Finite Group Databasebeta

← #14786407

Subgroups — #14786407

Order 2816.

1844 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
1C22×#66983C211yesmaximal, characteristic
2C2×#10622349C212yesmaximal, complemented
3C2×#10622825C211yesmaximal, characteristic, complemented
4#13069799C214yesmaximal, complemented
5#13068931C212yesmaximal, complemented
6#13068806C212yesmaximal, complemented
7#13068548C212yesmaximal, complemented
8C11×#1779C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×D44C2211yescharacteristic
12C22×C22⋊Dic11—21no—
13C2×#66983—21no—
14C2×#66983—21no—
15C2×#66983—28no—
16C2×#66983C2212yes—
17C2×#66983C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic, complemented
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C2×C11×C22⋊C8C2212yes—
23C2×C11×C22⋊C8C2212yescomplemented
24C2×C11×C22⋊C8C2212yescomplemented
25#10622825—21no—
26#10622825—21no—
27#10622825C2212yes—
28#10622825C2212yescomplemented
29C2×C11⋊#95—21no—
30C2×#66885C2214yescomplemented
31C2×#66885C2214yescomplemented
32C2×#66882C2214yescomplemented
33#10622349—28no—
34#10622189C2214yescomplemented
35C25×C11D411yescharacteristic
36C24×D11—21no—
37C23×C4×C11—24no—
38C23×C4×C11—24no—
39C23×C4×C11—42no—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—28no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—44no—
50C22×C22⋊D11—44no—
51C23×Dic11—21no—
52C23×Dic11—21no—
53C23×Dic11—21no—
54C22×D44—21no—
55C22×D44—24no—
56C22×D44—24no—
57C22×D44—42no—
58C22×D44C2312yes—
59C22×C8×C11C2314yes—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—44no—
63#66983—28no—
64#66983—28no—
65#66983—24no—
66#66983—24no—
67#66983—24no—
68#66983D418yes—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11C2312yes—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C11×C22⋊C8—24no—
82C11×C22⋊C8—24no—
83C11×C22⋊C8—42no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—28no—
87#66885—44no—
88#66882—28no—
89#24002—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—41no—
95C24×C11—41no—
96C24×C11D814yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C23×D11—24no—
101C23×D11—22no—
102C23×D11—42no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—416no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4114yes—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—28no—
132C2×C22⋊D11—28no—
133C2×C22⋊D11—432no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C2×C22⋊D11—44no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C2×D44—24no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—416no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44C2×D414yes—
158C2×C8×C11—24no—
159C2×C8×C11—24no—
160C2×C8×C11—24no—
161C22⋊Dic11—44no—
162C22⋊Dic11—44no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—28no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169C4⋊Dic11—42no—
170C4⋊Dic11—42no—
171C4⋊Dic11C2×D414yes—
172C22×#121—111no—
173C2×#480—112no—
174C2×#380—111no—
175#2033—114no—
176#1874—112no—
177#1852—112no—
178#1786—112no—
179#1779D1111yescharacteristic, complemented
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11#12012yes—
202C23×C11#12312yes—
203C23×C11C2×D812yes—
204C23×C11C2×D812yes—
205C23×C11C2×D812yes—
206C23×C11AGL(1,ℤ/8)12yes—
207C23×C11#13712yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—48no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—84no—
220C22×D11—84no—
221C22×D11—84no—
222C22×D11—84no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—28no—
228C2×C4×C11—28no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12312yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C22⋊D11—416no—
242C22⋊D11—416no—
243C2×Dic11—24no—
244C2×Dic11—48no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—84no—
254C2×Dic11—84no—
255D44—28no—
256D44—48no—
257D44—44no—
258C8×C11—44no—
259C23×D4—111no—
260C23×D4—221no—
261C24×C4C2×D1111yescharacteristic
262C2×#121—112no—
263C2×#121—112no—
264C2×#121—228no—
265C2×#121—221no—
266C2×#121—221no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—111no—
270C22×C22⋊C4—221no—
271C22×C22⋊C4—221no—
272#480—228no—
273C2×#107—114no—
274C2×#102—114no—
275C2×#102—114no—
276C2×C22⋊C8C2×D1112yes—
277C2×C22⋊C8C2×D1112yescomplemented
278C2×C22⋊C8C2×D1112yescomplemented
279#380—112no—
280#380—112no—
281#380—221no—
282#380—221no—
283C2×#95—221no—
284#340—114no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—416no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11#44714yes—
306C22×C11#48014yescomplemented
307C22×C11C2×#12011yescharacteristic
308C22×C11C2×#12311yescharacteristic
309C22×C11#53411yescharacteristic
310C22×C11C22×D811yescharacteristic
311C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C11C2×#13711yescharacteristic
313C22×C11#57511yescharacteristic
