 | no | — |
| 403 | C2×C32 | — | 2 | 2 | no | — |
| 404 | C2×C32 | — | 8 | 1 | no | — |
| 405 | C2×C32 | C2×#120 | 1 | 1 | yes | characteristic |
| 406 | C2×C32 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 407 | C2×C32 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 408 | C3⋊D3 | — | 2 | 2 | no | — |
| 409 | C3⋊D3 | — | 2 | 2 | no | — |
| 410 | C3×D3 | — | 4 | 8 | no | — |
| 411 | C24 | — | 6 | 2 | no | — |
| 412 | C24 | — | 9 | 1 | no | — |
| 413 | C24 | — | 18 | 2 | no | — |
| 414 | C24 | — | 18 | 2 | no | — |
| 415 | C24 | — | 18 | 8 | no | — |
| 416 | C24 | — | 36 | 4 | no | — |
| 417 | C24 | — | 36 | 4 | no | — |
| 418 | #41 | — | 18 | 4 | no | — |
| 419 | C2×Q8 | — | 9 | 1 | no | — |
| 420 | C2×D4 | — | 2 | 1 | no | — |
| 421 | C2×D4 | — | 3 | 4 | no | — |
| 422 | C2×D4 | — | 6 | 8 | no | — |
| 423 | C2×D4 | — | 6 | 2 | no | — |
| 424 | C2×D4 | — | 9 | 8 | no | — |
| 425 | C2×D4 | — | 18 | 4 | no | — |
| 426 | C2×D4 | — | 18 | 2 | no | — |
| 427 | C2×D4 | — | 18 | 2 | no | — |
| 428 | C2×D4 | — | 18 | 8 | no | — |
| 429 | C2×D4 | — | 18 | 8 | no | — |
| 430 | C2×D4 | — | 18 | 8 | no | — |
| 431 | C2×D4 | — | 18 | 8 | no | — |
| 432 | C2×D4 | — | 18 | 1 | no | — |
| 433 | C2×D4 | — | 18 | 1 | no | — |
| 434 | C2×D4 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 435 | C22×C4 | — | 9 | 1 | no | — |
| 436 | C22×C4 | — | 9 | 1 | no | — |
| 437 | C22×C4 | — | 9 | 1 | no | — |
| 438 | C22×C4 | — | 9 | 1 | no | — |
| 439 | C22×C4 | — | 9 | 1 | no | — |
| 440 | C22×C4 | — | 18 | 4 | no | — |
| 441 | C22×C4 | — | 18 | 1 | no | — |
| 442 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 443 | SD16 | — | 18 | 8 | no | — |
| 444 | D8 | — | 6 | 8 | no | — |
| 445 | M16 | — | 18 | 4 | no | — |
| 446 | C2×C8 | — | 3 | 4 | no | — |
| 447 | C4⋊C4 | — | 9 | 1 | no | — |
| 448 | C4⋊C4 | — | 18 | 1 | no | — |
| 449 | C4⋊C4 | — | 18 | 1 | no | — |
| 450 | C4⋊C4 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 451 | C22⋊C4 | — | 2 | 1 | no | — |
| 452 | C22⋊C4 | — | 18 | 1 | no | — |
| 453 | C22⋊C4 | — | 18 | 1 | no | — |
| 454 | C22⋊C4 | — | 18 | 1 | no | — |
| 455 | C22⋊C4 | — | 18 | 1 | no | — |
| 456 | C42 | — | 18 | 1 | no | — |
| 457 | C22×C3 | — | 2 | 2 | no | — |
| 458 | C22×C3 | — | 2 | 2 | no | — |
| 459 | C22×C3 | — | 2 | 1 | no | — |
| 460 | C22×C3 | — | 2 | 2 | no | — |
| 461 | C22×C3 | — | 4 | 1 | no | — |
| 462 | C22×C3 | — | 4 | 1 | no | — |
| 463 | C22×C3 | — | 4 | 2 | no | — |
