Finite Group DatabasebetaFinite Group DatabasebetaOrder 2304.
1511 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 1511 conjugacy classes of subgroups — too many to draw. Only its 170 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×#10596408 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#10596416 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C2×D4×AGL(1,𝔽9) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11824520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11824465 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11791996 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #11791470 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #11791443 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C4×AGL(1,𝔽9)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C23×AGL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 11 | C22×AΓL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 12 | C22×AΓL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 13 | C2×D4×#157 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C22⋊PSU(3,𝔽2) | C22 | 1 | 4 | yes | — |
| 15 | C2×C4⋊PSU(3,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#64242 | C22 | 1 | 4 | yes | — |
| 17 | C2×#64231 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C22⋊AGL(1,𝔽9) | C22 | 1 | 2 | yes | — |
| 19 | D4×AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 20 | C2×C4⋊AGL(1,𝔽9) | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4×AGL(1,𝔽9) | C22 | 1 | 1 | yes | characteristic |
| 22 | #10596416 | — | 2 | 16 | no | — |
| 23 | C2×AGL(1,𝔽9)⋊C4 | C22 | 1 | 2 | yes | — |
| 24 | C2×PSU(3,𝔽2)⋊C4 | C22 | 1 | 4 | yes | — |
| 25 | C2×GO+(4,𝔽2)⋊C4 | C22 | 1 | 4 | yes | — |
| 26 | #10596408 | — | 2 | 4 | no | — |
| 27 | #10595300 | — | 2 | 1 | no | — |
| 28 | #10593827 | — | 2 | 1 | no | — |
| 29 | #10593566 | — | 2 | 2 | no | — |
| 30 | #10593553 | — | 2 | 1 | no | — |
| 31 | C4×#3777 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10593530 | — | 2 | 2 | no | — |
| 33 | C4×#3773 | C22 | 1 | 1 | yes | characteristic |
| 34 | #10593405 | — | 2 | 1 | no | — |
| 35 | #10593166 | C22 | 1 | 2 | yes | — |
| 36 | C23×#157 | C23 | 1 | 2 | yes | — |
| 37 | C22×PSU(3,𝔽2) | C23 | 1 | 2 | yes | — |
| 38 | C22×GO+(4,𝔽2) | — | 2 | 1 | no | — |
| 39 | C22×GO+(4,𝔽2) | C23 | 1 | 2 | yes | — |
| 40 | C22×AGL(1,𝔽9) | — | 2 | 8 | no | — |
| 41 | C22×AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 42 | C22×AGL(1,𝔽9) | C23 | 1 | 2 | yes | — |
| 43 | C22×AGL(1,𝔽9) | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×AGL(1,𝔽9) | C23 | 1 | 1 | yes | characteristic |
| 45 | C2×AΓL(1,𝔽9) | — | 2 | 4 | no | — |
| 46 | C2×AΓL(1,𝔽9) | — | 2 | 4 | no | — |
| 47 | C2×AΓL(1,𝔽9) | — | 2 | 8 | no | — |
| 48 | C2×AΓL(1,𝔽9) | — | 4 | 4 | no | — |
| 49 | C2×D4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#3811 | — | 2 | 4 | no | — |
| 51 | C2×#3802 | — | 2 | 1 | no | — |
| 52 | C2×C22⋊#157 | — | 2 | 4 | no | — |
| 53 | C2×C22⋊#157 | D4 | 1 | 2 | yes | — |
| 54 | D4×#157 | — | 2 | 2 | no | — |
| 55 | D4×#157 | — | 2 | 2 | no | — |
| 56 | C2×C4⋊#157 | — | 2 | 1 | no | — |
