Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
886 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #22626258 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | D73⋊#359 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22626162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22625816 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22624704 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#14556666 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#14556664 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | D73⋊#108 | C22 | 1 | 2 | yes | complemented |
| 9 | #17989573 | — | 2 | 1 | no | — |
| 10 | #17989506 | — | 2 | 2 | no | — |
| 11 | #17989505 | — | 2 | 2 | no | — |
| 12 | #17989502 | — | 2 | 2 | no | — |
| 13 | #17989501 | — | 2 | 2 | no | — |
| 14 | #17989482 | — | 2 | 1 | no | — |
| 15 | C22⋊#11924031 | — | 2 | 1 | no | — |
| 16 | #17989456 | — | 2 | 1 | no | — |
| 17 | #17989423 | — | 2 | 1 | no | — |
| 18 | #17989403 | — | 2 | 2 | no | — |
| 19 | #17989397 | — | 2 | 2 | no | — |
| 20 | #17989396 | — | 2 | 2 | no | — |
| 21 | #17989391 | — | 2 | 2 | no | — |
| 22 | #17989387 | C4 | 1 | 1 | yes | characteristic |
| 23 | #17989384 | — | 2 | 1 | no | — |
| 24 | #17989384 | C4 | 1 | 2 | yes | — |
| 25 | C2×#14556611 | — | 2 | 1 | no | — |
| 26 | #135×D73 | — | 2 | 1 | no | — |
| 27 | #135×D73 | C22 | 1 | 2 | yes | — |
| 28 | C2×#14556599 | C22 | 1 | 1 | yes | characteristic |
| 29 | #575×C73 | C4 | 1 | 1 | yes | characteristic |
| 30 | D73⋊M16 | — | 2 | 2 | no | — |
| 31 | #14556666 | — | 2 | 2 | no | — |
| 32 | #14556664 | — | 2 | 2 | no | — |
| 33 | C2×#11924031 | — | 2 | 1 | no | — |
| 34 | C2×#11924031 | — | 2 | 1 | no | — |
| 35 | #14556662 | — | 2 | 2 | no | — |
| 36 | #14556661 | — | 2 | 2 | no | — |
| 37 | #14556652 | — | 4 | 1 | no | — |
| 38 | #14556651 | — | 4 | 1 | no | — |
| 39 | #14556639 | — | 2 | 2 | no | — |
| 40 | #14556638 | — | 2 | 2 | no | — |
| 41 | #14556638 | — | 4 | 1 | no | — |
| 42 | #14556637 | — | 2 | 2 | no | — |
| 43 | #14556637 | — | 4 | 1 | no | — |
| 44 | #14556636 | — | 2 | 2 | no | — |
| 45 | #14556636 | — | 4 | 1 | no | — |
| 46 | #14556636 | — | 4 | 1 | no | — |
| 47 | C2×#11924028 | — | 2 | 1 | no | — |
| 48 | C2×#11924028 | — | 4 | 2 | no | — |
| 49 | C2×#11924028 | D4 | 1 | 1 | yes | characteristic |
| 50 | #41×D73 | — | 2 | 2 | no | — |
| 51 | #41×D73 | — | 2 | 2 | no | — |
| 52 | #41×D73 | — | 4 | 2 | no | — |
| 53 | #14556624 | — | 2 | 2 | no | — |
| 54 | #14556623 | — | 2 | 2 | no | — |
| 55 | #14556623 | — | 2 | 2 | no | — |
| 56 | #14556620 | — | 2 | 2 | no | — |
| 57 | #14556620 | — | 2 | 2 | no | — |
| 58 | #14556619 | — | 2 | 2 | no | — |
| 59 | #14556618 | — | 2 | 2 | no | — |
| 60 | #14556618 | — | 2 | 2 | no | — |
| 61 | #14556615 | — | 2 | 2 | no | — |
| 62 | #14556615 | — | 2 | 2 | no | — |
| 63 | #14556614 | — | 2 | 1 | no | — |
| 64 | #14556614 | D4 | 1 | 2 | yes | — |
