Finite Group Databasebeta

← #14909224

Subgroups — #14909224

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C211yesmaximal, characteristic, complemented
2C2×#10622524C211yesmaximal, characteristic, complemented
3C2×#10622529C211yesmaximal, characteristic, complemented
4C2×D11×D16C211yesmaximal, characteristic, complemented
5#13079098C211yesmaximal, characteristic, complemented
6#13079096C211yesmaximal, characteristic, complemented
7#13070882C211yesmaximal, characteristic, complemented
8#13070881C211yesmaximal, characteristic, complemented
9#13070879C211yesmaximal, characteristic, complemented
10#13070876C211yesmaximal, characteristic, complemented
11#13070875C211yesmaximal, characteristic, complemented
12#13070865C211yesmaximal, characteristic, complemented
13#13070864C211yesmaximal, characteristic, complemented
14#13070214C211yesmaximal, characteristic, complemented
15C11×#2250C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66967—21no—
18C2×#66965C2211yescharacteristic
19C2×#66964—21no—
20C2×D8×D11C2211yescharacteristic
21C2×D8×D11C2211yescharacteristic
22#10623246—21no—
23#10623205—21no—
24C2×C11×SD32C2211yescharacteristic, complemented
25C2×C11×SD32C2211yescharacteristic, complemented
26C2×C11×D16C2211yescharacteristic
27C2×C11×D16C2211yescharacteristic, complemented
28C11×#495C2211yescharacteristic, complemented
29C11×#493C2211yescharacteristic, complemented
30#10622804C2211yescharacteristic, complemented
31C2×#66893C2211yescharacteristic, complemented
32C2×#66892C2211yescharacteristic, complemented
33#10622789—21no—
34#10622768C2211yescharacteristic, complemented
35#10622767—21no—
36#10622764C2211yescharacteristic, complemented
37#10622764C2211yescharacteristic, complemented
38C2×#66891C2211yescharacteristic, complemented
39C2×#66890C2211yescharacteristic
40C2×#66890C2211yescharacteristic
41C2×#66890C2211yescharacteristic, complemented
42C2×#66890C2211yescharacteristic, complemented
43C2×#66890C2211yescharacteristic, complemented
44#10622687—21no—
45#10622671—21no—
46#10622529—24no—
47#10622527—24no—
48#10622524—24no—
49D11×D16—24no—
50C2×#66864C2211yescharacteristic, complemented
51C2×#66864C2211yescharacteristic, complemented
52C2×D176C2211yescharacteristic
53C2×D176C2211yescharacteristic, complemented
54C2×#66862C2211yescharacteristic
55C2×C16×D11C2211yescharacteristic
56#10622309C2211yescharacteristic, complemented
57#10622308C2211yescharacteristic, complemented
58#10622302C2211yescharacteristic
59C11×#346C2211yescharacteristic, complemented
60#10622140C2211yescharacteristic, complemented
61C16×Dic11C2211yescharacteristic, complemented
62C4×C11⋊C16C2211yescharacteristic, complemented
63C2×#4343—21no—
64C2×#4341—21no—
65C2×D4×D11—21no—
66C2×D4×D11—21no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×D8—21no—
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C2×C11×D8C2311yescharacteristic
73C11×#127—21no—
74C11×#124—21no—
75#67000—21no—
76C2×#4325—21no—
77C2×#4325—21no—
78#66993—21no—
79#66993—21no—
80#66992—42no—
81#66990—42no—
82#66989—21no—
83C2×#4324—21no—
84C2×#4324—21no—
85C2×#4323—21no—
86C2×#4323—21no—
87C2×#4323—21no—
88C2×#4323—21no—
89#66972—22no—
90#66972—22no—
91#66967—44no—
92#66965—22no—
93#66965—22no—
94#66964—44no—
95D8×D11—22no—
96D8×D11—22no—
97D8×D11—22no—
98D8×D11—22no—
99C2×Dic44C2311yescharacteristic
100C2×D88—21no—
