Finite Group Databasebeta

← C11×#18278 #14595471

Subgroups — C11×#18278 #14595471

Order 2816.

910 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×#3563C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic, complemented
3C11×#3105C211yesmaximal, characteristic
4C11×#2562C211yesmaximal, characteristic, complemented
5C11×#1617C212yesmaximal, complemented
6C11×#1615C212yesmaximal, complemented
7C11×#1599C212yesmaximal, complemented
8C11×#1597C212yesmaximal
9C11×#1509C211yesmaximal, characteristic, complemented
10C11×#1503C211yesmaximal, characteristic, complemented
11C11×#1470C211yesmaximal, characteristic, complemented
12C11×#564—21no—
13C11×#563—21no—
14C11×#557—21no—
15C11×#554—21no—
16C11×#552—21no—
17C11×#552—21no—
18C11×#552—22no—
19C11×#544—21no—
20C11×#544C2212yes—
21C11×#541—21no—
22C11×#541—22no—
23C11×#539C2212yes—
24C11×#533C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#484C2212yes—
29C11×#484C2211yescharacteristic
30C11×#481C2211yescharacteristic
31C11×#478—21no—
32C11×#474—21no—
33C11×#463—21no—
34C11×#461—21no—
35C11×#450C2211yescharacteristic
36C11×#450C2212yes—
37C11×#447C2211yescharacteristic
38C11×#440—22no—
39C4×C11×SD16—21no—
40C4×C11×D8—21no—
41C11×#432C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C11×#400C2212yes—
44C11×#394C2212yes—
45C11×#388—22no—
46C11×#380—21no—
47C11×#380—21no—
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#328C2212yes—
50C11×#328C2212yes—
51C11×#328C2212yes—
52C11×#327C2212yes—
53C11×#324C2212yes—
54C11×#324C2212yes—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C2×C11×SD16—21no—
58C2×C11×SD16—22no—
59C2×C11×D8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×#126—22no—
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—22no—
69C11×#126—21no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#125—21no—
80C11×#125—21no—
81C11×#125—21no—
82C11×#125—21no—
83C11×#125—21no—
84C11×#125D411yescharacteristic
85C11×#124D411yescharacteristic
86C11×#123—22no—
87C11×#123—21no—
88C11×#123—22no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—21no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8C2311yescharacteristic
97C11×C22⋊Q8C2312yes—
98C11×#121C2311yescharacteristic
99C4×Q8×C11—21no—
100C4×Q8×C11—22no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11D411yescharacteristic
104C4×Q8×C11D412yes—
105C4×D4×C11—21no—
106C4×D4×C11—22no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11D411yescharacteristic
112C11×#117—22no—
113C11×#117—21no—
114C11×#117—21no—
115C11×#117—22no—
116C11×#117—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C4⋊C4D412yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—21no—
130C11×#107—22no—
131C11×#106—21no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×#103—21no—
135C11×#103—22no—
136C11×#102—21no—
137C11×#102—21no—
138C11×#102—21no—
139C11×#102—22no—
140C11×C22⋊C8C2312yes—
141C11×C22⋊C8C2311yescharacteristic
142C11×C22⋊C8C2311yescharacteristic
143C11×#97—21no—
144C4×C8×C11—21no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18278C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D412yes—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2411yescharacteristic
172C11×SD16—42no—
173C11×SD16—44no—
174C11×D8—42no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—44no—
219C11×C22⋊C4—41no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—82no—
222C42×C11—22no—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11—81no—
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232#3563C2×C1111yescharacteristic, complemented
233#3110C2×C1111yescharacteristic, complemented
234#3105C2×C1111yescharacteristic
235#2562C2×C1111yescharacteristic, complemented
236#1617C2×C1112yescomplemented
237#1615C2×C1112yescomplemented
238#1599C2×C1112yescomplemented
239#1597C2×C1112yes—
240#1509C2×C1111yescharacteristic, complemented
241#1503C2×C1111yescharacteristic, complemented
242#1470C2×C1111yescharacteristic, complemented
243C23×C11—22no—
244C23×C11—21no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252Q8×C11—41no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—82no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—82no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—42no—
296#564—21no—
297#563—21no—
298#557—21no—
299#554—21no—
300#552—21no—
301#552—21no—
302#552—22no—
303#544—21no—
304#544C22×C1112yes—
305#541—21no—
306#541—22no—
307#539C22×C1112yes—
308#533C22×C1111yescharacteristic
309#529C22×C1111yescharacteristic
310C2×#125C22×C1111yescharacteristic
311C2×C4×D4C22×C1111yescharacteristic
312#484C22×C1111yescharacteristic
313#484C22×C1112yes—
314#481C22×C1111yescharacteristic
315#478—21no—
316#474—21no—
317#463—21no—
318#461—21no—
319#450C22×C1111yescharacteristic
320#450C22×C1112yes—
321#447C22×C1111yescharacteristic
322#440—22no—
323C4×SD16—21no—
