Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1111 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1111 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 | #11722520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | SD16×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64123⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11721233 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11721200 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11720849 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11720838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D3×#914 | — | 3 | 2 | no | maximal |
| 13 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 14 | Q8×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | D4×#272 | C22 | 1 | 1 | yes | characteristic |
| 16 | #88722 | C22 | 1 | 2 | yes | complemented |
| 17 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 18 | #88677 | — | 2 | 1 | no | — |
| 19 | #88676 | — | 2 | 2 | no | — |
| 20 | #88655 | — | 2 | 1 | no | — |
| 21 | #88655 | C22 | 1 | 1 | yes | characteristic |
| 22 | #88655 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #88654 | C22 | 1 | 2 | yes | complemented |
| 24 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 25 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 26 | #88648 | — | 2 | 2 | no | — |
| 27 | #88648 | C22 | 1 | 2 | yes | complemented |
| 28 | SD16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #88549 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #88546 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #88528 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C8×#272 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #3755⋊C3 | C22 | 1 | 2 | yes | complemented |
| 34 | #3753⋊C3 | C22 | 1 | 2 | yes | complemented |
| 35 | #3745⋊C3 | C22 | 1 | 2 | yes | complemented |
| 36 | #3743⋊C3 | C22 | 1 | 2 | yes | complemented |
| 37 | #88438 | C22 | 1 | 2 | yes | complemented |
| 38 | #88436 | C22 | 1 | 2 | yes | complemented |
| 39 | #88434 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #88432 | C22 | 1 | 2 | yes | complemented |
| 41 | #88430 | C22 | 1 | 2 | yes | complemented |
| 42 | D3×#239 | — | 3 | 2 | no | — |
| 43 | D32×D4 | — | 3 | 2 | no | — |
| 44 | #64123 | D3 | 1 | 2 | yes | complemented |
| 45 | C3×#914 | — | 3 | 2 | no | — |
| 46 | C3×D3×SD16 | — | 3 | 2 | no | — |
| 47 | C3×D3×SD16 | — | 6 | 1 | no | — |
| 48 | #63941 | — | 3 | 2 | no | — |
| 49 | #63939 | — | 3 | 2 | no | — |
| 50 | D3×#215 | — | 3 | 2 | no | — |
| 51 | #63937 | — | 3 | 2 | no | — |
| 52 | #63934 | — | 3 | 2 | no | — |
| 53 | D3×#213 | — | 3 | 2 | no | — |
| 54 | #63798 | — | 3 | 2 | no | — |
| 55 | #63794 | — | 3 | 2 | no | — |
| 56 | D3×D24 | — | 3 | 2 | no | — |
| 57 | D3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 58 | C22×#272 | — | 2 | 1 | no | — |
| 59 | C22×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 60 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 61 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 62 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 63 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 64 | C2×((C3⋊D3)⋊C3)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 65 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 66 | D4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 67 | #6235 | — | 2 | 1 | no | — |
| 68 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 69 | C4×#272 | — | 2 | 1 | no | — |
| 70 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 71 | #6229 | — | 2 | 1 | no | — |