101C2×D88C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×D88C2311yescharacteristic
104C2×#4314—21no—
105C2×#4313D411yescharacteristic
106C2×C8×D11C2311yescharacteristic
107#66937—42no—
108#66935—42no—
109#66928—21no—
110#66927—21no—
111#66925D411yescharacteristic
112C11×SD32—22no—
113C11×SD32—22no—
114C11×D16—22no—
115C11×D16—22no—
116C2×C11×C16C2311yescharacteristic
117C2×C11×C16C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66893—22no—
120#66892—22no—
121#66891—22no—
122#66890—22no—
123#66890—22no—
124#66890—22no—
125#66890—22no—
126#66890—22no—
127#66879D411yescharacteristic
128C8×Dic11C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#66867D411yescharacteristic
132#66864—22no—
133#66864—22no—
134D176—22no—
135D176—22no—
136#66862D414yescomplemented
137C16×D11D414yescomplemented
138#33720—111nomaximal, Sylow
139C23×D11—41no—
140C23×D11—41no—
141C2×Q8×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—41no—
151C22×Dic11—41no—
152#4343—42no—
153#4343—42no—
154#4341—42no—
155#4341—42no—
156D4×D11—42no—
157D4×D11—42no—
158D4×D11—42no—
159D4×D11—42no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—41no—
164C2×D44—42no—
165C2×C4×D11—41no—
166C2×C4×D11C2×D411yescharacteristic
167C2×Dic22—21no—
168C11×Q16—21no—
169C11×Q16—21no—
170C11×SD16—42no—
171C11×D8—21no—
172C11×D8—21no—
173C11×D8—21no—
174C11×D8—21no—
175C11×D8—21no—
176C11×D8—21no—
177C11×D8—42no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2411yescharacteristic
180C11×C22⋊C4—42no—
181C42×C11C2×D411yescharacteristic
182C22⋊Dic11—42no—
183#4325—42no—
184#4325—42no—
185#4324—42no—
186#4324—42no—
187#4323—42no—
188#4323—42no—
189#4323—42no—
190#4323—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4D812yes—
194Dic11⋊C4D812yes—
195C4×Dic11C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198Dic44—21no—
199Dic44—21no—
200D88—21no—
201D88—21no—
202D88—21no—
203D88—21no—
204D88—21no—
205D88—21no—
206D88—42no—
207#4314—42no—
208#4313D814yes—
209C8×D11C2×D412yes—
210C8×D11C2×D412yes—
211C11×C16C2×D412yes—
212C11×C16C2×D412yes—
213C11⋊C16C2×D412yes—
214C11⋊C16C2×D412yes—
215C2×#509—111no—
216C2×#509—111no—
217C2×#508—111no—
218C22×D16—111no—
219#3155—111no—
220#3155—111no—
221#2250—111no—
222#2250—111no—
223#2250—111no—
224#2250D1111yescharacteristic, complemented
225#2249—111no—
226#2249—111no—
227#2246—111no—
228#2246—111no—
229#2108—111no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—162no—
239C22×D11—162no—
240C22×D11C2×D811yescharacteristic
241Q8×C11—41no—
242Q8×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—162no—
250C2×C4×C11—41no—
251C2×C4×C11C2×D812yes—
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—162no—
257C22⋊D11—162no—
258C2×Dic11—41no—
259C2×Dic11—82no—
260C2×Dic11C2×D812yes—
261C2×Dic11C2×D811yescharacteristic
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—82no—
269D44—162no—
270C4×D11—82no—
271C4×D11#12712yes—
272C4×D11C2×D812yes—
273Dic22—41no—
274Dic22—41no—
275C8×C11C2×D812yes—
276C8×C11C22×D411yescharacteristic
277C8×C11C22×D411yescharacteristic
278C11⋊C8#12712yes—
279C11⋊C8C2×D812yes—
280C2×AGL(1,ℤ/8)—221no—
281C2×AGL(1,ℤ/8)—221no—
282C2×#135—111no—
283C2×#135—111no—
284C22×D8—111no—
285C22×D8—111no—
286#535—221no—
287#535—221no—
288#509—224no—
289#509—224no—
290#508—224no—
291C2×Q32—111no—
292C2×SD32—111no—
293C2×SD32—111no—
294C2×SD32—111no—
295C2×SD32—111no—
