Finite Group Databasebeta

← #14910365

Subgroups — #14910365

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
2#13080370C211yesmaximal, characteristic, complemented
3D8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13070864C211yesmaximal, characteristic, complemented
5#13070719C211yesmaximal, characteristic, complemented
6#13070716C211yesmaximal, characteristic, complemented
7#13070654C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13SD32×Dic11C211yesmaximal, characteristic, complemented
14#13070446C211yesmaximal, characteristic, complemented
15C2×C11×#509C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17C22×C11×D8C2211yescharacteristic
18#10623365—21no—
19D4×C22⋊D11—21no—
20C2×#66972C2211yescharacteristic, complemented
21C2×D8×D11C2211yescharacteristic
22C11×#509—24no—
23C2×C11×SD32C2211yescharacteristic
24C2×C11×SD32C2211yescharacteristic, complemented
25C2×C11×D16C2211yescharacteristic
26C2×C11×D16C2211yescharacteristic, complemented
27C2×C11×M32C2211yescharacteristic, complemented
28#10622851—21no—
29#10622830—21no—
30Q16×Dic11C2211yescharacteristic, complemented
31C2×#66892C2211yescharacteristic, complemented
32#10622785—21no—
33#10622776—21no—
34#10622770C2211yescharacteristic
35#10622770C2211yescharacteristic, complemented
36#10622769—21no—
37#10622764C2211yescharacteristic
38#10622764C2211yescharacteristic, complemented
39#10622763—21no—
40D8×Dic11C2211yescharacteristic
41C2×#66890C2211yescharacteristic
42C2×#66890C2211yescharacteristic, complemented
43C2×#66890C2211yescharacteristic, complemented
44#10622728C2211yescharacteristic
45#10622728C2211yescharacteristic, complemented
46C8×C22⋊D11C2211yescharacteristic
47#10622527—24no—
48C2×D176C2211yescharacteristic, complemented
49C2×#66862C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56#10622147C2211yescharacteristic, complemented
57(C2×D11)⋊C16C2211yescharacteristic, complemented
58#10622143C2211yescharacteristic, complemented
59Dic11⋊C16C2211yescharacteristic, complemented
60C16×Dic11C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C22×D4×C11—21no—
63C22×C22⋊D11—41no—
64C2×#4343—21no—
65C2×D4×D11—21no—
66C11×#135—22no—
67C11×#135—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8—22no—
71C2×C11×D8—21no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77#67006—41no—
78Q8×Dic11—21no—
79C2×#4325—21no—
80#66993—21no—
81#66993—21no—
82#66993—41no—
83#66992—41no—
84#66991—21no—
85#66991—21no—
86#66991—41no—
87#66990—41no—
88D4×Dic11—21no—
89C2×#4323—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92#66983—21no—
93#66983—21no—
94#66983—41no—
95C4×C22⋊D11—41no—
96C4×C22⋊D11D411yescharacteristic
97#66972—22no—
98#66972—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×D88C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×SD32—22no—
105C11×SD32D414yescomplemented
106C11×D16—22no—
107C11×D16—22no—
108C11×M32—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66892—22no—
117#66890—22no—
118#66890—41no—
119#66890—41no—
120#66885—21no—
121#66885—21no—
122(C2×D11)⋊C8D411yescharacteristic
123#66882C2311yescharacteristic
124#66882C2311yescharacteristic
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129D176—22no—
130#66862—22no—
131#33840—111nomaximal, Sylow
132C24×C11—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—21no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C22×C4×C11—41no—
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—41no—
154C2×C22⋊D11—41no—
155C2×C22⋊D11—84no—
156C2×C22⋊D11D811yescharacteristic
157C22×Dic11—41no—
158#4343—42no—
159#4343—81no—
160D4×D11—42no—
161D4×D11—81no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—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—
174C11×D8—21no—
175C11×D8—42no—
176C11×D8C2×D412yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2411yescharacteristic
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11D811yescharacteristic
185#4325—42no—
186#4323—42no—
187#4323—81no—
188#4323—81no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4D811yescharacteristic
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—41no—
195Dic11⋊C4D811yescharacteristic
196C4×Dic11—41no—
197C4×Dic11C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200D88—21no—
201D88—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—
211C2×#509D1111yescharacteristic, complemented
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#2186—111no—
221#2184—111no—
222#2184—111no—
223C4×SD32—111no—
224#2169—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—161no—
231C23×C11C2×D811yescharacteristic
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—82no—
235C22×D11—82no—
236C22×D11—161no—
237C22×D11C2×D811yescharacteristic
238Q8×C11—22no—
239Q8×C11—41no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—82no—
247D4×C11—82no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—82no—
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C22⋊D11—22no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—82no—
259C22⋊D11—82no—
260C22⋊D11—161no—
261C22⋊D11—161no—
262C22⋊D11—161no—
263C22⋊D11—161no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—82no—
267C2×Dic11C2×D811yescharacteristic
268C2×Dic11C2×D811yescharacteristic
269C2×Dic11C2×D811yescharacteristic
270D44—41no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—82no—
275C4×D11—21no—
276C4×D11—21no—
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×D8C2×D1111yescharacteristic
287#550—221no—
288D42—221no—
289#509—24no—
290#509—224no—
291C2×SD32—111no—
292C2×SD32C2×D1111yescharacteristic
293C2×SD32C2×D1111yescharacteristic, complemented