| 72 | #6229 | C23 | 1 | 1 | yes | characteristic, complemented |
| 73 | #638⋊C3 | — | 2 | 2 | no | — |
| 74 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 2 | no | — |
| 75 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 76 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | complemented |
| 77 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 78 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 2 | yes | — |
| 79 | #6200 | — | 2 | 2 | no | — |
| 80 | #6199 | D4 | 1 | 1 | yes | characteristic |
| 81 | #6198 | — | 2 | 2 | no | — |
| 82 | #6198 | — | 2 | 1 | no | — |
| 83 | #6198 | — | 2 | 1 | no | — |
| 84 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 85 | ((C3⋊D3)⋊C3)⋊C4 | D4 | 1 | 2 | yes | — |
| 86 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic, complemented |
| 87 | #6180 | C23 | 1 | 1 | yes | characteristic, complemented |
| 88 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | complemented |
| 89 | D3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 90 | C2×#914 | — | 9 | 1 | no | — |
| 91 | C22×D32 | — | 6 | 2 | no | — |
| 92 | #3832 | C2×D3 | 1 | 2 | yes | complemented |
| 93 | D4×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 94 | C3×#239 | — | 3 | 2 | no | — |
| 95 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 96 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 97 | C3×D3×D4 | — | 3 | 2 | no | — |
| 98 | C3×D3×D4 | — | 3 | 2 | no | — |
| 99 | C3×D3×D4 | — | 6 | 1 | no | — |
| 100 | #3811 | — | 6 | 2 | no | — |
| 101 | D3×#67 | — | 6 | 2 | no | — |
| 102 | D3×#67 | — | 6 | 2 | no | — |
| 103 | #3802 | — | 3 | 2 | no | — |
| 104 | D3×D12 | — | 3 | 2 | no | — |
| 105 | D3×D12 | — | 3 | 2 | no | — |
| 106 | D3×D12 | — | 3 | 2 | no | — |
| 107 | D3×D12 | — | 6 | 2 | no | — |
| 108 | C4×D32 | — | 3 | 2 | no | — |
| 109 | C4×D32 | — | 6 | 2 | no | — |
| 110 | #3799 | — | 3 | 2 | no | — |
| 111 | #3799 | — | 6 | 2 | no | — |
| 112 | #3796 | — | 3 | 2 | no | — |
| 113 | #3796 | — | 6 | 2 | no | — |
| 114 | C32×SD16 | — | 2 | 1 | no | — |
| 115 | C32×SD16 | C2×D3 | 1 | 2 | yes | complemented |
| 116 | #3755 | C2×D3 | 1 | 2 | yes | complemented |
| 117 | #3753 | C2×D3 | 1 | 2 | yes | complemented |
| 118 | #3745 | C2×D3 | 1 | 2 | yes | complemented |
| 119 | #3743 | C2×D3 | 1 | 2 | yes | complemented |
| 120 | C3×#215 | — | 3 | 2 | no | — |
| 121 | C3×#215 | — | 3 | 2 | no | — |
| 122 | C3×#215 | — | 6 | 1 | no | — |
| 123 | C3×#214 | — | 3 | 2 | no | — |
| 124 | C3×#214 | — | 6 | 1 | no | — |
| 125 | C3×#213 | — | 3 | 2 | no | — |
| 126 | C3×D24 | — | 3 | 2 | no | — |
| 127 | C3×#204 | — | 3 | 2 | no | — |
| 128 | C3×#204 | — | 6 | 1 | no | — |
| 129 | C3×ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 130 | C3×D3×C8 | — | 3 | 2 | no | — |
| 131 | C3×D3×C8 | — | 6 | 1 | no | — |
| 132 | #3717 | — | 3 | 2 | no | — |
| 133 | #3715 | — | 3 | 2 | no | — |
| 134 | #3714 | — | 3 | 2 | no | — |
| 135 | #3714 | — | 3 | 2 | no | — |
| 136 | #3714 | — | 3 | 2 | no | — |
| 137 | #3713 | — | 3 | 2 | no | — |
| 138 | #3712 | — | 3 | 2 | no | — |
| 139 | #3711 | — | 3 | 2 | no | — |
| 140 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 141 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 142 | C2×#272 | — | 2 | 1 | no | — |
| 143 | C2×#272 | — | 4 | 2 | no | — |
| 144 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 146 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 147 | C2×(C3⋊D3)⋊C3 | — | 4 | 4 | no | — |
| 148 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 149 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 2 | no | — |
