Finite Group Databasebeta

← D11×#2025 #14781045

Subgroups — D11×#2025 #14781045

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×D11×#102C212yesmaximal
3D11×#390C211yesmaximal, characteristic
4#13069763C211yesmaximal, characteristic, complemented
5#13069762C211yesmaximal, characteristic, complemented
6#13069761C212yesmaximal, complemented
7#13069760C212yesmaximal, complemented
8#13069759C211yesmaximal, characteristic, complemented
9D11×#340C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2025C211yesmaximal, characteristic, complemented
12C22×D4×D11C2211yescharacteristic
13C2×C11×#125C2211yescharacteristic, complemented
14C22×C8×D11C2212yes—
15D11×#125—28no—
16C2×C4⋊C4×D11—22no—
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2212yes—
19C2×#66943C2212yescomplemented
20C2×#66942—22no—
21C2×C22⋊C4×D11—22no—
22C2×C42×D11C2211yescharacteristic
23C2×#66923C2211yescharacteristic, complemented
24C2×C11×#102C2212yes—
25C11×#390C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66885C2212yes—
29#10622601C2211yescharacteristic
30C2×#66873C2212yes—
31#10622570—22no—
32#10622552C2211yescharacteristic
33D11×#102—28no—
34C11×#340C2212yescomplemented
35C11×#336C2211yescharacteristic, complemented
36#10622189C2212yescomplemented
37#10622188C2212yescomplemented
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40#10622162C2211yescharacteristic, complemented
41C24×D11—21no—
42C22×D4×C11C2311yescharacteristic
43C22×C22⋊D11—21no—
44C2×D4×D11—24no—
45C2×D4×D11—24no—
46C2×D4×D11—22no—
47C2×D4×D11Q814yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—21no—
51C22×C4×D11D412yes—
52C22×C4×D11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×#125—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11D412yes—
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73C2×C8×D11—24no—
74C2×C8×D11—24no—
75C2×C8×D11—24no—
76C4⋊C4×D11—216no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—24no—
79C4⋊C4×D11D418yes—
80#66943—24no—
81#66943—24no—
82#66942—216no—
83C22⋊C4×D11—48no—
84C42×D11—24no—
85#66923—24no—
86C11×#102—24no—
87#66896—24no—
88#66885—24no—
89#66873—24no—
90C2×#2025—111nomaximal, Sylow
91C24×C11—21no—
92C23×D11—21no—
93C23×D11—24no—
94C23×D11—42no—
95C23×D11—42no—
96C23×D11—44no—
97C23×D11—44no—
98C23×D11C2×D411yescharacteristic
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—21no—
102C2×D4×C11C2×Q812yes—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—24no—
108C2×C22⋊D11—42no—
109C2×C22⋊D11—42no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11C2×D412yes—
113C22×Dic11C2×D411yescharacteristic
114D4×D11—216no—
115D4×D11—48no—
116C2×D44—22no—
117C2×D44—21no—
118C2×D44—22no—
119C2×D44C2×Q812yes—
120C2×C4×D11—24no—
121C2×C4×D11—28no—
122C2×C4×D11—24no—
123C2×C4×D11—24no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11C2×D414yes—
129C2×C4×D11C2×Q812yes—
130C2×C4×D11#4112yes—
131C2×C4×D11#4114yes—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—28no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D414yes—
139C11×C22⋊C4—44no—
140C42×C11—22no—
141C22⋊Dic11—44no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—44no—
144C4⋊Dic11—28no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11C2×D414yes—
148Dic11⋊C4—28no—
149Dic11⋊C4—28no—
150Dic11⋊C4—28no—
151Dic11⋊C4—42no—
152C4×Dic11—24no—
153C4×Dic11—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C8×D11—48no—
