Finite Group Databasebeta

← D11×#2647 #14920876

Subgroups — D11×#2647 #14920876

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074596C211yesmaximal, characteristic, complemented
2#13074595C211yesmaximal, characteristic, complemented
3#13074594C214yesmaximal, complemented
4#13074593C212yesmaximal, complemented
5#13074592C212yesmaximal, complemented
6#13074591C211yesmaximal, characteristic, complemented
7#13074590C214yesmaximal, complemented
8D11×#400C214yesmaximal
9D11×#398C214yesmaximal
10D11×#389C212yesmaximal
11D11×#389C212yesmaximal
12D11×#384C211yesmaximal, characteristic
13D11×#382C211yesmaximal, characteristic
14D11×#376C211yesmaximal, characteristic
15C11×#2647C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D11C2212yes—
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2214yes—
19C2×C4⋊C4×D11C2214yes—
20C2×C4⋊C4×D11C2214yes—
21C2×C42×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C11×#400C2214yes—
25C11×#398C2214yes—
26C11×#389C2212yes—
27C11×#389C2212yes—
28C11×#384C2211yescharacteristic
29C11×#382C2211yescharacteristic
30C11×#376C2211yescharacteristic
31#10622599C2214yes—
32#10622598C2212yes—
33#10622598C2212yes—
34#10622597C2214yes—
35#10622597C2214yes—
36#10622596C2214yes—
37#10622595C2214yes—
38#10622593C2214yes—
39#10622590C2212yes—
40#10622589C2214yes—
41#10622589C2212yes—
42#10622586C2212yes—
43#10622586C2212yes—
44#10622585C2214yes—
45#10622585C2214yes—
46#10622549C2211yescharacteristic
47#10622548C2211yescharacteristic
48#10622545C2211yescharacteristic
49#10622545C2211yescharacteristic
50#10622545C2211yescharacteristic
51#10622541C2212yes—
52#10622541C2212yes—
53D11×#95C2212yes—
54D11×#95C2212yes—
55D11×#95C2214yes—
56D11×#95C2214yes—
57D11×#95C2214yes—
58#10622274C2214yes—
59#10622273C2214yes—
60#10622273C2214yes—
61#10622272C2214yes—
62#10622271C2214yes—
63#10622271C2214yes—
64#10622270C2214yes—
65#10622270C2214yes—
66#10622263C2214yes—
67#10622261C2212yes—
68#10622261C2212yes—
69#10622260C2214yes—
70#10622260C2214yes—
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2312yes—
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2312yes—
77C22×C4×D11C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2314yes—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2312yes—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2311yescharacteristic
106C4⋊C4×D11—28no—
107C4⋊C4×D11—28no—
108C4⋊C4×D11—48no—
109C4⋊C4×D11—48no—
110C4⋊C4×D11—48no—
111C42×D11—24no—
112C42×D11—24no—
113C42×D11Q818yes—
114C11×#95C2314yes—
115C11×#95C2314yes—
116C11×#95C2312yes—
117C11×#95C2312yes—
118C11×#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2312yes—
122C11⋊#95C2312yes—
123C11⋊#95C2312yes—
124C11⋊#95C2312yes—
125C11⋊#95C2312yes—
126C11⋊#95C2312yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C2×#2647—111nomaximal, Sylow
135C23×D11C2411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11C2411yescharacteristic
144C22×Dic11C2412yes—
145C22×Dic11C2414yes—
146C22×Dic11C2411yescharacteristic
147C22×Dic11C2414yes—
148C22×Dic11C2412yes—
149C22×Dic11C2411yescharacteristic
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—24no—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—28no—
160C2×C4×D11—28no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—28no—
165C2×C4×D11C2×Q818yes—
166C2×C4×D11C2×Q814yes—
167C2×C4×D11#4114yes—
