Finite Group Databasebeta

← #14910276

Subgroups — #14910276

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2#13080332C211yesmaximal, characteristic, complemented
3#13080295C211yesmaximal, characteristic, complemented
4#13070884C211yesmaximal, characteristic, complemented
5#13070721C211yesmaximal, characteristic, complemented
6#13070712C211yesmaximal, characteristic, complemented
7#13070673C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070553C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070492C211yesmaximal, characteristic, complemented
14#13070441C211yesmaximal, characteristic, complemented
15C2×C11×#508C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic, complemented
18#10623360—21no—
19#10623355—21no—
20C2×#66965C2211yescharacteristic
21C2×D8×D11C2211yescharacteristic
22C11×#508—24no—
23C2×C11×Q32C2211yescharacteristic, complemented
24C2×C11×SD32C2211yescharacteristic
25C2×C11×SD32C2211yescharacteristic, complemented
26C2×C11×D16C2211yescharacteristic
27C22×C11×C16C2211yescharacteristic, complemented
28#10622852—21no—
29#10622851—21no—
30#10622804C2211yescharacteristic
31#10622801C2211yescharacteristic
32#10622801C2211yescharacteristic
33#10622794C2211yescharacteristic, complemented
34C2×#66893C2211yescharacteristic, complemented
35C2×#66892C2211yescharacteristic
36#10622786—21no—
37#10622782—21no—
38#10622778—21no—
39#10622775—21no—
40D8×Dic11C2211yescharacteristic
41D8×Dic11C2211yescharacteristic, complemented
42C2×#66891C2211yescharacteristic
43C2×#66890C2211yescharacteristic
44#10622729C2211yescharacteristic, complemented
45#10622728C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47#10622524—24no—
48C2×#66864C2211yescharacteristic
49C2×#66862C2211yescharacteristic
50#10622202C2211yescharacteristic, complemented
51#10622202C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic
56(C2×D11)⋊C16C2211yescharacteristic
57#10622143C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59#10622140C2211yescharacteristic, complemented
60Dic11⋊C16C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×#4341—21no—
64C2×D4×D11—21no—
65C11×#135—22no—
66C11×#135—22no—
67C11×#135—41no—
68C11×#135—41no—
69C2×C11×Q16C2311yescharacteristic
70C2×C11×Q16C2311yescharacteristic
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76#67000—21no—
77#66999—21no—
78#66999—21no—
79#66997—21no—
80C2×#4326—21no—
81C2×#4325—21no—
82#66992—41no—
83#66992—41no—
84#66990—41no—
85#66988—41no—
86D4×Dic11—21no—
87D4×Dic11—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90#66983—21no—
91#66982—41no—
92#66982—41no—
93C4×C22⋊D11D411yescharacteristic
94C2×(C2×D11)⋊C4—41no—
95#66977—21no—
96C2×Dic11⋊C4—41no—
97#66965—22no—
98#66965—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×Dic44C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×Q32—22no—
105C11×SD32—22no—
106C11×SD32—22no—
107C11×D16D414yescomplemented
108C2×C11×C16—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66899—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66893—41no—
117#66892—41no—
118#66891—22no—
119#66890—22no—
120#66885—21no—
121(C2×D11)⋊C8D411yescharacteristic
122#66882C2311yescharacteristic
123#66882C2311yescharacteristic
124#66880—21no—
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129#66864—22no—
130#66862—22no—
131#33833—111nomaximal, Sylow
132C23×D11—41no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—81no—
136C11×#41—81no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11D811yescharacteristic
150C22×Dic11—41no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153#4341—42no—
154#4341—81no—
155D4×D11—42no—
156D4×D11—81no—
157C2×D44—21no—
158C2×C4×D11C2×D411yescharacteristic
159C2×Dic22—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—21no—
164C11×SD16—42no—
165C11×SD16—42no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8C2×D412yes—
