Order 2048.
At least 7842 conjugacy classes of subgroups; only the 35072 normal subgroups are shown.
The subgroup lattice has 1748 nodes (normal subgroups only) — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D42 |
| commutator, Frattini, cosocle | C42 | C27 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6357777 | C2 | semidirect |
| 2. C2×#6348992 | C2 | semidirect |
| 3. C2×#6354085 | C2 | semidirect |
| 4. C2×#6354077 | C2 | semidirect |
| 5. C2×M16×AGL(1,ℤ/8) | C2 | semidirect |
| 6. C2×#6362952 | C2 | semidirect |
| 7. C2×#6362950 | C2 | semidirect |
| 8. C2×#6360217 | C2 | semidirect |
| 9. C2×#6361602 | C2 | semidirect |
| 10. C2×#6361594 | C2 | semidirect |
| 11. C2×#6360185 | C2 | semidirect |
| 12. C2×SD16×AGL(1,ℤ/8) | C2 | semidirect |
| 13. C2×#6360176 | C2 | semidirect |
| 14. C2×#6360208 | C2 | semidirect |
| 15. C2×#6349007 | C2 | semidirect |
| 16. C2×#41×AGL(1,ℤ/8) | C2 | semidirect |
| 17. C2×D8×AGL(1,ℤ/8) | C2 | semidirect |
| 18. C2×#6362966 | C2 | semidirect |
| 19. AGL(1,ℤ/8)2 | C2 | direct (N × H) |
| 20. C2×#6348967 | C2 | semidirect |
| 21. C22×D4×AGL(1,ℤ/8) | C2 | semidirect |
| 22. C2×#412 | C22 | semidirect |
| 23. C22×D4×#41 | C22 | semidirect |
| 24. C23×D42 | C22 | semidirect |
| 25. #41×AGL(1,ℤ/8) | C22 | semidirect |
| 26. C2×#61465 | C22 | semidirect |
| 27. C2×#61466 | C22 | semidirect |
| 28. C2×#61452 | C22 | semidirect |
| 29. C2×#61451 | C22 | semidirect |
| 30. C2×SD16×#41 | C22 | semidirect |
| 31. C2×D8×#41 | C22 | semidirect |
| 32. C2×#61439 | C22 | semidirect |
| 33. C2×#61437 | C22 | semidirect |
| 34. C2×#61402 | C22 | semidirect |
| 35. C2×#61252 | C22 | semidirect |
| 36. C2×#61321 | C22 | semidirect |
| 37. C2×#61317 | C22 | semidirect |
| 38. C2×#61161 | C22 | semidirect |
| 39. C2×#61155 | C22 | semidirect |
| 40. C2×Q8×AGL(1,ℤ/8) | C22 | semidirect |
| 42. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 43. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 44. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 45. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 46. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 47. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 48. C2×D4×AGL(1,ℤ/8) | C22 | semidirect |
| 49. C22×#3272 | C22 | semidirect |
| 50. C22×#3274 | C22 | semidirect |
| 51. C22×D4×SD16 | C22 | semidirect |
| 52. C22×D4×D8 | C22 | semidirect |
| 53. C2×#60968 | C22 | semidirect |
| 54. C2×#60798 | C22 | semidirect |
| 55. C2×#60700 | C22 | semidirect |
| 56. C22×#3151 | C22 | semidirect |
| 57. C2×#60561 | C22 | semidirect |
| 58. C2×#60558 | C22 | semidirect |
| 59. C22×#3038 | C22 | semidirect |
| 60. C22×#3036 | C22 | semidirect |
| 61. C2×M16×#41 | C22 | semidirect |
| 62. C22×D4×M16 | C22 | semidirect |
| 64. #6362966 | C22 | semidirect |
| 65. #6362952 | C22 | semidirect |
| 66. #6362950 | C22 | semidirect |
| 67. #6361602 | C22 | semidirect |
| 68. #6361594 | C22 | semidirect |
| 69. C2×#20314 | C22 | semidirect |
| 70. C2×#20310 | C22 | semidirect |
| 71. C2×#20309 | C22 | semidirect |
| 72. #6360217 | C22 | semidirect |
| 73. #6360208 | C22 | semidirect |
| 74. #6360185 | C22 | semidirect |
| 75. #6360176 | C22 | semidirect |
| 76. C2×#20202 | C22 | semidirect |
| 77. C2×#20195 | C22 | semidirect |
| 78. C2×#20192 | C22 | semidirect |
| 79. C2×#20190 | C22 | semidirect |
| 80. C2×#20170 | C22 | semidirect |
| 81. C2×#20163 | C22 | semidirect |
| 82. C2×#20160 | C22 | semidirect |
| 83. C2×#20158 | C22 | semidirect |
| 84. C2×#20084 | C22 | semidirect |
| 85. C2×#20072 | C22 | semidirect |
| 86. C2×#20067 | C22 | semidirect |
| 87. C2×#20059 | C22 | semidirect |
| 88. C2×#20054 | C22 | semidirect |
| 89. C2×#20053 | C22 | semidirect |
| 90. C2×#20030 | C22 | semidirect |
| 91. C2×#20024 | C22 | semidirect |
| 92. C2×#20023 | C22 | semidirect |
| 93. C2×#20022 | C22 | semidirect |
| 94. SD16×AGL(1,ℤ/8) | C22 | semidirect |
| 95. D8×AGL(1,ℤ/8) | C22 | semidirect |
| 96. C2×SD162 | C22 | semidirect |
| 97. C2×D8×SD16 | C22 | semidirect |
| 98. C2×D82 | C22 | semidirect |
| 99. C2×#19892 | C22 | semidirect |
| 100. C2×#19890 | C22 | semidirect |
