Finite Group Databasebeta

← #14900652

Subgroups — #14900652

Order 2816.

628 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
1C11⋊#2104C211yesmaximal, characteristic, complemented
2C11⋊#2104C211yesmaximal, characteristic, complemented
3#13069794C211yesmaximal, characteristic, complemented
4#13069793C211yesmaximal, characteristic, complemented
5#13069783C211yesmaximal, characteristic, complemented
6#13069744C211yesmaximal, characteristic
7#13069156C211yesmaximal, characteristic
8#13069155C211yesmaximal, characteristic
9#13069074C211yesmaximal, characteristic, complemented
10#13069030C211yesmaximal, characteristic, complemented
11#13069026C211yesmaximal, characteristic, complemented
12#13068723C211yesmaximal, characteristic, complemented
13#13068722C211yesmaximal, characteristic, complemented
14#13068693C211yesmaximal, characteristic, complemented
15C11×#1899C211yesmaximal, characteristic, complemented
16C2×C11×#123C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18#10623335C2211yescharacteristic
19#10623329C2211yescharacteristic
20C2×#66982C2211yescharacteristic
21#10623017C2211yescharacteristic
22#10623014C2211yescharacteristic
23C2×C11×#99C2211yescharacteristic
24C2×C11×#99C2211yescharacteristic
25C11×#381C2211yescharacteristic
26C2×#66898C2211yescharacteristic
27C2×#66898C2211yescharacteristic
28#10622824C2211yescharacteristic
29#10622824C2211yescharacteristic
30#10622824C2211yescharacteristic
31C2×#66870C2211yescharacteristic
32C2×#66870C2211yescharacteristic
33C2×#66870C2211yescharacteristic
34C2×#66870C2211yescharacteristic
35C11×#342C2211yescharacteristic
36C11×#342C2211yescharacteristic
37#10622165C2211yescharacteristic
38#10622165C2211yescharacteristic
39#10622165C2211yescharacteristic
40#10622165C2211yescharacteristic
41#10622165C2211yescharacteristic
42#10622165C2211yescharacteristic
43#10622165C2211yescharacteristic
44#10622165C2211yescharacteristic
45#10622164C2211yescharacteristic
46#10622164C2211yescharacteristic
47#10622164C2211yescharacteristic
48#10622164C2211yescharacteristic
49#10622164C2211yescharacteristic
50#10622164C2211yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11C2311yescharacteristic
54C11×#123—21no—
55C11×#123—21no—
56C11×#123—41no—
57C11×#117—41no—
58C11×#117—41no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4C2311yescharacteristic
67C2×C42×C11—21no—
68#67006—21no—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11C2311yescharacteristic
71C2×C22⋊Dic11C2311yescharacteristic
72C2×C22⋊Dic11C2311yescharacteristic
73C2×C22⋊Dic11C2311yescharacteristic
74C2×C22⋊Dic11C2311yescharacteristic
75C2×C22⋊Dic11C2311yescharacteristic
76C2×C22⋊Dic11C2311yescharacteristic
77#66992—41no—
78#66990—21no—
79#66988—21no—
80D4×Dic11—41no—
81D4×Dic11—41no—
82#66982—21no—
83#66982—21no—
84#66982—21no—
85#66982—41no—
86C4×C22⋊D11—41no—
87C2×(C2×D11)⋊C4—21no—
88#66979—21no—
89#66977—41no—
90C2×Dic11⋊C4—21no—
91(C22⋊D11)⋊C4—41no—
92C22⋊C4×D11—21no—
93#66931—41no—
94#66931—41no—
95#66930—21no—
96C11×#99—41no—
97C11×#99—41no—
98C11×#95—41no—
99#66898—41no—
100#66898—41no—
101C11⋊#95—41no—
102C11⋊#95—41no—
103C11⋊#95—41no—
104#66870—41no—
105#66870—41no—
106#66870—41no—
107#66870—41no—
108#32701—111nomaximal, Sylow
109C24×C11#4111yescharacteristic
110C24×C11C2411yescharacteristic
111C23×D11#4111yescharacteristic
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C2×C22⋊D11—21no—
133C2×C22⋊D11—21no—
134C2×C22⋊D11—21no—
135C2×C22⋊D11—21no—
136C2×C22⋊D11—21no—
137C2×C22⋊D11—21no—
138C2×C22⋊D11—41no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—41no—
147C22×Dic11#4111yescharacteristic
148C2×C4×D11—41no—
149C2×Dic22—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—42no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C11×C22⋊C4—21no—
161C11×C22⋊C4—21no—
162C11×C22⋊C4—21no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C42×C11—42no—
166C22⋊Dic11—21no—
167C22⋊Dic11—21no—
168C22⋊Dic11—21no—
169C22⋊Dic11—21no—
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179C22⋊Dic11—21no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186C4⋊Dic11—41no—
187C4⋊Dic11—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—42no—
193C4×Dic11—41no—
194C4×Dic11—41no—
195#2104—111no—
196#2104—111no—
197#2032—111no—
198#2032—111no—
199#2030—111no—
200#2022—111no—
201#1913—111no—
202#1913—111no—
203#1899—111no—
204#1899D1111yescharacteristic, complemented
205#1890—111no—
206#1890—111no—
207#1828—111no—
208#1828—111no—
209#1820—111no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—81no—
214C23×C11—81no—
215C23×C11C2×#4111yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11H(5,𝔽2)11yescharacteristic
219C23×C11H(5,𝔽2)11yescharacteristic
220C23×C11H(5,𝔽2)11yescharacteristic
221C23×C11H(5,𝔽2)11yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—81no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—81no—
249C2×C4×C11—81no—
250C2×C4×C11—81no—
251C2×C4×C11—81no—
252C2×C4×C11—81no—
253C22⋊D11—41no—
254C22⋊D11—41no—
255C22⋊D11—41no—
256C22⋊D11—41no—
257C22⋊D11—161no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—81no—
269C2×Dic11—81no—
270C2×Dic11—81no—
271C2×Dic11—81no—
