Finite Group Databasebeta

← C11×#32883 #14610076

Subgroups — C11×#32883 #14610076

Order 2816.

3926 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×#41C211yesmaximal, characteristic
2C2×C11×#452C214yesmaximal, complemented
3C2×C11×#451C211yesmaximal, characteristic, complemented
4C2×C11×#450C211yesmaximal, characteristic, complemented
5C11×#2848C211yesmaximal, characteristic, complemented
6C11×#1788C214yesmaximal, complemented
7C11×#1787C211yesmaximal, characteristic, complemented
8C11×#1786C211yesmaximal, characteristic, complemented
9C11×#1779C211yesmaximal, characteristic, complemented
10C22×C11×#41—216no—
11C22×C11×#41—24no—
12C22×C11×#41—24no—
13C22×C11×#41—22no—
14C22×C11×#41C2214yes—
15C23×Q8×C11C2211yescharacteristic
16C23×D4×C11—21no—
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11—21no—
19C24×C4×C11C2211yescharacteristic
20C22×C11×Q16C2212yescomplemented
21C22×C11×SD16C2212yescomplemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×C22⋊Q8C2212yescomplemented
24C11×#452—216no—
25C11×#451—24no—
26C11×#450—24no—
27C2×C11×#103C2212yescomplemented
28C2×C11×#103C2214yescomplemented
29C2×C11×#102C2212yescomplemented
30C2×C11×#102C2214yescomplemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2214yescomplemented
34C11×#385—22no—
35C11×#385—21no—
36C11×#380C2211yescharacteristic
37C11×#380C2212yescomplemented
38C11×#379—21no—
39C25×C11—21no—
40C25×C11D411yescharacteristic
41C2×C11×#41—264no—
42C2×C11×#41—264no—
43C2×C11×#41—216no—
44C2×C11×#41—216no—
45C2×C11×#41—216no—
46C2×C11×#41—28no—
47C2×C11×#41—28no—
48C2×C11×#41—28no—
49C2×C11×#41—28no—
50C2×C11×#41—28no—
51C2×C11×#41D4116yes—
52C22×Q8×C11—28no—
53C22×Q8×C11—22no—
54C22×Q8×C11—21no—
55C22×Q8×C11D414yes—
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C22×D4×C11—216no—
59C22×D4×C11—28no—
60C22×D4×C11—24no—
61C22×D4×C11—28no—
62C22×D4×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11D414yes—
65C22×D4×C11C2312yes—
66C23×C4×C11—216no—
67C23×C4×C11—28no—
68C23×C4×C11—21no—
69C23×C4×C11—24no—
70C23×C4×C11—22no—
71C23×C4×C11—22no—
72C23×C4×C11—28no—
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D412yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2312yes—
77C2×C11×Q16—24no—
78C2×C11×Q16—28no—
79C2×C11×SD16—24no—
80C2×C11×SD16—28no—
81C22×C8×C11C2312yes—
82C22×C8×C11C2312yes—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—28no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C11×#103—24no—
95C11×#103—28no—
96C11×#102—24no—
97C11×#102—28no—
98C11×C22⋊C8—22no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—28no—
101C11×#95—21no—
102C11×#95—22no—
103#32883C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—28no—
105C24×C11—24no—
106C24×C11—22no—
107C24×C11—24no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—42no—
112C24×C11—44no—
113C24×C11—42no—
114C24×C11—42no—
115C24×C11C2×D412yes—
116C24×C11C2×D411yescharacteristic
117C11×#41—2128no—
118C11×#41—232no—
119C11×#41—232no—
120C11×#41—232no—
121C11×#41—232no—
122C2×Q8×C11—216no—
123C2×Q8×C11—28no—
124C2×Q8×C11—216no—
125C2×Q8×C11—24no—
126C2×Q8×C11—24no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11C2×D418yes—
132C2×Q8×C11C2×D414yes—
133C2×D4×C11—264no—
134C2×D4×C11—216no—
135C2×D4×C11—216no—
136C2×D4×C11—28no—
137C2×D4×C11—216no—
138C2×D4×C11—216no—
139C2×D4×C11—216no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—24no—
143C2×D4×C11C2×D418yes—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—28no—
146C22×C4×C11—264no—
147C22×C4×C11—216no—
148C22×C4×C11—216no—
149C22×C4×C11—216no—
150C22×C4×C11—216no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—24no—
156C22×C4×C11—216no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D418yes—
171C22×C4×C11C2411yescharacteristic
172C11×Q16—48no—
173C11×SD16—48no—
174C2×C8×C11—22no—
175C2×C8×C11—24no—
176C2×C8×C11—24no—
177C2×C8×C11—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—44no—
182C11×C4⋊C4—42no—
183C11×C22⋊C4—44no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C23×#41C2×C1111yescharacteristic
188C2×#452C2×C1114yescomplemented
189C2×#451C2×C1111yescharacteristic, complemented
