Finite Group Databasebeta

← #14960746

Subgroups — #14960746

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13076904C212yesmaximal, complemented
4#13074966C218yesmaximal, complemented
5#13074865C218yesmaximal, complemented
6#13074424C212yesmaximal, complemented
7#13073991C212yesmaximal, complemented
8#13072267C212yesmaximal, complemented
9#13071944C212yesmaximal, complemented
10#13071944C212yesmaximal, complemented
11C11×#2312C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C2×#66977C2212yes—
20C2×#66977C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C2×#66950C2214yescomplemented
23C2×#66939C2214yescomplemented
24C2×#66939C2214yescomplemented
25C2×#66937—28no—
26C2×#66937C2218yes—
27#10623014—28no—
28C2×#66931C2214yescomplemented
29C2×#66931C2214yescomplemented
30C2×#66928C2214yescomplemented
31C11×#388C2218yescomplemented
32C11×#380C2212yes—
33C11×#379C2212yes—
34C4×C11×C22⋊C4C2212yes—
35#10622607C2218yescomplemented
36#10622600C2214yescomplemented
37#10622574C2218yescomplemented
38#10622574C2218yescomplemented
39#10622571C2214yescomplemented
40#10622571C2214yescomplemented
41#10622568C2214yes—
42#10622568C2214yes—
43#10622563C2214yes—
44#10622563C2214yes—
45#10622552C2214yescomplemented
46#10622541C2218yescomplemented
47#10622290C2214yescomplemented
48#10622286C2214yescomplemented
49#10622285C2218yescomplemented
50#10622281C2218yescomplemented
51#10622274C2214yescomplemented
52#10622269C2214yescomplemented
53C25×C11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11C2314yes—
63C22×C22⋊D11C2314yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C22×D44—24no—
69C22×D44—44no—
70C22×D44C2314yes—
71C22×C4×D11—24no—
72C22×C4×D11—44no—
73C22×C4×D11C2314yes—
74C22×Dic22C2312yes—
75C22×Dic22C2312yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4D418yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C42×C11C2314yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2314yes—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2318yes—
95C2×C4⋊Dic11C2318yes—
96#66977—28no—
97#66977—28no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102#66950—48no—
103#66939—48no—
104#66939—48no—
105#66937—232no—
106#66931—216no—
107#66931—216no—
108#66928—48no—
109C11×#95C2314yes—
110C11×#95C2314yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113#36718—111nomaximal, Sylow
114C24×C11—24no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11C2×D414yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—42no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11C2412yes—
129C23×D11C2412yes—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2418yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—28no—
141C2×C22⋊D11—44no—
142C2×C22⋊D11—44no—
143C2×C22⋊D11—416no—
144C2×C22⋊D11—416no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—42no—
151C22×Dic11—44no—
152C22×Dic11—44no—
153C22×Dic11C2412yes—
154C22×Dic11C2414yes—
155C22×Dic11C2414yes—
156C22×Dic11C2412yes—
157C2×D44—28no—
158C2×D44—28no—
159C2×D44—44no—
160C2×D44—416no—
161C2×C4×D11—28no—
162C2×C4×D11—28no—
163C2×C4×D11—44no—
164C2×C4×D11—416no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C11×C4⋊C4—44no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4C2×D4116yes—
174C42×C11—44no—
175C22⋊Dic11—28no—
176C22⋊Dic11—28no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182C4⋊Dic11—216no—
183C4⋊Dic11—24no—
184C4⋊Dic11—24no—
185C4⋊Dic11—48no—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189C2×#543—111no—
190C22×#121—111no—
191#2848—112no—
192#2681—118no—
193#2672—118no—
194#2626—112no—