| 65 | #14556613 | — | 2 | 1 | no | — |
| 66 | #14556613 | C2×C4 | 1 | 2 | yes | — |
| 67 | #14556612 | — | 2 | 2 | no | — |
| 68 | #14556612 | — | 2 | 2 | no | — |
| 69 | #14556611 | — | 2 | 2 | no | — |
| 70 | #14556611 | — | 2 | 2 | no | — |
| 71 | #14556611 | — | 2 | 2 | no | — |
| 72 | #14556611 | — | 2 | 2 | no | — |
| 73 | #14556610 | — | 2 | 1 | no | — |
| 74 | #14556610 | D4 | 1 | 2 | yes | — |
| 75 | C2×#11924018 | — | 2 | 1 | no | — |
| 76 | Q16×D73 | — | 2 | 1 | no | — |
| 77 | Q16×D73 | D4 | 1 | 2 | yes | — |
| 78 | C2×#11924016 | — | 2 | 1 | no | — |
| 79 | C2×#11924015 | — | 2 | 1 | no | — |
| 80 | SD16×D73 | — | 2 | 2 | no | — |
| 81 | SD16×D73 | — | 2 | 2 | no | — |
| 82 | C2×#11924013 | — | 2 | 1 | no | — |
| 83 | D8×D73 | — | 2 | 1 | no | — |
| 84 | D8×D73 | D4 | 1 | 2 | yes | — |
| 85 | #14556599 | — | 2 | 2 | no | — |
| 86 | #14556599 | — | 2 | 2 | no | — |
| 87 | C2×#11924011 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | C2×#11924011 | D4 | 1 | 1 | yes | characteristic |
| 89 | C22×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C8×D73 | D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C8×D73 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×#41×C73 | — | 2 | 1 | no | — |
| 93 | #137×C73 | — | 2 | 2 | no | — |
| 94 | AGL(1,ℤ/8)×C73 | — | 2 | 2 | no | — |
| 95 | #135×C73 | — | 2 | 1 | no | — |
| 96 | #135×C73 | C2×C4 | 1 | 2 | yes | — |
| 97 | C2×M16×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 98 | #11924038 | — | 4 | 2 | no | — |
| 99 | #11924037 | — | 4 | 2 | no | — |
| 100 | #11924036 | — | 4 | 2 | no | — |
| 101 | #11924031 | — | 4 | 1 | no | — |
| 102 | #11924031 | — | 4 | 1 | no | — |
| 103 | #11924029 | — | 2 | 2 | no | — |
| 104 | #11924029 | — | 2 | 2 | no | — |
| 105 | #11924029 | — | 4 | 2 | no | — |
| 106 | #11924028 | — | 2 | 2 | no | — |
| 107 | #11924028 | — | 2 | 2 | no | — |
| 108 | #11924028 | — | 2 | 2 | no | — |
| 109 | #11924028 | — | 2 | 2 | no | — |
| 110 | #11924028 | — | 4 | 2 | no | — |
| 111 | #11924028 | — | 4 | 2 | no | — |
| 112 | #11924028 | — | 4 | 2 | no | — |
| 113 | #11924028 | — | 4 | 2 | no | — |
| 114 | #11924028 | — | 4 | 2 | no | — |
| 115 | #11924028 | — | 4 | 1 | no | — |
| 116 | #11924028 | — | 4 | 1 | no | — |
| 117 | #11924028 | — | 4 | 2 | no | — |
| 118 | #11924027 | — | 2 | 2 | no | — |
| 119 | #11924027 | — | 2 | 2 | no | — |
| 120 | #11924027 | — | 4 | 2 | no | — |
| 121 | #11924027 | — | 4 | 2 | no | — |
| 122 | #11924027 | — | 4 | 2 | no | — |
| 123 | #11924027 | — | 4 | 2 | no | — |
| 124 | #11924027 | — | 4 | 2 | no | — |
| 125 | C2×Dic146 | — | 2 | 1 | no | — |
| 126 | C2×Dic146 | — | 4 | 2 | no | — |
| 127 | C2×Dic146 | D8 | 1 | 1 | yes | characteristic |
| 128 | Q8×D73 | — | 2 | 2 | no | — |
| 129 | Q8×D73 | — | 2 | 2 | no | — |
| 130 | Q8×D73 | — | 4 | 2 | no | — |
| 131 | C2×D292 | — | 2 | 1 | no | — |
| 132 | C2×D292 | — | 4 | 2 | no | — |
| 133 | C2×D292 | SD16 | 1 | 1 | yes | characteristic |
