Finite Group Databasebeta

← C11×#18216 #14595409

Subgroups — C11×#18216 #14595409

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic, complemented
2C11×#3105C212yesmaximal, complemented
3C11×#2598C211yesmaximal, characteristic, complemented
4C11×#1618C212yesmaximal, complemented
5C11×#1617C211yesmaximal, characteristic, complemented
6C11×#1616C211yesmaximal, characteristic, complemented
7C11×#1600C212yesmaximal, complemented
8C11×#1599C211yesmaximal, characteristic, complemented
9C11×#1598C211yesmaximal, characteristic, complemented
10C11×#1521C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#556—22no—
13C11×#555—22no—
14C11×#553—22no—
15C11×#552—22no—
16C11×#544C2211yescharacteristic
17C11×#538—21no—
18C11×#538C2212yes—
19C11×#537C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C11×#525—21no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#484C2212yes—
27C11×#481C2212yes—
28C11×#478—22no—
29C11×#463—22no—
30C11×#450C2212yes—
31C11×#447C2212yes—
32C4×C11×SD16—22no—
33C4×C11×D8—22no—
34C11×#431C2212yes—
35C11×#400C2211yescharacteristic
36C11×#399C2211yescharacteristic
37C11×#394C2211yescharacteristic
38C11×#392C2211yescharacteristic
39C11×#388—21no—
40C11×#386—21no—
41C11×#386—21no—
42C11×#385—21no—
43C11×#383C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2211yescharacteristic
49C11×#324C2211yescharacteristic
50C11×#323C2212yes—
51C2×C11×#41—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C2×C11×SD16—22no—
57C2×C11×D8—22no—
58C11×C4⋊Q8—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#125—21no—
64C11×#125—22no—
65C11×#125D412yescomplemented
66C11×#124—21no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124D412yescomplemented
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8C2312yes—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—21no—
84C11×#121C2312yes—
85C11×#120—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—21no—
88C4×Q8×C11D412yescomplemented
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11D412yescomplemented
98C11×#117—22no—
99C11×#117—22no—
100C11×#117—21no—
101C11×#117—22no—
102C11×#117—22no—
103C11×#117—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
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#18216C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C11×#41—42no—
138C11×#41—42no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—81no—
152C2×D4×C11C2×D412yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
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—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
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—42no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—22no—
214C42×C11C2×D412yes—
215C42×C11C2×D412yes—
216#3493C2×C1111yescharacteristic, complemented
217#3105C2×C1112yescomplemented
218#2598C2×C1111yescharacteristic, complemented
219#1618C2×C1112yescomplemented
220#1617C2×C1111yescharacteristic, complemented
221#1616C2×C1111yescharacteristic, complemented
222#1600C2×C1112yescomplemented
223#1599C2×C1111yescharacteristic, complemented
224#1598C2×C1111yescharacteristic, complemented
225#1521C2×C1112yescomplemented
226#1458C2×C1111yescharacteristic, complemented
227C23×C11—22no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—81no—
244D4×C11—24no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—82no—
251D4×C11—81no—
252D4×C11—82no—
253D4×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—41no—
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—82no—
280C2×C4×C11—84no—
281C2×C4×C11—82no—
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12012yes—
285C2×C4×C11#13512yes—
286C2×C4×C11C22×D412yes—
287C8×C11—42no—
288C8×C11—42no—
289#556—22no—
290#555—22no—
291#553—22no—
292#552—22no—
293#544C22×C1111yescharacteristic
294#538—21no—
295#538C22×C1112yes—
296#537C22×C1111yescharacteristic
297#529—21no—
298#529C22×C1112yes—
299#525—21no—
300#520—21no—
301C2×C4×D4C22×C1111yescharacteristic
302C2×#117C22×C1111yescharacteristic
303#484C22×C1112yes—
304#481C22×C1112yes—
305#478—22no—
306#463—22no—
307#450C22×C1112yes—
308#447C22×C1112yes—
309C4×SD16—22no—
310C4×D8—22no—
311#431C22×C1112yes—
312#400C22×C1111yescharacteristic
313#399C22×C1111yescharacteristic
314#394C22×C1111yescharacteristic
315#392C22×C1111yescharacteristic
316#388—21no—
317#386—21no—
318#386—21no—
319#385—21no—
320#383C22×C1111yescharacteristic
321#328C22×C1112yes—
322#328C22×C1112yes—
323#327C22×C1112yes—
324#327C22×C1112yes—
325#324C22×C1111yescharacteristic
326#324C22×C1111yescharacteristic