| 101. C2×#19885 | C22 | semidirect |
| 102. C2×#19883 | C22 | semidirect |
| 103. C2×#19804 | C22 | semidirect |
| 104. C2×#19803 | C22 | semidirect |
| 105. C2×#19764 | C22 | semidirect |
| 106. C2×#19763 | C22 | semidirect |
| 107. C2×#19756 | C22 | semidirect |
| 108. C2×#19756 | C22 | semidirect |
| 109. C2×#19755 | C22 | semidirect |
| 110. C2×#19755 | C22 | semidirect |
| 111. #6357777 | C22 | semidirect |
| 112. C2×#19747 | C22 | semidirect |
| 113. C2×#19745 | C22 | semidirect |
| 114. C2×#19676 | C22 | semidirect |
| 115. C2×#19671 | C22 | semidirect |
| 116. C2×#19629 | C22 | semidirect |
| 117. C2×#19621 | C22 | semidirect |
| 118. #6354085 | C22 | semidirect |
| 119. #6354077 | C22 | semidirect |
| 120. C2×#19320 | C22 | semidirect |
| 121. C2×#19312 | C22 | semidirect |
| 122. C2×#19306 | C22 | semidirect |
| 123. C2×#19304 | C22 | semidirect |
| 124. C2×#19292 | C22 | semidirect |
| 125. C2×#19291 | C22 | semidirect |
| 126. C2×#19280 | C22 | semidirect |
| 127. C2×#19279 | C22 | semidirect |
| 128. C2×#19267 | C22 | semidirect |
| 129. C2×#19266 | C22 | semidirect |
| 130. C2×#19255 | C22 | semidirect |
| 131. C2×#19254 | C22 | semidirect |
| 132. C2×#19170 | C22 | semidirect |
| 133. C2×#19170 | C22 | semidirect |
| 134. C2×#19169 | C22 | semidirect |
| 135. C2×#19166 | C22 | semidirect |
| 136. C2×#19164 | C22 | semidirect |
| 137. C2×#19162 | C22 | semidirect |
| 138. C2×#19162 | C22 | semidirect |
| 139. C2×#19162 | C22 | semidirect |
| 140. #6349007 | C22 | semidirect |
| 141. #6348992 | C22 | semidirect |
| 142. #6348967 | C22 | semidirect |
| 143. C2×#18799 | C22 | semidirect |
| 144. C2×#18799 | C22 | semidirect |
| 145. C2×#18792 | C22 | semidirect |
| 146. C2×#18790 | C22 | semidirect |
| 147. C2×#18788 | C22 | semidirect |
| 148. C2×#18786 | C22 | semidirect |
| 149. C2×#18786 | C22 | semidirect |
| 150. C2×#18786 | C22 | semidirect |
| 151. C2×#18782 | C22 | semidirect |
| 152. C2×#18770 | C22 | semidirect |
| 153. C2×#18758 | C22 | semidirect |
| 154. C2×#18747 | C22 | semidirect |
| 155. C2×#18747 | C22 | semidirect |
| 156. C2×#18746 | C22 | semidirect |
| 157. C2×#18746 | C22 | semidirect |
| 158. C2×#18746 | C22 | semidirect |
| 159. C2×#18554 | C22 | semidirect |
| 160. C2×#18554 | C22 | semidirect |
| 161. C2×#18548 | C22 | semidirect |
| 162. C2×#18537 | C22 | semidirect |
| 163. C2×#18529 | C22 | semidirect |
| 164. C2×#18527 | C22 | semidirect |
| 165. C2×#18524 | C22 | semidirect |
| 166. M16×AGL(1,ℤ/8) | C22 | semidirect |
| 167. C2×#18048 | C22 | semidirect |
| 168. C2×#18046 | C22 | semidirect |
| 169. C2×#18044 | C22 | semidirect |
| 170. C2×#18040 | C22 | semidirect |
| 171. C2×M16×SD16 | C22 | semidirect |
| 172. C2×M16×D8 | C22 | semidirect |
| 173. C2×#17891 | C22 | semidirect |
| 174. C2×#17871 | C22 | semidirect |
| 175. C2×#17869 | C22 | semidirect |
| 176. C2×C8×AGL(1,ℤ/8) | C22 | semidirect |
| 177. C2×#17796 | C22 | semidirect |
| 178. C2×#17752 | C22 | semidirect |
| 179. C2×#17745 | C22 | semidirect |
| 180. C2×#17741 | C22 | semidirect |
| 181. C2×#17451 | C22 | semidirect |
| 182. C2×#17448 | C22 | semidirect |
| 183. C2×M162 | C22 | semidirect |
| 185. #412 | C23 | semidirect |
| 186. C2×#3483 | C23 | semidirect |
| 187. C2×#3482 | C23 | semidirect |
| 188. C2×#3481 | C23 | semidirect |
| 189. C2×Q8×#41 | C23 | semidirect |
| 190. C2×#3480 | C23 | semidirect |
| 191. C2×#3475 | C23 | semidirect |
| 194. C2×D4×#41 | C23 | semidirect |
| 195. C2×D4×#41 | C23 | semidirect |
| 196. C2×D4×#41 | C23 | semidirect |
| 197. C2×D4×#41 | C23 | semidirect |
| 198. C22×#550 | C23 | semidirect |
| 199. C22×#547 | C23 | semidirect |
| 200. C22×D4×Q8 | C23 | semidirect |
| 204. C22×D42 | C23 | semidirect |
| 205. C22×D42 | C23 | semidirect |
| 211. #61466 | C23 | semidirect |
| 212. #61465 | C23 | semidirect |
| 213. #61452 | C23 | semidirect |
| 214. #61451 | C23 | semidirect |
| 215. #61439 | C23 | semidirect |
| 216. #61437 | C23 | semidirect |
| 217. SD16×#41 | C23 | semidirect |
| 218. D8×#41 | C23 | semidirect |
| 219. #61402 | C23 | semidirect |
| 220. C2×#3399 | C23 | semidirect |
