Finite Group Databasebeta

← C11×#18200 #14595393

Subgroups — C11×#18200 #14595393

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3490C211yesmaximal, characteristic
2C11×#3091C212yesmaximal, complemented
3C11×#2482C211yesmaximal, characteristic, complemented
4C11×#1618C212yesmaximal, complemented
5C11×#1614C211yesmaximal, characteristic, complemented
6C11×#1613C211yesmaximal, characteristic, complemented
7C11×#1612C212yesmaximal, complemented
8C11×#1608C211yesmaximal, characteristic, complemented
9C11×#1607C211yesmaximal, characteristic, complemented
10C11×#1516C212yesmaximal, complemented
11C2×C11×#323C211yesmaximal, characteristic, complemented
12C11×#551—22no—
13C11×#551—22no—
14C11×#546—22no—
15C11×#546—22no—
16C11×#543C2211yescharacteristic
17C11×#538—21no—
18C11×#538C2212yes—
19C11×#534C2211yescharacteristic
20C11×#525—21no—
21C11×#525C2212yes—
22C2×C11×#120—21no—
23C11×#518—21no—
24C2×C11×#117C2211yescharacteristic, complemented
25C22×C11×C22⋊C4C2211yescharacteristic
26C11×#485—22no—
27C11×#484C2212yescomplemented
28C11×#483C2212yescomplemented
29C11×#482—22no—
30C11×#481C2212yescomplemented
31C11×#480C2212yescomplemented
32C11×#427—22no—
33C11×#416—22no—
34C2×C11×C22⋊C8C2212yescomplemented
35C11×#399C2211yescharacteristic
36C11×#399C2211yescharacteristic, complemented
37C11×#397C2211yescharacteristic
38C11×#397C2211yescharacteristic, complemented
39C11×#388—21no—
40C11×#388—21no—
41C11×#385—21no—
42C11×#381C2211yescharacteristic, complemented
43C11×#379—21no—
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yescomplemented
47C11×#327C2212yescomplemented
48C11×#323C2211yescharacteristic
49C11×#323C2211yescharacteristic
50C11×#323C2212yescomplemented
51C25×C11D411yescharacteristic
52C2×C11×#41—21no—
53C2×C11×#41D412yes—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C8×C11—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#124—22no—
63C11×#124—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—21no—
79C11×#121D412yes—
80C11×#121C2312yes—
81C11×#120—22no—
82C11×#120—22no—
83C11×#120—22no—
84C11×#120—22no—
85C11×#120—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C11×#117—22no—
93C11×#117—21no—
94C11×#117—22no—
95C11×#117—22no—
96C11×#117D412yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
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⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4C2311yescharacteristic
117C2×C42×C11—21no—
118C11×#107—22no—
119C11×#107—22no—
120C11×#106—22no—
121C11×#106—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8C2312yes—
128C11×C22⋊C8C2312yes—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18200C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—22no—
139C24×C11—41no—
140C24×C11—42no—
141C24×C11—81no—
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C11×#41—44no—
146C11×#41—82no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D412yes—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—82no—
159C2×D4×C11—82no—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—42no—
173C22×C4×C11—81no—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2411yescharacteristic
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—44no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—81no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4C2×D412yes—
194C11×C4⋊C4C2×D412yes—
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—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—81no—
215C11×C22⋊C4—81no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—42no—
219#3490C2×C1111yescharacteristic
220#3091C2×C1112yescomplemented
221#2482C2×C1111yescharacteristic, complemented
222#1618C2×C1112yescomplemented
223#1614C2×C1111yescharacteristic, complemented
224#1613C2×C1111yescharacteristic, complemented
225#1612C2×C1112yescomplemented
226#1608C2×C1111yescharacteristic, complemented