| 134 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 135 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 136 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 137 | C2×C22⋊D73 | D8 | 1 | 1 | yes | characteristic |
| 138 | C2×C22⋊D73 | SD16 | 1 | 1 | yes | characteristic |
| 139 | D4×D73 | — | 2 | 2 | no | — |
| 140 | D4×D73 | — | 2 | 2 | no | — |
| 141 | D4×D73 | — | 4 | 2 | no | — |
| 142 | D4×D73 | — | 4 | 2 | no | — |
| 143 | D4×D73 | — | 4 | 2 | no | — |
| 144 | D4×D73 | — | 4 | 2 | no | — |
| 145 | D4×D73 | — | 4 | 2 | no | — |
| 146 | C2×C4×D73 | — | 4 | 2 | no | — |
| 147 | C2×C4×D73 | — | 4 | 1 | no | — |
| 148 | C2×C4×D73 | — | 4 | 2 | no | — |
| 149 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | Dic292 | — | 2 | 1 | no | — |
| 152 | Dic292 | C22⋊C4 | 1 | 2 | yes | — |
| 153 | #11924018 | — | 2 | 2 | no | — |
| 154 | #11924018 | — | 2 | 2 | no | — |
| 155 | #11924017 | — | 2 | 2 | no | — |
| 156 | #11924017 | — | 2 | 2 | no | — |
| 157 | #11924016 | — | 2 | 2 | no | — |
| 158 | #11924016 | — | 2 | 2 | no | — |
| 159 | #11924015 | — | 2 | 2 | no | — |
| 160 | #11924015 | — | 2 | 2 | no | — |
| 161 | D584 | — | 2 | 1 | no | — |
| 162 | D584 | C22⋊C4 | 1 | 2 | yes | — |
| 163 | #11924013 | — | 2 | 2 | no | — |
| 164 | #11924013 | — | 2 | 2 | no | — |
| 165 | #11924011 | — | 2 | 2 | no | — |
| 166 | #11924011 | — | 2 | 2 | no | — |
| 167 | C2×#10596831 | — | 2 | 1 | no | — |
| 168 | C2×#10596831 | — | 2 | 1 | no | — |
| 169 | C2×#10596831 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 170 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C8×D73 | — | 2 | 1 | no | — |
| 172 | C8×D73 | — | 2 | 1 | no | — |
| 173 | C8×D73 | C2×D4 | 1 | 2 | yes | — |
| 174 | C8×D73 | C2×D4 | 1 | 2 | yes | — |
| 175 | #41×C73 | — | 2 | 2 | no | — |
| 176 | #41×C73 | — | 2 | 2 | no | — |
| 177 | #41×C73 | — | 4 | 1 | no | — |
| 178 | #41×C73 | — | 4 | 1 | no | — |
| 179 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 180 | C2×D4×C73 | — | 2 | 1 | no | — |
| 181 | C2×D4×C73 | — | 4 | 1 | no | — |
| 182 | C22×C4×C73 | — | 4 | 1 | no | — |
| 183 | C22×C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 184 | Q16×C73 | — | 2 | 1 | no | — |
| 185 | Q16×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 186 | SD16×C73 | — | 2 | 2 | no | — |
| 187 | SD16×C73 | — | 2 | 2 | no | — |
| 188 | D8×C73 | — | 2 | 1 | no | — |
| 189 | D8×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 190 | M16×C73 | — | 2 | 2 | no | — |
| 191 | C2×C8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 192 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 193 | C23×C73 | — | 4 | 1 | no | — |
| 194 | C23×C73 | #102 | 1 | 1 | yes | characteristic |
| 195 | C22×D73 | — | 4 | 2 | no | — |
| 196 | C22×D73 | — | 4 | 1 | no | — |
| 197 | C22×D73 | — | 4 | 2 | no | — |
| 198 | C22×D73 | #102 | 1 | 1 | yes | characteristic |
