Finite Group Databasebeta

← C11×#19086 #14596279

Subgroups — C11×#19086 #14596279

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic, complemented
2C11×#3219C211yesmaximal, characteristic, complemented
3C11×#3214C211yesmaximal, characteristic, complemented
4C11×#3213C211yesmaximal, characteristic, complemented
5C11×#1662C212yesmaximal, complemented
6C11×#1659C212yesmaximal, complemented
7C11×#1656C212yesmaximal, complemented
8C11×#1655C212yesmaximal, complemented
9C11×#1536C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1533C211yesmaximal, characteristic, complemented
12C11×#562C2212yes—
13C11×H(3,𝔽4)C2212yes—
14C11×#559—21no—
15C11×#548—21no—
16C11×#546—22no—
17C11×#546—21no—
18D42×C11—21no—
19C11×#542—21no—
20C11×#538—22no—
21C11×#538—21no—
22C11×#535—21no—
23C11×#534—21no—
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic, complemented
26C11×#529C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C11×#497C2211yescharacteristic, complemented
29C11×#496C2211yescharacteristic, complemented
30C11×#496C2212yescomplemented
31C11×#496C2212yescomplemented
32C11×#491C2211yescharacteristic, complemented
33C11×#490C2211yescharacteristic, complemented
34C11×#489C2212yescomplemented
35C11×#489C2212yescomplemented
36C11×#464—21no—
37C11×#463—22no—
38C11×#463—21no—
39C11×#461—21no—
40C11×#459—21no—
41C11×#452—21no—
42C11×#449—22no—
43C11×#449—21no—
44C11×#448—21no—
45C11×#447—21no—
46C11×#432C2211yescharacteristic, complemented
47C11×#432C2211yescharacteristic, complemented
48C11×#432C2211yescharacteristic, complemented
49C11×#330C2212yescomplemented
50C11×#329C2212yescomplemented
51C11×#329C2212yescomplemented
52C11×#329C2212yescomplemented
53C11×#329C2212yescomplemented
54C11×#329C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41D412yes—
58C22×Q8×C11D411yescharacteristic
59C22×D4×C11—22no—
60C22×D4×C11—21no—
61C22×D4×C11D411yescharacteristic
62C2×C11×Q16—21no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×D8—22no—
68C2×C11×D8—22no—
69C2×C11×D8—21no—
70C11×C4⋊Q8D411yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127—21no—
73C11×#127D411yescharacteristic
74C11×#127C2311yescharacteristic
75C11×#126—22no—
76C11×#126—21no—
77C11×#125C2311yescharacteristic
78C11×#124—21no—
79C11×#124—22no—
80C11×#124—22no—
81C11×#124—22no—
82C11×#124—21no—
83C11×#124—21no—
84C11×#124—21no—
85C11×#124D412yes—
86C11×#124C2312yes—
87C11×#124C2312yes—
88C11×#124C2311yescharacteristic
89C11×#123—22no—
90C11×#123—22no—
91C11×#123—21no—
92C11×#123—22no—
93C11×#123—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8D411yescharacteristic
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121D411yescharacteristic
109C11×#120—22no—
110C11×#120—22no—
111C11×#120—22no—
112C11×#120—22no—
113C11×#120—22no—
114C4×Q8×C11—21no—
115C4×Q8×C11D411yescharacteristic
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11D411yescharacteristic
125C11×#117—21no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C42×C11C2311yescharacteristic
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—21no—
140C11×#102—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2312yes—
145C11×#97C2312yes—
146C11×#97C2311yescharacteristic
147C11×#97C2311yescharacteristic
148#19086C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—22no—
150C24×C11—21no—
151C11×#41—81no—
152C11×#41—81no—
153C11×#41—82no—
154C11×#41—82no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—81no—
158C2×Q8×C11C2×D412yes—
159C2×Q8×C11C2×D412yes—
160C2×Q8×C11C2×D411yescharacteristic
161C2×D4×C11—22no—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—41no—
175C2×D4×C11—81no—
176C2×D4×C11—82no—
177C2×D4×C11—84no—
178C2×D4×C11C2×D412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D411yescharacteristic
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—22no—
186C22×C4×C11—41no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C11×Q16—81no—
191C11×SD16—81no—
192C11×SD16—82no—
193C11×SD16—82no—
194C11×SD16—81no—
195C11×D8—81no—
196C11×D8—82no—
197C11×D8—82no—
198C2×C8×C11—21no—
199C2×C8×C11—22no—
200C2×C8×C11—22no—
201C2×C8×C11—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⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4C2×D411yescharacteristic
213C11×C4⋊C4C2×D411yescharacteristic
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—41no—
231C11×C22⋊C4—41no—
232C42×C11—22no—
233C42×C11—21no—
234C42×C11C2×D411yescharacteristic
