Finite Group Databasebeta

← #14910421

Subgroups — #14910421

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13080290C211yesmaximal, characteristic, complemented
4D8×C22⋊D11C211yesmaximal, characteristic, complemented
5#13070864C211yesmaximal, characteristic, complemented
6#13070701C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070650C211yesmaximal, characteristic, complemented
9#13070649C211yesmaximal, characteristic, complemented
10#13070530C211yesmaximal, characteristic, complemented
11#13070529C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
15C11×#2184C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic, complemented
17D4×C22⋊D11—21no—
18C2×D8×D11C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic, complemented
21#10623140—21no—
22C2×C11×D16C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic, complemented
25#10622830—21no—
26#10622770C2211yescharacteristic, complemented
27#10622769—21no—
28#10622764C2211yescharacteristic, complemented
29#10622764C2211yescharacteristic, complemented
30#10622763—21no—
31D8×Dic11C2211yescharacteristic, complemented
32C2×#66890—24no—
33C2×#66890C2211yescharacteristic
34C2×#66890C2211yescharacteristic, complemented
35C2×#66890C2211yescharacteristic, complemented
36C2×#66890C2211yescharacteristic, complemented
37C2×#66890C2211yescharacteristic, complemented
38#10622728C2211yescharacteristic, complemented
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic, complemented
41#10622649—21no—
42D11×D16—24no—
43C2×D176C2211yescharacteristic, complemented
44C2×D176C2211yescharacteristic, complemented
45C2×C16×D11C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic, complemented
47#10622485C2211yescharacteristic, complemented
48#10622399—21no—
49#10622386—21no—
50C11×#357C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C16×Dic11C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C22×C22⋊D11—41no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C2×D4×D11—41no—
66C22×D44—21no—
67C2×C11×D8—22no—
68C2×C11×D8—21no—
69C2×C11×D8—41no—
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C2×C11×D8C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#121—21no—
75#67006—41no—
76#66993—21no—
77#66993—21no—
78#66992—41no—
79#66991—21no—
80#66990—41no—
81#66990—41no—
82D4×Dic11—21no—
83C2×#4323—21no—
84C2×#4323—21no—
85C2×#4323—21no—
86C2×#4323—21no—
87#66983—21no—
88C4×C22⋊D11D411yescharacteristic
89D8×D11—22no—
90D8×D11—22no—
91D8×D11—41no—
92D8×D11—41no—
93C2×D88—22no—
94C2×D88—21no—
95C2×D88—41no—
96C2×D88C2311yescharacteristic
97C2×D88C2311yescharacteristic
98C2×D88C2311yescharacteristic
99C2×C8×D11C2311yescharacteristic
100#66948—21no—
101#66946—21no—
102#66937—41no—
103#66935—41no—
104C11×D16—22no—
105C11×D16—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110#66896—21no—
111#66896—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66890—22no—
114#66890—22no—
115#66890—22no—
116#66890—22no—
117#66890D414yescomplemented
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120#66882C2311yescharacteristic
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123C2×C11⋊C16—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128D176—22no—
129D176—41no—
130C16×D11—22no—
131D4×D16—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C23×D11—41no—
135C23×D11—41no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
