Finite Group Databasebeta

← #14910445

Subgroups — #14910445

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66891C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13080365C211yesmaximal, characteristic, complemented
4D8×C22⋊D11C211yesmaximal, characteristic
5#13070870C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070655C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070535C211yesmaximal, characteristic, complemented
12#13070531C211yesmaximal, characteristic, complemented
13#13070471C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17D4×C22⋊D11—21no—
18C2×Q16×D11C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic
20C22×Dic44C2211yescharacteristic, complemented
21#10623163—21no—
22C2×C11×SD32C2211yescharacteristic
23C2×C11×SD32C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic, complemented
25#10622830—21no—
26#10622794C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28#10622770C2211yescharacteristic
29#10622769—21no—
30#10622764C2211yescharacteristic
31#10622763—21no—
32D8×Dic11C2211yescharacteristic
33C2×#66891—24no—
34C2×#66891C2211yescharacteristic
35C2×#66891C2211yescharacteristic
36C2×#66891C2211yescharacteristic, complemented
37C2×#66891C2211yescharacteristic, complemented
38#10622728C2211yescharacteristic
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic, complemented
41#10622663—21no—
42D11×SD32—24no—
43C2×#66864C2211yescharacteristic, complemented
44C2×#66864C2211yescharacteristic, complemented
45C2×C16×D11C2211yescharacteristic, complemented
46#10622500C2211yescharacteristic, complemented
47#10622486C2211yescharacteristic, complemented
48#10622421—21no—
49#10622406—21no—
50C11×#357C2211yescharacteristic
51C11×#357C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic, complemented
53#10622202C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C16×Dic11C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60#10622128C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C22×C22⋊D11—41no—
63C2×Q8×D11—21no—
64C2×D4×D11—21no—
65C22×Dic22—21no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8—22no—
68C2×C11×D8—21no—
69C2×C11×D8—41no—
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C22⋊Q8—21no—
74#67006—41no—
75#66997—21no—
76C2×#4326—21no—
77C2×#4326—21no—
78#66993—21no—
79#66992—41no—
80#66991—21no—
81#66990—41no—
82D4×Dic11—21no—
83C2×#4323—21no—
84C2×#4323—21no—
85#66983—21no—
86C4×C22⋊D11D411yescharacteristic
87Q16×D11—22no—
88Q16×D11—41no—
89D8×D11—22no—
90D8×D11—41no—
91C2×Dic44—22no—
92C2×Dic44—21no—
93C2×Dic44—41no—
94C2×Dic44C2311yescharacteristic
95C2×Dic44C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×C8×D11C2311yescharacteristic
98#66950—21no—
99#66949—41no—
100#66941—41no—
101#66940—21no—
102(C22⋊D11)⋊C4—41no—
103#66931—41no—
104C11×SD32—22no—
105C11×SD32—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110#66896—21no—
111#66896—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66892—22no—
114#66891—22no—
115#66891—22no—
116#66891—22no—
117#66891D414yescomplemented
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120#66882C2311yescharacteristic
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123C2×C11⋊C16—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66874—21no—
127#66874—21no—
128#66864—22no—
129#66864—41no—
130C16×D11—22no—
131D4×SD32—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—41no—
139C2×D4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—84no—
147C2×C22⋊D11D811yescharacteristic
148C22×Dic11—41no—
149C22×Dic11—41no—
150Q8×D11—42no—
151Q8×D11—81no—
152D4×D11—42no—
153D4×D11—81no—
154C2×D44—21no—
155C2×C4×D11—41no—
156C2×C4×D11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—42no—
160C2×Dic22—41no—
161C2×Dic22—41no—
162C2×Dic22—81no—
163C11×Q16—21no—
164C11×Q16—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—42no—
169C11×D8C2×D412yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11D811yescharacteristic
180#4326—42no—
181#4326—81no—
182#4323—42no—
183#4323—81no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4D811yescharacteristic
187C4⋊Dic11—21no—
