Finite Group Databasebeta

← #14731346

Subgroups — #14731346

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079932C211yesmaximal, characteristic, complemented
2#13079171C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic, complemented
4#13067900C212yesmaximal, complemented
5#13067795C212yesmaximal, complemented
6#13067767C212yesmaximal, complemented
7#13067732C212yesmaximal, complemented
8#13067293C211yesmaximal, characteristic, complemented
9#13067067C211yesmaximal, characteristic, complemented
10C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3496C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)—21no—
13C11×#547—21no—
14C11×#547C2212yes—
15C11×#546—22no—
16C11×#546—22no—
17D42×C11—21no—
18D42×C11C2212yes—
19C11×#537—21no—
20C11×#534—22no—
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×#121—22no—
24C2×C4×D4×C11C2211yescharacteristic
25#10623001C2211yescharacteristic, complemented
26#10622828—21no—
27#10622707—21no—
28#10622706C2211yescharacteristic, complemented
29#10622692C2211yescharacteristic, complemented
30#10622689C2211yescharacteristic, complemented
31#10622688—21no—
32#10622683C2211yescharacteristic, complemented
33#10622654—22no—
34#10622654—22no—
35#10622632C2212yescomplemented
36C4×#4324—22no—
37#10622622—22no—
38#10622621C2212yescomplemented
39#10622621C2212yescomplemented
40#10622620C2212yescomplemented
41#10622577—21no—
42#10622537C2211yescharacteristic, complemented
43C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
44C2×C4×C11⋊C8C2211yescharacteristic, complemented
45#10622185C2212yescomplemented
46#10622182C2212yescomplemented
47D4⋊(C11⋊C8)C2212yescomplemented
48D4⋊(C11⋊C8)C2212yescomplemented
49D4⋊(C11⋊C8)C2212yescomplemented
50D4⋊(C11⋊C8)C2212yescomplemented
51C11×H(5,𝔽2)—44no—
52C11×H(5,𝔽2)—44no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×D4×C11—24no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11D411yescharacteristic
62C23×C4×C11—21no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#124—21no—
68C11×#124—21no—
69C11×#123—24no—
70C11×#123—24no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121D412yes—
82C11×#121D412yes—
83C11×#120—24no—
84C11×#120—24no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D412yes—
90C4×D4×C11D412yes—
91C4×D4×C11C2312yes—
92C4×D4×C11C2312yes—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11C2311yescharacteristic
98C2×#4324—22no—
99C2×#4324—22no—
100#66979—21no—
101#66977—21no—
102#66977—21no—
103C2×#4318—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106#66923—21no—
107#66922C2311yescharacteristic
108#66922C2311yescharacteristic
109C4×Dic22—21no—
110C4×Dic22—21no—
111#66896—22no—
112#66896—22no—
113#66896—22no—
114#66896—22no—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66872—22no—
119#66872—22no—
120#66871—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)C2312yes—
124C4⋊(C11⋊C8)C2312yes—
125C4×C11⋊C8—21no—
126C4×C11⋊C8C2311yescharacteristic
127C4×C11⋊C8C2311yescharacteristic
128#18663—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—24no—
131C11×#41—44no—
132C11×#41—48no—
133C11×#41—44no—
134C11×#41—42no—
135C11×#41—42no—
136C11×#41—42no—
137C11×#41—42no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—44no—
152C2×D4×C11—48no—
153C2×D4×C11—416no—
154C2×D4×C11—44no—
155C2×D4×C11—82no—
156C2×D4×C11—82no—
157C2×D4×C11SD1614yescomplemented
158C2×D4×C11C2×D412yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C2×Dic22—21no—
173C2×Dic22—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2411yescharacteristic
193C22⋊Dic11—41no—
194#4324—44no—