| 57 | C2×C4⋊#157 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×C4×#157 | — | 2 | 1 | no | — |
| 59 | C2×C4×#157 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22⋊PSU(3,𝔽2) | — | 2 | 8 | no | — |
| 61 | C22⋊PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 62 | C2×#3777 | — | 2 | 4 | no | — |
| 63 | C2×#3777 | — | 2 | 1 | no | — |
| 64 | C2×#3777 | C23 | 1 | 2 | yes | — |
| 65 | C4⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 66 | C4⋊PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 67 | #64242 | — | 2 | 8 | no | — |
| 68 | #64242 | — | 4 | 4 | no | — |
| 69 | C2×#3773 | C23 | 1 | 2 | yes | — |
| 70 | C2×D32⋊C4 | — | 2 | 4 | no | — |
| 71 | #64231 | — | 2 | 2 | no | — |
| 72 | #64231 | — | 2 | 2 | no | — |
| 73 | C22⋊AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 74 | C4⋊AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 75 | C4×AGL(1,𝔽9) | D4 | 1 | 4 | yes | complemented |
| 76 | AGL(1,𝔽9)⋊C4 | D4 | 1 | 8 | yes | complemented |
| 77 | PSU(3,𝔽2)⋊C4 | — | 2 | 8 | no | — |
| 78 | GO+(4,𝔽2)⋊C4 | — | 2 | 8 | no | — |
| 79 | C3×#940 | — | 4 | 1 | no | — |
| 80 | #63979 | — | 4 | 2 | no | — |
| 81 | #63911 | — | 4 | 1 | no | — |
| 82 | C4×#624 | — | 2 | 1 | no | — |
| 83 | #63747 | — | 2 | 1 | no | — |
| 84 | #63737 | — | 2 | 1 | no | — |
| 85 | #28482 | — | 9 | 1 | no | maximal, Sylow |
| 86 | D3×#127 | — | 12 | 1 | no | — |
| 87 | C23×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 88 | C22×D32 | — | 2 | 2 | no | — |
| 89 | C22×#157 | — | 2 | 2 | no | — |
| 90 | C22×#157 | — | 2 | 2 | no | — |
| 91 | C22×#157 | — | 2 | 4 | no | — |
| 92 | C22×#157 | — | 2 | 2 | no | — |
| 93 | C22×#157 | — | 2 | 4 | no | — |
| 94 | C22×#157 | — | 2 | 2 | no | — |
| 95 | C22×#157 | C2×D4 | 1 | 2 | yes | — |
| 96 | C22×#157 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×#157 | C24 | 1 | 1 | yes | characteristic |
| 98 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 99 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 100 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 101 | C2×PSU(3,𝔽2) | — | 2 | 4 | no | — |
| 102 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 103 | C2×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 104 | C2×GO+(4,𝔽2) | — | 2 | 2 | no | — |
| 105 | C2×GO+(4,𝔽2) | — | 2 | 4 | no | — |
| 106 | C2×GO+(4,𝔽2) | — | 4 | 2 | no | — |
| 107 | C2×GO+(4,𝔽2) | — | 8 | 2 | no | — |
| 108 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 109 | C2×AGL(1,𝔽9) | — | 2 | 4 | no | — |
| 110 | C2×AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 111 | C2×AGL(1,𝔽9) | — | 4 | 8 | no | — |
| 112 | C2×AGL(1,𝔽9) | C2×D4 | 1 | 2 | yes | — |
| 113 | C2×AGL(1,𝔽9) | C2×D4 | 1 | 4 | yes | — |
| 114 | C2×AGL(1,𝔽9) | C2×D4 | 1 | 2 | yes | — |
| 115 | AΓL(1,𝔽9) | — | 4 | 8 | no | — |
| 116 | AΓL(1,𝔽9) | — | 4 | 8 | no | — |
| 117 | C2×C32×D4 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 118 | C2×#638 | SD16 | 1 | 2 | yes | complemented |
| 119 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 120 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 121 | C2×C4⋊(C3⋊D3) | SD16 | 1 | 1 | yes | characteristic, complemented |
