Finite Group Databasebeta

← #14738875

Subgroups — #14738875

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079989C211yesmaximal, characteristic, complemented
2#13079631C211yesmaximal, characteristic
3#13078991C211yesmaximal, characteristic, complemented
4#13068184C211yesmaximal, characteristic, complemented
5#13068177C211yesmaximal, characteristic, complemented
6#13068156C211yesmaximal, characteristic, complemented
7#13068149C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068053C211yesmaximal, characteristic, complemented
10#13068032C211yesmaximal, characteristic, complemented
11#13068025C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067283C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×#66927C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#446C2211yescharacteristic, complemented
20C8×Q8×C11C2211yescharacteristic, complemented
21C11×#436—21no—
22C11×#436C2211yescharacteristic, complemented
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic, complemented
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622744—21no—
30#10622744—21no—
31#10622680—21no—
32#10622676—21no—
33#10622671—21no—
34#10622667—21no—
35#10622665—21no—
36#10622659—21no—
37#10622655—21no—
38#10622649—21no—
39#10622644C2211yescharacteristic, complemented
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622634C2211yescharacteristic, complemented
43#10622632C2211yescharacteristic, complemented
44#10622628C2211yescharacteristic
45#10622628C2211yescharacteristic
46#10622621C2211yescharacteristic, complemented
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622326—21no—
50#10622326—21no—
51#10622307C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622307C2211yescharacteristic
54#10622307C2211yescharacteristic
55#10622124C2211yescharacteristic, complemented
56#10622124C2211yescharacteristic, complemented
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622096C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C22×D44—21no—
68C22×D44—21no—
69C22×D44—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C22×C8×C11—21no—
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8D411yescharacteristic
79C11×#121D411yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C2×C42×C11C2311yescharacteristic
85C2×#4326—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90C2×#4323—21no—
91#66979—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318—21no—
95#66927—21no—
96#66927—21no—
97#66927—21no—
98#66927C2311yescharacteristic
99#66927C2311yescharacteristic
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117C4×C8×C11C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66899—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66885—21no—
123#66885—21no—
124#66885—21no—
125#66885—21no—
126#66885—21no—
127#66885—21no—
128#66885—21no—
129#66885—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—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
143#66867—21no—
144#19380—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11C2×D411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—42no—
161C2×D44—41no—
162C2×D44—41no—
163C2×D44—41no—
164C2×D44—81no—
165C2×D44—81no—
166C2×D44—82no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16—42no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—42no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C42×C11—21no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11#4111yescharacteristic
194C42×C11C2411yescharacteristic
195C22⋊Dic11—41no—
196#4326—81no—
197#4325—81no—
198#4325—81no—
199#4324—81no—
200#4323—81no—
201#4323—81no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208C4×Dic11—41no—
209#4318—81no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#3252—111no—
215#3217—111no—
216#3138—111no—
217#2969D1111yescharacteristic, complemented
218#1702—111no—
219#1701—111no—
220#1698—111no—
221#1697—111no—
222#1682—111no—
223#1681—111no—
224#1678—111no—
225#1677—111no—
226#1569—111no—
227#1554—111no—
228#1545—111no—
229C23×C11—21no—
230C23×C11#12111yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—82no—
236Q8×C11—21no—
237Q8×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—81no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—41no—
258C2×Dic11—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—81no—
268D44—81no—
269D44—82no—
270D44—82no—
271D44—82no—
272Dic22—41no—
273Dic22—41no—
274Dic22—81no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#533—111no—
286C2×#127—111no—
287#529C2×D1111yescharacteristic
288#496—221no—
289#490—221no—
290#490—221no—
291#490—221no—
292#486—111no—
293#486—111no—
294#486—111no—
295#486—111no—
296#479—221no—
297#477—111no—
298#476—111no—
299#470—221no—
300#468—221no—
301#464—221no—
302#462—111no—
303#461—111no—
304#460—111no—
305#460—111no—
306#459—111no—
307#459—111no—
308#450—221no—
309#447—221no—
310#446C2×D1111yescharacteristic, complemented
311C8×Q8C2×D1111yescharacteristic, complemented
312#436—21no—
313#436C2×D1111yescharacteristic, complemented
314#435—21no—
