Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
6608 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23778090 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | #23777800 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #23777662 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #23777407 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #23777377 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #23777323 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #23776697 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C79×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #19099311 | C22 | 1 | 12 | yes | complemented |
| 10 | #19099304 | C22 | 1 | 16 | yes | — |
| 11 | #19099273 | C22 | 1 | 12 | yes | complemented |
| 12 | #19099266 | C22 | 1 | 24 | yes | — |
| 13 | #19099266 | C22 | 1 | 48 | yes | complemented |
| 14 | #19099264 | C22 | 1 | 48 | yes | — |
| 15 | #19099254 | C22 | 1 | 24 | yes | — |
| 16 | #19099245 | C22 | 1 | 48 | yes | complemented |
| 17 | #19099235 | C22 | 1 | 24 | yes | — |
| 18 | #19099235 | C22 | 1 | 12 | yes | complemented |
| 19 | #19099216 | C22 | 1 | 24 | yes | — |
| 20 | #19099216 | C22 | 1 | 12 | yes | complemented |
| 21 | #19099174 | C22 | 1 | 12 | yes | complemented |
| 22 | #19099169 | C22 | 1 | 48 | yes | — |
| 23 | #19099169 | C22 | 1 | 12 | yes | complemented |
| 24 | #19099168 | C22 | 1 | 12 | yes | — |
| 25 | #19099161 | C22 | 1 | 48 | yes | — |
| 26 | #19099143 | C22 | 1 | 24 | yes | — |
| 27 | #19099118 | C22 | 1 | 6 | yes | — |
| 28 | #19099114 | C22 | 1 | 6 | yes | — |
| 29 | #19099114 | C22 | 1 | 12 | yes | complemented |
| 30 | #19099113 | C22 | 1 | 3 | yes | — |
| 31 | #19099100 | C22 | 1 | 12 | yes | — |
| 32 | #19099100 | C22 | 1 | 24 | yes | complemented |
| 33 | #19099099 | C22 | 1 | 12 | yes | — |
| 34 | #19099098 | C22 | 1 | 12 | yes | — |
| 35 | #125×D79 | C22 | 1 | 12 | yes | complemented |
| 36 | #19099076 | C22 | 1 | 12 | yes | — |
| 37 | #19099075 | C22 | 1 | 6 | yes | — |
| 38 | #19099045 | C22 | 1 | 24 | yes | complemented |
| 39 | C4×#11929625 | C22 | 1 | 12 | yes | — |
| 40 | #19099031 | C22 | 1 | 6 | yes | — |
| 41 | C2×C42×D79 | C22 | 1 | 1 | yes | characteristic |
| 42 | #564×C79 | C22 | 1 | 4 | yes | complemented |
| 43 | #557×C79 | C22 | 1 | 12 | yes | complemented |
| 44 | #541×C79 | C22 | 1 | 12 | yes | — |
| 45 | #533×C79 | C22 | 1 | 3 | yes | — |
| 46 | C2×#11929625 | C23 | 1 | 24 | yes | — |
| 47 | C2×#11929625 | C23 | 1 | 12 | yes | — |
| 48 | C2×#11929624 | C23 | 1 | 6 | yes | — |
| 49 | C22×C4×D79 | C23 | 1 | 3 | yes | — |
| 50 | #14579161 | C23 | 1 | 3 | yes | — |
| 51 | #14579158 | C23 | 1 | 12 | yes | — |
| 52 | #14579158 | C23 | 1 | 16 | yes | — |
| 53 | #14579158 | C23 | 1 | 3 | yes | — |
| 54 | #14579156 | C23 | 1 | 48 | yes | — |
| 55 | #14579156 | C23 | 1 | 24 | yes | — |
| 56 | #14579155 | C23 | 1 | 16 | yes | — |
| 57 | #14579153 | C23 | 1 | 12 | yes | — |
| 58 | #14579152 | C23 | 1 | 12 | yes | — |
| 59 | #14579151 | C23 | 1 | 48 | yes | — |