| 122 | C2×C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C3×#67 | — | 4 | 4 | no | — |
| 124 | C2×C3×D12 | — | 4 | 1 | no | — |
| 125 | #3811 | — | 4 | 8 | no | — |
| 126 | #3811 | — | 8 | 4 | no | — |
| 127 | C2×#626 | — | 4 | 4 | no | — |
| 128 | C2×#625 | — | 4 | 1 | no | — |
| 129 | C2×#624 | — | 2 | 2 | no | — |
| 130 | #3802 | — | 4 | 2 | no | — |
| 131 | #3802 | — | 4 | 2 | no | — |
| 132 | C22⋊#157 | — | 2 | 4 | no | — |
| 133 | C22⋊#157 | — | 4 | 8 | no | — |
| 134 | C4⋊#157 | — | 2 | 2 | no | — |
| 135 | C4⋊#157 | — | 4 | 2 | no | — |
| 136 | C4×#157 | — | 4 | 2 | no | — |
| 137 | C4×#157 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4×#157 | #41 | 1 | 2 | yes | — |
| 139 | #3777 | — | 2 | 2 | no | — |
| 140 | #3777 | — | 4 | 8 | no | — |
| 141 | #3777 | — | 4 | 2 | no | — |
| 142 | #3777 | C2×D4 | 1 | 4 | yes | — |
| 143 | #3773 | — | 2 | 2 | no | — |
| 144 | #3773 | C2×D4 | 1 | 4 | yes | — |
| 145 | D32⋊C4 | — | 4 | 8 | no | — |
| 146 | C3×C4×Dic3 | — | 4 | 1 | no | — |
| 147 | Dic32 | — | 4 | 1 | no | — |
| 148 | C2×#492 | — | 9 | 1 | no | — |
| 149 | C2×#465 | — | 9 | 4 | no | — |
| 150 | C2×C8×D4 | — | 9 | 1 | no | — |
| 151 | #2542 | — | 9 | 1 | no | — |
| 152 | #2541 | — | 9 | 1 | no | — |
| 153 | #2000 | — | 9 | 4 | no | — |
| 154 | #1982 | — | 9 | 1 | no | — |
| 155 | #1981 | — | 9 | 1 | no | — |
| 156 | C4×#106 | — | 9 | 1 | no | — |
| 157 | C2×D3×D4 | — | 12 | 1 | no | — |
| 158 | C2×D3×D4 | — | 12 | 1 | no | — |
| 159 | C2×D3×D4 | — | 12 | 4 | no | — |
| 160 | C3×#127 | — | 12 | 1 | no | — |
| 161 | #940 | — | 4 | 1 | no | — |
| 162 | #940 | — | 12 | 1 | no | — |
| 163 | #940 | — | 12 | 4 | no | — |
| 164 | #874 | — | 12 | 1 | no | — |
| 165 | C42×D3 | — | 12 | 1 | no | — |
| 166 | C23×C32 | C2×SD16 | 1 | 2 | yes | — |
| 167 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 168 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 169 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 170 | C22×C3⋊D3 | — | 2 | 4 | no | — |
| 171 | C22×C3⋊D3 | C2×SD16 | 1 | 2 | yes | — |
| 172 | C22×C3⋊D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 173 | C22×C3×D3 | — | 4 | 2 | no | — |
| 174 | C2×D32 | — | 4 | 2 | no | — |
| 175 | C2×D32 | — | 4 | 4 | no | — |
| 176 | C2×D32 | — | 4 | 2 | no | — |
| 177 | C2×D32 | — | 4 | 4 | no | — |
| 178 | C2×#157 | — | 2 | 2 | no | — |
| 179 | C2×#157 | — | 2 | 2 | no | — |
| 180 | C2×#157 | — | 2 | 4 | no | — |
| 181 | C2×#157 | — | 2 | 4 | no | — |
| 182 | C2×#157 | — | 4 | 2 | no | — |
| 183 | C2×#157 | — | 4 | 2 | no | — |
| 184 | C2×#157 | — | 4 | 2 | no | — |
| 185 | C2×#157 | — | 4 | 2 | no | — |
| 186 | C2×#157 | — | 4 | 4 | no | — |
| 187 | C2×#157 | — | 4 | 2 | no | — |
| 188 | C2×#157 | — | 4 | 4 | no | — |
| 189 | C2×#157 | #121 | 1 | 2 | yes | — |
| 190 | C2×#157 | C22×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×#157 | C22×D4 | 1 | 2 | yes | — |
| 192 | C2×#157 | C2×#41 | 1 | 1 | yes | characteristic |
| 193 | C2×#157 | H(5,𝔽2) | 1 | 2 | yes | — |
| 194 | PSU(3,𝔽2) | — | 4 | 2 | no | — |
| 195 | PSU(3,𝔽2) | — | 4 | 2 | no | — |