| 464 | C22×C3 | — | 4 | 2 | no | — |
| 465 | C22×C3 | — | 4 | 2 | no | — |
| 466 | C22×C3 | — | 4 | 2 | no | — |
| 467 | C22×C3 | — | 4 | 2 | no | — |
| 468 | C22×C3 | — | 4 | 2 | no | — |
| 469 | C22×C3 | — | 6 | 8 | no | — |
| 470 | C22×C3 | — | 12 | 16 | no | — |
| 471 | C22×C3 | — | 12 | 4 | no | — |
| 472 | C22×C3 | — | 12 | 4 | no | — |
| 473 | C22×C3 | #911 | 1 | 4 | yes | complemented |
| 474 | C22×C3 | C2×D3×D4 | 1 | 2 | yes | — |
| 475 | C2×D3 | — | 2 | 8 | no | — |
| 476 | C2×D3 | — | 3 | 4 | no | — |
| 477 | C2×D3 | — | 3 | 4 | no | — |
| 478 | C2×D3 | — | 4 | 16 | no | — |
| 479 | C2×D3 | — | 4 | 4 | no | — |
| 480 | C2×D3 | — | 4 | 4 | no | — |
| 481 | C2×D3 | — | 6 | 2 | no | — |
| 482 | C2×D3 | — | 6 | 2 | no | — |
| 483 | C2×D3 | — | 6 | 16 | no | — |
| 484 | C2×D3 | — | 6 | 2 | no | — |
| 485 | C2×D3 | — | 6 | 2 | no | — |
| 486 | C2×D3 | — | 6 | 2 | no | — |
| 487 | C2×D3 | — | 6 | 2 | no | — |
| 488 | C2×D3 | — | 12 | 1 | no | — |
| 489 | C2×D3 | — | 12 | 1 | no | — |
| 490 | C2×D3 | — | 12 | 1 | no | — |
| 491 | C2×D3 | — | 12 | 1 | no | — |
| 492 | C2×D3 | — | 12 | 8 | no | — |
| 493 | C2×D3 | — | 12 | 32 | no | — |
| 494 | C2×D3 | — | 12 | 32 | no | — |
| 495 | C3×C4 | — | 2 | 2 | no | — |
| 496 | C3×C4 | — | 2 | 2 | no | — |
| 497 | C3×C4 | — | 4 | 1 | no | — |
| 498 | C3×C4 | — | 4 | 2 | no | — |
| 499 | C3×C4 | — | 4 | 2 | no | — |
| 500 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 501 | Dic3 | — | 3 | 4 | no | — |
| 502 | Dic3 | — | 6 | 2 | no | — |
| 503 | Dic3 | — | 6 | 2 | no | — |
| 504 | Dic3 | — | 12 | 1 | no | — |
| 505 | Dic3 | — | 12 | 2 | no | — |
| 506 | Dic3 | — | 12 | 2 | no | — |
| 507 | Dic3 | — | 12 | 2 | no | — |
| 508 | Dic3 | — | 12 | 2 | no | — |
| 509 | C32 | #3003 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 510 | C23 | — | 2 | 1 | no | — |
| 511 | C23 | — | 6 | 8 | no | — |
| 512 | C23 | — | 6 | 4 | no | — |
| 513 | C23 | — | 9 | 1 | no | — |
| 514 | C23 | — | 9 | 1 | no | — |
| 515 | C23 | — | 12 | 4 | no | — |
| 516 | C23 | — | 12 | 4 | no | — |
| 517 | C23 | — | 18 | 2 | no | — |
| 518 | C23 | — | 18 | 2 | no | — |
| 519 | C23 | — | 18 | 8 | no | — |
| 520 | C23 | — | 18 | 8 | no | — |
| 521 | C23 | — | 18 | 2 | no | — |
| 522 | C23 | — | 36 | 4 | no | — |
| 523 | C23 | — | 36 | 32 | no | — |
| 524 | C23 | — | 36 | 4 | no | — |
| 525 | C23 | — | 36 | 4 | no | — |
| 526 | C23 | — | 36 | 4 | no | — |
