Finite Group Databasebeta

← #14910344

Subgroups — #14910344

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C2×#10622524C211yesmaximal, characteristic, complemented
3#13080332C211yesmaximal, characteristic, complemented
4#13080290C211yesmaximal, characteristic, complemented
5#13070870C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070727C211yesmaximal, characteristic, complemented
8#13070660C211yesmaximal, characteristic, complemented
9#13070649C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070540C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070445C211yesmaximal, characteristic, complemented
15C11×#2186C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17#10623355—21no—
18C2×#66965C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic
20C22×D88C2211yescharacteristic
21#10623140—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622852—21no—
26#10622806—24no—
27#10622801C2211yescharacteristic, complemented
28#10622794C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic, complemented
31#10622786—21no—
32#10622775—21no—
33#10622764C2211yescharacteristic
34D8×Dic11C2211yescharacteristic, complemented
35C2×#66891C2211yescharacteristic, complemented
36C2×#66890C2211yescharacteristic
37C2×#66890C2211yescharacteristic, complemented
38#10622729C2211yescharacteristic, complemented
39C8×C22⋊D11C2211yescharacteristic
40C2×#66876C2211yescharacteristic, complemented
41#10622649—21no—
42#10622524—24no—
43C2×#66864C2211yescharacteristic
44C2×#66864C2211yescharacteristic, 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#10622130C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C2×#4341—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—
74#66999—21no—
75#66997—21no—
76C2×#4326—21no—
77#66993—21no—
78#66992—41no—
79#66990—41no—
80#66988—41no—
81D4×Dic11—21no—
82C2×#4324—21no—
83C2×#4323—21no—
84C2×#4323—21no—
85#66982—41no—
86C4×C22⋊D11D411yescharacteristic
87#66977—21no—
88C2×Dic11⋊C4—41no—
89#66965—22no—
90#66965—41no—
91D8×D11—22no—
92D8×D11—41no—
93C2×Dic44C2311yescharacteristic
94C2×D88—22no—
95C2×D88—21no—
96C2×D88—41no—
97C2×D88C2311yescharacteristic
98C2×D88C2311yescharacteristic
99C2×C8×D11C2311yescharacteristic
100#66948—21no—
101#66946—21no—
102#66937—41no—
103#66935—41no—
104C11×SD32—41no—
105C11×D16—22no—
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#66892—22no—
115#66891—22no—
116#66890—22no—
117#66890D414yescomplemented
118(C2×D11)⋊C8D411yescharacteristic
119#66882C2311yescharacteristic
120#66880—21no—
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123#66876—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128#66864—22no—
129#66864—41no—
130#66862—22no—
131#33838—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⋊D11D811yescharacteristic
148C22×Dic11—41no—
149C22×Dic11—41no—
150#4341—42no—
151#4341—81no—
152D4×D11—42no—
153D4×D11—81no—
154D4×D11—84no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—42no—
158C2×D44—41no—
159C2×D44—41no—
160C2×D44—81no—
161C2×C4×D11—41no—
162C2×C4×D11C2×D411yescharacteristic
163C2×Dic22—21no—
164C11×Q16—21no—
165C11×Q16—21no—
166C11×SD16—42no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8C2×D412yescomplemented
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C22⋊C4—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11D811yescharacteristic
180#4326—81no—
181#4324—42no—
182#4323—42no—
183#4323—81no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4D811yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197Dic44—21no—
198Dic44—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#3283—111no—
213D4×D8—111no—
214#2248—111no—
215#2220—111no—
216#2220—111no—
217#2208—111no—
218#2206—111no—
219#2187—111no—
220#2187—111no—
221#2186—111no—
222#2186D1111yescharacteristic, complemented
223C4×D16—111no—
224#2169—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C2×D811yescharacteristic
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11—161no—
236C22×D11C2×D811yescharacteristic
237Q8×C11—41no—
238Q8×C11—41no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—82no—
244D4×C11—82no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C22⋊D11—22no—
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—161no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—82no—
260C2×Dic11—82no—
261C2×Dic11C2×D811yescharacteristic
262C2×Dic11C2×D811yescharacteristic
263C2×Dic11C2×D811yescharacteristic
264D44—22no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—82no—
269D44—82no—
270C4×D11—21no—
271C4×D11—21no—
272C4×D11—82no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—21no—
276C8×C11C22×D411yescharacteristic
277C8×C11H(5,𝔽2)11yescharacteristic
278C11⋊C8—21no—
279C11⋊C8—21no—
280C2×#135—111no—
281C2×#135C2×D1111yescharacteristic, complemented
282C22×D8—111no—
283C22×D8—111no—
284#547—221no—
285D42—221no—
286#509—224no—
287#509—224no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16—111no—
296C2×D16C2×D1111yescharacteristic, complemented
297C2×M32—111no—
298C2×M32—111no—
299#494—111no—
300#493—111no—
301#467—111no—
302#467—111no—
303#466—111no—
304#466C2×D1111yescharacteristic
305#461—221no—
306#459—221no—
307#452—221no—
308#452—221no—
309#447—221no—
310#447—221no—
311C4×D8—111no—
312C4×D8—111no—
313C8×D4—111no—
314#366—111no—
315C4⋊C16—111no—
316#358—111no—
317#358C2×D1111yescharacteristic, complemented
318#357—111no—
319#357—111no—
320#357—111no—
321#357C2×D1111yescharacteristic, complemented
322C22⋊C16—111no—
323C22⋊C16C2×D1111yescharacteristic, complemented