| 199 | C22×D73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 200 | Q8×C73 | — | 2 | 2 | no | — |
| 201 | Q8×C73 | — | 4 | 1 | no | — |
| 202 | D4×C73 | — | 2 | 2 | no | — |
| 203 | D4×C73 | — | 4 | 1 | no | — |
| 204 | D4×C73 | — | 4 | 2 | no | — |
| 205 | D4×C73 | — | 4 | 2 | no | — |
| 206 | C2×C4×C73 | — | 2 | 1 | no | — |
| 207 | C2×C4×C73 | — | 2 | 1 | no | — |
| 208 | C2×C4×C73 | — | 4 | 2 | no | — |
| 209 | C2×C4×C73 | — | 4 | 1 | no | — |
| 210 | C2×C4×C73 | — | 4 | 2 | no | — |
| 211 | C2×C4×C73 | #102 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C22⋊D73 | — | 2 | 2 | no | — |
| 214 | C22⋊D73 | — | 2 | 2 | no | — |
| 215 | C22⋊D73 | — | 4 | 2 | no | — |
| 216 | C22⋊D73 | — | 4 | 2 | no | — |
| 217 | C22⋊D73 | — | 4 | 2 | no | — |
| 218 | C22⋊D73 | — | 4 | 2 | no | — |
| 219 | C22⋊D73 | — | 4 | 2 | no | — |
| 220 | C22⋊D73 | — | 4 | 2 | no | — |
| 221 | C2×Dic73 | — | 4 | 2 | no | — |
| 222 | C2×Dic73 | — | 4 | 1 | no | — |
| 223 | C2×Dic73 | — | 4 | 2 | no | — |
| 224 | C2×Dic73 | #102 | 1 | 1 | yes | characteristic |
| 225 | C2×Dic73 | C2×D8 | 1 | 1 | yes | characteristic |
| 226 | D292 | — | 2 | 2 | no | — |
| 227 | D292 | — | 2 | 2 | no | — |
| 228 | D292 | — | 4 | 1 | no | — |
| 229 | D292 | — | 4 | 2 | no | — |
| 230 | D292 | — | 4 | 2 | no | — |
| 231 | C4×D73 | — | 2 | 1 | no | — |
| 232 | C4×D73 | — | 2 | 1 | no | — |
| 233 | C4×D73 | — | 4 | 2 | no | — |
| 234 | C4×D73 | — | 4 | 2 | no | — |
| 235 | C4×D73 | — | 4 | 2 | no | — |
| 236 | C4×D73 | — | 4 | 2 | no | — |
| 237 | C4×D73 | — | 4 | 2 | no | — |
| 238 | C4×D73 | — | 4 | 2 | no | — |
| 239 | C4×D73 | #120 | 1 | 2 | yes | — |
| 240 | C4×D73 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 241 | Dic146 | — | 2 | 2 | no | — |
| 242 | Dic146 | — | 2 | 2 | no | — |
| 243 | Dic146 | — | 4 | 2 | no | — |
| 244 | Dic146 | — | 4 | 1 | no | — |
| 245 | Dic146 | — | 4 | 2 | no | — |
| 246 | #10596833 | — | 8 | 2 | no | — |
| 247 | C8×C73 | — | 2 | 1 | no | — |
| 248 | C8×C73 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 249 | #10596831 | — | 2 | 1 | no | — |
| 250 | #10596831 | #120 | 1 | 1 | yes | characteristic |
| 251 | #10596831 | #120 | 1 | 1 | yes | characteristic |
| 252 | C22×C73 | — | 2 | 1 | no | — |
| 253 | C22×C73 | — | 4 | 1 | no | — |
| 254 | C22×C73 | — | 4 | 2 | no | — |
| 255 | C22×C73 | — | 16 | 1 | no | — |
| 256 | C22×C73 | C2×#102 | 1 | 1 | yes | characteristic |
| 257 | C2×D73 | — | 2 | 1 | no | — |
| 258 | C2×D73 | — | 4 | 1 | no | — |
| 259 | C2×D73 | — | 4 | 1 | no | — |
| 260 | C2×D73 | — | 4 | 2 | no | — |
| 261 | C2×D73 | — | 16 | 2 | no | — |
| 262 | C2×D73 | — | 16 | 2 | no | — |
| 263 | C2×D73 | — | 16 | 1 | no | — |
| 264 | C2×D73 | #450 | 1 | 2 | yes | — |
| 265 | C4×C73 | — | 2 | 1 | no | — |
| 266 | C4×C73 | — | 4 | 2 | no | — |
| 267 | C4×C73 | #379 | 1 | 1 | yes | characteristic |
| 268 | C4×C73 | #418 | 1 | 1 | yes | characteristic |
| 269 | Dic73 | — | 2 | 1 | no | — |
