← #72340434
Subgroups — #72340434
Order 2048.
Only the 6486 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 508 nodes (normal subgroups only) — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72340431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#418884 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #72340427 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #72340423 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #72340420 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #72340411 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C2×#356056 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72311879 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#6437630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #72310916 | C2 | 1 | 16 | yes | maximal, complemented |
| 11 | #72303769 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | C2×#10574841 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #72213423 | C2 | 1 | 16 | yes | maximal, complemented |
| 14 | C22×H(7,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#63090 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×#62852 | C22 | 1 | 2 | yes | — |
| 17 | #10575251 | C22 | 1 | 4 | yes | complemented |
| 18 | #10574916 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×#60398 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#60398 | C22 | 1 | 4 | yes | complemented |
| 21 | #10574841 | C22 | 1 | 32 | yes | complemented |
| 22 | C2×#60387 | C22 | 1 | 4 | yes | — |
| 23 | C2×#60387 | C22 | 1 | 4 | yes | — |
| 24 | C2×#60387 | C22 | 1 | 2 | yes | complemented |
| 25 | C22×#3019 | C22 | 1 | 8 | yes | complemented |
| 26 | C2×#60093 | C22 | 1 | 4 | yes | complemented |
| 27 | C22×#2888 | C22 | 1 | 2 | yes | — |
| 28 | #7630502 | C22 | 1 | 1 | yes | characteristic |
| 29 | #7630502 | C22 | 1 | 2 | yes | complemented |
| 30 | #6628902 | C22 | 1 | 8 | yes | complemented |
| 31 | #6628901 | C22 | 1 | 8 | yes | complemented |
| 32 | #6443344 | C22 | 1 | 32 | yes | complemented |
| 33 | #6443343 | C22 | 1 | 32 | yes | complemented |
| 34 | #6437970 | C22 | 1 | 16 | yes | complemented |
| 35 | #6437969 | C22 | 1 | 16 | yes | complemented |
| 36 | #6437630 | C22 | 1 | 16 | yes | complemented |
| 37 | C2×#23493 | C22 | 1 | 4 | yes | complemented |
| 38 | C2×#23445 | C22 | 1 | 4 | yes | complemented |
| 39 | C2×#23412 | C22 | 1 | 8 | yes | complemented |
| 40 | C2×#23412 | C22 | 1 | 8 | yes | complemented |
| 41 | #6431733 | C22 | 1 | 4 | yes | complemented |
| 42 | C2×#23402 | C22 | 1 | 4 | yes | complemented |
| 43 | C2×#21244 | C22 | 1 | 8 | yes | complemented |
| 44 | C2×#21014 | C22 | 1 | 4 | yes | complemented |
| 45 | #6371454 | C22 | 1 | 2 | yes | complemented |
| 46 | #6371369 | C22 | 1 | 4 | yes | complemented |
| 47 | #6371287 | C22 | 1 | 2 | yes | complemented |
| 48 | #6370746 | C22 | 1 | 2 | yes | complemented |
| 49 | #6370734 | C22 | 1 | 4 | yes | complemented |
| 50 | C2×#20586 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#20586 | C22 | 1 | 2 | yes | complemented |
