Finite Group Databasebeta

← D11×#1823 #14753545

Subgroups — D11×#1823 #14753545

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic
3D11×#380C211yesmaximal, characteristic
4#13068703C211yesmaximal, characteristic, complemented
5#13068702C211yesmaximal, characteristic, complemented
6#13068701C214yesmaximal, complemented
7#13068700C211yesmaximal, characteristic, complemented
8D11×#340C214yesmaximal, complemented
9C11×#1823C211yesmaximal, characteristic, complemented
10C23×C4×D11—21no—
11C23×C4×D11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C22×C8×D11C2212yes—
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11—24no—
19C2×C4⋊C4×D11C418yescomplemented
20C2×C4⋊C4×D11C2212yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C22⋊C4×D11—21no—
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29#10622600C2212yes—
30#10622555—21no—
31D11×C22⋊C8—24no—
32#10622280—21no—
33D11×#95—21no—
34C11×#340C2214yescomplemented
35#10622189C2214yescomplemented
36#10622167C2214yescomplemented
37#10622167C2214yescomplemented
38C24×D11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D411yescharacteristic
43C22×C4×D11—28no—
44C22×C4×D11—28no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11—44no—
49C22×C4×D11—44no—
50C22×C4×D11C2×C414yes—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D414yes—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2×C414yescomplemented
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C22⋊Dic11—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C414yescomplemented
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—28no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C22×C11⋊C8C2312yes—
75C2×C8×D11—24no—
76C2×C8×D11—28no—
77C4⋊C4×D11—28no—
78C4⋊C4×D11—28no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11—24no—
81C4⋊C4×D11—28no—
82C4⋊C4×D11C2×C418yes—
83C4⋊C4×D11C2×C418yescomplemented
84C22⋊C4×D11—44no—
85C11×C22⋊C8—22no—
86C11×#95—21no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—24no—
91C2×#1823—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—24no—
94C23×D11—24no—
95C23×D11C22⋊C414yes—
96C23×D11D814yes—
97C23×D11SD1614yes—
98C23×D11C2×D411yescharacteristic
99C23×D11C2×D411yescharacteristic
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—24no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11C22⋊C414yes—
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C2×C4×D11—24no—
120C2×C4×D11—216no—
121C2×C4×D11—216no—
122C2×C4×D11—28no—
123C2×C4×D11—28no—
124C2×C4×D11—24no—
125C2×C4×D11—24no—
126C2×C4×D11—432no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11C22⋊C414yes—
135C2×C4×D11C22⋊C414yes—
136C2×C4×D11C22×C412yes—
137C2×C4×D11C22×C412yes—
138C2×C4×D11C2×D412yes—
139C2×C4×D11C2×D412yes—
140C2×C4×D11#4118yes—
141C2×C8×C11—22no—
142C2×C8×C11—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4C22×C414yes—
147C11×C22⋊C4—42no—
148C22⋊Dic11—42no—
149(C2×D11)⋊C4—44no—
150C4⋊Dic11—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—24no—
153C4⋊Dic11C22×C414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—44no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—24no—
159C8×D11—48no—
160C23×C4⋊C4—111no—
161C22×C22⋊C8—111no—
162C2×#380—111no—
163#1823—111no—
164#1823—111no—
165#1823—114no—
166#1823—111no—
167#1823D1111yescharacteristic, direct product factor
168C2×#340—114no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11C2×C22⋊C412yes—
172C23×C11C2×D812yes—
173C23×C11C2×SD1612yes—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—28no—
178C22×D11—28no—
179C22×D11—216no—
180C22×D11—216no—
181C22×D11#102116yes—
182C22×D11C2×C22⋊C412yes—
183C22×D11C2×C22⋊C412yes—
184C22×D11#12314yes—
185C22×D11C2×D812yes—
186C22×D11C2×D812yes—
187C22×D11C2×SD1612yes—
188C22×D11C2×SD1612yes—
189C22×D11#13714yes—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—48no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4114yes—
204C2×Dic11—22no—
205C2×Dic11—28no—
206C2×Dic11—24no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—48no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C2×Dic11#12314yes—
216C4×D11—28no—
217C4×D11—24no—
218C4×D11—24no—
219C4×D11—28no—
220C4×D11—416no—
221C4×D11—416no—
222C4×D11—88no—
223C4×D11#11718yes—
224C4×D11#12318yes—
225C8×C11—42no—
226C11⋊C8—42no—
227C24×C4—111no—
228C24×C4—221no—
229C23×C8—112no—
230C22×C4⋊C4—111no—
231C22×C4⋊C4—112no—
232C22×C4⋊C4—112no—
233C22×C4⋊C4—118no—
234C22×C4⋊C4—112no—
235C22×C4⋊C4—221no—
236C22×C4⋊C4—221no—
237C22×C4⋊C4—224no—
238C22×C4⋊C4—221no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C22⋊C4—221no—
241C2×C22⋊C8—111no—
242C2×C22⋊C8—112no—
243C2×C22⋊C8—224no—
244C2×C22⋊C8C2×D1111yescharacteristic
245#380—111no—
246#380—112no—
247#380—221no—
248#380—221no—
249#380C2×D1111yescharacteristic
250C2×#95—221no—
251#340—114no—
252#340—114no—
253#340—114no—
254#340C2×D1114yescomplemented
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11C2×#10214yes—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11C2×#12312yes—
262C22×C11C22×D811yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×#13712yes—
265C2×D11—24no—
266C2×D11—24no—
267C2×D11—22no—
