Finite Group Databasebeta

← C11×#19042 #14596235

Subgroups — C11×#19042 #14596235

Order 2816.

1036 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×#3213C211yesmaximal, characteristic, complemented
3C11×#3180C211yesmaximal, characteristic, complemented
4C11×#3150C211yesmaximal, characteristic, complemented
5C11×#1661C212yesmaximal, complemented
6C11×#1659C212yesmaximal, complemented
7C11×#1656C212yesmaximal, complemented
8C11×#1655C212yesmaximal, complemented
9C11×#1532C211yesmaximal, characteristic, complemented
10C11×#1530C211yesmaximal, characteristic, complemented
11C2×C11×#329C211yesmaximal, characteristic, complemented
12C2×C11×#135—22no—
13C11×#562C2212yes—
14C11×H(3,𝔽4)C2212yes—
15C11×#559—21no—
16C11×#548—21no—
17C11×#546—22no—
18C11×#546—21no—
19D42×C11—21no—
20C11×#542—21no—
21C11×#538—22no—
22C11×#538—21no—
23C11×#535—21no—
24C11×#534—21no—
25C11×#532C2211yescharacteristic
26C11×#532C2211yescharacteristic, complemented
27C11×#529C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic
29C11×#501C2211yescharacteristic, complemented
30C11×#497—21no—
31C11×#497C2212yescomplemented
32C11×#496—21no—
33C11×#496C2212yescomplemented
34C11×#496C2211yescharacteristic, complemented
35C11×#496C2212yescomplemented
36C11×#490C2211yescharacteristic, complemented
37C11×#489C2211yescharacteristic, complemented
38C11×#489C2212yescomplemented
39C11×#466—21no—
40C11×#465—21no—
41C11×#463—22no—
42C11×#448—21no—
43C11×#447—21no—
44C11×#442—21no—
45C11×#440—21no—
46C11×#432C2211yescharacteristic, complemented
47C2×C11×#97C2211yescharacteristic, complemented
48C2×C11×#97C2211yescharacteristic, 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
62C11×#135—48no—
63C2×C11×Q16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—21no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×D8—22no—
69C2×C11×D8—21no—
70C2×C11×D8—22no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8D411yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127—21no—
76C11×#127D411yescharacteristic
77C11×#127C2311yescharacteristic
78C11×#126—22no—
79C11×#126—21no—
80C11×#125C2311yescharacteristic
81C11×#124—21no—
82C11×#124—22no—
83C11×#124—22no—
84C11×#124—22no—
85C11×#124—21no—
86C11×#124—21no—
87C11×#124—21no—
88C11×#124D412yes—
89C11×#124C2312yes—
90C11×#124C2311yescharacteristic
91C11×#124C2312yes—
92C11×#123—22no—
93C11×#123—22no—
94C11×#123—21no—
95C11×#123—22no—
96C11×#123—22no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8D411yescharacteristic
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—21no—
105C11×#121—22no—
106C11×#121—22no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121D411yescharacteristic
112C11×#120—22no—
113C11×#120—22no—
114C11×#120—22no—
115C11×#120—22no—
116C11×#120—22no—
117C4×Q8×C11—21no—
118C4×Q8×C11D411yescharacteristic
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11—21no—
126C4×D4×C11—21no—
127C4×D4×C11D411yescharacteristic
128C11×#117—21no—
129C2×C11×C22⋊C4—22no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11C2311yescharacteristic
133C11×#107—21no—
134C11×#106—21no—
135C11×C4⋊C8—21no—
136C11×#103—21no—
137C11×#103—22no—
138C11×#102—21no—
139C11×#102—22no—
140C11×#102—21no—
141C11×#102—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C11×#97—21no—
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2311yescharacteristic
148C11×#97C2312yes—
149#19042C1111yesmaximal, characteristic, direct product factor, Sylow
150C24×C11—22no—
151C24×C11—21no—
152C11×#41—44no—
153C11×#41—44no—
154C11×#41—82no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—81no—
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11C2×D412yes—
160C2×Q8×C11C2×D412yes—
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×D411yescharacteristic
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
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—44no—
191C11×SD16—42no—
192C11×SD16—44no—
193C11×SD16—44no—
194C11×SD16—82no—
195C11×D8—42no—
196C11×D8—44no—
197C11×D8—82no—
198C2×C8×C11—24no—
199C2×C8×C11—21no—
200C2×C8×C11—22no—
201C2×C8×C11—21no—
202C2×C8×C11—22no—
203C2×C8×C11—42no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