| 221. C2×#3397 | C23 | semidirect |
| 222. C2×#3392 | C23 | semidirect |
| 223. C2×#3391 | C23 | semidirect |
| 224. Q8×AGL(1,ℤ/8) | C23 | semidirect |
| 225. C2×#3386 | C23 | semidirect |
| 226. C2×#3384 | C23 | semidirect |
| 227. C2×Q8×SD16 | C23 | semidirect |
| 228. C2×Q8×D8 | C23 | semidirect |
| 229. #61321 | C23 | semidirect |
| 230. #61317 | C23 | semidirect |
| 231. C2×#3368 | C23 | semidirect |
| 232. C2×#3373 | C23 | semidirect |
| 233. C2×#3367 | C23 | semidirect |
| 234. C2×#3366 | C23 | semidirect |
| 235. C2×#3362 | C23 | semidirect |
| 236. C2×#3359 | C23 | semidirect |
| 237. C2×#3358 | C23 | semidirect |
| 238. C2×#3358 | C23 | semidirect |
| 239. #61252 | C23 | semidirect |
| 240. C2×#3354 | C23 | semidirect |
| 241. C2×#3353 | C23 | semidirect |
| 242. C2×#3335 | C23 | semidirect |
| 243. C2×#3334 | C23 | semidirect |
| 244. #61161 | C23 | semidirect |
| 245. #61155 | C23 | semidirect |
| 246. C2×#3332 | C23 | semidirect |
| 247. C2×#3330 | C23 | semidirect |
| 248. C2×#3325 | C23 | semidirect |
| 249. C2×#3324 | C23 | semidirect |
| 250. C2×#3298 | C23 | semidirect |
| 251. C2×#3295 | C23 | semidirect |
| 252. C2×#3294 | C23 | semidirect |
| 253. C2×#3294 | C23 | semidirect |
| 255. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 256. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 257. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 258. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 259. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 260. D4×AGL(1,ℤ/8) | C23 | semidirect |
| 263. C2×D4×SD16 | C23 | semidirect |
| 264. C2×D4×SD16 | C23 | semidirect |
| 265. C2×D4×SD16 | C23 | semidirect |
| 266. C2×D4×SD16 | C23 | semidirect |
| 269. C2×D4×D8 | C23 | semidirect |
| 270. C2×D4×D8 | C23 | semidirect |
| 271. C2×D4×D8 | C23 | semidirect |
| 272. C2×D4×D8 | C23 | semidirect |
| 275. C2×#3274 | C23 | semidirect |
| 276. C2×#3274 | C23 | semidirect |
| 277. C2×#3274 | C23 | semidirect |
| 278. C2×#3274 | C23 | semidirect |
| 281. C2×#3272 | C23 | semidirect |
| 282. C2×#3272 | C23 | semidirect |
| 283. C2×#3272 | C23 | semidirect |
| 284. C2×#3272 | C23 | semidirect |
| 285. #60968 | C23 | semidirect |
| 286. C2×#3227 | C23 | semidirect |
| 287. #60798 | C23 | semidirect |
| 288. C2×#3208 | C23 | semidirect |
| 289. C2×#3205 | C23 | semidirect |
| 290. C2×#3205 | C23 | semidirect |
| 291. #60700 | C23 | semidirect |
| 292. C2×#3184 | C23 | semidirect |
| 293. C2×#3184 | C23 | semidirect |
| 294. C2×#3182 | C23 | semidirect |
| 295. C2×#3169 | C23 | semidirect |
| 296. C2×#3167 | C23 | semidirect |
| 297. C2×#3165 | C23 | semidirect |
| 300. C2×#3151 | C23 | semidirect |
| 301. C2×#3151 | C23 | semidirect |
| 302. C2×#3151 | C23 | semidirect |
| 303. C2×#3151 | C23 | semidirect |
| 304. C22×#493 | C23 | semidirect |
| 305. C22×#492 | C23 | semidirect |
| 306. C2×#3141 | C23 | semidirect |
| 307. C2×#3138 | C23 | semidirect |
| 308. C2×#3138 | C23 | semidirect |
| 309. #60561 | C23 | semidirect |
| 310. #60558 | C23 | semidirect |
| 311. C2×#3110 | C23 | semidirect |
| 312. C2×#3109 | C23 | semidirect |
| 313. C2×#3115 | C23 | semidirect |
| 314. C2×#3115 | C23 | semidirect |
| 315. C2×#3103 | C23 | semidirect |
| 318. C2×#3100 | C23 | semidirect |
| 319. C2×#3079 | C23 | semidirect |
| 320. C2×#3079 | C23 | semidirect |
| 321. C2×#3077 | C23 | semidirect |
| 322. C2×#3077 | C23 | semidirect |
| 325. C2×#3038 | C23 | semidirect |
| 326. C2×#3038 | C23 | semidirect |
| 327. C2×#3038 | C23 | semidirect |
| 328. C2×#3038 | C23 | semidirect |
| 329. C2×#3038 | C23 | semidirect |
| 333. C2×#3036 | C23 | semidirect |
| 334. C2×#3036 | C23 | semidirect |
| 335. C2×#3036 | C23 | semidirect |
| 336. C22×#460 | C23 | semidirect |
| 339. C22×#459 | C23 | semidirect |
| 340. M16×#41 | C23 | semidirect |
| 341. C2×#2971 | C23 | semidirect |
| 342. C2×#2970 | C23 | semidirect |
| 343. C2×#2965 | C23 | semidirect |
| 344. C2×C8×#41 | C23 | semidirect |
| 345. C2×Q8×M16 | C23 | semidirect |
| 346. C2×Q8×M16 | C23 | semidirect |
| 367. C2×D4×M16 | C23 | semidirect |
| 368. C2×D4×M16 | C23 | semidirect |