| 52 | C2×#20401 | C22 | 1 | 4 | yes | complemented |
| 53 | #418884 | C22 | 1 | 64 | yes | complemented |
| 54 | #417800 | C22 | 1 | 32 | yes | complemented |
| 55 | #417798 | C22 | 1 | 32 | yes | complemented |
| 56 | #394288 | C22 | 1 | 32 | yes | complemented |
| 57 | #394287 | C22 | 1 | 32 | yes | complemented |
| 58 | #394043 | C22 | 1 | 64 | yes | complemented |
| 59 | #366636 | C22 | 1 | 64 | yes | complemented |
| 60 | C2×#11119 | C22 | 1 | 8 | yes | complemented |
| 61 | C2×#11033 | C22 | 1 | 8 | yes | complemented |
| 62 | #357577 | C22 | 1 | 8 | yes | complemented |
| 63 | #357493 | C22 | 1 | 4 | yes | complemented |
| 64 | #356056 | C22 | 1 | 16 | yes | complemented |
| 65 | C2×#10939 | C22 | 1 | 4 | yes | complemented |
| 66 | #354051 | C22 | 1 | 4 | yes | complemented |
| 67 | C2×#10771 | C22 | 1 | 4 | yes | complemented |
| 68 | C2×H(7,𝔽2) | C23 | 1 | 8 | yes | — |
| 69 | C22×#585 | C23 | 1 | 4 | yes | — |
| 70 | C22×#585 | C23 | 1 | 2 | yes | — |
| 71 | C23×H(5,𝔽2) | C23 | 1 | 1 | yes | characteristic |
| 72 | C23×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 73 | #63090 | C23 | 1 | 32 | yes | complemented |
| 74 | C22×#575 | C23 | 1 | 8 | yes | — |
| 75 | C22×#575 | C23 | 1 | 8 | yes | — |
| 76 | C22×#575 | C23 | 1 | 4 | yes | complemented |
| 77 | C22×#568 | C23 | 1 | 4 | yes | — |
| 78 | #62852 | C23 | 1 | 16 | yes | — |
| 79 | C2×#3449 | C23 | 1 | 4 | yes | — |
| 80 | C2×#3449 | C23 | 1 | 2 | yes | — |
| 81 | C2×#3449 | C23 | 1 | 4 | yes | — |
| 82 | C2×#3449 | C23 | 1 | 4 | yes | complemented |
| 83 | C22×#535 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×#535 | C23 | 1 | 4 | yes | — |
| 85 | C2×#3428 | C23 | 1 | 2 | yes | — |
| 86 | #60645 | C23 | 1 | 16 | yes | complemented |
| 87 | #60644 | C23 | 1 | 16 | yes | complemented |
| 88 | #60455 | C23 | 1 | 16 | yes | complemented |
| 89 | #60454 | C23 | 1 | 16 | yes | complemented |
| 90 | #60398 | C23 | 1 | 32 | yes | complemented |
| 91 | C2×#3028 | C23 | 1 | 16 | yes | complemented |
| 92 | C2×#3027 | C23 | 1 | 16 | yes | complemented |
| 93 | #60387 | D4 | 1 | 32 | yes | complemented |
| 94 | #60387 | C23 | 1 | 32 | yes | — |
| 95 | #60387 | C23 | 1 | 32 | yes | — |
| 96 | C2×#3022 | D4 | 1 | 16 | yes | complemented |
| 97 | C2×#3022 | C23 | 1 | 8 | yes | complemented |
| 98 | C2×#3021 | D4 | 1 | 16 | yes | complemented |
| 99 | C2×#3021 | C23 | 1 | 8 | yes | complemented |
| 100 | C2×#3019 | C23 | 1 | 64 | yes | complemented |
| 101 | C2×#2911 | C23 | 1 | 4 | yes | complemented |
| 102 | #60093 | C23 | 1 | 32 | yes | complemented |
| 103 | C22×#421 | C23 | 1 | 8 | yes | — |
| 104 | C22×#421 | C23 | 1 | 8 | yes | — |
| 105 | C22×#421 | C23 | 1 | 4 | yes | complemented |
| 106 | C22×#421 | C23 | 1 | 4 | yes | complemented |
| 107 | C2×#2896 | C23 | 1 | 4 | yes | complemented |
| 108 | C2×#2896 | C23 | 1 | 4 | yes | complemented |
| 109 | C2×#2888 | D4 | 1 | 16 | yes | complemented |
| 110 | C2×#2888 | C23 | 1 | 16 | yes | — |
| 111 | C22×#413 | D4 | 1 | 8 | yes | complemented |
| 112 | C22×#413 | C23 | 1 | 2 | yes | — |
| 113 | C22×#413 | C23 | 1 | 2 | yes | — |