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⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C42×C11—22no—
235C42×C11—21no—
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D411yescharacteristic
238C42×C11C2×D411yescharacteristic
239C42×C11C2411yescharacteristic
240#3558C2×C1111yescharacteristic, complemented
241#3213C2×C1111yescharacteristic, complemented
242#3180C2×C1111yescharacteristic, complemented
243#3150C2×C1111yescharacteristic, complemented
244#1661C2×C1112yescomplemented
245#1659C2×C1112yescomplemented
246#1656C2×C1112yescomplemented
247#1655C2×C1112yescomplemented
248#1532C2×C1111yescharacteristic, complemented
249#1530C2×C1111yescharacteristic, complemented
250C2×#329C2×C1111yescharacteristic, complemented
251C23×C11—22no—
252C23×C11—21no—
253C23×C11—22no—
254C23×C11—42no—
255C23×C11—41no—
256C23×C11—81no—
257C23×C11—81no—
258C23×C11—82no—
259C23×C11—82no—
260C23×C11—82no—
261C23×C11#12011yescharacteristic
262Q8×C11—42no—
263Q8×C11—41no—
264Q8×C11—42no—
265Q8×C11—42no—
266Q8×C11—42no—
267D4×C11—42no—
268D4×C11—41no—
269D4×C11—42no—
270D4×C11—42no—
271D4×C11—42no—
272D4×C11—42no—
273D4×C11—41no—
274D4×C11—42no—
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—22no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
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—24no—
307C8×C11—22no—
308C8×C11—41no—
309C8×C11—42no—
310C2×#135—22no—
311#562C22×C1112yes—
312H(3,𝔽4)C22×C1112yes—
313#559—21no—
314#548—21no—
315#546—22no—
316#546—21no—
317D42—21no—
318#542—21no—
319#538—22no—
320#538—21no—
321#535—21no—
322#534—21no—
323#532C22×C1111yescharacteristic
324#532C22×C1111yescharacteristic, complemented
325#529C22×C1111yescharacteristic
326C2×#124C22×C1111yescharacteristic
327#501C22×C1111yescharacteristic, complemented
328#497—21no—
329#497C22×C1112yescomplemented
330#496—21no—
331#496C22×C1112yescomplemented
332#496C22×C1111yescharacteristic, complemented
333#496C22×C1112yescomplemented
334#490C22×C1111yescharacteristic, complemented
335#489C22×C1111yescharacteristic, complemented
336#489C22×C1112yescomplemented
337#466—21no—
338#465—21no—
339#463—22no—
340#448—21no—
341#447—21no—
342#442—21no—
343#440—21no—
344#432C22×C1111yescharacteristic, complemented
345C2×#97C22×C1111yescharacteristic, complemented
346C2×#97C22×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—42no—
356C22×C11—42no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—41no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—162no—
368C22×C11—164no—
369C22×C11#45312yes—
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—42no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—81no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41D4×C1112yes—
386C22×Q8D4×C1111yescharacteristic
387C22×D4—22no—
388C22×D4—21no—
389C22×D4D4×C1111yescharacteristic
390#135—48no—
391C2×Q16—22no—
392C2×SD16—22no—
393C2×SD16—21no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×D8—22no—
397C2×D8—21no—
398C2×D8—22no—
399C22×C8—21no—
400C22×C8—21no—
401C4⋊Q8D4×C1111yescharacteristic
402C4⋊Q8C23×C1111yescharacteristic
403#127—21no—
404#127D4×C1111yescharacteristic
405#127C23×C1111yescharacteristic
406#126—22no—
407#126—21no—
408#125C23×C1111yescharacteristic
409#124—21no—
410#124—22no—
411#124—22no—
412#124—22no—
413#124—21no—
414#124—21no—
415#124—21no—
416#124D4×C1112yes—
417#124C23×C1112yes—
418#124C23×C1111yescharacteristic
419#124C23×C1112yes—
420#123—22no—
421#123—22no—
422#123—21no—
423#123—22no—
424#123—22no—
425C22⋊Q8—21no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8D4×C1111yescharacteristic
429#121—22no—
430#121—22no—
431#121—22no—
432#121—21no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—21no—
437#121—21no—
438#121—21no—
439#121D4×C1111yescharacteristic
440#120—22no—
441#120—22no—
442#120—22no—
443#120—22no—
444#120—22no—
445C4×Q8—21no—
446C4×Q8D4×C1111yescharacteristic
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4D4×C1111yescharacteristic
456#117—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42C23×C1111yescharacteristic
461#107—21no—
462#106—21no—
463C4⋊C8—21no—
464#103—21no—
465#103—22no—
466#102—21no—
467#102—22no—
468#102—21no—
469#102—21no—
470C22⋊C8—21no—
471#97—21no—
472#97—21no—