190C2×#450C2×C1111yescharacteristic, complemented
191#2848C2×C1111yescharacteristic, complemented
192#1788C2×C1114yescomplemented
193#1787C2×C1111yescharacteristic, complemented
194#1786C2×C1111yescharacteristic, complemented
195#1779C2×C1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—28no—
199C23×C11—216no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—28no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—416no—
211C23×C11—44no—
212C23×C11—48no—
213C23×C11—416no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—48no—
219C23×C11#12014yes—
220C23×C11#12012yes—
221C23×C11#13512yes—
222C23×C11#13712yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—216no—
225Q8×C11—24no—
226Q8×C11—28no—
227Q8×C11—42no—
228Q8×C11—42no—
229Q8×C11#12018yes—
230D4×C11—264no—
231D4×C11—216no—
232D4×C11—28no—
233D4×C11—24no—
234D4×C11#12018yes—
235C2×C4×C11—28no—
236C2×C4×C11—216no—
237C2×C4×C11—264no—
238C2×C4×C11—216no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—28no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11#12014yes—
256C2×C4×C11#12012yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D414yes—
259C2×C4×C11C22×D411yescharacteristic
260C8×C11—42no—
261C8×C11—42no—
262C22×#41—216no—
263C22×#41—24no—
264C22×#41—24no—
265C22×#41—22no—
266C22×#41C22×C1114yes—
267C23×Q8C22×C1111yescharacteristic
268C23×D4—21no—
269C23×D4C22×C1111yescharacteristic
270C24×C4—21no—
271C24×C4C22×C1111yescharacteristic
272C22×Q16C22×C1112yescomplemented
273C22×SD16C22×C1112yescomplemented
274C2×C22⋊Q8C22×C1111yescharacteristic
275C2×C22⋊Q8C22×C1112yescomplemented
276#452—216no—
277#451—24no—
278#450—24no—
279C2×#103C22×C1112yescomplemented
280C2×#103C22×C1114yescomplemented
281C2×#102C22×C1112yescomplemented
282C2×#102C22×C1114yescomplemented
283C2×C22⋊C8C22×C1111yescharacteristic
284C2×C22⋊C8C22×C1111yescharacteristic
285C2×C22⋊C8C22×C1114yescomplemented
286#385—22no—
287#385—21no—
288#380C22×C1111yescharacteristic
289#380C22×C1112yescomplemented
290#379—21no—
291C22×C11—22no—
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—28no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—416no—
300C22×C11—432no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—48no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—48no—
309C22×C11#45214yescomplemented
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#12012yes—
312C22×C11C2×#13511yescharacteristic
313C22×C11C2×#13711yescharacteristic
314C22×C11#57512yes—
315C4×C11—24no—
316C4×C11—28no—
317C4×C11—22no—
318C4×C11—81no—
319C4×C11—82no—
320C4×C11—81no—
321C4×C11C2×#12012yes—
322C4×C11C2×#12012yes—
323C25—21no—
324C25D4×C1111yescharacteristic
325C2×#41—264no—
326C2×#41—264no—
327C2×#41—216no—
328C2×#41—216no—
329C2×#41—216no—
330C2×#41—28no—
331C2×#41—28no—
332C2×#41—28no—
333C2×#41—28no—
334C2×#41—28no—
335C2×#41D4×C11116yes—
336C22×Q8—28no—
337C22×Q8—22no—
338C22×Q8—21no—
339C22×Q8D4×C1114yes—
340C22×Q8C23×C1111yescharacteristic
341C22×Q8C23×C1112yes—
342C22×D4—216no—
343C22×D4—28no—
344C22×D4—24no—
345C22×D4—28no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4D4×C1114yes—
349C22×D4C23×C1112yes—
350C23×C4—216no—
351C23×C4—28no—
352C23×C4—21no—
353C23×C4—24no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—28no—
357C23×C4D4×C1111yescharacteristic
358C23×C4D4×C1112yes—
359C23×C4C23×C1111yescharacteristic
360C23×C4C23×C1112yes—
361C2×Q16—24no—
362C2×Q16—28no—
363C2×SD16—24no—
364C2×SD16—28no—
365C22×C8C23×C1112yes—
366C22×C8C23×C1112yes—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—28no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4C23×C1111yescharacteristic
373C2×C4⋊C4C23×C1112yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378#103—24no—
379#103—28no—
380#102—24no—
381#102—28no—
382C22⋊C8—22no—
383C22⋊C8—22no—
384C22⋊C8—28no—
385#95—21no—
386#95—22no—
387C2×C11—24no—
388C2×C11—44no—
389C2×C11—48no—
390C2×C11#284611yescharacteristic
391C2×C11C2×#45211yescharacteristic
392C2×C11#300212yes—
393C2×C11#300511yescharacteristic
394C2×C11#300712yes—
395C24—28no—
396C24—24no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—42no—
403C24—44no—
404C24—42no—
405C24—42no—