168C2×C4×D11#4114yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—44no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4—44no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11C2×Q814yes—
177C4⋊Dic11—24no—
178C4⋊Dic11—24no—
179C4⋊Dic11—44no—
180C4⋊Dic11—44no—
181C4⋊Dic11—44no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—44no—
185Dic11⋊C4—44no—
186Dic11⋊C4—44no—
187Dic11⋊C4—44no—
188Dic11⋊C4—44no—
189Dic11⋊C4—44no—
190C4×Dic11—22no—
191C4×Dic11—24no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11C2×Q818yes—
196C4×Dic11C2×Q814yes—
197#2647—114no—
198#2647—114no—
199#2647—112no—
200#2647—112no—
201#2647—111no—
202#2647—111no—
203#2647—111no—
204#2647D1111yescharacteristic, direct product factor
205C2×#400—114no—
206C2×#398—114no—
207C2×#389—112no—
208C2×#389—112no—
209C2×#384—111no—
210C2×#382—111no—
211C2×#376—111no—
212C23×C11C2511yescharacteristic
213C22×D11C22×Q812yes—
214C22×D11C2×#4112yes—
215C22×D11C2×#4112yes—
216C22×D11H(5,𝔽2)14yes—
217C22×D112−1+414yes—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11C22×Q814yes—
234C2×C4×C11C22×Q812yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C11C2×#4112yes—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11C22×Q814yes—
253C2×Dic11C22×Q812yes—
254C2×Dic11C2×#4112yes—
255C2×Dic11C2×#4112yes—
256C4×D11—216no—
257C4×D11—44no—
258C4×D11—416no—
259C4×D11—44no—
260C4×D11—48no—
261C4×D11—416no—
262C4×D11#125116yes—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—114no—
266C22×C4⋊C4—114no—
267C22×C4⋊C4—114no—
268C22×C42—111no—
269C22×C42—111no—
270C22×C42—111no—
271#400—114no—
272#400—114no—
273#400—114no—
274#400—114no—
275#400—114no—
276#400—114no—
277#400—114no—
278#400C2×D1114yes—
279#398—114no—
280#398—114no—
281#398—114no—
282#398—114no—
283#398—114no—
284#398—114no—
285#398—114no—
286#398C2×D1114yes—
287#389—114no—
288#389—114no—
289#389—112no—
290#389—112no—
291#389—112no—
292#389—112no—
293#389—112no—
294#389—112no—
295#389—114no—
296#389—114no—
297#389C2×D1112yes—
298#389C2×D1112yes—
299#384—114no—
300#384—112no—
301#384—111no—
302#384C2×D1111yescharacteristic
303#382—112no—
304#382—111no—
305#382—114no—
306#382C2×D1111yescharacteristic
307#376—111no—
308#376—111no—
309#376—111no—
310#376—112no—
311#376—112no—
312#376C2×D1111yescharacteristic
313C2×#95—112no—
314C2×#95—114no—
315C2×#95—114no—
316C2×#95—112no—
317C2×#95—114no—
318C22×C11C23×Q811yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C2×H(5,𝔽2)12yes—
322C22×C11C2×2−1+412yes—
323C2×D11C2×#12514yes—
324C2×D11#54014yes—
325C2×D11#54114yes—
326C2×D11#54218yes—
327C2×D11#54418yes—
328C4×C11—24no—
329C4×C11—41no—
330C4×C11—44no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11C2×#12514yes—
335Dic11—24no—
336Dic11—41no—
337Dic11—44no—
338Dic11—41no—
339Dic11—42no—
340Dic11—44no—
341Dic11C2×#12514yes—
342C23×C4—111no—
343C23×C4—112no—
344C23×C4—114no—
345C23×C4—111no—
346C23×C4—114no—
347C23×C4—112no—
348C23×C4—111no—
349C2×C4⋊C4—114no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4—448no—
365C2×C4⋊C4—448no—
366C2×C4⋊C4—448no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1112yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C42—112no—
373C2×C42—111no—
374C2×C42—118no—
375C2×C42—111no—
376C2×C42—112no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—224no—
381C2×C42—224no—
382C2×C42C22×D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385#95—112no—