324C4×D8—21no—
325#432C22×C1111yescharacteristic
326#431C22×C1111yescharacteristic
327#400C22×C1112yes—
328#394C22×C1112yes—
329#388—22no—
330#380—21no—
331#380—21no—
332C4×C4⋊C4C22×C1111yescharacteristic
333#328C22×C1112yes—
334#328C22×C1112yes—
335#328C22×C1112yes—
336#327C22×C1112yes—
337#324C22×C1112yes—
338#324C22×C1112yes—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C2×#12011yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57811yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—82no—
367C4×C11—81no—
368C4×C11#45412yes—
369C22×D4C23×C1111yescharacteristic
370C23×C4—21no—
371C2×SD16—21no—
372C2×SD16—22no—
373C2×D8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377C4⋊Q8D4×C1111yescharacteristic
378C4⋊Q8D4×C1111yescharacteristic
379#126—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#126—21no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—21no—
389#125—22no—
390#125—22no—
391#125—22no—
392#125—22no—
393#125—21no—
394#125—21no—
395#125—21no—
396#125—21no—
397#125—21no—
398#125D4×C1111yescharacteristic
399#124D4×C1111yescharacteristic
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—22no—
410C22⋊Q8C23×C1111yescharacteristic
411C22⋊Q8C23×C1112yes—
412#121C23×C1111yescharacteristic
413C4×Q8—21no—
414C4×Q8—22no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8D4×C1111yescharacteristic
418C4×Q8D4×C1112yes—
419C4×D4—21no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4D4×C1111yescharacteristic
426#117—22no—
427#117—21no—
428#117—21no—
429#117—22no—
430#117—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1111yescharacteristic
434C2×C4⋊C4D4×C1112yes—
435C2×C4⋊C4D4×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1112yes—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C42—21no—
442C2×C42C23×C1111yescharacteristic
443#107—21no—
444#107—22no—
445#106—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448#103—21no—
449#103—22no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—22no—
454C22⋊C8C23×C1112yes—
455C22⋊C8C23×C1111yescharacteristic
456C22⋊C8C23×C1111yescharacteristic
457#97—21no—
458C4×C8—21no—
459#95—22no—
460#95—22no—
461#95C23×C1112yes—
462C2×C11—21no—
463C2×C11—21no—
464C2×C11—81no—
465C2×C11—82no—
466C2×C11#301311yescharacteristic
467C2×C11C2×#45411yescharacteristic
468C2×C11#302511yescharacteristic
469C24—21no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8C2×D4×C1112yes—
473C2×Q8C2×D4×C1111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4C2×D4×C1111yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4C2×D4×C1112yes—
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1112yes—
491C22×C4C24×C1111yescharacteristic
492SD16—42no—
493SD16—44no—
494D8—42no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4C2×D4×C1111yescharacteristic
527C4⋊C4C2×D4×C1111yescharacteristic
528C4⋊C4C2×D4×C1112yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—44no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—82no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—21no—
547C42—81no—
548C42C2×D4×C1111yescharacteristic
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C2×D4×C1111yescharacteristic
552C11#1827811yescharacteristic, direct product factor, Sylow
553C23—22no—
554C23—21no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×D4×C1111yescharacteristic
562Q8—41no—
563Q8—42no—
564Q8—42no—
565Q8—82no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4C11×#12011yescharacteristic
598C2×C4C11×#12011yescharacteristic
599C2×C4C11×#12011yescharacteristic
600C2×C4C11×#12011yescharacteristic
601C2×C4C22×D4×C1111yescharacteristic
602C2×C4C22×D4×C1111yescharacteristic
603C8—41no—
604C8—41no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22C2×C11×#12011yescharacteristic
619C22C11×#57711yescharacteristic
620C22C11×#57811yescharacteristic
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—41no—
633C4—82no—
634C4—81no—
635C4C11×#45412yes—
636C2—21no—
637C2—21no—
638C2—82no—
639C2—81no—
640C2C11×#301311yescharacteristic
641C2C2×C11×#45411yescharacteristic
642C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#447C22
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×#3563C2semidirect
2. C11×#3110C2semidirect
4. C11×#2562C2semidirect
5. C11×#1617C2semidirect
6. C11×#1615C2semidirect
7. C11×#1599C2semidirect
9. C11×#1509C2semidirect
10. C11×#1503C2semidirect
11. C11×#1470C2semidirect
148. #18278C11direct (N × H)
232. #3563C2×C11semidirect
233. #3110C2×C11semidirect
235. #2562C2×C11semidirect
236. #1617C2×C11semidirect
237. #1615C2×C11semidirect
238. #1599C2×C11semidirect
240. #1509C2×C11semidirect
241. #1503C2×C11semidirect
242. #1470C2×C11semidirect
552. C11#18278direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#31102
C11×#31052
C11×#25622
C11×#16172
C11×#16152
C11×#15992
C11×#15972
C11×#15092
C11×#15032
C11×#14702
#1827811