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—84no—
153C2×C22⋊D11D811yescharacteristic
154C22×Dic11—41no—
155D4×D11—42no—
156D4×D11—42no—
157D4×D11—81no—
158D4×D11—81no—
159D4×D11—84no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—42no—
164C2×D44—41no—
165C2×D44—41no—
166C2×D44—81no—
167C2×C4×D11—41no—
168C2×C4×D11C2×D411yescharacteristic
169C11×D8—21no—
170C11×D8—21no—
171C11×D8—21no—
172C11×D8—21no—
173C11×D8—21no—
174C11×D8—42no—
175C11×D8C2×D412yescomplemented
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C22⋊C4—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11D811yescharacteristic
185#4323—42no—
186#4323—42no—
187#4323—81no—
188#4323—81no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4D811yescharacteristic
193C4⋊Dic11—21no—
194Dic11⋊C4D811yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198D88—21no—
199D88—21no—
200D88—21no—
201D88—21no—
202D88—21no—
203D88—42no—
204D88C2×D412yescomplemented
205C8×D11—21no—
206C8×D11—21no—
207C11×C16—21no—
208C11×C16—21no—
209C11⋊C16—21no—
210C11⋊C16C2×D412yescomplemented
211C22×D16—111no—
212C22×D16—111no—
213D4×D8—111no—
214D4×D8—111no—
215#2246—111no—
216#2215—111no—
217#2215—111no—
218#2206—111no—
219#2206—111no—
220#2184—111no—
221#2184—111no—
222#2184—111no—
223#2184D1111yescharacteristic, complemented
224C4×D16—111no—
225D4×C16—111no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—161no—
232C23×C11C2×D811yescharacteristic
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—82no—
240C22×D11—82no—
241C22×D11—82no—
242C22×D11—161no—
243C22×D11—161no—
244C22×D11—161no—
245C22×D11C2×D811yescharacteristic
246D4×C11—22no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—82no—
253D4×C11—82no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11C2×D811yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C22⋊D11—82no—
260C22⋊D11—82no—
261C22⋊D11—82no—
262C22⋊D11—82no—
263C22⋊D11—82no—
264C22⋊D11—82no—
265C22⋊D11—161no—
266C22⋊D11—161no—
267C22⋊D11D1614yescomplemented
268C2×Dic11—41no—
269C2×Dic11—82no—
270C2×Dic11C2×D811yescharacteristic
271C2×Dic11C2×D811yescharacteristic
272C2×Dic11C2×D811yescharacteristic
273D44—22no—
274D44—41no—
275D44—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—82no—
280D44—82no—
281C4×D11—21no—
282C4×D11—21no—
283C4×D11—82no—
284C8×C11—21no—
285C8×C11C22×D411yescharacteristic
286C8×C11H(5,𝔽2)11yescharacteristic
287C11⋊C8—21no—
288C11⋊C8—21no—
289C22×D8—111no—
290C22×D8—111no—
291C22×D8—111no—
292C22×D8C2×D1111yescharacteristic, complemented
293D42—221no—
294D42—221no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—111no—
298C2×D16—111no—
299C2×D16—111no—
300C2×D16—111no—
301C2×D16—111no—
302C2×D16—224no—
303C2×D16—224no—
304C2×D16C2×D1111yescharacteristic, complemented
305C2×D16C2×D1111yescharacteristic, complemented
306C22×C16—111no—
307C22×C16—111no—
308#493—111no—
309#493—111no—
310#466—111no—
311#466—111no—
312#466—111no—
313#466C2×D1111yescharacteristic, complemented
314#459—221no—
315#459—221no—
316#447—221no—
317#447—221no—
318#447—221no—
319#447—221no—
320C4×D8—111no—
321C4×D8—111no—
322C8×D4—111no—
323#366—111no—
324C4⋊C16—111no—
325#357—111no—
326#357—111no—
327#357—111no—
328#357—111no—
329#357C2×D1111yescharacteristic, complemented
330#357C2×D1111yescharacteristic, complemented
331C22⋊C16—111no—
332C22⋊C16C2×D1111yescharacteristic, complemented