| 150 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 4 | no | — |
| 151 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 152 | ((C3⋊D3)⋊C3)⋊C2 | — | 4 | 2 | no | — |
| 153 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 154 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 155 | #1084 | — | 2 | 1 | no | — |
| 156 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 158 | D3×#41 | — | 9 | 2 | no | — |
| 159 | C2×#239 | — | 9 | 1 | no | — |
| 160 | C2×D3×D4 | — | 9 | 1 | no | — |
| 161 | C2×D3×D4 | — | 9 | 2 | no | — |
| 162 | C3×AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 163 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 164 | #949 | — | 9 | 2 | no | — |
| 165 | C2×#215 | — | 9 | 1 | no | — |
| 166 | #932 | — | 9 | 2 | no | — |
| 167 | C2×#213 | — | 9 | 1 | no | — |
| 168 | #914 | — | 3 | 2 | no | — |
| 169 | #914 | — | 9 | 2 | no | — |
| 170 | #914 | — | 9 | 2 | no | — |
| 171 | #914 | — | 9 | 2 | no | — |
| 172 | #914 | — | 9 | 2 | no | — |
| 173 | #914 | — | 9 | 2 | no | — |
| 174 | D3×SD16 | — | 3 | 2 | no | — |
| 175 | D3×SD16 | — | 6 | 1 | no | — |
| 176 | D3×SD16 | — | 9 | 2 | no | — |
| 177 | #911 | — | 9 | 2 | no | — |
| 178 | #911 | — | 9 | 2 | no | — |
| 179 | D3×D8 | — | 9 | 2 | no | — |
| 180 | D3×D8 | — | 9 | 2 | no | — |
| 181 | #908 | — | 9 | 2 | no | — |
| 182 | D3×M16 | — | 9 | 2 | no | — |
| 183 | C2×D24 | — | 9 | 1 | no | — |
| 184 | C2×ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 185 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 186 | C22×C3×D3 | — | 6 | 2 | no | — |
| 187 | C22×C3×D3 | — | 6 | 2 | no | — |
| 188 | C22×C3×D3 | — | 12 | 1 | no | — |
| 189 | C2×D32 | — | 3 | 2 | no | — |
| 190 | C2×D32 | — | 6 | 2 | no | — |
| 191 | C2×D32 | — | 6 | 2 | no | — |
| 192 | C2×D32 | — | 6 | 2 | no | — |
| 193 | C2×D32 | — | 6 | 2 | no | — |
| 194 | C2×D32 | — | 12 | 8 | no | — |
| 195 | C32×Q8 | — | 2 | 1 | no | — |
| 196 | C32×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 197 | C32×D4 | — | 2 | 1 | no | — |
| 198 | C32×D4 | C22×D3 | 1 | 2 | yes | — |
| 199 | #638 | — | 2 | 2 | no | — |
| 200 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 201 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 202 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | complemented |
| 203 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 204 | C4×C3⋊D3 | C22×D3 | 1 | 2 | yes | — |
| 205 | C3×#67 | — | 6 | 2 | no | — |
| 206 | C3×#67 | — | 6 | 2 | no | — |
| 207 | C3×#67 | — | 12 | 1 | no | — |
| 208 | C3×D12 | — | 3 | 2 | no | — |
| 209 | C3×D12 | — | 3 | 2 | no | — |
| 210 | C3×D12 | — | 3 | 2 | no | — |
| 211 | C3×D12 | — | 6 | 1 | no | — |
| 212 | C3×D12 | — | 6 | 2 | no | — |
| 213 | C3×C4×D3 | — | 3 | 2 | no | — |
| 214 | C3×C4×D3 | — | 3 | 2 | no | — |
| 215 | C3×C4×D3 | — | 6 | 1 | no | — |
| 216 | C3×C4×D3 | — | 6 | 2 | no | — |
| 217 | C3×C4×D3 | — | 6 | 2 | no | — |
| 218 | C3×C4×D3 | — | 12 | 1 | no | — |
| 219 | C3×Dic6 | — | 3 | 2 | no | — |
| 220 | C3×Dic6 | — | 6 | 1 | no | — |
| 221 | C3×Dic6 | — | 6 | 2 | no | — |
| 222 | C3×Dic6 | — | 12 | 1 | no | — |
| 223 | #626 | — | 6 | 2 | no | — |
| 224 | #626 | — | 6 | 2 | no | — |
| 225 | #626 | — | 6 | 2 | no | — |
| 226 | #626 | — | 6 | 2 | no | — |
| 227 | #626 | — | 6 | 2 | no | — |
| 228 | #625 | — | 6 | 2 | no | — |
| 229 | #624 | — | 3 | 2 | no | — |
| 230 | #624 | — | 6 | 2 | no | — |
| 231 | D3×Dic3 | — | 3 | 2 | no | — |
| 232 | D3×Dic3 | — | 3 | 2 | no | — |
| 233 | D3×Dic3 | — | 6 | 2 | no | — |
| 234 | C32×C8 | — | 2 | 1 | no | — |