195#4324—82no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202C4×Dic11—41no—
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—81no—
210#3496D1111yescharacteristic
211#3246—111no—
212#3167—111no—
213#3077—111no—
214#1654—112no—
215#1639—112no—
216#1635—112no—
217#1629—112no—
218#1547—111no—
219#1492—111no—
220C2×D4⋊C8—111no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—48no—
226C23×C11—81no—
227C23×C11—81no—
228C23×C11—84no—
229C23×C11—84no—
230C23×C11#12011yescharacteristic
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—42no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—24no—
238D4×C11—42no—
239D4×C11—48no—
240D4×C11—48no—
241D4×C11—44no—
242D4×C11—44no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—42no—
248D4×C11—81no—
249D4×C11—84no—
250D4×C11C2×SD1614yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—48no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—44no—
263C2×C4×C11—82no—
264C2×C4×C11—81no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11C2×SD1612yes—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×Dic11—41no—
274C2×Dic11—41no—
275Dic22—42no—
276Dic22—41no—
277Dic22—41no—
278C11⋊C8—22no—
279C11⋊C8—41no—
280C11⋊C8—42no—
281C11⋊C8—42no—
282C2×H(5,𝔽2)—21no—
283#547—21no—
284#547C2×D1112yes—
285#546—22no—
286#546—22no—
287D42—21no—
288D42C2×D1112yes—
289#537—21no—
290#534—22no—
291#533—111no—
292#532C2×D1111yescharacteristic
293#532C2×D1111yescharacteristic
294C2×#121—22no—
295C2×C4×D4C2×D1111yescharacteristic
296#498—111no—
297#492—111no—
298#487—111no—
299#486—111no—
300#478—222no—
301#476—112no—
302#476—112no—
303#475—221no—
304#474—112no—
305#465—222no—
306#465—222no—
307#461—112no—
308#460—221no—
309C4×SD16—222no—
310#428—221no—
311#423—111no—
312C2×C4⋊C8—111no—
313#418—221no—
314C2×C4×C8—111no—
315#332—112no—
316#331—112no—
317D4⋊C8—112no—
318D4⋊C8—112no—
319D4⋊C8—112no—
320D4⋊C8—112no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—24no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—84no—
333C22×C11—168no—
334C22×C11#45012yes—
335C22×C11C2×#12011yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11#45012yes—
343C4×C11C22×SD1611yescharacteristic
344C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57711yescharacteristic
347Dic11—81no—
348Dic11—81no—
349H(5,𝔽2)—44no—
350H(5,𝔽2)—44no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—21no—
354C2×#41—21no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C22⋊D1111yescharacteristic
360C23×C4—21no—
361C2×SD16—222no—
362C2×SD16—222no—
363C2×M16—221no—
364C22×C8—221no—
365C22×C8—221no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368C4⋊Q8C22⋊D1111yescharacteristic
369C4⋊Q8C22×D1111yescharacteristic
370#127C22⋊D1111yescharacteristic
371#127C22×D1111yescharacteristic
372#125—221no—
373#124—21no—
374#124—21no—
375#123—24no—
376#123—24no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381#121—24no—
382#121—24no—
383#121—22no—
384#121—22no—
385#121—21no—
386#121—21no—
387#121—22no—
388#121—22no—
389#121C22⋊D1112yes—
390#121C22⋊D1112yes—
391#120—24no—
392#120—24no—
393C4×Q8—221no—
394C4×Q8—221no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C22⋊D1112yes—
400C4×D4C22⋊D1112yes—
401C4×D4C22×D1112yes—
402C4×D4C22×D1112yes—
403#117—221no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C22⋊C4—24no—
407C2×C22⋊C4—21no—
408C2×C42C22×D1111yescharacteristic
409#107—222no—
410#106—222no—
411#106—222no—
412#106—222no—
413C4⋊C8—112no—
414C4⋊C8—112no—
415C4⋊C8—221no—
416C4⋊C8—221no—
417#103—222no—
418#103—222no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—222no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C2×C11—22no—
