Finite Group Databasebeta

← #14910364

Subgroups — #14910364

Order 2816.

748 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622527C211yesmaximal, characteristic, complemented
2C2×#10622806C211yesmaximal, characteristic, complemented
3#13080370C211yesmaximal, characteristic, complemented
4#13080290C211yesmaximal, characteristic, complemented
5#13070864C211yesmaximal, characteristic, complemented
6#13070718C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070650C211yesmaximal, characteristic, complemented
10#13070542C211yesmaximal, characteristic, complemented
11#13070530C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070445C211yesmaximal, characteristic, complemented
15C11×#2186C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17#10623365—21no—
18C2×#66972C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic
20C22×D88C2211yescharacteristic
21#10623140—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622851—21no—
26#10622806—24no—
27Q16×Dic11C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic, complemented
30#10622785—21no—
31#10622776—21no—
32#10622770C2211yescharacteristic, complemented
33#10622764C2211yescharacteristic
34#10622764C2211yescharacteristic, complemented
35C2×#66890C2211yescharacteristic
36C2×#66890C2211yescharacteristic, complemented
37C2×#66890C2211yescharacteristic, complemented
38#10622728C2211yescharacteristic, complemented
39C8×C22⋊D11C2211yescharacteristic
40C2×#66876C2211yescharacteristic, complemented
41#10622649—21no—
42#10622527—24no—
43C2×D176C2211yescharacteristic
44C2×D176C2211yescharacteristic, complemented
45C2×#66862C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic
47#10622485C2211yescharacteristic
48#10622399—21no—
49#10622386—21no—
50C11×#358C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C16×Dic11C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60#10622128C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C2×#4343—21no—
63C2×D4×D11—21no—
64C2×D4×D11—41no—
65C22×D44—21no—
66C11×#135—22no—
67C11×#135—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#121—21no—
74Q8×Dic11—21no—
75C2×#4325—21no—
76#66993—21no—
77#66993—21no—
78#66993—41no—
79#66991—21no—
80#66991—41no—
81#66990—41no—
82C2×#4323—21no—
83C2×#4323—21no—
84C2×#4323—21no—
85#66983—21no—
86#66983—41no—
87C4×C22⋊D11—41no—
88C4×C22⋊D11D411yescharacteristic
89#66972—22no—
90#66972—41no—
91D8×D11—22no—
92D8×D11—41no—
93C2×D88—22no—
94C2×D88—21no—
95C2×D88—41no—
96C2×D88C2311yescharacteristic
97C2×D88C2311yescharacteristic
98C2×D88C2311yescharacteristic
99C2×C8×D11C2311yescharacteristic
100#66948—21no—
101#66946—21no—
102#66937—41no—
103#66935—41no—
104C11×SD32—22no—
105C11×D16—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110#66899—21no—
111#66896—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66892—22no—
114#66892D414yescomplemented
115#66890—22no—
116#66890—22no—
117#66890—22no—
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120#66882C2311yescharacteristic
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123#66876—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128D176—22no—
129D176—41no—
130#66862—22no—
131#33840—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C11×#41—42no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C2×D411yescharacteristic
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11D811yescharacteristic
151#4343—42no—
152#4343—81no—
153D4×D11—42no—
154D4×D11—81no—
155D4×D11—84no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—41no—
161C2×D44—41no—
162C2×D44—41no—
163C2×D44—81no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11C2×D411yescharacteristic
167C11×Q16—21no—
168C11×Q16C2×D412yescomplemented
169C11×SD16—42no—
170C11×D8—21no—
171C11×D8—21no—
172C11×D8—21no—
173C11×D8—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C22⋊C4—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11D811yescharacteristic
182#4325—42no—
183#4323—42no—
184#4323—81no—
185#4323—81no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192Dic11⋊C4D811yescharacteristic
193C4×Dic11—41no—
194C4×Dic11C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197D88—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—21no—
