Finite Group Databasebeta

← #14738989

Subgroups — #14738989

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079756C211yesmaximal, characteristic, complemented
2#13078408C211yesmaximal, characteristic
3D11×#461C211yesmaximal, characteristic
4#13077637C211yesmaximal, characteristic
5#13068038C211yesmaximal, characteristic, complemented
6#13068037C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13067992C211yesmaximal, characteristic, complemented
9#13067991C211yesmaximal, characteristic, complemented
10#13067990C211yesmaximal, characteristic, complemented
11#13067989C211yesmaximal, characteristic, complemented
12#13067385C211yesmaximal, characteristic, complemented
13#13067286C211yesmaximal, characteristic, complemented
14#13067272C211yesmaximal, characteristic, complemented
15C11×#1679C211yesmaximal, characteristic, complemented
16C2×SD16×D11—21no—
17#10623259C2211yescharacteristic
18D11×C4⋊Q8C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C11×#487C2211yescharacteristic, complemented
21C11×#474C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24#10622775—21no—
25C8×C22⋊D11—21no—
26C2×(C2×D11)⋊C8—21no—
27#10622700C2211yescharacteristic
28#10622696C2211yescharacteristic
29#10622694C2211yescharacteristic, complemented
30#10622692C2211yescharacteristic, complemented
31#10622632C2211yescharacteristic
32D4×C11⋊C8C2211yescharacteristic
33#10622621C2211yescharacteristic
34#10622504—21no—
35#10622494—21no—
36#10622455C2211yescharacteristic
37#10622454C2211yescharacteristic
38#10622450C2211yescharacteristic
39#10622447C2211yescharacteristic
40#10622446C2211yescharacteristic
41D11×C4⋊C8C2211yescharacteristic
42#10622431—21no—
43#10622418—21no—
44#10622418—21no—
45D11×#103—21no—
46#10622404—21no—
47#10622404—21no—
48#10622383—21no—
49#10622376—21no—
50(C22⋊D11)⋊C8—21no—
51D11×C22⋊C8—21no—
52C8×D44C2211yescharacteristic
53#10622298C2211yescharacteristic
54#10622293C2211yescharacteristic, complemented
55C11×#334C2211yescharacteristic, 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#10622118C2211yescharacteristic, complemented
65#10622118C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11D411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×SD16—21no—
71C22×C8×C11—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75#66999—21no—
76Q8×Dic11—21no—
77#66997—21no—
78C2×#4325—21no—
79D4×Dic11D411yescharacteristic
80C2×#4324—21no—
81C4×C22⋊D11—21no—
82C22×C11⋊C8—21no—
83SD16×D11—44no—
84C2×#4314—21no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66950—21no—
90#66946D411yescharacteristic
91#66945—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—21no—
94C4⋊C4×D11D411yescharacteristic
95#66943—21no—
96#66941—21no—
97#66941—21no—
98#66940—21no—
99(C22⋊D11)⋊C4—21no—
100C22⋊C4×D11—21no—
101C4×D44C2311yescharacteristic
102C42×D11C2311yescharacteristic
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120#66885—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8D411yescharacteristic
125(C2×D11)⋊C8D411yescharacteristic
126#66881—21no—
127#66881—21no—
128#66881—21no—
129#66880—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8D411yescharacteristic
133Dic11⋊C8D411yescharacteristic
134C8×Dic11—21no—
135#66874—21no—
136#66873—21no—
137#66872—21no—
138#66872—21no—
139#66872—21no—
140#66871—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19390—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153Q8×D11—42no—
154Q8×D11—42no—
155D4×D11—22no—
156D4×D11SD1614yes—
157C2×D44C2×D411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—41no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×C4×D11#4111yescharacteristic
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—41no—
170C11×SD16—42no—
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#4325—42no—
186#4324—42no—
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#4314—42no—
211#4313—42no—
212C8×D11—42no—
213C8×D11—81no—
214C8×D11—81no—
215#3229—111no—
216#3077—111no—
217C2×#461—111no—
218#2972—111no—
219#1679—111no—
220#1679—111no—
221#1679—111no—
222#1679D1111yescharacteristic, complemented
223#1671—111no—
224#1671—111no—
225#1671—111no—
226#1671—111no—
227#1570—111no—
228#1546—111no—
229#1542—111no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11—24no—
233C22×D11—81no—
234C22×D11—81no—
235C22×D11#12111yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240D4×C11—21no—
241D4×C11C2×SD1612yes—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—24no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—81no—
255C2×Dic11#12111yescharacteristic
256C2×Dic11#12111yescharacteristic
257C2×Dic11#12111yescharacteristic
258D44—21no—
259D44C2×SD1612yes—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—81no—
266C4×D11—81no—
267C4×D11—82no—
268C4×D11C2×SD1612yes—
269C4×D11#13512yes—
270Dic22—41no—
271Dic22—41no—
272Dic22—82no—
273Dic22—81no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C22×SD16—221no—
285#533—111no—
286C2×C4⋊Q8—111no—
287C2×C4×D4—111no—
288#498—111no—
289#498—111no—
290#487—111no—
291#487C2×D1111yescharacteristic, complemented
292#483—221no—
293#483—221no—
294#478—221no—
295#478—221no—
296#476—111no—
297#476—111no—
298#475—221no—
299#475—221no—
300#474—111no—
301#474C2×D1111yescharacteristic
302#461—111no—
303#461—111no—
304#461—111no—
305#461—221no—
306#461—221no—
307#461C2×D1111yescharacteristic
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—111no—
311C8×D4—221no—
312C8×D4—221no—