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—111no—
298C2×D16C2×D1111yescharacteristic
299C2×D16C2×D1111yescharacteristic, complemented
300C2×M32—111no—
301C2×M32C2×D1111yescharacteristic, complemented
302#493—111no—
303#493—111no—
304#466—111no—
305#466—111no—
306#466—111no—
307#466—111no—
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#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357—111no—
324#357—111no—
325C22⋊C16—111no—
326C22⋊C16—111no—
327C4×C16—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
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—164no—
341C22×C11C22×D811yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—164no—
352C4×C11—21no—
353C4×C11—42no—
354C4×C11D4211yescharacteristic
355C4×C11#57611yescharacteristic
356Dic11—21no—
357Dic11—21no—
358Dic11—81no—
359Dic11—81no—
360Dic11#50912yescomplemented
361C2×#41—21no—
362C2×#41—221no—
363C22×D4—21no—
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—22no—
374C2×D8—21no—
375C2×D8—41no—
376C2×D8—111no—
377C2×D8—111no—
378C2×D8—221no—
379C2×D8—221no—
380C2×D8—221no—
381C2×D8—222no—
382C2×D8—441no—
383C2×D8C22×D1111yescharacteristic
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388#127—221no—
389#127—221no—
390#127—441no—
391#121—221no—
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—222no—
406SD32C22⋊D1114yescomplemented
407D16—22no—
408D16—22no—
409D16—222no—
410D16—222no—
411D16—441no—
412D16—441no—
413M32—22no—
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16C22×D1111yescharacteristic
418C2×C16C22×D1111yescharacteristic
419#107—111no—
420#107—111no—
421C4⋊C8—111no—
422#103—221no—
423#102—221no—
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—82no—
433C2×C11—161no—
434C2×C11—161no—
435C2×C11D4×D811yescharacteristic
436C2×C11C2×#50911yescharacteristic
437C2×C11#341511yescharacteristic
438D11—41no—
439D11—161no—
440D11—161no—
441C24—41no—
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—21no—
451C2×D4—42no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—81no—
455C2×D4—111no—
456C2×D4—221no—
457C2×D4—221no—
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—441no—
469C2×D4—881no—
470C2×D4—884no—
471C22×C4—41no—
472C22×C4—111no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4D4×D1111yescharacteristic
476Q16—21no—
477Q16C2×C22⋊D1112yescomplemented
478SD16—42no—
479SD16—442no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—21no—
485D8—42no—
486D8—221no—
487D8—221no—
488D8—221no—
489D8—221no—
490D8—442no—
491D8—881no—
492D8—881no—
493D8C2×C22⋊D1112yes—
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—111no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—441no—
506C22⋊C4—111no—
507C22⋊C4—111no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C42—111no—
514C42—441no—
515C16—21no—
516C16—221no—
517C16—221no—
518C16C2×C22⋊D1112yescomplemented
519C11#3384011yescharacteristic, complemented, Sylow
520C23—41no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—111no—
526C23—161no—
527C23—441no—
528C23—441no—
529C23—882no—
530C23—882no—
531C23—1761no—
532C23D8×D1111yescharacteristic
533Q8—22no—
534Q8—41no—
535D4—22no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—82no—
542D4—82no—
543D4—222no—
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—82no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4D8×D1111yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C8—21no—
574C8—221no—
575C8—221no—
576C8#6703711yescharacteristic
577C8C22×C22⋊D1111yescharacteristic
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—164no—
591C22—221no—
592C22—221no—
593C22—221no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—1764no—
601C22C2×D8×D1111yescharacteristic
602C4—21no—
603C4—42no—
604C4—112no—
605C4—221no—
606C4—221no—
607C4—881no—
608C4—881no—
609C4#1062328811yescharacteristic
610C4D4×C22⋊D1111yescharacteristic
611C2—41no—
612C2—82no—
613C2—161no—
614C2—161no—
615C2—441no—
616C2—1761no—
617C2—1761no—
618C2D8×C22⋊D1111yescharacteristic
619C2D11×#50911yescharacteristic
620C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33840
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. #13080370C2semidirect
3. D8×C22⋊D11C2semidirect
4. #13070864C2semidirect
5. #13070719C2semidirect
6. #13070716C2semidirect
7. #13070654C2semidirect
8. #13070649C2semidirect
9. #13070539C2semidirect
10. #13070538C2semidirect
11. #13070528C2semidirect
12. #13070526C2semidirect
13. SD32×Dic11C2semidirect
14. #13070446C2semidirect
15. C2×C11×#509C2semidirect
16. C2×C11×#135C22semidirect
20. C2×#66972C22semidirect
24. C2×C11×SD32C22semidirect
26. C2×C11×D16C22semidirect
27. C2×C11×M32C22semidirect
30. Q16×Dic11C22semidirect
31. C2×#66892C22semidirect
35. #10622770C22semidirect
38. #10622764C22semidirect
42. C2×#66890C22semidirect
43. C2×#66890C22semidirect
45. #10622728C22semidirect
48. C2×D176C22semidirect
49. C2×#66862C22semidirect
50. #10622202C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622147C22semidirect
56. #10622147C22semidirect
57. (C2×D11)⋊C16C22semidirect
58. #10622143C22semidirect
59. Dic11⋊C16C22semidirect
60. C16×Dic11C22semidirect
105. C11×SD32D4semidirect
168. C11×Q16C2×D4semidirect
207. C11×C16C2×D4semidirect
211. C2×#509D11semidirect
284. C2×#135C2×D11semidirect
293. C2×SD32C2×D11semidirect
299. C2×D16C2×D11semidirect
301. C2×M32C2×D11semidirect
360. Dic11#509semidirect
406. SD32C22⋊D11semidirect
477. Q16C2×C22⋊D11semidirect
518. C16C2×C22⋊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
#130803702
D8×C22⋊D112
#130708642
#130707192
#130707162
#130706542
#130706492
#130705392
#130705382
#130705282
#130705262
SD32×Dic112
#130704462
C2×C11×#5092
#3384011