Finite Group Databasebeta

← C11×#18299 #14595492

Subgroups — C11×#18299 #14595492

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic
2C11×#3190C212yesmaximal, complemented
3C11×#2638C211yesmaximal, characteristic, complemented
4C11×#1612C212yesmaximal, complemented
5C11×#1611C211yesmaximal, characteristic, complemented
6C11×#1610C211yesmaximal, characteristic, complemented
7C11×#1606C212yesmaximal, complemented
8C11×#1605C211yesmaximal, characteristic, complemented
9C11×#1604C211yesmaximal, characteristic, complemented
10C11×#1516C212yesmaximal, complemented
11C11×#1459C211yesmaximal, characteristic, complemented
12C11×#544C2211yescharacteristic
13C11×#542—22no—
14C11×#540—22no—
15C11×#538—21no—
16C11×#538C2212yes—
17C11×#537C2211yescharacteristic
18C11×#535—21no—
19C11×#532—22no—
20C11×#529—22no—
21C11×#525—21no—
22C11×#525C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C4×C11×#41—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#485—22no—
27C11×#483C2212yes—
28C11×#480C2212yes—
29C11×#467—22no—
30C11×#465—22no—
31C11×#452—22no—
32C11×#451C2212yes—
33C11×#448C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C11×#398C2211yescharacteristic
36C11×#397—21no—
37C11×#397C2211yescharacteristic
38C11×#395C2211yescharacteristic
39C11×#394—21no—
40C11×#393C2211yescharacteristic
41C11×#387—21no—
42C11×#385—21no—
43C11×#381C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2211yescharacteristic
49C11×#324C2211yescharacteristic
50C11×#323C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41D412yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C22×C8×C11—22no—
61C11×C4⋊Q8—22no—
62C11×#127—22no—
63C11×#126—22no—
64C11×#126—22no—
65C11×#125—22no—
66C11×#124—22no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8D412yes—
79C11×C22⋊Q8C2312yes—
80C11×#121—21no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—21no—
87C11×#121D412yes—
88C11×#121C2312yes—
89C11×#120—22no—
90C11×#120—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C11×#117—22no—
102C11×#117—21no—
103C11×#117—21no—
104C11×#117D412yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
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×C11—22no—
117C2×C42×C11D411yescharacteristic
118C11×#107—22no—
119C11×#106—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#103—22no—
123C11×#102—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18299C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11C2×D411yescharacteristic
136C24×C11C2×D411yescharacteristic
137C11×#41—42no—
138C11×#41—42no—
139C11×#41—82no—
140C11×#41—82no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—22no—
144C2×Q8×C11—81no—
145C2×Q8×C11C2×D412yes—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D412yes—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—81no—
167C22×C4×C11—81no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2411yescharacteristic
175C11×Q16—82no—
176C11×SD16—82no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—82no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—81no—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×D412yes—
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—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—42no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C42×C11—22no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11—22no—
215C42×C11—21no—
216#3460C2×C1111yescharacteristic
217#3190C2×C1112yescomplemented
218#2638C2×C1111yescharacteristic, complemented
219#1612C2×C1112yescomplemented
220#1611C2×C1111yescharacteristic, complemented
221#1610C2×C1111yescharacteristic, complemented
222#1606C2×C1112yescomplemented
223#1605C2×C1111yescharacteristic, complemented
224#1604C2×C1111yescharacteristic, complemented
225#1516C2×C1112yescomplemented
226#1459C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—22no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11#12012yes—
238C23×C11C22×D411yescharacteristic
239Q8×C11—42no—
240Q8×C11—42no—
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—81no—
244D4×C11—44no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11—81no—
253D4×C11—82no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—44no—
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—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—81no—
283C2×C4×C11—82no—
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#13512yes—
287C2×C4×C11C22×D412yes—
288C8×C11—42no—
289C8×C11—42no—
290#544C22×C1111yescharacteristic
291#542—22no—
292#540—22no—
293#538—21no—
294#538C22×C1112yes—
295#537C22×C1111yescharacteristic
296#535—21no—
297#532—22no—
298#529—22no—
299#525—21no—
300#525C22×C1112yes—
301C2×C22⋊Q8C22×C1111yescharacteristic
302C4×#41—21no—
303C2×C4×D4C22×C1111yescharacteristic