| 60 | #14579150 | C23 | 1 | 12 | yes | — |
| 61 | #14579149 | C23 | 1 | 6 | yes | — |
| 62 | #14579146 | C23 | 1 | 24 | yes | — |
| 63 | #14579146 | C23 | 1 | 48 | yes | — |
| 64 | #14579146 | C23 | 1 | 48 | yes | — |
| 65 | #14579146 | C23 | 1 | 48 | yes | — |
| 66 | #14579145 | C23 | 1 | 12 | yes | — |
| 67 | #14579141 | C23 | 1 | 12 | yes | — |
| 68 | #14579139 | C23 | 1 | 48 | yes | — |
| 69 | #14579137 | C23 | 1 | 24 | yes | — |
| 70 | #14579137 | C23 | 1 | 12 | yes | — |
| 71 | #14579136 | C23 | 1 | 48 | yes | — |
| 72 | #14579136 | C23 | 1 | 24 | yes | — |
| 73 | #14579136 | C23 | 1 | 48 | yes | — |
| 74 | #14579136 | C23 | 1 | 12 | yes | — |
| 75 | #14579136 | C23 | 1 | 48 | yes | — |
| 76 | #14579136 | C23 | 1 | 12 | yes | — |
| 77 | #14579135 | C23 | 1 | 12 | yes | — |
| 78 | #14579134 | C23 | 1 | 48 | yes | — |
| 79 | #14579131 | C23 | 1 | 12 | yes | — |
| 80 | Q8×Dic79 | C23 | 1 | 12 | yes | — |
| 81 | #14579126 | C23 | 1 | 12 | yes | — |
| 82 | C4×D316 | C23 | 1 | 48 | yes | — |
| 83 | C4×D316 | C23 | 1 | 24 | yes | — |
| 84 | C4×D316 | C23 | 1 | 24 | yes | — |
| 85 | C4×D316 | C23 | 1 | 12 | yes | — |
| 86 | #14579123 | C23 | 1 | 24 | yes | — |
| 87 | #14579123 | C23 | 1 | 48 | yes | — |
| 88 | #14579123 | C23 | 1 | 12 | yes | — |
| 89 | #14579123 | C23 | 1 | 12 | yes | — |
| 90 | (C22⋊D79)⋊C4 | C23 | 1 | 24 | yes | — |
| 91 | #14579119 | C23 | 1 | 24 | yes | — |
| 92 | #14579119 | C23 | 1 | 12 | yes | — |
| 93 | #14579118 | C23 | 1 | 48 | yes | — |
| 94 | #14579118 | C23 | 1 | 12 | yes | — |
| 95 | C4⋊C4×D79 | C23 | 1 | 24 | yes | — |
| 96 | C4⋊C4×D79 | C23 | 1 | 48 | yes | — |
| 97 | C2×C4×Dic79 | C23 | 1 | 3 | yes | — |
| 98 | C42×D79 | C23 | 1 | 6 | yes | — |
| 99 | C42×D79 | C23 | 1 | 2 | yes | — |
| 100 | C42×D79 | C23 | 1 | 12 | yes | — |
| 101 | C4⋊Q8×C79 | C23 | 1 | 12 | yes | — |
| 102 | C4⋊Q8×C79 | C23 | 1 | 6 | yes | — |
| 103 | #126×C79 | C23 | 1 | 16 | yes | — |
| 104 | #125×C79 | C23 | 1 | 48 | yes | — |
| 105 | #125×C79 | C23 | 1 | 12 | yes | — |
| 106 | #125×C79 | C23 | 1 | 6 | yes | — |
| 107 | C22⋊Q8×C79 | C23 | 1 | 12 | yes | — |
| 108 | C4×Q8×C79 | C23 | 1 | 24 | yes | — |
| 109 | C4×Q8×C79 | C23 | 1 | 12 | yes | — |
| 110 | #117×C79 | C23 | 1 | 6 | yes | — |
| 111 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 112 | C23×D79 | C24 | 1 | 1 | yes | characteristic |
| 113 | #11929625 | — | 4 | 24 | no | — |
| 114 | #11929625 | — | 4 | 48 | no | — |
| 115 | #11929624 | — | 4 | 12 | no | — |
| 116 | C2×Dic158 | C24 | 1 | 6 | yes | — |
| 117 | C2×D316 | C24 | 1 | 12 | yes | — |
| 118 | C2×D316 | C24 | 1 | 6 | yes | — |
| 119 | C2×D316 | C24 | 1 | 24 | yes | — |
| 120 | C2×D316 | C24 | 1 | 48 | yes | — |
| 121 | C2×C22⋊D79 | C24 | 1 | 12 | yes | — |
| 122 | C22×Dic79 | C24 | 1 | 3 | yes | — |
| 123 | C2×C4×D79 | — | 4 | 6 | no | — |
| 124 | C2×C4×D79 | C24 | 1 | 12 | yes | — |
| 125 | C2×C4×D79 | C24 | 1 | 6 | yes | — |
| 126 | C2×C4×D79 | C24 | 1 | 24 | yes | — |
| 127 | C2×C4×D79 | C24 | 1 | 48 | yes | — |