296C2×SD32C2×D1111yescharacteristic, complemented
297C2×SD32C2×D1111yescharacteristic, complemented
298C2×D16—111no—
299C2×D16—111no—
300C2×D16—111no—
301C2×D16—111no—
302C2×D16—111no—
303C2×D16—111no—
304C2×D16—111no—
305C2×D16—224no—
306C2×D16C2×D1111yescharacteristic
307C2×D16C2×D1111yescharacteristic, complemented
308C2×M32—111no—
309C22×C16—111no—
310#496—221no—
311#496—221no—
312#496—221no—
313#496—221no—
314#495—111no—
315#495—111no—
316#495—111no—
317#495C2×D1111yescharacteristic, complemented
318#493—111no—
319#493—111no—
320#493—111no—
321#493C2×D1111yescharacteristic, complemented
322#405—111no—
323#346—111no—
324#346C2×D1111yescharacteristic, complemented
325C4×C16—111no—
326C4×C16—111no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11C22×D811yescharacteristic
334C2×D11—22no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—82no—
339C2×D11—82no—
340C2×D11—82no—
341C2×D11—164no—
342C2×D11—164no—
343C2×D11#49312yes—
344C4×C11—22no—
345C4×C11—81no—
346C4×C11C2×#12711yescharacteristic
347C4×C11C22×D811yescharacteristic
348Dic11—22no—
349Dic11—81no—
350Dic11#49312yes—
351C2×#41—221no—
352C2×#41—221no—
353C22×D4—221no—
354C22×D4—221no—
355AGL(1,ℤ/8)—444no—
356AGL(1,ℤ/8)—444no—
357#135—222no—
358#135—222no—
359#135—222no—
360#135—222no—
361C2×Q16—111no—
362C2×Q16C22×D1111yescharacteristic
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×D8—21no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—222no—
374C2×D8—222no—
375C2×D8—222no—
376C2×D8—222no—
377C2×D8—221no—
378C2×D8—221no—
379C2×D8—221no—
380C2×D8—221no—
381C2×D8—221no—
382C2×D8C22×D1111yescharacteristic
383C2×D8C22×D1111yescharacteristic
384C2×D8C22×D1111yescharacteristic
385C2×M16—111no—
386C22×C8—111no—
387#127—21no—
388#127—221no—
389#127—221no—
390#127—221no—
391#124—21no—
392#124—221no—
393#124—221no—
394#124—221no—
395#121—442no—
396#121—442no—
397#120—442no—
398#120—442no—
399#117—111no—
400Q32—222no—
401SD32—22no—
402SD32—22no—
403SD32—222no—
404SD32—222no—
405SD32—222no—
406SD32—222no—
407D16—22no—
408D16—22no—
409D16—222no—
410D16—222no—
411D16—222no—
412D16—222no—
413D16—222no—
414D16—222no—
415D16—222no—
416M32—114no—
417C2×C16—111no—
418C2×C16—111no—
419C2×C16—114no—
420C2×C16C22×D1111yescharacteristic
421C2×C16C22×D1111yescharacteristic
422#97—111no—
423#97—111no—
424C4×C8—111no—
425C4×C8C22×D1111yescharacteristic
426C2×C11—161no—
427C2×C11—161no—
428C2×C11—161no—
429C2×C11C2×#49311yescharacteristic
430C2×C11#341512yes—
431D11—22no—
432D11—161no—
433D11—161no—
434D11—161no—
435C24—441no—
436C24—441no—
437#41—442no—
438#41—442no—
439#41—442no—
440#41—442no—
441C2×Q8—21no—
442C2×Q8—221no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—42no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—441no—
451C2×D4—442no—
452C2×D4—442no—
453C2×D4—442no—
454C2×D4—442no—
455C2×D4—441no—
456C2×D4—441no—
457C2×D4—442no—
458C2×D4—442no—
459C2×D4—441no—
460C2×D4—442no—
461C22×C4—111no—
462C22×C4—441no—
463C22×C4—441no—
464Q16—21no—
465Q16—21no—
466Q16—221no—
467Q16—221no—
468SD16—42no—
469SD16—442no—
470SD16—442no—
471SD16—442no—
472SD16—442no—
473SD16—442no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—21no—
479D8—21no—
480D8—42no—
481D8—221no—
482D8—221no—
483D8—221no—
484D8—221no—
485D8—221no—
486D8—221no—
487D8—442no—
488D8—442no—
489D8—442no—
490D8—442no—
491D8—442no—
