Finite Group Databasebeta

← D11×#2088 #14782815

Subgroups — D11×#2088 #14782815

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#106C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3D11×#389C211yesmaximal, characteristic
4D11×#389C211yesmaximal, characteristic
5#13070120C211yesmaximal, characteristic, complemented
6#13070119C211yesmaximal, characteristic, complemented
7#13070118C211yesmaximal, characteristic, complemented
8#13070117C211yesmaximal, characteristic, complemented
9#13070116C211yesmaximal, characteristic, complemented
10#13070115C211yesmaximal, characteristic, complemented
11#13070114C211yesmaximal, characteristic, complemented
12D11×#340C211yesmaximal, characteristic
13D11×#340C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#2088C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37#10622585—21no—
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43D11×#106—24no—
44D11×C4⋊C8—24no—
45D11×#95—21no—
46D11×#95—21no—
47#10622260—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×C8×D11—22no—
97C2×C8×D11—22no—
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101C2×C8×D11D414yes—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—44no—
109C4⋊C4×D11—44no—
110C4⋊C4×D11Q814yes—
111C4⋊C4×D11Q814yes—
112C42×D11—22no—
113C42×D11—22no—
114C11×#106—22no—
115C11×C4⋊C8—22no—
116C11×#95—21no—
117C11×#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66881—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—22no—
127#66872—22no—
128#66872—22no—
129C4⋊(C11⋊C8)—22no—
130C2×#2088—111nomaximal, Sylow
131C23×D11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11SD1614yes—
164C2×C4×D11C2×D412yes—
165C2×C4×D11C2×Q812yes—
166C2×C4×D11C2×Q812yes—
167C2×C4×D11#4112yes—
168C2×C4×D11#4112yes—
169C2×C4×D11#4112yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4C2×Q812yes—
185C11×C4⋊C4C2×Q812yes—
186C42×C11—21no—
187C42×C11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11C2×Q812yes—
197C4⋊Dic11C2×Q812yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C8×D11—28no—
217C8×D11—44no—
218C22×#106—111no—
219C22×C4⋊C8—111no—
220C2×#389—111no—
221C2×#389—111no—
222#2088—111no—
223#2088—111no—
224#2088—111no—
225#2088—111no—
226#2088—111no—
227#2088—111no—
228#2088—111no—
229#2088D1111yescharacteristic, direct product factor
230C2×#340—111no—
231C2×#340—111no—
232C2×#340—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11#12112yes—
235C22×D11C22⋊Q812yes—
236C22×D11C22⋊Q812yes—
237C22×D11C2×SD1612yes—
238C22×D11#13512yes—
239C22×D11AGL(1,ℤ/8)12yes—
240C22×D11#13712yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C2×SD1612yes—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11#12112yes—
283C2×Dic11C22⋊Q812yes—
284C2×Dic11C22⋊Q812yes—
285C2×Dic11C2×SD1612yes—
286C4×D11—28no—
287C4×D11—44no—
288C4×D11—48no—
289C4×D11—48no—
290C4×D11—84no—
291C4×D11—84no—
292C4×D11#12314yes—
293C4×D11#12514yes—
294C4×D11#12514yes—
295C4×D11C4⋊Q814yes—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C23×C8—111no—
301C23×C8—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—221no—
307C22×C4⋊C4—221no—
308C22×C42—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×#106—224no—
313C2×#106C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×C4⋊C8—224no—
318C2×C4⋊C8C2×D1111yescharacteristic
319#389—111no—
320#389—111no—
321#389—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#389—221no—
326#389—221no—
327#389—221no—
328#389—221no—
329#389C2×D1111yescharacteristic
330#389C2×D1111yescharacteristic
331C2×#95—221no—
332C2×#95—221no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345C22×C11C2×#12111yescharacteristic
346C22×C11C2×C22⋊Q811yescharacteristic
347C22×C11C2×C22⋊Q811yescharacteristic
348C22×C11C22×SD1611yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C2×D11#39814yes—
353C2×D11#46514yes—
354C2×D11#46814yes—
355C2×D11#47514yes—
356C2×D11#47614yes—
357C2×D11#47814yes—
358C2×D11#47914yes—
359C4×C11—22no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11C2×#12311yescharacteristic