202D88—42no—
203D88C2×D412yes—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
210C2×#509—111no—
211C2×#509—111no—
212#3287—111no—
213D4×D8—111no—
214#2246—111no—
215#2218—111no—
216#2218—111no—
217#2207—111no—
218#2206—111no—
219#2186—111no—
220#2186D1111yescharacteristic, complemented
221#2184—111no—
222#2184—111no—
223C4×SD32—111no—
224#2169—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C2×D811yescharacteristic
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—161no—
236C22×D11—161no—
237C22×D11C2×D811yescharacteristic
238Q8×C11—22no—
239Q8×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—82no—
245D4×C11—82no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—22no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—161no—
258C22⋊D11—161no—
259C22⋊D11—161no—
260C22⋊D11—161no—
261C2×Dic11—41no—
262C2×Dic11C2×D811yescharacteristic
263C2×Dic11C2×D811yescharacteristic
264C2×Dic11C2×D811yescharacteristic
265D44—22no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—82no—
272D44—82no—
273D44—82no—
274C4×D11—21no—
275C4×D11—21no—
276C4×D11—82no—
277C4×D11—82no—
278C8×C11—21no—
279C8×C11C22×D411yescharacteristic
280C8×C11H(5,𝔽2)11yescharacteristic
281C11⋊C8—21no—
282C11⋊C8—21no—
283C2×#135—111no—
284C2×#135C2×D1111yescharacteristic, complemented
285C22×D8—111no—
286C22×D8—111no—
287#550—221no—
288D42—221no—
289#509—224no—
290#509—224no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—111no—
298C2×D16—111no—
299C2×D16C2×D1111yescharacteristic, complemented
300C2×M32—111no—
301C2×M32—111no—
302#493—111no—
303#493—111no—
304#466—111no—
305#466—111no—
306#466—111no—
307#466C2×D1111yescharacteristic
308#460—221no—
309#459—221no—
310#449—221no—
311#449—221no—
312#447—221no—
313#447—221no—
314C4×Q16—111no—
315C4×D8—111no—
316C8×D4—111no—
317#367—111no—
318C4⋊C16—111no—
319#358C2×D1111yescharacteristic, complemented
320#357—111no—
321#357—111no—
322#357—111no—
323#357—111no—
324#357C2×D1111yescharacteristic, complemented
325C22⋊C16—111no—
326C22⋊C16C2×D1111yescharacteristic, complemented
327C4×C16—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C22×D811yescharacteristic
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—42no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—164no—
351C2×D11—164no—
352C4×C11—21no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11D4211yescharacteristic
356C4×C11#57611yescharacteristic
357Dic11—21no—
358Dic11—21no—
359Dic11—81no—
360Dic11#50912yescomplemented
361C2×#41—21no—
362C2×#41—221no—
363C22×D4—221no—
364C22×D4—221no—
365C22×D4—441no—
366#135—22no—
367#135—41no—
368#135—222no—
369#135—441no—
370C2×Q16C22×D1111yescharacteristic
371C2×SD16—21no—
372C2×SD16—221no—
373C2×D8—111no—
374C2×D8—111no—
375C2×D8—111no—
376C2×D8—222no—
377C2×D8—221no—
378C2×D8—221no—
379C2×D8—221no—
380C2×D8—222no—
381C2×D8—221no—
382C2×D8—441no—
383C2×D8—441no—
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388#127—221no—
389#127—221no—
390#127—441no—
391#121—21no—
392#121—221no—
393#121—221no—
394#121—221no—
395#121—441no—
396#121—441no—
397#121—441no—
398#120—441no—
399#120—441no—
400C4×Q8—221no—
401C4×D4—111no—
402C4×D4—221no—
403C4×D4—441no—
404SD32—22no—
405SD32—114no—
406SD32—222no—
407D16—41no—
408D16—222no—
409D16—222no—
410D16—222no—
411D16—222no—
412D16—441no—
413M32—222no—
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16C22×D1111yescharacteristic
418C2×C16C22×D1111yescharacteristic
419#107—111no—
420#107C22×D1111yescharacteristic
421C4⋊C8—111no—
422#103—221no—
423#102—21no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428C22⋊C8—111no—
429C22⋊C8—111no—
430C4×C8—111no—
431C2×C11—41no—
432C2×C11—161no—
433C2×C11—161no—
434C2×C11D4×D811yescharacteristic
435C2×C11C2×#50911yescharacteristic
436C2×C11#341511yescharacteristic
437D11—41no—
438D11—82no—
439D11—161no—
440D11—161no—
441C24—441no—
442C24—441no—
443#41—42no—
444#41—81no—
445#41—442no—
446#41—881no—
447C2×Q8—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—111no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—442no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—441no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—441no—
