Finite Group Databasebeta

← #14738955

Subgroups — #14738955

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079560C211yesmaximal, characteristic, complemented
2#13078408C211yesmaximal, characteristic
3D11×#474C211yesmaximal, characteristic
4#13077637C211yesmaximal, characteristic
5#13068068C211yesmaximal, characteristic, complemented
6#13068067C211yesmaximal, characteristic, complemented
7#13068066C211yesmaximal, characteristic, complemented
8#13068065C211yesmaximal, characteristic, complemented
9#13067980C211yesmaximal, characteristic, complemented
10#13067979C211yesmaximal, characteristic, complemented
11#13067978C211yesmaximal, characteristic, complemented
12#13067389C211yesmaximal, characteristic, complemented
13#13067299C211yesmaximal, characteristic, complemented
14#13067272C211yesmaximal, characteristic, complemented
15C11×#1669C211yesmaximal, characteristic, complemented
16#10623259C2211yescharacteristic
17D11×C4⋊Q8C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#494C2211yescharacteristic, complemented
20C11×#474C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622799—21no—
24#10622799—21no—
25#10622795—21no—
26#10622795—21no—
27C8×C22⋊D11—21no—
28C2×(C2×D11)⋊C8—21no—
29#10622705C2211yescharacteristic, complemented
30#10622700C2211yescharacteristic
31#10622700C2211yescharacteristic
32#10622694C2211yescharacteristic, complemented
33D4×C11⋊C8C2211yescharacteristic
34#10622621C2211yescharacteristic
35#10622620C2211yescharacteristic
36#10622504—21no—
37#10622503—21no—
38#10622494—21no—
39D11×#107—21no—
40#10622459C2211yescharacteristic
41#10622455C2211yescharacteristic
42#10622450C2211yescharacteristic
43#10622447C2211yescharacteristic
44#10622446C2211yescharacteristic
45D11×C4⋊C8C2211yescharacteristic
46#10622383—21no—
47D11×#102—21no—
48#10622376—21no—
49#10622372—21no—
50(C22⋊D11)⋊C8—21no—
51D11×C22⋊C8—21no—
52C8×D44C2211yescharacteristic
53#10622298C2211yescharacteristic
54#10622294C2211yescharacteristic, complemented
55C11×#335C2211yescharacteristic, complemented
56C11×#332C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622185C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622120C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622096C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11D411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C4×D4×C11C2311yescharacteristic
76#66999—21no—
77Q8×Dic11—21no—
78#66997—21no—
79C2×#4326—21no—
80C2×#4326—21no—
81D4×Dic11D411yescharacteristic
82C4×C22⋊D11—21no—
83C22×C11⋊C8—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66950—21no—
89#66946D411yescharacteristic
90#66945—21no—
91C4⋊C4×D11—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11D411yescharacteristic
94#66943—21no—
95#66941—21no—
96#66941—21no—
97#66940—21no—
98(C22⋊D11)⋊C4—21no—
99C22⋊C4×D11—21no—
100C4×D44C2311yescharacteristic
101C42×D11C2311yescharacteristic
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#107—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8—21no—
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115#66896—21no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118#66885—21no—
119#66885—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8D411yescharacteristic
124(C2×D11)⋊C8D411yescharacteristic
125#66882—21no—
126#66881—21no—
127#66880—21no—
128#66880—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8D411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133C8×Dic11—21no—
134#66873—21no—
135#66873—21no—
136#66872—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19387—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11C2×D411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152Q8×D11—81no—
153Q8×D11—81no—
154D4×D11—22no—
155D4×D11Q1614yescomplemented
156C2×D44C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—41no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11#4111yescharacteristic
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—41no—
169C11×Q16—81no—
170C11×Q16—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—81no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—81no—
186#4326—81no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—41no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—41no—
195C4⋊Dic11C2×D411yescharacteristic
196Dic11⋊C4—21no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11#4111yescharacteristic
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4313—42no—
211C8×D11—42no—
212C8×D11—81no—
213C8×D11—81no—
214#3209—111no—
215#3077—111no—
216C2×#474—111no—
217#2972—111no—
218#1683—111no—
219#1683—111no—
220#1683—111no—
221#1683—111no—
222#1669—111no—
223#1669—111no—
224#1669—111no—
225#1669D1111yescharacteristic, complemented
226#1571—111no—
227#1549—111no—
228#1542—111no—
229C23×C11—21no—
230C22×D11—21no—
231C22×D11—24no—
232C22×D11—81no—
233C22×D11—81no—
234C22×D11#12111yescharacteristic
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239D4×C11—21no—
240D4×C11C2×Q1612yes—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—24no—
250C2×Dic11—21no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—81no—
254C2×Dic11#12111yescharacteristic
255C2×Dic11#12111yescharacteristic
256C2×Dic11#12111yescharacteristic
257D44—21no—
258D44C2×Q1612yes—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—81no—
265C4×D11—81no—
266C4×D11—82no—
267C4×D11C2×Q1612yes—
268C4×D11#13512yes—
269Dic22—41no—
270Dic22—41no—
271Dic22—82no—
272Dic22—81no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283#533—111no—
284C2×C4⋊Q8—111no—
285C2×C4×D4—111no—
286#494—111no—
287#494C2×D1111yescharacteristic, complemented
288#487—111no—
289#487—111no—
290#478—221no—
291#478—221no—
292#476—111no—
