Finite Group Databasebeta

← #14738995

Subgroups — #14738995

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079745C211yesmaximal, characteristic, complemented
2D11×#476C211yesmaximal, characteristic, complemented
3#13078081C211yesmaximal, characteristic
4#13077637C211yesmaximal, characteristic, complemented
5#13068028C211yesmaximal, characteristic, complemented
6#13068027C211yesmaximal, characteristic, complemented
7#13068026C211yesmaximal, characteristic, complemented
8#13068025C211yesmaximal, characteristic, complemented
9#13067990C211yesmaximal, characteristic, complemented
10#13067989C211yesmaximal, characteristic, complemented
11#13067988C211yesmaximal, characteristic, complemented
12#13067385C211yesmaximal, characteristic, complemented
13#13067295C211yesmaximal, characteristic, complemented
14#13067264C211yesmaximal, characteristic, complemented
15C11×#1671C211yesmaximal, characteristic, complemented
16C2×#66967—21no—
17#10623256C2211yescharacteristic
18D11×C4⋊Q8C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C11×#498C2211yescharacteristic, complemented
21C11×#476C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24#10622778—21no—
25C8×C22⋊D11—21no—
26C2×(C2×D11)⋊C8—21no—
27#10622701C2211yescharacteristic, complemented
28#10622697C2211yescharacteristic
29#10622696C2211yescharacteristic
30#10622692C2211yescharacteristic, complemented
31#10622628C2211yescharacteristic
32D4×C11⋊C8C2211yescharacteristic
33#10622621C2211yescharacteristic
34#10622483—21no—
35#10622483—21no—
36#10622483—21no—
37#10622476—21no—
38#10622476—21no—
39D11×#106—21no—
40#10622456C2211yescharacteristic
41#10622455C2211yescharacteristic
42#10622450C2211yescharacteristic
43#10622447C2211yescharacteristic
44#10622446C2211yescharacteristic
45D11×C4⋊C8C2211yescharacteristic
46#10622432—21no—
47#10622416—21no—
48D11×#102—21no—
49#10622374—21no—
50(C22⋊D11)⋊C8—21no—
51D11×C22⋊C8—21no—
52#10622307C2211yescharacteristic, complemented
53C8×D44C2211yescharacteristic
54#10622298C2211yescharacteristic
55C11×#334C2211yescharacteristic, complemented
56C11×#333C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622123C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622118C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×#4343—21no—
68C2×Q8×D11—21no—
69C2×D4×D11D411yescharacteristic
70C22×C4×D11—21no—
71C2×C11×SD16—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C4×D4×C11C2311yescharacteristic
76#67000—21no—
77#66997—21no—
78C2×#4325—21no—
79D4×Dic11D411yescharacteristic
80C2×#4323—21no—
81C4×C22⋊D11—21no—
82C22×C11⋊C8—21no—
83#66967—44no—
84C2×D88—21no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66948—21no—
90#66948—21no—
91#66946—21no—
92#66946—21no—
93#66946D411yescharacteristic
94C4⋊C4×D11—21no—
95C4⋊C4×D11—21no—
96C4⋊C4×D11D411yescharacteristic
97#66941—21no—
98#66941—21no—
99(C22⋊D11)⋊C4—21no—
100C22⋊C4×D11—21no—
101#66927C2311yescharacteristic
102C4×D44C2311yescharacteristic
103C42×D11C2311yescharacteristic
104#66922C2311yescharacteristic
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66896—21no—
117C22⋊(C11⋊C8)—21no—
118#66885—21no—
119#66885—21no—
120#66885—21no—
121#66885—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8D411yescharacteristic
126(C2×D11)⋊C8D411yescharacteristic
127#66881—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133#66873—21no—
134#66873—21no—
135#66873—21no—
136#66873—21no—
137#66872—21no—
138#66872—21no—
139#66872—21no—
140#66872—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19391—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—
153#4343—42no—
154#4343—42no—
155Q8×D11—82no—
156D4×D11—22no—
157D4×D11SD1614yes—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—41no—
162C2×D44C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—41no—
167C2×C4×D11—41no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11#4111yescharacteristic
173C2×Dic22—21no—
174C2×Dic22—41no—
175C11×SD16—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—81no—