| 235 | C32×C8 | C22×D3 | 1 | 2 | yes | complemented |
| 236 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | complemented |
| 237 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 238 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 239 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 240 | C2×AGL(1,ℤ/8) | — | 27 | 1 | no | Sylow |
| 241 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 242 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 243 | #272 | — | 4 | 1 | no | — |
| 244 | #272 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 245 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 246 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 247 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 248 | C23×D3 | — | 18 | 1 | no | — |
| 249 | C23×D3 | — | 18 | 2 | no | — |
| 250 | C3×#41 | — | 9 | 2 | no | — |
| 251 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 252 | C2×C3×D4 | — | 9 | 2 | no | — |
| 253 | C2×C3×D4 | — | 9 | 1 | no | — |
| 254 | C2×#67 | — | 18 | 1 | no | — |
| 255 | C2×#67 | — | 18 | 2 | no | — |
| 256 | #239 | — | 3 | 2 | no | — |
| 257 | #239 | — | 9 | 2 | no | — |
| 258 | #239 | — | 9 | 2 | no | — |
| 259 | #239 | — | 18 | 2 | no | — |
| 260 | D3×Q8 | — | 3 | 2 | no | — |
| 261 | D3×Q8 | — | 6 | 1 | no | — |
| 262 | #237 | — | 9 | 2 | no | — |
| 263 | #237 | — | 18 | 2 | no | — |
| 264 | D3×D4 | — | 3 | 2 | no | — |
| 265 | D3×D4 | — | 3 | 2 | no | — |
| 266 | D3×D4 | — | 6 | 1 | no | — |
| 267 | D3×D4 | — | 9 | 2 | no | — |
| 268 | D3×D4 | — | 9 | 2 | no | — |
| 269 | D3×D4 | — | 9 | 2 | no | — |
| 270 | D3×D4 | — | 9 | 2 | no | — |
| 271 | D3×D4 | — | 9 | 2 | no | — |
| 272 | D3×D4 | — | 18 | 2 | no | — |
| 273 | D3×D4 | — | 18 | 2 | no | — |
| 274 | D3×D4 | — | 18 | 2 | no | — |
| 275 | D3×D4 | — | 18 | 2 | no | — |
| 276 | #235 | — | 9 | 2 | no | — |
| 277 | #235 | — | 18 | 2 | no | — |
| 278 | C2×D12 | — | 9 | 1 | no | — |
| 279 | C2×D12 | — | 9 | 1 | no | — |
| 280 | C2×D12 | — | 9 | 2 | no | — |
| 281 | C2×D12 | — | 18 | 1 | no | — |
| 282 | C2×C4×D3 | — | 9 | 1 | no | — |
| 283 | C2×C4×D3 | — | 9 | 2 | no | — |
| 284 | C2×C4×D3 | — | 18 | 1 | no | — |
| 285 | C2×C4×D3 | — | 18 | 2 | no | — |
| 286 | C3×SD16 | — | 3 | 2 | no | — |
| 287 | C3×SD16 | — | 6 | 1 | no | — |
| 288 | C3×SD16 | — | 9 | 2 | no | — |
| 289 | C3×SD16 | — | 9 | 1 | no | — |
| 290 | C3×SD16 | — | 9 | 1 | no | — |
| 291 | C3×SD16 | — | 9 | 1 | no | — |
| 292 | C3×SD16 | D32 | 1 | 1 | yes | characteristic |
| 293 | C3×D8 | — | 9 | 2 | no | — |
| 294 | C3×D8 | — | 9 | 2 | no | — |
| 295 | C3×M16 | — | 9 | 2 | no | — |
| 296 | C2×C3×C8 | — | 9 | 1 | no | — |
| 297 | #215 | — | 3 | 2 | no | — |
| 298 | #215 | — | 3 | 2 | no | — |
| 299 | #215 | — | 6 | 1 | no | — |
| 300 | #215 | — | 9 | 2 | no | — |
| 301 | #215 | — | 9 | 2 | no | — |
| 302 | #214 | — | 3 | 2 | no | — |
| 303 | #214 | — | 6 | 1 | no | — |
| 304 | #214 | — | 9 | 2 | no | — |
| 305 | #213 | — | 3 | 2 | no | — |
| 306 | #213 | — | 9 | 2 | no | — |
| 307 | #213 | — | 9 | 2 | no | — |
| 308 | #213 | — | 9 | 2 | no | — |
| 309 | #213 | — | 9 | 2 | no | — |
| 310 | #213 | — | 9 | 2 | no | — |
| 311 | #208 | — | 9 | 2 | no | — |
| 312 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 313 | D24 | — | 3 | 2 | no | — |
| 314 | D24 | — | 9 | 2 | no | — |
| 315 | D24 | — | 9 | 2 | no | — |
| 316 | D24 | — | 9 | 2 | no | — |
| 317 | #204 | — | 3 | 2 | no | — |
| 318 | #204 | — | 6 | 1 | no | — |
| 319 | #204 | — | 9 | 2 | no | — |
| 320 | ΓL(1,𝔽25) | — | 3 | 2 | no | — |