| 114 | C23×#100 | D4 | 1 | 8 | yes | complemented |
| 115 | C23×#100 | C23 | 1 | 4 | yes | — |
| 116 | C22×#410 | C23 | 1 | 4 | yes | — |
| 117 | C22×#410 | C23 | 1 | 8 | yes | — |
| 118 | C22×#410 | C23 | 1 | 8 | yes | complemented |
| 119 | C2×#2873 | C23 | 1 | 4 | yes | complemented |
| 120 | #35616 | C23 | 1 | 4 | yes | — |
| 121 | #35616 | C23 | 1 | 8 | yes | complemented |
| 122 | #35527 | C23 | 1 | 4 | yes | — |
| 123 | #35527 | C23 | 1 | 8 | yes | complemented |
| 124 | #34044 | C23 | 1 | 4 | yes | — |
| 125 | #34044 | C23 | 1 | 2 | yes | — |
| 126 | C2×#2309 | C23 | 1 | 2 | yes | — |
| 127 | C2×#2309 | C23 | 1 | 1 | yes | characteristic |
| 128 | #23493 | C23 | 1 | 32 | yes | complemented |
| 129 | #23445 | C23 | 1 | 32 | yes | complemented |
| 130 | #23412 | C23 | 1 | 64 | yes | complemented |
| 131 | C2×#2009 | C23 | 1 | 32 | yes | complemented |
| 132 | C2×#2008 | C23 | 1 | 32 | yes | complemented |
| 133 | #23406 | C23 | 1 | 32 | yes | complemented |
| 134 | C2×#2004 | C23 | 1 | 16 | yes | complemented |
| 135 | C2×#2002 | C23 | 1 | 16 | yes | complemented |
| 136 | #21244 | C23 | 1 | 64 | yes | complemented |
| 137 | #21014 | C23 | 1 | 32 | yes | complemented |
| 138 | #20956 | C23 | 1 | 8 | yes | complemented |
| 139 | #20955 | C23 | 1 | 8 | yes | complemented |
| 140 | #20903 | C23 | 1 | 32 | yes | complemented |
| 141 | #20855 | C23 | 1 | 16 | yes | complemented |
| 142 | #20615 | C23 | 1 | 16 | yes | complemented |
| 143 | #20608 | C23 | 1 | 32 | yes | complemented |
| 144 | #20586 | D4 | 1 | 8 | yes | — |
| 145 | #20586 | C23 | 1 | 8 | yes | — |
| 146 | #20586 | C23 | 1 | 16 | yes | complemented |
| 147 | C2×#1781 | D4 | 1 | 8 | yes | — |
| 148 | #20401 | C23 | 1 | 32 | yes | complemented |
| 149 | C22×#344 | C23 | 1 | 8 | yes | complemented |
| 150 | C2×#1742 | C23 | 1 | 4 | yes | complemented |
| 151 | C2×#1740 | C23 | 1 | 4 | yes | complemented |
| 152 | C2×#1733 | C23 | 1 | 4 | yes | complemented |
| 153 | C2×#1733 | C23 | 1 | 4 | yes | complemented |
| 154 | #11119 | C23 | 1 | 64 | yes | complemented |
| 155 | #11033 | C23 | 1 | 64 | yes | complemented |
| 156 | #11019 | C23 | 1 | 64 | yes | complemented |
| 157 | #11007 | C23 | 1 | 16 | yes | complemented |
| 158 | #11006 | C23 | 1 | 16 | yes | complemented |
| 159 | #10959 | C23 | 1 | 32 | yes | complemented |
| 160 | #10939 | C23 | 1 | 32 | yes | complemented |
| 161 | #10771 | C23 | 1 | 32 | yes | complemented |
| 162 | C2×#585 | C2×D4 | 1 | 16 | yes | — |
| 163 | C2×#585 | C2×D4 | 1 | 16 | yes | — |
| 164 | C2×#585 | C24 | 1 | 8 | yes | — |
| 165 | C2×#585 | C24 | 1 | 16 | yes | — |
| 166 | C22×H(5,𝔽2) | C2×D4 | 1 | 8 | yes | — |
| 167 | C22×H(5,𝔽2) | C2×D4 | 1 | 4 | yes | — |
| 168 | C22×H(5,𝔽2) | C24 | 1 | 4 | yes | — |
| 169 | C22×H(5,𝔽2) | C24 | 1 | 8 | yes | — |
| 170 | C23×#41 | C2×D4 | 1 | 4 | yes | — |
| 171 | C23×#41 | C24 | 1 | 2 | yes | — |
| 172 | C23×#41 | C24 | 1 | 4 | yes | — |
| 173 | C23×#41 | C24 | 1 | 4 | yes | — |
| 174 | C23×#41 | C24 | 1 | 1 | yes | characteristic |
| 175 | C24×D4 | C2×D4 | 1 | 4 | yes | — |