| 196 | PSU(3,𝔽2) | — | 4 | 4 | no | — |
| 197 | GO+(4,𝔽2) | — | 4 | 2 | no | — |
| 198 | GO+(4,𝔽2) | — | 4 | 2 | no | — |
| 199 | GO+(4,𝔽2) | — | 4 | 4 | no | — |
| 200 | GO+(4,𝔽2) | — | 8 | 4 | no | — |
| 201 | AGL(1,𝔽9) | — | 2 | 2 | no | — |
| 202 | AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 203 | AGL(1,𝔽9) | #127 | 1 | 4 | yes | complemented |
| 204 | C32×D4 | — | 2 | 2 | no | — |
| 205 | C2×C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 206 | #638 | — | 2 | 4 | no | — |
| 207 | C2×C3⋊Dic3 | C2×SD16 | 1 | 1 | yes | characteristic |
| 208 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 209 | C4×C3⋊D3 | #121 | 1 | 2 | yes | — |
| 210 | C4×C3⋊D3 | #135 | 1 | 2 | yes | — |
| 211 | C3×#67 | — | 8 | 8 | no | — |
| 212 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 213 | C3×D12 | — | 8 | 2 | no | — |
| 214 | #626 | — | 8 | 8 | no | — |
| 215 | #625 | — | 8 | 2 | no | — |
| 216 | #624 | — | 2 | 4 | no | — |
| 217 | #624 | — | 4 | 2 | no | — |
| 218 | C22×SD16 | — | 9 | 2 | no | — |
| 219 | C22×SD16 | — | 9 | 2 | no | — |
| 220 | C23×C8 | — | 9 | 2 | no | — |
| 221 | C2×C4⋊Q8 | — | 9 | 1 | no | — |
| 222 | C2×#127 | — | 9 | 1 | no | — |
| 223 | C2×#127 | — | 18 | 1 | no | — |
| 224 | C2×C22⋊Q8 | — | 9 | 4 | no | — |
| 225 | C2×#121 | — | 9 | 4 | no | — |
| 226 | C2×C4×D4 | — | 9 | 1 | no | — |
| 227 | #492 | — | 18 | 4 | no | — |
| 228 | #465 | — | 18 | 16 | no | — |
| 229 | C8×D4 | — | 18 | 4 | no | — |
| 230 | C2×#106 | — | 9 | 2 | no | — |
| 231 | C2×C4⋊C8 | — | 9 | 1 | no | — |
| 232 | C2×#103 | — | 9 | 4 | no | — |
| 233 | C2×#102 | — | 9 | 4 | no | — |
| 234 | C2×C22⋊C8 | — | 9 | 2 | no | — |
| 235 | C2×C4×C8 | — | 9 | 1 | no | — |
| 236 | #399 | — | 18 | 2 | no | — |
| 237 | #392 | — | 18 | 2 | no | — |
| 238 | #390 | — | 18 | 1 | no | — |
| 239 | #390 | — | 18 | 1 | no | — |
| 240 | #384 | — | 18 | 1 | no | — |
| 241 | C4×C4⋊C4 | — | 9 | 1 | no | — |
| 242 | C4×C4⋊C4 | — | 9 | 1 | no | — |
| 243 | #340 | — | 9 | 2 | no | — |
| 244 | C23×D3 | — | 12 | 2 | no | — |
| 245 | C23×D3 | — | 12 | 2 | no | — |
| 246 | C2×C3×D4 | — | 4 | 1 | no | — |
| 247 | C2×C3×D4 | — | 12 | 1 | no | — |
| 248 | C2×C3×D4 | — | 12 | 4 | no | — |
| 249 | C2×#67 | — | 4 | 4 | no | — |
| 250 | C2×#67 | — | 12 | 2 | no | — |
| 251 | C2×#67 | — | 12 | 4 | no | — |
| 252 | C2×#67 | — | 12 | 2 | no | — |
| 253 | D3×D4 | — | 24 | 2 | no | — |
| 254 | D3×D4 | — | 24 | 2 | no | — |
| 255 | D3×D4 | — | 24 | 2 | no | — |
| 256 | D3×D4 | — | 24 | 2 | no | — |
| 257 | D3×D4 | — | 24 | 8 | no | — |
| 258 | D3×D4 | — | 24 | 8 | no | — |
| 259 | C2×D12 | — | 4 | 1 | no | — |
| 260 | C2×D12 | — | 12 | 1 | no | — |
| 261 | C2×D12 | — | 12 | 4 | no | — |
| 262 | C2×C4×D3 | — | 12 | 1 | no | — |
| 263 | C2×C4×D3 | — | 12 | 2 | no | — |
| 264 | C3×C42 | — | 12 | 1 | no | — |
| 265 | C4×Dic3 | — | 4 | 1 | no | — |
| 266 | C4×Dic3 | — | 12 | 2 | no | — |
| 267 | C22×C32 | — | 2 | 4 | no | — |
| 268 | C22×C32 | — | 2 | 2 | no | — |
| 269 | C22×C32 | C22×SD16 | 1 | 1 | yes | characteristic |