| 128 | C2×C4×D79 | C24 | 1 | 6 | yes | — |
| 129 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 130 | C4⋊Dic79 | C24 | 1 | 24 | yes | — |
| 131 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 132 | Dic79⋊C4 | C24 | 1 | 48 | yes | — |
| 133 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 134 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 135 | (C2×D79)⋊C4 | C24 | 1 | 48 | yes | — |
| 136 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 137 | (C2×D79)⋊C4 | C24 | 1 | 24 | yes | — |
| 138 | C4×Dic79 | C24 | 1 | 3 | yes | — |
| 139 | C4×Dic79 | C24 | 1 | 3 | yes | — |
| 140 | C4×Dic79 | C24 | 1 | 6 | yes | — |
| 141 | C4×Dic79 | C24 | 1 | 24 | yes | — |
| 142 | C2×Q8×C79 | C24 | 1 | 12 | yes | — |
| 143 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 144 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 145 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 146 | C4⋊C4×C79 | C24 | 1 | 24 | yes | — |
| 147 | C4⋊C4×C79 | C24 | 1 | 48 | yes | — |
| 148 | C22⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 149 | C42×C79 | C24 | 1 | 3 | yes | — |
| 150 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 151 | C42×C79 | C24 | 1 | 12 | yes | — |
| 152 | C42×C79 | C24 | 1 | 16 | yes | — |
| 153 | C23×C79 | C25 | 1 | 1 | yes | characteristic |
| 154 | C22×D79 | — | 4 | 3 | no | — |
| 155 | C22×D79 | C25 | 1 | 2 | yes | — |
| 156 | C22×D79 | C25 | 1 | 12 | yes | — |
| 157 | Q8×C79 | — | 2 | 24 | no | — |
| 158 | C2×C4×C79 | — | 2 | 6 | no | — |
| 159 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 160 | C2×C4×C79 | C25 | 1 | 24 | yes | — |
| 161 | C2×C4×C79 | C25 | 1 | 3 | yes | — |
| 162 | C22⋊D79 | — | 4 | 12 | no | — |
| 163 | C2×Dic79 | — | 4 | 3 | no | — |
| 164 | C2×Dic79 | C25 | 1 | 6 | yes | — |
| 165 | C2×Dic79 | C25 | 1 | 12 | yes | — |
| 166 | D316 | — | 2 | 24 | no | — |
| 167 | D316 | — | 4 | 6 | no | — |
| 168 | D316 | — | 4 | 48 | no | — |
| 169 | D316 | — | 4 | 24 | no | — |
| 170 | C4×D79 | — | 2 | 12 | no | — |
| 171 | C4×D79 | — | 2 | 24 | no | — |
| 172 | C4×D79 | — | 4 | 6 | no | — |
| 173 | C4×D79 | — | 4 | 48 | no | — |
| 174 | C4×D79 | — | 4 | 24 | no | — |
| 175 | Dic158 | — | 4 | 6 | no | — |
| 176 | C22×C79 | — | 2 | 3 | no | — |
| 177 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 178 | C2×D79 | — | 2 | 12 | no | — |
| 179 | C2×D79 | — | 2 | 6 | no | — |
| 180 | C2×D79 | — | 2 | 24 | no | — |
| 181 | C2×D79 | — | 4 | 4 | no | — |
| 182 | C4×C79 | — | 2 | 3 | no | — |
| 183 | C4×C79 | — | 2 | 24 | no | — |
| 184 | C4×C79 | #585 | 1 | 6 | yes | — |
| 185 | Dic79 | — | 2 | 12 | no | — |
| 186 | Dic79 | — | 2 | 6 | no | — |
| 187 | #62840 | — | 79 | 1 | no | maximal, Sylow |
| 188 | C2×C79 | — | 4 | 1 | no | — |
| 189 | C2×C79 | C2×#585 | 1 | 3 | yes | — |
| 190 | D79 | — | 4 | 12 | no | — |
| 191 | D79 | — | 4 | 2 | no | — |
| 192 | #3567 | — | 79 | 8 | no | — |
| 193 | #3556 | D79 | 1 | 1 | yes | characteristic, complemented |