188C4⋊Dic11—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4D811yescharacteristic
193C4×Dic11—41no—
194C4×Dic11C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197Dic44—21no—
198Dic44—21no—
199Dic44—21no—
200Dic44—42no—
201Dic44C2×D412yescomplemented
202D88—21no—
203D88—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
210C22×SD32—111no—
211C22×SD32—111no—
212D4×Q16—111no—
213D4×D8—111no—
214#2248—111no—
215#2217—111no—
216#2217—111no—
217#2208—111no—
218#2207—111no—
219#2187—111no—
220#2187D1111yescharacteristic, complemented
221#2185—111no—
222#2185—111no—
223C4×SD32—111no—
224D4×C16—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—161no—
230C23×C11C2×D811yescharacteristic
231C22×D11—41no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C22⋊D11—82no—
250C22⋊D11—82no—
251C22⋊D11—82no—
252C22⋊D11—82no—
253C22⋊D11—161no—
254C22⋊D11SD3214yescomplemented
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—82no—
259C2×Dic11—82no—
260C2×Dic11C2×D811yescharacteristic
261C2×Dic11C2×D811yescharacteristic
262C2×Dic11C2×D811yescharacteristic
263D44—41no—
264D44—41no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—82no—
268Dic22—22no—
269Dic22—41no—
270Dic22—41no—
271Dic22—41no—
272Dic22—82no—
273Dic22—82no—
274C8×C11—21no—
275C8×C11C22×D411yescharacteristic
276C8×C11H(5,𝔽2)11yescharacteristic
277C11⋊C8—21no—
278C11⋊C8—21no—
279C22×Q16—111no—
280C22×Q16—111no—
281C22×D8—111no—
282C22×D8C2×D1111yescharacteristic
283D4×Q8—221no—
284D42—221no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—224no—
293C2×SD32—224no—
294C2×SD32C2×D1111yescharacteristic
295C2×SD32C2×D1111yescharacteristic, complemented
296C22×C16—111no—
297C22×C16—111no—
298#494—111no—
299#493—111no—
300#467—111no—
301#467C2×D1111yescharacteristic, complemented
302#466—111no—
303#466—111no—
304#462—221no—
305#459—221no—
306#451—221no—
307#451—221no—
308#447—221no—
309#447—221no—
310C4×Q16—111no—
311C4×D8—111no—
312C8×D4—111no—
313#367—111no—
314C4⋊C16—111no—
315#358—111no—
316#358—111no—
317#358—111no—
318#357—111no—
319#357C2×D1111yescharacteristic
320#357C2×D1111yescharacteristic, complemented
321C22⋊C16—111no—
322C22⋊C16C2×D1111yescharacteristic, complemented
323C4×C16—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—42no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—164no—
333C22×C11C2×SD3212yescomplemented
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—164no—
341C2×D11C2×SD3212yescomplemented
342C4×C11—21no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11D4211yescharacteristic
346C4×C11#57611yescharacteristic
347Dic11—21no—
348Dic11—21no—
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352Dic11C2×SD3212yescomplemented
353C22×Q8—221no—
354C22×Q8—221no—
355C22×D4—21no—
356C22×D4—221no—
357C22×D4—441no—
358C2×Q16—111no—
359C2×Q16—111no—
360C2×Q16—222no—
361C2×Q16—221no—
362C2×Q16—221no—
363C2×Q16—222no—
364C2×Q16—221no—
365C2×Q16—441no—
366C2×Q16—441no—
367C2×Q16C22×D1111yescharacteristic
368C2×D8—22no—
369C2×D8—21no—
370C2×D8—41no—
371C2×D8—111no—
372C2×D8—221no—
373C2×D8—221no—
374C2×D8—222no—
375C2×D8—441no—
376C2×D8C22×D1111yescharacteristic
377C2×D8C22×D1111yescharacteristic
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C4⋊Q8—221no—
381C4⋊Q8—441no—
382#127—221no—
383C22⋊Q8—21no—
384C22⋊Q8—221no—
385C22⋊Q8—441no—
386C22⋊Q8—441no—
387#121—221no—
388#121—221no—
389#121—441no—
390#120—441no—
391#120—441no—
392C4×Q8—221no—
393C4×D4—111no—
394C4×D4—221no—
395C4×D4—441no—
396SD32—22no—
397SD32—41no—
398SD32—114no—
399SD32—222no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405C2×C16—111no—
406C2×C16—111no—
407C2×C16—222no—
408C2×C16—222no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107—111no—
412#107C22×D1111yescharacteristic
413C4⋊C8—111no—
414#103—21no—
415#103—221no—
416#103—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8—111no—
423C2×C11—22no—
424C2×C11—82no—
425C2×C11—161no—
426C2×C11D4×D811yescharacteristic
427C2×C11C22×SD3211yescharacteristic
428C2×C11#341611yescharacteristic
429D11—22no—
430D11—161no—
431C24—41no—
432C24—441no—
433C2×Q8—21no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—442no—
