Finite Group Databasebeta

← D11×#2659 #14920316

Subgroups — D11×#2659 #14920316

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C212yesmaximal
2#13074733C214yesmaximal, complemented
3#13074732C212yesmaximal, complemented
4#13074731C214yesmaximal, complemented
5#13074730C211yesmaximal, characteristic, complemented
6#13074729C214yesmaximal, complemented
7D11×#398C214yesmaximal, complemented
8D11×#395C214yesmaximal, complemented
9D11×#380C214yesmaximal
10C2×D11×#95C211yesmaximal, characteristic
11C11×#2659C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C2×C11×C22⋊Q8C2212yes—
16C2×#66999C2212yes—
17C2×#66977C2212yes—
18D11×C22⋊Q8—216no—
19C2×#66950C2212yes—
20C2×#66949C2214yes—
21C2×C4⋊C4×D11C2214yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C4⋊C4×D11C2214yes—
24C2×C4⋊C4×D11C2214yes—
25C2×C22⋊C4×D11C2214yes—
26C2×#66931C2214yes—
27C11×#398C2214yescomplemented
28C11×#395C2214yescomplemented
29C11×#380C2214yes—
30C2×C11×#95C2211yescharacteristic
31#10622842C2214yescomplemented
32#10622825C2214yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35#10622600C2214yes—
36#10622600C2214yes—
37#10622597C2218yescomplemented
38#10622596C2214yescomplemented
39#10622593C2214yescomplemented
40#10622592C2218yescomplemented
41#10622592C2214yescomplemented
42#10622555C2218yes—
43#10622280C2218yes—
44D11×#95C2214yes—
45D11×#95C2214yes—
46D11×#95C2218yes—
47#10622274C2214yescomplemented
48#10622270C2218yescomplemented
49#10622269C2214yescomplemented
50#10622269C2218yescomplemented
51C24×D11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2312yes—
57C2×Q8×D11—28no—
58C2×Q8×D11—48no—
59C22×C4×D11—44no—
60C22×C4×D11—44no—
61C22×C4×D11—44no—
62C22×C4×D11D418yes—
63C22×C4×D11Q8116yescomplemented
64C22×C4×D11C2314yes—
65C22×C4×D11C2314yes—
66C22×C4×D11C2312yes—
67C22×C4×D11C2314yes—
68C22×C4×D11C2312yes—
69C22×C4×D11C2314yes—
70C22×Dic22C2314yes—
71C22×Dic22C2312yes—
72C11×C22⋊Q8—28no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78C2×C22⋊Dic11C2314yes—
79#66999—28no—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×C4⋊Dic11C2314yes—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86#66977—28no—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2314yes—
89C2×Dic11⋊C4C2314yes—
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92#66950—28no—
93#66949—216no—
94C4⋊C4×D11—28no—
95C4⋊C4×D11—216no—
96C4⋊C4×D11—48no—
97C4⋊C4×D11—48no—
98C22⋊C4×D11—216no—
99#66931—216no—
100C11×#95C2318yes—
101C11×#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C2×#2659—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11—24no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11C2×D414yes—
113C23×D11C2×Q818yes—
114C23×D11C2411yescharacteristic
115C23×D11C2411yescharacteristic
116C2×Q8×C11—24no—
117C2×Q8×C11—44no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×Q818yescomplemented
123C22×C4×C11C2414yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2414yes—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11C2×D414yes—
131C22×Dic11C2×Q818yescomplemented
132C22×Dic11C2414yes—
133C22×Dic11C2414yes—
134C22×Dic11C2412yes—
135C22×Dic11C2414yes—
136Q8×D11—432no—
137C2×C4×D11—28no—
138C2×C4×D11—28no—
139C2×C4×D11—28no—
140C2×C4×D11—28no—
141C2×C4×D11—28no—
142C2×C4×D11—28no—
143C2×C4×D11—216no—
144C2×C4×D11—28no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11—44no—
148C2×C4×D11—416no—
149C2×C4×D11—432no—
150C2×C4×D11C2×D418yes—
151C2×C4×D11C2×D418yes—
152C2×C4×D11C2×Q8116yes—
153C2×C4×D11C2×Q8116yescomplemented
154C2×Dic22—28no—
155C2×Dic22—24no—
156C2×Dic22—44no—
157C2×Dic22—48no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—44no—
161C11×C4⋊C4—44no—
162C11×C22⋊C4—28no—
163C22⋊Dic11—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166C4⋊Dic11—28no—
167C4⋊Dic11—24no—