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2411yescharacteristic
238#3558C2×C1111yescharacteristic, complemented
239#3219C2×C1111yescharacteristic, complemented
240#3214C2×C1111yescharacteristic, complemented
241#3213C2×C1111yescharacteristic, complemented
242#1662C2×C1112yescomplemented
243#1659C2×C1112yescomplemented
244#1656C2×C1112yescomplemented
245#1655C2×C1112yescomplemented
246#1536C2×C1111yescharacteristic, complemented
247#1535C2×C1111yescharacteristic, complemented
248#1533C2×C1111yescharacteristic, complemented
249C23×C11—21no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—42no—
253C23×C11—41no—
254C23×C11—81no—
255C23×C11—81no—
256C23×C11—82no—
257C23×C11—82no—
258C23×C11—82no—
259C23×C11#12011yescharacteristic
260Q8×C11—41no—
261Q8×C11—42no—
262Q8×C11—42no—
263Q8×C11—42no—
264Q8×C11—41no—
265Q8×C11—41no—
266D4×C11—41no—
267D4×C11—42no—
268D4×C11—42no—
269D4×C11—42no—
270D4×C11—42no—
271D4×C11—41no—
272D4×C11—42no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—42no—
277D4×C11—44no—
278D4×C11—81no—
279D4×C11—82no—
280D4×C11—82no—
281D4×C11—82no—
282D4×C11—82no—
283D4×C11—82no—
284D4×C11—82no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—82no—
296C2×C4×C11—82no—
297C2×C4×C11—81no—
298C2×C4×C11—82no—
299C2×C4×C11—82no—
300C2×C4×C11#12011yescharacteristic
301C2×C4×C11#12011yescharacteristic
302C2×C4×C11#12011yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C8×C11—42no—
307C8×C11—42no—
308C8×C11—41no—
309C8×C11—41no—
310#562C22×C1112yes—
311H(3,𝔽4)C22×C1112yes—
312#559—21no—
313#548—21no—
314#546—22no—
315#546—21no—
316D42—21no—
317#542—21no—
318#538—22no—
319#538—21no—
320#535—21no—
321#534—21no—
322#532C22×C1111yescharacteristic
323#532C22×C1111yescharacteristic, complemented
324#529C22×C1111yescharacteristic
325C2×#124C22×C1111yescharacteristic
326#497C22×C1111yescharacteristic, complemented
327#496C22×C1111yescharacteristic, complemented
328#496C22×C1112yescomplemented
329#496C22×C1112yescomplemented
330#491C22×C1111yescharacteristic, complemented
331#490C22×C1111yescharacteristic, complemented
332#489C22×C1112yescomplemented
333#489C22×C1112yescomplemented
334#464—21no—
335#463—22no—
336#463—21no—
337#461—21no—
338#459—21no—
339#452—21no—
340#449—22no—
341#449—21no—
342#448—21no—
343#447—21no—
344#432C22×C1111yescharacteristic, complemented
345#432C22×C1111yescharacteristic, complemented
346#432C22×C1111yescharacteristic, complemented
347#330C22×C1112yescomplemented
348#329C22×C1112yescomplemented
349#329C22×C1112yescomplemented
350#329C22×C1112yescomplemented
351#329C22×C1112yescomplemented
352#329C22×C1112yescomplemented
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—41no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—162no—
369C22×C11—164no—
370C22×C11C2×#12011yescharacteristic
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—21no—
376C4×C11—21no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—81no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41D4×C1112yes—
386C22×Q8D4×C1111yescharacteristic
387C22×D4—22no—
388C22×D4—21no—
389C22×D4D4×C1111yescharacteristic
390C2×Q16—21no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—21no—
398C4⋊Q8D4×C1111yescharacteristic
399C4⋊Q8C23×C1111yescharacteristic
400#127—21no—
401#127D4×C1111yescharacteristic
402#127C23×C1111yescharacteristic
403#126—22no—
404#126—21no—
405#125C23×C1111yescharacteristic
406#124—21no—
407#124—22no—
408#124—22no—
409#124—22no—
410#124—21no—
411#124—21no—
412#124—21no—
413#124D4×C1112yes—
414#124C23×C1112yes—
415#124C23×C1111yescharacteristic
416#124C23×C1112yes—
417#123—22no—
418#123—22no—
419#123—21no—
420#123—22no—
421#123—22no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8D4×C1111yescharacteristic
426#121—22no—
427#121—22no—
428#121—22no—
429#121—21no—
430#121—22no—
431#121—22no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121D4×C1111yescharacteristic
437#120—22no—
438#120—22no—
439#120—22no—
440#120—22no—
441#120—22no—
442C4×Q8—21no—
443C4×Q8D4×C1111yescharacteristic
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4D4×C1111yescharacteristic
453#117—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C42C23×C1111yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461#103—22no—
462#103—22no—
463#103—21no—
464#103—21no—
465#102—22no—
466#102—22no—
467#102—21no—
468#102—21no—
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472#97C23×C1111yescharacteristic
