Finite Group Databasebeta

← D11×#1989 #14758278

Subgroups — D11×#1989 #14758278

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3C4×C4⋊C4×D11C211yesmaximal, characteristic
4#13069574C211yesmaximal, characteristic, complemented
5#13069573C211yesmaximal, characteristic, complemented
6#13069572C212yesmaximal, complemented
7#13069571C211yesmaximal, characteristic, complemented
8#13069570C212yesmaximal, complemented
9D11×#340C212yesmaximal
10D11×#340C212yesmaximal
11C11×#1989C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C22×C8×D11C2212yes—
14D11×#125—24no—
15D11×#125C418yescomplemented
16C2×C4⋊C4×D11—21no—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2212yes—
21C2×#66943C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×#66942—21no—
24C2×#66942—21no—
25C2×C42×D11—21no—
26C2×C42×D11C2211yescharacteristic
27C2×#66923C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×Dic11⋊C8C2212yes—
31C4⋊C4×Dic11C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33C4×Dic11⋊C4—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35D11×C4⋊C8—24no—
36D11×#95—21no—
37#10622262—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×C4×D11—22no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×#125—22no—
54C11×#125C2×C414yescomplemented
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2312yes—
80C2×C8×D11—24no—
81C2×C8×D11—28no—
82C4⋊C4×D11—28no—
83C4⋊C4×D11—28no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11C2×C414yes—
88C4⋊C4×D11C2×C414yes—
89C4⋊C4×D11Q818yes—
90#66943—22no—
91#66943—22no—
92#66943C2×C414yescomplemented
93#66943C2×C414yescomplemented
94#66942—28no—
95#66942—28no—
96C42×D11—44no—
97C42×D11C2×C414yes—
98C42×D11D414yes—
99#66923—22no—
100#66923C2×C414yescomplemented
101C11×C4⋊C8—22no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105Dic11⋊C8—24no—
106C4⋊(C11⋊C8)—22no—
107C2×#1989—111nomaximal, Sylow
108C23×D11C2×D411yescharacteristic
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C2×C4×D11—24no—
122C2×C4×D11—24no—
123C2×C4×D11—28no—
124C2×C4×D11—24no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11C22⋊C414yes—
133C2×C4×D11C22⋊C414yes—
134C2×C4×D11C22×C412yes—
135C2×C4×D11C2×D412yes—
136C2×C4×D11C2×Q814yes—
137C2×C4×D11#4114yes—
138C2×C8×C11—22no—
139C2×C8×C11—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C22×C412yes—
146C11×C4⋊C4C22×C412yes—
147C11×C4⋊C4C2×Q814yes—
148C42×C11—42no—
149C42×C11C22×C412yes—
150C42×C11C2×D412yes—
151C4⋊Dic11—24no—
152C4⋊Dic11—24no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11C22×C412yes—
157C4⋊Dic11C22×C412yes—
158C4⋊Dic11C2×Q814yes—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—28no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166C4×Dic11—42no—
167C4×Dic11—44no—
168C4×Dic11C22⋊C414yes—
169C4×Dic11C22⋊C414yes—
170C4×Dic11C22×C412yes—
171C4×Dic11C2×D412yes—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—24no—
174C8×D11—48no—
175C22×#125—111no—
176C22×C4⋊C8—111no—
177C2×C4×C4⋊C4—111no—
178#1989—111no—
179#1989—111no—
180#1989—112no—
181#1989—112no—
182#1989—111no—
183#1989D1111yescharacteristic, direct product factor
184C2×#340—112no—
185C2×#340—112no—
186C23×C11C22×D411yescharacteristic
187C22×D11C2×C22⋊C412yes—
188C22×D11C22⋊Q814yes—
189C22×D11#13514yes—
190C22×D11AGL(1,ℤ/8)12yes—
191C22×D11#13712yes—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q812yes—
208C2×C4×C11C2×#4112yes—
209C2×Dic11—22no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C412yes—
222C2×Dic11C2×C22⋊C412yes—
223C2×Dic11C22⋊Q814yes—
224C4×D11—28no—
225C4×D11—28no—
226C4×D11—48no—
227C4×D11—48no—
228C4×D11—416no—
229C4×D11C4×Q818yes—
230C4×D11#12414yes—
231C4×D11C4⋊Q814yes—
232C8×C11—42no—
233C11⋊C8—42no—
234C23×C8—112no—
235C2×#125—118no—
236C2×#125—111no—
237C2×#125—111no—
238C2×#125—111no—
239C2×#125—221no—
240C2×#125—221no—
241C2×#125—224no—
242C2×#125C2×D1111yescharacteristic
243C22×C4⋊C4—111no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4—221no—
247C22×C4⋊C4—221no—
248C22×C42—111no—
249C22×C42—221no—
250C2×C4⋊C8—112no—
251C2×C4⋊C8—111no—
252C2×C4⋊C8—224no—
253C2×C4⋊C8C2×D1111yescharacteristic
254C4×C4⋊C4—112no—
255C4×C4⋊C4—111no—
256C4×C4⋊C4—221no—
257C4×C4⋊C4—221no—
258C4×C4⋊C4C2×D1111yescharacteristic
259C2×#95—221no—
260#340—112no—
261#340—112no—
262#340—112no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340C2×D1112yes—
267#340C2×D1112yes—
268C22×C11C22×C22⋊C411yescharacteristic
269C22×C11C2×C22⋊Q812yes—
270C22×C11C2×#13512yes—
