Finite Group Databasebeta

← #14769204

Subgroups — #14769204

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic
3C2×D11×#103C212yesmaximal, complemented
4#13071516C211yesmaximal, characteristic
5#13069540C211yesmaximal, characteristic, complemented
6#13069036C212yesmaximal, complemented
7#13068920C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9#13068549C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999C2212yes—
15C22×C8×D11C2212yes—
16#10623258—24no—
17#10623258C418yescomplemented
18C2×#66949—22no—
19C2×#66946—21no—
20C2×#66946—21no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66941—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622602—22no—
35#10622600C2212yes—
36#10622586—21no—
37C2×#66874C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40D11×#103—28no—
41C8×D44—24no—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44#10622167C2212yes—
45C22×Q8×C11C2312yes—
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—42no—
50C2×Q8×D11—42no—
51C2×Q8×D11C2×C418yescomplemented
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11C2312yes—
56C22×Dic22—22no—
57C22×Dic22C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2×C414yescomplemented
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66999—24no—
69#66999C2×C418yescomplemented
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8C2312yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11—42no—
86#66949—216no—
87#66946—28no—
88#66946—44no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—42no—
91#66941—28no—
92C4×D44C2×C414yes—
93C4×D44D414yes—
94C4×Dic22—22no—
95C4×Dic22C2×C414yescomplemented
96C11×#103—24no—
97C11×#103—42no—
98C4×C8×C11—22no—
99#66899—24no—
100#66899—42no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103(C2×D11)⋊C8—24no—
104#66880—22no—
105#66880D414yescomplemented
106#66874—24no—
107C4⋊(C11⋊C8)—22no—
108D4×#103—111nomaximal, Sylow
109C23×D11C2×D412yes—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C414yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11C2×D412yes—
126Q8×D11—216no—
127Q8×D11—48no—
128Q8×D11—48no—
129Q8×D11—48no—
130C2×D44C22⋊C414yes—
131C2×D44SD1614yes—
132C2×D44Q1614yes—
133C2×C4×D11—28no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—44no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11—82no—
143C2×C4×D11C22×C414yes—
144C2×C4×D11C2×D414yes—
145C2×Dic22—28no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—44no—
150C2×Dic22—44no—
151C2×Dic22C22×C412yes—
152C2×Dic22C2×D412yes—
153C2×Dic22#4112yes—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C2×D412yes—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—81no—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—44no—
170(C2×D11)⋊C4C22⋊C418yes—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C22⋊C414yes—
176C4⋊Dic11C22×C412yes—
177C4⋊Dic11C2×D412yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—24no—
180Dic11⋊C4—44no—
181C4×Dic11—24no—
182C4×Dic11—42no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C8×D11—48no—
187C2×D4×Q8—111no—
188C2×C8×D4—111no—
189C22×#103—112no—
190D4×C4⋊C4—111no—
191#1981—111no—
192#1956D1111yescharacteristic, complemented
193#1892—112no—
194#1872—112no—
195#1803—111no—
196#1787—112no—
197C4×#103—111no—
198C23×C11C22×D411yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11C2×C22⋊C414yes—
204C22×D11C2×SD1614yes—
205C22×D11C2×Q1614yes—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C2×SD1612yes—
221C2×C4×C11C2×Q1612yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11C2×C22⋊C414yes—
243D44#103116yescomplemented
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—416no—
249C4×D11—88no—
250Dic22—22no—
251Dic22—22no—
252Dic22—22no—
253Dic22—416no—
254Dic22C4×D414yescomplemented
255C8×C11—22no—
256C8×C11—41no—
257C11⋊C8—42no—
258C23×Q8—112no—
259C23×C8—112no—
260D4×Q8—118no—
261D4×Q8—224no—
262C2×C4⋊Q8—221no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×C22⋊Q8—112no—
265C2×C22⋊Q8—222no—
266C2×C4×Q8—111no—
267C2×C4×D4—111no—
268C2×C4×D4—221no—
269C2×C4×D4—221no—
270C22×C4⋊C4—112no—
271C8×D4—224no—
272C2×C4⋊C8—111no—
273C2×#103—111no—
274C2×#103—112no—
275C2×#103—111no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103—228no—
279C2×#103C2×D1112yes—
280C2×#103C2×D1112yes—
281C2×C22⋊C8—112no—
282C2×C4×C8C2×D1111yescharacteristic
283#389—221no—
284#385—222no—
285#384C2×D1111yescharacteristic
286#380—112no—
287C4×C4⋊C4—111no—
288#340—111no—
289#340—111no—
290#340—112no—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11D4211yescharacteristic
293C22×C11#54611yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C22×Q1611yescharacteristic
296C22×C11#57711yescharacteristic
297C22×C11#57811yescharacteristic
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11C2×#10318yescomplemented
305C4×C11—22no—
306C4×C11—44no—
307C4×C11—82no—
308C4×C11C2×#10314yescomplemented
309C4×C11C2×C4×D411yescharacteristic