333C4×C16—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—42no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—164no—
346C22×C11C2×D1612yescomplemented
347C22×C11C22×D811yescharacteristic
348C2×D11—21no—
349C2×D11—21no—
350C2×D11—42no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—164no—
360C2×D11—164no—
361C2×D11—164no—
362C2×D11C2×D1612yescomplemented
363C4×C11—21no—
364C4×C11—81no—
365C4×C11D4211yescharacteristic
366C4×C11#57611yescharacteristic
367Dic11—21no—
368Dic11—21no—
369Dic11—81no—
370Dic11C2×D1612yescomplemented
371C22×D4—21no—
372C22×D4—221no—
373C22×D4—221no—
374C22×D4—221no—
375C22×D4—441no—
376C22×D4—441no—
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—111no—
381C2×D8—111no—
382C2×D8—111no—
383C2×D8—222no—
384C2×D8—221no—
385C2×D8—221no—
386C2×D8—221no—
387C2×D8—221no—
388C2×D8—222no—
389C2×D8—222no—
390C2×D8—221no—
391C2×D8—441no—
392C2×D8—441no—
393C2×D8—441no—
394C2×D8C22×D1111yescharacteristic
395C2×D8C22×D1111yescharacteristic
396C2×D8C22×D1111yescharacteristic
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399#127—221no—
400#127—221no—
401#121—21no—
402#121—221no—
403#121—221no—
404#121—221no—
405#121—441no—
406#121—441no—
407#120—441no—
408#120—441no—
409#120—441no—
410#120—441no—
411C4×D4—111no—
412C4×D4—221no—
413C4×D4—221no—
414D16—22no—
415D16—41no—
416D16—114no—
417D16—222no—
418D16—222no—
419D16—222no—
420D16—222no—
421D16—222no—
422D16—441no—
423C2×C16—111no—
424C2×C16—111no—
425C2×C16—222no—
426C2×C16—222no—
427C2×C16C22×D1111yescharacteristic
428C2×C16C22×D1111yescharacteristic
429#107—111no—
430#107C22×D1111yescharacteristic
431C4⋊C8—111no—
432#102—21no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438C22⋊C8—111no—
439C22⋊C8—111no—
440C4×C8—111no—
441C2×C11—22no—
442C2×C11—82no—
443C2×C11—161no—
444C2×C11—161no—
445C2×C11D4×D811yescharacteristic
446C2×C11C22×D1611yescharacteristic
447C2×C11#341511yescharacteristic
448D11—22no—
449D11—82no—
450D11—161no—
451D11—161no—
452C24—41no—
453C24—441no—
454C24—441no—
455C24—441no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—81no—
463C2×D4—111no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—442no—
468C2×D4—441no—
469C2×D4—441no—
470C2×D4—441no—
471C2×D4—441no—
472C2×D4—441no—
473C2×D4—441no—
474C2×D4—441no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4—441no—
478C2×D4—441no—
479C2×D4—441no—
480C2×D4—881no—
481C2×D4—881no—
482C2×D4—881no—
483C2×D4—884no—
484C2×D4—884no—
485C22×C4—111no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4D4×D1111yescharacteristic
489D8—21no—
490D8—21no—
491D8—21no—
492D8—21no—
493D8—21no—
494D8—42no—
495D8—112no—
496D8—221no—
497D8—221no—
498D8—221no—
499D8—221no—
500D8—221no—
501D8—442no—
502D8—442no—
503D8—442no—
504D8—881no—
505D8—881no—
506D8D4×D1112yescomplemented
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8D4×D1111yescharacteristic
514C2×C8C23×D1111yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—111no—
517C4⋊C4—221no—
518C22⋊C4—41no—
519C22⋊C4—111no—
520C22⋊C4—111no—
521C22⋊C4—441no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C42—111no—
527C16—21no—
528C16—21no—
529C16—112no—
530C16—221no—
531C11D4×D1611yescharacteristic, complemented, Sylow
532C23—41no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—111no—
538C23—161no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—882no—
543C23—882no—
544C23—882no—
545C23—882no—
546C23—882no—
547C23—882no—