| 369. C2×D4×M16 | C23 | semidirect |
| 370. C2×D4×M16 | C23 | semidirect |
| 371. C22×#436 | C23 | semidirect |
| 372. C22×C8×D4 | C23 | semidirect |
| 380. #20314 | C23 | semidirect |
| 381. #20310 | C23 | semidirect |
| 382. #20309 | C23 | semidirect |
| 383. #20202 | C23 | semidirect |
| 384. #20195 | C23 | semidirect |
| 385. #20192 | C23 | semidirect |
| 386. #20190 | C23 | semidirect |
| 387. #20170 | C23 | semidirect |
| 388. #20163 | C23 | semidirect |
| 389. #20160 | C23 | semidirect |
| 390. #20158 | C23 | semidirect |
| 391. #20084 | C23 | semidirect |
| 392. #20072 | C23 | semidirect |
| 393. #20067 | C23 | semidirect |
| 394. #20059 | C23 | semidirect |
| 395. #20054 | C23 | semidirect |
| 396. #20053 | C23 | semidirect |
| 397. #20030 | C23 | semidirect |
| 398. #20024 | C23 | semidirect |
| 399. #20023 | C23 | semidirect |
| 400. #20022 | C23 | semidirect |
| 401. SD162 | C23 | semidirect |
| 402. D8×SD16 | C23 | semidirect |
| 403. D82 | C23 | semidirect |
| 404. #19892 | C23 | semidirect |
| 405. #19890 | C23 | semidirect |
| 406. #19885 | C23 | semidirect |
| 407. #19883 | C23 | semidirect |
| 408. #19804 | C23 | semidirect |
| 409. #19803 | C23 | semidirect |
| 410. #19764 | C23 | semidirect |
| 411. #19763 | C23 | semidirect |
| 412. #19756 | C23 | semidirect |
| 413. #19756 | C23 | semidirect |
| 414. #19755 | C23 | semidirect |
| 415. #19755 | C23 | semidirect |
| 416. #19747 | C23 | semidirect |
| 417. #19745 | C23 | semidirect |
| 418. #19676 | C23 | semidirect |
| 419. #19671 | C23 | semidirect |
| 420. #19629 | C23 | semidirect |
| 421. #19621 | C23 | semidirect |
| 422. C2×#1721 | C23 | semidirect |
| 423. C2×#1721 | C23 | semidirect |
| 424. C2×#1721 | C23 | semidirect |
| 425. C2×#1717 | C23 | semidirect |
| 426. C2×#1715 | C23 | semidirect |
| 427. C2×#1715 | C23 | semidirect |
| 428. C2×#1714 | C23 | semidirect |
| 429. C2×#1712 | C23 | semidirect |
| 430. C2×#1706 | C23 | semidirect |
| 431. C2×#1705 | C23 | semidirect |
| 432. #19320 | C23 | semidirect |
| 433. #19312 | C23 | semidirect |
| 434. #19306 | C23 | semidirect |
| 435. #19304 | C23 | semidirect |
| 436. #19292 | C23 | semidirect |
| 437. #19291 | C23 | semidirect |
| 438. #19280 | C23 | semidirect |
| 439. #19279 | C23 | semidirect |
| 440. #19267 | C23 | semidirect |
| 441. #19266 | C23 | semidirect |
| 442. #19255 | C23 | semidirect |
| 443. #19254 | C23 | semidirect |
| 444. #19170 | C23 | semidirect |
| 445. #19170 | C23 | semidirect |
| 446. #19169 | C23 | semidirect |
| 447. #19166 | C23 | semidirect |
| 448. #19164 | C23 | semidirect |
| 449. #19162 | C23 | semidirect |
| 450. #19162 | C23 | semidirect |
| 451. #19162 | C23 | semidirect |
| 452. C2×#1688 | C23 | semidirect |
| 453. C2×#1688 | C23 | semidirect |
| 454. C2×#1686 | C23 | semidirect |
| 455. C2×#1686 | C23 | semidirect |
| 456. C2×#1701 | C23 | semidirect |
| 457. C2×#1701 | C23 | semidirect |
| 458. C2×#1699 | C23 | semidirect |
| 459. C2×#1697 | C23 | semidirect |
| 460. C2×#1693 | C23 | semidirect |
| 461. C2×#1691 | C23 | semidirect |
| 462. C2×#1687 | C23 | semidirect |
| 463. C2×#1687 | C23 | semidirect |
| 464. C2×#1687 | C23 | semidirect |
| 465. C2×#1685 | C23 | semidirect |
| 466. C2×#1685 | C23 | semidirect |
| 467. C2×#1685 | C23 | semidirect |
| 468. C2×#1668 | C23 | semidirect |
| 469. C2×#1668 | C23 | semidirect |
| 470. C2×#1666 | C23 | semidirect |
| 471. C2×#1666 | C23 | semidirect |
| 472. C2×#1681 | C23 | semidirect |
| 473. C2×#1681 | C23 | semidirect |
| 474. C2×#1679 | C23 | semidirect |
| 475. C2×#1677 | C23 | semidirect |
| 476. C2×#1673 | C23 | semidirect |
| 477. C2×#1671 | C23 | semidirect |
| 478. C2×#1667 | C23 | semidirect |
| 479. C2×#1667 | C23 | semidirect |
| 480. C2×#1667 | C23 | semidirect |
| 481. C2×#1665 | C23 | semidirect |
| 482. C2×#1665 | C23 | semidirect |
| 483. C2×#1665 | C23 | semidirect |
| 484. #18799 | C23 | semidirect |
| 485. #18799 | C23 | semidirect |
| 486. #18792 | C23 | semidirect |
| 487. #18790 | C23 | semidirect |
| 488. #18788 | C23 | semidirect |
| 489. #18786 | C23 | semidirect |
| 490. #18786 | C23 | semidirect |
