Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
Only the 4277 normal subgroups are shown; non-normal subgroups are omitted.
The subgroup lattice has 517 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72232048 |
| commutator, Frattini, cosocle | C26 | C26 |
| LCS | G ▷ C26 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C26 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72305956 | C2 | semidirect |
| 2. #72303484 | C2 | semidirect |
| 3. #72303475 | C2 | semidirect |
| 4. #72303394 | C22 | semidirect |
| 5. #72303387 | C22 | semidirect |
| 6. #72302137 | C2 | semidirect |
| 7. #72302130 | C22 | semidirect |
| 8. #72302092 | C22 | semidirect |
| 9. #72300151 | C2 | semidirect |
| 10. #72300149 | C22 | semidirect |
| 11. #72271167 | C22 | semidirect |
| 12. #72266864 | C22 | semidirect |
| 13. #72266581 | C2 | semidirect |
| 14. #72266555 | C22 | semidirect |
| 15. #72266521 | C22 | semidirect |
| 16. #72266509 | C22 | semidirect |
| 17. #72258968 | C2 | semidirect |
| 18. #72256119 | C22 | semidirect |
| 19. #72238595 | C22 | semidirect |
| 20. #72238595 | C22 | semidirect |
| 21. #72237302 | C22 | semidirect |
| 22. #72234651 | C2 | semidirect |
| 23. #72234650 | C22 | semidirect |
| 24. #72234647 | C22 | semidirect |
| 25. #72234641 | C22 | semidirect |
| 26. #72234639 | C2 | semidirect |
| 27. #72234638 | C22 | semidirect |
| 28. #72234637 | C22 | semidirect |
| 29. #72234636 | C22 | semidirect |
| 30. #72234633 | C22 | semidirect |
| 31. #72234623 | C22 | semidirect |
| 32. #72234622 | C22 | semidirect |
| 33. #72234621 | C22 | semidirect |
| 34. #72234608 | C22 | semidirect |
| 35. #72234607 | C22 | semidirect |
| 36. #72234606 | C22 | semidirect |
| 37. #72234598 | C22 | semidirect |
| 38. #72234597 | C22 | semidirect |
| 39. #72234595 | C22 | semidirect |
| 40. #72234593 | C22 | semidirect |
| 41. #72233067 | C22 | semidirect |
| 42. #72233067 | C22 | semidirect |
| 43. #72225712 | C22 | semidirect |
| 44. #72224136 | C22 | semidirect |
| 45. #72219311 | C22 | semidirect |
| 47. #72219254 | C22 | semidirect |
| 48. #72218180 | C22 | semidirect |
| 49. #72216662 | C2 | semidirect |
| 50. #72216629 | C22 | semidirect |
| 51. #72216625 | C22 | semidirect |
| 52. #72216620 | C22 | semidirect |
| 53. #72216616 | C22 | semidirect |
| 54. #72216587 | C22 | semidirect |
| 55. #72216481 | C22 | semidirect |
| 57. #72215858 | C22 | semidirect |
| 58. #1202 | C22 | semidirect |
| 59. #72211223 | C2 | semidirect |
| 60. #72211186 | C22 | semidirect |
| 61. #72211186 | C22 | semidirect |
| 62. #72211163 | C22 | semidirect |
| 63. #72211144 | C22 | semidirect |
| 64. #72210600 | C22 | semidirect |
| 65. #72210578 | C22 | semidirect |
| 66. #72209716 | C22 | semidirect |
| 67. #72209716 | C22 | semidirect |
| 68. #72209699 | C22 | semidirect |
| 73. C24×#120 | C23 | semidirect |
| 74. C2×#46996 | C23 | semidirect |
| 90. #6342371 | C23 | semidirect |
| 91. #6342371 | C23 | semidirect |
| 92. #6342371 | C23 | semidirect |
| 93. #5034875 | C23 | semidirect |
| 94. #5025789 | D4 | semidirect |
| 96. #5024691 | C23 | semidirect |