| 270 | Dic73 | — | 4 | 2 | no | — |
| 271 | Dic73 | #447 | 1 | 2 | yes | — |
| 272 | #12746 | — | 73 | 1 | no | maximal, Sylow |
| 273 | C2×C73 | — | 2 | 1 | no | — |
| 274 | C2×C73 | — | 4 | 1 | no | — |
| 275 | C2×C73 | — | 8 | 2 | no | — |
| 276 | C2×C73 | #1786 | 1 | 1 | yes | characteristic |
| 277 | D73 | — | 2 | 2 | no | — |
| 278 | D73 | — | 4 | 1 | no | — |
| 279 | D73 | — | 8 | 2 | no | — |
| 280 | #3584 | — | 73 | 1 | no | — |
| 281 | #2148 | — | 73 | 2 | no | — |
| 282 | C2×#359 | — | 73 | 2 | no | — |
| 283 | #2113 | — | 73 | 1 | no | — |
| 284 | #1813 | — | 73 | 1 | no | — |
| 285 | C73 | #12746 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 286 | #585 | — | 146 | 1 | no | — |
| 287 | #578 | — | 146 | 2 | no | — |
| 288 | #577 | — | 146 | 2 | no | — |
| 289 | #577 | — | 146 | 2 | no | — |
| 290 | #576 | — | 146 | 2 | no | — |
| 291 | #575 | — | 73 | 2 | no | — |
| 292 | #575 | — | 73 | 1 | no | — |
| 293 | #575 | — | 146 | 1 | no | — |
| 294 | #575 | #64408 | 1 | 1 | yes | characteristic |
| 295 | C2×#135 | — | 73 | 2 | no | — |
| 296 | C2×#135 | — | 146 | 1 | no | — |
| 297 | C2×#135 | — | 146 | 1 | no | — |
| 298 | C2×#131 | — | 73 | 1 | no | — |
| 299 | C2×M32 | — | 73 | 1 | no | — |
| 300 | C22×C16 | — | 73 | 1 | no | — |
| 301 | C2×#108 | — | 73 | 2 | no | — |
| 302 | #413 | — | 146 | 1 | no | — |
| 303 | #362 | — | 146 | 2 | no | — |
| 304 | #361 | — | 146 | 2 | no | — |
| 305 | #359 | — | 146 | 2 | no | — |
| 306 | #359 | — | 146 | 2 | no | — |
| 307 | C22⋊C16 | — | 146 | 1 | no | — |
| 308 | C22⋊C16 | — | 146 | 1 | no | — |
| 309 | #338 | — | 146 | 1 | no | — |
| 310 | 2−1+4 | — | 292 | 1 | no | — |
| 311 | 2−1+4 | — | 146 | 2 | no | — |
| 312 | 2−1+4 | — | 146 | 2 | no | — |
| 313 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 314 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 315 | H(5,𝔽2) | — | 292 | 1 | no | — |
| 316 | H(5,𝔽2) | — | 146 | 2 | no | — |
| 317 | H(5,𝔽2) | — | 146 | 2 | no | — |
| 318 | C2×#41 | — | 2 | 1 | no | — |
| 319 | C2×#41 | — | 292 | 2 | no | — |
| 320 | C2×#41 | — | 292 | 2 | no | — |
| 321 | C2×#41 | — | 73 | 1 | no | — |
| 322 | C2×#41 | — | 146 | 2 | no | — |
| 323 | C2×#41 | — | 146 | 2 | no | — |
| 324 | C2×#41 | — | 146 | 1 | no | — |
| 325 | #137 | — | 2 | 2 | no | — |
| 326 | #137 | — | 146 | 2 | no | — |
| 327 | #137 | — | 146 | 2 | no | — |
| 328 | #137 | — | 146 | 2 | no | — |
| 329 | #137 | — | 146 | 2 | no | — |
| 330 | #137 | — | 146 | 2 | no | — |
| 331 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 332 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 333 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 334 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 335 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 336 | AGL(1,ℤ/8) | — | 146 | 2 | no | — |
| 337 | #135 | — | 2 | 1 | no | — |
| 338 | #135 | — | 73 | 2 | no | — |
| 339 | #135 | — | 73 | 2 | no | — |
| 340 | #135 | — | 73 | 2 | no | — |
