Finite Group Databasebeta

← C11×#18386 #14595579

Subgroups — C11×#18386 #14595579

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3491C211yesmaximal, characteristic, complemented
2C11×#3211C212yesmaximal, complemented
3C11×#2610C211yesmaximal, characteristic, complemented
4C11×#1603C212yesmaximal, complemented
5C11×#1602C211yesmaximal, characteristic, complemented
6C11×#1601C211yesmaximal, characteristic, complemented
7C11×#1597C212yesmaximal, complemented
8C11×#1596C211yesmaximal, characteristic, complemented
9C11×#1595C211yesmaximal, characteristic
10C11×#1500C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#552—22no—
13C11×#552—22no—
14C11×#551—22no—
15C11×#551—22no—
16C11×#543C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#534C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C2×C11×#124C2211yescharacteristic, complemented
23C2×C11×#123—21no—
24C11×#518—21no—
25C2×C11×#117C2211yescharacteristic
26C11×#495—22no—
27C11×#488—22no—
28C11×#464—22no—
29C11×#463—22no—
30C11×#451C2212yescomplemented
31C11×#450C2212yescomplemented
32C11×#448C2212yes—
33C11×#447C2212yes—
34C11×#431C2212yescomplemented
35C11×#395C2211yescharacteristic, complemented
36C11×#394C2211yescharacteristic, complemented
37C11×#393C2211yescharacteristic
38C11×#392C2211yescharacteristic
39C11×#390—21no—
40C11×#388—21no—
41C11×#388—21no—
42C11×#386—21no—
43C11×#376C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yescomplemented
49C11×#323C2211yescharacteristic
50C11×#323C2211yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11D411yescharacteristic
56C2×C11×Q16—22no—
57C2×C11×SD16—22no—
58C2×C11×SD16—22no—
59C2×C11×D8—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#126—22no—
64C11×#125—21no—
65C11×#125—22no—
66C11×#125—22no—
67C11×#125D412yescomplemented
68C11×#124—21no—
69C11×#124—22no—
70C11×#124—22no—
71C11×#124D412yescomplemented
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8C2312yes—
85C11×#121—21no—
86C11×#121C2312yes—
87C11×#120—22no—
88C4×Q8×C11—21no—
89C4×Q8×C11D412yescomplemented
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11D412yescomplemented
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117—22no—
100C11×#117—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4C2311yescharacteristic
118C2×C42×C11—21no—
119C2×C42×C11D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×C4⋊C8—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#102—22no—
125C11×#102—22no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C4×C8×C11—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18386C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11—81no—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—81no—
151C2×D4×C11—81no—
152C2×D4×C11C2×D412yes—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×Q16—82no—
172C11×SD16—82no—
173C11×SD16—82no—
174C11×D8—82no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
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—22no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C42×C11—22no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—22no—
215C42×C11—42no—
216C42×C11C2×D412yes—
217C42×C11C2×D412yes—
218#3491C2×C1111yescharacteristic, complemented
219#3211C2×C1112yescomplemented
220#2610C2×C1111yescharacteristic, complemented
221#1603C2×C1112yescomplemented
222#1602C2×C1111yescharacteristic, complemented
223#1601C2×C1111yescharacteristic, complemented
224#1597C2×C1112yescomplemented
225#1596C2×C1111yescharacteristic, complemented
226#1595C2×C1111yescharacteristic
227#1500C2×C1112yescomplemented
228#1458C2×C1111yescharacteristic, complemented
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—81no—
243C23×C11—81no—
244C23×C11#13512yes—
245C23×C11C22×D411yescharacteristic
246Q8×C11—42no—
247Q8×C11—42no—
248Q8×C11—42no—
249Q8×C11—81no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—42no—
253D4×C11—44no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—81no—
257D4×C11—84no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—41no—
274C2×C4×C11—42no—
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—41no—
283C2×C4×C11—41no—
284C2×C4×C11—82no—
285C2×C4×C11—81no—
286C2×C4×C11—82no—
287C2×C4×C11—81no—
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12012yes—
291C2×C4×C11C22×D412yes—
292C8×C11—42no—
293C8×C11—42no—
294#552—22no—
295#552—22no—
296#551—22no—
297#551—22no—
298#543C22×C1111yescharacteristic
299#539—21no—
300#539C22×C1112yes—
301#534C22×C1111yescharacteristic
302#529—21no—
303#529C22×C1112yes—
304C2×#124C22×C1111yescharacteristic, complemented
305C2×#123—21no—
306#518—21no—
307C2×#117C22×C1111yescharacteristic
308#495—22no—
309#488—22no—
310#464—22no—
311#463—22no—
312#451C22×C1112yescomplemented
313#450C22×C1112yescomplemented
314#448C22×C1112yes—
315#447C22×C1112yes—
316#431C22×C1112yescomplemented
317#395C22×C1111yescharacteristic, complemented
318#394C22×C1111yescharacteristic, complemented
319#393C22×C1111yescharacteristic
320#392C22×C1111yescharacteristic
321#390—21no—
322#388—21no—
323#388—21no—
324#386—21no—
325#376C22×C1111yescharacteristic, complemented
326#328C22×C1112yescomplemented
327#328C22×C1112yescomplemented
328#327C22×C1112yes—
329#327C22×C1112yes—
330#324C22×C1112yescomplemented