| 176 | C24×D4 | C2×D4 | 1 | 4 | yes | — |
| 177 | C24×D4 | C24 | 1 | 1 | yes | characteristic |
| 178 | C2×#575 | C2×D4 | 1 | 32 | yes | complemented |
| 179 | C2×#575 | C24 | 1 | 32 | yes | — |
| 180 | C2×#575 | C24 | 1 | 32 | yes | — |
| 181 | C22×#137 | C2×D4 | 1 | 16 | yes | complemented |
| 182 | C22×#137 | C24 | 1 | 8 | yes | complemented |
| 183 | C22×AGL(1,ℤ/8) | C2×D4 | 1 | 16 | yes | complemented |
| 184 | C22×AGL(1,ℤ/8) | C24 | 1 | 8 | yes | complemented |
| 185 | C2×#568 | C2×D4 | 1 | 16 | yes | — |
| 186 | C2×#568 | C24 | 1 | 16 | yes | — |
| 187 | C23×M16 | C2×D4 | 1 | 16 | yes | — |
| 188 | C23×M16 | C24 | 1 | 4 | yes | — |
| 189 | C23×M16 | C24 | 1 | 4 | yes | — |
| 190 | #3449 | C2×D4 | 1 | 16 | yes | — |
| 191 | #3449 | C24 | 1 | 16 | yes | — |
| 192 | #3449 | C24 | 1 | 16 | yes | complemented |
| 193 | C2×#536 | C2×D4 | 1 | 8 | yes | — |
| 194 | C2×#536 | C24 | 1 | 4 | yes | — |
| 195 | C2×#536 | C24 | 1 | 8 | yes | — |
| 196 | C2×#535 | C2×D4 | 1 | 8 | yes | — |
| 197 | C2×#535 | C24 | 1 | 4 | yes | — |
| 198 | C2×#535 | C24 | 1 | 16 | yes | — |
| 199 | C2×#535 | C24 | 1 | 8 | yes | — |
| 200 | C22×#127 | C24 | 1 | 2 | yes | — |
| 201 | C22×#124 | C24 | 1 | 2 | yes | — |
| 202 | #3428 | C24 | 1 | 8 | yes | — |
| 203 | C22×#117 | C24 | 1 | 4 | yes | — |
| 204 | C22×#117 | C24 | 1 | 4 | yes | — |
| 205 | C22×#117 | C24 | 1 | 2 | yes | — |
| 206 | C22×#117 | C24 | 1 | 1 | yes | characteristic |
| 207 | #3022 | C2×D4 | 1 | 128 | yes | complemented |
| 208 | #3021 | C2×D4 | 1 | 128 | yes | complemented |
| 209 | #2911 | C24 | 1 | 16 | yes | complemented |
| 210 | C2×#421 | C2×D4 | 1 | 32 | yes | complemented |
| 211 | C2×#421 | C2×D4 | 1 | 32 | yes | complemented |
| 212 | C2×#421 | C24 | 1 | 32 | yes | — |
| 213 | C2×#421 | C24 | 1 | 32 | yes | — |
| 214 | C2×#421 | C24 | 1 | 16 | yes | complemented |
| 215 | C22×#104 | C24 | 1 | 16 | yes | complemented |
| 216 | #2896 | C24 | 1 | 16 | yes | complemented |
| 217 | C2×#419 | C24 | 1 | 8 | yes | complemented |
| 218 | C2×#418 | C24 | 1 | 8 | yes | complemented |
| 219 | C2×#413 | C2×D4 | 1 | 16 | yes | — |
| 220 | C2×#413 | C2×D4 | 1 | 16 | yes | — |
| 221 | C2×#413 | C2×D4 | 1 | 8 | yes | — |
| 222 | C2×#413 | C2×D4 | 1 | 8 | yes | — |
| 223 | C2×#413 | C2×D4 | 1 | 64 | yes | complemented |
| 224 | C2×#413 | C24 | 1 | 8 | yes | — |
| 225 | C2×#413 | C24 | 1 | 8 | yes | — |
| 226 | C22×#101 | C2×D4 | 1 | 4 | yes | — |
| 227 | C22×#101 | C2×D4 | 1 | 4 | yes | — |
| 228 | C22×#100 | C2×D4 | 1 | 4 | yes | — |
| 229 | C22×#100 | C2×D4 | 1 | 4 | yes | — |
| 230 | C22×#100 | C2×D4 | 1 | 16 | yes | — |
| 231 | C22×#100 | C2×D4 | 1 | 16 | yes | — |
| 232 | C22×#100 | C2×D4 | 1 | 64 | yes | complemented |
| 233 | C22×#100 | C24 | 1 | 16 | yes | — |
| 234 | C2×#410 | C2×D4 | 1 | 16 | yes | — |
| 235 | C2×#410 | C24 | 1 | 32 | yes | — |
| 236 | C2×#410 | C24 | 1 | 16 | yes | — |
| 237 | C2×#410 | C24 | 1 | 32 | yes | complemented |
| 238 | C22×#99 | C2×D4 | 1 | 16 | yes | — |
| 239 | #2873 | C24 | 1 | 16 | yes | complemented |
