Finite Group Databasebeta

← C11×#19043 #14596236

Subgroups — C11×#19043 #14596236

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic
2C11×#3215C211yesmaximal, characteristic, complemented
3C11×#3181C211yesmaximal, characteristic, complemented
4C11×#3135C211yesmaximal, characteristic, complemented
5C11×#1662C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1659C212yesmaximal, complemented
8C11×#1659C212yesmaximal, complemented
9C11×#1532C211yesmaximal, characteristic, complemented
10C11×#1530C211yesmaximal, characteristic, complemented
11C2×C11×#329C211yesmaximal, 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×#533C2211yescharacteristic, complemented
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C11×#501C2211yescharacteristic, complemented
29C11×#497C2211yescharacteristic, complemented
30C11×#497C2212yescomplemented
31C11×#491—21no—
32C11×#491C2211yescharacteristic, complemented
33C11×#490—21no—
34C11×#489C2211yescharacteristic, complemented
35C11×#489C2212yescomplemented
36C11×#489C2212yescomplemented
37C11×#489C2212yescomplemented
38C11×#467—21no—
39C11×#465—21no—
40C11×#464—22no—
41C11×#451—21no—
42C11×#450—21no—
43C11×#441—21no—
44C11×#440—21no—
45C11×#432C2211yescharacteristic, complemented
46C11×#416—22no—
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×#41D412yes—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C2×C11×Q16—21no—
62C2×C11×Q16—22no—
63C2×C11×SD16—21no—
64C2×C11×SD16—22no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127—21no—
71C11×#127D411yescharacteristic
72C11×#126—22no—
73C11×#126—21no—
74C11×#125—21no—
75C11×#125C2311yescharacteristic
76C11×#124—21no—
77C11×#124—22no—
78C11×#124—22no—
79C11×#124—22no—
80C11×#124—21no—
81C11×#124—21no—
82C11×#124D412yes—
83C11×#124C2312yes—
84C11×#124C2312yes—
85C11×#124C2311yescharacteristic
86C11×#123—22no—
87C11×#123—22no—
88C11×#123—21no—
89C11×#123—22no—
90C11×#123—22no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8D411yescharacteristic
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—21no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—21no—
104C11×#121—21no—
105C11×#121D411yescharacteristic
106C11×#120—22no—
107C11×#120—22no—
108C11×#120—22no—
109C11×#120—22no—
110C11×#120—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11—21no—
114C4×Q8×C11D411yescharacteristic
115C4×D4×C11—22no—
116C4×D4×C11—22no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11D411yescharacteristic
122C11×#117—21no—
123C11×#117—21no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—21no—
129C11×#106—21no—
130C11×C4⋊C8—21no—
131C11×#103—22no—
132C11×#103—22no—
133C11×#103—21no—
134C11×#103—22no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#102—21no—
140C11×#102—22no—
141C11×C22⋊C8—21no—
142C11×#97—21no—
143C11×#97—21no—
144C11×#97C2312yes—
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2311yescharacteristic
148#19043C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—22no—
150C24×C11—21no—
151C11×#41—44no—
152C11×#41—82no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—81no—
157C2×Q8×C11C2×D412yes—
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11C2×D412yes—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—81no—
171C2×D4×C11—82no—
172C2×D4×C11—84no—
173C2×D4×C11C2×D412yes—
174C2×D4×C11C2×D411yescharacteristic
175C2×D4×C11C2×D412yes—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C11×Q16—42no—
185C11×Q16—82no—
186C11×SD16—42no—
187C11×SD16—82no—
188C2×C8×C11—21no—
189C2×C8×C11—22no—
190C2×C8×C11—21no—
191C2×C8×C11—22no—
192C2×C8×C11—42no—
193C2×C8×C11—42no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—41no—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D411yescharacteristic
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—41no—
227C42×C11—22no—
228C42×C11—21no—
229C42×C11—41no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2411yescharacteristic
234#3558C2×C1111yescharacteristic
235#3215C2×C1111yescharacteristic, complemented
236#3181C2×C1111yescharacteristic, complemented
237#3135C2×C1111yescharacteristic, complemented
238#1662C2×C1112yescomplemented
239#1661C2×C1112yescomplemented
240#1659C2×C1112yescomplemented
241#1659C2×C1112yescomplemented
242#1532C2×C1111yescharacteristic, complemented
243#1530C2×C1111yescharacteristic, complemented
244C2×#329C2×C1111yescharacteristic, complemented
245C23×C11—22no—
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—42no—
249C23×C11—81no—
250C23×C11—81no—
251C23×C11—82no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11#12011yescharacteristic
255Q8×C11—41no—
256Q8×C11—42no—
257Q8×C11—42no—
258Q8×C11—42no—
259Q8×C11—41no—