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C42×C11C2411yescharacteristic
189C22⋊Dic11—21no—
190#4325—42no—
191#4323—42no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C2×D411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204C4×Dic11#4111yescharacteristic
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88—42no—
212#4313—42no—
213C8×D11—42no—
214C8×D11—81no—
215C8×D11—81no—
216#3227—111no—
217C2×#476—111no—
218#3036—111no—
219#2972—111no—
220#1677—111no—
221#1677—111no—
222#1677—111no—
223#1677—111no—
224#1671—111no—
225#1671—111no—
226#1671—111no—
227#1671D1111yescharacteristic, complemented
228#1570—111no—
229#1548—111no—
230#1540—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—24no—
234C22×D11—41no—
235C22×D11—81no—
236C22×D11—81no—
237C22×D11#12111yescharacteristic
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—81no—
241D4×C11—21no—
242D4×C11C2×SD1612yes—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—24no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—81no—
255C2×Dic11#12111yescharacteristic
256C2×Dic11#12111yescharacteristic
257C2×Dic11#12111yescharacteristic
258D44—21no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—81no—
264D44—82no—
265D44C2×SD1612yes—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—81no—
272C4×D11—81no—
273C4×D11—82no—
274C4×D11—82no—
275C4×D11C2×SD1612yes—
276C4×D11#13512yes—
277Dic22—82no—
278Dic22—81no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C11⋊C8—21no—
285C11⋊C8—21no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C2×AGL(1,ℤ/8)—221no—
290#532—111no—
291C2×C4⋊Q8—111no—
292C2×C4×D4—111no—
293#498—111no—
294#498C2×D1111yescharacteristic, complemented
295#486—111no—
296#486—111no—
297#481—221no—
298#481—221no—
299#476—111no—
300#476—111no—
301#476—111no—
302#476—221no—
303#476—221no—
304#476—221no—
305#476—221no—
306#476C2×D1111yescharacteristic
307#463—221no—
308#463—221no—
309#461—111no—
310#461C2×D1111yescharacteristic
311#459—111no—
312#459—111no—
313C8×D4—111no—
314C8×D4—111no—
315C8×D4—111no—
316C8×D4—221no—
317C8×D4—221no—
318C8×D4C2×D1111yescharacteristic
319#431—111no—
320#431—111no—
321C2×#106—221no—
322#423—111no—
323C2×C4⋊C8—111no—
324#417—221no—
325C2×#102—221no—
326C2×C22⋊C8—221no—
327C2×C22⋊C8—221no—
328#334—111no—
329#334—111no—
330#334—111no—
331#334C2×D1111yescharacteristic, complemented
332#333—111no—
333#333—111no—
334#333—111no—
335#333C2×D1111yescharacteristic, complemented
336#332—111no—
337#332C2×D1111yescharacteristic, complemented
338#331—111no—
339#331—111no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×#12111yescharacteristic
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—84no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11#46512yes—
354C4×C11—21no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C22×SD1611yescharacteristic
359C4×C11C2×#13511yescharacteristic
360C4×C11#57711yescharacteristic
361C4×C11#57711yescharacteristic
362Dic11—21no—
363Dic11—21no—
364Dic11—41no—
365Dic11—81no—
366Dic11#46512yes—
367C2×#41—221no—
368C22×Q8—221no—
369C22×D4—111no—
370C23×C4—221no—
371AGL(1,ℤ/8)—444no—
372C2×SD16—21no—
373C2×SD16—221no—
374C2×D8—221no—
375C2×D8—221no—
376C2×M16—221no—
377C22×C8—21no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C22×C8—221no—
382C4⋊Q8—111no—
383C4⋊Q8—221no—
384C4⋊Q8—221no—
385C4⋊Q8—221no—
386C4⋊Q8C22×D1111yescharacteristic
387C4⋊Q8C22×D1111yescharacteristic
388#127—111no—
389#124—221no—
390#121—221no—
391#121—221no—
392C4×D4—111no—
393C4×D4—111no—
394C4×D4—111no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4C22×D1111yescharacteristic
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—221no—
409#106—221no—
410#106—221no—
411#106—221no—
412#106—221no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8—111no—
416C4⋊C8—111no—
417C4⋊C8—111no—
418C4⋊C8—221no—
419C4⋊C8—221no—
420C4⋊C8C22×D1111yescharacteristic
421C4⋊C8C22×D1111yescharacteristic
422C4⋊C8C22×D1111yescharacteristic
423#103—21no—
424#103—221no—
425#102—21no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431#102—221no—