| 321 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 322 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 323 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 324 | D3×C8 | — | 3 | 2 | no | — |
| 325 | D3×C8 | — | 6 | 1 | no | — |
| 326 | D3×C8 | — | 9 | 2 | no | — |
| 327 | C22×C32 | — | 2 | 2 | no | — |
| 328 | C22×C32 | — | 4 | 1 | no | — |
| 329 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 330 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 331 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 332 | C2×C3⋊D3 | D3×D4 | 1 | 2 | yes | — |
| 333 | C2×C3×D3 | — | 3 | 2 | no | — |
| 334 | C2×C3×D3 | — | 3 | 2 | no | — |
| 335 | C2×C3×D3 | — | 6 | 1 | no | — |
| 336 | C2×C3×D3 | — | 6 | 2 | no | — |
| 337 | C2×C3×D3 | — | 6 | 2 | no | — |
| 338 | C2×C3×D3 | — | 6 | 2 | no | — |
| 339 | C2×C3×D3 | — | 12 | 1 | no | — |
| 340 | C2×C3×D3 | — | 12 | 4 | no | — |
| 341 | C2×C3×D3 | — | 12 | 4 | no | — |
| 342 | C2×C3×D3 | — | 24 | 2 | no | — |
| 343 | D32 | — | 6 | 4 | no | — |
| 344 | D32 | — | 12 | 4 | no | — |
| 345 | D32 | — | 12 | 4 | no | — |
| 346 | D32 | — | 12 | 4 | no | — |
| 347 | D32 | — | 12 | 4 | no | — |
| 348 | C32×C4 | — | 2 | 2 | no | — |
| 349 | C32×C4 | — | 2 | 1 | no | — |
| 350 | C32×C4 | — | 4 | 1 | no | — |
| 351 | C32×C4 | C23×D3 | 1 | 2 | yes | — |
| 352 | C3⋊Dic3 | D3×D4 | 1 | 2 | yes | — |
| 353 | C3×Dic3 | — | 3 | 2 | no | — |
| 354 | C3×Dic3 | — | 3 | 2 | no | — |
| 355 | C3×Dic3 | — | 6 | 1 | no | — |
| 356 | C3×Dic3 | — | 6 | 2 | no | — |
| 357 | C3×Dic3 | — | 12 | 1 | no | — |
| 358 | C2×#41 | — | 27 | 1 | no | — |
| 359 | C22×D4 | — | 27 | 1 | no | — |
| 360 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 361 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 362 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 363 | AGL(1,ℤ/8) | — | 27 | 2 | no | — |
| 364 | C2×SD16 | — | 9 | 1 | no | — |
| 365 | C2×SD16 | — | 27 | 1 | no | — |
| 366 | C2×D8 | — | 27 | 1 | no | — |
| 367 | C2×D8 | — | 27 | 1 | no | — |
| 368 | C2×M16 | — | 27 | 1 | no | — |
| 369 | H(3,𝔽3) | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 370 | C23×C3 | — | 18 | 1 | no | — |
| 371 | C23×C3 | — | 18 | 2 | no | — |
| 372 | C22×D3 | — | 6 | 2 | no | — |
| 373 | C22×D3 | — | 6 | 2 | no | — |
| 374 | C22×D3 | — | 9 | 1 | no | — |
| 375 | C22×D3 | — | 9 | 2 | no | — |
| 376 | C22×D3 | — | 12 | 1 | no | — |
| 377 | C22×D3 | — | 18 | 2 | no | — |
| 378 | C22×D3 | — | 18 | 2 | no | — |
| 379 | C22×D3 | — | 18 | 2 | no | — |
| 380 | C22×D3 | — | 18 | 2 | no | — |
| 381 | C22×D3 | — | 18 | 1 | no | — |
| 382 | C22×D3 | — | 18 | 1 | no | — |
| 383 | C22×D3 | — | 18 | 2 | no | — |
| 384 | C22×D3 | — | 18 | 2 | no | — |
| 385 | C22×D3 | — | 36 | 4 | no | — |
| 386 | C22×D3 | — | 36 | 8 | no | — |
| 387 | C3×Q8 | — | 3 | 2 | no | — |
| 388 | C3×Q8 | — | 6 | 1 | no | — |
| 389 | C3×Q8 | — | 9 | 1 | no | — |
| 390 | C3×Q8 | — | 18 | 1 | no | — |
| 391 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 392 | C3×D4 | — | 3 | 2 | no | — |
| 393 | C3×D4 | — | 6 | 1 | no | — |
| 394 | C3×D4 | — | 9 | 2 | no | — |
| 395 | C3×D4 | — | 9 | 2 | no | — |
| 396 | C3×D4 | — | 9 | 1 | no | — |
| 397 | C3×D4 | — | 18 | 2 | no | — |
| 398 | C3×D4 | — | 18 | 1 | no | — |
| 399 | C3×D4 | — | 18 | 2 | no | — |
| 400 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 401 | C2×C3×C4 | — | 9 | 2 | no | — |
| 402 | C2×C3×C4 | — | 9 | 1 | no | — |
| 403 | C2×C3×C4 | — | 18 | 1 | no | — |
| 404 | C2×C3×C4 | — | 18 | 2 | no | — |
| 405 | #67 | — | 6 | 2 | no | — |
| 406 | #67 | — | 6 | 2 | no | — |
| 407 | #67 | — | 12 | 1 | no | — |