272C2×Dic11—81no—
273C2×Dic11—81no—
274C2×Dic11—81no—
275C2×Dic11—161no—
276C4×D11—161no—
277Dic22—161no—
278#543—111no—
279#534—111no—
280C2×#123—111no—
281C2×#123C2×D1111yescharacteristic
282#518—111no—
283#518—111no—
284C2×#117C2×D1111yescharacteristic
285C2×#99—111no—
286C2×#99—111no—
287C2×#99—111no—
288C2×#99—111no—
289C2×#99—111no—
290C2×#99—111no—
291C2×#99C2×D1111yescharacteristic
292C2×#99C2×D1111yescharacteristic
293#381—111no—
294#381—111no—
295#381—111no—
296#381C2×D1111yescharacteristic
297#342—111no—
298#342—111no—
299#342—111no—
300#342—111no—
301#342—111no—
302#342—111no—
303#342—111no—
304#342—111no—
305#342—111no—
306#342—111no—
307#342—111no—
308#342—111no—
309#342—111no—
310#342—111no—
311#342C2×D1111yescharacteristic
312#342C2×D1111yescharacteristic
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11#53811yescharacteristic
325C22×C11#53811yescharacteristic
326C22×C11#53811yescharacteristic
327C22×C11#55111yescharacteristic
328C22×C11#55111yescharacteristic
329C22×C11#55111yescharacteristic
330C22×C11#56011yescharacteristic
331C2×D11—41no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×D4—111no—
352C22×D4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354#123—21no—
355#123—21no—
356#123—41no—
357#123—221no—
358#123—221no—
359#123—221no—
360#123—221no—
361#123—441no—
362C22⋊Q8—441no—
363C22⋊Q8—441no—
364C22⋊Q8—441no—
365#121—441no—
366#120—221no—
367#120—221no—
368C4×D4—441no—
369C4×D4—441no—
370C4×D4—441no—
371C4×D4—441no—
372#117—41no—
373#117—41no—
374#117—221no—
375#117—221no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—221no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—111no—
381C2×C22⋊C4—111no—
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—111no—
385C2×C22⋊C4—111no—
386C2×C22⋊C4—111no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4C22×D1111yescharacteristic
392C2×C22⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4C22×D1111yescharacteristic
395C2×C42—21no—
396#99—41no—
397#99—41no—
398#99—441no—
399#99—441no—
400#99—441no—
401#99—441no—
402#99—441no—
403#99—441no—
404#95—41no—
405#95—441no—
406#95—441no—
407#95—441no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—21no—
411C2×C11—21no—
412C2×C11—21no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—81no—
416C2×C11#276011yescharacteristic
417D11—81no—
418C24—111no—
419C24#433911yescharacteristic
420C24C23×D1111yescharacteristic
421C2×Q8—441no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—441no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4#433911yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4#434111yescharacteristic
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—42no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C4⋊C4—442no—
468C4⋊C4—441no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C22⋊C4—221no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C42—42no—
502C42—441no—
503C42—441no—
504C11#3270111yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—81no—
509C23—81no—
510C23—221no—
511C23—221no—
512C23—221no—
513C23—881no—
514C23C2×#433911yescharacteristic
515C23C2×#434111yescharacteristic
516C23#6703711yescharacteristic
517C23#6703711yescharacteristic
518C23#6703711yescharacteristic
519C23#41×D1111yescharacteristic
520C23#6704211yescharacteristic
521Q8—1761no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—441no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—1761no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—881no—
565C2×C4—881no—
566C2×C4—881no—
567C2×C4—881no—
568C2×C4—881no—
569C2×C4—881no—
570C2×C4—881no—
571C2×C4—1761no—
572C2×C4—1761no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—441no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22#1062302611yescharacteristic
589C22#1062308711yescharacteristic
590C22#1062309111yescharacteristic
591C22#1062312411yescharacteristic
592C22#1062314411yescharacteristic
593C22#1062315111yescharacteristic
594C22#1062318911yescharacteristic
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—441no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4—881no—
610C4—881no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—81no—
619C2—881no—
620C2#1307599211yescharacteristic
subgroupG/H
centerC2#13075992
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#1899C2
socleC2×C11#2760
prime radical#10623335C22
hypercenter#1899D11
hypocenterC11#32701
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C24 ◁ #1899

Complements

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

NH ≅ G/Ntype
1. C11⋊#2104C2semidirect
2. C11⋊#2104C2semidirect
3. #13069794C2semidirect
4. #13069793C2semidirect
5. #13069783C2semidirect
9. #13069074C2semidirect
10. #13069030C2semidirect
11. #13069026C2semidirect
12. #13068723C2semidirect
13. #13068722C2semidirect
14. #13068693C2semidirect
15. C11×#1899C2semidirect
204. #1899D11semidirect
504. C11#32701semidirect

Maximal subgroups

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

subgroupindex
C11⋊#21042
#130697942
#130697932
#130697832
#130697442
#130691562
#130691552
#130690742
#130690302
#130690262
#130687232
#130687222
#130686932
C11×#18992
#3270111