327#323C22×C1112yes—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11C2×#12011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11#57511yescharacteristic
348C4×C11—22no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C2×#41—21no—
362C22×D4—21no—
363C22×D4C23×C1111yescharacteristic
364C23×C4—21no—
365C23×C4D4×C1111yescharacteristic
366C2×SD16—22no—
367C2×D8—22no—
368C4⋊Q8—22no—
369#126—22no—
370#126—22no—
371#126—22no—
372#126—22no—
373#125—21no—
374#125—22no—
375#125D4×C1112yescomplemented
376#124—21no—
377#124—22no—
378#124—22no—
379#124D4×C1112yescomplemented
380#123—22no—
381#123—22no—
382#123—22no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8C23×C1112yes—
388#121—21no—
389#121—21no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121C23×C1112yes—
395#120—22no—
396C4×Q8—22no—
397C4×Q8—21no—
398C4×Q8D4×C1112yescomplemented
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4D4×C1112yescomplemented
408#117—22no—
409#117—22no—
410#117—21no—
411#117—22no—
412#117—22no—
413#117—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4D4×C1111yescharacteristic
417C2×C4⋊C4C23×C1111yescharacteristic
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4D4×C1111yescharacteristic
425C2×C22⋊C4C23×C1111yescharacteristic
426C2×C42D4×C1111yescharacteristic
427C2×C42C23×C1111yescharacteristic
428#107—22no—
429#106—22no—
430C4⋊C8—22no—
431#103—22no—
432#102—22no—
433#102—22no—
434#102—22no—
435C22⋊C8C23×C1112yes—
436C22⋊C8C23×C1112yes—
437C4×C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95C23×C1111yescharacteristic
443#95C23×C1111yescharacteristic
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—82no—
447C2×C11—81no—
448C2×C11—82no—
449C2×C11#300211yescharacteristic
450C2×C11#302111yescharacteristic
451C2×C11#302511yescharacteristic
452C24—21no—
453C24C2×D4×C1111yescharacteristic
454#41—42no—
455#41—42no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C1112yes—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—81no—
469C2×D4C2×D4×C1112yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C24×C1111yescharacteristic
489SD16—44no—
490D8—44no—
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—81no—
507C4⋊C4C2×D4×C1112yes—
508C4⋊C4C2×D4×C1112yes—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
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—42no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C42—22no—
527C42—22no—
528C42—21no—
529C42—21no—
530C42—22no—
531C42C2×D4×C1112yes—
532C42C2×D4×C1112yes—
533C11#1821611yescharacteristic, direct product factor, Sylow
534C23—22no—
535C23—21no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C22×D4×C1111yescharacteristic
548Q8—42no—
549Q8—42no—
550Q8—81no—
551D4—24no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—82no—
558D4—81no—
559D4—82no—
560D4—84no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—84no—
588C2×C4—82no—
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C11×#12012yes—
592C2×C4C11×#13512yes—
593C2×C4C22×D4×C1112yes—
594C8—42no—
595C8—42no—
596C22—21no—
597C22—21no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—42no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22C2×C11×#12011yescharacteristic
614C22C2×C11×#13511yescharacteristic
615C22C11×#57511yescharacteristic
616C4—22no—
617C4—21no—
618C4—21no—
619C4—22no—
620C4—22no—
621C4—42no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—42no—
626C4—81no—
627C4—81no—
628C4—81no—
629C2—21no—
630C2—21no—
631C2—81no—
632C2—82no—
633C2—82no—
634C2C11×#300211yescharacteristic
635C2C11×#302111yescharacteristic
636C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
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×#3493C2semidirect
2. C11×#3105C2semidirect
3. C11×#2598C2semidirect
4. C11×#1618C2semidirect
5. C11×#1617C2semidirect
6. C11×#1616C2semidirect
7. C11×#1600C2semidirect
8. C11×#1599C2semidirect
9. C11×#1598C2semidirect
10. C11×#1521C2semidirect
11. C11×#1458C2semidirect
65. C11×#125D4semidirect
69. C11×#124D4semidirect
88. C4×Q8×C11D4semidirect
97. C4×D4×C11D4semidirect
134. #18216C11direct (N × H)
216. #3493C2×C11semidirect
217. #3105C2×C11semidirect
218. #2598C2×C11semidirect
219. #1618C2×C11semidirect
220. #1617C2×C11semidirect
221. #1616C2×C11semidirect
222. #1600C2×C11semidirect
223. #1599C2×C11semidirect
224. #1598C2×C11semidirect
225. #1521C2×C11semidirect
226. #1458C2×C11semidirect
375. #125D4×C11semidirect
379. #124D4×C11semidirect
398. C4×Q8D4×C11semidirect
407. C4×D4D4×C11semidirect
533. C11#18216direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#31052
C11×#25982
C11×#16182
C11×#16172
C11×#16162
C11×#16002
C11×#15992
C11×#15982
C11×#15212
C11×#14582
#1821611