| 240 | #2309 | C2×D4 | 1 | 8 | yes | — |
| 241 | #2309 | C24 | 1 | 4 | yes | — |
| 242 | #2309 | C24 | 1 | 8 | yes | — |
| 243 | #2297 | C24 | 1 | 16 | yes | — |
| 244 | #2297 | C24 | 1 | 8 | yes | — |
| 245 | C2×#379 | C2×D4 | 1 | 8 | yes | — |
| 246 | #1781 | C2×D4 | 1 | 64 | yes | — |
| 247 | C2×#344 | C24 | 1 | 32 | yes | complemented |
| 248 | #1742 | C24 | 1 | 16 | yes | complemented |
| 249 | #1740 | C24 | 1 | 16 | yes | complemented |
| 250 | #1733 | C24 | 1 | 16 | yes | complemented |
| 251 | C2×#339 | C24 | 1 | 16 | yes | complemented |
| 252 | C26 | #127 | 1 | 4 | yes | — |
| 253 | C26 | C22×D4 | 1 | 2 | yes | — |
| 254 | #585 | C22×D4 | 1 | 64 | yes | — |
| 255 | C22×#41 | #127 | 1 | 16 | yes | — |
| 256 | C22×#41 | C22×D4 | 1 | 16 | yes | — |
| 257 | C22×#41 | C22×D4 | 1 | 4 | yes | — |
| 258 | C22×#41 | C22×D4 | 1 | 4 | yes | — |
| 259 | C22×#41 | C22×D4 | 1 | 8 | yes | — |
| 260 | C22×#41 | C22×D4 | 1 | 8 | yes | — |
| 261 | C22×#41 | C22×D4 | 1 | 4 | yes | — |
| 262 | C22×#41 | C22×D4 | 1 | 16 | yes | — |
| 263 | C22×#41 | C22×D4 | 1 | 16 | yes | — |
| 264 | C22×#41 | C22×D4 | 1 | 8 | yes | — |
| 265 | C22×#41 | H(5,𝔽2) | 1 | 8 | yes | — |
| 266 | C22×#41 | H(5,𝔽2) | 1 | 8 | yes | — |
| 267 | C22×#41 | H(5,𝔽2) | 1 | 8 | yes | — |
| 268 | C22×#41 | C25 | 1 | 4 | yes | — |
| 269 | C22×#41 | C25 | 1 | 8 | yes | — |
| 270 | C22×#41 | C25 | 1 | 8 | yes | — |
| 271 | C23×Q8 | C22×D4 | 1 | 2 | yes | — |
| 272 | C23×Q8 | C22×D4 | 1 | 4 | yes | — |
| 273 | C23×Q8 | H(5,𝔽2) | 1 | 4 | yes | — |
| 274 | C23×Q8 | C25 | 1 | 1 | yes | characteristic |
| 275 | C23×D4 | #127 | 1 | 8 | yes | — |
| 276 | C23×D4 | #127 | 1 | 16 | yes | — |
| 277 | C23×D4 | #127 | 1 | 16 | yes | — |
| 278 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 279 | C23×D4 | C22×D4 | 1 | 16 | yes | — |
| 280 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 281 | C23×D4 | C22×D4 | 1 | 2 | yes | — |
| 282 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 283 | C23×D4 | C22×D4 | 1 | 16 | yes | — |
| 284 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 285 | C23×D4 | C22×D4 | 1 | 4 | yes | — |
| 286 | C23×D4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 287 | C23×D4 | C25 | 1 | 1 | yes | characteristic |
| 288 | C23×D4 | C25 | 1 | 2 | yes | — |
| 289 | C24×C4 | #127 | 1 | 4 | yes | — |
| 290 | C24×C4 | C22×D4 | 1 | 4 | yes | — |
| 291 | C24×C4 | C25 | 1 | 1 | yes | characteristic |
| 292 | C2×#137 | C22×D4 | 1 | 64 | yes | complemented |
| 293 | C2×AGL(1,ℤ/8) | C22×D4 | 1 | 64 | yes | complemented |
| 294 | C22×M16 | C22×D4 | 1 | 8 | yes | — |
| 295 | C22×M16 | C22×D4 | 1 | 8 | yes | — |
| 296 | C22×M16 | C22×D4 | 1 | 16 | yes | — |
| 297 | C22×M16 | C22×D4 | 1 | 16 | yes | — |
| 298 | C22×M16 | C22×D4 | 1 | 8 | yes | — |
| 299 | C22×M16 | C22×D4 | 1 | 8 | yes | — |
| 300 | C22×M16 | C22×D4 | 1 | 64 | yes | — |
| 301 | C22×M16 | C25 | 1 | 8 | yes | — |
| 302 | C22×M16 | C25 | 1 | 8 | yes | — |
| 303 | #536 | C22×D4 | 1 | 32 | yes | — |
| 304 | #535 | C22×D4 | 1 | 32 | yes | — |
| 305 | C2×#117 | C22×D4 | 1 | 8 | yes | — |