366C4×C11C2×#12511yescharacteristic
367C4×C11C2×#12511yescharacteristic
368C4×C11C2×C4⋊Q811yescharacteristic
369Dic11—22no—
370Dic11—42no—
371Dic11—41no—
372Dic11—42no—
373Dic11—81no—
374Dic11—81no—
375Dic11#39814yes—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4—221no—
383C22×C8—111no—
384C22×C8—114no—
385C22×C8—111no—
386C22×C8—222no—
387C22×C8—222no—
388C22×C8—222no—
389C22×C8—222no—
390C22×C8—222no—
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—444no—
418C2×C4⋊C4—444no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—222no—
427C2×C42—222no—
428C2×C42C22×D1111yescharacteristic
429#106—22no—
430#106—222no—
431#106—222no—
432#106—222no—
433C4⋊C8—22no—
434C4⋊C8—222no—
435C4⋊C8—222no—
436C4⋊C8—222no—
437#95—21no—
438#95—21no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11C2×#39811yescharacteristic
446C2×C11C2×#46511yescharacteristic
447C2×C11C2×#46811yescharacteristic
448C2×C11C2×#47611yescharacteristic
449C2×C11C2×#47811yescharacteristic
450C2×C11C2×#47511yescharacteristic
451C2×C11C2×#47911yescharacteristic
452D11#208818yesdirect product factor
453C24—111no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—111no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—111no—
466C22×C4—114no—
467C22×C4—111no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—112no—
498C2×C8—228no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—444no—
505C2×C8D4×D1112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—224no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4Q8×D1112yes—
533C4⋊C4Q8×D1112yes—
534C42—21no—
535C42—21no—
536C42—222no—
537C42—222no—
538C42—221no—
539C42—221no—
540C11C2×#208811yescharacteristic, complemented, Sylow
541C23—112no—
542C23—112no—
543C23—112no—
544C23—112no—
545C23—112no—
546C23—112no—
547C23—112no—
548C23C2×D4×D1111yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—112no—
567C2×C4—112no—
568C2×C4—112no—
569C2×C4—114no—
570C2×C4—114no—
571C2×C4—114no—
572C2×C4—114no—
573C2×C4—112no—
574C2×C4—228no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—444no—
583C2×C4—448no—
584C2×C4—448no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—884no—
596C2×C4—884no—
597C2×C4SD16×D1112yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×Q8×D1111yescharacteristic
600C2×C4C2×Q8×D1111yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C8—22no—
605C8—41no—
606C8—222no—
607C8—441no—
608C22—114no—
609C22—114no—
610C22—114no—
611C22—114no—
612C22—114no—
613C22—114no—
614C22—114no—
615C22D11×#12111yescharacteristic
616C22D11×C22⋊Q811yescharacteristic
617C22D11×C22⋊Q811yescharacteristic
618C22C2×SD16×D1111yescharacteristic
619C22D11×#13511yescharacteristic
620C22D11×AGL(1,ℤ/8)11yescharacteristic
621C22D11×#13711yescharacteristic
622C4—22no—
623C4—42no—
624C4—42no—
625C4—41no—
626C4—81no—
627C4—81no—
628C4—114no—
629C4—222no—
630C4—442no—
631C4—442no—
632C4—441no—
633C4—881no—
634C4—881no—
635C4D11×#12311yescharacteristic
636C4D11×#12511yescharacteristic
637C4D11×#12511yescharacteristic
638C4D11×C4⋊Q811yescharacteristic
639C2—118no—
640C2D11×#39811yescharacteristic
641C2D11×#46511yescharacteristic
642C2D11×#46811yescharacteristic
643C2D11×#47611yescharacteristic
644C2D11×#47811yescharacteristic
645C2D11×#47511yescharacteristic
646C2D11×#47911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2088C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2088D11
hypocenterC11C2×#2088
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #13070120C2semidirect
6. #13070119C2semidirect
7. #13070118C2semidirect
8. #13070117C2semidirect
9. #13070116C2semidirect
10. #13070115C2semidirect
11. #13070114C2semidirect
15. C11×#2088C2semidirect
229. #2088D11direct (N × H)
452. D11#2088direct (N × H)
540. C11C2×#2088semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1062
C2×D11×C4⋊C82
D11×#3892
#130701202
#130701192
#130701182
#130701172
#130701162
#130701152
#130701142
D11×#3402
C11×#20882
C2×#208811