464C2×D4—442no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4—441no—
468C2×D4—881no—
469C2×D4—881no—
470C2×D4—884no—
471C22×C4—41no—
472C22×C4—111no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4D4×D1111yescharacteristic
476Q16—21no—
477Q16D4×D1112yescomplemented
478SD16—42no—
479SD16—442no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—112no—
485D8—221no—
486D8—221no—
487D8—221no—
488D8—221no—
489D8—221no—
490D8—442no—
491D8—442no—
492D8—881no—
493D8—881no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8D4×D1111yescharacteristic
501C2×C8C23×D1111yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—111no—
504C4⋊C4—221no—
505C4⋊C4—441no—
506C22⋊C4—41no—
507C22⋊C4—111no—
508C22⋊C4—111no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C42—111no—
514C42—441no—
515C16—21no—
516C16—21no—
517C16—112no—
518C16—221no—
519C11#3384011yescharacteristic, complemented, Sylow
520C23—41no—
521C23—41no—
522C23—111no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—882no—
527C23—882no—
528C23—882no—
529C23—882no—
530C23—1761no—
531C23—1761no—
532C23D8×D1111yescharacteristic
533Q8—22no—
534Q8—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—82no—
540D4—82no—
541D4—222no—
542D4—222no—
543D4—441no—
544D4—441no—
545D4—441no—
546D4—441no—
547D4—441no—
548D4—882no—
549D4—882no—
550D4—882no—
551D4—882no—
552D4—882no—
553D4—882no—
554D4—1761no—
555D4—1761no—
556D4—1761no—
557D4—1761no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—82no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—111no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—441no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4D8×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C8—21no—
574C8—221no—
575C8—221no—
576C8C2×D4×D1111yescharacteristic
577C8#6703711yescharacteristic
578C22—21no—
579C22—21no—
580C22—21no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—221no—
588C22—221no—
589C22—221no—
590C22—442no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—1764no—
600C22—1764no—
601C22C2×D8×D1111yescharacteristic
602C4—21no—
603C4—42no—
604C4—81no—
605C4—112no—
606C4—221no—
607C4—221no—
608C4—881no—
609C4#1062312111yescharacteristic
610C4#1062330511yescharacteristic
611C2—41no—
612C2—161no—
613C2—161no—
614C2—441no—
615C2—882no—
616C2—1761no—
617C2—1761no—
618C2#1308028611yescharacteristic
619C2D11×#50911yescharacteristic
620C2#1308175411yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2186C2
socleC22×C11C22×D8
hypercenter#2186D11
hypocenterC11#33840
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×#10622806C2semidirect
3. #13080370C2semidirect
4. #13080290C2semidirect
5. #13070864C2semidirect
6. #13070718C2semidirect
7. #13070717C2semidirect
8. #13070654C2semidirect
9. #13070650C2semidirect
10. #13070542C2semidirect
11. #13070530C2semidirect
12. #13070526C2semidirect
13. #13070465C2semidirect
14. #13070445C2semidirect
15. C11×#2186C2semidirect
16. C2×C11×#135C22semidirect
18. C2×#66972C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×D16C22semidirect
27. Q16×Dic11C22semidirect
29. C2×#66892C22semidirect
32. #10622770C22semidirect
34. #10622764C22semidirect
36. C2×#66890C22semidirect
37. C2×#66890C22semidirect
38. #10622728C22semidirect
40. C2×#66876C22semidirect
44. C2×D176C22semidirect
45. C2×#66862C22semidirect
50. C11×#358C22semidirect
51. C11×#357C22semidirect
52. C11×C22⋊C16C22semidirect
53. #10622200C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. C16×Dic11C22semidirect
59. #10622129C22semidirect
60. #10622128C22semidirect
114. #66892D4semidirect
168. C11×Q16C2×D4semidirect
209. C11⋊C16C2×D4semidirect
220. #2186D11semidirect
284. C2×#135C2×D11semidirect
293. C2×SD32C2×D11semidirect
299. C2×D16C2×D11semidirect
319. #358C2×D11semidirect
324. #357C2×D11semidirect
326. C22⋊C16C2×D11semidirect
360. Dic11#509semidirect
477. Q16D4×D11semidirect
519. C11#33840semidirect

Maximal subgroups

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

subgroupindex
C2×#106225272
C2×#106228062
#130803702
#130802902
#130708642
#130707182
#130707172
#130706542
#130706502
#130705422
#130705302
#130705262
#130704652
#130704452
C11×#21862
#3384011