| 491. #18786 | C23 | semidirect |
| 492. #18782 | C23 | semidirect |
| 493. #18770 | C23 | semidirect |
| 494. #18758 | C23 | semidirect |
| 495. #18747 | C23 | semidirect |
| 496. #18747 | C23 | semidirect |
| 497. #18746 | C23 | semidirect |
| 498. #18746 | C23 | semidirect |
| 499. #18746 | C23 | semidirect |
| 500. #18554 | C23 | semidirect |
| 501. #18554 | C23 | semidirect |
| 502. #18548 | C23 | semidirect |
| 503. #18537 | C23 | semidirect |
| 504. #18529 | C23 | semidirect |
| 505. #18527 | C23 | semidirect |
| 506. #18524 | C23 | semidirect |
| 507. C2×#1642 | C23 | semidirect |
| 508. C2×#1642 | C23 | semidirect |
| 509. C2×#1624 | C23 | semidirect |
| 510. C2×#1623 | C23 | semidirect |
| 511. C2×#1621 | C23 | semidirect |
| 512. C2×#1621 | C23 | semidirect |
| 513. C2×#1621 | C23 | semidirect |
| 514. C2×#1651 | C23 | semidirect |
| 515. C2×#1651 | C23 | semidirect |
| 516. C2×#1654 | C23 | semidirect |
| 517. C2×#1654 | C23 | semidirect |
| 518. C2×#1628 | C23 | semidirect |
| 519. C2×#1626 | C23 | semidirect |
| 520. C2×#1627 | C23 | semidirect |
| 521. C2×#1627 | C23 | semidirect |
| 522. C2×#1627 | C23 | semidirect |
| 523. C2×#1625 | C23 | semidirect |
| 524. C2×#1625 | C23 | semidirect |
| 525. C2×#1625 | C23 | semidirect |
| 527. C2×#1639 | C23 | semidirect |
| 528. C2×#1639 | C23 | semidirect |
| 529. C2×#1639 | C23 | semidirect |
| 530. C2×#1639 | C23 | semidirect |
| 531. C2×#1639 | C23 | semidirect |
| 532. C2×#1620 | C23 | semidirect |
| 533. C2×#1622 | C23 | semidirect |
| 535. C2×#1629 | C23 | semidirect |
| 536. C2×#1629 | C23 | semidirect |
| 538. C2×#1619 | C23 | semidirect |
| 539. C2×#1619 | C23 | semidirect |
| 540. C2×#1619 | C23 | semidirect |
| 541. C2×#1619 | C23 | semidirect |
| 542. C2×#1619 | C23 | semidirect |
| 543. #18048 | C23 | semidirect |
| 544. #18046 | C23 | semidirect |
| 545. #18044 | C23 | semidirect |
| 546. #18040 | C23 | semidirect |
| 547. M16×SD16 | C23 | semidirect |
| 548. M16×D8 | C23 | semidirect |
| 549. #17891 | C23 | semidirect |
| 550. C2×#1594 | C23 | semidirect |
| 551. C2×#1592 | C23 | semidirect |
| 552. C2×#1590 | C23 | semidirect |
| 553. C2×#1589 | C23 | semidirect |
| 554. #17871 | C23 | semidirect |
| 555. #17869 | C23 | semidirect |
| 556. C2×#1588 | C23 | semidirect |
| 557. C2×#1586 | C23 | semidirect |
| 558. C2×#1586 | C23 | semidirect |
| 559. C2×#1585 | C23 | semidirect |
| 560. C2×#1582 | C23 | semidirect |
| 561. C2×#1583 | C23 | semidirect |
| 562. C2×#1581 | C23 | semidirect |
| 563. C2×#1581 | C23 | semidirect |
| 564. C8×AGL(1,ℤ/8) | C23 | semidirect |
| 565. C2×#1580 | C23 | semidirect |
| 566. C2×SD16⋊C8 | C23 | semidirect |
| 567. C2×C8×SD16 | C23 | semidirect |
| 568. C2×C8×D8 | C23 | semidirect |
| 569. #17796 | C23 | semidirect |
| 570. C2×#1569 | C23 | semidirect |
| 571. C2×#1567 | C23 | semidirect |
| 572. C2×#1566 | C23 | semidirect |
| 573. C2×#1565 | C23 | semidirect |
| 574. C2×#1565 | C23 | semidirect |
| 575. #17752 | C23 | semidirect |
| 576. #17745 | C23 | semidirect |
| 577. #17741 | C23 | semidirect |
| 578. C2×#1561 | C23 | semidirect |
| 579. C2×#1560 | C23 | semidirect |
| 580. C2×#1557 | C23 | semidirect |
| 581. C2×#1555 | C23 | semidirect |
| 582. C2×#1550 | C23 | semidirect |
| 583. C2×#1549 | C23 | semidirect |
| 584. C2×#1547 | C23 | semidirect |
| 585. C2×#1547 | C23 | semidirect |
| 586. C2×#1547 | C23 | semidirect |
| 587. C2×#1545 | C23 | semidirect |
| 588. C2×#1545 | C23 | semidirect |
| 589. C2×#1545 | C23 | semidirect |
| 590. #17451 | C23 | semidirect |
| 591. #17448 | C23 | semidirect |
| 592. C2×#1489 | C23 | semidirect |
| 593. C2×#1489 | C23 | semidirect |
| 594. C2×#1490 | C23 | semidirect |
| 595. C2×#1487 | C23 | semidirect |
| 598. C2×#1486 | C23 | semidirect |
| 599. C2×#1477 | C23 | semidirect |
| 600. C2×#1477 | C23 | semidirect |
| 601. C2×#1478 | C23 | semidirect |
| 602. C2×#1478 | C23 | semidirect |
| 603. M162 | C23 | semidirect |
| 604. C2×#1455 | C23 | semidirect |
| 605. C2×#1451 | C23 | semidirect |
| 606. C2×C8×M16 | C23 | semidirect |
| 620. #3483 | C24 | semidirect |
| 621. #3482 | C24 | semidirect |
