Finite Group Databasebeta

← D11×#2815 #14959893

Subgroups — D11×#2815 #14959893

Order 2816.

3774 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C212yesmaximal, complemented
2#13076641C214yesmaximal, complemented
3#13076640C211yesmaximal, characteristic, complemented
4#13076639C214yesmaximal, complemented
5#13076638C212yesmaximal, complemented
6#13076637C214yesmaximal, complemented
7D11×#397C214yesmaximal, complemented
8D11×#392C214yesmaximal, complemented
9D11×#392C214yesmaximal, complemented
10D11×#381C211yesmaximal, characteristic, complemented
11C11×#2815C211yesmaximal, characteristic, complemented
12C22×D4×D11C2214yes—
13C22×D4×D11C2212yes—
14C22×D4×D11C2214yes—
15C23×C4×D11C2211yescharacteristic
16C2×C11×#121C2212yescomplemented
17C2×#66992C2214yescomplemented
18C2×#66991C2212yescomplemented
19C2×#66983C2212yescomplemented
20D11×#121—216no—
21C2×#66948C2212yescomplemented
22C2×C4⋊C4×D11C2212yes—
23C2×#66937C2214yescomplemented
24C2×C22⋊C4×D11C2214yes—
25C2×C22⋊C4×D11C2212yes—
26C2×C22⋊C4×D11C2218yes—
27C11×#397C2214yescomplemented
28C11×#392C2214yescomplemented
29C11×#392C2214yescomplemented
30C11×#381C2211yescharacteristic, complemented
31#10622836C2214yescomplemented
32#10622836C2214yescomplemented
33#10622836C2218yescomplemented
34#10622836C2218yescomplemented
35#10622824C2211yescharacteristic, complemented
36#10622606C2214yescomplemented
37#10622573C2218yescomplemented
38#10622573C2214yescomplemented
39#10622573C2218yescomplemented
40#10622573C2214yescomplemented
41#10622566C2214yescomplemented
42#10622565C2218yescomplemented
43#10622556C2212yescomplemented
44#10622288C2218yescomplemented
45#10622287C2214yescomplemented
46#10622284C2214yescomplemented
47#10622284C2214yescomplemented
48#10622277C2214yescomplemented
49D11×#95C2214yes—
50D11×#95C2214yes—
51C24×D11C2314yes—
52C24×D11C2311yescharacteristic
53C22×D4×C11C2312yes—
54C22×D4×C11C2314yes—
55C22×D4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11C2314yes—
58C22×C22⋊D11C2314yes—
59C22×C22⋊D11C2314yes—
60C22×C22⋊D11C2318yes—
61C23×Dic11C2311yescharacteristic
62C2×D4×D11—216no—
63C2×D4×D11—28no—
64C2×D4×D11—48no—
65C2×D4×D11—416no—
66C2×D4×D11—48no—
67C2×D4×D11—416no—
68C22×D44C2314yes—
69C22×D44C2312yes—
70C22×D44C2314yes—
71C22×C4×D11—44no—
72C22×C4×D11D418yescomplemented
73C22×C4×D11C2314yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2312yes—
76C22×C4×D11C2312yes—
77C11×#121—28no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2312yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2312yes—
84C2×C22⋊Dic11C2318yes—
85#66992—216no—
86#66991—28no—
87#66983—28no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11C2312yes—
94C2×Dic11⋊C4C2314yes—
95#66948—28no—
96C4⋊C4×D11—28no—
97#66937—216no—
98C22⋊C4×D11—216no—
99C22⋊C4×D11—44no—
100C22⋊C4×D11—416no—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C2×#2815—111nomaximal, Sylow
108C24×C11C2414yes—
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—28no—
112C23×D11—28no—
113C23×D11—28no—
114C23×D11—216no—
115C23×D11—216no—
116C23×D11—28no—
117C23×D11C2×D414yes—
118C23×D11C2414yes—
119C23×D11C2411yescharacteristic
120C23×D11C2411yescharacteristic
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—44no—
124C2×D4×C11—48no—
125C2×D4×C11—44no—
126C2×D4×C11—48no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D414yescomplemented
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C2×C22⋊D11—28no—
133C2×C22⋊D11—28no—
134C2×C22⋊D11—28no—
135C2×C22⋊D11—48no—
136C2×C22⋊D11—48no—
137C2×C22⋊D11—48no—
138C2×C22⋊D11—48no—
139C2×C22⋊D11—48no—
140C2×C22⋊D11—48no—
141C22×Dic11—42no—