315C8×D4C2×D1111yescharacteristic, complemented
316#433—21no—
317#432—111no—
318#431C2×D1111yescharacteristic
319#423—111no—
320#418—221no—
321#418—221no—
322#405—21no—
323C4×M16C2×D1111yescharacteristic
324#335—111no—
325#335—111no—
326#334—111no—
327#334—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×#12111yescharacteristic
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—164no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#57511yescharacteristic
358C4×C11#57511yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361Dic11—81no—
362Dic11—81no—
363C22×D4—221no—
364C22×D4—221no—
365C22×D4—221no—
366C2×Q16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×D8—221no—
371C2×D8—221no—
372C2×M16—21no—
373C2×M16—221no—
374C2×M16C22⋊D1111yescharacteristic
375C2×M16C22⋊D1111yescharacteristic
376C22×C8—21no—
377C4⋊Q8—111no—
378C4⋊Q8—111no—
379#127—111no—
380#127—111no—
381#127—221no—
382#127—221no—
383#127—221no—
384#126—21no—
385#125—221no—
386#125D4411yescharacteristic
387#124D4411yescharacteristic
388#123—21no—
389C22⋊Q8—221no—
390C22⋊Q8—221no—
391C22⋊Q8D4411yescharacteristic
392#121D4411yescharacteristic
393C4×Q8—221no—
394C4×Q8—221no—
395C4×Q8C22×D1111yescharacteristic
396C4×D4—21no—
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399#117—221no—
400C2×C42C22×D1111yescharacteristic
401#107—221no—
402#106—221no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—221no—
413#103—221no—
414#103—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—221no—
432#97—21no—
433#97—221no—
434#97C22⋊D1111yescharacteristic
435#97C22⋊D1111yescharacteristic
436C4×C8—21no—
437C4×C8—21no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—41no—
441C2×C11—81no—
442C2×C11#304011yescharacteristic
443C2×C11#306211yescharacteristic
444C2×C11#306811yescharacteristic
445D11—161no—
446D11—161no—
447C24—441no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8C2×D4411yescharacteristic
451C2×D4—21no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—442no—
459C2×D4—442no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—881no—
464C2×D4—881no—
465C2×D4—882no—
466C2×D4C2×D4411yescharacteristic
467C22×C4—21no—
468C22×C4C2×D4411yescharacteristic
469C22×C4#433911yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471Q16—881no—
472SD16—881no—
473SD16—881no—
474SD16—881no—
475D8—881no—
476D8—881no—
477M16—41no—
478M16—41no—
479M16—42no—
480M16—881no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C2×C8C2×C22⋊D1111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4C2×D4411yescharacteristic
503C4⋊C4C2×D4411yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—441no—
510C42—21no—
511C42—441no—
512C42C2×D4411yescharacteristic
513C42#433911yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1938011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—441no—
519C23—441no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23#6698311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—441no—
527Q8—441no—
528Q8—881no—
529D4—21no—
530D4—21no—
531D4—81no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—881no—
541D4—881no—
542D4—882no—
543D4—882no—
544D4—882no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6698311yescharacteristic
558C2×C4#6698311yescharacteristic
559C2×C4#6698311yescharacteristic
560C2×C4C22×D4411yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—1764no—
586C22C2×#6698311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—881no—
595C4—881no—
596C4#1062328211yescharacteristic
597C4#1062328311yescharacteristic
598C4#1062335311yescharacteristic
599C4#1062335311yescharacteristic
600C2—41no—
601C2—81no—
602C2—1761no—
603C2—1761no—
604C2#1307811011yescharacteristic
605C2#1307829611yescharacteristic
606C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#2969D11
hypocenterC11#19380
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. #13079989C2semidirect
3. #13078991C2semidirect
4. #13068184C2semidirect
5. #13068177C2semidirect
6. #13068156C2semidirect
7. #13068149C2semidirect
8. #13068060C2semidirect
9. #13068053C2semidirect
10. #13068032C2semidirect
11. #13068025C2semidirect
12. #13067383C2semidirect
13. #13067324C2semidirect
14. #13067283C2semidirect
15. C11×#2969C2semidirect
19. C11×#446C22semidirect
20. C8×Q8×C11C22semidirect
22. C11×#436C22semidirect
24. C8×D4×C11C22semidirect
39. #10622644C22semidirect
42. #10622634C22semidirect
43. #10622632C22semidirect
46. #10622621C22semidirect
55. #10622124C22semidirect
56. #10622124C22semidirect
61. #10622119C22semidirect
62. #10622119C22semidirect
63. #10622096C22semidirect
64. #10622096C22semidirect
65. #10622095C22semidirect
66. #10622095C22semidirect
217. #2969D11semidirect
310. #446C2×D11semidirect
311. C8×Q8C2×D11semidirect
313. #436C2×D11semidirect
315. C8×D4C2×D11semidirect
516. C11#19380semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130796312
#130789912
#130681842
#130681772
#130681562
#130681492
#130680602
#130680532
#130680322
#130680252
#130673832
#130673242
#130672832
C11×#29692
#1938011