227#1607C2×C1111yescharacteristic, complemented
228#1516C2×C1112yescomplemented
229C2×#323C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—22no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—22no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—41no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—81no—
250C23×C11—81no—
251C23×C11—81no—
252C23×C11—81no—
253C23×C11—84no—
254C23×C11—84no—
255C23×C11#12011yescharacteristic
256C23×C11#12011yescharacteristic
257C23×C11#13512yes—
258C23×C11C22×D411yescharacteristic
259Q8×C11—42no—
260Q8×C11—81no—
261D4×C11—42no—
262D4×C11—44no—
263D4×C11—44no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—44no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—81no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—41no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—82no—
296C2×C4×C11—81no—
297C2×C4×C11—81no—
298C2×C4×C11—81no—
299C2×C4×C11—82no—
300C2×C4×C11#12012yes—
301C2×C4×C11C22×D412yes—
302C8×C11—42no—
303C8×C11—42no—
304#551—22no—
305#551—22no—
306#546—22no—
307#546—22no—
308#543C22×C1111yescharacteristic
309#538—21no—
310#538C22×C1112yes—
311#534C22×C1111yescharacteristic
312#525—21no—
313#525C22×C1112yes—
314C2×#120—21no—
315#518—21no—
316C2×#117C22×C1111yescharacteristic, complemented
317C22×C22⋊C4C22×C1111yescharacteristic
318#485—22no—
319#484C22×C1112yescomplemented
320#483C22×C1112yescomplemented
321#482—22no—
322#481C22×C1112yescomplemented
323#480C22×C1112yescomplemented
324#427—22no—
325#416—22no—
326C2×C22⋊C8C22×C1112yescomplemented
327#399C22×C1111yescharacteristic
328#399C22×C1111yescharacteristic, complemented
329#397C22×C1111yescharacteristic
330#397C22×C1111yescharacteristic, complemented
331#388—21no—
332#388—21no—
333#385—21no—
334#381C22×C1111yescharacteristic, complemented
335#379—21no—
336#328C22×C1112yescomplemented
337#328C22×C1112yescomplemented
338#327C22×C1112yescomplemented
339#327C22×C1112yescomplemented
340#323C22×C1111yescharacteristic
341#323C22×C1111yescharacteristic
342#323C22×C1112yescomplemented
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—42no—
358C22×C11—41no—
359C22×C11—42no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11—41no—
363C22×C11—81no—
364C22×C11—84no—
365C22×C11—81no—
366C22×C11—84no—
367C22×C11—162no—
368C22×C11#45812yes—
369C22×C11C2×#12011yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11#57511yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C25D4×C1111yescharacteristic
384C2×#41—21no—
385C2×#41D4×C1112yes—
386C22×D4—21no—
387C22×D4—21no—
388C22×D4—21no—
389C23×C4D4×C1111yescharacteristic
390C23×C4C23×C1111yescharacteristic
391C22×C8—22no—
392#126—22no—
393#126—22no—
394#124—22no—
395#124—22no—
396#123—22no—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8D4×C1112yes—
406C22⋊Q8C23×C1112yes—
407#121—21no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121D4×C1112yes—
412#121C23×C1112yes—
413#120—22no—
414#120—22no—
415#120—22no—
416#120—22no—
417#120—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424#117—22no—
425#117—21no—
426#117—22no—
427#117—22no—
428#117D4×C1112yes—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C22⋊C4—22no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4D4×C1111yescharacteristic
446C2×C22⋊C4D4×C1111yescharacteristic
447C2×C22⋊C4C23×C1111yescharacteristic
448C2×C22⋊C4C23×C1111yescharacteristic
449C2×C42—21no—
450#107—22no—
451#107—22no—
452#106—22no—
453#106—22no—
454#103—22no—
455#103—22no—
456#102—22no—
457#102—22no—
458C22⋊C8—22no—
459C22⋊C8C23×C1112yes—
460C22⋊C8C23×C1112yes—
461#95—21no—
462#95—21no—
463#95—21no—
464#95C23×C1111yescharacteristic
465#95C23×C1111yescharacteristic
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—22no—
469C2×C11—41no—
470C2×C11—42no—
471C2×C11—81no—
472C2×C11—82no—
473C2×C11#300211yescharacteristic