| 97. #5021140 | D4 | semidirect |
| 99. #5020751 | C23 | semidirect |
| 100. #5020751 | C23 | semidirect |
| 101. #4432226 | C23 | semidirect |
| 102. #4430405 | C23 | semidirect |
| 103. #4430395 | C23 | semidirect |
| 104. #4422949 | D4 | semidirect |
| 106. #4386402 | C23 | semidirect |
| 107. #4381895 | D4 | semidirect |
| 108. #4379766 | C23 | semidirect |
| 110. #4308128 | C23 | semidirect |
| 111. #4308128 | C23 | semidirect |
| 112. #763333 | D4 | semidirect |
| 113. #712928 | D4 | semidirect |
| 114. #686187 | D4 | semidirect |
| 115. #648360 | C23 | semidirect |
| 116. #647670 | C23 | semidirect |
| 117. #647657 | D4 | semidirect |
| 119. #631793 | D4 | semidirect |
| 120. #617161 | C23 | semidirect |
| 121. #616969 | C23 | semidirect |
| 122. #616969 | C23 | semidirect |
| 123. #616961 | D4 | semidirect |
| 124. #616960 | D4 | semidirect |
| 126. #612459 | C23 | semidirect |
| 127. #612424 | C23 | semidirect |
| 128. C2×#15947 | D4 | semidirect |
| 129. #576160 | C23 | semidirect |
| 130. #561414 | C23 | semidirect |
| 133. C22⋊C4×#120 | C23 | semidirect |
| 134. #517411 | C23 | semidirect |
| 135. #394058 | C23 | semidirect |
| 136. #392675 | C23 | semidirect |
| 137. #392109 | C23 | semidirect |
| 138. #359501 | C23 | semidirect |
| 139. #238077 | C23 | semidirect |
| 140. #233541 | C23 | semidirect |
| 141. #201687 | C23 | semidirect |
| 142. #201664 | C23 | semidirect |
| 143. #190116 | C23 | semidirect |
| 154. #119911 | C23 | semidirect |
| 155. #119556 | C23 | semidirect |
| 156. #119556 | C23 | semidirect |
| 157. #119550 | C23 | semidirect |
| 158. #119550 | C23 | semidirect |
| 159. #116022 | C23 | semidirect |
| 160. #116022 | C23 | semidirect |
| 161. #115995 | C23 | semidirect |
| 162. #115690 | C23 | semidirect |
| 163. #115690 | C23 | semidirect |
| 164. #115690 | C23 | semidirect |
| 165. #115690 | C23 | semidirect |
| 166. #115690 | C23 | semidirect |
| 167. #115690 | C23 | semidirect |
| 168. #115631 | C23 | semidirect |
| 169. #115631 | C23 | semidirect |
| 170. #115204 | C23 | semidirect |
| 171. #115163 | C23 | semidirect |
| 172. #110180 | C23 | semidirect |
| 173. #110180 | C23 | semidirect |
| 174. #110086 | C23 | semidirect |
| 175. #107114 | C23 | semidirect |
| 176. #106766 | C23 | semidirect |
| 177. #106654 | C23 | semidirect |
| 178. C28 | C24 | semidirect |
| 190. C22×#534 | C2×D4 | semidirect |
| 193. C23×#120 | C2×D4 | semidirect |
| 194. C23×#120 | C2×D4 | semidirect |
| 196. C23×#120 | C24 | semidirect |
| 197. C24×C22⋊C4 | C24 | semidirect |
| 198. C2×#2840 | C24 | semidirect |
| 199. C2×#2849 | C2×D4 | semidirect |
| 200. C2×#2849 | C2×D4 | semidirect |
| 201. C2×#2847 | C2×D4 | semidirect |
| 202. C2×#2846 | C2×D4 | semidirect |
| 208. C2×#2433 | C2×D4 | semidirect |
| 209. C2×#2408 | C2×D4 | semidirect |
| 210. C2×#2410 | C2×D4 | semidirect |
| 212. C2×#2403 | C2×D4 | semidirect |
| 214. C2×#2403 | C24 | semidirect |
| 215. C2×#2613 | C2×D4 | semidirect |
| 216. C2×#2613 | C2×D4 | semidirect |
| 221. C2×#2308 | C2×D4 | semidirect |
| 223. C2×#2308 | C24 | semidirect |