| 408 | #67 | — | 18 | 2 | no | — |
| 409 | #67 | — | 18 | 2 | no | — |
| 410 | #67 | — | 18 | 2 | no | — |
| 411 | #67 | — | 18 | 2 | no | — |
| 412 | #67 | — | 18 | 2 | no | — |
| 413 | #67 | — | 18 | 2 | no | — |
| 414 | #67 | — | 18 | 2 | no | — |
| 415 | C2×Dic3 | — | 9 | 1 | no | — |
| 416 | C2×Dic3 | — | 9 | 2 | no | — |
| 417 | C2×Dic3 | — | 18 | 2 | no | — |
| 418 | D12 | — | 3 | 2 | no | — |
| 419 | D12 | — | 3 | 2 | no | — |
| 420 | D12 | — | 3 | 2 | no | — |
| 421 | D12 | — | 6 | 1 | no | — |
| 422 | D12 | — | 6 | 2 | no | — |
| 423 | D12 | — | 9 | 2 | no | — |
| 424 | D12 | — | 9 | 2 | no | — |
| 425 | D12 | — | 18 | 2 | no | — |
| 426 | D12 | — | 18 | 1 | no | — |
| 427 | D12 | — | 18 | 1 | no | — |
| 428 | D12 | — | 18 | 2 | no | — |
| 429 | D12 | — | 18 | 2 | no | — |
| 430 | C4×D3 | — | 3 | 2 | no | — |
| 431 | C4×D3 | — | 3 | 2 | no | — |
| 432 | C4×D3 | — | 6 | 1 | no | — |
| 433 | C4×D3 | — | 6 | 2 | no | — |
| 434 | C4×D3 | — | 6 | 2 | no | — |
| 435 | C4×D3 | — | 9 | 2 | no | — |
| 436 | C4×D3 | — | 9 | 2 | no | — |
| 437 | C4×D3 | — | 9 | 2 | no | — |
| 438 | C4×D3 | — | 9 | 2 | no | — |
| 439 | C4×D3 | — | 12 | 1 | no | — |
| 440 | C4×D3 | — | 18 | 2 | no | — |
| 441 | C4×D3 | — | 18 | 2 | no | — |
| 442 | C4×D3 | — | 18 | 2 | no | — |
| 443 | Dic6 | — | 3 | 2 | no | — |
| 444 | Dic6 | — | 6 | 1 | no | — |
| 445 | Dic6 | — | 6 | 2 | no | — |
| 446 | Dic6 | — | 12 | 1 | no | — |
| 447 | C3×C8 | — | 3 | 2 | no | — |
| 448 | C3×C8 | — | 6 | 1 | no | — |
| 449 | C3×C8 | — | 9 | 2 | no | — |
| 450 | C3×C8 | — | 9 | 1 | no | — |
| 451 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 452 | C3⋊C8 | — | 3 | 2 | no | — |
| 453 | C3⋊C8 | — | 3 | 2 | no | — |
| 454 | C3⋊C8 | — | 6 | 1 | no | — |
| 455 | C3⋊C8 | — | 9 | 2 | no | — |
| 456 | C2×C32 | — | 2 | 1 | no | — |
| 457 | C2×C32 | — | 4 | 2 | no | — |
| 458 | C2×C32 | — | 8 | 1 | no | — |
| 459 | C2×C32 | C2×D3×D4 | 1 | 2 | yes | — |
| 460 | C3⋊D3 | — | 2 | 2 | no | — |
| 461 | C3⋊D3 | — | 4 | 2 | no | — |
| 462 | C3⋊D3 | — | 4 | 2 | no | — |
| 463 | C3×D3 | — | 3 | 4 | no | — |
| 464 | C3×D3 | — | 6 | 2 | no | — |
| 465 | C3×D3 | — | 6 | 2 | no | — |
| 466 | C3×D3 | — | 12 | 2 | no | — |
| 467 | C3×D3 | — | 12 | 2 | no | — |
| 468 | C3×D3 | — | 12 | 2 | no | — |
| 469 | C3×D3 | — | 24 | 1 | no | — |
| 470 | C24 | — | 54 | 1 | no | — |
| 471 | #41 | — | 9 | 2 | no | — |
| 472 | #41 | — | 27 | 2 | no | — |
| 473 | #41 | — | 54 | 2 | no | — |
| 474 | C2×Q8 | — | 9 | 1 | no | — |
| 475 | C2×D4 | — | 9 | 1 | no | — |
| 476 | C2×D4 | — | 9 | 2 | no | — |
| 477 | C2×D4 | — | 27 | 1 | no | — |
| 478 | C2×D4 | — | 27 | 1 | no | — |
| 479 | C2×D4 | — | 27 | 2 | no | — |
| 480 | C2×D4 | — | 54 | 1 | no | — |
| 481 | C2×D4 | — | 54 | 1 | no | — |
| 482 | C2×D4 | — | 54 | 2 | no | — |
| 483 | C22×C4 | — | 27 | 1 | no | — |
| 484 | C22×C4 | — | 54 | 1 | no | — |
| 485 | SD16 | — | 9 | 1 | no | — |
| 486 | SD16 | — | 9 | 2 | no | — |
| 487 | SD16 | — | 9 | 1 | no | — |
| 488 | SD16 | — | 9 | 1 | no | — |
| 489 | SD16 | — | 27 | 2 | no | — |
| 490 | SD16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 491 | D8 | — | 9 | 2 | no | — |
| 492 | D8 | — | 9 | 2 | no | — |
| 493 | D8 | — | 27 | 2 | no | — |
| 494 | D8 | — | 27 | 2 | no | — |
| 495 | M16 | — | 9 | 2 | no | — |
| 496 | M16 | — | 27 | 2 | no | — |
| 497 | C2×C8 | — | 9 | 1 | no | — |
| 498 | C2×C8 | — | 27 | 1 | no | — |
| 499 | C22×C3 | — | 2 | 1 | no | — |
| 500 | C22×C3 | — | 6 | 2 | no | — |
| 501 | C22×C3 | — | 9 | 2 | no | — |
| 502 | C22×C3 | — | 9 | 1 | no | — |