| 527 | C23 | #3811 | 1 | 1 | yes | characteristic |
| 528 | Q8 | — | 18 | 2 | no | — |
| 529 | D4 | — | 2 | 2 | no | — |
| 530 | D4 | — | 3 | 8 | no | — |
| 531 | D4 | — | 4 | 2 | no | — |
| 532 | D4 | — | 6 | 8 | no | — |
| 533 | D4 | — | 6 | 4 | no | — |
| 534 | D4 | — | 18 | 8 | no | — |
| 535 | D4 | — | 18 | 8 | no | — |
| 536 | D4 | — | 36 | 2 | no | — |
| 537 | D4 | — | 36 | 2 | no | — |
| 538 | C2×C4 | — | 2 | 2 | no | — |
| 539 | C2×C4 | — | 2 | 1 | no | — |
| 540 | C2×C4 | — | 9 | 1 | no | — |
| 541 | C2×C4 | — | 9 | 4 | no | — |
| 542 | C2×C4 | — | 9 | 1 | no | — |
| 543 | C2×C4 | — | 18 | 2 | no | — |
| 544 | C2×C4 | — | 18 | 2 | no | — |
| 545 | C2×C4 | — | 18 | 2 | no | — |
| 546 | C2×C4 | — | 18 | 2 | no | — |
| 547 | C2×C4 | — | 18 | 1 | no | — |
| 548 | C2×C4 | — | 18 | 1 | no | — |
| 549 | C2×C4 | — | 36 | 2 | no | — |
| 550 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 551 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 552 | C8 | — | 6 | 4 | no | — |
| 553 | C2×C3 | — | 2 | 4 | no | — |
| 554 | C2×C3 | — | 2 | 1 | no | — |
| 555 | C2×C3 | — | 2 | 1 | no | — |
| 556 | C2×C3 | — | 2 | 1 | no | — |
| 557 | C2×C3 | — | 4 | 2 | no | — |
| 558 | C2×C3 | — | 8 | 2 | no | — |
| 559 | C2×C3 | — | 8 | 2 | no | — |
| 560 | C2×C3 | — | 12 | 8 | no | — |
| 561 | C2×C3 | D3×#120 | 1 | 2 | yes | — |
| 562 | C2×C3 | C2×#911 | 1 | 2 | yes | — |
| 563 | C2×C3 | D3×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 564 | D3 | — | 4 | 8 | no | — |
| 565 | D3 | — | 6 | 4 | no | — |
| 566 | D3 | — | 6 | 4 | no | — |
| 567 | D3 | — | 12 | 2 | no | — |
| 568 | D3 | — | 12 | 2 | no | — |
| 569 | C22 | — | 2 | 1 | no | — |
| 570 | C22 | — | 2 | 1 | no | — |
| 571 | C22 | — | 4 | 1 | no | — |
| 572 | C22 | — | 4 | 1 | no | — |
| 573 | C22 | — | 4 | 1 | no | — |
| 574 | C22 | — | 6 | 8 | no | — |
| 575 | C22 | — | 9 | 2 | no | — |
| 576 | C22 | — | 9 | 2 | no | — |
| 577 | C22 | — | 12 | 16 | no | — |
| 578 | C22 | — | 12 | 4 | no | — |
| 579 | C22 | — | 12 | 4 | no | — |
| 580 | C22 | — | 18 | 8 | no | — |
| 581 | C22 | — | 18 | 1 | no | — |
| 582 | C22 | — | 18 | 1 | no | — |
| 583 | C22 | — | 18 | 1 | no | — |
| 584 | C22 | — | 18 | 1 | no | — |
| 585 | C22 | — | 36 | 16 | no | — |
| 586 | C22 | — | 36 | 16 | no | — |
| 587 | C22 | #63927 | 1 | 2 | yes | complemented |
| 588 | C22 | C2×#3811 | 1 | 1 | yes | characteristic |
| 589 | C4 | — | 2 | 1 | no | — |
| 590 | C4 | — | 4 | 1 | no | — |