427C2×C11—44no—
428C2×C11—82no—
429C2×C11—82no—
430C2×C11C2×#45011yescharacteristic
431C2×C11#301211yescharacteristic
432C2×C11#301811yescharacteristic
433C24—21no—
434C24—24no—
435#41—44no—
436#41—48no—
437#41—44no—
438#41—42no—
439#41—42no—
440#41—42no—
441#41—42no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—44no—
458C2×D4—48no—
459C2×D4—416no—
460C2×D4—44no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4#432414yescomplemented
464C2×D4C2×C22⋊D1112yes—
465C2×D4C2×C22⋊D1112yes—
466C2×D4C2×C22⋊D1112yes—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478SD16—444no—
479SD16—882no—
480M16—442no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—442no—
486C2×C8—881no—
487C4⋊C4—24no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—441no—
496C4⋊C4—441no—
497C4⋊C4C2×C22⋊D1112yes—
498C4⋊C4C2×C22⋊D1112yes—
499C4⋊C4C2×C22⋊D1112yes—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—441no—
509C42—441no—
510C42C2×C22⋊D1111yescharacteristic
511C42C2×C22⋊D1111yescharacteristic
512C42C2×C22⋊D1111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1866311yescharacteristic, complemented, Sylow
515C23—22no—
516C23—24no—
517C23—22no—
518C23—22no—
519C23—48no—
520C23—81no—
521C23—81no—
522C23—84no—
523C23—84no—
524C23#6700611yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—42no—
528Q8—442no—
529Q8—441no—
530Q8—441no—
531D4—22no—
532D4—24no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—48no—
537D4—48no—
538D4—44no—
539D4—44no—
540D4—41no—
541D4—41no—
542D4—42no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—84no—
547D4C2×#432414yes—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—48no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4#6698512yes—
565C2×C4C2×#432412yes—
566C2×C4#6700611yescharacteristic
567C2×C4#6700611yescharacteristic
568C2×C4#6700611yescharacteristic
569C2×C4C22×C22⋊D1111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C8—222no—
573C8—441no—
574C8—442no—
575C8—442no—
576C22—21no—
577C22—21no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—84no—
588C22—168no—
589C22#1062283112yes—
590C22C2×#6700611yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—881no—
598C4—881no—
599C4#1062283112yes—
600C4C2×#6698511yescharacteristic
601C4C22×#432411yescharacteristic
602C4#1062336611yescharacteristic
603C4#1062336711yescharacteristic
604C2—22no—
605C2—44no—
606C2—82no—
607C2—82no—
608C2C2×#1062283111yescharacteristic
609C2#1307792011yescharacteristic
610C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18663
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13079932C2semidirect
2. #13079171C2semidirect
3. #13078413C2semidirect
4. #13067900C2semidirect
5. #13067795C2semidirect
6. #13067767C2semidirect
7. #13067732C2semidirect
8. #13067293C2semidirect
9. #13067067C2semidirect
10. C2×D4⋊(C11⋊C8)C2semidirect
25. #10623001C22semidirect
28. #10622706C22semidirect
29. #10622692C22semidirect
30. #10622689C22semidirect
32. #10622683C22semidirect
35. #10622632C22semidirect
38. #10622621C22semidirect
39. #10622621C22semidirect
40. #10622620C22semidirect
42. #10622537C22semidirect
43. C2×C4⋊(C11⋊C8)C22semidirect
44. C2×C4×C11⋊C8C22semidirect
45. #10622185C22semidirect
46. #10622182C22semidirect
47. D4⋊(C11⋊C8)C22semidirect
48. D4⋊(C11⋊C8)C22semidirect
49. D4⋊(C11⋊C8)C22semidirect
50. D4⋊(C11⋊C8)C22semidirect
157. C2×D4×C11SD16semidirect
463. C2×D4#4324semidirect
514. C11#18663semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130791712
#130784132
#130679002
#130677952
#130677672
#130677322
#130672932
#130670672
C2×D4⋊(C11⋊C8)2
C11×#34962
#1866311