| 194 | #3548 | — | 79 | 3 | no | — |
| 195 | #3539 | — | 79 | 12 | no | — |
| 196 | #3517 | — | 79 | 12 | no | — |
| 197 | #3515 | — | 79 | 12 | no | — |
| 198 | #3512 | — | 79 | 12 | no | — |
| 199 | #3444 | — | 79 | 3 | no | — |
| 200 | C79 | #62840 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 201 | #564 | C2×D79 | 1 | 4 | yes | complemented |
| 202 | #562 | — | 79 | 12 | no | — |
| 203 | #560 | — | 79 | 16 | no | — |
| 204 | #557 | C2×D79 | 1 | 12 | yes | complemented |
| 205 | #554 | — | 79 | 12 | no | — |
| 206 | #553 | — | 79 | 48 | no | — |
| 207 | #553 | — | 79 | 24 | no | — |
| 208 | #553 | — | 79 | 48 | no | — |
| 209 | #552 | — | 79 | 48 | no | — |
| 210 | #552 | — | 79 | 24 | no | — |
| 211 | #550 | — | 79 | 24 | no | — |
| 212 | #550 | — | 79 | 12 | no | — |
| 213 | #547 | — | 79 | 24 | no | — |
| 214 | #547 | — | 79 | 12 | no | — |
| 215 | #541 | — | 79 | 12 | no | — |
| 216 | #541 | C2×D79 | 1 | 12 | yes | — |
| 217 | #540 | — | 79 | 48 | no | — |
| 218 | #540 | — | 79 | 12 | no | — |
| 219 | #540 | — | 79 | 12 | no | — |
| 220 | #539 | — | 79 | 48 | no | — |
| 221 | #537 | — | 79 | 24 | no | — |
| 222 | #533 | — | 79 | 6 | no | — |
| 223 | #533 | C2×D79 | 1 | 3 | yes | — |
| 224 | #532 | — | 79 | 6 | no | — |
| 225 | #532 | — | 79 | 12 | no | — |
| 226 | #532 | — | 79 | 3 | no | — |
| 227 | #529 | — | 79 | 12 | no | — |
| 228 | #529 | — | 79 | 12 | no | — |
| 229 | #529 | — | 79 | 12 | no | — |
| 230 | #529 | — | 79 | 24 | no | — |
| 231 | C2×#125 | — | 79 | 12 | no | — |
| 232 | #525 | — | 79 | 12 | no | — |
| 233 | #525 | — | 79 | 6 | no | — |
| 234 | #520 | — | 79 | 24 | no | — |
| 235 | C4×#41 | — | 79 | 12 | no | — |
| 236 | C4×#41 | — | 79 | 6 | no | — |
| 237 | C22×C42 | — | 79 | 1 | no | — |
| 238 | C2×#41 | — | 79 | 12 | no | — |
| 239 | C2×#41 | — | 79 | 24 | no | — |
| 240 | C2×#41 | — | 79 | 6 | no | — |
| 241 | C23×C4 | — | 79 | 3 | no | — |
| 242 | C4⋊Q8 | — | 79 | 3 | no | — |
| 243 | C4⋊Q8 | C22×D79 | 1 | 6 | yes | — |
| 244 | C4⋊Q8 | C22×D79 | 1 | 12 | yes | — |
| 245 | #127 | — | 79 | 3 | no | — |
| 246 | #127 | — | 79 | 12 | no | — |
| 247 | #127 | — | 79 | 16 | no | — |
| 248 | #126 | — | 79 | 24 | no | — |
| 249 | #126 | — | 79 | 48 | no | — |
| 250 | #126 | — | 79 | 16 | no | — |
| 251 | #126 | C22×D79 | 1 | 16 | yes | — |
| 252 | #125 | — | 79 | 12 | no | — |
| 253 | #125 | — | 79 | 48 | no | — |
| 254 | #125 | — | 79 | 12 | no | — |
| 255 | #125 | C22×D79 | 1 | 12 | yes | — |
| 256 | #125 | C22×D79 | 1 | 6 | yes | — |
| 257 | #125 | C22×D79 | 1 | 48 | yes | — |
| 258 | #124 | — | 79 | 12 | no | — |
| 259 | #124 | — | 79 | 6 | no | — |
| 260 | #123 | — | 79 | 24 | no | — |
| 261 | #123 | — | 79 | 48 | no | — |
| 262 | #123 | — | 79 | 48 | no | — |
| 263 | #123 | — | 79 | 48 | no | — |
| 264 | #123 | — | 79 | 12 | no | — |
| 265 | C22⋊Q8 | — | 79 | 12 | no | — |
| 266 | C22⋊Q8 | — | 79 | 24 | no | — |
| 267 | C22⋊Q8 | — | 79 | 12 | no | — |
| 268 | C22⋊Q8 | — | 79 | 48 | no | — |
| 269 | C22⋊Q8 | C22×D79 | 1 | 12 | yes | — |