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C2×D11#39114yes—
274C2×D11#41614yes—
275C2×D11#41714yes—
276C2×D11#47818yes—
277C2×D11#47918yes—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—44no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11C2×C4×Q812yes—
284C4×C11C2×#12411yescharacteristic
285C4×C11C2×C4⋊Q811yescharacteristic
286Dic11—22no—
287Dic11—22no—
288Dic11—44no—
289Dic11—42no—
290Dic11—42no—
291Dic11#39114yes—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—221no—
296C23×C4—221no—
297C23×C4—222no—
298C22×C8—112no—
299C22×C8—228no—
300C22×C8—224no—
301C22×C8C22×D1112yes—
302#125—22no—
303#125—114no—
304#125—114no—
305#125—114no—
306#125—228no—
307#125—228no—
308#125—222no—
309#125—222no—
310#125—222no—
311#125C4×D1114yescomplemented
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—114no—
319C2×C4⋊C4—118no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—224no—
323C2×C4⋊C4—228no—
324C2×C4⋊C4—228no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1112yes—
337C2×C42—21no—
338C2×C42—111no—
339C2×C42—111no—
340C2×C42—111no—
341C2×C42—114no—
342C2×C42—114no—
343C2×C42—222no—
344C2×C42—221no—
345C2×C42—444no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—22no—
348C4⋊C8—224no—
349C4⋊C8—222no—
350#95—21no—
351#95—222no—
352#95—221no—
353C2×C11C2×#39111yescharacteristic
354C2×C11C2×#41611yescharacteristic
355C2×C11C2×#41711yescharacteristic
356C2×C11C2×#47812yes—
357C2×C11C2×#47912yes—
358D11#198918yesdirect product factor
359C24—111no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—111no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—114no—
367C22×C4—114no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—114no—
371C22×C4—114no—
372C22×C4—222no—
373C22×C4—224no—
374C22×C4—222no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—228no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—444no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4D4×D1111yescharacteristic
387C22×C4D4×D1111yescharacteristic
388C22×C4C23×D1111yescharacteristic
389C2×C8—22no—
390C2×C8—24no—
391C2×C8—222no—
392C2×C8—224no—
393C2×C8—448no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—112no—
400C4⋊C4—112no—
401C4⋊C4—114no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—228no—
405C4⋊C4—224no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4C2×C4×D1112yes—
415C4⋊C4C2×C4×D1112yes—
416C4⋊C4Q8×D1114yes—
417C42—42no—
418C42—114no—
419C42—114no—
420C42—112no—
421C42—112no—
422C42—442no—
423C42—444no—
424C42C2×C4×D1112yes—
425C42D4×D1112yes—
426C11C2×#198911yescharacteristic, complemented, Sylow
427C23—112no—
428C23—114no—
429C23—112no—
430C23—112no—
431C23—114no—
432C23C2×D4×D1111yescharacteristic
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—112no—
445C2×C4—114no—
446C2×C4—114no—
447C2×C4—118no—
448C2×C4—114no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—228no—
452C2×C4—228no—
453C2×C4—222no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—224no—
459C2×C4—4416no—
460C2×C4—448no—
461C2×C4—448no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4C22⋊C4×D1112yes—
468C2×C4C22⋊C4×D1112yes—
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4C2×Q8×D1112yes—
472C2×C4#41×D1112yes—
473C8—42no—
474C8—442no—
475C22—118no—
476C22—114no—
477C22—118no—
478C22—114no—
479C22—114no—
480C22C2×C22⋊C4×D1111yescharacteristic
481C22D11×C22⋊Q812yes—
482C22D11×#13512yes—
483C22D11×AGL(1,ℤ/8)11yescharacteristic
484C22D11×#13711yescharacteristic
485C4—22no—
486C4—22no—
487C4—44no—
488C4—42no—
489C4—42no—
490C4—114no—
491C4—222no—
492C4—222no—
493C4—444no—
494C4—442no—
495C4—442no—
496C4C4×Q8×D1112yes—
497C4D11×#12411yescharacteristic
498C4D11×C4⋊Q811yescharacteristic
499C2—118no—
500C2D11×#39111yescharacteristic
501C2D11×#41611yescharacteristic
502C2D11×#41711yescharacteristic
503C2D11×#47812yes—
504C2D11×#47912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11C2×#1989
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
4. #13069574C2semidirect
5. #13069573C2semidirect
6. #13069572C2semidirect
7. #13069571C2semidirect
8. #13069570C2semidirect
11. C11×#1989C2semidirect
15. D11×#125C4semidirect
54. C11×#125C2×C4semidirect
92. #66943C2×C4semidirect
93. #66943C2×C4semidirect
100. #66923C2×C4semidirect
183. #1989D11direct (N × H)
311. #125C4×D11semidirect
358. D11#1989direct (N × H)
426. C11C2×#1989semidirect

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×C4⋊C82
C4×C4⋊C4×D112
#130695742
#130695732
#130695722
#130695712
#130695702
D11×#3402
C11×#19892
C2×#198911