195#2583—112no—
196#2435—112no—
197#2405—112no—
198#2405—112no—
199#2312D1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—28no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—88no—
209C23×C11C22×D414yes—
210C23×C11C22×D412yes—
211C23×C112−1+414yes—
212C23×C11C2511yescharacteristic
213C22×D11—28no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—416no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—88no—
229C22×D11H(5,𝔽2)14yes—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—28no—
233C2×C4×C11—28no—
234C2×C4×C11—28no—
235C2×C4×C11—44no—
236C2×C4×C11—44no—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D414yes—
239C22⋊D11—416no—
240C22⋊D11—416no—
241C2×Dic11—28no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—28no—
248C2×Dic11—24no—
249C2×Dic11—28no—
250C2×Dic11—44no—
251C2×Dic11—84no—
252C2×Dic11—84no—
253C2×Dic11H(5,𝔽2)14yes—
254D44—416no—
255C4×D11—416no—
256Dic22—84no—
257Dic22—84no—
258C23×D4—111no—
259C23×D4—111no—
260C23×D4—111no—
261C24×C4—111no—
262#543—228no—
263C2×#124—114no—
264C2×#123—114no—
265C2×#123—114no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—114no—
269C2×C22⋊Q8—114no—
270C2×C22⋊Q8—114no—
271C2×#121—118no—
272C2×#121—228no—
273C22×C4⋊C4—111no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4C2×D1111yescharacteristic
277#399—114no—
278#398—114no—
279#396—118no—
280#395—114no—
281#394—118no—
282#394—118no—
283#394—118no—
284#393—114no—
285#390—114no—
286#389—118no—
287#388C2×D1118yescomplemented
288#386—114no—
289#386—114no—
290#385—114no—
291#385—114no—
292#385—118no—
293#380—114no—
294#380C2×D1112yes—
295#379—114no—
296#379—114no—
297#379C2×D1112yes—
298C4×C22⋊C4C2×D1112yes—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—28no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—48no—
306C22×C11—88no—
307C22×C11#53614yes—
308C22×C11C23×D411yescharacteristic
309C22×C11C2×H(5,𝔽2)12yes—
310C22×C11C2×H(5,𝔽2)12yes—
311C22×C11C2×2−1+412yes—
312C2×D11—24no—
313C2×D11—28no—
314C2×D11—416no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—44no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—48no—
322C2×D11—88no—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—48no—
326Dic11—24no—
327Dic11—44no—
328Dic11—44no—
329Dic11—42no—
330C25—111no—
331C25—111no—
332C25C22×D1111yescharacteristic
333C22×Q8—112no—
334C22×Q8—112no—
335C22×D4—114no—
336C22×D4—114no—
337C22×D4—114no—
338C22×D4—224no—
339C22×D4—224no—
340C22×D4—224no—
341C22×D4—444no—
342C22×D4—444no—
343C22×D4—444no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—114no—
349C23×C4—224no—
350C23×C4—444no—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353#124—448no—
354#123—448no—
355#123—448no—
356C22⋊Q8—228no—
357C22⋊Q8—228no—
358C22⋊Q8—2216no—
359C22⋊Q8—2216no—
360C22⋊Q8—448no—
361#121—2232no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—118no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4C22×D1114yes—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4D4418yes—
381C2×C22⋊C4C22×D1114yes—
382C2×C22⋊C4C22×D1114yes—
383C2×C22⋊C4C22×D1114yes—
384C2×C22⋊C4C22×D1114yes—
385C2×C42C22×D1114yes—
386#95—118no—
387#95—118no—
388#95C22×D1114yes—
389#95C22×D1114yes—
390C2×C11—24no—
391C2×C11—44no—
392C2×C11C2×#53611yescharacteristic
393C2×C11#348411yescharacteristic
394C2×C11#348411yescharacteristic
395C2×C11#353614yes—
396D11—44no—
397D11—82no—
398C24—24no—
399C24—42no—
400C24—42no—
401C24—112no—
402C24—112no—
403C24—224no—
404C24—222no—
405C24—222no—
406C24—224no—
407C24—224no—
408C24—442no—
409C24—442no—
410C24—442no—
