Finite Group Databasebeta

← C11×#19088 #14596281

Subgroups — C11×#19088 #14596281

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3559C211yesmaximal, characteristic, complemented
2C11×#3234C211yesmaximal, characteristic, complemented
3C11×#3219C211yesmaximal, characteristic, complemented
4C11×#3214C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1657C212yesmaximal, complemented
8C11×#1656C212yesmaximal, complemented
9C11×#1536C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1534C211yesmaximal, characteristic, complemented
12C11×#563C2212yes—
13C11×#562C2212yes—
14C11×#554—21no—
15C11×#553—21no—
16C11×#553—21no—
17C11×#547—22no—
18C11×#547—21no—
19C11×#544—21no—
20C11×#540—21no—
21C11×#539—22no—
22C11×#539—21no—
23C11×#537—21no—
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#125C2211yescharacteristic
28C11×#501C2212yes—
29C11×#497C2211yescharacteristic
30C11×#496C2211yescharacteristic
31C11×#496C2212yes—
32C11×#491C2211yescharacteristic
33C11×#490C2212yes—
34C11×#490C2211yescharacteristic
35C11×#489C2212yes—
36C11×#481—21no—
37C11×#480—21no—
38C11×#478—22no—
39C11×#464—21no—
40C11×#463—21no—
41C11×#461—21no—
42C11×#459—21no—
43C11×#452—21no—
44C11×#449—22no—
45C11×#449—21no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#329C2212yes—
53C11×#329C2212yes—
54C11×#329C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41—21no—
57C2×C11×#41D412yes—
58C2×C11×Q16—21no—
59C2×C11×SD16—22no—
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×D8—22no—
63C2×C11×D8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×#127D411yescharacteristic
69C11×#127C2311yescharacteristic
70C11×#126—22no—
71C11×#126—22no—
72C11×#126—21no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—21no—
76C11×#125—21no—
77C11×#125D412yes—
78C11×#125C2311yescharacteristic
79C11×#125C2312yes—
80C11×#124—21no—
81C11×#124C2312yes—
82C11×#124C2311yescharacteristic
83C11×#123—22no—
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—22no—
87C11×#123—21no—
88C11×#123—22no—
89C11×#123—22no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8D411yescharacteristic
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—21no—
100C11×#121—21no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121D411yescharacteristic
108C4×Q8×C11D411yescharacteristic
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11D411yescharacteristic
119C11×#117—21no—
120C11×#117—21no—
121C2×C11×C4⋊C4—22no—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4D411yescharacteristic
126C2×C11×C4⋊C4D411yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#106—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—22no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#102—22no—
137C11×#102—21no—
138C11×#102—21no—
139C11×#102—22no—
140C11×#102—22no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2312yes—
145C11×#97C2312yes—
146C11×#97C2311yescharacteristic
147C11×#97C2311yescharacteristic
148#19088C1111yesmaximal, characteristic, direct product factor, Sylow
149C11×#41—84no—
150C11×#41—81no—
151C11×#41—81no—
152C11×#41—82no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—41no—
167C2×D4×C11C2×D412yes—
168C2×D4×C11C2×D411yescharacteristic
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—41no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C11×Q16—81no—
181C11×SD16—81no—
182C11×SD16—82no—
183C11×SD16—81no—
184C11×D8—81no—
185C11×D8—82no—
186C2×C8×C11—22no—
187C2×C8×C11—21no—
188C2×C8×C11—22no—
189C2×C8×C11—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C42×C11—22no—
227C42×C11—21no—
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2411yescharacteristic
232#3559C2×C1111yescharacteristic, complemented
233#3234C2×C1111yescharacteristic, complemented
234#3219C2×C1111yescharacteristic, complemented
235#3214C2×C1111yescharacteristic, complemented
236#1664C2×C1112yescomplemented
237#1661C2×C1112yescomplemented
238#1657C2×C1112yescomplemented
239#1656C2×C1112yescomplemented
240#1536C2×C1111yescharacteristic, complemented
241#1535C2×C1111yescharacteristic, complemented
242#1534C2×C1111yescharacteristic, complemented
243C23×C11—22no—
244C23×C11—21no—
245C23×C11—41no—
246C23×C11#12011yescharacteristic
247Q8×C11—41no—
248Q8×C11—42no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—82no—
252D4×C11—41no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—42no—
260D4×C11—44no—
261D4×C11—42no—
262D4×C11—81no—
263D4×C11—82no—
264D4×C11—82no—
265D4×C11—82no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—82no—
279C2×C4×C11—82no—
280C2×C4×C11—81no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11—82no—
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C8×C11—42no—
291C8×C11—42no—
292C8×C11—41no—
293C8×C11—41no—
294#563C22×C1112yes—
295#562C22×C1112yes—
296#554—21no—
297#553—21no—
298#553—21no—
299#547—22no—
300#547—21no—
301#544—21no—
302#540—21no—
303#539—22no—
304#539—21no—
305#537—21no—
306#532C22×C1111yescharacteristic
307#532C22×C1111yescharacteristic
308#529C22×C1111yescharacteristic
309C2×#125C22×C1111yescharacteristic