492M16—114no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—112no—
496C2×C8—112no—
497C2×C8D4×D1111yescharacteristic
498C2×C8C23×D1111yescharacteristic
499C4⋊C4—112no—
500C22⋊C4—42no—
501C22⋊C4—112no—
502C22⋊C4—442no—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C42—111no—
506C42D4×D1111yescharacteristic
507C16—112no—
508C16—112no—
509C16D4×D1112yes—
510C16D4×D1112yes—
511C11#3372011yescharacteristic, complemented, Sylow
512C23—41no—
513C23—41no—
514C23—41no—
515C23—111no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—882no—
520C23—882no—
521C23—1762no—
522C23—1762no—
523Q8—41no—
524Q8—41no—
525Q8—441no—
526Q8—441no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—162no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—441no—
539D4—441no—
540D4—882no—
541D4—882no—
542D4—882no—
543D4—882no—
544D4—1762no—
545D4—1762no—
546D4—1762no—
547C2×C4—41no—
548C2×C4—111no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—441no—
553C2×C4—882no—
554C2×C4—882no—
555C2×C4D8×D1112yes—
556C2×C4C2×D4×D1111yescharacteristic
557C8—112no—
558C8—112no—
559C8D8×D1112yes—
560C8C2×D4×D1111yescharacteristic
561C8C2×D4×D1111yescharacteristic
562C22—82no—
563C22—82no—
564C22—82no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—112no—
569C22—222no—
570C22—882no—
571C22—882no—
572C22—882no—
573C22—881no—
574C22—881no—
575C22—881no—
576C22—1764no—
577C22—1764no—
578C22C2×D8×D1111yescharacteristic
579C4—22no—
580C4—81no—
581C4—112no—
582C4—222no—
583C4—881no—
584C4D11×#12711yescharacteristic
585C4C2×D8×D1111yescharacteristic
586C2—161no—
587C2—161no—
588C2—161no—
589C2—222no—
590C2—1761no—
591C2—1761no—
592C2—1761no—
593C2D11×#49311yescharacteristic
594C2#1308175612yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2250C2
socleC22×C11C22×D8
hypercenter#2250D11
hypocenterC11#33720
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×#10622524C2semidirect
3. C2×#10622529C2semidirect
4. C2×D11×D16C2semidirect
5. #13079098C2semidirect
6. #13079096C2semidirect
7. #13070882C2semidirect
8. #13070881C2semidirect
9. #13070879C2semidirect
10. #13070876C2semidirect
11. #13070875C2semidirect
12. #13070865C2semidirect
13. #13070864C2semidirect
14. #13070214C2semidirect
15. C11×#2250C2semidirect
24. C2×C11×SD32C22semidirect
25. C2×C11×SD32C22semidirect
27. C2×C11×D16C22semidirect
28. C11×#495C22semidirect
29. C11×#493C22semidirect
30. #10622804C22semidirect
31. C2×#66893C22semidirect
32. C2×#66892C22semidirect
34. #10622768C22semidirect
36. #10622764C22semidirect
37. #10622764C22semidirect
38. C2×#66891C22semidirect
41. C2×#66890C22semidirect
42. C2×#66890C22semidirect
43. C2×#66890C22semidirect
50. C2×#66864C22semidirect
51. C2×#66864C22semidirect
53. C2×D176C22semidirect
56. #10622309C22semidirect
57. #10622308C22semidirect
59. C11×#346C22semidirect
60. #10622140C22semidirect
61. C16×Dic11C22semidirect
62. C4×C11⋊C16C22semidirect
136. #66862D4semidirect
137. C16×D11D4semidirect
224. #2250D11semidirect
296. C2×SD32C2×D11semidirect
297. C2×SD32C2×D11semidirect
307. C2×D16C2×D11semidirect
317. #495C2×D11semidirect
321. #493C2×D11semidirect
324. #346C2×D11semidirect
511. C11#33720semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
C2×#106225242
C2×#106225292
C2×D11×D162
#130790982
#130790962
#130708822
#130708812
#130708792
#130708762
#130708752
#130708652
#130708642
#130702142
C11×#22502
#3372011