| 306 | C2×#117 | C22×D4 | 1 | 8 | yes | — |
| 307 | C2×#117 | C22×D4 | 1 | 8 | yes | — |
| 308 | C2×#117 | C25 | 1 | 8 | yes | — |
| 309 | C2×#117 | C25 | 1 | 8 | yes | — |
| 310 | C2×#117 | C25 | 1 | 4 | yes | — |
| 311 | C22×C22⋊C4 | C22×D4 | 1 | 8 | yes | — |
| 312 | C22×C42 | C25 | 1 | 2 | yes | — |
| 313 | #421 | C22×D4 | 1 | 128 | yes | complemented |
| 314 | #413 | #120 | 1 | 64 | yes | complemented |
| 315 | #413 | C22×D4 | 1 | 64 | yes | — |
| 316 | C2×#101 | #120 | 1 | 16 | yes | complemented |
| 317 | C2×#101 | #120 | 1 | 16 | yes | complemented |
| 318 | C2×#101 | C22×D4 | 1 | 16 | yes | — |
| 319 | C2×#101 | C22×D4 | 1 | 16 | yes | — |
| 320 | C2×#100 | #120 | 1 | 16 | yes | complemented |
| 321 | C2×#100 | #120 | 1 | 16 | yes | complemented |
| 322 | C2×#100 | C22×D4 | 1 | 16 | yes | — |
| 323 | C2×#100 | C22×D4 | 1 | 64 | yes | — |
| 324 | C2×#100 | C22×D4 | 1 | 16 | yes | — |
| 325 | C2×#99 | C22×D4 | 1 | 64 | yes | — |
| 326 | #379 | C22×D4 | 1 | 32 | yes | — |
| 327 | C25 | C2×#127 | 1 | 4 | yes | — |
| 328 | C25 | C2×#127 | 1 | 4 | yes | — |
| 329 | C25 | C2×#127 | 1 | 16 | yes | — |
| 330 | C25 | C2×#127 | 1 | 4 | yes | — |
| 331 | C25 | C23×D4 | 1 | 4 | yes | — |
| 332 | C25 | C23×D4 | 1 | 1 | yes | characteristic |
| 333 | C2×#41 | C2×#120 | 1 | 16 | yes | — |
| 334 | C2×#41 | #535 | 1 | 16 | yes | — |
| 335 | C2×#41 | D42 | 1 | 16 | yes | — |
| 336 | C2×#41 | D42 | 1 | 16 | yes | — |
| 337 | C2×#41 | D42 | 1 | 16 | yes | — |
| 338 | C2×#41 | D42 | 1 | 16 | yes | — |
| 339 | C2×#41 | D42 | 1 | 16 | yes | — |
| 340 | C2×#41 | D42 | 1 | 16 | yes | — |
| 341 | C2×#41 | C23×D4 | 1 | 16 | yes | — |
| 342 | C2×#41 | C23×D4 | 1 | 32 | yes | — |
| 343 | C2×#41 | C2×H(5,𝔽2) | 1 | 16 | yes | — |
| 344 | C22×Q8 | C2×#120 | 1 | 4 | yes | — |
| 345 | C22×Q8 | C2×#120 | 1 | 4 | yes | — |
| 346 | C22×Q8 | C2×#127 | 1 | 4 | yes | — |
| 347 | C22×Q8 | #535 | 1 | 4 | yes | — |
| 348 | C22×Q8 | #535 | 1 | 4 | yes | — |
| 349 | C22×Q8 | D42 | 1 | 16 | yes | — |
| 350 | C22×Q8 | C23×D4 | 1 | 8 | yes | — |
| 351 | C22×Q8 | C23×D4 | 1 | 4 | yes | — |
| 352 | C22×Q8 | C2×H(5,𝔽2) | 1 | 8 | yes | — |
| 353 | C22×D4 | C2×#120 | 1 | 4 | yes | — |
| 354 | C22×D4 | C2×#120 | 1 | 4 | yes | — |
| 355 | C22×D4 | C2×#127 | 1 | 4 | yes | — |
| 356 | C22×D4 | C2×#127 | 1 | 8 | yes | — |
| 357 | C22×D4 | C2×#127 | 1 | 32 | yes | — |
| 358 | C22×D4 | C2×#127 | 1 | 8 | yes | — |
| 359 | C22×D4 | #535 | 1 | 4 | yes | — |
| 360 | C22×D4 | #535 | 1 | 4 | yes | — |
| 361 | C22×D4 | D42 | 1 | 16 | yes | — |
| 362 | C22×D4 | D42 | 1 | 16 | yes | — |
| 363 | C22×D4 | D42 | 1 | 16 | yes | — |
| 364 | C22×D4 | C23×D4 | 1 | 8 | yes | — |
| 365 | C22×D4 | C23×D4 | 1 | 4 | yes | — |
| 366 | C22×D4 | C23×D4 | 1 | 8 | yes | — |
| 367 | C22×D4 | C23×D4 | 1 | 8 | yes | — |
| 368 | C22×D4 | C2×H(5,𝔽2) | 1 | 8 | yes | — |
| 369 | C23×C4 | C2×#127 | 1 | 4 | yes | — |
| 370 | C23×C4 | C2×#127 | 1 | 8 | yes | — |
| 371 | C23×C4 | C2×#127 | 1 | 16 | yes | — |
| 372 | C23×C4 | D42 | 1 | 16 | yes | — |
| 373 | C23×C4 | D42 | 1 | 16 | yes | — |
| 374 | C23×C4 | C23×D4 | 1 | 2 | yes | — |