406C24C2×D4×C1112yes—
407C24C2×D4×C1111yescharacteristic
408#41—2128no—
409#41—232no—
410#41—232no—
411#41—232no—
412#41—232no—
413C2×Q8—216no—
414C2×Q8—28no—
415C2×Q8—216no—
416C2×Q8—24no—
417C2×Q8—24no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—24no—
421C2×Q8—21no—
422C2×Q8C2×D4×C1118yes—
423C2×Q8C2×D4×C1114yes—
424C2×D4—264no—
425C2×D4—216no—
426C2×D4—216no—
427C2×D4—28no—
428C2×D4—216no—
429C2×D4—216no—
430C2×D4—216no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—24no—
434C2×D4C2×D4×C1118yes—
435C2×D4C2×D4×C1114yes—
436C22×C4—28no—
437C22×C4—264no—
438C22×C4—216no—
439C22×C4—216no—
440C22×C4—216no—
441C22×C4—216no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—216no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4C2×D4×C1112yes—
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1112yes—
460C22×C4C2×D4×C1112yes—
461C22×C4C2×D4×C1118yes—
462C22×C4C24×C1111yescharacteristic
463Q16—48no—
464SD16—48no—
465C2×C8—22no—
466C2×C8—24no—
467C2×C8—24no—
468C2×C8—22no—
469C4⋊C4—21no—
470C4⋊C4—24no—
471C4⋊C4—21no—
472C4⋊C4—44no—
473C4⋊C4—42no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C11#3288311yescharacteristic, direct product factor, Sylow
479C23—22no—
480C23—22no—
481C23—28no—
482C23—216no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—28no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—48no—
492C23—48no—
493C23—416no—
494C23—44no—
495C23—48no—
496C23—416no—
497C23—42no—
498C23—42no—
499C23—44no—
500C23—44no—
501C23—48no—
502C23C11×#12014yes—
503C23C11×#12012yes—
504C23C11×#13512yes—
505C23C11×#13712yes—
506C23C22×D4×C1111yescharacteristic
507Q8—216no—
508Q8—24no—
509Q8—28no—
510Q8—42no—
511Q8—42no—
512Q8C11×#12018yes—
513D4—264no—
514D4—216no—
515D4—28no—
516D4—24no—
517D4C11×#12018yes—
518C2×C4—28no—
519C2×C4—216no—
520C2×C4—264no—
521C2×C4—216no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—28no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4C11×#12014yes—
539C2×C4C11×#12012yes—
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C22×D4×C1114yes—
542C2×C4C22×D4×C1111yescharacteristic
543C8—42no—
544C8—42no—
545C22—24no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—28no—
553C22—416no—
554C22—432no—
555C22—42no—
556C22—44no—
557C22—42no—
558C22—48no—
559C22—42no—
560C22—44no—
561C22—42no—
562C22—48no—
563C22C11×#45214yescomplemented
564C22C2×C11×#12011yescharacteristic
565C22C2×C11×#12012yes—
566C22C2×C11×#13511yescharacteristic
567C22C2×C11×#13711yescharacteristic
568C22C11×#57512yes—
569C4—24no—
570C4—28no—
571C4—22no—
572C4—82no—
573C4—81no—
574C4—81no—
575C4C2×C11×#12012yes—
576C4C2×C11×#12012yes—
577C2—24no—
578C2—44no—
579C2—48no—
580C2C11×#284611yescharacteristic
581C2C2×C11×#45211yescharacteristic
582C2C11×#300212yes—
583C2C11×#300511yescharacteristic
584C2C11×#300712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×C11×#41C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#452C2semidirect
3. C2×C11×#451C2semidirect
4. C2×C11×#450C2semidirect
5. C11×#2848C2semidirect
6. C11×#1788C2semidirect
7. C11×#1787C2semidirect
8. C11×#1786C2semidirect
9. C11×#1779C2semidirect
20. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
23. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#102C22semidirect
33. C2×C11×C22⋊C8C22semidirect
37. C11×#380C22semidirect
103. #32883C11direct (N × H)
188. C2×#452C2×C11semidirect
189. C2×#451C2×C11semidirect
190. C2×#450C2×C11semidirect
191. #2848C2×C11semidirect
192. #1788C2×C11semidirect
193. #1787C2×C11semidirect
194. #1786C2×C11semidirect
195. #1779C2×C11semidirect
272. C22×Q16C22×C11semidirect
273. C22×SD16C22×C11semidirect
275. C2×C22⋊Q8C22×C11semidirect
279. C2×#103C22×C11semidirect
280. C2×#103C22×C11semidirect
281. C2×#102C22×C11semidirect
282. C2×#102C22×C11semidirect
285. C2×C22⋊C8C22×C11semidirect
289. #380C22×C11semidirect
309. C22×C11#452semidirect
478. C11#32883direct (N × H)
563. C22C11×#452semidirect

Maximal subgroups

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

subgroupindex
C23×C11×#412
C2×C11×#4522
C2×C11×#4512
C2×C11×#4502
C11×#28482
C11×#17882
C11×#17872
C11×#17862
C11×#17792
#3288311