Finite Group Databasebeta

← C11×#18208 #14595401

Subgroups — C11×#18208 #14595401

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3491C211yesmaximal, characteristic, complemented
2C11×#3105C212yesmaximal, complemented
3C11×#2598C211yesmaximal, characteristic, complemented
4C11×#1615C212yesmaximal, complemented
5C11×#1614C211yesmaximal, characteristic, complemented
6C11×#1613C211yesmaximal, characteristic, complemented
7C11×#1597C212yesmaximal, complemented
8C11×#1596C211yesmaximal, characteristic, complemented
9C11×#1595C211yesmaximal, characteristic
10C11×#1521C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#552—22no—
13C11×#552—22no—
14C11×#551—22no—
15C11×#551—22no—
16C11×#543C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#534C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C2×C11×#123—21no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic, complemented
25C2×C11×#117C2211yescharacteristic
26C11×#484C2212yescomplemented
27C11×#481C2212yes—
28C11×#478—22no—
29C11×#463—22no—
30C11×#450C2212yescomplemented
31C11×#447C2212yes—
32C4×C11×SD16—22no—
33C4×C11×D8—22no—
34C11×#431C2212yescomplemented
35C11×#400C2211yescharacteristic, complemented
36C11×#399C2211yescharacteristic
37C11×#394C2211yescharacteristic, complemented
38C11×#392C2211yescharacteristic
39C11×#388—21no—
40C11×#386—21no—
41C11×#386—21no—
42C11×#385—21no—
43C11×#383C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yescomplemented
49C11×#323C2211yescharacteristic
50C11×#323C2211yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C2×C11×SD16—22no—
57C2×C11×D8—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#125—21no—
63C11×#125—22no—
64C11×#125—22no—
65C11×#125D412yescomplemented
66C11×#124—21no—
67C11×#124D412yescomplemented
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8C2312yes—
81C11×#121—21no—
82C11×#121C2312yes—
83C11×#120—22no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yescomplemented
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11D412yescomplemented
94C11×#117—22no—
95C11×#117—22no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—22no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C42×C11D411yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×C4⋊C8—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C4×C8×C11—22no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18208C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—81no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11—42no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×SD16—44no—
173C11×D8—44no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—22no—
214C42×C11C2×D412yes—
215C42×C11C2×D412yes—
216#3491C2×C1111yescharacteristic, complemented
217#3105C2×C1112yescomplemented
218#2598C2×C1111yescharacteristic, complemented
219#1615C2×C1112yescomplemented
220#1614C2×C1111yescharacteristic, complemented
221#1613C2×C1111yescharacteristic, complemented
222#1597C2×C1112yescomplemented
223#1596C2×C1111yescharacteristic, complemented
224#1595C2×C1111yescharacteristic
225#1521C2×C1112yescomplemented
226#1458C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—81no—
241C23×C11—81no—
242C23×C11#13512yes—
243C23×C11C22×D411yescharacteristic
244Q8×C11—42no—
245Q8×C11—81no—
246D4×C11—24no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—44no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—81no—
253D4×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—82no—
281C2×C4×C11—84no—
282C2×C4×C11—81no—
283C2×C4×C11—82no—
284C2×C4×C11—81no—
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11#12012yes—
288C2×C4×C11C22×D412yes—
289C8×C11—42no—
290C8×C11—42no—
291#552—22no—
292#552—22no—
293#551—22no—
294#551—22no—
295#543C22×C1111yescharacteristic
296#539—21no—
297#539C22×C1112yes—
298#534C22×C1111yescharacteristic
299#529—21no—
300#529C22×C1112yes—
301C2×#123—21no—
302#518—21no—
303C2×C4×D4C22×C1111yescharacteristic, complemented
304C2×#117C22×C1111yescharacteristic
305#484C22×C1112yescomplemented
306#481C22×C1112yes—
307#478—22no—
308#463—22no—
309#450C22×C1112yescomplemented
310#447C22×C1112yes—
311C4×SD16—22no—
312C4×D8—22no—
313#431C22×C1112yescomplemented
314#400C22×C1111yescharacteristic, complemented
315#399C22×C1111yescharacteristic
316#394C22×C1111yescharacteristic, complemented
317#392C22×C1111yescharacteristic
318#388—21no—
319#386—21no—
320#386—21no—
321#385—21no—
322#383C22×C1111yescharacteristic, complemented
323#328C22×C1112yescomplemented
324#328C22×C1112yescomplemented
325#327C22×C1112yes—
326#327C22×C1112yes—
327#324C22×C1112yescomplemented
328#323C22×C1111yescharacteristic
329#323C22×C1111yescharacteristic