| 375 | C23×C4 | C23×D4 | 1 | 2 | yes | — |
| 376 | C23×C4 | C23×D4 | 1 | 4 | yes | — |
| 377 | C23×C4 | C23×D4 | 1 | 4 | yes | — |
| 378 | C23×C4 | C23×D4 | 1 | 8 | yes | — |
| 379 | C23×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 380 | C23×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 381 | C23×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 382 | C23×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 383 | C23×C4 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 384 | C23×C4 | C26 | 1 | 1 | yes | characteristic |
| 385 | C2×M16 | C2×#120 | 1 | 16 | yes | — |
| 386 | C2×M16 | C2×#120 | 1 | 16 | yes | — |
| 387 | C2×M16 | C2×#120 | 1 | 32 | yes | — |
| 388 | C2×M16 | C23×D4 | 1 | 16 | yes | — |
| 389 | C2×M16 | C23×D4 | 1 | 32 | yes | — |
| 390 | C2×M16 | C23×D4 | 1 | 16 | yes | — |
| 391 | #117 | C23×D4 | 1 | 16 | yes | — |
| 392 | C2×C22⋊C4 | C23×D4 | 1 | 16 | yes | — |
| 393 | #101 | C2×#120 | 1 | 64 | yes | — |
| 394 | #100 | C2×#120 | 1 | 64 | yes | — |
| 395 | C24 | #2433 | 1 | 8 | yes | — |
| 396 | C24 | #2433 | 1 | 8 | yes | — |
| 397 | C24 | C22×#127 | 1 | 1 | yes | characteristic |
| 398 | C24 | C22×#127 | 1 | 1 | yes | characteristic |
| 399 | C24 | C22×#127 | 1 | 8 | yes | — |
| 400 | C24 | C22×#127 | 1 | 8 | yes | — |
| 401 | C24 | C2×D42 | 1 | 4 | yes | — |
| 402 | C24 | C2×D42 | 1 | 4 | yes | — |
| 403 | C24 | #3484 | 1 | 2 | yes | — |
| 404 | C24 | #3484 | 1 | 2 | yes | — |
| 405 | C24 | C24×D4 | 1 | 1 | yes | characteristic |
| 406 | C2×Q8 | #2433 | 1 | 8 | yes | — |
| 407 | C2×Q8 | #2433 | 1 | 8 | yes | — |
| 408 | C2×Q8 | C22×#120 | 1 | 8 | yes | — |
| 409 | C2×Q8 | C2×#535 | 1 | 8 | yes | — |
| 410 | C2×Q8 | C2×D42 | 1 | 16 | yes | — |
| 411 | C2×D4 | #2433 | 1 | 8 | yes | — |
| 412 | C2×D4 | #2433 | 1 | 8 | yes | — |
| 413 | C2×D4 | #2433 | 1 | 32 | yes | — |
| 414 | C2×D4 | C22×#120 | 1 | 8 | yes | — |
| 415 | C2×D4 | C2×#535 | 1 | 8 | yes | — |
| 416 | C2×D4 | C2×D42 | 1 | 32 | yes | — |
| 417 | C2×D4 | C2×D42 | 1 | 16 | yes | — |
| 418 | C22×C4 | #2433 | 1 | 8 | yes | — |
| 419 | C22×C4 | #2433 | 1 | 8 | yes | — |
| 420 | C22×C4 | #2433 | 1 | 32 | yes | — |
| 421 | C22×C4 | C22×#120 | 1 | 2 | yes | — |
| 422 | C22×C4 | C22×#120 | 1 | 2 | yes | — |
| 423 | C22×C4 | C22×#120 | 1 | 4 | yes | — |
| 424 | C22×C4 | C22×#127 | 1 | 2 | yes | — |
| 425 | C22×C4 | C22×#127 | 1 | 8 | yes | — |
| 426 | C22×C4 | C2×#535 | 1 | 2 | yes | — |
| 427 | C22×C4 | C2×#535 | 1 | 2 | yes | — |
| 428 | C22×C4 | C2×#535 | 1 | 4 | yes | — |
| 429 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 430 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 431 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 432 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 433 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 434 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 435 | C22×C4 | C2×D42 | 1 | 8 | yes | — |
| 436 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 437 | C22×C4 | C2×D42 | 1 | 4 | yes | — |
| 438 | C22×C4 | C2×D42 | 1 | 32 | yes | — |
