Finite Group Databasebeta

← C11×#18289 #14595482

Subgroups — C11×#18289 #14595482

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#539C211yesmaximal, characteristic
2C11×#3189C211yesmaximal, characteristic, complemented
3C11×#3187C211yesmaximal, characteristic
4C11×#2627C211yesmaximal, characteristic, complemented
5C11×#1615C214yesmaximal, complemented
6C11×#1603C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic
9C2×C11×#324C211yesmaximal, characteristic, complemented
10C11×#539—22no—
11C11×#539—22no—
12C11×#539—22no—
13C11×#539C2214yes—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#484—21no—
25C11×#484C2212yescomplemented
26C11×#483—21no—
27C11×#481C2212yes—
28C11×#467—22no—
29C11×#465—22no—
30C11×#451—21no—
31C11×#451C2212yescomplemented
32C11×#450—21no—
33C11×#448C2212yes—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#400C2212yescomplemented
37C11×#398—22no—
38C11×#395C2212yescomplemented
39C11×#385—21no—
40C11×#381—21no—
41C11×#380C2211yescharacteristic
42C11×#328C2214yescomplemented
43C11×#327C2214yes—
44C11×#324C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×Q16—22no—
54C2×C11×SD16—22no—
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C11×#126—24no—
58C11×#126—24no—
59C11×#125—24no—
60C11×#125—24no—
61C11×#123—24no—
62C11×#123—24no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121D412yes—
78C11×#121C2312yes—
79C4×D4×C11—24no—
80C4×D4×C11—24no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C11×#107—22no—
106C11×#106—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#102—22no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8C2312yes—
114C11×C22⋊C8C2312yes—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18289C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—21no—
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—81no—
126C2×Q8×C11—81no—
127C2×Q8×C11C2×D412yes—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—81no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11—82no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C11×Q16—82no—
160C11×SD16—82no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—81no—
164C2×C8×C11—81no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4—82no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—42no—
194C42×C11—24no—
195C2×#539C2×C1111yescharacteristic
196#3189C2×C1111yescharacteristic, complemented
197#3187C2×C1111yescharacteristic
198#2627C2×C1111yescharacteristic, complemented
199#1615C2×C1114yescomplemented
200#1603C2×C1114yescomplemented
201#1520C2×C1111yescharacteristic, complemented
202#1519C2×C1111yescharacteristic
203C2×#324C2×C1111yescharacteristic, complemented
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11#12011yescharacteristic
211C23×C11#12011yescharacteristic
212C23×C11#13512yes—
213C23×C11#13712yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—81no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—44no—
223D4×C11—81no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—81no—
252C2×C4×C11—84no—
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C8×C11—42no—
258C8×C11—42no—
259#539—22no—
260#539—22no—
261#539—22no—
262#539C22×C1114yes—
263C2×#126—21no—
264C2×#125—21no—
265C2×#123—21no—
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8C22×C1111yescharacteristic
269C2×C22⋊Q8C22×C1111yescharacteristic
270C2×#121C22×C1111yescharacteristic
271C2×C4×D4—21no—
272C22×C4⋊C4C22×C1111yescharacteristic
273#484—21no—
274#484C22×C1112yescomplemented
275#483—21no—
276#481C22×C1112yes—
277#467—22no—
278#465—22no—
279#451—21no—
280#451C22×C1112yescomplemented
281#450—21no—
282#448C22×C1112yes—
283C2×C22⋊C8C22×C1111yescharacteristic
284C2×C22⋊C8C22×C1111yescharacteristic
285#400C22×C1112yescomplemented
286#398—22no—
287#395C22×C1112yescomplemented
288#385—21no—
289#381—21no—
290#380C22×C1111yescharacteristic
291#328C22×C1114yescomplemented
292#327C22×C1114yes—
293#324C22×C1114yescomplemented
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—84no—