| 270 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 271 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 272 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 273 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 274 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 275 | C2×C3⋊D3 | C2×#121 | 1 | 1 | yes | characteristic |
| 276 | C2×C3⋊D3 | D42 | 1 | 2 | yes | — |
| 277 | C2×C3⋊D3 | C2×#135 | 1 | 1 | yes | characteristic |
| 278 | C2×C3⋊D3 | #577 | 1 | 2 | yes | — |
| 279 | C2×C3×D3 | — | 8 | 4 | no | — |
| 280 | C2×C3×D3 | — | 8 | 2 | no | — |
| 281 | D32 | — | 8 | 4 | no | — |
| 282 | D32 | — | 8 | 2 | no | — |
| 283 | D32 | — | 8 | 2 | no | — |
| 284 | #157 | — | 2 | 2 | no | — |
| 285 | #157 | — | 4 | 4 | no | — |
| 286 | #157 | — | 4 | 2 | no | — |
| 287 | #157 | — | 8 | 2 | no | — |
| 288 | #157 | C2×#127 | 1 | 1 | yes | characteristic |
| 289 | #157 | #535 | 1 | 1 | yes | characteristic |
| 290 | #157 | #550 | 1 | 2 | yes | — |
| 291 | C32×C4 | #465 | 1 | 2 | yes | complemented |
| 292 | C3⋊Dic3 | #465 | 1 | 2 | yes | complemented |
| 293 | C3×Dic3 | — | 4 | 4 | no | — |
| 294 | C22×Q8 | — | 9 | 2 | no | — |
| 295 | C22×D4 | — | 9 | 1 | no | — |
| 296 | C22×D4 | — | 9 | 2 | no | — |
| 297 | C22×D4 | — | 18 | 1 | no | — |
| 298 | C22×D4 | — | 18 | 1 | no | — |
| 299 | C22×D4 | — | 18 | 4 | no | — |
| 300 | C23×C4 | — | 9 | 2 | no | — |
| 301 | C2×SD16 | — | 18 | 8 | no | — |
| 302 | C2×SD16 | — | 18 | 4 | no | — |
| 303 | C2×SD16 | — | 18 | 4 | no | — |
| 304 | C2×SD16 | — | 36 | 4 | no | — |
| 305 | C22×C8 | — | 9 | 1 | no | — |
| 306 | C22×C8 | — | 9 | 1 | no | — |
| 307 | C22×C8 | — | 9 | 2 | no | — |
| 308 | C22×C8 | — | 18 | 4 | no | — |
| 309 | C22×C8 | — | 18 | 8 | no | — |
| 310 | C4⋊Q8 | — | 18 | 2 | no | — |
| 311 | C4⋊Q8 | — | 18 | 2 | no | — |
| 312 | #127 | — | 12 | 1 | no | — |
| 313 | #127 | — | 18 | 2 | no | — |
| 314 | #127 | — | 18 | 2 | no | — |
| 315 | #127 | — | 36 | 1 | no | — |
| 316 | #127 | — | 36 | 2 | no | — |
| 317 | C22⋊Q8 | — | 18 | 8 | no | — |
| 318 | C22⋊Q8 | — | 36 | 4 | no | — |
| 319 | #121 | — | 18 | 8 | no | — |
| 320 | #121 | — | 36 | 4 | no | — |
| 321 | C4×D4 | — | 18 | 2 | no | — |
| 322 | C4×D4 | — | 18 | 2 | no | — |
| 323 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 324 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 325 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 326 | C2×C4⋊C4 | — | 18 | 4 | no | — |
| 327 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 328 | C2×C4⋊C4 | — | 18 | 1 | no | — |
| 329 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 330 | C2×C22⋊C4 | — | 18 | 4 | no | — |
| 331 | C2×C22⋊C4 | — | 18 | 4 | no | — |
| 332 | C2×C42 | — | 9 | 1 | no | — |
| 333 | C2×C42 | — | 18 | 1 | no | — |
| 334 | C2×C42 | — | 18 | 1 | no | — |
| 335 | #106 | — | 9 | 8 | no | — |
| 336 | C4⋊C8 | — | 18 | 2 | no | — |
| 337 | #103 | — | 18 | 8 | no | — |
| 338 | #102 | — | 18 | 8 | no | — |
| 339 | C22⋊C8 | — | 18 | 4 | no | — |
| 340 | C4×C8 | — | 9 | 4 | no | — |
| 341 | #95 | — | 18 | 1 | no | — |
| 342 | #95 | — | 18 | 1 | no | — |
| 343 | C23×C3 | — | 4 | 2 | no | — |
| 344 | C23×C3 | — | 12 | 2 | no | — |