| 270 | #121 | — | 79 | 12 | no | — |
| 271 | #121 | — | 79 | 12 | no | — |
| 272 | #121 | — | 79 | 12 | no | — |
| 273 | #121 | — | 79 | 24 | no | — |
| 274 | #121 | — | 79 | 48 | no | — |
| 275 | #121 | — | 79 | 48 | no | — |
| 276 | #121 | — | 79 | 48 | no | — |
| 277 | #121 | — | 79 | 48 | no | — |
| 278 | #120 | — | 79 | 12 | no | — |
| 279 | C4×Q8 | — | 79 | 12 | no | — |
| 280 | C4×Q8 | — | 79 | 12 | no | — |
| 281 | C4×Q8 | C22×D79 | 1 | 12 | yes | — |
| 282 | C4×Q8 | C22×D79 | 1 | 24 | yes | — |
| 283 | C4×D4 | — | 79 | 12 | no | — |
| 284 | C4×D4 | — | 79 | 24 | no | — |
| 285 | C4×D4 | — | 79 | 12 | no | — |
| 286 | C4×D4 | — | 79 | 48 | no | — |
| 287 | C4×D4 | — | 79 | 24 | no | — |
| 288 | C4×D4 | — | 79 | 24 | no | — |
| 289 | C4×D4 | — | 79 | 12 | no | — |
| 290 | C4×D4 | — | 79 | 48 | no | — |
| 291 | C4×D4 | — | 79 | 24 | no | — |
| 292 | #117 | — | 79 | 12 | no | — |
| 293 | #117 | — | 79 | 24 | no | — |
| 294 | #117 | — | 79 | 12 | no | — |
| 295 | #117 | — | 79 | 48 | no | — |
| 296 | #117 | C22×D79 | 1 | 6 | yes | — |
| 297 | C2×C4⋊C4 | — | 79 | 24 | no | — |
| 298 | C2×C4⋊C4 | — | 79 | 48 | no | — |
| 299 | C2×C42 | — | 79 | 3 | no | — |
| 300 | C2×C42 | — | 79 | 12 | no | — |
| 301 | C2×C42 | — | 79 | 6 | no | — |
| 302 | C2×C42 | — | 79 | 2 | no | — |
| 303 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 304 | C24 | — | 79 | 1 | no | — |
| 305 | #41 | — | 316 | 12 | no | — |
| 306 | #41 | — | 316 | 24 | no | — |
| 307 | #41 | — | 316 | 48 | no | — |
| 308 | C2×Q8 | — | 79 | 6 | no | — |
| 309 | C2×Q8 | C23×D79 | 1 | 12 | yes | — |
| 310 | C2×D4 | — | 79 | 12 | no | — |
| 311 | C2×D4 | — | 79 | 24 | no | — |
| 312 | C2×D4 | — | 79 | 6 | no | — |
| 313 | C2×D4 | — | 79 | 48 | no | — |
| 314 | C2×D4 | — | 79 | 12 | no | — |
| 315 | C22×C4 | — | 316 | 6 | no | — |
| 316 | C22×C4 | — | 79 | 3 | no | — |
| 317 | C22×C4 | — | 79 | 6 | no | — |
| 318 | C22×C4 | — | 79 | 24 | no | — |
| 319 | C22×C4 | — | 79 | 48 | no | — |
| 320 | C22×C4 | — | 79 | 6 | no | — |
| 321 | C22×C4 | — | 79 | 12 | no | — |
| 322 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 323 | C4⋊C4 | — | 79 | 24 | no | — |
| 324 | C4⋊C4 | — | 79 | 48 | no | — |
| 325 | C4⋊C4 | — | 79 | 12 | no | — |
| 326 | C4⋊C4 | — | 79 | 24 | no | — |
| 327 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 328 | C4⋊C4 | C23×D79 | 1 | 48 | yes | — |
| 329 | C4⋊C4 | C23×D79 | 1 | 24 | yes | — |
| 330 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 331 | C22⋊C4 | — | 79 | 24 | no | — |
| 332 | C22⋊C4 | — | 79 | 24 | no | — |
| 333 | C22⋊C4 | — | 79 | 24 | no | — |
| 334 | C22⋊C4 | — | 79 | 48 | no | — |
| 335 | C22⋊C4 | — | 79 | 24 | no | — |
| 336 | C22⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 337 | C42 | — | 79 | 3 | no | — |
| 338 | C42 | — | 79 | 3 | no | — |
| 339 | C42 | — | 79 | 6 | no | — |
| 340 | C42 | — | 79 | 24 | no | — |
| 341 | C42 | C23×D79 | 1 | 3 | yes | — |