168C4⋊Dic11—44no—
169C4⋊Dic11—44no—
170Dic11⋊C4—28no—
171Dic11⋊C4—28no—
172Dic11⋊C4—28no—
173Dic11⋊C4—48no—
174Dic11⋊C4—48no—
175C22×C22⋊Q8—112no—
176#2659—114no—
177#2659—114no—
178#2659—114no—
179#2659—111no—
180#2659—112no—
181#2659D1111yescharacteristic, direct product factor
182C2×#398—114no—
183C2×#395—114no—
184C2×#380—114no—
185C22×#95—111no—
186C23×C11—22no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11C22×D412yes—
190C23×C11C22×Q814yes—
191C23×C11C2511yescharacteristic
192C22×D11—22no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—28no—
196C22×D11—28no—
197C22×D11—216no—
198C22×D11—216no—
199C22×D11C4⋊Q8116yes—
200C22×D11C22×D412yes—
201C22×D11C22×D412yes—
202C22×D11C22×Q814yes—
203C22×D11C22×Q814yes—
204C22×D11H(5,𝔽2)14yes—
205C22×D11H(5,𝔽2)12yes—
206C22×D112−1+412yes—
207Q8×C11—48no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—44no—
217C2×C4×C11—48no—
218C2×C4×C11C22×D414yes—
219C2×C4×C11C22×Q818yes—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—28no—
227C2×Dic11—24no—
228C2×Dic11—44no—
229C2×Dic11—48no—
230C2×Dic11C22×D414yes—
231C2×Dic11C22×Q818yes—
232C4×D11—216no—
233C4×D11—232no—
234C4×D11—48no—
235C4×D11—416no—
236C4×D11—416no—
237C4×D11—416no—
238Dic22—416no—
239Dic22—48no—
240C23×Q8—112no—
241C24×C4—111no—
242C24×C4—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×C22⋊Q8—114no—
246C2×C22⋊Q8—112no—
247C2×C22⋊Q8—114no—
248C2×C22⋊Q8—2216no—
249C2×C22⋊Q8C2×D1112yes—
250C22×C4⋊C4—114no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—114no—
253C22×C4⋊C4—114no—
254C22×C22⋊C4—114no—
255#398—114no—
256#398—114no—
257#398—118no—
258#398—118no—
259#398—114no—
260#398C2×D1114yescomplemented
261#395—114no—
262#395—118no—
263#395—114no—
264#395—118no—
265#395—114no—
266#395C2×D1114yescomplemented
267#380—114no—
268#380—114no—
269#380—114no—
270#380—118no—
271#380—118no—
272#380C2×D1114yes—
273C2×#95—112no—
274C2×#95—111no—
275C2×#95—114no—
276C2×#95—118no—
277C2×#95—114no—
278C2×#95C2×D1111yescharacteristic
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11C2×C4⋊Q814yes—
284C22×C11C23×D411yescharacteristic
285C22×C11C23×Q812yes—
286C22×C11C2×H(5,𝔽2)12yes—
287C22×C11C2×H(5,𝔽2)11yescharacteristic
288C22×C11C2×2−1+411yescharacteristic
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—232no—
294C2×D11C2×C4⋊Q814yes—
295C2×D11C2×C4⋊Q814yes—
296C2×D11#53414yes—
297C2×D11#53714yes—
298C2×D11#54318yes—
299C2×D11#54418yes—
300C4×C11—24no—
301C4×C11—28no—
302C4×C11—44no—
303C4×C11—44no—
304Dic11—24no—
305Dic11—28no—
306Dic11—44no—
307Dic11—44no—
308C25—111no—
309C22×Q8—114no—
310C22×Q8—112no—
311C22×Q8—228no—
312C22×Q8—448no—
313C22×Q8C22×D1112yes—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4—112no—
317C23×C4—114no—
318C23×C4—118no—
319C23×C4—1116no—
320C23×C4—112no—
321C23×C4—114no—
322C23×C4—114no—
323C23×C4—114no—
324C23×C4—444no—
325C23×C4—444no—
326C23×C4—444no—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1112yes—
329C22⋊Q8—28no—
330C22⋊Q8—2216no—
331C22⋊Q8—2216no—
332C22⋊Q8—228no—
333C22⋊Q8—228no—
334C22⋊Q8—228no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—228no—
345C2×C4⋊C4—2216no—
346C2×C4⋊C4—448no—
347C2×C4⋊C4—448no—
348C2×C4⋊C4C22×D1114yes—
349C2×C4⋊C4C22×D1112yes—
350C2×C4⋊C4C22×D1114yes—
351C2×C4⋊C4C22×D1114yes—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—114no—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—2216no—
356C2×C22⋊C4C22×D1114yes—
357#95—114no—
358#95—118no—
359#95—118no—
360#95—118no—
361#95—118no—
362#95C22×D1114yes—
363#95C22×D1118yes—
364C2×C11—24no—
365C2×C11C22×C4⋊Q811yescharacteristic
366C2×C11C2×#53411yescharacteristic
367C2×C11C2×#53711yescharacteristic
368C2×C11C2×#54312yes—
369C2×C11C2×#54412yes—
370D11—24no—
371D11#265918yesdirect product factor
372C24—111no—