473#97C23×C1111yescharacteristic
474#97C23×C1112yes—
475#97C23×C1112yes—
476C2×C11—41no—
477C2×C11—82no—
478C2×C11—81no—
479C2×C11—82no—
480C2×C11—161no—
481C2×C11#301911yescharacteristic
482C2×C11#301911yescharacteristic
483C2×C11#302111yescharacteristic
484C24—22no—
485C24—21no—
486#41—81no—
487#41—81no—
488#41—82no—
489#41—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—81no—
493C2×Q8C2×D4×C1112yes—
494C2×Q8C2×D4×C1112yes—
495C2×Q8C2×D4×C1111yescharacteristic
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—41no—
510C2×D4—81no—
511C2×D4—82no—
512C2×D4—84no—
513C2×D4C2×D4×C1112yes—
514C2×D4C2×D4×C1112yes—
515C2×D4C2×D4×C1111yescharacteristic
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C2×D4×C1111yescharacteristic
525Q16—81no—
526SD16—82no—
527SD16—82no—
528SD16—81no—
529SD16—81no—
530D8—81no—
531D8—82no—
532D8—82no—
533C2×C8—21no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4C2×D4×C1111yescharacteristic
548C4⋊C4C2×D4×C1111yescharacteristic
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—21no—
557C22⋊C4—22no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C42—22no—
568C42—21no—
569C42C2×D4×C1111yescharacteristic
570C42C2×D4×C1111yescharacteristic
571C42C2×D4×C1111yescharacteristic
572C42C24×C1111yescharacteristic
573C11#1908611yescharacteristic, direct product factor, Sylow
574C23—21no—
575C23—22no—
576C23—22no—
577C23—42no—
578C23—41no—
579C23—81no—
580C23—81no—
581C23—82no—
582C23—82no—
583C23—82no—
584C23C11×#12011yescharacteristic
585Q8—41no—
586Q8—42no—
587Q8—42no—
588Q8—42no—
589Q8—41no—
590Q8—41no—
591D4—41no—
592D4—42no—
593D4—42no—
594D4—42no—
595D4—42no—
596D4—41no—
597D4—42no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—42no—
602D4—44no—
603D4—81no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608D4—82no—
609D4—82no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—82no—
621C2×C4—82no—
622C2×C4—81no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4C11×#12011yescharacteristic
626C2×C4C11×#12011yescharacteristic
627C2×C4C11×#12011yescharacteristic
628C2×C4C22×D4×C1111yescharacteristic
629C2×C4C22×D4×C1111yescharacteristic
630C2×C4C22×D4×C1111yescharacteristic
631C8—42no—
632C8—42no—
633C8—41no—
634C8—41no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—41no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—162no—
651C22—164no—
652C22C2×C11×#12011yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—81no—
665C2—41no—
666C2—81no—
667C2—82no—
668C2—82no—
669C2—161no—
670C2C11×#301911yescharacteristic
671C2C11×#301911yescharacteristic
672C2C11×#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×#3558C2semidirect
2. C11×#3219C2semidirect
3. C11×#3214C2semidirect
4. C11×#3213C2semidirect
5. C11×#1662C2semidirect
6. C11×#1659C2semidirect
7. C11×#1656C2semidirect
8. C11×#1655C2semidirect
9. C11×#1536C2semidirect
10. C11×#1535C2semidirect
11. C11×#1533C2semidirect
25. C11×#532C22semidirect
28. C11×#497C22semidirect
29. C11×#496C22semidirect
30. C11×#496C22semidirect
31. C11×#496C22semidirect
32. C11×#491C22semidirect
33. C11×#490C22semidirect
34. C11×#489C22semidirect
35. C11×#489C22semidirect
46. C11×#432C22semidirect
47. C11×#432C22semidirect
48. C11×#432C22semidirect
49. C11×#330C22semidirect
50. C11×#329C22semidirect
51. C11×#329C22semidirect
52. C11×#329C22semidirect
53. C11×#329C22semidirect
54. C11×#329C22semidirect
148. #19086C11direct (N × H)
238. #3558C2×C11semidirect
239. #3219C2×C11semidirect
240. #3214C2×C11semidirect
241. #3213C2×C11semidirect
242. #1662C2×C11semidirect
243. #1659C2×C11semidirect
244. #1656C2×C11semidirect
245. #1655C2×C11semidirect
246. #1536C2×C11semidirect
247. #1535C2×C11semidirect
248. #1533C2×C11semidirect
323. #532C22×C11semidirect
326. #497C22×C11semidirect
327. #496C22×C11semidirect
328. #496C22×C11semidirect
329. #496C22×C11semidirect
330. #491C22×C11semidirect
331. #490C22×C11semidirect
332. #489C22×C11semidirect
333. #489C22×C11semidirect
344. #432C22×C11semidirect
345. #432C22×C11semidirect
346. #432C22×C11semidirect
347. #330C22×C11semidirect
348. #329C22×C11semidirect
349. #329C22×C11semidirect
350. #329C22×C11semidirect
351. #329C22×C11semidirect
352. #329C22×C11semidirect
573. C11#19086direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35582
C11×#32192
C11×#32142
C11×#32132
C11×#16622
C11×#16592
C11×#16562
C11×#16552
C11×#15362
C11×#15352
C11×#15332
#1908611