142C22×Dic11C2×D414yescomplemented
143C22×Dic11C2414yes—
144C22×Dic11C2414yes—
145C22×Dic11C2412yes—
146D4×D11—464no—
147D4×D11—432no—
148D4×D11—464no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—44no—
152C2×D44—48no—
153C2×D44—44no—
154C2×D44—48no—
155C2×C4×D11—28no—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—216no—
159C2×C4×D11—216no—
160C2×C4×D11—44no—
161C2×C4×D11—416no—
162C2×C4×D11C2×D418yes—
163C2×C4×D11C2×D418yescomplemented
164C11×C4⋊C4—24no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—48no—
168C22⋊Dic11—28no—
169C22⋊Dic11—42no—
170C22⋊Dic11—48no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—48no—
175(C2×D11)⋊C4—48no—
176C4⋊Dic11—24no—
177Dic11⋊C4—28no—
178C22×#121—112no—
179#2815—114no—
180#2815—114no—
181#2815—114no—
182#2815—111no—
183#2815—112no—
184#2815D1111yescharacteristic, direct product factor
185C2×#397—114no—
186C2×#392—114no—
187C2×#392—114no—
188C2×#381—111no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—24no—
196C23×C11C22×D412yes—
197C23×C11C2511yescharacteristic
198C22×D11—22no—
199C22×D11—24no—
200C22×D11—28no—
201C22×D11—216no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—28no—
205C22×D11—24no—
206C22×D11—28no—
207C22×D11—416no—
208C22×D11—416no—
209C22×D11—416no—
210C22×D11—416no—
211C22×D11—432no—
212C22×D11—432no—
213C22×D11C22×D412yes—
214C22×D11C22×D412yes—
215C22×D11H(5,𝔽2)14yes—
216C22×D11H(5,𝔽2)18yes—
217D4×C11—48no—
218D4×C11—416no—
219D4×C11—416no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—28no—
223C2×C4×C11—24no—
224C2×C4×C11—28no—
225C2×C4×C11—44no—
226C2×C4×C11C22×D414yes—
227C22⋊D11—416no—
228C22⋊D11—416no—
229C22⋊D11—416no—
230C22⋊D11—432no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—28no—
234C2×Dic11—24no—
235C2×Dic11—28no—
236C2×Dic11—44no—
237C2×Dic11C22×D414yes—
238D44—48no—
239D44—416no—
240D44—416no—
241C4×D11—216no—
242C4×D11—48no—
243C4×D11—416no—
244C4×D11—416no—
245C23×D4—112no—
246C23×D4—114no—
247C23×D4—114no—
248C24×C4—111no—
249C2×#121—112no—
250C2×#121—114no—
251C2×#121—112no—
252C2×#121—112no—
253C2×#121—114no—
254C2×#121—2216no—
255C2×#121C2×D1112yescomplemented
256C22×C4⋊C4—112no—
257C22×C22⋊C4—114no—
258C22×C22⋊C4—118no—
259C22×C22⋊C4—112no—
260#397—114no—
261#397—118no—
262#397—114no—
263#397—114no—
264#397—118no—
265#397C2×D1114yescomplemented
266#392—118no—
267#392—114no—
268#392—118no—
269#392—114no—
270#392—118no—
271#392—114no—
272#392—118no—
273#392—114no—
274#392—114no—
275#392—114no—
276#392C2×D1114yescomplemented
277#392C2×D1114yescomplemented
278#381—111no—
279#381—112no—
280#381—114no—
281#381C2×D1111yescharacteristic, complemented
282C2×#95—114no—
283C2×#95—114no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—48no—
291C22×C11—48no—
292C22×C11C23×D411yescharacteristic
293C22×C11C2×H(5,𝔽2)12yes—
294C22×C11C2×H(5,𝔽2)14yes—
295C2×D11—22no—
296C2×D11—24no—
297C2×D11—44no—
298C2×D11—416no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—48no—
303C2×D11—48no—
304C2×D11—832no—
305C2×D11#53414yes—
306C2×D11#53518yes—
307C2×D11#560116yes—
308C4×C11—24no—
309C4×C11—44no—
310C4×C11—44no—
311Dic11—24no—
312Dic11—44no—
313Dic11—44no—
314C25—111no—
315C25—114no—
316C22×D4—114no—
317C22×D4—114no—
318C22×D4—114no—
319C22×D4—118no—
320C22×D4—114no—
321C22×D4—112no—
322C22×D4—114no—
323C22×D4—228no—
324C22×D4—2216no—
325C22×D4—448no—
326C22×D4—4416no—
327C22×D4—448no—
328C22×D4—4416no—
329C22×D4C22×D1114yes—
330C22×D4C22×D1112yes—
331C22×D4C22×D1114yes—
332C23×C4—111no—
333C23×C4—112no—
334C23×C4—118no—
335C23×C4—112no—
336C23×C4—114no—
337C23×C4—114no—
338C23×C4—444no—
339C23×C4C22×D1111yescharacteristic
340#121—28no—
341#121—2216no—
342#121—228no—
343#121—228no—
344#121—2216no—
345#121—228no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—114no—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—112no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—118no—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—2216no—
359C2×C22⋊C4—444no—
360C2×C22⋊C4—4416no—
361C2×C22⋊C4C22×D1114yes—
362C2×C22⋊C4C22×D1112yes—
363C2×C22⋊C4C22×D1118yes—
364#95—118no—
365#95—114no—
366#95—118no—
367#95—114no—
368#95C22×D1114yes—
369#95C22×D1114yes—
370C2×C11—42no—
371C2×C11—84no—
372C2×C11C2×#53411yescharacteristic
373C2×C11C2×#53512yes—
374C2×C11C2×#56014yes—
375D11—42no—
376D11—84no—
377D11#281518yesdirect product factor
378C24—111no—
379C24—114no—
380C24—111no—
381C24—114no—
382C24—224no—
383C24—228no—
384C24—228no—
385C24—228no—
386C24—2216no—
387C24—2216no—
388C24—228no—
389C24C23×D1114yes—
390C24C23×D1111yescharacteristic
391C2×D4—28no—
392C2×D4—24no—
393C2×D4—44no—
394C2×D4—48no—
395C2×D4—44no—
396C2×D4—48no—
397C2×D4—228no—
398C2×D4—228no—
399C2×D4—228no—
400C2×D4—228no—
401C2×D4—224no—
402C2×D4—444no—
403C2×D4—448no—
404C2×D4—444no—
405C2×D4—448no—
406C2×D4—4432no—
407C2×D4—448no—
408C2×D4—448no—
409C2×D4—448no—
410C2×D4—448no—
411C2×D4—448no—
412C2×D4—448no—
413C2×D4—4464no—
414C2×D4—4464no—
415C22×C4—42no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—118no—
419C22×C4—118no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—228no—
423C22×C4—228no—
424C22×C4—2216no—
425C22×C4—228no—
426C22×C4—2216no—
427C22×C4—444no—
428C22×C4—4416no—
429C22×C4—442no—
430C22×C4D4×D1114yescomplemented
431C22×C4C23×D1114yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1112yes—
434C4⋊C4—24no—
435C4⋊C4—228no—
436C4⋊C4—224no—
437C22⋊C4—28no—
438C22⋊C4—42no—
439C22⋊C4—48no—
440C22⋊C4—228no—
441C22⋊C4—228no—
442C22⋊C4—228no—
443C22⋊C4—444no—
444C22⋊C4—448no—
445C22⋊C4—448no—
446C22⋊C4—442no—
447C22⋊C4—448no—
448C11C2×#281511yescharacteristic, complemented, Sylow
449C23—22no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—28no—
454C23—28no—
455C23—24no—
456C23—112no—
457C23—114no—
458C23—118no—
459C23—112no—
460C23—228no—
461C23—2216no—
462C23—222no—
463C23—224no—
464C23—224no—
465C23—224no—
466C23—228no—
467C23—228no—
468C23—224no—
469C23—4416no—
470C23—4416no—
471C23—4416no—
472C23—4432no—
473C23—4416no—
474C23—4432no—
475C23C2×D4×D1112yes—
476C23C24×D1111yescharacteristic
477D4—48no—
478D4—416no—
479D4—416no—
480D4—448no—
481D4—4416no—
482D4—4416no—
483D4—4416no—
484D4—4416no—
485D4—4416no—
486D4—4432no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—28no—
490C2×C4—24no—
491C2×C4—28no—
492C2×C4—44no—
493C2×C4—114no—
494C2×C4—2216no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—228no—
498C2×C4—224no—
499C2×C4—228no—
500C2×C4—448no—
501C2×C4—4416no—
502C2×C4—4416no—
503C2×C4—444no—
504C2×C4C2×D4×D1114yes—
505C22—22no—
506C22—24no—
507C22—44no—
508C22—44no—
509C22—44no—
510C22—44no—
511C22—48no—
512C22—48no—
513C22—114no—
514C22—118no—
515C22—1116no—
516C22—222no—
517C22—224no—
518C22—4416no—
519C22—444no—
520C22—444no—
521C22—444no—
522C22—444no—
523C22—448no—
524C22—448no—
525C22—8832no—
526C22C22×D4×D1111yescharacteristic
527C22D11×H(5,𝔽2)12yes—
528C22D11×H(5,𝔽2)14yes—
529C4—24no—
530C4—44no—
531C4—44no—
532C4—224no—
533C4—444no—
534C4—444no—
535C2—42no—
536C2—84no—
537C2—118no—
538C2—442no—
539C2—884no—
540C2D11×#53411yescharacteristic
541C2D11×#53512yes—
542C2D11×#56014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2815C2
hypercenter#2815D11
hypocenterC11C2×#2815
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2815