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—22no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—162no—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11#57511yescharacteristic
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11—81no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4C23×C1111yescharacteristic
367C23×C4—21no—
368C23×C4D4×C1111yescharacteristic
369C2×SD16—22no—
370C2×D8—22no—
371#126—22no—
372#126—22no—
373#126—22no—
374#126—22no—
375#125—21no—
376#125—22no—
377#125—22no—
378#125D4×C1112yescomplemented
379#124—21no—
380#124D4×C1112yescomplemented
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—22no—
393C22⋊Q8C23×C1112yes—
394#121—21no—
395#121C23×C1112yes—
396#120—22no—
397C4×Q8—21no—
398C4×Q8D4×C1112yescomplemented
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4D4×C1112yescomplemented
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4D4×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4D4×C1111yescharacteristic
428C2×C22⋊C4C23×C1111yescharacteristic
429C2×C42D4×C1111yescharacteristic
430C2×C42C23×C1111yescharacteristic
431#107—22no—
432#106—22no—
433C4⋊C8—22no—
434#103—22no—
435#102—22no—
436#102—22no—
437#102—22no—
438C22⋊C8C23×C1112yes—
439C22⋊C8C23×C1112yes—
440C4×C8—22no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C23×C1111yescharacteristic
446#95C23×C1111yescharacteristic
447C2×C11—21no—
448C2×C11—21no—
449C2×C11—42no—
450C2×C11—82no—
451C2×C11—82no—
452C2×C11#300211yescharacteristic
453C2×C11#302111yescharacteristic
454C2×C11#302511yescharacteristic
455C24—21no—
456C24—21no—
457C24C2×D4×C1111yescharacteristic
458C2×Q8—21no—
459C2×Q8C2×D4×C1112yes—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—81no—
470C2×D4C2×D4×C1112yes—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C24×C1111yescharacteristic
492SD16—44no—
493D8—44no—
494C2×C8—22no—
495C2×C8—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—81no—
510C4⋊C4C2×D4×C1112yes—
511C4⋊C4C2×D4×C1112yes—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—81no—
529C22⋊C4—81no—
530C42—22no—
531C42—21no—
532C42—21no—
533C42—22no—
534C42C2×D4×C1112yes—
535C42C2×D4×C1112yes—
536C11#1820811yescharacteristic, direct product factor, Sylow
537C23—21no—
538C23—21no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—81no—
551C23—81no—
552C23C11×#13512yes—
553C23C22×D4×C1111yescharacteristic
554Q8—42no—
555Q8—81no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—84no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—82no—
591C2×C4—84no—
592C2×C4—81no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4C11×#12011yescharacteristic
596C2×C4C11×#12011yescharacteristic
597C2×C4C11×#12012yes—
598C2×C4C22×D4×C1112yes—
599C8—42no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—22no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—162no—
619C22C2×C11×#12011yescharacteristic
620C22C2×C11×#13511yescharacteristic
621C22C11×#57511yescharacteristic
622C4—21no—
623C4—21no—
624C4—22no—
625C4—22no—
626C4—41no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C2—21no—
636C2—21no—
637C2—42no—
638C2—82no—
639C2—82no—
640C2C11×#300211yescharacteristic
641C2C11×#302111yescharacteristic
642C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#1595C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3491C2semidirect
2. C11×#3105C2semidirect
3. C11×#2598C2semidirect
4. C11×#1615C2semidirect
5. C11×#1614C2semidirect
6. C11×#1613C2semidirect
7. C11×#1597C2semidirect
8. C11×#1596C2semidirect
10. C11×#1521C2semidirect
11. C11×#1458C2semidirect
24. C2×C4×D4×C11C22semidirect
26. C11×#484C22semidirect
30. C11×#450C22semidirect
34. C11×#431C22semidirect
35. C11×#400C22semidirect
37. C11×#394C22semidirect
43. C11×#383C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
48. C11×#324C22semidirect
65. C11×#125D4semidirect
67. C11×#124D4semidirect
85. C4×Q8×C11D4semidirect
93. C4×D4×C11D4semidirect
134. #18208C11direct (N × H)
216. #3491C2×C11semidirect
217. #3105C2×C11semidirect
218. #2598C2×C11semidirect
219. #1615C2×C11semidirect
220. #1614C2×C11semidirect
221. #1613C2×C11semidirect
222. #1597C2×C11semidirect
223. #1596C2×C11semidirect
225. #1521C2×C11semidirect
226. #1458C2×C11semidirect
303. C2×C4×D4C22×C11semidirect
305. #484C22×C11semidirect
309. #450C22×C11semidirect
313. #431C22×C11semidirect
314. #400C22×C11semidirect
316. #394C22×C11semidirect
322. #383C22×C11semidirect
323. #328C22×C11semidirect
324. #328C22×C11semidirect
327. #324C22×C11semidirect
378. #125D4×C11semidirect
380. #124D4×C11semidirect
398. C4×Q8D4×C11semidirect
406. C4×D4D4×C11semidirect
536. C11#18208direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34912
C11×#31052
C11×#25982
C11×#16152
C11×#16142
C11×#16132
C11×#15972
C11×#15962
C11×#15952
C11×#15212
C11×#14582
#1820811