| 341 | #135 | — | 146 | 2 | no | — |
| 342 | #135 | — | 146 | 2 | no | — |
| 343 | #135 | — | 146 | 2 | no | — |
| 344 | #135 | — | 146 | 1 | no | — |
| 345 | #135 | — | 146 | 2 | no | — |
| 346 | #135 | — | 146 | 1 | no | — |
| 347 | #135 | — | 146 | 2 | no | — |
| 348 | #135 | — | 146 | 2 | no | — |
| 349 | #135 | — | 146 | 1 | no | — |
| 350 | #135 | C2×#64408 | 1 | 2 | yes | — |
| 351 | C2×Q16 | — | 73 | 2 | no | — |
| 352 | C2×Q16 | — | 146 | 1 | no | — |
| 353 | C2×Q16 | — | 146 | 1 | no | — |
| 354 | C2×SD16 | — | 146 | 2 | no | — |
| 355 | C2×SD16 | — | 146 | 2 | no | — |
| 356 | C2×SD16 | — | 146 | 1 | no | — |
| 357 | C2×SD16 | — | 146 | 1 | no | — |
| 358 | C2×D8 | — | 73 | 2 | no | — |
| 359 | C2×D8 | — | 146 | 1 | no | — |
| 360 | C2×D8 | — | 146 | 1 | no | — |
| 361 | #131 | — | 146 | 2 | no | — |
| 362 | #131 | — | 146 | 2 | no | — |
| 363 | C2×M16 | — | 73 | 1 | no | — |
| 364 | C2×M16 | — | 73 | 1 | no | — |
| 365 | C2×M16 | — | 146 | 2 | no | — |
| 366 | C2×M16 | C2×#64408 | 1 | 1 | yes | characteristic |
| 367 | C22×C8 | — | 73 | 1 | no | — |
| 368 | C22×C8 | — | 73 | 1 | no | — |
| 369 | C22×C8 | — | 73 | 1 | no | — |
| 370 | M32 | — | 146 | 2 | no | — |
| 371 | C2×C16 | — | 146 | 1 | no | — |
| 372 | C2×C16 | — | 146 | 1 | no | — |
| 373 | C2×C16 | — | 146 | 2 | no | — |
| 374 | #108 | — | 146 | 2 | no | — |
| 375 | #108 | — | 146 | 2 | no | — |
| 376 | #101 | — | 292 | 1 | no | — |
| 377 | #100 | — | 292 | 1 | no | — |
| 378 | #41 | — | 2 | 2 | no | — |
| 379 | #41 | — | 2 | 2 | no | — |
| 380 | #41 | — | 4 | 1 | no | — |
| 381 | #41 | — | 4 | 1 | no | — |
| 382 | #41 | — | 292 | 1 | no | — |
| 383 | #41 | — | 292 | 2 | no | — |
| 384 | #41 | — | 292 | 2 | no | — |
| 385 | #41 | — | 292 | 2 | no | — |
| 386 | #41 | — | 292 | 2 | no | — |
| 387 | #41 | — | 292 | 2 | no | — |
| 388 | #41 | — | 292 | 2 | no | — |
| 389 | #41 | — | 292 | 2 | no | — |
| 390 | #41 | — | 292 | 2 | no | — |
| 391 | #41 | — | 292 | 2 | no | — |
| 392 | #41 | — | 292 | 2 | no | — |
| 393 | #41 | — | 292 | 2 | no | — |
| 394 | #41 | — | 292 | 2 | no | — |
| 395 | #41 | — | 292 | 1 | no | — |
| 396 | #41 | — | 146 | 2 | no | — |
| 397 | #41 | — | 146 | 2 | no | — |
| 398 | #41 | — | 146 | 2 | no | — |
| 399 | #41 | — | 146 | 2 | no | — |
| 400 | #41 | — | 146 | 2 | no | — |
| 401 | #41 | — | 146 | 2 | no | — |
| 402 | #41 | — | 146 | 2 | no | — |
| 403 | #41 | — | 146 | 2 | no | — |
| 404 | C2×Q8 | — | 2 | 1 | no | — |
| 405 | C2×Q8 | — | 292 | 2 | no | — |
| 406 | C2×Q8 | — | 292 | 2 | no | — |
| 407 | C2×Q8 | — | 73 | 1 | no | — |
| 408 | C2×Q8 | — | 146 | 1 | no | — |
| 409 | C2×Q8 | — | 146 | 2 | no | — |
| 410 | C2×Q8 | — | 146 | 2 | no | — |
| 411 | C2×D4 | — | 2 | 1 | no | — |
| 412 | C2×D4 | — | 4 | 1 | no | — |
| 413 | C2×D4 | — | 292 | 2 | no | — |
| 414 | C2×D4 | — | 292 | 2 | no | — |
| 415 | C2×D4 | — | 292 | 2 | no | — |
| 416 | C2×D4 | — | 292 | 2 | no | — |