| 345 | C22×D3 | — | 4 | 2 | no | — |
| 346 | C22×D3 | — | 12 | 1 | no | — |
| 347 | C22×D3 | — | 12 | 2 | no | — |
| 348 | C22×D3 | — | 24 | 2 | no | — |
| 349 | C22×D3 | — | 24 | 4 | no | — |
| 350 | C22×D3 | — | 24 | 2 | no | — |
| 351 | C22×D3 | — | 24 | 4 | no | — |
| 352 | C22×D3 | — | 24 | 4 | no | — |
| 353 | C22×D3 | — | 24 | 2 | no | — |
| 354 | C22×D3 | — | 24 | 2 | no | — |
| 355 | C22×D3 | — | 24 | 4 | no | — |
| 356 | C3×D4 | — | 8 | 2 | no | — |
| 357 | C3×D4 | — | 24 | 2 | no | — |
| 358 | C3×D4 | — | 24 | 8 | no | — |
| 359 | C2×C3×C4 | — | 4 | 1 | no | — |
| 360 | C2×C3×C4 | — | 12 | 2 | no | — |
| 361 | #67 | — | 8 | 8 | no | — |
| 362 | #67 | — | 24 | 4 | no | — |
| 363 | #67 | — | 24 | 8 | no | — |
| 364 | #67 | — | 24 | 4 | no | — |
| 365 | C2×Dic3 | — | 4 | 2 | no | — |
| 366 | C2×Dic3 | — | 12 | 1 | no | — |
| 367 | D12 | — | 8 | 2 | no | — |
| 368 | D12 | — | 24 | 2 | no | — |
| 369 | D12 | — | 24 | 8 | no | — |
| 370 | C4×D3 | — | 12 | 2 | no | — |
| 371 | C4×D3 | — | 12 | 2 | no | — |
| 372 | C4×D3 | — | 12 | 4 | no | — |
| 373 | C4×D3 | — | 12 | 4 | no | — |
| 374 | C2×C32 | — | 4 | 2 | no | — |
| 375 | C2×C32 | C2×#465 | 1 | 1 | yes | characteristic |
| 376 | C2×C32 | D4×SD16 | 1 | 2 | yes | — |
| 377 | C3⋊D3 | — | 4 | 2 | no | — |
| 378 | C3⋊D3 | #2541 | 1 | 1 | yes | characteristic |
| 379 | C3⋊D3 | #3057 | 1 | 1 | yes | characteristic |
| 380 | C3⋊D3 | #3284 | 1 | 2 | yes | — |
| 381 | C3×D3 | — | 16 | 2 | no | — |
| 382 | C24 | — | 9 | 2 | no | — |
| 383 | C24 | — | 18 | 2 | no | — |
| 384 | C2×Q8 | — | 18 | 4 | no | — |
| 385 | C2×Q8 | — | 18 | 4 | no | — |
| 386 | C2×Q8 | — | 18 | 2 | no | — |
| 387 | C2×Q8 | — | 18 | 2 | no | — |
| 388 | C2×D4 | — | 9 | 2 | no | — |
| 389 | C2×D4 | — | 9 | 1 | no | — |
| 390 | C2×D4 | — | 12 | 4 | no | — |
| 391 | C2×D4 | — | 12 | 1 | no | — |
| 392 | C2×D4 | — | 18 | 2 | no | — |
| 393 | C2×D4 | — | 18 | 2 | no | — |
| 394 | C2×D4 | — | 18 | 4 | no | — |
| 395 | C2×D4 | — | 18 | 4 | no | — |
| 396 | C2×D4 | — | 18 | 2 | no | — |
| 397 | C2×D4 | — | 18 | 2 | no | — |
| 398 | C2×D4 | — | 36 | 2 | no | — |
| 399 | C2×D4 | — | 36 | 2 | no | — |
| 400 | C2×D4 | — | 36 | 1 | no | — |
| 401 | C2×D4 | — | 36 | 2 | no | — |
| 402 | C2×D4 | — | 36 | 4 | no | — |
| 403 | C2×D4 | — | 36 | 8 | no | — |
| 404 | C2×D4 | — | 72 | 2 | no | — |
| 405 | C2×D4 | — | 72 | 4 | no | — |
| 406 | C2×D4 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 407 | C22×C4 | — | 9 | 1 | no | — |
| 408 | C22×C4 | — | 9 | 1 | no | — |
| 409 | C22×C4 | — | 9 | 1 | no | — |
| 410 | C22×C4 | — | 9 | 2 | no | — |
| 411 | C22×C4 | — | 18 | 2 | no | — |
| 412 | C22×C4 | — | 18 | 2 | no | — |
| 413 | C22×C4 | — | 18 | 4 | no | — |
| 414 | C22×C4 | — | 18 | 4 | no | — |
| 415 | C22×C4 | — | 18 | 2 | no | — |
| 416 | C22×C4 | — | 18 | 2 | no | — |
| 417 | C22×C4 | — | 18 | 2 | no | — |
| 418 | SD16 | — | 36 | 8 | no | — |
| 419 | SD16 | — | 36 | 8 | no | — |
| 420 | C2×C8 | — | 9 | 2 | no | — |
| 421 | C2×C8 | — | 9 | 4 | no | — |
| 422 | C2×C8 | — | 9 | 2 | no | — |
| 423 | C2×C8 | — | 18 | 2 | no | — |
