Finite Group Databasebeta

← #25253426

Subgroups — #25253426

Order 11008.

622 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146984C211yesmaximal, characteristic, complemented
2#19146269C211yesmaximal, characteristic
3#19136817C211yesmaximal, characteristic, complemented
4#19136782C211yesmaximal, characteristic, complemented
5#19136778C211yesmaximal, characteristic, complemented
6#19136741C211yesmaximal, characteristic, complemented
7#19136694C211yesmaximal, characteristic, complemented
8#19136633C211yesmaximal, characteristic, complemented
9#19136523C211yesmaximal, characteristic, complemented
10#19136522C211yesmaximal, characteristic, complemented
11#19136444C211yesmaximal, characteristic, complemented
12C16×C22⋊D43C211yesmaximal, characteristic, complemented
13C2×#14582701C211yesmaximal, characteristic, complemented
14#357×D43C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C2×D8×D43C2211yescharacteristic
18#14583607—21no—
19#14583533—21no—
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic, complemented
22C2×C16×D43C2211yescharacteristic, complemented
23#14583303C2211yescharacteristic, complemented
24#14583274C2211yescharacteristic
25#14583233—21no—
26#14583232—21no—
27#14583192—21no—
28#14583137C2211yescharacteristic, complemented
29#14583136C2211yescharacteristic
30#14583093—21no—
31#14583034—21no—
32#14583032—21no—
33Q16×Dic43C2211yescharacteristic, complemented
34#14582981C2211yescharacteristic
35C8×C22⋊D43C2211yescharacteristic
36C2×#13063259C2211yescharacteristic, complemented
37#107×D43C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40Dic43⋊C16C2211yescharacteristic, complemented
41#14582701C2211yescharacteristic
42#14582701C2211yescharacteristic
43#14582701C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic, complemented
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C2×SD32×C43C2211yescharacteristic, complemented
53C22×C16×C43C2211yescharacteristic, complemented
54C43×#467C2211yescharacteristic, complemented
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×#357C2211yescharacteristic, complemented
59C22×D172—21no—
60C2×D4×D43—21no—
61C2×D4×D43—41no—
62C2×D344—22no—
63C2×D344—21no—
64C2×D344—41no—
65C2×D344C2311yescharacteristic
66C2×D344C2311yescharacteristic
67C2×#10621882—21no—
68C2×#10621882—21no—
69D8×D43—22no—
70D8×D43—41no—
71C2×C8×D43C2311yescharacteristic
72#13063324—21no—
73#13063321—21no—
74#13063315—41no—
75#13063305—41no—
76#13063302—41no—
77#13063301—21no—
78#13063300—21no—
79#13063298—41no—
80#13063295—41no—
81#13063293—41no—
82Q8×Dic43—21no—
83#13063287—21no—
84C4×C22⋊D43D411yescharacteristic
85(C22⋊D43)⋊C4—41no—
86C2×C4⋊Dic43—21no—
87C4⋊C4×D43—21no—
88#13063268—22no—
89#13063268—41no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92C16×D43—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98Dic43⋊C8D411yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)D411yescharacteristic
104(C2×D43)⋊C8D411yescharacteristic
105C8×Dic43C2311yescharacteristic
106C2×Q16×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110#121×C43—21no—
111SD32×C43—41no—
112C2×C16×C43—41no—
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115#107×C43C2311yescharacteristic
116#107×C43C2311yescharacteristic
117#103×C43—21no—
118#102×C43—21no—
119C23×D43—41no—
120C23×D43—41no—
121C2×Q8×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×C22⋊D43D811yescharacteristic
129C22×Dic43—41no—
130D4×D43—42no—
131D4×D43—81no—
132D4×D43—84no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—41no—
136C2×D172—41no—
137C2×D172—42no—
138C2×D172—81no—
139C2×C4×D43—41no—
140C2×C4×D43—41no—
141C2×C4×D43C2×D411yescharacteristic
142C2×Dic86—41no—
143Q16×C43—21no—
144Q16×C43—21no—
145D8×C43—21no—
146D8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43C2×D411yescharacteristic
150C2×C8×C43C2411yescharacteristic
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C22⋊Dic43D811yescharacteristic
157#10621882—42no—
158#10621882—81no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4D811yescharacteristic
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170Dic43⋊C4D811yescharacteristic