| 591 | C4 | — | 9 | 2 | no | — |
| 592 | C4 | — | 18 | 1 | no | — |
| 593 | C4 | — | 36 | 1 | no | — |
| 594 | C4 | — | 36 | 1 | no | — |
| 595 | C4 | D32×D4 | 1 | 2 | yes | — |
| 596 | C3 | — | 2 | 1 | no | — |
| 597 | C3 | #80002 | 1 | 2 | yes | complemented |
| 598 | C2 | — | 2 | 2 | no | — |
| 599 | C2 | — | 8 | 1 | no | — |
| 600 | C2 | — | 12 | 8 | no | — |
| 601 | C2 | — | 18 | 2 | no | — |
| 602 | C2 | — | 18 | 2 | no | — |
| 603 | C2 | C2×#63927 | 1 | 1 | yes | characteristic |
| 604 | C2 | #10595278 | 1 | 1 | yes | characteristic |
| 605 | C2 | #10595458 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#3802 | C2 | semidirect |
| 2. #10596077 | C2 | semidirect |
| 3. C2×#63927 | C2 | semidirect |
| 4. C3×#5036 | C2 | semidirect |
| 5. #10591516 | C2 | semidirect |
| 6. #10591172 | C2 | semidirect |
| 7. #10591159 | C2 | semidirect |
| 8. #10590597 | C2 | semidirect |
| 9. #10590594 | C2 | semidirect |
| 12. C2×#3830 | C22 | semidirect |
| 21. C32×#121 | C22 | semidirect |
| 22. #64147 | C22 | semidirect |
| 25. #64133 | C22 | semidirect |
| 26. #64106 | C22 | semidirect |
| 27. #64101 | C22 | semidirect |
| 30. C2×C3×#213 | C22 | semidirect |
| 32. C2×#3716 | C22 | semidirect |
| 33. C2×#3712 | C22 | semidirect |
| 34. C3×#830 | C22 | semidirect |
| 35. C3×#809 | C22 | semidirect |
| 36. #63563 | C22 | semidirect |
| 37. #63557 | C22 | semidirect |
| 45. #5036 | D3 | semidirect |
| 58. C2×C32×D4 | C23 | semidirect |
| 70. C2×#634 | C23 | semidirect |
| 81. #3802 | D4 | semidirect |
| 82. C32×C4⋊C4 | C23 | semidirect |
| 89. C4⋊(C3⋊Dic3) | C23 | semidirect |
| 93. C2×C3×C3⋊C8 | C23 | semidirect |
| 112. C3×#121 | C2×D3 | semidirect |
| 120. C2×#213 | C2×D3 | semidirect |
| 137. #830 | C2×D3 | semidirect |
| 140. #809 | C2×D3 | semidirect |
| 208. C2×C3×D4 | C22×D3 | semidirect |
| 248. C3×C4⋊C4 | C22×D3 | semidirect |
| 269. C2×C3⋊C8 | C22×D3 | semidirect |
| 277. C22×C32 | AGL(1,ℤ/8) | semidirect |
| 285. C2×C3⋊D3 | AGL(1,ℤ/8) | semidirect |
| 317. #121 | D32 | semidirect |
| 434. C2×D4 | C2×D32 | semidirect |
| 450. C4⋊C4 | C2×D32 | semidirect |
| 473. C22×C3 | #911 | semidirect |
| 509. C32 | #3003 | semidirect |
| 587. C22 | #63927 | semidirect |
| 597. C3 | #80002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3802 | 2 |
| #10596077 | 2 |
| C2×#63927 | 2 |
| C3×#5036 | 2 |
| #10591516 | 2 |
| #10591172 | 2 |
| #10591159 | 2 |
| #10590597 | 2 |
| #10590594 | 2 |
| #80002 | 3 |