411C24C2×D4414yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×Q8—224no—
415C2×Q8—224no—
416C2×Q8—444no—
417C2×Q8—444no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—228no—
424C2×D4—444no—
425C2×D4—4416no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—4416no—
429C2×D4—4416no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—228no—
443C22×C4—444no—
444C22×C4—4416no—
445C22×C4—442no—
446C22×C4—444no—
447C22×C4—444no—
448C22×C4C2×D4414yes—
449C22×C4C2×D4414yes—
450C22×C4C23×D1118yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—44no—
454C4⋊C4—2216no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—448no—
461C22⋊C4—28no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—2216no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C22⋊C4C2×D44116yes—
472C42—44no—
473C11#3671811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—28no—
480C23—44no—
481C23—44no—
482C23—88no—
483C23—114no—
484C23—228no—
485C23—222no—
486C23—224no—
487C23—224no—
488C23—222no—
489C23—222no—
490C23—224no—
491C23—224no—
492C23—224no—
493C23—4416no—
494C23—444no—
495C23—444no—
496C23—444no—
497C23—444no—
498C23—444no—
499C23—888no—
500C23C22×D4414yes—
501C23C22×D4412yes—
502C23#6704314yes—
503C23C24×D1111yescharacteristic
504Q8—884no—
505Q8—884no—
506D4—4416no—
507D4—4416no—
508D4—4416no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—28no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—114no—
517C2×C4—228no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—228no—
525C2×C4—224no—
526C2×C4—4416no—
527C2×C4—444no—
528C2×C4—884no—
529C2×C4—884no—
530C2×C4C22×D4414yes—
531C2×C4C22×D4414yes—
532C22—22no—
533C22—22no—
534C22—28no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—48no—
539C22—88no—
540C22—224no—
541C22—228no—
542C22—4416no—
543C22—442no—
544C22—442no—
545C22—444no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—448no—
550C22—888no—
551C22#1062305714yes—
552C22C23×D4411yescharacteristic
553C22C2×#6704312yes—
554C22D11×H(5,𝔽2)12yes—
555C22D11×H(5,𝔽2)12yes—
556C4—24no—
557C4—24no—
558C4—48no—
559C4—224no—
560C4—442no—
561C4—444no—
562C4—444no—
563C2—24no—
564C2—44no—
565C2—444no—
566C2—882no—
567C2C2×#1062305711yescharacteristic
568C2#1308225211yescharacteristic
569C2#1308225211yescharacteristic
570C2#1308283714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2312C2
prime radicalC22×#66937C2
hypercenter#2312D11
hypocenterC11#36718
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2312

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13076904C2semidirect
4. #13074966C2semidirect
5. #13074865C2semidirect
6. #13074424C2semidirect
7. #13073991C2semidirect
8. #13072267C2semidirect
9. #13071944C2semidirect
10. #13071944C2semidirect
11. C11×#2312C2semidirect
22. C2×#66950C22semidirect
23. C2×#66939C22semidirect
24. C2×#66939C22semidirect
28. C2×#66931C22semidirect
29. C2×#66931C22semidirect
30. C2×#66928C22semidirect
31. C11×#388C22semidirect
35. #10622607C22semidirect
36. #10622600C22semidirect
37. #10622574C22semidirect
38. #10622574C22semidirect
39. #10622571C22semidirect
40. #10622571C22semidirect
45. #10622552C22semidirect
46. #10622541C22semidirect
47. #10622290C22semidirect
48. #10622286C22semidirect
49. #10622285C22semidirect
50. #10622281C22semidirect
51. #10622274C22semidirect
52. #10622269C22semidirect
199. #2312D11semidirect
287. #388C2×D11semidirect
473. C11#36718semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
C22×#669372
#130769042
#130749662
#130748652
#130744242
#130739912
#130722672
#130719442
C11×#23122
#3671811