| 424 | C2×C8 | — | 18 | 2 | no | — |
| 425 | C2×C8 | — | 18 | 4 | no | — |
| 426 | C2×C8 | — | 36 | 8 | no | — |
| 427 | C4⋊C4 | — | 9 | 4 | no | — |
| 428 | C4⋊C4 | — | 9 | 4 | no | — |
| 429 | C4⋊C4 | — | 18 | 2 | no | — |
| 430 | C4⋊C4 | — | 18 | 2 | no | — |
| 431 | C4⋊C4 | — | 18 | 2 | no | — |
| 432 | C4⋊C4 | — | 36 | 2 | no | — |
| 433 | C4⋊C4 | — | 36 | 2 | no | — |
| 434 | C4⋊C4 | — | 36 | 8 | no | — |
| 435 | C22⋊C4 | — | 18 | 4 | no | — |
| 436 | C22⋊C4 | — | 36 | 8 | no | — |
| 437 | C22⋊C4 | — | 36 | 8 | no | — |
| 438 | C42 | — | 9 | 2 | no | — |
| 439 | C42 | — | 9 | 2 | no | — |
| 440 | C42 | — | 12 | 1 | no | — |
| 441 | C42 | — | 36 | 1 | no | — |
| 442 | C42 | — | 36 | 2 | no | — |
| 443 | C22×C3 | — | 4 | 1 | no | — |
| 444 | C22×C3 | — | 8 | 4 | no | — |
| 445 | C22×C3 | — | 8 | 2 | no | — |
| 446 | C22×C3 | — | 24 | 2 | no | — |
| 447 | C22×C3 | — | 24 | 4 | no | — |
| 448 | C2×D3 | — | 8 | 2 | no | — |
| 449 | C2×D3 | — | 8 | 4 | no | — |
| 450 | C2×D3 | — | 12 | 1 | no | — |
| 451 | C2×D3 | — | 12 | 2 | no | — |
| 452 | C2×D3 | — | 12 | 1 | no | — |
| 453 | C2×D3 | — | 12 | 2 | no | — |
| 454 | C2×D3 | — | 24 | 2 | no | — |
| 455 | C2×D3 | — | 24 | 4 | no | — |
| 456 | C2×D3 | — | 48 | 2 | no | — |
| 457 | C2×D3 | — | 48 | 4 | no | — |
| 458 | C2×D3 | — | 48 | 2 | no | — |
| 459 | C2×D3 | — | 48 | 2 | no | — |
| 460 | C2×D3 | — | 48 | 2 | no | — |
| 461 | C2×D3 | — | 48 | 4 | no | — |
| 462 | C3×C4 | — | 4 | 2 | no | — |
| 463 | C3×C4 | — | 12 | 4 | no | — |
| 464 | Dic3 | — | 4 | 4 | no | — |
| 465 | Dic3 | — | 12 | 2 | no | — |
| 466 | C32 | #28482 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 467 | C23 | — | 9 | 1 | no | — |
| 468 | C23 | — | 9 | 2 | no | — |
| 469 | C23 | — | 12 | 2 | no | — |
| 470 | C23 | — | 18 | 2 | no | — |
| 471 | C23 | — | 18 | 4 | no | — |
| 472 | C23 | — | 18 | 2 | no | — |
| 473 | C23 | — | 18 | 4 | no | — |
| 474 | C23 | — | 36 | 4 | no | — |
| 475 | C23 | — | 36 | 2 | no | — |
| 476 | C23 | — | 36 | 2 | no | — |
| 477 | C23 | — | 36 | 4 | no | — |
| 478 | C23 | C2×AΓL(1,𝔽9) | 1 | 2 | yes | — |
| 479 | Q8 | — | 36 | 2 | no | — |
| 480 | Q8 | — | 36 | 2 | no | — |
| 481 | Q8 | — | 36 | 4 | no | — |
| 482 | D4 | — | 2 | 2 | no | — |
| 483 | D4 | — | 18 | 4 | no | — |
| 484 | D4 | — | 18 | 2 | no | — |
| 485 | D4 | — | 24 | 8 | no | — |
| 486 | D4 | — | 24 | 2 | no | — |
| 487 | D4 | — | 36 | 2 | no | — |
| 488 | D4 | — | 36 | 2 | no | — |
| 489 | D4 | — | 36 | 4 | no | — |
| 490 | D4 | — | 72 | 2 | no | — |
| 491 | D4 | — | 72 | 8 | no | — |
| 492 | D4 | — | 72 | 4 | no | — |
| 493 | C2×C4 | — | 9 | 1 | no | — |
| 494 | C2×C4 | — | 9 | 1 | no | — |
| 495 | C2×C4 | — | 9 | 2 | no | — |
| 496 | C2×C4 | — | 9 | 2 | no | — |
| 497 | C2×C4 | — | 9 | 1 | no | — |
| 498 | C2×C4 | — | 9 | 2 | no | — |
| 499 | C2×C4 | — | 9 | 2 | no | — |
| 500 | C2×C4 | — | 9 | 2 | no | — |
| 501 | C2×C4 | — | 12 | 2 | no | — |
| 502 | C2×C4 | — | 18 | 4 | no | — |
| 503 | C2×C4 | — | 18 | 2 | no | — |
| 504 | C2×C4 | — | 18 | 2 | no | — |
| 505 | C2×C4 | — | 18 | 4 | no | — |
| 506 | C2×C4 | — | 18 | 4 | no | — |