158C22×#125—111no—
159C22×#102—112no—
160C2×#390—111no—
161#2025—112no—
162#2025—111no—
163#2025—112no—
164#2025—111no—
165#2025—111no—
166#2025D1111yescharacteristic, direct product factor
167C2×#340—112no—
168C2×#336—111no—
169C23×C11—22no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—48no—
181C22×D11—416no—
182C22×D11—88no—
183C22×D11—84no—
184C22×D11—84no—
185C22×D11#12012yes—
186C22×D11C22⋊Q812yes—
187C22×D11#12412yes—
188C22×D11#13514yes—
189C22×D11AGL(1,ℤ/8)14yes—
190D4×C11—24no—
191D4×C11—42no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11C22×D412yes—
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4112yes—
203C2×C4×C11C2×#4111yescharacteristic
204C22⋊D11—48no—
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11#12012yes—
214C2×Dic11C22⋊Q812yes—
215C2×Dic11#12412yes—
216D44—24no—
217D44—42no—
218C4×D11—48no—
219C4×D11—416no—
220C4×D11—84no—
221C4×D11C22⋊Q818yes—
222C4×D11#12418yes—
223C8×C11—42no—
224C11⋊C8—42no—
225C23×D4—111no—
226C23×C8—112no—
227C2×#125—112no—
228C2×#125—111no—
229C2×#125—222no—
230C2×#125—228no—
231C2×#125C2×D1111yescharacteristic, complemented
232C22×C4⋊C4—112no—
233C22×C4⋊C4—111no—
234C22×C4⋊C4—222no—
235C22×C22⋊C4—222no—
236C22×C42—111no—
237C2×#102—112no—
238C2×#102—112no—
239C2×#102—112no—
240C2×#102—228no—
241C2×#102C2×D1112yes—
242#390—111no—
243#390—111no—
244#390—111no—
245#390—222no—
246#390C2×D1111yescharacteristic
247#340—112no—
248#340—112no—
249#340—112no—
250#340C2×D1112yescomplemented
251#336—112no—
252#336—111no—
253#336C2×D1111yescharacteristic, complemented
254C22×C11—44no—
255C22×C11—42no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—82no—
259C22×C11C2×#12011yescharacteristic
260C22×C11C2×C22⋊Q811yescharacteristic
261C22×C11C2×#12411yescharacteristic
262C22×C11C2×#13512yes—
263C22×C11C2×AGL(1,ℤ/8)12yes—
264C2×D11—44no—
265C2×D11—42no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—82no—
269C2×D11—816no—
270C2×D11#39314yes—
271C2×D11#44918yes—
272C2×D11#47818yes—
273C2×D11#48814yes—
274C2×D11#49014yes—
275C4×C11—42no—
276C4×C11—44no—
277C4×C11—81no—
278C4×C11C2×C22⋊Q812yes—
279C4×C11C2×#12412yes—
280Dic11—42no—
281Dic11—44no—
282Dic11—81no—
283Dic11#39314yes—
284C25—221no—
285C22×D4—114no—
286C22×D4—111no—
287C22×D4—224no—
288C22×D4—224no—
289C22×D4—222no—
290C22×D4—221no—
291C22×D4C22×D1111yescharacteristic
292C23×C4—111no—
293C23×C4—112no—
294C23×C4—222no—
295C23×C4—221no—
296C22×C8—112no—
297C22×C8—224no—
298C22×C8—224no—
299C22×C8—224no—
300C22×C8C22×D1112yes—
301#125—24no—
302#125—224no—
303#125—224no—
304#125—2216no—
305#125—224no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4—118no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—224no—
311C2×C4⋊C4—2216no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1112yes—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—448no—
325C2×C42—112no—
326C2×C42—111no—
327C2×C42—224no—
328C2×C42C22×D1111yescharacteristic
329#102—24no—
330#102—224no—
331#102—224no—
332#102—224no—
333C2×C11—82no—
334C2×C11C2×#39311yescharacteristic
335C2×C11C2×#44912yes—
336C2×C11C2×#47812yes—
337C2×C11C2×#48811yescharacteristic
338C2×C11C2×#49011yescharacteristic
339D11—82no—
340D11#202518yesdirect product factor
341C24—21no—
342C24—111no—
343C24—224no—
344C24—221no—
345C24—444no—
346C24—442no—
347C24—442no—
348C24—444no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—112no—