293#476—111no—
294#474—111no—
295#474—111no—
296#474—111no—
297#474—111no—
298#474—221no—
299#474—221no—
300#474C2×D1111yescharacteristic
301#474C2×D1111yescharacteristic
302#462—221no—
303#462—221no—
304#451—221no—
305#451—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—221no—
310C8×D4—221no—
311C8×D4C2×D1111yescharacteristic
312#431—111no—
313#431—111no—
314#428—221no—
315C2×#107—221no—
316#423—111no—
317C2×C4⋊C8—111no—
318#418—221no—
319C2×#102—221no—
320C2×C22⋊C8—221no—
321C2×C22⋊C8—221no—
322#335—111no—
323#335—111no—
324#335—111no—
325#335C2×D1111yescharacteristic, complemented
326#333—111no—
327#333—111no—
328#332—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#332C2×D1111yescharacteristic, complemented
333#332C2×D1111yescharacteristic, complemented
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×#12111yescharacteristic
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—22no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—84no—
344C2×D11#46712yes—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C22×Q1611yescharacteristic
350C4×C11C2×#13511yescharacteristic
351C4×C11#57611yescharacteristic
352C4×C11#57611yescharacteristic
353Dic11—21no—
354Dic11—21no—
355Dic11—41no—
356Dic11—81no—
357Dic11—81no—
358Dic11#46712yes—
359C22×Q8—221no—
360C22×D4—111no—
361C23×C4—221no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—221no—
365C2×Q16—221no—
366C2×M16—221no—
367C22×C8—21no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C4⋊Q8—111no—
373C4⋊Q8—111no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8—221no—
377C4⋊Q8C22×D1111yescharacteristic
378C4⋊Q8C22×D1111yescharacteristic
379#125—221no—
380C22⋊Q8—221no—
381C22⋊Q8—221no—
382C4×Q8—221no—
383C4×Q8—221no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—221no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—111no—
396#107—21no—
397#107—21no—
398#107—221no—
399#107—221no—
400#107—221no—
401#107—221no—
402#106—221no—
403#106—221no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414#103—221no—
415#103—221no—
416#103—221no—
417#103—221no—
418#102—21no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426C22⋊C8—21no—
427C22⋊C8—111no—
428C22⋊C8—111no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C2×C11—42no—
437C2×C11#304111yescharacteristic
438C2×C11C2×#46711yescharacteristic
439C2×C11#306911yescharacteristic
440D11—22no—
441D11—42no—
442C24—221no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—441no—
448C2×Q8—881no—
449C2×Q8—881no—
450C2×D4—114no—
451C2×D4—111no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4D4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—441no—
464C22×C4—881no—
465C22×C4—881no—
466Q16—81no—
467Q16—81no—
468Q16—881no—
469Q16—881no—
470M16—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—442no—
481C2×C8—881no—
482C2×C8—881no—
483C2×C8—881no—
484C2×C8D4×D1111yescharacteristic
485C2×C8D4×D1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—111no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C4⋊C4—441no—
499C4⋊C4—441no—
500C4⋊C4D4×D1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—441no—
506C42—111no—
507C42—111no—
508C42—111no—
509C42—441no—
510C42C23×D1111yescharacteristic
511C11#1938711yescharacteristic, complemented, Sylow
512C23—21no—
513C23—111no—
514C23—224no—
515C23—221no—
516C23—881no—
517C23—881no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—441no—
523Q8—441no—
524Q8—881no—
525Q8—882no—
526D4—21no—
527D4—112no—
528D4—224no—
529D4—221no—
530D4Q16×D1112yes—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—111no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4—882no—
552C2×C4—881no—
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—221no—
562C8—221no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—112no—
570C22—221no—
571C22—221no—
572C22—222no—
573C22—441no—
574C22—441no—
575C22—884no—
576C22D11×#12111yescharacteristic
577C4—21no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—112no—
582C4—221no—
583C4—221no—
584C4—441no—
585C4—881no—
586C4—881no—
587C4#1062328811yescharacteristic
588C4C2×Q16×D1111yescharacteristic
589C4D11×#13511yescharacteristic
590C4#1062330511yescharacteristic
591C2—42no—
592C2—222no—
593C2—442no—
594C2#1307811411yescharacteristic
595C2D11×#46711yescharacteristic
596C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1669C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1669D11
hypocenterC11#19387
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1669

Complements

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

NH ≅ G/Ntype
1. #13079560C2semidirect
5. #13068068C2semidirect
6. #13068067C2semidirect
7. #13068066C2semidirect
8. #13068065C2semidirect
9. #13067980C2semidirect
10. #13067979C2semidirect
11. #13067978C2semidirect
12. #13067389C2semidirect
13. #13067299C2semidirect
14. #13067272C2semidirect
15. C11×#1669C2semidirect
19. C11×#494C22semidirect
29. #10622705C22semidirect
32. #10622694C22semidirect
54. #10622294C22semidirect
55. C11×#335C22semidirect
56. C11×#332C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622185C22semidirect
60. #10622124C22semidirect
61. #10622120C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622117C22semidirect
66. #10622096C22semidirect
155. D4×D11Q16semidirect
225. #1669D11semidirect
287. #494C2×D11semidirect
325. #335C2×D11semidirect
332. #332C2×D11semidirect
333. #332C2×D11semidirect
511. C11#19387semidirect

Maximal subgroups

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

subgroupindex
#130795602
#130784082
D11×#4742
#130776372
#130680682
#130680672
#130680662
#130680652
#130679802
#130679792
#130679782
#130673892
#130672992
#130672722
C11×#16692
#1938711