310#501C22×C1112yes—
311#497C22×C1111yescharacteristic
312#496C22×C1111yescharacteristic
313#496C22×C1112yes—
314#491C22×C1111yescharacteristic
315#490C22×C1112yes—
316#490C22×C1111yescharacteristic
317#489C22×C1112yes—
318#481—21no—
319#480—21no—
320#478—22no—
321#464—21no—
322#463—21no—
323#461—21no—
324#459—21no—
325#452—21no—
326#449—22no—
327#449—21no—
328#432C22×C1111yescharacteristic
329#432C22×C1111yescharacteristic
330#432C22×C1111yescharacteristic
331#330C22×C1112yes—
332#330C22×C1112yes—
333#330C22×C1112yes—
334#329C22×C1112yes—
335#329C22×C1112yes—
336#329C22×C1112yes—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—42no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—41no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11C2×#12011yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—81no—
363C2×#41—22no—
364C2×#41—21no—
365C2×#41D4×C1112yes—
366C2×Q16—21no—
367C2×SD16—22no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×D8—22no—
371C2×D8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—22no—
374C4⋊Q8D4×C1111yescharacteristic
375C4⋊Q8C23×C1111yescharacteristic
376#127D4×C1111yescharacteristic
377#127C23×C1111yescharacteristic
378#126—22no—
379#126—22no—
380#126—21no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125D4×C1112yes—
386#125C23×C1112yes—
387#125C23×C1111yescharacteristic
388#124—21no—
389#124C23×C1111yescharacteristic
390#124C23×C1112yes—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—21no—
396#123—22no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8D4×C1111yescharacteristic
405#121—22no—
406#121—22no—
407#121—21no—
408#121—21no—
409#121—22no—
410#121—22no—
411#121—21no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121D4×C1111yescharacteristic
416C4×Q8D4×C1111yescharacteristic
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4D4×C1111yescharacteristic
427#117—21no—
428#117—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1111yescharacteristic
434C2×C4⋊C4D4×C1111yescharacteristic
435C2×C42C23×C1111yescharacteristic
436#107—22no—
437#106—22no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441#103—22no—
442#103—21no—
443#103—21no—
444#102—22no—
445#102—21no—
446#102—21no—
447#102—22no—
448#102—22no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97C23×C1112yes—
453#97C23×C1111yescharacteristic
454#97C23×C1111yescharacteristic
455#97C23×C1112yes—
456C2×C11—41no—
457C2×C11—82no—
458C2×C11—81no—
459C2×C11—161no—
460C2×C11#301911yescharacteristic
461C2×C11#302011yescharacteristic
462C2×C11#302111yescharacteristic
463#41—84no—
464#41—81no—
465#41—81no—
466#41—82no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8C2×D4×C1112yes—
470C2×Q8C2×D4×C1111yescharacteristic
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4C2×D4×C1112yes—
482C2×D4C2×D4×C1111yescharacteristic
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494Q16—81no—
495SD16—82no—
496SD16—81no—
497SD16—81no—
498D8—81no—
499D8—82no—
500C2×C8—22no—
501C2×C8—21no—
502C2×C8—22no—
503C2×C8—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4C2×D4×C1111yescharacteristic
523C4⋊C4C2×D4×C1111yescharacteristic
524C4⋊C4C2×D4×C1112yes—
525C4⋊C4C2×D4×C1112yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C42—22no—
541C42—21no—
542C42C2×D4×C1111yescharacteristic
543C42C2×D4×C1111yescharacteristic
544C42C2×D4×C1111yescharacteristic
545C42C24×C1111yescharacteristic
546C11#1908811yescharacteristic, direct product factor, Sylow
547C23—22no—
548C23—21no—
549C23—41no—
550C23C11×#12011yescharacteristic
551Q8—41no—
552Q8—42no—
553Q8—41no—
554Q8—41no—
555Q8—82no—
556D4—41no—
557D4—42no—
558D4—42no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4C11×#12011yescharacteristic
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C22×D4×C1111yescharacteristic
593C2×C4C22×D4×C1111yescharacteristic
594C8—42no—
595C8—41no—
596C8—41no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×C11×#12011yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—81no—
624C2—41no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C11×#301911yescharacteristic
629C2C11×#302011yescharacteristic
630C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ 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×#3559C2semidirect
2. C11×#3234C2semidirect
3. C11×#3219C2semidirect
4. C11×#3214C2semidirect
5. C11×#1664C2semidirect
6. C11×#1661C2semidirect
7. C11×#1657C2semidirect
8. C11×#1656C2semidirect
9. C11×#1536C2semidirect
10. C11×#1535C2semidirect
11. C11×#1534C2semidirect
148. #19088C11direct (N × H)
232. #3559C2×C11semidirect
233. #3234C2×C11semidirect
234. #3219C2×C11semidirect
235. #3214C2×C11semidirect
236. #1664C2×C11semidirect
237. #1661C2×C11semidirect
238. #1657C2×C11semidirect
239. #1656C2×C11semidirect
240. #1536C2×C11semidirect
241. #1535C2×C11semidirect
242. #1534C2×C11semidirect
546. C11#19088direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35592
C11×#32342
C11×#32192
C11×#32142
C11×#16642
C11×#16612
C11×#16572
C11×#16562
C11×#15362
C11×#15352
C11×#15342
#1908811