169C11×D8C2×D412yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2411yescharacteristic
174C22⋊Dic11—41no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11D811yescharacteristic
178#4326—81no—
179#4325—81no—
180#4324—42no—
181#4323—42no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195Dic11⋊C4D811yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199Dic44—21no—
200Dic44—21no—
201D88—21no—
202D88—21no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#509—111no—
210C2×#508D1111yescharacteristic, complemented
211#3283—111no—
212#3280—111no—
213#2251—111no—
214#2219—111no—
215#2217—111no—
216#2210—111no—
217#2208—111no—
218#2189—111no—
219#2189—111no—
220#2187—111no—
221#2186—111no—
222#2177—111no—
223#2168—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C2×D811yescharacteristic
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—161no—
231C22×D11C2×D811yescharacteristic
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—82no—
241D4×C11—82no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11C2×D811yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—41no—
251C22⋊D11—82no—
252C22⋊D11—82no—
253C22⋊D11—161no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—82no—
258C2×Dic11—82no—
259C2×Dic11—161no—
260C2×Dic11C2×D811yescharacteristic
261C2×Dic11C2×D811yescharacteristic
262C2×Dic11C2×D811yescharacteristic
263D44—41no—
264D44—41no—
265C4×D11—21no—
266C4×D11—21no—
267Dic22—41no—
268Dic22—41no—
269C8×C11—21no—
270C8×C11C22×D411yescharacteristic
271C8×C11H(5,𝔽2)11yescharacteristic
272C11⋊C8—21no—
273C11⋊C8—21no—
274C2×#135—111no—
275C2×#135C2×D1111yescharacteristic
276C2×#135C2×D1111yescharacteristic, complemented
277C22×D8—111no—
278#547—221no—
279#546—221no—
280#509—224no—
281#508—24no—
282C2×Q32—111no—
283C2×Q32C2×D1111yescharacteristic, complemented
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32C2×D1111yescharacteristic
288C2×SD32C2×D1111yescharacteristic, complemented
289C2×D16—111no—
290C2×D16C2×D1111yescharacteristic
291C2×M32—111no—
292C22×C16C2×D1111yescharacteristic, complemented
293#495—111no—
294#494—111no—
295#467—111no—
296#467—111no—
297#467—111no—
298#466—111no—
299#463—221no—
300#461—221no—
301#452—221no—
302#452—221no—
303#450—221no—
304#449—221no—
305C4×D8—111no—
306C4×D8—111no—
307C8×D4—111no—
308#367—111no—
309C4⋊C16—111no—
310#358—111no—
311#358—111no—
312#358—111no—
313#357—111no—
314#357—111no—
315#357—111no—
316C22⋊C16—111no—
317C22⋊C16—111no—
318#346—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11C22×D811yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—164no—
336C4×C11—21no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11D4211yescharacteristic
340C4×C11#57611yescharacteristic
341Dic11—21no—
342Dic11—21no—
343Dic11—21no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—221no—
350C22×D4—221no—
351#135—22no—
352#135—22no—
353#135—41no—
354#135—41no—
355#135—222no—
356#135—441no—
357C2×Q16—111no—
358C2×Q16—221no—
359C2×Q16C22×D1111yescharacteristic
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×D8—111no—
366C2×D8—221no—
367C2×D8—222no—
368C2×D8—441no—
369C2×D8C22×D1111yescharacteristic
370C2×D8C22×D1111yescharacteristic
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C4⋊Q8—221no—
374#124—221no—
375#123—441no—
376#123—441no—
377#123—441no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381#121—221no—
382#121—441no—
383#121—441no—
384#120—441no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4—221no—
388C2×C4⋊C4—441no—
389C2×C22⋊C4—441no—
390Q32—22no—
391Q32—441no—
392SD32—22no—
393SD32—22no—
394SD32—222no—
395SD32—222no—
396SD32—441no—
397D16—222no—
398D16C22⋊D1114yescomplemented
399M32—222no—
400C2×C16—22no—
401C2×C16—111no—
402C2×C16—111no—
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107—111no—
406#107—111no—
407C4⋊C8—111no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C4×C8—111no—