353C2×D4—2216no—
354C2×D4—224no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—221no—
358C2×D4—448no—
359C2×D4—442no—
360C2×D4—442no—
361C2×D4Q8×D1112yes—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—111no—
365C22×C4—114no—
366C22×C4—112no—
367C22×C4—114no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—224no—
371C22×C4—224no—
372C22×C4—228no—
373C22×C4—224no—
374C22×C4—222no—
375C22×C4—221no—
376C22×C4—444no—
377C22×C4—444no—
378C22×C4—444no—
379C22×C4—442no—
380C22×C4D4×D1112yes—
381C22×C4C23×D1111yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—448no—
389C4⋊C4—28no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—114no—
393C4⋊C4—228no—
394C4⋊C4—228no—
395C4⋊C4—228no—
396C4⋊C4—228no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—442no—
400C4⋊C4D4×D1114yes—
401C22⋊C4—44no—
402C22⋊C4—444no—
403C22⋊C4—444no—
404C22⋊C4—444no—
405C42—22no—
406C42—224no—
407C42—222no—
408C11C2×#202511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23—114no—
415C23—114no—
416C23—112no—
417C23—112no—
418C23—112no—
419C23—222no—
420C23—448no—
421C23—4416no—
422C23—442no—
423C23—442no—
424C23—441no—
425C23—441no—
426C23—888no—
427C23—884no—
428C23—884no—
429C23C2×D4×D1111yescharacteristic
430D4—24no—
431D4—42no—
432D4—224no—
433D4—448no—
434D4—442no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—112no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—118no—
447C2×C4—118no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—224no—
452C2×C4—448no—
453C2×C4—4416no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—884no—
459C2×C4C2×D4×D1112yes—
460C2×C4C2×Q8×D1111yescharacteristic
461C2×C4#41×D1112yes—
462C2×C4#41×D1111yescharacteristic
463C8—42no—
464C8—442no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—81no—
469C22—81no—
470C22—118no—
471C22—118no—
472C22—114no—
473C22—114no—
474C22—114no—
475C22—444no—
476C22—442no—
477C22—8816no—
478C22—882no—
479C22—881no—
480C22—881no—
481C22D11×#12011yescharacteristic
482C22D11×C22⋊Q811yescharacteristic
483C22D11×#12411yescharacteristic
484C22D11×#13512yes—
485C22D11×AGL(1,ℤ/8)12yes—
486C4—42no—
487C4—44no—
488C4—81no—
489C4—114no—
490C4—442no—
491C4—444no—
492C4—881no—
493C4D11×C22⋊Q812yes—
494C4D11×#12412yes—
495C2—82no—
496C2—118no—
497C2—882no—
498C2D11×#39311yescharacteristic
499C2D11×#44912yes—
500C2D11×#47812yes—
501C2D11×#48811yescharacteristic
502C2D11×#49011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2025C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#2025D11
hypocenterC11C2×#2025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
4. #13069763C2semidirect
5. #13069762C2semidirect
6. #13069761C2semidirect
7. #13069760C2semidirect
8. #13069759C2semidirect
9. D11×#340C2semidirect
10. D11×#336C2semidirect
11. C11×#2025C2semidirect
13. C2×C11×#125C22semidirect
19. C2×#66943C22semidirect
23. C2×#66923C22semidirect
34. C11×#340C22semidirect
35. C11×#336C22semidirect
36. #10622189C22semidirect
37. #10622188C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
40. #10622162C22semidirect
166. #2025D11direct (N × H)
231. C2×#125C2×D11semidirect
250. #340C2×D11semidirect
253. #336C2×D11semidirect
340. D11#2025direct (N × H)
408. C11C2×#2025semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×D11×#1022
D11×#3902
#130697632
#130697622
#130697612
#130697602
#130697592
D11×#3402
D11×#3362
C11×#20252
C2×#202511