Finite Group Databasebeta

← #14910231

Subgroups — #14910231

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2#13080301C211yesmaximal, characteristic, complemented
3D8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13070879C211yesmaximal, characteristic, complemented
5#13070716C211yesmaximal, characteristic, complemented
6#13070712C211yesmaximal, characteristic, complemented
7#13070669C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic, complemented
10#13070536C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070492C211yesmaximal, characteristic, complemented
14#13070441C211yesmaximal, characteristic, complemented
15C22×C11×D16C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic, complemented
18#10623337—21no—
19D4×C22⋊D11—21no—
20C2×#66965C2211yescharacteristic, complemented
21C2×D8×D11C2211yescharacteristic, complemented
22C2×C11×D16—24no—
23C2×C11×D16C2211yescharacteristic
24C2×C11×D16C2211yescharacteristic
25C2×C11×D16C2211yescharacteristic, complemented
26C2×C11×D16C2211yescharacteristic, complemented
27C22×C11×C16C2211yescharacteristic, complemented
28#10622831—21no—
29#10622830—21no—
30#10622771—21no—
31#10622770C2211yescharacteristic, complemented
32#10622770C2211yescharacteristic, complemented
33#10622769—21no—
34#10622768C2211yescharacteristic, complemented
35#10622766—21no—
36#10622764C2211yescharacteristic, complemented
37#10622763—21no—
38D8×Dic11C2211yescharacteristic, complemented
39D8×Dic11C2211yescharacteristic, complemented
40C2×#66891C2211yescharacteristic, complemented
41C2×#66891C2211yescharacteristic, complemented
42C2×#66890C2211yescharacteristic, complemented
43C2×#66890C2211yescharacteristic, complemented
44#10622729C2211yescharacteristic, complemented
45#10622728C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47#10622524—24no—
48C2×#66864C2211yescharacteristic, complemented
49C2×#66862C2211yescharacteristic, complemented
50#10622200C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622143C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59#10622140C2211yescharacteristic, complemented
60Dic11⋊C16C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×C22⋊D11—41no—
64C2×#4341—21no—
65C2×D4×D11—21no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8—21no—
69C2×C11×D8—21no—
70C2×C11×D8—41no—
71C2×C11×D8—41no—
72C2×C11×D8C2311yescharacteristic
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77#67006—41no—
78#67006—41no—
79C2×C22⋊Dic11—41no—
80#66993—21no—
81#66992—41no—
82#66992—41no—
83#66991—21no—
84#66991—21no—
85#66990—41no—
86#66989—21no—
87#66988—41no—
88D4×Dic11—21no—
89D4×Dic11—21no—
90C2×#4324—21no—
91C2×#4324—21no—
92C2×#4323—21no—
93C2×#4323—21no—
94#66983—21no—
95C4×C22⋊D11D411yescharacteristic
96#66977—21no—
97#66965—22no—
98#66965—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×Dic44C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×D16—22no—
105C11×D16—22no—
106C11×D16—22no—
107C11×D16D414yescomplemented
108C2×C11×C16—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66896—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66891—22no—
117#66891—41no—
118#66890—22no—
119#66890—41no—
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#33830—111nomaximal, Sylow
132C24×C11—41no—
133C24×C11—41no—
134C23×D11—41no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C2×D4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—84no—
154C2×C22⋊D11D811yescharacteristic
155C22×Dic11—41no—
156C22×Dic11—41no—
157C22×Dic11—41no—
158#4341—42no—
159#4341—81no—
160D4×D11—42no—
161D4×D11—81no—
162C2×D44—21no—
163C2×C4×D11C2×D411yescharacteristic
164C2×Dic22—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—21no—
171C11×D8—42no—
172C11×D8—42no—
173C11×D8C2×D412yes—
174C11×D8C2×D412yescomplemented
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2411yescharacteristic
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C22⋊Dic11D811yescharacteristic
187#4324—42no—
188#4324—81no—
189#4323—42no—
190#4323—81no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4D811yescharacteristic
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4D811yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200Dic44—21no—
201Dic44—21no—
202D88—21no—
203D88—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C2×#509—111no—
211C22×D16D1111yescharacteristic, complemented
212#3280—111no—
213D4×D8—111no—
214#2250—111no—
215#2218—111no—
216#2217—111no—
217#2210—111no—
218#2206—111no—
219#2187—111no—
220#2186—111no—
221#2184—111no—
222#2184—111no—
223#2177—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—82no—
232C23×C11—82no—
233C23×C11—161no—
234C23×C11—161no—
235C23×C11C2×D811yescharacteristic
236C22×D11—41no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—161no—
240C22×D11C2×D811yescharacteristic
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—82no—
250D4×C11—82no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11C2×D811yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C22⋊D11—22no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—82no—
259C22⋊D11—82no—
260C22⋊D11—82no—
261C22⋊D11—161no—
262C22⋊D11—161no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—82no—
267C2×Dic11—82no—
268C2×Dic11—161no—
269C2×Dic11C2×D811yescharacteristic
270C2×Dic11C2×D811yescharacteristic
271C2×Dic11C2×D811yescharacteristic
272D44—41no—
273D44—41no—
274C4×D11—21no—
275C4×D11—21no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—21no—
279C8×C11C22×D411yescharacteristic
280C8×C11H(5,𝔽2)11yescharacteristic
281C11⋊C8—21no—
282C11⋊C8—21no—
283C2×#135—111no—
284C22×D8—111no—
285C22×D8C2×D1111yescharacteristic
286C22×D8C2×D1111yescharacteristic, complemented
287#546—221no—
288D42—221no—
289#509—224no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×D16—24no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16C2×D1111yescharacteristic
297C2×D16C2×D1111yescharacteristic
298C2×D16C2×D1111yescharacteristic, complemented
299C2×D16C2×D1111yescharacteristic, complemented
300C2×M32—111no—
301C22×C16C2×D1111yescharacteristic, complemented
302#495—111no—
303#493—111no—
304#467—111no—
305#466—111no—
306#466—111no—
307#466—111no—
308#463—221no—
309#459—221no—
310#450—221no—
311#449—221no—
312#447—221no—
313#447—221no—
314C4×D8—111no—
315C4×D8—111no—
316C8×D4—111no—
317#367—111no—
318C4⋊C16—111no—
319#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357—111no—
324#357—111no—
325C22⋊C16—111no—
326C22⋊C16—111no—
327#346—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—164no—
343C22×C11—164no—
344C22×C11#50912yescomplemented
345C22×C11C22×D811yescharacteristic
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—164no—
353C4×C11—21no—
354C4×C11D4211yescharacteristic
355C4×C11#57611yescharacteristic
356Dic11—21no—
357Dic11—21no—
358Dic11—21no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C2×#41—221no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—221no—
366C22×D4—441no—
367#135—222no—
368#135—441no—
369C2×Q16—111no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×D8—22no—
373C2×D8—22no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—41no—
377C2×D8—41no—
378C2×D8—111no—
379C2×D8—221no—
380C2×D8—221no—
381C2×D8—222no—
382C2×D8—441no—
383C2×D8C22×D1111yescharacteristic
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C2×D8C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389#127—221no—
390#124—221no—
391#123—441no—
392C22⋊Q8—221no—
393#121—221no—
394#121—221no—
395#121—221no—
396#121—441no—
397#121—441no—
398#120—441no—
399#120—441no—
400#120—441no—
401C4×D4—111no—
402C4×D4—221no—
403C4×D4—221no—
404C2×C22⋊C4—441no—
405SD32—222no—
406SD32—222no—
407SD32—441no—
408D16—22no—
409D16—22no—
410D16—22no—
411D16—222no—
412D16—441no—
413D16C22⋊D1114yescomplemented
414M32—222no—
415C2×C16—22no—
416C2×C16—111no—
417C2×C16—111no—
418C2×C16C22×D1111yescharacteristic
419C2×C16C22×D1111yescharacteristic
420#107—111no—
421#107—111no—
422C4⋊C8—111no—
423#103—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C4×C8—111no—
432C2×C11—22no—
433C2×C11—82no—
434C2×C11—82no—
435C2×C11—161no—
436C2×C11—161no—
437C2×C11D4×D811yescharacteristic
438C2×C11C2×#50911yescharacteristic
439C2×C11#341511yescharacteristic
440D11—41no—
441D11—161no—
442C24—41no—
443C24—41no—
444C24—441no—
445#41—442no—
446#41—881no—
447C2×Q8—221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4—111no—
459C2×D4—221no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—442no—
464C2×D4—441no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4—441no—
468C2×D4—881no—
469C2×D4—884no—
470C22×C4—111no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4D4×D1111yescharacteristic
475Q16—221no—
476Q16—221no—
477SD16—442no—
478SD16—881no—
479D8—21no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—21no—
485D8—42no—
486D8—42no—
487D8—221no—
488D8—221no—
489D8—442no—
490D8—881no—
491D8C2×C22⋊D1112yes—
492D8C2×C22⋊D1112yescomplemented
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—111no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C22⋊C4—111no—
506C22⋊C4—111no—
507C22⋊C4—441no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42—111no—
516C16—21no—
517C16—221no—
518C16—221no—
519C16C2×C22⋊D1112yescomplemented
520C11#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—82no—
529C23—111no—
530C23—161no—
531C23—161no—
532C23—441no—
533C23—882no—
534C23—882no—
535C23—1761no—
536C23D8×D1111yescharacteristic
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—82no—
548D4—82no—
549D4—222no—
550D4—441no—
551D4—441no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4—882no—
556D4—882no—
557D4—1761no—
558D4—1761no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—111no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4—1761no—
572C2×C4D8×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C8—21no—
575C8—221no—
576C8—221no—
577C8#6703711yescharacteristic
578C8C22×C22⋊D1111yescharacteristic
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—164no—
594C22—164no—
595C22—221no—
596C22—221no—
597C22—221no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22—1764no—
602C22#1062252412yescomplemented
603C22C2×D8×D1111yescharacteristic
604C4—21no—
605C4—221no—
606C4—221no—
607C4—221no—
608C4—881no—
609C4—881no—
610C4—881no—
611C4#1062328811yescharacteristic
612C4D4×C22⋊D1111yescharacteristic
613C2—22no—
614C2—82no—
615C2—82no—
616C2—161no—
617C2—161no—
618C2—441no—
619C2—1761no—
620C2D8×C22⋊D1111yescharacteristic
621C2C2×#1062252411yescharacteristic
622C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×D16C2
socleC22×C11C22×D8
hypercenterC22×D16D11
hypocenterC11#33830
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. #13080301C2semidirect
3. D8×C22⋊D11C2semidirect
4. #13070879C2semidirect
5. #13070716C2semidirect
6. #13070712C2semidirect
7. #13070669C2semidirect
8. #13070649C2semidirect
9. #13070545C2semidirect
10. #13070536C2semidirect
11. #13070528C2semidirect
12. #13070526C2semidirect
13. #13070492C2semidirect
14. #13070441C2semidirect
15. C22×C11×D16C2semidirect
17. C22×C11×D8C22semidirect
20. C2×#66965C22semidirect
21. C2×D8×D11C22semidirect
25. C2×C11×D16C22semidirect
26. C2×C11×D16C22semidirect
27. C22×C11×C16C22semidirect
31. #10622770C22semidirect
32. #10622770C22semidirect
34. #10622768C22semidirect
36. #10622764C22semidirect
38. D8×Dic11C22semidirect
39. D8×Dic11C22semidirect
40. C2×#66891C22semidirect
41. C2×#66891C22semidirect
42. C2×#66890C22semidirect
43. C2×#66890C22semidirect
44. #10622729C22semidirect
48. C2×#66864C22semidirect
49. C2×#66862C22semidirect
50. #10622200C22semidirect
51. #10622200C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622143C22semidirect
58. #10622141C22semidirect
59. #10622140C22semidirect
60. Dic11⋊C16C22semidirect
107. C11×D16D4semidirect
174. C11×D8C2×D4semidirect
207. C11×C16C2×D4semidirect
211. C22×D16D11semidirect
286. C22×D8C2×D11semidirect
298. C2×D16C2×D11semidirect
299. C2×D16C2×D11semidirect
301. C22×C16C2×D11semidirect
344. C22×C11#509semidirect
413. D16C22⋊D11semidirect
492. D8C2×C22⋊D11semidirect
519. C16C2×C22⋊D11semidirect
520. C11#33830semidirect
602. C22#10622524semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
#130803012
D8×C22⋊D112
#130708792
#130707162
#130707122
#130706692
#130706492
#130705452
#130705362
#130705282
#130705262
#130704922
#130704412
C22×C11×D162
#3383011