| 622. #3481 | C24 | semidirect |
| 623. #3480 | C24 | semidirect |
| 624. C2×#559 | C24 | semidirect |
| 625. Q8×#41 | C24 | semidirect |
| 626. C2×Q82 | C24 | semidirect |
| 627. C2×#557 | C24 | semidirect |
| 628. #3475 | C24 | semidirect |
| 629. C2×#556 | C24 | semidirect |
| 630. C2×#555 | C24 | semidirect |
| 631. C2×#554 | C24 | semidirect |
| 634. D4×#41 | C24 | semidirect |
| 635. D4×#41 | C24 | semidirect |
| 636. D4×#41 | C24 | semidirect |
| 639. C2×#550 | C24 | semidirect |
| 640. C2×#550 | C24 | semidirect |
| 643. C2×D4×Q8 | C24 | semidirect |
| 644. C2×D4×Q8 | C24 | semidirect |
| 647. C2×#547 | C24 | semidirect |
| 648. C2×#547 | C24 | semidirect |
| 657. C2×D42 | C24 | semidirect |
| 658. C2×D42 | C24 | semidirect |
| 699. #3399 | C24 | semidirect |
| 700. #3397 | C24 | semidirect |
| 701. #3392 | C24 | semidirect |
| 702. #3391 | C24 | semidirect |
| 703. #3386 | C24 | semidirect |
| 704. #3384 | C24 | semidirect |
| 705. Q8×SD16 | C24 | semidirect |
| 706. Q8×D8 | C24 | semidirect |
| 707. #3373 | C24 | semidirect |
| 708. #3368 | C24 | semidirect |
| 709. #3367 | C24 | semidirect |
| 710. #3366 | C24 | semidirect |
| 711. #3362 | C24 | semidirect |
| 712. #3359 | C24 | semidirect |
| 713. #3358 | C24 | semidirect |
| 714. #3358 | C24 | semidirect |
| 715. #3354 | C24 | semidirect |
| 716. #3353 | C24 | semidirect |
| 717. #3335 | C24 | semidirect |
| 718. #3334 | C24 | semidirect |
| 719. #3332 | C24 | semidirect |
| 720. #3330 | C24 | semidirect |
| 721. #3325 | C24 | semidirect |
| 722. #3324 | C24 | semidirect |
| 723. #3298 | C24 | semidirect |
| 724. #3295 | C24 | semidirect |
| 725. #3294 | C24 | semidirect |
| 726. #3294 | C24 | semidirect |
| 729. D4×SD16 | C24 | semidirect |
| 730. D4×SD16 | C24 | semidirect |
| 731. D4×SD16 | C24 | semidirect |
| 734. D4×D8 | C24 | semidirect |
| 735. D4×D8 | C24 | semidirect |
| 736. D4×D8 | C24 | semidirect |
| 739. #3274 | C24 | semidirect |
| 740. #3274 | C24 | semidirect |
| 741. #3274 | C24 | semidirect |
| 744. #3272 | C24 | semidirect |
| 745. #3272 | C24 | semidirect |
| 746. #3272 | C24 | semidirect |
| 747. #3227 | C24 | semidirect |
| 748. #3208 | C24 | semidirect |
| 749. #3205 | C24 | semidirect |
| 750. #3205 | C24 | semidirect |
| 751. #3184 | C24 | semidirect |
| 752. #3184 | C24 | semidirect |
| 753. #3182 | C24 | semidirect |
| 754. #3169 | C24 | semidirect |
| 755. #3167 | C24 | semidirect |
| 756. #3165 | C24 | semidirect |
| 757. C2×#500 | C24 | semidirect |
| 758. C2×#498 | C24 | semidirect |
| 759. C2×#498 | C24 | semidirect |
| 762. #3151 | C24 | semidirect |
| 763. #3151 | C24 | semidirect |
| 764. #3151 | C24 | semidirect |
| 768. C2×#493 | C24 | semidirect |
| 769. C2×#493 | C24 | semidirect |
| 770. C2×#493 | C24 | semidirect |
| 774. C2×#492 | C24 | semidirect |
| 775. C2×#492 | C24 | semidirect |
| 776. #3141 | C24 | semidirect |
| 777. #3138 | C24 | semidirect |
| 778. #3138 | C24 | semidirect |
| 779. C2×#487 | C24 | semidirect |
| 781. C2×#486 | C24 | semidirect |
| 782. C2×#486 | C24 | semidirect |
| 783. C2×#486 | C24 | semidirect |
| 784. C2×#486 | C24 | semidirect |
| 785. #3115 | C24 | semidirect |
| 786. #3115 | C24 | semidirect |
| 787. #3110 | C24 | semidirect |
| 788. #3109 | C24 | semidirect |
| 789. #3103 | C24 | semidirect |
| 792. #3100 | C24 | semidirect |
| 793. #3079 | C24 | semidirect |
| 794. #3079 | C24 | semidirect |
| 795. #3077 | C24 | semidirect |
| 796. #3077 | C24 | semidirect |
| 797. C2×#475 | C24 | semidirect |
| 798. C2×#475 | C24 | semidirect |
| 803. C2×#474 | C24 | semidirect |
| 804. C2×#474 | C24 | semidirect |
| 807. #3038 | C24 | semidirect |
| 808. #3038 | C24 | semidirect |
| 809. #3038 | C24 | semidirect |
| 810. #3038 | C24 | semidirect |
| 814. #3036 | C24 | semidirect |
| 815. #3036 | C24 | semidirect |
| 818. C2×#460 | C24 | semidirect |
| 819. C2×#460 | C24 | semidirect |
| 820. C2×#460 | C24 | semidirect |
| 833. C2×#459 | C24 | semidirect |
| 834. C2×#459 | C24 | semidirect |
| 835. C2×#459 | C24 | semidirect |
| 836. #2971 | C24 | semidirect |
| 837. #2970 | C24 | semidirect |