| 439 | C22×C4 | #3484 | 1 | 4 | yes | — |
| 440 | C22×C4 | #3484 | 1 | 4 | yes | — |
| 441 | C22×C4 | #3484 | 1 | 8 | yes | — |
| 442 | C22×C4 | #3484 | 1 | 8 | yes | — |
| 443 | C22×C4 | #3484 | 1 | 8 | yes | — |
| 444 | C22×C4 | #3484 | 1 | 8 | yes | — |
| 445 | C22×C4 | #3484 | 1 | 8 | yes | — |
| 446 | C22×C4 | #3484 | 1 | 4 | yes | — |
| 447 | C22×C4 | #3532 | 1 | 8 | yes | — |
| 448 | C22×C4 | #3532 | 1 | 4 | yes | — |
| 449 | C22×C4 | #3532 | 1 | 4 | yes | — |
| 450 | C22×C4 | C24×D4 | 1 | 2 | yes | — |
| 451 | C22×C4 | C24×D4 | 1 | 4 | yes | — |
| 452 | C22×C4 | C22×H(5,𝔽2) | 1 | 4 | yes | — |
| 453 | C22×C4 | C22×H(5,𝔽2) | 1 | 4 | yes | — |
| 454 | M16 | C22×#120 | 1 | 32 | yes | — |
| 455 | C23 | C2×#2433 | 1 | 16 | yes | — |
| 456 | C23 | C2×#2433 | 1 | 2 | yes | — |
| 457 | C23 | C2×#2433 | 1 | 2 | yes | — |
| 458 | C23 | C2×#2433 | 1 | 4 | yes | — |
| 459 | C23 | #35390 | 1 | 1 | yes | characteristic |
| 460 | C23 | #35390 | 1 | 1 | yes | characteristic |
| 461 | C23 | #35390 | 1 | 2 | yes | — |
| 462 | C23 | #58990 | 1 | 8 | yes | — |
| 463 | C23 | #58990 | 1 | 4 | yes | — |
| 464 | C23 | #58990 | 1 | 4 | yes | — |
| 465 | C23 | C23×#127 | 1 | 1 | yes | characteristic |
| 466 | C23 | C22×D42 | 1 | 4 | yes | — |
| 467 | C23 | C2×#3484 | 1 | 2 | yes | — |
| 468 | C2×C4 | C2×#2433 | 1 | 4 | yes | — |
| 469 | C2×C4 | C2×#2433 | 1 | 2 | yes | — |
| 470 | C2×C4 | C2×#2433 | 1 | 2 | yes | — |
| 471 | C2×C4 | C2×#2433 | 1 | 16 | yes | — |
| 472 | C2×C4 | #35390 | 1 | 4 | yes | — |
| 473 | C2×C4 | D4×#120 | 1 | 4 | yes | — |
| 474 | C2×C4 | D4×#120 | 1 | 4 | yes | — |
| 475 | C2×C4 | D4×#120 | 1 | 4 | yes | — |
| 476 | C2×C4 | D4×#120 | 1 | 4 | yes | — |
| 477 | C2×C4 | D4×#120 | 1 | 8 | yes | — |
| 478 | C2×C4 | D4×#120 | 1 | 8 | yes | — |
| 479 | C2×C4 | #37645 | 1 | 4 | yes | — |
| 480 | C2×C4 | #37645 | 1 | 4 | yes | — |
| 481 | C2×C4 | #37645 | 1 | 4 | yes | — |
| 482 | C2×C4 | #37645 | 1 | 4 | yes | — |
| 483 | C2×C4 | #37645 | 1 | 8 | yes | — |
| 484 | C2×C4 | #37645 | 1 | 8 | yes | — |
| 485 | C2×C4 | #58990 | 1 | 8 | yes | — |
| 486 | C2×C4 | #58990 | 1 | 4 | yes | — |
| 487 | C2×C4 | #58990 | 1 | 4 | yes | — |
| 488 | C2×C4 | C23×#120 | 1 | 2 | yes | — |
| 489 | C2×C4 | C22×#535 | 1 | 2 | yes | — |
| 490 | C2×C4 | C22×D42 | 1 | 4 | yes | — |
| 491 | C2×C4 | C22×D42 | 1 | 4 | yes | — |
| 492 | C2×C4 | C2×#3532 | 1 | 4 | yes | — |
| 493 | C2×C4 | C2×#3484 | 1 | 8 | yes | — |
| 494 | C2×C4 | C2×#3484 | 1 | 4 | yes | — |
| 495 | C22 | #648360 | 1 | 2 | yes | — |
| 496 | C22 | #648360 | 1 | 1 | yes | characteristic |
| 497 | C22 | #648360 | 1 | 1 | yes | characteristic |
| 498 | C22 | #648360 | 1 | 4 | yes | — |
| 499 | C22 | C22×#2433 | 1 | 2 | yes | — |
| 500 | C22 | C2×#35390 | 1 | 1 | yes | characteristic |
| 501 | C22 | C2×#58990 | 1 | 4 | yes | — |
| 502 | C4 | #648360 | 1 | 4 | yes | — |
| 503 | C4 | #648360 | 1 | 4 | yes | — |
| 504 | C4 | C2×D4×#120 | 1 | 4 | yes | — |
| 505 | C4 | C2×#37645 | 1 | 4 | yes | — |
| 506 | C2 | C2×#648360 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta