Finite Group Databasebeta

← D11×#2812 #14959887

Subgroups — D11×#2812 #14959887

Order 2816.

4438 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#120C212yesmaximal, complemented
2#13076614C213yesmaximal, complemented
3#13076613C211yesmaximal, characteristic, complemented
4#13076612C216yesmaximal, complemented
5#13076611C212yesmaximal, complemented
6#13076610C213yesmaximal, complemented
7D11×#397C213yesmaximal, complemented
8D11×#394C216yesmaximal, complemented
9D11×#392C213yesmaximal, complemented
10D11×#379C211yesmaximal, characteristic, complemented
11C11×#2812C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C22×D4×D11C2216yes—
14C22×D4×D11C2211yescharacteristic, complemented
15C2×C11×#120C2212yescomplemented
16C2×#67006C2212yescomplemented
17C2×#66990C2216yescomplemented
18D11×#120—216no—
19C2×C4⋊C4×D11C2213yescomplemented
20C2×#66935C2216yescomplemented
21C2×C22⋊C4×D11C2216yes—
22C2×C22⋊C4×D11C2213yes—
23C2×C22⋊C4×D11C2213yes—
24C2×C22⋊C4×D11C2216yescomplemented
25C11×#397C2213yescomplemented
26C11×#394C2216yescomplemented
27C11×#392C2213yescomplemented
28C11×#379C2211yescharacteristic, complemented
29#10622860C2211yescharacteristic, complemented
30#10622836C2213yescomplemented
31#10622836C2216yescomplemented
32#10622835C2216yescomplemented
33#10622606C2213yescomplemented
34#10622604C2216yescomplemented
35#10622574C2216yescomplemented
36#10622574C2216yescomplemented
37#10622573C2216yescomplemented
38#10622573C2213yescomplemented
39#10622572C2216yescomplemented
40#10622572C2216yescomplemented
41#10622568C2213yescomplemented
42#10622568C2213yescomplemented
43#10622566C2213yescomplemented
44#10622565C2216yescomplemented
45#10622288C2216yescomplemented
46#10622287C2213yescomplemented
47#10622285C2216yescomplemented
48#10622284C2213yescomplemented
49D11×#95C2213yescomplemented
50D11×#95C2213yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11—46no—
53C24×D11—46no—
54C24×D11D418yescomplemented
55C24×D11C2312yes—
56C24×D11C2313yes—
57C24×D11C2313yes—
58C22×D4×C11C2316yes—
59C22×D4×C11C2311yescharacteristic, complemented
60C22×C22⋊D11C2316yes—
61C22×C22⋊D11C2316yes—
62C22×C22⋊D11C2312yescomplemented
63C2×D4×D11—224no—
64C2×D4×D11—412no—
65C2×D4×D11—412no—
66C2×D4×D11—46no—
67C22×D44C2316yes—
68C22×D44C2311yescharacteristic, complemented
69C22×C4×D11C2313yes—
70C22×C4×D11C2311yescharacteristic
71C22×C4×D11C2316yes—
72C11×#120—28no—
73C2×C11×C4⋊C4C2313yescomplemented
74C2×C11×C22⋊C4C2316yes—
75C2×C11×C22⋊C4C2313yes—
76C2×C11×C22⋊C4C2313yes—
77C2×C11×C22⋊C4C2316yescomplemented
78#67006—28no—
79C2×C22⋊Dic11C2316yes—
80C2×C22⋊Dic11C2313yes—
81C2×C22⋊Dic11C2313yes—
82C2×C22⋊Dic11C2316yescomplemented
83#66990—224no—
84C2×(C2×D11)⋊C4C2316yes—
85C2×(C2×D11)⋊C4C2316yes—
86C2×(C2×D11)⋊C4C2313yes—
87C2×(C2×D11)⋊C4C2316yes—
88C2×(C2×D11)⋊C4C2313yes—
89C2×(C2×D11)⋊C4C2316yescomplemented
90C2×(C2×D11)⋊C4C2316yescomplemented
91C2×C4⋊Dic11C2313yescomplemented
92C2×Dic11⋊C4C2316yescomplemented
93C4⋊C4×D11—46no—
94#66935—224no—
95C22⋊C4×D11—224no—
96C22⋊C4×D11—46no—
97C22⋊C4×D11—46no—
98C22⋊C4×D11—412no—
99C11×#95C2313yescomplemented
100C11×#95C2313yescomplemented
101C11⋊#95C2316yescomplemented
102C11⋊#95C2313yescomplemented
103C11⋊#95C2316yescomplemented
104C11⋊#95C2313yescomplemented
105C2×#2812—111nomaximal, Sylow
106C24×C11—43no—
107C24×C11—43no—
108C24×C11C2×D414yescomplemented
109C24×C11C2412yes—
110C24×C11C2413yes—
111C23×D11—26no—
112C23×D11—26no—
113C23×D11—212no—
114C23×D11—212no—
115C23×D11—24no—
116C23×D11—212no—
117C23×D11—212no—
118C23×D11—448no—
119C23×D11—46no—
120C23×D11—46no—
121C23×D11—43no—
122C23×D11—43no—
123C23×D11—448no—
124C23×D11—416no—
125C23×D11C2×D4112yes—
126C23×D11C2×D4112yescomplemented
127C23×D11C2412yes—
128C23×D11C2413yes—
129C23×D11C2411yescharacteristic
130C2×D4×C11—212no—
131C2×D4×C11—46no—
132C2×D4×C11—46no—
133C2×D4×C11—43no—
134C22×C4×C11C2411yescharacteristic
135C22×C4×C11C2416yes—
136C22×C4×C11C2413yes—
137C2×C22⋊D11—212no—
138C2×C22⋊D11—212no—
139C2×C22⋊D11—46no—
140C2×C22⋊D11—46no—
141C2×C22⋊D11—46no—
142C2×C22⋊D11—46no—
143C2×C22⋊D11—46no—
144C22×Dic11C2411yescharacteristic
145C22×Dic11C2416yes—
146C22×Dic11C2413yes—
147D4×D11—496no—
148D4×D11—416no—
149C2×D44—212no—
150C2×D44—46no—
151C2×D44—46no—
152C2×D44—43no—
153C2×C4×D11—212no—
154C2×C4×D11—212no—
155C2×C4×D11—26no—
156C2×C4×D11—212no—
157C2×C4×D11—26no—
158C2×C4×D11—212no—
159C11×C4⋊C4—43no—
160C11×C22⋊C4—212no—
161C11×C22⋊C4—43no—
162C11×C22⋊C4—43no—
163C11×C22⋊C4—46no—
164C22⋊Dic11—212no—
165C22⋊Dic11—43no—
166C22⋊Dic11—43no—
167C22⋊Dic11—46no—
168(C2×D11)⋊C4—212no—
169(C2×D11)⋊C4—212no—
170(C2×D11)⋊C4—43no—
171(C2×D11)⋊C4—46no—
172(C2×D11)⋊C4—43no—
173(C2×D11)⋊C4—46no—
174(C2×D11)⋊C4—46no—
175C4⋊Dic11—43no—
176Dic11⋊C4—46no—
177C22×#120—112no—
178#2812—113no—
179#2812—116no—
180#2812—113no—
181#2812—111no—
182#2812—112no—
183#2812D1111yescharacteristic, direct product factor
184C2×#397—113no—
185C2×#394—116no—
186C2×#392—113no—
187C2×#379—111no—
188C23×C11—23no—
189C23×C11—23no—
190C23×C11—26no—
191C23×C11—26no—
192C23×C11—22no—
193C23×C11—26no—
194C23×C11—26no—
195C23×C11—412no—
196C23×C11—412no—
197C23×C11—44no—
198C23×C11C22×D416yes—
199C23×C11C2511yescharacteristic
200C22×D11—23no—
201C22×D11—23no—
202C22×D11—26no—
203C22×D11—26no—
204C22×D11—248no—
205C22×D11—224no—
206C22×D11—22no—
207C22×D11—26no—
208C22×D11—26no—
209C22×D11—424no—
210C22×D11—412no—
211C22×D11—412no—
212C22×D11—424no—
213C22×D11—412no—
214C22×D11—4128no—
215C22×D11—424no—
216C22×D11—412no—
217C22×D11—412no—
218C22×D11—424no—
219C22×D11—424no—
220C22×D11—48no—
221C22×D11C22×D416yes—
222C22×D11C22×D412yes—
223C22×D11H(5,𝔽2)16yes—
224C22×D11H(5,𝔽2)16yes—
225D4×C11—424no—
226D4×C11—44no—
227C2×C4×C11—26no—
228C2×C4×C11—26no—
229C2×C4×C11—23no—
230C2×C4×C11—26no—
231C2×C4×C11—26no—
232C2×C4×C11—23no—
233C22⋊D11—424no—
234C22⋊D11—424no—
235C22⋊D11—48no—
236C2×Dic11—26no—
237C2×Dic11—23no—
238C2×Dic11—26no—
239C2×Dic11—26no—
240C2×Dic11—26no—
241C2×Dic11—23no—
242D44—424no—
243D44—44no—
244C4×D11—424no—
245C4×D11—412no—
246C4×D11—44no—
247C26—111no—
248C23×D4—116no—
249C23×D4—111no—
250C2×#120—112no—
251C2×#120—116no—
252C2×#120—116no—
253C2×#120—2216no—
254C2×#120C2×D1112yescomplemented
255C22×C4⋊C4—113no—
256C22×C22⋊C4—116no—
257C22×C22⋊C4—113no—
258C22×C22⋊C4—113no—
259C22×C22⋊C4—116no—
260#397—113no—
261#397—116no—
262#397—113no—
263#397—113no—
264#397—116no—
265#397C2×D1113yescomplemented
266#394—116no—
267#394—116no—
268#394—116no—
269#394—116no—
270#394—116no—
271#394—116no—
272#394—116no—
273#394C2×D1116yescomplemented
274#392—116no—
275#392—113no—
276#392—113no—
277#392—116no—
278#392—113no—
279#392C2×D1113yescomplemented
280#379—111no—
281#379—113no—
282#379—113no—
283#379C2×D1111yescharacteristic, complemented
284C2×#95—113no—
285C2×#95—113no—
286C22×C11—212no—
287C22×C11—26no—
288C22×C11—416no—
289C22×C11—46no—
290C22×C11—43no—
291C22×C11—43no—
292C22×C11—46no—
293C22×C11—46no—
294C22×C11—42no—
295C22×C11C23×D411yescharacteristic
296C22×C11C2×H(5,𝔽2)13yes—
297C22×C11C2×H(5,𝔽2)13yes—
298C2×D11—26no—
299C2×D11—212no—
300C2×D11—448no—
301C2×D11—46no—
302C2×D11—43no—
303C2×D11—43no—
304C2×D11—448no—
305C2×D11—46no—
306C2×D11—46no—
307C2×D11—42no—
308C2×D11—816no—
309C2×D11#534112yes—
310C2×D11#560112yes—
311C2×D11H(3,𝔽4)14yes—
312C4×C11—46no—
313C4×C11—43no—
314C4×C11—41no—
315Dic11—46no—
316Dic11—43no—
317Dic11—41no—
318C25—113no—
319C25—118no—
320C25—113no—
321C25—112no—
322C25—446no—
323C25—446no—
324C25C22×D1111yescharacteristic
325C22×D4—116no—
326C22×D4—116no—
327C22×D4—112no—
328C22×D4—116no—
329C22×D4—111no—
330C22×D4—2224no—
331C22×D4—4412no—
332C22×D4—446no—
333C22×D4—4412no—
334C22×D4C22×D1116yes—
335C22×D4C22×D1111yescharacteristic, complemented
336C23×C4—113no—
337C23×C4—116no—
338C23×C4—111no—
339#120—28no—
340#120—2224no—
341#120—2224no—
342#120—228no—
343C2×C4⋊C4—116no—
344C2×C4⋊C4—113no—
345C2×C4⋊C4—446no—
346C2×C4⋊C4C22×D1113yescomplemented
347C2×C22⋊C4—116no—
348C2×C22⋊C4—116no—
349C2×C22⋊C4—116no—
350C2×C22⋊C4—113no—
351C2×C22⋊C4—113no—
352C2×C22⋊C4—116no—
353C2×C22⋊C4—113no—
354C2×C22⋊C4—113no—
355C2×C22⋊C4—116no—
356C2×C22⋊C4—116no—
357C2×C22⋊C4—116no—
358C2×C22⋊C4—2224no—
359C2×C22⋊C4—446no—
360C2×C22⋊C4—446no—
361C2×C22⋊C4—4412no—
362C2×C22⋊C4C22×D1116yes—
363C2×C22⋊C4C22×D1113yes—
364C2×C22⋊C4C22×D1113yes—
365C2×C22⋊C4C22×D1116yescomplemented
366#95—116no—
367#95—113no—
368#95—113no—
369#95—116no—
370#95C22×D1113yescomplemented
371#95C22×D1113yescomplemented
372C2×C11—46no—
373C2×C11—82no—
374C2×C11C2×#53413yes—
375C2×C11C2×#56013yes—
376C2×C11C2×H(3,𝔽4)11yescharacteristic
377D11—46no—
378D11—82no—
379D11#281218yesdirect product factor
380C24—43no—
381C24—43no—
382C24—111no—
383C24—1112no—
384C24—113no—
385C24—1112no—
386C24—112no—
387C24—226no—
388C24—226no—
389C24—2212no—
390C24—2212no—
391C24—2212no—
392C24—224no—
393C24—2212no—
394C24—443no—
395C24—443no—
396C24—446no—
397C24—446no—
398C24—4448no—
399C24—4448no—
400C24—4416no—
401C24D4×D1114yescomplemented
402C24C23×D1112yes—
403C24C23×D1113yes—
404C2×D4—212no—
405C2×D4—46no—
406C2×D4—46no—
407C2×D4—43no—
408C2×D4—2212no—
409C2×D4—2212no—
410C2×D4—2212no—
411C2×D4—446no—
412C2×D4—443no—
413C2×D4—446no—
414C2×D4—446no—
415C2×D4—446no—
416C2×D4—446no—
417C2×D4—446no—
418C2×D4—446no—
419C2×D4—4496no—
420C2×D4—4416no—
421C22×C4—111no—
422C22×C4—116no—
423C22×C4—113no—
424C22×C4—2212no—
425C22×C4—2212no—
426C22×C4—226no—
427C22×C4—2212no—
428C22×C4—226no—
429C22×C4—2212no—
430C22×C4C23×D1111yescharacteristic
431C22×C4C23×D1116yes—
432C22×C4C23×D1113yes—
433C4⋊C4—43no—
434C4⋊C4—446no—
435C4⋊C4—443no—
436C22⋊C4—212no—
437C22⋊C4—43no—
438C22⋊C4—43no—
439C22⋊C4—46no—
440C22⋊C4—2212no—
441C22⋊C4—2212no—
442C22⋊C4—2212no—
443C22⋊C4—446no—
444C22⋊C4—446no—
445C22⋊C4—443no—
446C22⋊C4—446no—
447C22⋊C4—443no—
448C22⋊C4—443no—
449C22⋊C4—446no—
450C22⋊C4—443no—
451C11C2×#281211yescharacteristic, complemented, Sylow
452C23—23no—
453C23—23no—
454C23—26no—
455C23—26no—
456C23—22no—
457C23—26no—
458C23—26no—
459C23—412no—
460C23—412no—
461C23—44no—
462C23—112no—
463C23—116no—
464C23—116no—
465C23—116no—
466C23—2248no—
467C23—2224no—
468C23—223no—
469C23—223no—
470C23—226no—
471C23—226no—
472C23—222no—
473C23—226no—
474C23—226no—
475C23—4424no—
476C23—4412no—
477C23—4424no—
478C23—4412no—
479C23—4412no—
480C23—4424no—
481C23—448no—
482C23—4424no—
483C23—44128no—
484C23—4424no—
485C23—4412no—
486C23—4412no—
487C23C2×D4×D1116yes—
488C23C24×D1111yescharacteristic
489D4—424no—
490D4—44no—
491D4—4424no—
492D4—444no—
493D4—4424no—
494D4—4424no—
495D4—448no—
496C2×C4—26no—
497C2×C4—26no—
498C2×C4—23no—
499C2×C4—26no—
500C2×C4—23no—
501C2×C4—26no—
502C2×C4—226no—
503C2×C4—226no—
504C2×C4—223no—
505C2×C4—226no—
506C2×C4—223no—
507C2×C4—226no—
508C2×C4—4424no—
509C2×C4—444no—
510C2×C4—4412no—
511C22—212no—
512C22—26no—
513C22—416no—
514C22—46no—
515C22—43no—
516C22—43no—
517C22—46no—
518C22—46no—
519C22—42no—
520C22—1112no—
521C22—1112no—
522C22—114no—
523C22—2212no—
524C22—226no—
525C22—4448no—
526C22—4448no—
527C22—446no—
528C22—443no—
529C22—443no—
530C22—446no—
531C22—446no—
532C22—442no—
533C22—8816no—
534C22C22×D4×D1111yescharacteristic
535C22D11×H(5,𝔽2)13yes—
536C22D11×H(5,𝔽2)13yes—
537C4—46no—
538C4—43no—
539C4—41no—
540C4—446no—
541C4—443no—
542C4—441no—
543C2—46no—
544C2—82no—
545C2—118no—
546C2—446no—
547C2—882no—
548C2D11×#53413yes—
549C2D11×#56013yes—
550C2D11×H(3,𝔽4)11yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2812C2
hypercenter#2812D11
hypocenterC11C2×#2812
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2812

Complements

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

NH ≅ G/Ntype
1. C2×D11×#120C2semidirect
2. #13076614C2semidirect
3. #13076613C2semidirect
4. #13076612C2semidirect
5. #13076611C2semidirect
6. #13076610C2semidirect
7. D11×#397C2semidirect
8. D11×#394C2semidirect
9. D11×#392C2semidirect
10. D11×#379C2semidirect
11. C11×#2812C2semidirect
14. C22×D4×D11C22semidirect
15. C2×C11×#120C22semidirect
16. C2×#67006C22semidirect
17. C2×#66990C22semidirect
19. C2×C4⋊C4×D11C22semidirect
20. C2×#66935C22semidirect
24. C2×C22⋊C4×D11C22semidirect
25. C11×#397C22semidirect
26. C11×#394C22semidirect
27. C11×#392C22semidirect
28. C11×#379C22semidirect
29. #10622860C22semidirect
30. #10622836C22semidirect
31. #10622836C22semidirect
32. #10622835C22semidirect
33. #10622606C22semidirect
34. #10622604C22semidirect
35. #10622574C22semidirect
36. #10622574C22semidirect
37. #10622573C22semidirect
38. #10622573C22semidirect
39. #10622572C22semidirect
40. #10622572C22semidirect
41. #10622568C22semidirect
42. #10622568C22semidirect
43. #10622566C22semidirect
44. #10622565C22semidirect
45. #10622288C22semidirect
46. #10622287C22semidirect
47. #10622285C22semidirect
48. #10622284C22semidirect
49. D11×#95C22semidirect
50. D11×#95C22semidirect
54. C24×D11D4semidirect
59. C22×D4×C11C23semidirect
62. C22×C22⋊D11C23semidirect
68. C22×D44C23semidirect
73. C2×C11×C4⋊C4C23semidirect
77. C2×C11×C22⋊C4C23semidirect
82. C2×C22⋊Dic11C23semidirect
89. C2×(C2×D11)⋊C4C23semidirect
90. C2×(C2×D11)⋊C4C23semidirect
91. C2×C4⋊Dic11C23semidirect
92. C2×Dic11⋊C4C23semidirect
99. C11×#95C23semidirect
100. C11×#95C23semidirect
101. C11⋊#95C23semidirect
102. C11⋊#95C23semidirect
103. C11⋊#95C23semidirect
104. C11⋊#95C23semidirect
108. C24×C11C2×D4semidirect
126. C23×D11C2×D4semidirect
183. #2812D11direct (N × H)
254. C2×#120C2×D11semidirect
265. #397C2×D11semidirect
273. #394C2×D11semidirect
279. #392C2×D11semidirect
283. #379C2×D11semidirect
335. C22×D4C22×D11semidirect
346. C2×C4⋊C4C22×D11semidirect
365. C2×C22⋊C4C22×D11semidirect
370. #95C22×D11semidirect
371. #95C22×D11semidirect
379. D11#2812direct (N × H)
401. C24D4×D11semidirect
451. C11C2×#2812semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1202
#130766142
#130766132
#130766122
#130766112
#130766102
D11×#3972
D11×#3942
D11×#3922
D11×#3792
C11×#28122
C2×#281211