473#97C23×C1111yescharacteristic
474#97C23×C1111yescharacteristic
475#97C23×C1112yes—
476#97C23×C1112yes—
477C2×C11—22no—
478C2×C11—82no—
479C2×C11—82no—
480C2×C11—81no—
481C2×C11—161no—
482C2×C11C2×#45311yescharacteristic
483C2×C11#301811yescharacteristic
484C2×C11#301911yescharacteristic
485C24—22no—
486C24—21no—
487#41—44no—
488#41—44no—
489#41—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—81no—
493C2×Q8C2×D4×C1111yescharacteristic
494C2×Q8C2×D4×C1112yes—
495C2×Q8C2×D4×C1112yes—
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×C1111yescharacteristic
514C2×D4C2×D4×C1112yes—
515C2×D4C2×D4×C1112yes—
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—44no—
526SD16—44no—
527SD16—44no—
528SD16—42no—
529SD16—82no—
530D8—44no—
531D8—42no—
532D8—82no—
533C2×C8—24no—
534C2×C8—21no—
535C2×C8—22no—
536C2×C8—21no—
537C2×C8—22no—
538C2×C8—42no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4C2×D4×C1111yescharacteristic
550C4⋊C4C2×D4×C1111yescharacteristic
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—21no—
557C22⋊C4—22no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C42—22no—
570C42—21no—
571C42C2×D4×C1111yescharacteristic
572C42C2×D4×C1111yescharacteristic
573C42C2×D4×C1111yescharacteristic
574C42C24×C1111yescharacteristic
575C11#1904211yescharacteristic, direct product factor, Sylow
576C23—22no—
577C23—21no—
578C23—22no—
579C23—42no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—82no—
584C23—82no—
585C23—82no—
586C23C11×#12011yescharacteristic
587Q8—42no—
588Q8—41no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592D4—42no—
593D4—41no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—41no—
599D4—42no—
600D4—41no—
601D4—42no—
602D4—44no—
603D4—81no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608D4—82no—
609D4—82no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
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—24no—
632C8—22no—
633C8—41no—
634C8—42no—
635C22—21no—
636C22—21no—
637C22—42no—
638C22—42no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—42no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—162no—
650C22—164no—
651C22C11×#45312yes—
652C22C2×C11×#12011yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C2—22no—
666C2—82no—
667C2—81no—
668C2—82no—
669C2—161no—
670C2C2×C11×#45311yescharacteristic
671C2C11×#301811yescharacteristic
672C2C11×#301911yescharacteristic
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×#3213C2semidirect
3. C11×#3180C2semidirect
4. C11×#3150C2semidirect
5. C11×#1661C2semidirect
6. C11×#1659C2semidirect
7. C11×#1656C2semidirect
8. C11×#1655C2semidirect
9. C11×#1532C2semidirect
10. C11×#1530C2semidirect
11. C2×C11×#329C2semidirect
26. C11×#532C22semidirect
29. C11×#501C22semidirect
31. C11×#497C22semidirect
33. C11×#496C22semidirect
34. C11×#496C22semidirect
35. C11×#496C22semidirect
36. C11×#490C22semidirect
37. C11×#489C22semidirect
38. C11×#489C22semidirect
46. C11×#432C22semidirect
47. C2×C11×#97C22semidirect
48. C2×C11×#97C22semidirect
49. C11×#330C22semidirect
50. C11×#329C22semidirect
51. C11×#329C22semidirect
52. C11×#329C22semidirect
53. C11×#329C22semidirect
54. C11×#329C22semidirect
149. #19042C11direct (N × H)
240. #3558C2×C11semidirect
241. #3213C2×C11semidirect
242. #3180C2×C11semidirect
243. #3150C2×C11semidirect
244. #1661C2×C11semidirect
245. #1659C2×C11semidirect
246. #1656C2×C11semidirect
247. #1655C2×C11semidirect
248. #1532C2×C11semidirect
249. #1530C2×C11semidirect
250. C2×#329C2×C11semidirect
324. #532C22×C11semidirect
327. #501C22×C11semidirect
329. #497C22×C11semidirect
331. #496C22×C11semidirect
332. #496C22×C11semidirect
333. #496C22×C11semidirect
334. #490C22×C11semidirect
335. #489C22×C11semidirect
336. #489C22×C11semidirect
344. #432C22×C11semidirect
345. C2×#97C22×C11semidirect
346. C2×#97C22×C11semidirect
347. #330C22×C11semidirect
348. #329C22×C11semidirect
349. #329C22×C11semidirect
350. #329C22×C11semidirect
351. #329C22×C11semidirect
352. #329C22×C11semidirect
575. C11#19042direct (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×#32132
C11×#31802
C11×#31502
C11×#16612
C11×#16592
C11×#16562
C11×#16552
C11×#15322
C11×#15302
C2×C11×#3292
#1904211