| 342 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 343 | C42 | C23×D79 | 1 | 12 | yes | — |
| 344 | C42 | C23×D79 | 1 | 16 | yes | — |
| 345 | C23 | — | 316 | 3 | no | — |
| 346 | C23 | — | 79 | 2 | no | — |
| 347 | C23 | — | 79 | 12 | no | — |
| 348 | C23 | C24×D79 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 24 | no | — |
| 350 | Q8 | — | 316 | 6 | no | — |
| 351 | D4 | — | 316 | 6 | no | — |
| 352 | D4 | — | 316 | 24 | no | — |
| 353 | D4 | — | 316 | 48 | no | — |
| 354 | D4 | — | 316 | 12 | no | — |
| 355 | D4 | — | 158 | 24 | no | — |
| 356 | C2×C4 | — | 2 | 6 | no | — |
| 357 | C2×C4 | — | 316 | 6 | no | — |
| 358 | C2×C4 | — | 316 | 24 | no | — |
| 359 | C2×C4 | — | 316 | 48 | no | — |
| 360 | C2×C4 | — | 316 | 3 | no | — |
| 361 | C2×C4 | — | 79 | 6 | no | — |
| 362 | C2×C4 | — | 79 | 12 | no | — |
| 363 | C2×C4 | — | 158 | 12 | no | — |
| 364 | C2×C4 | — | 158 | 24 | no | — |
| 365 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 366 | C2×C4 | C24×D79 | 1 | 24 | yes | — |
| 367 | C2×C4 | C24×D79 | 1 | 3 | yes | — |
| 368 | C22 | — | 2 | 3 | no | — |
| 369 | C22 | — | 316 | 4 | no | — |
| 370 | C22 | — | 158 | 24 | no | — |
| 371 | C22 | — | 158 | 6 | no | — |
| 372 | C22 | — | 158 | 12 | no | — |
| 373 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 374 | C4 | — | 2 | 3 | no | — |
| 375 | C4 | — | 2 | 24 | no | — |
| 376 | C4 | — | 158 | 6 | no | — |
| 377 | C4 | — | 158 | 12 | no | — |
| 378 | C4 | #19099400 | 1 | 6 | yes | — |
| 379 | C2 | — | 4 | 1 | no | — |
| 380 | C2 | — | 316 | 2 | no | — |
| 381 | C2 | — | 316 | 12 | no | — |
| 382 | C2 | C2×#19099400 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D79 |
| commutator, socle, cosocle | C22×C79 | C26 |
| Fitting | C79×#3556 | C2 |
| hypercenter | #3556 | D79 |
| hypocenter | C79 | #62840 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #3556 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23778090 | C2 | semidirect |
| 2. #23777800 | C2 | semidirect |
| 3. #23777662 | C2 | semidirect |
| 4. #23777407 | C2 | semidirect |
| 5. #23777377 | C2 | semidirect |
| 6. #23777323 | C2 | semidirect |
| 7. #23776697 | C2 | semidirect |
| 8. C79×#3556 | C2 | semidirect |
| 9. #19099311 | C22 | semidirect |
| 11. #19099273 | C22 | semidirect |
| 13. #19099266 | C22 | semidirect |
| 16. #19099245 | C22 | semidirect |
| 18. #19099235 | C22 | semidirect |
| 20. #19099216 | C22 | semidirect |
| 21. #19099174 | C22 | semidirect |
| 23. #19099169 | C22 | semidirect |
| 29. #19099114 | C22 | semidirect |
| 32. #19099100 | C22 | semidirect |
| 35. #125×D79 | C22 | semidirect |
| 38. #19099045 | C22 | semidirect |
| 42. #564×C79 | C22 | semidirect |
| 43. #557×C79 | C22 | semidirect |
| 193. #3556 | D79 | semidirect |
| 200. C79 | #62840 | semidirect |
| 201. #564 | C2×D79 | semidirect |
| 204. #557 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778090 | 2 |
| #23777800 | 2 |
| #23777662 | 2 |
| #23777407 | 2 |
| #23777377 | 2 |
| #23777323 | 2 |
| #23776697 | 2 |
| C79×#3556 | 2 |
| #62840 | 79 |