432#102—221no—
433#102—221no—
434#102—221no—
435C22⋊C8—21no—
436C22⋊C8—111no—
437C22⋊C8—111no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442C4×C8—111no—
443C4×C8—221no—
444C4×C8C22×D1111yescharacteristic
445C2×C11—42no—
446C2×C11#304211yescharacteristic
447C2×C11C2×#46511yescharacteristic
448C2×C11#306811yescharacteristic
449D11—22no—
450D11—42no—
451D11—161no—
452C24—221no—
453#41—442no—
454#41—442no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—221no—
458C2×Q8—441no—
459C2×Q8—882no—
460C2×D4—114no—
461C2×D4—111no—
462C2×D4—222no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—441no—
468C2×D4D4×D1111yescharacteristic
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—441no—
478C22×C4—441no—
479C22×C4—881no—
480C22×C4—881no—
481SD16—42no—
482SD16—442no—
483D8—442no—
484D8—442no—
485M16—442no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—442no—
496C2×C8—881no—
497C2×C8—881no—
498C2×C8—881no—
499C2×C8D4×D1111yescharacteristic
500C2×C8D4×D1111yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—111no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—441no—
510C4⋊C4—441no—
511C4⋊C4D4×D1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—441no—
517C22⋊C4—441no—
518C42—111no—
519C42—111no—
520C42—111no—
521C42C23×D1111yescharacteristic
522C11#1939111yescharacteristic, complemented, Sylow
523C23—21no—
524C23—111no—
525C23—224no—
526C23—221no—
527C23—441no—
528C23—881no—
529C23—881no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533Q8—881no—
534Q8—882no—
535D4—21no—
536D4—112no—
537D4—224no—
538D4—221no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—441no—
543D4—881no—
544D4—882no—
545D4SD16×D1112yes—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—111no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—111no—
555C2×C4—111no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—881no—
564C2×C4—881no—
565C2×C4—882no—
566C2×C4—882no—
567C2×C4—881no—
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—221no—
577C8—221no—
578C8—441no—
579C8—441no—
580C8—441no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—112no—
585C22—221no—
586C22—221no—
587C22—222no—
588C22—441no—
589C22—441no—
590C22—884no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22D11×#12111yescharacteristic
595C4—21no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—112no—
600C4—221no—
601C4—221no—
602C4—441no—
603C4—881no—
604C4C2×SD16×D1111yescharacteristic
605C4#1062329311yescharacteristic
606C4D11×#13511yescharacteristic
607C4#1062330911yescharacteristic
608C2—42no—
609C2—222no—
610C2—442no—
611C2—1761no—
612C2#1307812311yescharacteristic
613C2D11×#46511yescharacteristic
614C2#1307833911yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1671C2
socleC22×C11C2×#121
prime radical#13078081C2
hypercenter#1671D11
hypocenterC11#19391
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #13079745C2semidirect
2. D11×#476C2semidirect
4. #13077637C2semidirect
5. #13068028C2semidirect
6. #13068027C2semidirect
7. #13068026C2semidirect
8. #13068025C2semidirect
9. #13067990C2semidirect
10. #13067989C2semidirect
11. #13067988C2semidirect
12. #13067385C2semidirect
13. #13067295C2semidirect
14. #13067264C2semidirect
15. C11×#1671C2semidirect
20. C11×#498C22semidirect
27. #10622701C22semidirect
30. #10622692C22semidirect
52. #10622307C22semidirect
55. C11×#334C22semidirect
56. C11×#333C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622184C22semidirect
60. #10622123C22semidirect
61. #10622123C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622118C22semidirect
66. #10622095C22semidirect
227. #1671D11semidirect
294. #498C2×D11semidirect
331. #334C2×D11semidirect
335. #333C2×D11semidirect
337. #332C2×D11semidirect
522. C11#19391semidirect

Maximal subgroups

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

subgroupindex
#130797452
D11×#4762
#130780812
#130776372
#130680282
#130680272
#130680262
#130680252
#130679902
#130679892
#130679882
#130673852
#130672952
#130672642
C11×#16712
#1939111