171C4×Dic43—41no—
172C4×Dic43C2×D411yescharacteristic
173C2×C43⋊C8C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175D344—21no—
176D344—21no—
177D344—21no—
178D344—42no—
179D344#4112yes—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—82no—
194C22×D43—161no—
195C22×D43—161no—
196C22×D43C2×D811yescharacteristic
197Q8×C43—41no—
198Q8×C43—41no—
199D4×C43—41no—
200D4×C43—41no—
201D4×C43—82no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C22⋊D43—82no—
210C22⋊D43—82no—
211C22⋊D43—161no—
212C22⋊D43SD3214yescomplemented
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—161no—
216C2×Dic43C2×D811yescharacteristic
217C2×Dic43C2×D811yescharacteristic
218C2×Dic43C2×D811yescharacteristic
219D172—22no—
220D172—41no—
221D172—41no—
222D172—41no—
223D172—82no—
224D172—82no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—82no—
228C4×D43—161no—
229Dic86—161no—
230C8×C43—21no—
231C8×C43C2×#4111yescharacteristic
232C8×C43H(5,𝔽2)11yescharacteristic
233C43⋊C8—21no—
234C43⋊C8—21no—
235#33862—431nomaximal, Sylow
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43C2×SD3212yes—
242C22×C43C22×D811yescharacteristic
243C2×D43—21no—
244C2×D43—21no—
245C2×D43—42no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—81no—
251C2×D43—164no—
252C2×D43—164no—
253C2×D43C2×SD3212yes—
254C4×C43—21no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43#54611yescharacteristic
259C4×C43#57711yescharacteristic
260Dic43—21no—
261Dic43—21no—
262Dic43—81no—
263Dic43—81no—
264Dic43C2×SD3212yes—
265#3338—431no—
266D4×D8—431no—
267#2240—431no—
268#2233—431no—
269#2233—431no—
270#2226—431no—
271#2217—431no—
272#2217D4311yescharacteristic, complemented
273#2207—431no—
274#2187—431no—
275#2187—431no—
276C4×SD32—431no—
277D4×C16—431no—
278C2×#357—431no—
279C2×#357—431no—
280C2×C43—22no—
281C2×C43—161no—
282C2×C43#329411yescharacteristic
283C2×C43C22×SD3211yescharacteristic
284C2×C43#341511yescharacteristic
285D43—22no—
286D43—82no—
287D43—161no—
288C22×D8—431no—
289C22×D8—431no—
290#554—861no—
291D42—861no—
292C2×SD32—431no—
293C2×SD32—431no—
294C2×SD32C2×D4311yescharacteristic, complemented
295C22×C16—431no—
296C22×C16C2×D4311yescharacteristic, complemented
297#500—431no—
298#493—431no—
299#484—861no—
300#484—861no—
301#477—861no—
302#467—431no—
303#467C2×D4311yescharacteristic, complemented
304#466—431no—
305#466C2×D4311yescharacteristic
306#459—861no—
307#447—861no—
308#447—861no—
309C4×Q16—431no—
310C4×D8—431no—
311C8×D4—431no—
312C2×#107—431no—
313C2×#107—431no—
314#367—431no—
315#367—431no—
316#367C2×D4311yescharacteristic, complemented
317C4⋊C16—431no—
318#358C2×D4311yescharacteristic, complemented
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325#357—431no—
326#357—431no—
327#357C2×D4311yescharacteristic, complemented
328C22⋊C16—431no—
329C22⋊C16—431no—
330C4×C16—431no—
331C43#3386211yescharacteristic, complemented, Sylow
332C22×D4—861no—
333C22×D4—861no—
334C22×D4—1721no—
335C2×Q16C22×D4311yescharacteristic
336C2×D8—431no—
337C2×D8—431no—
338C2×D8—862no—
339C2×D8—861no—
340C2×D8—861no—
341C2×D8—862no—
342C2×D8—861no—
343C2×D8—1721no—
344C2×D8—1721no—
345C2×D8C22×D4311yescharacteristic
346C22×C8—431no—
347C22×C8C22×D4311yescharacteristic
348C4⋊Q8—861no—
349#127—861no—
350#125—1721no—
351C22⋊Q8—21no—
352C22⋊Q8—861no—
353C22⋊Q8—1721no—
354C22⋊Q8—1721no—
355#121—21no—
356#121—861no—
357#121—1721no—
358#120—1721no—
359#120—1721no—
360C4×Q8—861no—
361C4×D4—431no—
362C4×D4—861no—
363C4×D4—1721no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366SD32—41no—
367SD32—862no—
368SD32—1721no—
369C2×C16—41no—
370C2×C16—431no—
371C2×C16—431no—
372C2×C16—1721no—
373C2×C16C22×D4311yescharacteristic
374C2×C16C22×D4311yescharacteristic
375#107—431no—
376#107—431no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107C22×D4311yescharacteristic
381#107C22×D4311yescharacteristic
382C4⋊C8—431no—
383#103—21no—
384#103—861no—
385#103—861no—
386#102—21no—
387#102—861no—
388#102—861no—
389C22⋊C8—431no—
390C22⋊C8—431no—
391C4×C8—431no—
392C24—1721no—
393C24—1721no—
394C2×Q8—21no—
395C2×Q8—1721no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—431no—