314C2×D11—44no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—816no—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—41no—
325C4×C11#54614yes—
326Dic11—44no—
327Dic11—82no—
328Dic11—82no—
329C25—221no—
330C25D4411yescharacteristic
331C22×D4—112no—
332C22×D4—224no—
333C22×D4—228no—
334C22×D4—222no—
335C22×D4—222no—
336C22×D4—221no—
337C22×D4—224no—
338C22×D4—442no—
339C22×D4—444no—
340C22×D4—444no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—42no—
344C23×C4—221no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4D4411yescharacteristic
348C23×C4D4411yescharacteristic
349C23×C4D4411yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C22×C8C22×D1114yes—
354#121—118no—
355#121—224no—
356#121—224no—
357#121—228no—
358#121—228no—
359#121—224no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—442no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—444no—
375#107—228no—
376#102—228no—
377#102—444no—
378C22⋊C8—24no—
379C22⋊C8—24no—
380C22⋊C8—42no—
381#95—222no—
382#95—222no—
383C2×C11—24no—
384C2×C11—24no—
385C2×C11—42no—
386C2×C11#240511yescharacteristic
387C2×C11C2×#44711yescharacteristic
388C2×C11#300711yescharacteristic
389C2×C11C2×#48011yescharacteristic
390C2×C11#309411yescharacteristic
391C2×C11#318611yescharacteristic
392C2×C11#319311yescharacteristic
393D11—84no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—41no—
399C24—41no—
400C24—224no—
401C24—222no—
402C24—442no—
403C24—442no—
404C24—442no—
405C24—442no—
406C24—442no—
407C24—442no—
408C24D8814yes—
409C24C2×D4411yescharacteristic
410C24C2×D4411yescharacteristic
411C24C2×D4411yescharacteristic
412C2×D4—114no—
413C2×D4—224no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—222no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—4416no—
420C2×D4—442no—
421C2×D4—4432no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—442no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—416no—
444C22×C4—224no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4411yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4D4×D1114yes—
460C22×C4#434114yes—
461C22×C4C23×D1111yescharacteristic
462C2×C8—24no—
463C2×C8—24no—
464C2×C8—24no—
465C4⋊C4—114no—
466C4⋊C4—224no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C22⋊C4—444no—
475C22⋊C4—444no—
476C11#2400211yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—28no—
492C23—28no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—224no—
499C23—448no—
500C23—448no—
501C23—448no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—884no—
509C23—884no—
510C23—884no—
511C23—884no—
512C23#6693512yes—
513C23#6693912yes—
514C23C2×D8812yes—
515C23C2×D8812yes—
516C23C2×D8812yes—
517C23#6696112yes—
518C23#6696212yes—
519C23C22×D4411yescharacteristic
520D4—228no—
521D4—448no—
522D4—4416no—
523D4—4416no—
524D4—444no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—224no—
539C2×C4—448no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—884no—
549C2×C4—884no—
550C2×C4#6693512yes—
551C2×C4#6693912yes—
552C2×C4C2×D4×D1112yes—
553C2×C4C2×#434112yes—
554C2×C4#6703712yes—
555C8—44no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—416no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—8816no—
580C22—882no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22#1062234514yes—
585C22#1062234914yescomplemented
586C22C2×#6693511yescharacteristic
587C22C2×#6693911yescharacteristic
588C22#1062302411yescharacteristic
589C22C22×D8811yescharacteristic
590C22C2×#6696111yescharacteristic
591C22C2×#6696211yescharacteristic
592C22#1062327911yescharacteristic
593C4—22no—
594C4—22no—
595C4—41no—
596C4—444no—
597C4—882no—
598C4—882no—
599C4#1062312214yes—
600C2—24no—
601C2—24no—
602C2—42no—
603C2—884no—
604C2#1307194411yescharacteristic
605C2C2×#1062234511yescharacteristic
606C2#1307787811yescharacteristic
607C2C2×#1062234911yescharacteristic
608C2#1307855711yescharacteristic
609C2#1307936711yescharacteristic
610C2#1307942311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1779C2
socleC23×C11C22×D4
prime radicalC22×#66983C2
hypercenter#1779D11
hypocenterC11#24002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#10622349C2semidirect
3. C2×#10622825C2semidirect
4. #13069799C2semidirect
5. #13068931C2semidirect
6. #13068806C2semidirect
7. #13068548C2semidirect
8. C11×#1779C2semidirect
20. C22×C4⋊Dic11C22semidirect
21. C22×C4⋊Dic11C22semidirect
23. C2×C11×C22⋊C8C22semidirect
24. C2×C11×C22⋊C8C22semidirect
28. #10622825C22semidirect
30. C2×#66885C22semidirect
31. C2×#66885C22semidirect
32. C2×#66882C22semidirect
34. #10622189C22semidirect
179. #1779D11semidirect
277. C2×C22⋊C8C2×D11semidirect
278. C2×C22⋊C8C2×D11semidirect
306. C22×C11#480semidirect
476. C11#24002semidirect
585. C22#10622349semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106223492
C2×#106228252
#130697992
#130689312
#130688062
#130685482
C11×#17792
#2400211