| 417 | C2×D4 | — | 292 | 2 | no | — |
| 418 | C2×D4 | — | 292 | 2 | no | — |
| 419 | C2×D4 | — | 292 | 1 | no | — |
| 420 | C2×D4 | — | 292 | 2 | no | — |
| 421 | C2×D4 | — | 292 | 2 | no | — |
| 422 | C2×D4 | — | 73 | 1 | no | — |
| 423 | C2×D4 | — | 73 | 1 | no | — |
| 424 | C2×D4 | — | 73 | 1 | no | — |
| 425 | C2×D4 | — | 146 | 1 | no | — |
| 426 | C2×D4 | — | 146 | 2 | no | — |
| 427 | C2×D4 | — | 146 | 2 | no | — |
| 428 | C22×C4 | — | 4 | 1 | no | — |
| 429 | C22×C4 | — | 292 | 1 | no | — |
| 430 | C22×C4 | — | 292 | 2 | no | — |
| 431 | C22×C4 | — | 292 | 2 | no | — |
| 432 | C22×C4 | — | 73 | 1 | no | — |
| 433 | C22×C4 | — | 73 | 1 | no | — |
| 434 | C22×C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 435 | Q16 | — | 2 | 1 | no | — |
| 436 | Q16 | — | 73 | 2 | no | — |
| 437 | Q16 | — | 146 | 1 | no | — |
| 438 | Q16 | — | 146 | 2 | no | — |
| 439 | Q16 | — | 146 | 2 | no | — |
| 440 | Q16 | C22⋊#64408 | 1 | 2 | yes | — |
| 441 | SD16 | — | 2 | 2 | no | — |
| 442 | SD16 | — | 2 | 2 | no | — |
| 443 | SD16 | — | 146 | 2 | no | — |
| 444 | SD16 | — | 146 | 2 | no | — |
| 445 | SD16 | — | 146 | 2 | no | — |
| 446 | SD16 | — | 146 | 2 | no | — |
| 447 | SD16 | — | 146 | 2 | no | — |
| 448 | SD16 | — | 146 | 2 | no | — |
| 449 | D8 | — | 2 | 1 | no | — |
| 450 | D8 | — | 73 | 2 | no | — |
| 451 | D8 | — | 146 | 1 | no | — |
| 452 | D8 | — | 146 | 2 | no | — |
| 453 | D8 | — | 146 | 2 | no | — |
| 454 | D8 | C22⋊#64408 | 1 | 2 | yes | — |
| 455 | M16 | — | 2 | 2 | no | — |
| 456 | M16 | — | 292 | 2 | no | — |
| 457 | M16 | — | 292 | 2 | no | — |
| 458 | M16 | — | 146 | 2 | no | — |
| 459 | M16 | — | 146 | 2 | no | — |
| 460 | C2×C8 | — | 292 | 2 | no | — |
| 461 | C2×C8 | — | 73 | 1 | no | — |
| 462 | C2×C8 | — | 73 | 2 | no | — |
| 463 | C2×C8 | — | 73 | 2 | no | — |
| 464 | C2×C8 | — | 73 | 1 | no | — |
| 465 | C2×C8 | — | 146 | 1 | no | — |
| 466 | C2×C8 | — | 146 | 1 | no | — |
| 467 | C2×C8 | — | 146 | 1 | no | — |
| 468 | C2×C8 | — | 146 | 1 | no | — |
| 469 | C2×C8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 470 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 471 | C16 | — | 292 | 1 | no | — |
| 472 | C16 | — | 292 | 1 | no | — |
| 473 | C23 | — | 4 | 1 | no | — |
| 474 | C23 | — | 292 | 1 | no | — |
| 475 | C23 | — | 292 | 2 | no | — |
| 476 | C23 | — | 292 | 2 | no | — |
| 477 | C23 | — | 73 | 1 | no | — |
| 478 | C23 | — | 73 | 1 | no | — |
| 479 | C23 | #14556653 | 1 | 1 | yes | characteristic |
| 480 | Q8 | — | 2 | 2 | no | — |
| 481 | Q8 | — | 4 | 1 | no | — |
| 482 | Q8 | — | 292 | 1 | no | — |
| 483 | Q8 | — | 292 | 2 | no | — |
| 484 | Q8 | — | 292 | 2 | no | — |
| 485 | Q8 | — | 146 | 2 | no | — |
| 486 | Q8 | — | 146 | 2 | no | — |
| 487 | D4 | — | 2 | 2 | no | — |
| 488 | D4 | — | 4 | 1 | no | — |
| 489 | D4 | — | 4 | 2 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 292 | 1 | no | — |
| 492 | D4 | — | 292 | 2 | no | — |