386#95—112no—
387#95—112no—
388#95—112no—
389#95—112no—
390#95—112no—
391#95—114no—
392#95—114no—
393#95—114no—
394#95—114no—
395#95—114no—
396#95—114no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95C22×D1112yes—
401#95C22×D1112yes—
402#95C22×D1114yes—
403#95C22×D1114yes—
404#95C22×D1114yes—
405C2×C11C22×#12511yescharacteristic
406C2×C11C2×#54011yescharacteristic
407C2×C11C2×#54111yescharacteristic
408C2×C11C2×#54212yes—
409C2×C11C2×#54412yes—
410D11#264718yesdirect product factor
411C24—111no—
412C22×C4—111no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—118no—
418C22×C4—111no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—111no—
422C22×C4—114no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—222no—
428C22×C4—228no—
429C22×C4—228no—
430C22×C4—228no—
431C22×C4—228no—
432C22×C4—224no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—228no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4C23×D1111yescharacteristic
439C22×C4C23×D1112yes—
440C22×C4C23×D1114yes—
441C22×C4C23×D1111yescharacteristic
442C22×C4C23×D1114yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1111yescharacteristic
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—44no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—444no—
455C4⋊C4—444no—
456C4⋊C4—444no—
457C4⋊C4—444no—
458C4⋊C4—444no—
459C4⋊C4—444no—
460C4⋊C4—444no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C42—22no—
464C42—22no—
465C42—118no—
466C42—114no—
467C42—222no—
468C42—222no—
469C42—224no—
470C42—222no—
471C42—222no—
472C42Q8×D1114yes—
473C11C2×#264711yescharacteristic, complemented, Sylow
474C23—112no—
475C23—112no—
476C23—112no—
477C23—114no—
478C23—114no—
479C23C24×D1111yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—1116no—
499C2×C4—114no—
500C2×C4—2216no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—444no—
517C2×C4—4416no—
518C2×C4—444no—
519C2×C4—448no—
520C2×C4—4416no—
521C2×C4C2×Q8×D1114yes—
522C2×C4C2×Q8×D1112yes—
523C2×C4#41×D1112yes—
524C2×C4#41×D1112yes—
525C22—114no—
526C22—114no—
527C22—114no—
528C22—118no—
529C22—118no—
530C22C22×Q8×D1111yescharacteristic
531C22C2×#41×D1111yescharacteristic
532C22C2×#41×D1111yescharacteristic
533C22D11×H(5,𝔽2)12yes—
534C22D11×2−1+412yes—
535C4—24no—
536C4—41no—
537C4—44no—
538C4—41no—
539C4—42no—
540C4—44no—
541C4—114no—
542C4—224no—
543C4—441no—
544C4—444no—
545C4—441no—
546C4—442no—
547C4—444no—
548C4D11×#12514yes—
549C2—118no—
550C2C2×D11×#12511yescharacteristic
551C2D11×#54011yescharacteristic
552C2D11×#54111yescharacteristic
553C2D11×#54212yes—
554C2D11×#54412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2647C2
prime radicalC23×D11C24
hypercenter#2647D11
hypocenterC11C2×#2647
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2647

Complements

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

NH ≅ G/Ntype
1. #13074596C2semidirect
2. #13074595C2semidirect
3. #13074594C2semidirect
4. #13074593C2semidirect
5. #13074592C2semidirect
6. #13074591C2semidirect
7. #13074590C2semidirect
15. C11×#2647C2semidirect
204. #2647D11direct (N × H)
410. D11#2647direct (N × H)
473. C11C2×#2647semidirect

Maximal subgroups

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

subgroupindex
#130745962
#130745952
#130745942
#130745932
#130745922
#130745912
#130745902
D11×#4002
D11×#3982
D11×#3892
D11×#3842
D11×#3822
D11×#3762
C11×#26472
C2×#264711