Finite Group Databasebeta

← #14739226

Subgroups — #14739226

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079574C211yesmaximal, characteristic, complemented
2#13078767C211yesmaximal, characteristic
3#13078687C211yesmaximal, characteristic, complemented
4#13068060C211yesmaximal, characteristic, complemented
5#13068053C211yesmaximal, characteristic, complemented
6#13068046C211yesmaximal, characteristic, complemented
7#13068039C211yesmaximal, characteristic, complemented
8#13067986C211yesmaximal, characteristic, complemented
9#13067981C211yesmaximal, characteristic, complemented
10#13067964C211yesmaximal, characteristic, complemented
11#13067957C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067314C211yesmaximal, characteristic, complemented
14#13067266C211yesmaximal, characteristic, complemented
15C11×#2988C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×D4×C11—21no—
22C8×D4×C11—21no—
23C8×D4×C11C2211yescharacteristic
24C8×D4×C11C2211yescharacteristic
25C11×#431—21no—
26C11×#431C2211yescharacteristic
27C2×C11×C4⋊C8—21no—
28C2×C11×C4⋊C8C2211yescharacteristic
29#10622852—21no—
30#10622851—21no—
31#10622644C2211yescharacteristic
32C4×#4326—21no—
33#10622640C2211yescharacteristic
34#10622639—21no—
35#10622633C2211yescharacteristic
36#10622633C2211yescharacteristic
37#10622632C2211yescharacteristic
38C4×#4324—21no—
39#10622628C2211yescharacteristic
40#10622627—21no—
41#10622620C2211yescharacteristic
42#10622620C2211yescharacteristic
43#10622616—21no—
44#10622609—21no—
45#10622539C2211yescharacteristic
46#10622538C2211yescharacteristic
47#10622458—21no—
48#10622458—21no—
49#10622346—21no—
50#10622346—21no—
51#10622312C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622306C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C4×Q8×C11D411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11D411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—21no—
83C2×#4325—21no—
84C2×#4324—21no—
85C2×#4323—21no—
86#66983—21no—
87#66983—21no—
88#66979—21no—
89#66977—21no—
90#66977—21no—
91C2×Dic44—21no—
92C2×Dic44—21no—
93C2×#4314—21no—
94C2×#4314—21no—
95#66928—21no—
96#66927C2311yescharacteristic
97C4×D44—21no—
98C4×D44—21no—
99#66923—21no—
100#66922C2311yescharacteristic
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8D411yescharacteristic
109C11×C4⋊C8D411yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D411yescharacteristic
116C4×C8×C11—21no—
117C4×C8×C11—21no—
118C4×C8×C11C2311yescharacteristic
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66885—21no—
127#66885—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66872—21no—
135#66872—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19413—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—41no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×C4×D11—41no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C2×C8×C11—81no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—41no—
190#4326—42no—
191#4325—42no—
192#4324—42no—
193#4323—42no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204C4×Dic11—41no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209Dic44—81no—
210Dic44—81no—
211#4314—81no—
212#4314—81no—
213#3210—111no—
214#3115—111no—
215#3107—111no—
216#2988D1111yescharacteristic, complemented
217#1682—111no—
218#1681—111no—
219#1680—111no—
220#1679—111no—
221#1670—111no—
222#1669—111no—
223#1666—111no—
224#1665—111no—
225#1572—111no—
226#1552—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11#12111yescharacteristic
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11#13512yes—
233D4×C11—24no—
234D4×C11—21no—
235D4×C11#13512yes—
236C2×C4×C11—24no—
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—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—82no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—81no—
263C4×D11—82no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533—111no—
281#532—111no—
282C4×#41C2×D1111yescharacteristic
283#494—111no—
284#492—111no—
285#487—111no—
286#486—111no—
287#485—221no—
288#482—221no—
289#475—111no—
290#475—111no—
291#474—111no—
292#474—111no—
293#464—221no—
294#464—221no—
295#462—111no—
296#461—111no—
297#460—111no—
298#459—111no—
299#452—221no—
300#452—221no—
301#452—221no—
302#449—221no—
303C8×Q8C2×D1111yescharacteristic