268C2×D11—22no—
269C2×D11—232no—
270C2×D11#38114yes—
271C2×D11C2×#10214yes—
272C2×D11C2×#10214yes—
273C2×D11#41914yes—
274C2×D11#48018yes—
275C2×D11#48318yes—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11—82no—
279C4×C11C2×#11712yes—
280C4×C11C2×#12312yes—
281Dic11—22no—
282Dic11—44no—
283Dic11—82no—
284Dic11#38114yes—
285C25—111no—
286C23×C4—21no—
287C23×C4—111no—
288C23×C4—111no—
289C23×C4—114no—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—114no—
293C23×C4—111no—
294C23×C4—228no—
295C23×C4—228no—
296C23×C4—222no—
297C23×C4—222no—
298C23×C4—222no—
299C23×C4—221no—
300C23×C4—444no—
301C23×C4—444no—
302C23×C4C22×D1111yescharacteristic
303C22×C8—112no—
304C22×C8—228no—
305C22×C8—224no—
306C22×C8C22×D1112yes—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—114no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—118no—
312C2×C4⋊C4—118no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—228no—
315C2×C4⋊C4—228no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—228no—
319C2×C4⋊C4—228no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4C4×D1114yescomplemented
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1112yes—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—444no—
332C22⋊C8—22no—
333C22⋊C8—224no—
334C22⋊C8—222no—
335#95—21no—
336#95—222no—
337#95—221no—
338C2×C11—24no—
339C2×C11C2×#38111yescharacteristic
340C2×C11C22×#10211yescharacteristic
341C2×C11C2×#41911yescharacteristic
342C2×C11C2×#48012yes—
343C2×C11C2×#48312yes—
344D11—24no—
345D11#182318yesdirect product factor
346C24—111no—
347C24—114no—
348C24—114no—
349C24—114no—
350C24—111no—
351C24—224no—
352C24—224no—
353C24D4×D1111yescharacteristic
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—111no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—118no—
364C22×C4—114no—
365C22×C4—111no—
366C22×C4—114no—
367C22×C4—114no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—224no—
371C22×C4—2216no—
372C22×C4—2216no—
373C22×C4—224no—
374C22×C4—228no—
375C22×C4—228no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—224no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—444no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—444no—
385C22×C4—4432no—
386C22×C4—444no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4C2×C4×D1112yes—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1112yes—
394C22×C4C23×D1111yescharacteristic
395C2×C8—22no—
396C2×C8—24no—
397C2×C8—222no—
398C2×C8—224no—
399C2×C8—448no—
400C4⋊C4—24no—
401C4⋊C4—22no—
402C4⋊C4—24no—
403C4⋊C4—114no—
404C4⋊C4—228no—
405C4⋊C4—228no—
406C4⋊C4—224no—
407C4⋊C4—222no—
408C4⋊C4—224no—
409C4⋊C4—444no—
410C4⋊C4C2×C4×D1114yes—
411C22⋊C4—42no—
412C22⋊C4—444no—
413C22⋊C4—442no—
414C11C2×#182311yescharacteristic, complemented, Sylow
415C23—22no—
416C23—22no—
417C23—112no—
418C23—112no—
419C23—112no—
420C23—114no—
421C23—114no—
422C23—112no—
423C23—112no—
424C23—112no—
425C23—1116no—
426C23—228no—
427C23—228no—
428C23—2216no—
429C23—2216no—
430C23—222no—
431C23—222no—
432C23C22⋊C4×D1112yes—
433C23D8×D1112yes—
434C23SD16×D1112yes—
435C23C2×D4×D1111yescharacteristic
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—48no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—112no—
447C2×C4—114no—
448C2×C4—118no—
449C2×C4—118no—
450C2×C4—112no—
451C2×C4—228no—
452C2×C4—228no—
453C2×C4—228no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—4416no—
459C2×C4—4416no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—448no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—888no—
467C2×C4C22⋊C4×D1112yes—
468C2×C4C22×C4×D1111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4#41×D1114yes—
471C8—42no—
472C8—442no—
473C22—22no—
474C22—22no—
475C22—24no—
476C22—24no—
477C22—114no—
478C22—114no—
479C22—114no—
480C22—118no—
481C22—118no—
482C22—114no—
483C22—2232no—
484C22—222no—
485C22—222no—
486C22—224no—
487C22—224no—
488C22D11×#10214yes—
489C22C2×C22⋊C4×D1111yescharacteristic
490C22D11×#12312yes—
491C22C2×D8×D1111yescharacteristic
492C22C2×SD16×D1111yescharacteristic
493C22D11×#13712yes—
494C4—22no—
495C4—44no—
496C4—82no—
497C4—114no—
498C4—222no—
499C4—444no—
500C4—882no—
501C4D11×#11712yes—
502C4D11×#12312yes—
503C2—24no—
504C2—118no—
505C2—224no—
506C2D11×#38111yescharacteristic
507C2C2×D11×#10211yescharacteristic
508C2D11×#41911yescharacteristic
509C2D11×#48012yes—
510C2D11×#48312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11C2×#1823
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13068703C2semidirect
5. #13068702C2semidirect
6. #13068701C2semidirect
7. #13068700C2semidirect
8. D11×#340C2semidirect
9. C11×#1823C2semidirect
19. C2×C4⋊C4×D11C4semidirect
34. C11×#340C22semidirect
35. #10622189C22semidirect
36. #10622167C22semidirect
37. #10622167C22semidirect
59. C2×C11×C4⋊C4C2×C4semidirect
67. C2×C4⋊Dic11C2×C4semidirect
83. C4⋊C4×D11C2×C4semidirect
167. #1823D11direct (N × H)
254. #340C2×D11semidirect
325. C2×C4⋊C4C4×D11semidirect
345. D11#1823direct (N × H)
414. C11C2×#1823semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×D11×C22⋊C82
D11×#3802
#130687032
#130687022
#130687012
#130687002
D11×#3402
C11×#18232
C2×#182311