373C24—114no—
374C24—118no—
375C24—111no—
376C24—224no—
377C24—222no—
378C24—222no—
379C24C23×D1111yescharacteristic
380C2×Q8—24no—
381C2×Q8—44no—
382C2×Q8—228no—
383C2×Q8—224no—
384C2×Q8—444no—
385C2×Q8—448no—
386C2×Q8—4432no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—114no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—118no—
394C22×C4—118no—
395C22×C4—1116no—
396C22×C4—118no—
397C22×C4—1116no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—228no—
401C22×C4—228no—
402C22×C4—228no—
403C22×C4—228no—
404C22×C4—228no—
405C22×C4—228no—
406C22×C4—2216no—
407C22×C4—228no—
408C22×C4—444no—
409C22×C4—444no—
410C22×C4—444no—
411C22×C4—4416no—
412C22×C4—4432no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4D4×D1114yes—
417C22×C4Q8×D1118yescomplemented
418C22×C4C23×D1114yes—
419C22×C4C23×D1114yes—
420C22×C4C23×D1112yes—
421C22×C4C23×D1114yes—
422C4⋊C4—24no—
423C4⋊C4—28no—
424C4⋊C4—44no—
425C4⋊C4—44no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—224no—
431C4⋊C4—448no—
432C4⋊C4—448no—
433C4⋊C4—444no—
434C4⋊C4—444no—
435C22⋊C4—28no—
436C22⋊C4—228no—
437C22⋊C4—228no—
438C22⋊C4—228no—
439C11C2×#265911yescharacteristic, complemented, Sylow
440C23—22no—
441C23—21no—
442C23—21no—
443C23—112no—
444C23—114no—
445C23—114no—
446C23—112no—
447C23—112no—
448C23—1116no—
449C23—112no—
450C23—114no—
451C23—228no—
452C23—2216no—
453C23—228no—
454C23—2216no—
455C23—222no—
456C23—221no—
457C23—221no—
458C23C2×D4×D1112yes—
459C23C2×Q8×D1114yes—
460C23C24×D1111yescharacteristic
461Q8—48no—
462Q8—448no—
463Q8—4416no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—28no—
471C2×C4—24no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—114no—
475C2×C4—118no—
476C2×C4—2216no—
477C2×C4—2232no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—228no—
485C2×C4—224no—
486C2×C4—448no—
487C2×C4—4416no—
488C2×C4—4416no—
489C2×C4—4416no—
490C2×C4—444no—
491C2×C4—448no—
492C2×C4C2×D4×D1114yes—
493C2×C4C2×Q8×D1118yes—
494C22—22no—
495C22—22no—
496C22—24no—
497C22—24no—
498C22—114no—
499C22—114no—
500C22—114no—
501C22—118no—
502C22—118no—
503C22—114no—
504C22—2232no—
505C22—222no—
506C22—222no—
507C22—224no—
508C22—224no—
509C22D11×C4⋊Q814yes—
510C22C22×D4×D1111yescharacteristic
511C22C22×Q8×D1112yes—
512C22D11×H(5,𝔽2)12yes—
513C22D11×H(5,𝔽2)11yescharacteristic
514C22D11×2−1+411yescharacteristic
515C4—24no—
516C4—28no—
517C4—44no—
518C4—44no—
519C4—224no—
520C4—228no—
521C4—444no—
522C4—444no—
523C2—24no—
524C2—118no—
525C2—224no—
526C2C2×D11×C4⋊Q811yescharacteristic
527C2D11×#53411yescharacteristic
528C2D11×#53711yescharacteristic
529C2D11×#54312yes—
530C2D11×#54412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2659C2
prime radicalC24×D11C23
hypercenter#2659D11
hypocenterC11C2×#2659
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
2. #13074733C2semidirect
3. #13074732C2semidirect
4. #13074731C2semidirect
5. #13074730C2semidirect
6. #13074729C2semidirect
7. D11×#398C2semidirect
8. D11×#395C2semidirect
11. C11×#2659C2semidirect
27. C11×#398C22semidirect
28. C11×#395C22semidirect
31. #10622842C22semidirect
37. #10622597C22semidirect
38. #10622596C22semidirect
39. #10622593C22semidirect
40. #10622592C22semidirect
41. #10622592C22semidirect
47. #10622274C22semidirect
48. #10622270C22semidirect
49. #10622269C22semidirect
50. #10622269C22semidirect
63. C22×C4×D11Q8semidirect
122. C22×C4×C11C2×Q8semidirect
131. C22×Dic11C2×Q8semidirect
153. C2×C4×D11C2×Q8semidirect
181. #2659D11direct (N × H)
260. #398C2×D11semidirect
266. #395C2×D11semidirect
371. D11#2659direct (N × H)
417. C22×C4Q8×D11semidirect
439. C11C2×#2659semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
#130747332
#130747322
#130747312
#130747302
#130747292
D11×#3982
D11×#3952
D11×#3802
C2×D11×#952
C11×#26592
C2×#265911