310C4×C11#51811yescharacteristic
311C4×C11D4211yescharacteristic
312C4×C11#54611yescharacteristic
313Dic11—24no—
314Dic11—24no—
315Dic11—42no—
316Dic11—42no—
317Dic11—81no—
318C22×Q8—118no—
319C22×Q8—111no—
320C22×Q8—222no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×Q8—224no—
324C22×Q8—442no—
325C22×Q8—442no—
326C22×Q8C22×D1112yes—
327C22×D4—111no—
328C23×C4—112no—
329C23×C4—222no—
330C23×C4—222no—
331C22×C8—112no—
332C22×C8—224no—
333C22×C8—224no—
334C22×C8—442no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C4⋊Q8—22no—
338C4⋊Q8—228no—
339C4⋊Q8C4×D1114yescomplemented
340C22⋊Q8—118no—
341C22⋊Q8—2216no—
342C22⋊Q8—224no—
343C4×Q8—114no—
344C4×Q8—222no—
345C4×D4—114no—
346C4×D4—114no—
347C4×D4—228no—
348C4×D4—444no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—442no—
362C2×C4⋊C4C22×D1112yes—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C42—221no—
367C2×C42—221no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—222no—
370#103—24no—
371#103—42no—
372#103—114no—
373#103—224no—
374#103—224no—
375#103—222no—
376#103—442no—
377C22⋊C8—224no—
378C4×C8—22no—
379#95—222no—
380#95—221no—
381C2×C11D4×C22⋊C411yescharacteristic
382C2×C11C22×#10311yescharacteristic
383C2×C11#289811yescharacteristic
384C2×C11D4×SD1611yescharacteristic
385C2×C11D4×Q1611yescharacteristic
386C2×C11#329811yescharacteristic
387C2×C11#329911yescharacteristic
388D11—28no—
389C24—112no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—112no—
396C2×Q8—112no—
397C2×Q8—112no—
398C2×Q8—228no—
399C2×Q8—221no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—2216no—
403C2×Q8—444no—
404C2×Q8—444no—
405C2×Q8—448no—
406C2×Q8—448no—
407C2×Q8—448no—
408C2×Q8C2×C4×D1114yes—
409C2×D4—114no—
410C2×D4—114no—
411C2×D4—114no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—112no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—228no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4—444no—
429C22×C4—444no—
430C22×C4—882no—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—448no—
443C2×C8D4×D1112yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—81no—
450C4⋊C4—114no—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—228no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—444no—
460C22⋊C4—118no—
461C22⋊C4—228no—
462C22⋊C4—444no—
463C42—224no—
464C42—442no—
465C42C2×C4×D1112yes—
466C42D4×D1112yes—
467C11D4×#10311yescharacteristic, complemented, Sylow
468C23—114no—
469C23—114no—
470C23—114no—
471C23—222no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23C2×D4×D1111yescharacteristic
476Q8—24no—
477Q8—24no—
478Q8—42no—
479Q8—42no—
480Q8—114no—
481Q8—222no—
482Q8—222no—
483Q8—222no—
484Q8—4416no—
485D4—1116no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—114no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—4416no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—888no—
515C2×C4C22⋊C4×D1112yes—
516C2×C4C22⋊C4×D1112yes—
517C2×C4SD16×D1112yes—
518C2×C4Q16×D1112yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4#6703711yescharacteristic
523C2×C4#41×D1111yescharacteristic
524C2×C4#6704211yescharacteristic
525C8—22no—
526C8—41no—
527C8—442no—
528C22—118no—
529C22—224no—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—224no—
534C22—224no—
535C22C2×C22⋊C4×D1111yescharacteristic
536C22#1062320711yescharacteristic
537C22#1062324811yescharacteristic
538C22C2×SD16×D1111yescharacteristic
539C22#1062329311yescharacteristic
540C22C2×Q16×D1111yescharacteristic
541C22#1062329711yescharacteristic
542C4—22no—
543C4—44no—
544C4—82no—
545C4—224no—
546C4—224no—
547C4—442no—
548C4—442no—
549C4—881no—
550C4D11×#10314yescomplemented
551C4C4×D4×D1111yescharacteristic
552C4#1062307611yescharacteristic
553C4#1062314011yescharacteristic
554C4#1062314311yescharacteristic
555C2—228no—
556C2#1307143711yescharacteristic
557C2C2×D11×#10311yescharacteristic
558C2#1307714411yescharacteristic
559C2#1308031111yescharacteristic
560C2#1308036611yescharacteristic
561C2#1308048011yescharacteristic
562C2#1308049111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1956D11
hypocenterC11D4×#103
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
3. C2×D11×#103C2semidirect
5. #13069540C2semidirect
6. #13069036C2semidirect
7. #13068920C2semidirect
8. #13068618C2semidirect
9. #13068549C2semidirect
10. C4×#66880C2semidirect
11. C11×#1956C2semidirect
17. #10623258C4semidirect
51. C2×Q8×D11C2×C4semidirect
61. C11×C4⋊Q8C2×C4semidirect
69. #66999C2×C4semidirect
95. C4×Dic22C2×C4semidirect
105. #66880D4semidirect
192. #1956D11semidirect
243. D44#103semidirect
254. Dic22C4×D4semidirect
304. C2×D11C2×#103semidirect
308. C4×C11C2×#103semidirect
339. C4⋊Q8C4×D11semidirect
467. C11D4×#103semidirect
550. C4D11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×C8×D442
C2×D11×#1032
#130715162
#130695402
#130690362
#130689202
#130686182
#130685492
C4×#668802
C11×#19562
D4×#10311