| 503 | C22×C3 | — | 12 | 1 | no | — |
| 504 | C22×C3 | — | 18 | 2 | no | — |
| 505 | C22×C3 | — | 18 | 2 | no | — |
| 506 | C22×C3 | — | 18 | 1 | no | — |
| 507 | C22×C3 | — | 36 | 2 | no | — |
| 508 | C22×C3 | — | 36 | 4 | no | — |
| 509 | C2×D3 | — | 3 | 2 | no | — |
| 510 | C2×D3 | — | 3 | 2 | no | — |
| 511 | C2×D3 | — | 6 | 1 | no | — |
| 512 | C2×D3 | — | 6 | 2 | no | — |
| 513 | C2×D3 | — | 6 | 2 | no | — |
| 514 | C2×D3 | — | 6 | 2 | no | — |
| 515 | C2×D3 | — | 9 | 2 | no | — |
| 516 | C2×D3 | — | 12 | 1 | no | — |
| 517 | C2×D3 | — | 12 | 4 | no | — |
| 518 | C2×D3 | — | 12 | 4 | no | — |
| 519 | C2×D3 | — | 18 | 2 | no | — |
| 520 | C2×D3 | — | 18 | 2 | no | — |
| 521 | C2×D3 | — | 18 | 4 | no | — |
| 522 | C2×D3 | — | 18 | 2 | no | — |
| 523 | C2×D3 | — | 24 | 2 | no | — |
| 524 | C2×D3 | — | 36 | 4 | no | — |
| 525 | C2×D3 | — | 36 | 4 | no | — |
| 526 | C2×D3 | — | 36 | 4 | no | — |
| 527 | C2×D3 | — | 36 | 4 | no | — |
| 528 | C2×D3 | — | 36 | 2 | no | — |
| 529 | C2×D3 | — | 36 | 2 | no | — |
| 530 | C2×D3 | — | 36 | 4 | no | — |
| 531 | C2×D3 | — | 36 | 4 | no | — |
| 532 | C3×C4 | — | 2 | 1 | no | — |
| 533 | C3×C4 | — | 3 | 2 | no | — |
| 534 | C3×C4 | — | 6 | 2 | no | — |
| 535 | C3×C4 | — | 6 | 1 | no | — |
| 536 | C3×C4 | — | 9 | 2 | no | — |
| 537 | C3×C4 | — | 9 | 1 | no | — |
| 538 | C3×C4 | — | 12 | 1 | no | — |
| 539 | C3×C4 | — | 18 | 1 | no | — |
| 540 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 541 | Dic3 | — | 3 | 2 | no | — |
| 542 | Dic3 | — | 3 | 2 | no | — |
| 543 | Dic3 | — | 6 | 1 | no | — |
| 544 | Dic3 | — | 6 | 2 | no | — |
| 545 | Dic3 | — | 9 | 2 | no | — |
| 546 | Dic3 | — | 12 | 1 | no | — |
| 547 | C32 | — | 2 | 1 | no | — |
| 548 | C32 | D3×AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 549 | C23 | — | 18 | 1 | no | — |
| 550 | C23 | — | 18 | 2 | no | — |
| 551 | C23 | — | 27 | 1 | no | — |
| 552 | C23 | — | 54 | 1 | no | — |
| 553 | C23 | — | 54 | 1 | no | — |
| 554 | C23 | — | 54 | 2 | no | — |
| 555 | C23 | — | 108 | 4 | no | — |
| 556 | Q8 | — | 9 | 1 | no | — |
| 557 | Q8 | — | 18 | 1 | no | — |
| 558 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 559 | D4 | — | 9 | 2 | no | — |
| 560 | D4 | — | 9 | 2 | no | — |
| 561 | D4 | — | 9 | 1 | no | — |
| 562 | D4 | — | 18 | 2 | no | — |
| 563 | D4 | — | 18 | 1 | no | — |
| 564 | D4 | — | 18 | 2 | no | — |
| 565 | D4 | — | 54 | 2 | no | — |
| 566 | D4 | — | 54 | 1 | no | — |
| 567 | D4 | — | 54 | 1 | no | — |
| 568 | D4 | — | 54 | 2 | no | — |
| 569 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 570 | C2×C4 | — | 9 | 1 | no | — |
| 571 | C2×C4 | — | 9 | 2 | no | — |
| 572 | C2×C4 | — | 18 | 2 | no | — |
| 573 | C2×C4 | — | 18 | 1 | no | — |
| 574 | C2×C4 | — | 27 | 1 | no | — |
| 575 | C2×C4 | — | 27 | 2 | no | — |
| 576 | C2×C4 | — | 54 | 2 | no | — |
| 577 | C8 | — | 9 | 1 | no | — |
| 578 | C8 | — | 9 | 2 | no | — |
| 579 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 580 | C2×C3 | — | 3 | 2 | no | — |
| 581 | C2×C3 | — | 4 | 1 | no | — |
| 582 | C2×C3 | — | 6 | 1 | no | — |
| 583 | C2×C3 | — | 9 | 2 | no | — |
| 584 | C2×C3 | — | 12 | 2 | no | — |
| 585 | C2×C3 | — | 18 | 2 | no | — |
| 586 | C2×C3 | — | 24 | 1 | no | — |
| 587 | C2×C3 | — | 36 | 2 | no | — |
| 588 | C2×C3 | — | 36 | 2 | no | — |
| 589 | C2×C3 | — | 36 | 1 | no | — |
| 590 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 591 | D3 | — | 3 | 4 | no | — |
| 592 | D3 | — | 6 | 2 | no | — |
| 593 | D3 | — | 6 | 2 | no | — |
| 594 | D3 | — | 12 | 2 | no | — |
| 595 | D3 | — | 12 | 2 | no | — |
| 596 | D3 | — | 12 | 2 | no | — |