313C8×D4C2×D1111yescharacteristic
314#431—111no—
315#431—111no—
316#428—221no—
317#423—111no—
318C2×C4⋊C8—111no—
319#418—221no—
320C2×#103—221no—
321C2×C22⋊C8—221no—
322C2×C22⋊C8—221no—
323#334—111no—
324#334—111no—
325#334—111no—
326#334C2×D1111yescharacteristic, complemented
327#333—111no—
328#333—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#332—111no—
333#332C2×D1111yescharacteristic, complemented
334#332C2×D1111yescharacteristic, complemented
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×#12111yescharacteristic
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—84no—
345C2×D11#46512yes—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C22×SD1611yescharacteristic
351C4×C11C2×#13511yescharacteristic
352C4×C11#57711yescharacteristic
353C4×C11#57711yescharacteristic
354Dic11—21no—
355Dic11—21no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359Dic11#46512yes—
360C22×Q8—221no—
361C22×D4—111no—
362C23×C4—221no—
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—444no—
368C2×M16—221no—
369C22×C8—21no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C4⋊Q8—111no—
375C4⋊Q8—111no—
376C4⋊Q8—221no—
377C4⋊Q8—221no—
378C4⋊Q8—221no—
379C4⋊Q8C22×D1111yescharacteristic
380C4⋊Q8C22×D1111yescharacteristic
381#125—221no—
382C22⋊Q8—221no—
383C22⋊Q8—221no—
384C4×Q8—221no—
385C4×Q8—221no—
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4C22×D1111yescharacteristic
392#117—221no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—111no—
398#107—21no—
399#107—221no—
400#106—221no—
401#106—221no—
402#106—221no—
403#106—221no—
404#106—221no—
405#106—221no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—111no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8C22×D1111yescharacteristic
414C4⋊C8C22×D1111yescharacteristic
415C4⋊C8C22×D1111yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—221no—
420#103—221no—
421#103—221no—
422#103—221no—
423#103—221no—
424#102—21no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—21no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C2×C11—42no—
439C2×C11#304211yescharacteristic
440C2×C11C2×#46511yescharacteristic
441C2×C11#306911yescharacteristic
442D11—22no—
443D11—42no—
444C24—221no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—441no—
450C2×Q8—442no—
451C2×Q8—442no—
452C2×D4—114no—
453C2×D4—111no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4D4×D1111yescharacteristic
457C22×C4—21no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—441no—
466C22×C4—881no—
467C22×C4—881no—
468SD16—42no—
469SD16—442no—
470SD16—442no—
471SD16—442no—
472M16—442no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—442no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8D4×D1111yescharacteristic
487C2×C8D4×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—111no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—441no—
499C4⋊C4—441no—
500C4⋊C4—441no—
501C4⋊C4—441no—
502C4⋊C4D4×D1111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—441no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42—441no—
512C42C23×D1111yescharacteristic
513C11#1939011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—111no—
516C23—224no—
517C23—221no—
518C23—881no—
519C23—881no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526Q8—881no—
527Q8—882no—
528D4—21no—
529D4—112no—
530D4—224no—
531D4—221no—
532D4SD16×D1112yes—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—111no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4—882no—
554C2×C4—881no—
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—441no—
566C8—441no—
567C8—441no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—112no—
572C22—221no—
573C22—221no—
574C22—222no—
575C22—441no—
576C22—441no—
577C22—884no—
578C22D11×#12111yescharacteristic
579C4—21no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—112no—
584C4—221no—
585C4—221no—
586C4—441no—
587C4—881no—
588C4—881no—
589C4C2×SD16×D1111yescharacteristic
590C4D11×#13511yescharacteristic
591C4#1062330111yescharacteristic
592C4#1062330611yescharacteristic
593C2—42no—
594C2—222no—
595C2—442no—
596C2#1307812611yescharacteristic
597C2D11×#46511yescharacteristic
598C2#1307835111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1679C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1679D11
hypocenterC11#19390
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
1. #13079756C2semidirect
5. #13068038C2semidirect
6. #13068037C2semidirect
7. #13068036C2semidirect
8. #13067992C2semidirect
9. #13067991C2semidirect
10. #13067990C2semidirect
11. #13067989C2semidirect
12. #13067385C2semidirect
13. #13067286C2semidirect
14. #13067272C2semidirect
15. C11×#1679C2semidirect
20. C11×#487C22semidirect
29. #10622694C22semidirect
30. #10622692C22semidirect
54. #10622293C22semidirect
55. C11×#334C22semidirect
56. C11×#332C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622185C22semidirect
60. #10622124C22semidirect
61. #10622120C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622118C22semidirect
66. #10622095C22semidirect
222. #1679D11semidirect
291. #487C2×D11semidirect
326. #334C2×D11semidirect
333. #332C2×D11semidirect
334. #332C2×D11semidirect
513. C11#19390semidirect

Maximal subgroups

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

subgroupindex
#130797562
#130784082
D11×#4612
#130776372
#130680382
#130680372
#130680362
#130679922
#130679912
#130679902
#130679892
#130673852
#130672862
#130672722
C11×#16792
#1939011