417C2×C11—41no—
418C2×C11—82no—
419C2×C11—82no—
420C2×C11D4×D811yescharacteristic
421C2×C11#341411yescharacteristic
422C2×C11#341611yescharacteristic
423D11—41no—
424D11—161no—
425C24—441no—
426#41—42no—
427#41—42no—
428#41—81no—
429#41—81no—
430#41—442no—
431#41—881no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—221no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4—441no—
442C2×D4—442no—
443C2×D4—441no—
444C2×D4—441no—
445C2×D4—881no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—111no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4D4×D1111yescharacteristic
453Q16—21no—
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—221no—
458Q16—221no—
459Q16—881no—
460SD16—42no—
461SD16—42no—
462SD16—442no—
463SD16—881no—
464D8—21no—
465D8—21no—
466D8—221no—
467D8—221no—
468D8—442no—
469D8C2×C22⋊D1112yes—
470D8C2×C22⋊D1112yes—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8D4×D1111yescharacteristic
478C2×C8C23×D1111yescharacteristic
479C4⋊C4—111no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—441no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4—441no—
487C22⋊C4—111no—
488C22⋊C4—111no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C42—111no—
498C16—21no—
499C16—221no—
500C16—221no—
501C16C2×C22⋊D1112yes—
502C11#3383311yescharacteristic, complemented, Sylow
503C23—41no—
504C23—41no—
505C23—111no—
506C23—441no—
507C23—882no—
508C23—882no—
509C23—1761no—
510C23D8×D1111yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—441no—
516Q8—441no—
517D4—22no—
518D4—22no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—882no—
527D4—882no—
528D4—1761no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4—1761no—
546C2×C4D8×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C8—21no—
549C8—221no—
550C8—221no—
551C8#6703711yescharacteristic
552C8C22×C22⋊D1111yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—42no—
557C22—42no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—221no—
563C22—221no—
564C22—221no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—1764no—
569C22C2×D8×D1111yescharacteristic
570C4—21no—
571C4—81no—
572C4—81no—
573C4—221no—
574C4—221no—
575C4—221no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4#1062328811yescharacteristic
580C4D4×C22⋊D1111yescharacteristic
581C2—41no—
582C2—82no—
583C2—82no—
584C2—441no—
585C2—1761no—
586C2D8×C22⋊D1111yescharacteristic
587C2#1308174911yescharacteristic
588C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#508C2
socleC22×C11C22×D8
hypercenterC2×#508D11
hypocenterC11#33833
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. #13080332C2semidirect
3. #13080295C2semidirect
4. #13070884C2semidirect
5. #13070721C2semidirect
6. #13070712C2semidirect
7. #13070673C2semidirect
8. #13070659C2semidirect
9. #13070556C2semidirect
10. #13070553C2semidirect
11. #13070543C2semidirect
12. #13070539C2semidirect
13. #13070492C2semidirect
14. #13070441C2semidirect
15. C2×C11×#508C2semidirect
17. C2×C11×#135C22semidirect
23. C2×C11×Q32C22semidirect
25. C2×C11×SD32C22semidirect
27. C22×C11×C16C22semidirect
33. #10622794C22semidirect
34. C2×#66893C22semidirect
41. D8×Dic11C22semidirect
44. #10622729C22semidirect
50. #10622202C22semidirect
51. #10622202C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
57. #10622143C22semidirect
58. #10622141C22semidirect
59. #10622140C22semidirect
60. Dic11⋊C16C22semidirect
107. C11×D16D4semidirect
210. C2×#508D11semidirect
276. C2×#135C2×D11semidirect
283. C2×Q32C2×D11semidirect
288. C2×SD32C2×D11semidirect
292. C22×C16C2×D11semidirect
398. D16C22⋊D11semidirect
502. C11#33833semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
#130803322
#130802952
#130708842
#130707212
#130707122
#130706732
#130706592
#130705562
#130705532
#130705432
#130705392
#130704922
#130704412
C2×C11×#5082
#3383311