Finite Group Databasebeta

← #14737433

Subgroups — #14737433

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C211yesmaximal, characteristic, complemented
2#13079588C211yesmaximal, characteristic
3#13079334C211yesmaximal, characteristic, complemented
4#13068177C211yesmaximal, characteristic, complemented
5#13068163C211yesmaximal, characteristic, complemented
6#13068134C211yesmaximal, characteristic, complemented
7#13068088C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068046C211yesmaximal, characteristic, complemented
10#13068005C211yesmaximal, characteristic, complemented
11#13067957C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067280C211yesmaximal, characteristic, complemented
14#13067263C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622747—21no—
30#10622747—21no—
31#10622681—21no—
32#10622676—21no—
33#10622672—21no—
34#10622667—21no—
35#10622664—21no—
36#10622660—21no—
37#10622654—21no—
38#10622650—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622632C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622628C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622323—21no—
50#10622323—21no—
51#10622307C2211yescharacteristic
52#10622306C2211yescharacteristic
53#10622295C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4326—21no—
85C2×#4325—21no—
86C2×#4324—21no—
87C2×#4324—21no—
88C2×#4323—21no—
89#66983—21no—
90#66983—21no—
91#66979—21no—
92#66977—21no—
93#66977—21no—
94C22×C11⋊C8—21no—
95C2×#4314—21no—
96C2×#4314—21no—
97#66928—21no—
98#66927C2311yescharacteristic
99C4×D44—21no—
100C4×D44—21no—
101#66923—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×#97—21no—
115C11×#97D411yescharacteristic
116C11×#97D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11—21no—
119C4×C8×C11C2311yescharacteristic
120C4×C8×C11C2311yescharacteristic
121#66899—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66882—21no—
127#66882—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874—21no—
134#66873—21no—
135#66873—21no—
136#66872—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8—21no—
144#19246—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—41no—
153#4339—81no—
154#4339—81no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×C4×D11—41no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—42no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—42no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—81no—
190#4326—81no—
191#4325—81no—
192#4324—81no—
193#4324—81no—
194#4323—81no—
195(C2×D11)⋊C4—41no—
196(C2×D11)⋊C4—41no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203Dic11⋊C4—41no—
204Dic11⋊C4—41no—
205C4×Dic11—41no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—81no—
211#4314—42no—
212#4314—42no—
213#3248—111no—
214#3212—111no—
215#3182—111no—
216#2969D1111yescharacteristic, complemented
217#1701—111no—
218#1699—111no—
219#1694—111no—
220#1686—111no—
221#1682—111no—
222#1680—111no—
223#1673—111no—
224#1665—111no—
225#1565—111no—
226#1544—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—81no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—81no—
261C4×D11—82no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11#13512yes—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278#533—111no—
279#532—111no—
280#529C2×D1111yescharacteristic
281#500—111no—
282#495—221no—
283#492—111no—
284#488—221no—
285#487—111no—
286#486—111no—
287#479—221no—
288#475—111no—
289#474—111no—
290#468—221no—
291#468—221no—
292#467—221no—
293#465—221no—
294#464—221no—
295#462—111no—
296#462—111no—
297#461—111no—
298#461—111no—
299#460—111no—
300#459—111no—
301#452—221no—
302#449—221no—
303#446C2×D1111yescharacteristic
304C8×Q8C2×D1111yescharacteristic
305#440—221no—
306#440—221no—
307#436—21no—
308#436C2×D1111yescharacteristic
309#435—21no—
310C8×D4C2×D1111yescharacteristic
311#433—21no—
312#431—111no—
313#431C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315#405—21no—
316C4×M16C2×D1111yescharacteristic
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×#12111yescharacteristic
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C2×#13511yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57611yescharacteristic
349C4×C11#57711yescharacteristic
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353C2×#41—221no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×D8—221no—
362C2×M16—21no—
363C2×M16C22⋊D1111yescharacteristic
364C2×M16C22⋊D1111yescharacteristic
365C22×C8—21no—
366C22×C8—221no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370#127—111no—
371#126—21no—
372#125—221no—
373#125D4411yescharacteristic
374#124—221no—
375#124D4411yescharacteristic
376#123—21no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8D4411yescharacteristic
380#121—221no—
381#121—221no—
382#121D4411yescharacteristic
383C4×Q8—221no—
384C4×Q8—221no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—21no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391#117—221no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#107—221no—
395#107—221no—
396#106—221no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405C4⋊C8C22×D1111yescharacteristic
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#102—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—221no—
422#97—21no—
423#97C22⋊D1111yescharacteristic
424#97C22⋊D1111yescharacteristic
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—221no—
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C2×C11—41no—
431C2×C11—81no—
432C2×C11#303511yescharacteristic
433C2×C11#306211yescharacteristic
434C2×C11#306911yescharacteristic
435D11—161no—
436#41—881no—
437#41—881no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8C2×D4411yescharacteristic
442C2×D4—21no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4C2×D4411yescharacteristic
448C22×C4—21no—
449C22×C4—441no—
450C22×C4C2×D4411yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453Q16—881no—
454Q16—881no—
455SD16—442no—
456SD16—442no—
457SD16—881no—
458SD16—881no—
459SD16—881no—
460D8—881no—
461M16—22no—
462M16—41no—
463M16—42no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—881no—
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C2×C8C2×C22⋊D1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4C2×D4411yescharacteristic
489C4⋊C4C2×D4411yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C42—21no—
499C42—441no—
500C42C2×D4411yescharacteristic
501C42#433911yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1924611yescharacteristic, complemented, Sylow
505C23—21no—
506C23—441no—
507C23#6698311yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—441no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516D4—21no—
517D4—21no—
518D4—81no—
519D4—441no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—881no—
524D4—882no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—882no—
539C2×C4#6698311yescharacteristic
540C2×C4#6698311yescharacteristic
541C2×C4#6698311yescharacteristic
542C2×C4C22×D4411yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—441no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8#6700312yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22C2×#6698311yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—881no—
573C4—881no—
574C4—881no—
575C4#1062328211yescharacteristic
576C4#1062328311yescharacteristic
577C4C2×#6700311yescharacteristic
578C4#1062335311yescharacteristic
579C2—41no—
580C2—81no—
581C2—1761no—
582C2#1307807111yescharacteristic
583C2#1307829611yescharacteristic
584C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radical#13079588C2
hypercenter#2969D11
hypocenterC11#19246
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
1. #13079953C2semidirect
3. #13079334C2semidirect
4. #13068177C2semidirect
5. #13068163C2semidirect
6. #13068134C2semidirect
7. #13068088C2semidirect
8. #13068060C2semidirect
9. #13068046C2semidirect
10. #13068005C2semidirect
11. #13067957C2semidirect
12. #13067368C2semidirect
13. #13067280C2semidirect
14. #13067263C2semidirect
15. C11×#2969C2semidirect
216. #2969D11semidirect
504. C11#19246semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130795882
#130793342
#130681772
#130681632
#130681342
#130680882
#130680602
#130680462
#130680052
#130679572
#130673682
#130672802
#130672632
C11×#29692
#1924611