304C8×Q8C2×D1111yescharacteristic
305#442—221no—
306#440—221no—
307C4×Q16—221no—
308C4×SD16—221no—
309C8×D4—21no—
310C8×D4—21no—
311C8×D4C2×D1111yescharacteristic
312C8×D4C2×D1111yescharacteristic
313#432—111no—
314#431—21no—
315#431—111no—
316#431C2×D1111yescharacteristic
317C2×C4⋊C8—21no—
318C2×C4⋊C8C2×D1111yescharacteristic
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—22no—
334C22×C11—21no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11C2×#13511yescharacteristic
349C4×C11C2×#13511yescharacteristic
350C4×C11#57611yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355C2×#41—221no—
356C2×#41D4411yescharacteristic
357C2×Q16—221no—
358C2×Q16—221no—
359C2×Q16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—221no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8—111no—
369C4⋊Q8—111no—
370C4⋊Q8—111no—
371#127—111no—
372#125—221no—
373#124—221no—
374C22⋊Q8—221no—
375C22⋊Q8—221no—
376#121—221no—
377#121—221no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8D4411yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—221no—
385C4×D4—221no—
386C4×D4D4411yescharacteristic
387C4×D4C22×D1111yescharacteristic
388#117—21no—
389#117—221no—
390#117D4411yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#107—221no—
395#106—221no—
396#106—221no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8C22⋊D1111yescharacteristic
405C4⋊C8C22⋊D1111yescharacteristic
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8C22⋊D1111yescharacteristic
425C22⋊C8C22⋊D1111yescharacteristic
426#97—221no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11—42no—
434C2×C11#304511yescharacteristic
435C2×C11#305011yescharacteristic
436C2×C11#306911yescharacteristic
437D11—161no—
438#41—22no—
439#41—22no—
440#41—881no—
441#41—881no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8C2×D4411yescharacteristic
446C2×D4—21no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—441no—
451C2×D4C2×D4411yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—441no—
456C22×C4C2×D4411yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—442no—
460Q16—881no—
461Q16—881no—
462SD16—442no—
463SD16—442no—
464SD16—881no—
465SD16—881no—
466D8—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4C2×D4411yescharacteristic
491C4⋊C4C2×D4411yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—441no—
502C42C2×D4411yescharacteristic
503C42#433911yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1941311yescharacteristic, complemented, Sylow
507C23—21no—
508C23—441no—
509C23#6698311yescharacteristic
510Q8—21no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517Q8#6695712yes—
518D4—24no—
519D4—21no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—881no—
525D4—882no—
526D4#6695712yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—81no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6698311yescharacteristic
544C2×C4#6698311yescharacteristic
545C2×C4#6698311yescharacteristic
546C2×C4C22×D4411yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8—441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6698311yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—41no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4C2×#6695711yescharacteristic
580C4C2×#6695711yescharacteristic
581C4#1062336611yescharacteristic
582C4#1062336811yescharacteristic
583C2—41no—
584C2—42no—
585C2—1761no—
586C2#1307815511yescharacteristic
587C2#1307819711yescharacteristic
588C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×#121
prime radical#13078767C2
hypercenter#2988D11
hypocenterC11#19413
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #13079574C2semidirect
3. #13078687C2semidirect
4. #13068060C2semidirect
5. #13068053C2semidirect
6. #13068046C2semidirect
7. #13068039C2semidirect
8. #13067986C2semidirect
9. #13067981C2semidirect
10. #13067964C2semidirect
11. #13067957C2semidirect
12. #13067396C2semidirect
13. #13067314C2semidirect
14. #13067266C2semidirect
15. C11×#2988C2semidirect
216. #2988D11semidirect
506. C11#19413semidirect

Maximal subgroups

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

subgroupindex
#130795742
#130787672
#130786872
#130680602
#130680532
#130680462
#130680392
#130679862
#130679812
#130679642
#130679572
#130673962
#130673142
#130672662
C11×#29882
#1941311