Complements

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

NH ≅ G/Ntype
1. C2×D11×#121C2semidirect
2. #13076641C2semidirect
3. #13076640C2semidirect
4. #13076639C2semidirect
5. #13076638C2semidirect
6. #13076637C2semidirect
7. D11×#397C2semidirect
8. D11×#392C2semidirect
9. D11×#392C2semidirect
10. D11×#381C2semidirect
11. C11×#2815C2semidirect
16. C2×C11×#121C22semidirect
17. C2×#66992C22semidirect
18. C2×#66991C22semidirect
19. C2×#66983C22semidirect
21. C2×#66948C22semidirect
23. C2×#66937C22semidirect
27. C11×#397C22semidirect
28. C11×#392C22semidirect
29. C11×#392C22semidirect
30. C11×#381C22semidirect
31. #10622836C22semidirect
32. #10622836C22semidirect
33. #10622836C22semidirect
34. #10622836C22semidirect
35. #10622824C22semidirect
36. #10622606C22semidirect
37. #10622573C22semidirect
38. #10622573C22semidirect
39. #10622573C22semidirect
40. #10622573C22semidirect
41. #10622566C22semidirect
42. #10622565C22semidirect
43. #10622556C22semidirect
44. #10622288C22semidirect
45. #10622287C22semidirect
46. #10622284C22semidirect
47. #10622284C22semidirect
48. #10622277C22semidirect
72. C22×C4×D11D4semidirect
128. C22×C4×C11C2×D4semidirect
142. C22×Dic11C2×D4semidirect
163. C2×C4×D11C2×D4semidirect
184. #2815D11direct (N × H)
255. C2×#121C2×D11semidirect
265. #397C2×D11semidirect
276. #392C2×D11semidirect
277. #392C2×D11semidirect
281. #381C2×D11semidirect
377. D11#2815direct (N × H)
430. C22×C4D4×D11semidirect
448. C11C2×#2815semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
#130766412
#130766402
#130766392
#130766382
#130766372
D11×#3972
D11×#3922
D11×#3812
C11×#28152
C2×#281511