| 838. #2965 | C24 | semidirect |
| 839. C8×#41 | C24 | semidirect |
| 840. Q8×M16 | C24 | semidirect |
| 841. Q8×M16 | C24 | semidirect |
| 842. C2×#446 | C24 | semidirect |
| 843. C2×#446 | C24 | semidirect |
| 844. C2×C8×Q8 | C24 | semidirect |
| 845. C2×C8×Q8 | C24 | semidirect |
| 904. D4×M16 | C24 | semidirect |
| 905. D4×M16 | C24 | semidirect |
| 906. D4×M16 | C24 | semidirect |
| 909. C2×#436 | C24 | semidirect |
| 910. C2×#436 | C24 | semidirect |
| 911. C2×#436 | C24 | semidirect |
| 914. C2×C8×D4 | C24 | semidirect |
| 915. C2×C8×D4 | C24 | semidirect |
| 916. C2×C8×D4 | C24 | semidirect |
| 966. #1721 | C24 | semidirect |
| 967. #1721 | C24 | semidirect |
| 968. #1721 | C24 | semidirect |
| 969. #1717 | C24 | semidirect |
| 970. #1715 | C24 | semidirect |
| 971. #1715 | C24 | semidirect |
| 972. #1714 | C24 | semidirect |
| 973. #1712 | C24 | semidirect |
| 974. #1706 | C24 | semidirect |
| 975. #1705 | C24 | semidirect |
| 976. #1701 | C24 | semidirect |
| 977. #1701 | C24 | semidirect |
| 978. #1699 | C24 | semidirect |
| 979. #1697 | C24 | semidirect |
| 980. #1693 | C24 | semidirect |
| 981. #1691 | C24 | semidirect |
| 982. #1688 | C24 | semidirect |
| 983. #1688 | C24 | semidirect |
| 984. #1687 | C24 | semidirect |
| 985. #1687 | C24 | semidirect |
| 986. #1687 | C24 | semidirect |
| 987. #1686 | C24 | semidirect |
| 988. #1686 | C24 | semidirect |
| 989. #1685 | C24 | semidirect |
| 990. #1685 | C24 | semidirect |
| 991. #1685 | C24 | semidirect |
| 992. #1681 | C24 | semidirect |
| 993. #1681 | C24 | semidirect |
| 994. #1679 | C24 | semidirect |
| 995. #1677 | C24 | semidirect |
| 996. #1673 | C24 | semidirect |
| 997. #1671 | C24 | semidirect |
| 998. #1668 | C24 | semidirect |
| 999. #1668 | C24 | semidirect |
| 1000. #1667 | C24 | semidirect |
| 1001. #1667 | C24 | semidirect |
| 1002. #1667 | C24 | semidirect |
| 1003. #1666 | C24 | semidirect |
| 1004. #1666 | C24 | semidirect |
| 1005. #1665 | C24 | semidirect |
| 1006. #1665 | C24 | semidirect |
| 1007. #1665 | C24 | semidirect |
| 1008. #1654 | C24 | semidirect |
| 1009. #1654 | C24 | semidirect |
| 1010. #1651 | C24 | semidirect |
| 1011. #1651 | C24 | semidirect |
| 1012. #1642 | C24 | semidirect |
| 1013. #1642 | C24 | semidirect |
| 1015. #1639 | C24 | semidirect |
| 1016. #1639 | C24 | semidirect |
| 1017. #1639 | C24 | semidirect |
| 1018. #1639 | C24 | semidirect |
| 1019. #1639 | C24 | semidirect |
| 1021. #1629 | C24 | semidirect |
| 1022. #1629 | C24 | semidirect |
| 1023. #1628 | C24 | semidirect |
| 1024. #1627 | C24 | semidirect |
| 1025. #1627 | C24 | semidirect |
| 1026. #1627 | C24 | semidirect |
| 1027. #1626 | C24 | semidirect |
| 1028. #1625 | C24 | semidirect |
| 1029. #1625 | C24 | semidirect |
| 1030. #1625 | C24 | semidirect |
| 1031. #1624 | C24 | semidirect |
| 1032. #1623 | C24 | semidirect |
| 1033. #1622 | C24 | semidirect |
| 1034. #1621 | C24 | semidirect |
| 1035. #1621 | C24 | semidirect |
| 1036. #1621 | C24 | semidirect |
| 1037. #1620 | C24 | semidirect |
| 1039. #1619 | C24 | semidirect |
| 1040. #1619 | C24 | semidirect |
| 1041. #1619 | C24 | semidirect |
| 1042. #1619 | C24 | semidirect |
| 1043. #1619 | C24 | semidirect |
| 1044. #1594 | C24 | semidirect |
| 1045. #1592 | C24 | semidirect |
| 1046. #1590 | C24 | semidirect |
| 1047. #1589 | C24 | semidirect |
| 1048. #1588 | C24 | semidirect |
| 1049. #1586 | C24 | semidirect |
| 1050. #1586 | C24 | semidirect |
| 1051. #1585 | C24 | semidirect |
| 1052. #1583 | C24 | semidirect |
| 1053. #1582 | C24 | semidirect |
| 1054. #1581 | C24 | semidirect |
| 1055. #1581 | C24 | semidirect |
| 1056. #1580 | C24 | semidirect |
| 1057. SD16⋊C8 | C24 | semidirect |
| 1058. C8×SD16 | C24 | semidirect |
| 1059. C8×D8 | C24 | semidirect |
| 1060. #1569 | C24 | semidirect |
| 1061. #1567 | C24 | semidirect |
| 1062. #1566 | C24 | semidirect |
| 1063. #1565 | C24 | semidirect |
| 1064. #1565 | C24 | semidirect |
| 1065. C2×#335 | C24 | semidirect |
| 1066. C2×#335 | C24 | semidirect |
| 1067. C2×#334 | C24 | semidirect |
| 1068. C2×#334 | C24 | semidirect |
| 1069. #1561 | C24 | semidirect |