| 493 | D4 | — | 292 | 2 | no | — |
| 494 | D4 | — | 292 | 2 | no | — |
| 495 | D4 | — | 292 | 2 | no | — |
| 496 | D4 | — | 292 | 2 | no | — |
| 497 | D4 | — | 292 | 2 | no | — |
| 498 | D4 | — | 292 | 2 | no | — |
| 499 | D4 | — | 292 | 2 | no | — |
| 500 | D4 | — | 146 | 2 | no | — |
| 501 | D4 | — | 146 | 2 | no | — |
| 502 | D4 | — | 146 | 2 | no | — |
| 503 | D4 | — | 146 | 2 | no | — |
| 504 | C2×C4 | — | 2 | 1 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 4 | 2 | no | — |
| 507 | C2×C4 | — | 4 | 1 | no | — |
| 508 | C2×C4 | — | 4 | 2 | no | — |
| 509 | C2×C4 | — | 292 | 2 | no | — |
| 510 | C2×C4 | — | 292 | 2 | no | — |
| 511 | C2×C4 | — | 292 | 2 | no | — |
| 512 | C2×C4 | — | 292 | 2 | no | — |
| 513 | C2×C4 | — | 292 | 2 | no | — |
| 514 | C2×C4 | — | 292 | 1 | no | — |
| 515 | C2×C4 | — | 292 | 2 | no | — |
| 516 | C2×C4 | — | 292 | 2 | no | — |
| 517 | C2×C4 | — | 292 | 2 | no | — |
| 518 | C2×C4 | — | 73 | 1 | no | — |
| 519 | C2×C4 | — | 73 | 2 | no | — |
| 520 | C2×C4 | — | 73 | 2 | no | — |
| 521 | C2×C4 | — | 73 | 1 | no | — |
| 522 | C2×C4 | — | 146 | 1 | no | — |
| 523 | C2×C4 | — | 146 | 1 | no | — |
| 524 | C2×C4 | #14556653 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 526 | C8 | — | 2 | 1 | no | — |
| 527 | C8 | — | 584 | 2 | no | — |
| 528 | C8 | — | 73 | 1 | no | — |
| 529 | C8 | — | 73 | 1 | no | — |
| 530 | C8 | — | 146 | 1 | no | — |
| 531 | C8 | C2×C22⋊#64408 | 1 | 2 | yes | — |
| 532 | C22 | — | 2 | 1 | no | — |
| 533 | C22 | — | 4 | 1 | no | — |
| 534 | C22 | — | 4 | 2 | no | — |
| 535 | C22 | — | 16 | 1 | no | — |
| 536 | C22 | — | 292 | 1 | no | — |
| 537 | C22 | — | 292 | 1 | no | — |
| 538 | C22 | — | 292 | 2 | no | — |
| 539 | C22 | — | 73 | 2 | no | — |
| 540 | C22 | — | 1168 | 1 | no | — |
| 541 | C22 | — | 1168 | 2 | no | — |
| 542 | C22 | — | 1168 | 2 | no | — |
| 543 | C22 | — | 146 | 1 | no | — |
| 544 | C22 | C2×#14556653 | 1 | 1 | yes | characteristic |
| 545 | C4 | — | 2 | 1 | no | — |
| 546 | C4 | — | 4 | 2 | no | — |
| 547 | C4 | — | 292 | 2 | no | — |
| 548 | C4 | — | 73 | 2 | no | — |
| 549 | C4 | — | 146 | 1 | no | — |
| 550 | C4 | #17989528 | 1 | 1 | yes | characteristic |
| 551 | C4 | #17989579 | 1 | 1 | yes | characteristic |
| 552 | C2 | — | 2 | 1 | no | — |
| 553 | C2 | — | 4 | 1 | no | — |
| 554 | C2 | — | 8 | 2 | no | — |
| 555 | C2 | — | 292 | 1 | no | — |
| 556 | C2 | — | 584 | 2 | no | — |
| 557 | C2 | — | 146 | 2 | no | — |
| 558 | C2 | #22625769 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626258 | C2 | semidirect |
| 2. D73⋊#359 | C2 | semidirect |
| 3. #22626162 | C2 | semidirect |
| 4. #22625816 | C2 | semidirect |
| 6. C2×#14556666 | C22 | semidirect |
| 7. C2×#14556664 | C22 | semidirect |
| 8. D73⋊#108 | C22 | semidirect |
| 285. C73 | #12746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626258 | 2 |
| D73⋊#359 | 2 |
| #22626162 | 2 |
| #22625816 | 2 |
| #22624704 | 2 |
| #12746 | 73 |