| 507 | C2×C4 | — | 36 | 2 | no | — |
| 508 | C2×C4 | — | 36 | 2 | no | — |
| 509 | C2×C4 | — | 36 | 4 | no | — |
| 510 | C2×C4 | — | 36 | 2 | no | — |
| 511 | C2×C4 | — | 36 | 2 | no | — |
| 512 | C2×C4 | — | 36 | 2 | no | — |
| 513 | C2×C4 | — | 36 | 4 | no | — |
| 514 | C2×C4 | — | 36 | 2 | no | — |
| 515 | C2×C4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 516 | C8 | — | 9 | 4 | no | — |
| 517 | C8 | — | 18 | 2 | no | — |
| 518 | C8 | — | 36 | 2 | no | — |
| 519 | C2×C3 | — | 4 | 1 | no | — |
| 520 | C2×C3 | — | 4 | 2 | no | — |
| 521 | C2×C3 | — | 16 | 2 | no | — |
| 522 | C2×C3 | — | 48 | 2 | no | — |
| 523 | D3 | — | 12 | 2 | no | — |
| 524 | D3 | — | 12 | 1 | no | — |
| 525 | D3 | — | 12 | 1 | no | — |
| 526 | D3 | — | 16 | 2 | no | — |
| 527 | D3 | — | 48 | 2 | no | — |
| 528 | C22 | — | 2 | 2 | no | — |
| 529 | C22 | — | 2 | 4 | no | — |
| 530 | C22 | — | 9 | 1 | no | — |
| 531 | C22 | — | 9 | 1 | no | — |
| 532 | C22 | — | 9 | 2 | no | — |
| 533 | C22 | — | 9 | 2 | no | — |
| 534 | C22 | — | 18 | 2 | no | — |
| 535 | C22 | — | 18 | 4 | no | — |
| 536 | C22 | — | 24 | 2 | no | — |
| 537 | C22 | — | 24 | 4 | no | — |
| 538 | C22 | — | 36 | 2 | no | — |
| 539 | C22 | — | 36 | 2 | no | — |
| 540 | C22 | — | 36 | 4 | no | — |
| 541 | C22 | — | 72 | 2 | no | — |
| 542 | C22 | — | 72 | 2 | no | — |
| 543 | C22 | — | 72 | 4 | no | — |
| 544 | C22 | C22×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 545 | C4 | — | 9 | 1 | no | — |
| 546 | C4 | — | 9 | 1 | no | — |
| 547 | C4 | — | 9 | 2 | no | — |
| 548 | C4 | — | 9 | 2 | no | — |
| 549 | C4 | — | 12 | 4 | no | — |
| 550 | C4 | — | 18 | 2 | no | — |
| 551 | C4 | — | 36 | 2 | no | — |
| 552 | C4 | — | 36 | 4 | no | — |
| 553 | C4 | — | 72 | 2 | no | — |
| 554 | C4 | #10596416 | 1 | 2 | yes | complemented |
| 555 | C3 | — | 4 | 1 | no | — |
| 556 | C2 | — | 4 | 2 | no | — |
| 557 | C2 | — | 9 | 1 | no | — |
| 558 | C2 | — | 9 | 1 | no | — |
| 559 | C2 | — | 9 | 2 | no | — |
| 560 | C2 | — | 36 | 2 | no | — |
| 561 | C2 | — | 48 | 2 | no | — |
| 562 | C2 | C2×#10596416 | 1 | 1 | yes | characteristic |
| 563 | C2 | D4×AΓL(1,𝔽9) | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10596408 | C2 | semidirect |
| 2. C2×#10596416 | C2 | semidirect |
| 3. C2×D4×AGL(1,𝔽9) | C2 | semidirect |
| 4. #11824520 | C2 | semidirect |
| 6. #11791996 | C2 | semidirect |
| 7. #11791470 | C2 | semidirect |
| 8. #11791443 | C2 | semidirect |
| 9. C4×AGL(1,𝔽9)⋊C4 | C2 | semidirect |
| 75. C4×AGL(1,𝔽9) | D4 | semidirect |
| 76. AGL(1,𝔽9)⋊C4 | D4 | semidirect |
| 117. C2×C32×D4 | SD16 | semidirect |
| 118. C2×#638 | SD16 | semidirect |
| 121. C2×C4⋊(C3⋊D3) | SD16 | semidirect |
| 203. AGL(1,𝔽9) | #127 | semidirect |
| 291. C32×C4 | #465 | semidirect |
| 292. C3⋊Dic3 | #465 | semidirect |
| 406. C2×D4 | AΓL(1,𝔽9) | semidirect |
| 466. C32 | #28482 | semidirect |
| 554. C4 | #10596416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596408 | 2 |
| C2×#10596416 | 2 |
| C2×D4×AGL(1,𝔽9) | 2 |
| #11824520 | 2 |
| #11824465 | 2 |
| #11791996 | 2 |
| #11791470 | 2 |
| #11791443 | 2 |
| C4×AGL(1,𝔽9)⋊C4 | 2 |
| #28482 | 9 |