Finite Group Databasebeta

← #14737765

Subgroups — #14737765

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078939C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic, complemented
3#13078767C211yesmaximal, characteristic
4#13068074C211yesmaximal, characteristic, complemented
5#13068067C211yesmaximal, characteristic, complemented
6#13068060C211yesmaximal, characteristic, complemented
7#13068053C211yesmaximal, characteristic, complemented
8#13068046C211yesmaximal, characteristic, complemented
9#13068039C211yesmaximal, characteristic, complemented
10#13068032C211yesmaximal, characteristic, complemented
11#13068025C211yesmaximal, characteristic, complemented
12#13067379C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067319C211yesmaximal, characteristic, complemented
15C8×C11×#41C211yesmaximal, 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×C4×C8×C11—21no—
28C2×C4×C8×C11C2211yescharacteristic
29#10622852—21no—
30#10622851—21no—
31#10622726—21no—
32#10622726—21no—
33#10622644C2211yescharacteristic
34#10622643—21no—
35#10622640C2211yescharacteristic
36#10622639—21no—
37#10622634C2211yescharacteristic
38#10622633C2211yescharacteristic
39#10622632C2211yescharacteristic
40#10622631—21no—
41#10622628C2211yescharacteristic
42#10622627—21no—
43#10622621C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622616—21no—
46#10622609—21no—
47#10622539C2211yescharacteristic
48#10622539C2211yescharacteristic
49#10622310—21no—
50#10622310—21no—
51#10622307C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11D411yescharacteristic
72C22×C8×C11D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4325—21no—
85C2×#4324—21no—
86C2×#4323—21no—
87#66983—21no—
88#66983—21no—
89#66979—21no—
90#66977—21no—
91#66977—21no—
92#66928—21no—
93#66927C2311yescharacteristic
94C4×D44—21no—
95C4×D44—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11—21no—
111C4×C8×C11—21no—
112C4×C8×C11D411yescharacteristic
113C4×C8×C11D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66885—21no—
123#66885—21no—
124#66885—21no—
125#66885—21no—
126#66880—21no—
127#66880—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—
143#66867—21no—
144#19278—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—42no—
158#4339—42no—
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—41no—
169C2×C8×C11—41no—
170C2×C8×C11—42no—
171C2×C8×C11—42no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190C22⋊Dic11—41no—
191#4326—42no—
192#4325—42no—
193#4324—42no—
194#4323—42no—
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—
210#3131—111no—
211#3116—111no—
212#3115—111no—
213C8×#41D1111yescharacteristic, complemented
214#1684—111no—
215#1683—111no—
216#1682—111no—
217#1681—111no—
218#1680—111no—
219#1679—111no—
220#1678—111no—
221#1677—111no—
222#1568—111no—
223#1554—111no—
224#1553—111no—
225C23×C11—21no—
226C23×C11#12111yescharacteristic
227C22×D11—41no—
228Q8×C11—21no—
229Q8×C11#13512yes—
230D4×C11—24no—
231D4×C11—21no—
232D4×C11#13512yes—
233C2×C4×C11—24no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—82no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—81no—
260C4×D11—82no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—81no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#533—111no—
277#532—111no—
278C4×#41C2×D1111yescharacteristic
279#488—221no—
280#488—221no—
281#487—111no—
282#487—111no—
283#486—111no—
284#486—111no—
285#485—221no—
286#482—221no—
287#477—111no—
288#476—111no—
289#475—111no—
290#474—111no—
291#462—111no—
292#461—111no—
293#460—111no—
294#459—111no—
295#452—221no—
296#449—221no—
297C8×Q8C2×D1111yescharacteristic
298C8×Q8C2×D1111yescharacteristic
299#442—221no—
300#441—221no—
301#440—221no—
302#440—221no—
303C8×D4—21no—
304C8×D4—21no—
305C8×D4C2×D1111yescharacteristic
306C8×D4C2×D1111yescharacteristic
307#432—111no—
308#432—111no—
309#431—21no—
310#431C2×D1111yescharacteristic
311#416—221no—
312#416—221no—
313C2×C4×C8—21no—
314C2×C4×C8C2×D1111yescharacteristic
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319#333—111no—
320#333—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#331—111no—
326#331—111no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—22no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×#12111yescharacteristic
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×#13511yescharacteristic
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57511yescharacteristic
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C2×#41—221no—
352C2×#41D4411yescharacteristic
353C2×Q16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×D8—221no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8C22⋊D1111yescharacteristic
360C22×C8C22⋊D1111yescharacteristic
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8—111no—
364#127—111no—
365#125—221no—
366#124—221no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369#121—221no—
370#121—221no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8D4411yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4D4411yescharacteristic
380C4×D4C22×D1111yescharacteristic
381#117—21no—
382#117—221no—
383#117D4411yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C22⋊D1111yescharacteristic
425C4×C8C22⋊D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—42no—
430C2×C11#304011yescharacteristic
431C2×C11#305011yescharacteristic
432C2×C11#306711yescharacteristic
433D11—161no—
434#41—22no—
435#41—22no—
436#41—442no—
437#41—442no—
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—21no—
450C22×C4—21no—
451C22×C4—441no—
452C22×C4C2×D4411yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456SD16—442no—
457SD16—442no—
458D8—442no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—42no—
464C2×C8—42no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4C2×D4411yescharacteristic
484C4⋊C4C2×D4411yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—441no—
495C42C2×D4411yescharacteristic
496C42#433911yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1927811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—441no—
502C23#6698311yescharacteristic
503Q8—21no—
504Q8—441no—
505Q8—441no—
506Q8—441no—
507Q8—441no—
508Q8—881no—
509Q8#6695712yes—
510D4—24no—
511D4—21no—
512D4—441no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—881no—
517D4—882no—
518D4#6695712yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—882no—
535C2×C4#6698311yescharacteristic
536C2×C4#6698311yescharacteristic
537C2×C4#6698311yescharacteristic
538C2×C4C22×D4411yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22C2×#6698311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4C2×#6695711yescharacteristic
572C4C2×#6695711yescharacteristic
573C4#1062335311yescharacteristic
574C4#1062335311yescharacteristic
575C2—41no—
576C2—42no—
577C2—1761no—
578C2#1307811011yescharacteristic
579C2#1307819711yescharacteristic
580C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radical#13078767C2
hypercenterC8×#41D11
hypocenterC11#19278
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #13078939C2semidirect
2. #13078778C2semidirect
4. #13068074C2semidirect
5. #13068067C2semidirect
6. #13068060C2semidirect
7. #13068053C2semidirect
8. #13068046C2semidirect
9. #13068039C2semidirect
10. #13068032C2semidirect
11. #13068025C2semidirect
12. #13067379C2semidirect
13. #13067324C2semidirect
14. #13067319C2semidirect
15. C8×C11×#41C2semidirect
213. C8×#41D11semidirect
499. C11#19278semidirect

Maximal subgroups

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

subgroupindex
#130789392
#130787782
#130787672
#130680742
#130680672
#130680602
#130680532
#130680462
#130680392
#130680322
#130680252
#130673792
#130673242
#130673192
C8×C11×#412
#1927811