| 597 | D3 | — | 18 | 2 | no | — |
| 598 | D3 | — | 24 | 1 | no | — |
| 599 | D3 | — | 36 | 2 | no | — |
| 600 | D3 | — | 36 | 2 | no | — |
| 601 | C22 | — | 2 | 1 | no | — |
| 602 | C22 | — | 9 | 1 | no | — |
| 603 | C22 | — | 9 | 2 | no | — |
| 604 | C22 | — | 18 | 2 | no | — |
| 605 | C22 | — | 18 | 1 | no | — |
| 606 | C22 | — | 18 | 2 | no | — |
| 607 | C22 | — | 36 | 2 | no | — |
| 608 | C22 | — | 36 | 4 | no | — |
| 609 | C22 | — | 54 | 2 | no | — |
| 610 | C22 | — | 108 | 2 | no | — |
| 611 | C22 | — | 108 | 2 | no | — |
| 612 | C22 | — | 108 | 4 | no | — |
| 613 | C4 | — | 2 | 1 | no | — |
| 614 | C4 | — | 9 | 2 | no | — |
| 615 | C4 | — | 9 | 1 | no | — |
| 616 | C4 | — | 18 | 1 | no | — |
| 617 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 618 | C3 | — | 3 | 2 | no | — |
| 619 | C3 | — | 6 | 1 | no | — |
| 620 | C3 | #10594740 | 1 | 1 | yes | characteristic |
| 621 | C2 | — | 4 | 1 | no | — |
| 622 | C2 | — | 9 | 2 | no | — |
| 623 | C2 | — | 18 | 2 | no | — |
| 624 | C2 | — | 36 | 1 | no | — |
| 625 | C2 | — | 36 | 2 | no | — |
| 626 | C2 | — | 36 | 2 | no | — |
| 627 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722520 | C2 | semidirect |
| 2. D4×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 3. SD16×#272 | C2 | semidirect |
| 4. #64123⋊C3 | C2 | semidirect |
| 5. #11721233 | C2 | semidirect |
| 6. #11721228 | C2 | semidirect |
| 7. #11721200 | C2 | semidirect |
| 8. #11721190 | C2 | semidirect |
| 9. #11720849 | C2 | semidirect |
| 10. #11720838 | C2 | semidirect |
| 11. #11720836 | C2 | semidirect |
| 14. Q8×#272 | C22 | semidirect |
| 16. #88722 | C22 | semidirect |
| 17. D4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 22. #88655 | C22 | semidirect |
| 23. #88654 | C22 | semidirect |
| 27. #88648 | C22 | semidirect |
| 28. SD16×H(3,𝔽3) | C22 | semidirect |
| 29. #88549 | C22 | semidirect |
| 30. #88546 | C22 | semidirect |
| 31. #88528 | C22 | semidirect |
| 32. C8×#272 | C22 | semidirect |
| 33. #3755⋊C3 | C22 | semidirect |
| 34. #3753⋊C3 | C22 | semidirect |
| 35. #3745⋊C3 | C22 | semidirect |
| 36. #3743⋊C3 | C22 | semidirect |
| 37. #88438 | C22 | semidirect |
| 38. #88436 | C22 | semidirect |
| 39. #88434 | C22 | semidirect |
| 40. #88432 | C22 | semidirect |
| 41. #88430 | C22 | semidirect |
| 44. #64123 | D3 | semidirect |
| 65. Q8×H(3,𝔽3) | C23 | semidirect |
| 72. #6229 | C23 | semidirect |
| 76. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 86. C8×H(3,𝔽3) | C23 | semidirect |
| 87. #6180 | C23 | semidirect |
| 88. (C3⋊(C3⋊C8))⋊C3 | C23 | semidirect |
| 92. #3832 | C2×D3 | semidirect |
| 93. D4×C3⋊D3 | C2×D3 | semidirect |
| 115. C32×SD16 | C2×D3 | semidirect |
| 116. #3755 | C2×D3 | semidirect |
| 117. #3753 | C2×D3 | semidirect |
| 118. #3745 | C2×D3 | semidirect |
| 119. #3743 | C2×D3 | semidirect |
| 196. C32×Q8 | C22×D3 | semidirect |
| 202. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 235. C32×C8 | C22×D3 | semidirect |
| 236. C3⋊(C3⋊C8) | C22×D3 | semidirect |
| 244. #272 | AGL(1,ℤ/8) | semidirect |
| 369. H(3,𝔽3) | C2×AGL(1,ℤ/8) | semidirect |
| 490. SD16 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 548. C32 | D3×AGL(1,ℤ/8) | semidirect |
| 558. Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 579. C8 | C2×((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722520 | 2 |
| D4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| SD16×#272 | 2 |
| #64123⋊C3 | 2 |
| #11721233 | 2 |
| #11721228 | 2 |
| #11721200 | 2 |
| #11721190 | 2 |
| #11720849 | 2 |
| #11720838 | 2 |
| #11720836 | 2 |
| D3×#914 | 3 |