331#323C22×C1111yescharacteristic
332#323C22×C1111yescharacteristic
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—22no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—162no—
351C22×C11C2×#12011yescharacteristic
352C22×C11C2×#13511yescharacteristic
353C22×C11#57511yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C22×Q8C23×C1111yescharacteristic
368C22×D4—21no—
369C22×D4—21no—
370C22×D4C23×C1111yescharacteristic
371C23×C4D4×C1111yescharacteristic
372C2×Q16—22no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×D8—22no—
376#126—22no—
377#126—22no—
378#126—22no—
379#126—22no—
380#125—21no—
381#125—22no—
382#125—22no—
383#125D4×C1112yescomplemented
384#124—21no—
385#124—22no—
386#124—22no—
387#124D4×C1112yescomplemented
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8C23×C1112yes—
401#121—21no—
402#121C23×C1112yes—
403#120—22no—
404C4×Q8—21no—
405C4×Q8D4×C1112yescomplemented
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4D4×C1112yescomplemented
412#117—22no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C1111yescharacteristic
421C2×C4⋊C4C23×C1111yescharacteristic
422C2×C22⋊C4—22no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4D4×C1111yescharacteristic
433C2×C22⋊C4C23×C1111yescharacteristic
434C2×C42—21no—
435C2×C42D4×C1111yescharacteristic
436C2×C42C23×C1111yescharacteristic
437C4⋊C8—22no—
438#103—22no—
439#103—22no—
440#102—22no—
441#102—22no—
442C22⋊C8C23×C1112yes—
443C22⋊C8C23×C1112yes—
444C4×C8—22no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95C23×C1111yescharacteristic
449#95C23×C1111yescharacteristic
450C2×C11—21no—
451C2×C11—21no—
452C2×C11—42no—
453C2×C11—82no—
454C2×C11—161no—
455C2×C11#300211yescharacteristic
456C2×C11#301811yescharacteristic
457C2×C11#302711yescharacteristic
458C24—21no—
459C24—21no—
460C24C2×D4×C1111yescharacteristic
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—81no—
464C2×Q8C2×D4×C1112yes—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4C2×D4×C1112yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C24×C1111yescharacteristic
494Q16—82no—
495SD16—82no—
496SD16—82no—
497D8—82no—
498C2×C8—22no—
499C2×C8—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—81no—
513C4⋊C4C2×D4×C1112yes—
514C4⋊C4C2×D4×C1112yes—
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—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—42no—
532C22⋊C4—81no—
533C22⋊C4—81no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42—22no—
538C42—42no—
539C42C2×D4×C1112yes—
540C42C2×D4×C1112yes—
541C11#1838611yescharacteristic, direct product factor, Sylow
542C23—21no—
543C23—21no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—81no—
556C23—81no—
557C23C11×#13512yes—
558C23C22×D4×C1111yescharacteristic
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—81no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—44no—
567D4—42no—
568D4—42no—
569D4—81no—
570D4—84no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—82no—
598C2×C4—81no—
599C2×C4—82no—
600C2×C4—81no—
601C2×C4C11×#12011yescharacteristic
602C2×C4C11×#12011yescharacteristic
603C2×C4C11×#12012yes—
604C2×C4C22×D4×C1112yes—
605C8—42no—
606C8—42no—
607C22—21no—
608C22—21no—
609C22—22no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—162no—
625C22C2×C11×#12011yescharacteristic
626C22C2×C11×#13511yescharacteristic
627C22C11×#57511yescharacteristic
628C4—21no—
629C4—21no—
630C4—22no—
631C4—22no—
632C4—42no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—41no—
638C4—42no—
639C4—81no—
640C4—81no—
641C2—21no—
642C2—21no—
643C2—42no—
644C2—82no—
645C2—161no—
646C2C11×#300211yescharacteristic
647C2C11×#301811yescharacteristic
648C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#1595C2
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×#3491C2semidirect
2. C11×#3211C2semidirect
3. C11×#2610C2semidirect
4. C11×#1603C2semidirect
5. C11×#1602C2semidirect
6. C11×#1601C2semidirect
7. C11×#1597C2semidirect
8. C11×#1596C2semidirect
10. C11×#1500C2semidirect
11. C11×#1458C2semidirect
22. C2×C11×#124C22semidirect
30. C11×#451C22semidirect
31. C11×#450C22semidirect
34. C11×#431C22semidirect
35. C11×#395C22semidirect
36. C11×#394C22semidirect
43. C11×#376C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
48. C11×#324C22semidirect
67. C11×#125D4semidirect
71. C11×#124D4semidirect
89. C4×Q8×C11D4semidirect
95. C4×D4×C11D4semidirect
134. #18386C11direct (N × H)
218. #3491C2×C11semidirect
219. #3211C2×C11semidirect
220. #2610C2×C11semidirect
221. #1603C2×C11semidirect
222. #1602C2×C11semidirect
223. #1601C2×C11semidirect
224. #1597C2×C11semidirect
225. #1596C2×C11semidirect
227. #1500C2×C11semidirect
228. #1458C2×C11semidirect
304. C2×#124C22×C11semidirect
312. #451C22×C11semidirect
313. #450C22×C11semidirect
316. #431C22×C11semidirect
317. #395C22×C11semidirect
318. #394C22×C11semidirect
325. #376C22×C11semidirect
326. #328C22×C11semidirect
327. #328C22×C11semidirect
330. #324C22×C11semidirect
383. #125D4×C11semidirect
387. #124D4×C11semidirect
405. C4×Q8D4×C11semidirect
411. C4×D4D4×C11semidirect
541. C11#18386direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34912
C11×#32112
C11×#26102
C11×#16032
C11×#16022
C11×#16012
C11×#15972
C11×#15962
C11×#15952
C11×#15002
C11×#14582
#1838611