| 1070. #1560 | C24 | semidirect |
| 1071. #1557 | C24 | semidirect |
| 1072. #1555 | C24 | semidirect |
| 1073. #1550 | C24 | semidirect |
| 1074. #1549 | C24 | semidirect |
| 1075. #1547 | C24 | semidirect |
| 1076. #1547 | C24 | semidirect |
| 1077. #1547 | C24 | semidirect |
| 1078. #1545 | C24 | semidirect |
| 1079. #1545 | C24 | semidirect |
| 1080. #1545 | C24 | semidirect |
| 1081. C2×#333 | C24 | semidirect |
| 1082. C2×#332 | C24 | semidirect |
| 1083. C2×#332 | C24 | semidirect |
| 1084. C2×#332 | C24 | semidirect |
| 1088. C2×#331 | C24 | semidirect |
| 1089. C2×#331 | C24 | semidirect |
| 1090. C2×#331 | C24 | semidirect |
| 1091. #1490 | C24 | semidirect |
| 1092. #1489 | C24 | semidirect |
| 1093. #1489 | C24 | semidirect |
| 1094. #1487 | C24 | semidirect |
| 1097. #1486 | C24 | semidirect |
| 1098. #1478 | C24 | semidirect |
| 1099. #1478 | C24 | semidirect |
| 1100. #1477 | C24 | semidirect |
| 1101. #1477 | C24 | semidirect |
| 1102. C2×Q8⋊C8 | C24 | semidirect |
| 1103. C2×Q8⋊C8 | C24 | semidirect |
| 1108. C2×D4⋊C8 | C24 | semidirect |
| 1109. C2×D4⋊C8 | C24 | semidirect |
| 1110. #1455 | C24 | semidirect |
| 1111. #1451 | C24 | semidirect |
| 1112. C8×M16 | C24 | semidirect |
| 1113. C2×#322 | C24 | semidirect |
| 1114. C2×#322 | C24 | semidirect |
| 1115. C2×C82 | C24 | semidirect |
| 1130. C2×AGL(1,ℤ/8) | AGL(1,ℤ/8) | direct (N × H) |
| 1157. #559 | C25 | semidirect |
| 1158. Q82 | C25 | semidirect |
| 1159. #557 | C25 | semidirect |
| 1160. #556 | C25 | semidirect |
| 1161. #555 | C25 | semidirect |
| 1162. #554 | C25 | semidirect |
| 1165. #550 | C25 | semidirect |
| 1168. D4×Q8 | C25 | semidirect |
| 1171. #547 | C25 | semidirect |
| 1177. D42 | C25 | semidirect |
| 1270. #500 | C25 | semidirect |
| 1271. #498 | C25 | semidirect |
| 1272. #498 | C25 | semidirect |
| 1276. #493 | C25 | semidirect |
| 1277. #493 | C25 | semidirect |
| 1281. #492 | C25 | semidirect |
| 1282. #487 | C25 | semidirect |
| 1284. #486 | C25 | semidirect |
| 1285. #486 | C25 | semidirect |
| 1286. #486 | C25 | semidirect |
| 1287. #486 | C25 | semidirect |
| 1290. #475 | C25 | semidirect |
| 1291. #475 | C25 | semidirect |
| 1294. #474 | C25 | semidirect |
| 1295. #474 | C25 | semidirect |
| 1302. #460 | C25 | semidirect |
| 1303. #460 | C25 | semidirect |
| 1310. #459 | C25 | semidirect |
| 1311. #459 | C25 | semidirect |
| 1312. #446 | C25 | semidirect |
| 1313. #446 | C25 | semidirect |
| 1314. C8×Q8 | C25 | semidirect |
| 1315. C8×Q8 | C25 | semidirect |
| 1358. #436 | C25 | semidirect |
| 1359. #436 | C25 | semidirect |
| 1362. C8×D4 | C25 | semidirect |
| 1363. C8×D4 | C25 | semidirect |
| 1445. #335 | C25 | semidirect |
| 1446. #335 | C25 | semidirect |
| 1447. #334 | C25 | semidirect |
| 1448. #334 | C25 | semidirect |
| 1449. #333 | C25 | semidirect |
| 1450. #332 | C25 | semidirect |
| 1451. #332 | C25 | semidirect |
| 1452. #332 | C25 | semidirect |
| 1456. #331 | C25 | semidirect |
| 1457. #331 | C25 | semidirect |
| 1458. #331 | C25 | semidirect |
| 1459. Q8⋊C8 | C25 | semidirect |
| 1460. Q8⋊C8 | C25 | semidirect |
| 1465. D4⋊C8 | C25 | semidirect |
| 1466. D4⋊C8 | C25 | semidirect |
| 1467. #322 | C25 | semidirect |
| 1468. #322 | C25 | semidirect |
| 1469. C82 | C25 | semidirect |
| 1471. C2×#41 | C2×AGL(1,ℤ/8) | semidirect |
| 1479. C22×D4 | C2×AGL(1,ℤ/8) | semidirect |
| 1503. AGL(1,ℤ/8) | C2×AGL(1,ℤ/8) | direct (N × H) |
| 1504. C2×SD16 | C2×AGL(1,ℤ/8) | semidirect |
| 1509. C2×D8 | C2×AGL(1,ℤ/8) | semidirect |
| 1514. C2×M16 | C2×AGL(1,ℤ/8) | semidirect |
| 1647. #41 | C22×AGL(1,ℤ/8) | semidirect |
| 1648. C2×Q8 | C22×AGL(1,ℤ/8) | semidirect |
| 1652. C2×D4 | C22×AGL(1,ℤ/8) | semidirect |
| 1653. C2×D4 | C22×AGL(1,ℤ/8) | semidirect |
| 1682. SD16 | C22×AGL(1,ℤ/8) | semidirect |
| 1683. D8 | C22×AGL(1,ℤ/8) | semidirect |
| 1684. M16 | C22×AGL(1,ℤ/8) | semidirect |
| 1685. C2×C8 | C22×AGL(1,ℤ/8) | semidirect |
| 1717. Q8 | C23×AGL(1,ℤ/8) | semidirect |
| 1719. D4 | C23×AGL(1,ℤ/8) | semidirect |
| 1735. C8 | C23×AGL(1,ℤ/8) | semidirect |
| 1745. C2 | AGL(1,ℤ/8)2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.