324C4×C16—111no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—42no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—164no—
345C2×D11—164no—
346C4×C11—21no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11D4211yescharacteristic
350C4×C11#57611yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—81no—
354Dic11—81no—
355Dic11#50912yescomplemented
356C2×#41—21no—
357C2×#41—221no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—441no—
361#135—22no—
362#135—41no—
363#135—222no—
364#135—441no—
365C2×Q16—111no—
366C2×Q16—221no—
367C2×Q16C22×D1111yescharacteristic
368C2×SD16—21no—
369C2×SD16—221no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—222no—
376C2×D8—221no—
377C2×D8—441no—
378C2×D8—441no—
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383C4⋊Q8—221no—
384#127—221no—
385#123—441no—
386#123—441no—
387C22⋊Q8—221no—
388C22⋊Q8—221no—
389#121—21no—
390#121—221no—
391#121—441no—
392#121—441no—
393#120—441no—
394#120—441no—
395C4×D4—111no—
396C4×D4—221no—
397C4×D4—221no—
398C2×C4⋊C4—441no—
399SD32—41no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405D16—22no—
406D16—114no—
407D16—222no—
408M32—222no—
409M32—222no—
410C2×C16—111no—
411C2×C16—111no—
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107—111no—
415#107C22×D1111yescharacteristic
416C4⋊C8—111no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C4×C8—111no—
426C2×C11—41no—
427C2×C11—82no—
428C2×C11—161no—
429C2×C11D4×D811yescharacteristic
430C2×C11C2×#50911yescharacteristic
431C2×C11#341611yescharacteristic
432D11—41no—
433D11—82no—
434D11—161no—
435C24—441no—
436C24—441no—
437#41—42no—
438#41—81no—
439#41—442no—
440#41—881no—
441C2×Q8—21no—
442C2×Q8—221no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—442no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—442no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—881no—
459C2×D4—881no—
460C2×D4—884no—
461C22×C4—41no—
462C22×C4—111no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4D4×D1111yescharacteristic
467Q16—21no—
468Q16—21no—
469Q16—221no—
470Q16—221no—
471Q16—881no—
472SD16—42no—
473SD16—442no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—112no—
478D8—221no—
479D8—221no—
480D8—221no—
481D8—442no—
482D8—442no—
483D8—881no—
484D8D4×D1112yescomplemented
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8D4×D1111yescharacteristic
492C2×C8C23×D1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—111no—
495C4⋊C4—221no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C4⋊C4—441no—
499C4⋊C4—441no—
500C22⋊C4—41no—
501C22⋊C4—111no—
502C22⋊C4—111no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—111no—
509C16—21no—
510C16—21no—
511C16—112no—
512C16—221no—
513C11#3383811yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—111no—
517C23—441no—
518C23—441no—
519C23—882no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23—1761no—
524C23—1761no—
525C23D8×D1111yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—441no—
529Q8—441no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—82no—
535D4—82no—
536D4—222no—
537D4—222no—
538D4—441no—
539D4—441no—
540D4—441no—
541D4—882no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—1761no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—111no—
553C2×C4—111no—
554C2×C4—111no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—882no—
560C2×C4—882no—
561C2×C4—882no—
562C2×C4D8×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C8—21no—
565C8—221no—
566C8—221no—
567C8C2×D4×D1111yescharacteristic
568C8#6703711yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—221no—
579C22—221no—
580C22—221no—
581C22—442no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22—1764no—
588C22—1764no—
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—81no—
592C4—81no—
593C4—112no—
594C4—221no—
595C4—221no—
596C4—881no—
597C4—881no—
598C4#1062312111yescharacteristic
599C4#1062330511yescharacteristic
600C2—41no—
601C2—82no—
602C2—161no—
603C2—441no—
604C2—882no—
605C2—1761no—
606C2#1308028611yescharacteristic
607C2D11×#50911yescharacteristic
608C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2186C2
socleC22×C11C22×D8
hypercenter#2186D11
hypocenterC11#33838
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×#10622806C2semidirect
2. C2×#10622524C2semidirect
3. #13080332C2semidirect
4. #13080290C2semidirect
5. #13070870C2semidirect
6. #13070732C2semidirect
7. #13070727C2semidirect
8. #13070660C2semidirect
9. #13070649C2semidirect
10. #13070547C2semidirect
11. #13070543C2semidirect
12. #13070540C2semidirect
13. #13070460C2semidirect
14. #13070445C2semidirect
15. C11×#2186C2semidirect
16. C2×C11×#135C22semidirect
18. C2×#66965C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×D16C22semidirect
27. #10622801C22semidirect
28. #10622794C22semidirect
30. C2×#66892C22semidirect
34. D8×Dic11C22semidirect
35. C2×#66891C22semidirect
37. C2×#66890C22semidirect
38. #10622729C22semidirect
40. C2×#66876C22semidirect
44. C2×#66864C22semidirect
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. #10622130C22semidirect
60. #10622127C22semidirect
117. #66890D4semidirect
170. C11×D8C2×D4semidirect
209. C11⋊C16C2×D4semidirect
222. #2186D11semidirect
281. C2×#135C2×D11semidirect
293. C2×SD32C2×D11semidirect
296. C2×D16C2×D11semidirect
317. #358C2×D11semidirect
321. #357C2×D11semidirect
323. C22⋊C16C2×D11semidirect
355. Dic11#509semidirect
484. D8D4×D11semidirect
513. C11#33838semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106225242
#130803322
#130802902
#130708702
#130707322
#130707272
#130706602
#130706492
#130705472
#130705432
#130705402
#130704602
#130704452
C11×#21862
#3383811