306C22×C11#45212yes—
307C22×C11#45212yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#13511yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11—82no—
321C4×C11—81no—
322C4×C11—81no—
323C22×Q8D4×C1111yescharacteristic
324C22×Q8C23×C1111yescharacteristic
325C22×D4—21no—
326C22×D4D4×C1111yescharacteristic
327C23×C4—21no—
328C23×C4D4×C1111yescharacteristic
329C23×C4D4×C1111yescharacteristic
330C23×C4C23×C1111yescharacteristic
331C2×Q16—22no—
332C2×SD16—22no—
333C22×C8—21no—
334C22×C8—21no—
335#126—24no—
336#126—24no—
337#125—24no—
338#125—24no—
339#123—24no—
340#123—24no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8D4×C1112yes—
352C22⋊Q8C23×C1112yes—
353#121—21no—
354#121—21no—
355#121D4×C1112yes—
356#121C23×C1112yes—
357C4×D4—24no—
358C4×D4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4D4×C1112yes—
371C2×C4⋊C4D4×C1111yescharacteristic
372C2×C4⋊C4D4×C1111yescharacteristic
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1112yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383#107—22no—
384#106—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8C23×C1112yes—
392C22⋊C8C23×C1112yes—
393#95—22no—
394#95—22no—
395#95—22no—
396#95C23×C1112yes—
397C2×C11—21no—
398C2×C11—22no—
399C2×C11—21no—
400C2×C11—22no—
401C2×C11—82no—
402C2×C11C2×#45211yescharacteristic
403C2×C11#302011yescharacteristic
404C2×C11#302611yescharacteristic
405C24—21no—
406C24C2×D4×C1111yescharacteristic
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—81no—
411C2×Q8—81no—
412C2×Q8C2×D4×C1112yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—81no—
419C2×D4C2×D4×C1112yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—82no—
436C22×C4C2×D4×C1112yes—
437C22×C4C2×D4×C1112yes—
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C24×C1111yescharacteristic
444Q16—82no—
445SD16—82no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—81no—
449C2×C8—81no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—81no—
466C4⋊C4—82no—
467C4⋊C4C2×D4×C1112yes—
468C4⋊C4C2×D4×C1112yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—42no—
479C42—24no—
480C11#1828911yescharacteristic, direct product factor, Sylow
481C23—22no—
482C23—41no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23C11×#12011yescharacteristic
488C23C11×#12011yescharacteristic
489C23C11×#13512yes—
490C23C11×#13712yes—
491C23C22×D4×C1111yescharacteristic
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—81no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—44no—
500D4—81no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—84no—
530C2×C4C11×#12011yescharacteristic
531C2×C4C11×#12011yescharacteristic
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C8—42no—
535C8—42no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—84no—
548C22C11×#45212yes—
549C22C11×#45212yes—
550C22C2×C11×#12011yescharacteristic
551C22C2×C11×#13511yescharacteristic
552C22C2×C11×#13711yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—81no—
564C4—81no—
565C2—21no—
566C2—22no—
567C2—21no—
568C2—22no—
569C2—82no—
570C2C2×C11×#45211yescharacteristic
571C2C11×#302011yescharacteristic
572C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3189C2semidirect
4. C11×#2627C2semidirect
5. C11×#1615C2semidirect
6. C11×#1603C2semidirect
7. C11×#1520C2semidirect
9. C2×C11×#324C2semidirect
25. C11×#484C22semidirect
31. C11×#451C22semidirect
36. C11×#400C22semidirect
38. C11×#395C22semidirect
42. C11×#328C22semidirect
44. C11×#324C22semidirect
119. #18289C11direct (N × H)
196. #3189C2×C11semidirect
198. #2627C2×C11semidirect
199. #1615C2×C11semidirect
200. #1603C2×C11semidirect
201. #1520C2×C11semidirect
203. C2×#324C2×C11semidirect
274. #484C22×C11semidirect
280. #451C22×C11semidirect
285. #400C22×C11semidirect
287. #395C22×C11semidirect
291. #328C22×C11semidirect
293. #324C22×C11semidirect
480. C11#18289direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5392
C11×#31892
C11×#31872
C11×#26272
C11×#16152
C11×#16032
C11×#15202
C11×#15192
C2×C11×#3242
#1828911