548C23—1761no—
549C23—1761no—
550C23—1761no—
551C23D8×D1111yescharacteristic
552D4—22no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—82no—
559D4—82no—
560D4—114no—
561D4—222no—
562D4—441no—
563D4—441no—
564D4—441no—
565D4—441no—
566D4—441no—
567D4—882no—
568D4—882no—
569D4—882no—
570D4—882no—
571D4—882no—
572D4—882no—
573D4—882no—
574D4—882no—
575D4—1761no—
576D4—1761no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—111no—
581C2×C4—111no—
582C2×C4—111no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—441no—
586C2×C4—882no—
587C2×C4—882no—
588C2×C4D8×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C8—21no—
591C8—221no—
592C8—221no—
593C8C2×D4×D1111yescharacteristic
594C8#6703711yescharacteristic
595C22—21no—
596C22—21no—
597C22—42no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—112no—
607C22—164no—
608C22—221no—
609C22—221no—
610C22—442no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22—1764no—
620C22—1764no—
621C22—1764no—
622C22D11×D1612yescomplemented
623C22C2×D8×D1111yescharacteristic
624C4—21no—
625C4—81no—
626C4—112no—
627C4—221no—
628C4—221no—
629C4—881no—
630C4#1062312111yescharacteristic
631C4#1062330511yescharacteristic
632C2—22no—
633C2—82no—
634C2—161no—
635C2—161no—
636C2—222no—
637C2—882no—
638C2—1761no—
639C2—1761no—
640C2#1308028611yescharacteristic
641C2C2×D11×D1611yescharacteristic
642C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11D4×D16
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. C22×#66890C2semidirect
2. C2×D11×D16C2semidirect
3. #13080290C2semidirect
4. D8×C22⋊D11C2semidirect
5. #13070864C2semidirect
6. #13070701C2semidirect
7. #13070700C2semidirect
8. #13070650C2semidirect
9. #13070649C2semidirect
10. #13070530C2semidirect
11. #13070529C2semidirect
12. #13070526C2semidirect
13. #13070460C2semidirect
14. (C22⋊D11)⋊C16C2semidirect
15. C11×#2184C2semidirect
16. C22×C11×D8C22semidirect
18. C2×D8×D11C22semidirect
19. C2×D8×D11C22semidirect
20. C22×D88C22semidirect
22. C2×C11×D16C22semidirect
23. C2×C11×D16C22semidirect
24. C11×#466C22semidirect
26. #10622770C22semidirect
28. #10622764C22semidirect
29. #10622764C22semidirect
31. D8×Dic11C22semidirect
34. C2×#66890C22semidirect
35. C2×#66890C22semidirect
36. C2×#66890C22semidirect
37. C2×#66890C22semidirect
38. #10622728C22semidirect
40. C22×C11⋊C16C22semidirect
43. C2×D176C22semidirect
44. C2×D176C22semidirect
45. C2×C16×D11C22semidirect
46. #10622496C22semidirect
47. #10622485C22semidirect
50. C11×#357C22semidirect
51. C11×#357C22semidirect
52. C11×C22⋊C16C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. C16×Dic11C22semidirect
59. #10622129C22semidirect
60. #10622127C22semidirect
117. #66890D4semidirect
175. C11×D8C2×D4semidirect
204. D88C2×D4semidirect
210. C11⋊C16C2×D4semidirect
223. #2184D11semidirect
267. C22⋊D11D16semidirect
292. C22×D8C2×D11semidirect
304. C2×D16C2×D11semidirect
305. C2×D16C2×D11semidirect
313. #466C2×D11semidirect
329. #357C2×D11semidirect
330. #357C2×D11semidirect
332. C22⋊C16C2×D11semidirect
346. C22×C11C2×D16semidirect
362. C2×D11C2×D16semidirect
370. Dic11C2×D16semidirect
506. D8D4×D11semidirect
531. C11D4×D16semidirect
622. C22D11×D16semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
C2×D11×D162
#130802902
D8×C22⋊D112
#130708642
#130707012
#130707002
#130706502
#130706492
#130705302
#130705292
#130705262
#130704602
(C22⋊D11)⋊C162
C11×#21842
D4×D1611