| 224. C2×C4×#120 | C2×D4 | semidirect |
| 225. C22×#379 | C2×D4 | semidirect |
| 234. C2×#1781 | C24 | semidirect |
| 235. #16032 | C2×D4 | semidirect |
| 237. #15984 | C2×D4 | semidirect |
| 238. #15982 | C2×D4 | semidirect |
| 239. #15950 | C2×D4 | semidirect |
| 241. #15948 | C2×D4 | semidirect |
| 242. #15948 | C2×D4 | semidirect |
| 243. #15948 | C2×D4 | semidirect |
| 244. #15948 | C2×D4 | semidirect |
| 245. #15948 | C2×D4 | semidirect |
| 249. #15947 | C2×D4 | semidirect |
| 250. #15947 | C2×D4 | semidirect |
| 251. #15947 | C2×D4 | semidirect |
| 252. #15947 | C2×D4 | semidirect |
| 253. #15947 | C2×D4 | semidirect |
| 254. #15947 | C2×D4 | semidirect |
| 255. #15262 | C2×D4 | semidirect |
| 257. #15259 | C2×D4 | semidirect |
| 258. #15259 | C2×D4 | semidirect |
| 259. #15259 | C2×D4 | semidirect |
| 260. #15259 | C2×D4 | semidirect |
| 261. #15259 | C2×D4 | semidirect |
| 262. #15259 | C2×D4 | semidirect |
| 269. #15257 | C2×D4 | semidirect |
| 270. #15257 | C2×D4 | semidirect |
| 271. #15257 | C2×D4 | semidirect |
| 272. #15257 | C2×D4 | semidirect |
| 273. #15257 | C2×D4 | semidirect |
| 274. #15257 | C2×D4 | semidirect |
| 275. #14679 | C24 | semidirect |
| 276. #14679 | C24 | semidirect |
| 277. #14679 | C24 | semidirect |
| 278. #14679 | C24 | semidirect |
| 279. #14659 | C2×D4 | semidirect |
| 280. #14658 | C2×D4 | semidirect |
| 283. #14344 | C2×D4 | semidirect |
| 284. #14335 | C2×D4 | semidirect |
| 286. #14290 | C2×D4 | semidirect |
| 287. #14287 | C2×D4 | semidirect |
| 288. #14262 | C24 | semidirect |
| 289. #14262 | C24 | semidirect |
| 290. #14255 | C2×D4 | semidirect |
| 293. #14167 | C2×D4 | semidirect |
| 294. #14134 | C2×D4 | semidirect |
| 296. #13940 | C2×D4 | semidirect |
| 297. #13877 | C24 | semidirect |
| 298. #13869 | C2×D4 | semidirect |
| 299. #13867 | C2×D4 | semidirect |
| 301. #13867 | C24 | semidirect |
| 302. C2×#1438 | C2×D4 | semidirect |
| 303. C2×#1438 | C2×D4 | semidirect |
| 304. #13827 | C24 | semidirect |
| 305. #13827 | C24 | semidirect |
| 306. C22⋊C42 | C24 | semidirect |
| 307. #10735 | C24 | semidirect |
| 308. #8101 | C24 | semidirect |
| 309. #8101 | C24 | semidirect |
| 310. #8101 | C24 | semidirect |
| 311. C27 | #120 | semidirect |
| 315. C23×#41 | #120 | semidirect |
| 324. C22×#127 | #120 | semidirect |
| 326. C22×#126 | #120 | semidirect |
| 327. C22×#126 | #120 | semidirect |
| 328. C22×#124 | #120 | semidirect |
| 331. C22×#123 | #120 | semidirect |
| 337. C22×C22⋊Q8 | #120 | semidirect |
| 338. C22×#121 | #120 | semidirect |
| 343. C22×#120 | #120 | semidirect |
| 344. C22×#120 | #120 | semidirect |
| 345. C22×#120 | #120 | semidirect |
| 369. C22×C4×D4 | #120 | semidirect |
| 371. C22×#117 | #120 | semidirect |
| 372. C23×C22⋊C4 | #120 | semidirect |
| 373. C23×C22⋊C4 | #120 | semidirect |
| 488. C25 | #3532 | semidirect |
| 499. C23×C4 | #3532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72305956 | 2 |
| #72303484 | 2 |
| #72303475 | 2 |
| #72302137 | 2 |
| #72300151 | 2 |
| #72266581 | 2 |
| #72258968 | 2 |
| #72234651 | 2 |
| #72234639 | 2 |
| #72216662 | 2 |
| #72211223 | 2 |