399C2×D4—861no—
400C2×D4—861no—
401C2×D4—3441no—
402C2×D4—3441no—
403C2×D4—3444no—
404C2×D4—1722no—
405C2×D4—1721no—
406C2×D4—1721no—
407C2×D4—1721no—
408C2×D4—1721no—
409C2×D4—1722no—
410C2×D4—1721no—
411C22×C4—431no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4D4×D4311yescharacteristic
416Q16—21no—
417Q16—21no—
418D8—21no—
419D8—21no—
420D8—432no—
421D8—861no—
422D8—861no—
423D8—861no—
424D8—3441no—
425D8—1722no—
426D8—1722no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—431no—
430C2×C8—431no—
431C2×C8—861no—
432C2×C8—861no—
433C2×C8D4×D4311yescharacteristic
434C2×C8C23×D4311yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—41no—
438C4⋊C4—431no—
439C4⋊C4—861no—
440C4⋊C4—861no—
441C4⋊C4—1721no—
442C4⋊C4—1721no—
443C4⋊C4—1721no—
444C4⋊C4—1721no—
445C4⋊C4—1721no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—431no—
449C22⋊C4—431no—
450C22⋊C4—1721no—
451C22⋊C4—1721no—
452C22⋊C4—1721no—
453C42—431no—
454C42—1721no—
455C16—21no—
456C16—21no—
457C16—861no—
458C16—861no—
459C23—41no—
460C23—431no—
461C23—3442no—
462C23—3442no—
463C23—3442no—
464C23—3442no—
465C23—1721no—
466C23—1721no—
467C23—6881no—
468C23—6881no—
469C23D8×D4311yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—6881no—
473D4—41no—
474D4—41no—
475D4—82no—
476D4—434no—
477D4—862no—
478D4—3442no—
479D4—3442no—
480D4—3442no—
481D4—3442no—
482D4—1721no—
483D4—1721no—
484D4—1721no—
485D4—6881no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—431no—
492C2×C4—431no—
493C2×C4—431no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—3442no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—6881no—
500C2×C4—6881no—
501C2×C4D8×D4311yescharacteristic
502C2×C4C2×D4×D4311yescharacteristic
503C8—21no—
504C8—861no—
505C8—861no—
506C8#41×D4311yescharacteristic
507C8#1306337011yescharacteristic
508C22—21no—
509C22—21no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—432no—
514C22—861no—
515C22—861no—
516C22—3441no—
517C22—3441no—
518C22—3441no—
519C22—3441no—
520C22—3441no—
521C22—1722no—
522C22—6884no—
523C22—6884no—
524C22SD32×D4312yes—
525C22C2×D8×D4311yescharacteristic
526C4—21no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—432no—
531C4—861no—
532C4—861no—
533C4—3441no—
534C4—3441no—
535C4#1458353811yescharacteristic
536C4#1458370611yescharacteristic
537C2—22no—
538C2—161no—
539C2—862no—
540C2—3442no—
541C2—6881no—
542C2#1914640311yescharacteristic
543C2C2×SD32×D4311yescharacteristic
544C2#1914773311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#19146269C2
hypercenter#2217D43
hypocenterC43#33862
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19146984C2semidirect
3. #19136817C2semidirect
4. #19136782C2semidirect
5. #19136778C2semidirect
6. #19136741C2semidirect
7. #19136694C2semidirect
8. #19136633C2semidirect
9. #19136523C2semidirect
10. #19136522C2semidirect
11. #19136444C2semidirect
12. C16×C22⋊D43C2semidirect
13. C2×#14582701C2semidirect
14. #357×D43C2semidirect
15. C43×#2217C2semidirect
21. C2×#13063268C22semidirect
22. C2×C16×D43C22semidirect
23. #14583303C22semidirect
28. #14583137C22semidirect
33. Q16×Dic43C22semidirect
36. C2×#13063259C22semidirect
37. #107×D43C22semidirect
38. #14582726C22semidirect
39. #14582726C22semidirect
40. Dic43⋊C16C22semidirect
43. #14582701C22semidirect
44. #14582701C22semidirect
45. #14582700C22semidirect
46. #14582700C22semidirect
48. #14582699C22semidirect
49. C22⋊(C43⋊C16)C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. C16×Dic43C22semidirect
52. C2×SD32×C43C22semidirect
53. C22×C16×C43C22semidirect
54. C43×#467C22semidirect
56. C43×#367C22semidirect
57. C43×#358C22semidirect
58. C43×#357C22semidirect
212. C22⋊D43SD32semidirect
272. #2217D43semidirect
294. C2×SD32C2×D43semidirect
296. C22×C16C2×D43semidirect
303. #467C2×D43semidirect
316. #367C2×D43semidirect
318. #358C2×D43semidirect
327. #357C2×D43semidirect
331. C43#33862semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191469842
#191462692
#191368172
#191367822
#191367782
#191367412
#191366942
#191366332
#191365232
#191365222
#191364442
C16×C22⋊D432
C2×#145827012
#357×D432
C43×#22172
#3386243