437C2×Q8—441no—
438C2×Q8—442no—
439C2×Q8—441no—
440C2×Q8—881no—
441C2×Q8—881no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—442no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—881no—
456C2×D4—884no—
457C22×C4—111no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4D4×D1111yescharacteristic
462Q16—21no—
463Q16—21no—
464Q16—112no—
465Q16—221no—
466Q16—221no—
467Q16—221no—
468Q16—442no—
469Q16—442no—
470Q16—881no—
471D8—21no—
472D8—21no—
473D8—21no—
474D8—42no—
475D8—221no—
476D8—221no—
477D8—442no—
478D8—881no—
479D8D4×D1112yes—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8D4×D1111yescharacteristic
487C2×C8C23×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—111no—
491C4⋊C4—221no—
492C4⋊C4—441no—
493C4⋊C4—441no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C22⋊C4—41no—
497C22⋊C4—111no—
498C22⋊C4—111no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C42—111no—
504C42—441no—
505C16—21no—
506C16—21no—
507C16—112no—
508C16—221no—
509C11D4×SD3211yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—111no—
515C23—161no—
516C23—441no—
517C23—882no—
518C23—882no—
519C23—1761no—
520C23D8×D1111yescharacteristic
521Q8—41no—
522Q8—41no—
523Q8—222no—
524Q8—441no—
525Q8—441no—
526Q8—441no—
527Q8—882no—
528Q8—882no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—82no—
534D4—114no—
535D4—441no—
536D4—441no—
537D4—882no—
538D4—882no—
539D4—882no—
540D4—882no—
541D4—1761no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—111no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—882no—
555C2×C4—882no—
556C2×C4—882no—
557C2×C4D8×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C8—21no—
560C8—221no—
561C8—221no—
562C8C2×D4×D1111yescharacteristic
563C8#6703711yescharacteristic
564C22—21no—
565C22—21no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—112no—
573C22—164no—
574C22—221no—
575C22—221no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—1764no—
580C22D11×SD3212yescomplemented
581C22C2×D8×D1111yescharacteristic
582C4—21no—
583C4—81no—
584C4—81no—
585C4—112no—
586C4—221no—
587C4—221no—
588C4—442no—
589C4—881no—
590C4—881no—
591C4#1062312111yescharacteristic
592C4#1062330511yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—222no—
597C2—1761no—
598C2#1308028611yescharacteristic
599C2C2×D11×SD3211yescharacteristic
600C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radicalD8×C22⋊D11C2
hypercenter#2187D11
hypocenterC11D4×SD32
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. C22×#66891C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080365C2semidirect
5. #13070870C2semidirect
6. #13070714C2semidirect
7. #13070711C2semidirect
8. #13070659C2semidirect
9. #13070655C2semidirect
10. #13070546C2semidirect
11. #13070535C2semidirect
12. #13070531C2semidirect
13. #13070471C2semidirect
14. (C22⋊D11)⋊C16C2semidirect
15. C11×#2187C2semidirect
18. C2×Q16×D11C22semidirect
20. C22×Dic44C22semidirect
23. C2×C11×SD32C22semidirect
24. C11×#467C22semidirect
26. #10622794C22semidirect
27. C2×#66892C22semidirect
36. C2×#66891C22semidirect
37. C2×#66891C22semidirect
40. C22×C11⋊C16C22semidirect
43. C2×#66864C22semidirect
44. C2×#66864C22semidirect
45. C2×C16×D11C22semidirect
46. #10622500C22semidirect
47. #10622486C22semidirect
51. C11×#357C22semidirect
52. C11×C22⋊C16C22semidirect
53. #10622202C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. Dic11⋊C16C22semidirect
58. C16×Dic11C22semidirect
59. #10622129C22semidirect
60. #10622128C22semidirect
117. #66891D4semidirect
201. Dic44C2×D4semidirect
209. C11⋊C16C2×D4semidirect
220. #2187D11semidirect
254. C22⋊D11SD32semidirect
295. C2×SD32C2×D11semidirect
301. #467C2×D11semidirect
320. #357C2×D11semidirect
322. C22⋊C16C2×D11semidirect
333. C22×C11C2×SD32semidirect
341. C2×D11C2×SD32semidirect
352. Dic11C2×SD32semidirect
509. C11D4×SD32semidirect
580. C22D11×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×#668912
C2×D11×SD322
#130803652
D8×C22⋊D112
#130708702
#130707142
#130707112
#130706592
#130706552
#130705462
#130705352
#130705312
#130704712
(C22⋊D11)⋊C162
C11×#21872
D4×SD3211