304#485—22no—
305#483C22×C1112yes—
306#480C22×C1112yes—
307#467—22no—
308#465—22no—
309#452—22no—
310#451C22×C1112yes—
311#448C22×C1112yes—
312C2×C22⋊C8C22×C1112yes—
313#398C22×C1111yescharacteristic
314#397—21no—
315#397C22×C1111yescharacteristic
316#395C22×C1111yescharacteristic
317#394—21no—
318#393C22×C1111yescharacteristic
319#387—21no—
320#385—21no—
321#381C22×C1111yescharacteristic
322#328C22×C1112yes—
323#328C22×C1112yes—
324#327C22×C1112yes—
325#327C22×C1112yes—
326#324C22×C1111yescharacteristic
327#324C22×C1111yescharacteristic
328#323C22×C1112yes—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11C2×#12011yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11#57511yescharacteristic
347C4×C11—22no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—22no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41D4×C1112yes—
363C22×Q8C23×C1111yescharacteristic
364C22×D4D4×C1111yescharacteristic
365C23×C4D4×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C2×Q16—22no—
368C2×SD16—22no—
369C22×C8—22no—
370C4⋊Q8—22no—
371#127—22no—
372#126—22no—
373#126—22no—
374#125—22no—
375#124—22no—
376#124—22no—
377#124—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8D4×C1112yes—
388C22⋊Q8C23×C1112yes—
389#121—21no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121D4×C1112yes—
397#121C23×C1112yes—
398#120—22no—
399#120—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410#117—22no—
411#117—21no—
412#117—21no—
413#117D4×C1112yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
424C2×C22⋊C4C23×C1111yescharacteristic
425C2×C42—22no—
426C2×C42D4×C1111yescharacteristic
427#107—22no—
428#106—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#102—22no—
433C22⋊C8—22no—
434C22⋊C8C23×C1112yes—
435C22⋊C8C23×C1112yes—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95C23×C1111yescharacteristic
442#95C23×C1111yescharacteristic
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—42no—
446C2×C11—82no—
447C2×C11—81no—
448C2×C11#300211yescharacteristic
449C2×C11#302211yescharacteristic
450C2×C11#302611yescharacteristic
451C24C2×D4×C1111yescharacteristic
452C24C2×D4×C1111yescharacteristic
453#41—42no—
454#41—42no—
455#41—82no—
456#41—82no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—81no—
461C2×Q8C2×D4×C1112yes—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—41no—
472C2×D4C2×D4×C1112yes—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1112yes—
489C22×C4C2×D4×C1112yes—
490C22×C4C24×C1111yescharacteristic
491Q16—82no—
492SD16—82no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—82no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—42no—
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—42no—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—22no—
531C42—21no—
532C11#1829911yescharacteristic, direct product factor, Sylow
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23C11×#12012yes—
544C23C22×D4×C1111yescharacteristic
545Q8—42no—
546Q8—42no—
547Q8—42no—
548Q8—42no—
549Q8—81no—
550D4—44no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—81no—
559D4—82no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—41no—
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—41no—
587C2×C4—41no—
588C2×C4—81no—
589C2×C4—82no—
590C2×C4C11×#12011yescharacteristic
591C2×C4C11×#12011yescharacteristic
592C2×C4C11×#13512yes—
593C2×C4C22×D4×C1112yes—
594C8—42no—
595C8—42no—
596C22—21no—
597C22—21no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—42no—
603C22—41no—
604C22—42no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×C11×#12011yescharacteristic
612C22C2×C11×#13511yescharacteristic
613C22C11×#57511yescharacteristic
614C4—22no—
615C4—22no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—81no—
627C2—21no—
628C2—21no—
629C2—42no—
630C2—81no—
631C2—82no—
632C2C11×#300211yescharacteristic
633C2C11×#302211yescharacteristic
634C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3460C2
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×#3190C2semidirect
3. C11×#2638C2semidirect
4. C11×#1612C2semidirect
5. C11×#1611C2semidirect
6. C11×#1610C2semidirect
7. C11×#1606C2semidirect
8. C11×#1605C2semidirect
9. C11×#1604C2semidirect
10. C11×#1516C2semidirect
11. C11×#1459C2semidirect
134. #18299C11direct (N × H)
217. #3190C2×C11semidirect
218. #2638C2×C11semidirect
219. #1612C2×C11semidirect
220. #1611C2×C11semidirect
221. #1610C2×C11semidirect
222. #1606C2×C11semidirect
223. #1605C2×C11semidirect
224. #1604C2×C11semidirect
225. #1516C2×C11semidirect
226. #1459C2×C11semidirect
532. C11#18299direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34602
C11×#31902
C11×#26382
C11×#16122
C11×#16112
C11×#16102
C11×#16062
C11×#16052
C11×#16042
C11×#15162
C11×#14592
#1829911