474C2×C11#301911yescharacteristic
475C2×C11C2×#45811yescharacteristic
476C24—21no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—41no—
481C24—42no—
482C24—81no—
483C24C2×D4×C1111yescharacteristic
484C24C2×D4×C1111yescharacteristic
485C24C2×D4×C1111yescharacteristic
486#41—44no—
487#41—82no—
488C2×Q8—21no—
489C2×Q8C2×D4×C1112yes—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—82no—
500C2×D4—82no—
501C2×D4C2×D4×C1112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—81no—
515C22×C4C2×D4×C1112yes—
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1112yes—
520C22×C4C24×C1111yescharacteristic
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—44no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4C2×D4×C1112yes—
535C4⋊C4C2×D4×C1112yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—22no—
558C42—22no—
559C42—42no—
560C11#1820011yescharacteristic, direct product factor, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—22no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—21no—
569C23—21no—
570C23—41no—
571C23—42no—
572C23—42no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—84no—
585C23—84no—
586C23C11×#12011yescharacteristic
587C23C11×#12011yescharacteristic
588C23C11×#13512yes—
589C23C22×D4×C1111yescharacteristic
590Q8—42no—
591Q8—81no—
592D4—42no—
593D4—44no—
594D4—44no—
595D4—42no—
596D4—42no—
597D4—44no—
598D4—82no—
599D4—82no—
600D4—81no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—82no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—82no—
631C2×C4C11×#12012yes—
632C2×C4C22×D4×C1112yes—
633C8—42no—
634C8—42no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—22no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—41no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—41no—
655C22—81no—
656C22—84no—
657C22—81no—
658C22—84no—
659C22—162no—
660C22C11×#45812yes—
661C22C2×C11×#12011yescharacteristic
662C22C2×C11×#13511yescharacteristic
663C22C11×#57511yescharacteristic
664C4—22no—
665C4—22no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—81no—
674C4—81no—
675C2—21no—
676C2—21no—
677C2—22no—
678C2—41no—
679C2—42no—
680C2—81no—
681C2—82no—
682C2C11×#300211yescharacteristic
683C2C11×#301911yescharacteristic
684C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3490C2
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×#3091C2semidirect
3. C11×#2482C2semidirect
4. C11×#1618C2semidirect
5. C11×#1614C2semidirect
6. C11×#1613C2semidirect
7. C11×#1612C2semidirect
8. C11×#1608C2semidirect
9. C11×#1607C2semidirect
10. C11×#1516C2semidirect
11. C2×C11×#323C2semidirect
24. C2×C11×#117C22semidirect
27. C11×#484C22semidirect
28. C11×#483C22semidirect
30. C11×#481C22semidirect
31. C11×#480C22semidirect
34. C2×C11×C22⋊C8C22semidirect
36. C11×#399C22semidirect
38. C11×#397C22semidirect
42. C11×#381C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
46. C11×#327C22semidirect
47. C11×#327C22semidirect
50. C11×#323C22semidirect
134. #18200C11direct (N × H)
220. #3091C2×C11semidirect
221. #2482C2×C11semidirect
222. #1618C2×C11semidirect
223. #1614C2×C11semidirect
224. #1613C2×C11semidirect
225. #1612C2×C11semidirect
226. #1608C2×C11semidirect
227. #1607C2×C11semidirect
228. #1516C2×C11semidirect
229. C2×#323C2×C11semidirect
316. C2×#117C22×C11semidirect
319. #484C22×C11semidirect
320. #483C22×C11semidirect
322. #481C22×C11semidirect
323. #480C22×C11semidirect
326. C2×C22⋊C8C22×C11semidirect
328. #399C22×C11semidirect
330. #397C22×C11semidirect
334. #381C22×C11semidirect
336. #328C22×C11semidirect
337. #328C22×C11semidirect
338. #327C22×C11semidirect
339. #327C22×C11semidirect
342. #323C22×C11semidirect
560. C11#18200direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34902
C11×#30912
C11×#24822
C11×#16182
C11×#16142
C11×#16132
C11×#16122
C11×#16082
C11×#16072
C11×#15162
C2×C11×#3232
#1820011