260Q8×C11—42no—
261Q8×C11—41no—
262D4×C11—41no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—44no—
269D4×C11—81no—
270D4×C11—82no—
271D4×C11—82no—
272D4×C11—82no—
273D4×C11—82no—
274D4×C11—82no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—82no—
287C2×C4×C11—81no—
288C2×C4×C11—82no—
289C2×C4×C11—82no—
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C8×C11—22no—
297C8×C11—42no—
298C8×C11—41no—
299C8×C11—42no—
300#562C22×C1112yes—
301H(3,𝔽4)C22×C1112yes—
302#559—21no—
303#548—21no—
304#546—22no—
305#546—21no—
306D42—21no—
307#542—21no—
308#538—22no—
309#538—21no—
310#535—21no—
311#534—21no—
312#533C22×C1111yescharacteristic, complemented
313#532C22×C1111yescharacteristic
314#529C22×C1111yescharacteristic
315C2×#124C22×C1111yescharacteristic
316#501C22×C1111yescharacteristic, complemented
317#497C22×C1111yescharacteristic, complemented
318#497C22×C1112yescomplemented
319#491—21no—
320#491C22×C1111yescharacteristic, complemented
321#490—21no—
322#489C22×C1112yescomplemented
323#489C22×C1112yescomplemented
324#489C22×C1111yescharacteristic, complemented
325#489C22×C1112yescomplemented
326#467—21no—
327#465—21no—
328#464—22no—
329#451—21no—
330#450—21no—
331#441—21no—
332#440—21no—
333#432C22×C1111yescharacteristic, complemented
334#416—22no—
335C2×#97C22×C1111yescharacteristic, complemented
336C2×#97C22×C1111yescharacteristic, complemented
337#330C22×C1112yescomplemented
338#329C22×C1112yescomplemented
339#329C22×C1112yescomplemented
340#329C22×C1112yescomplemented
341#329C22×C1112yescomplemented
342#329C22×C1112yescomplemented
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—41no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—162no—
355C22×C11—164no—
356C22×C11#45512yes—
357C22×C11C2×#12011yescharacteristic
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C2×#41—21no—
372C2×#41D4×C1112yes—
373C22×Q8D4×C1111yescharacteristic
374C22×D4—22no—
375C22×D4—21no—
376C22×D4D4×C1111yescharacteristic
377C2×Q16—21no—
378C2×Q16—22no—
379C2×SD16—21no—
380C2×SD16—22no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8D4×C1111yescharacteristic
384C4⋊Q8C23×C1111yescharacteristic
385C4⋊Q8C23×C1111yescharacteristic
386#127—21no—
387#127D4×C1111yescharacteristic
388#126—22no—
389#126—21no—
390#125—21no—
391#125C23×C1111yescharacteristic
392#124—21no—
393#124—22no—
394#124—22no—
395#124—22no—
396#124—21no—
397#124—21no—
398#124D4×C1112yes—
399#124C23×C1112yes—
400#124C23×C1111yescharacteristic
401#124C23×C1112yes—
402#123—22no—
403#123—22no—
404#123—21no—
405#123—22no—
406#123—22no—
407C22⋊Q8—21no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8D4×C1111yescharacteristic
413#121—22no—
414#121—22no—
415#121—22no—
416#121—21no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—21no—
421#121D4×C1111yescharacteristic
422#120—22no—
423#120—22no—
424#120—22no—
425#120—22no—
426#120—22no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8D4×C1111yescharacteristic
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4D4×C1111yescharacteristic
438#117—21no—
439#117—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C42C23×C1111yescharacteristic
444#107—21no—
445#106—21no—
446C4⋊C8—21no—
447#103—22no—
448#103—22no—
449#103—21no—
450#103—22no—
451#103—21no—
452#103—21no—
453#102—22no—
454#102—22no—
455#102—21no—
456#102—22no—
457C22⋊C8—21no—
458#97—21no—
459#97—21no—
460#97C23×C1111yescharacteristic
461#97C23×C1111yescharacteristic
462#97C23×C1112yes—
463#97C23×C1112yes—
464C2×C11—22no—
465C2×C11—82no—
466C2×C11—82no—
467C2×C11—81no—
468C2×C11C2×#45511yescharacteristic
469C2×C11#301811yescharacteristic
470C2×C11#301911yescharacteristic
471C24—22no—
472C24—21no—
473#41—44no—
474#41—82no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—81no—
479C2×Q8C2×D4×C1112yes—
480C2×Q8C2×D4×C1111yescharacteristic
481C2×Q8C2×D4×C1112yes—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—81no—
493C2×D4—82no—
494C2×D4—84no—
495C2×D4C2×D4×C1112yes—
496C2×D4C2×D4×C1111yescharacteristic
497C2×D4C2×D4×C1112yes—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1111yescharacteristic
505C22×C4C2×D4×C1111yescharacteristic
506Q16—42no—
507Q16—82no—
508SD16—42no—
509SD16—82no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—21no—
513C2×C8—22no—
514C2×C8—42no—
515C2×C8—42no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C1111yescharacteristic
531C4⋊C4C2×D4×C1111yescharacteristic
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—41no—
549C42—22no—
550C42—21no—
551C42—41no—
552C42C2×D4×C1111yescharacteristic
553C42C2×D4×C1111yescharacteristic
554C42C2×D4×C1111yescharacteristic
555C42C24×C1111yescharacteristic
556C11#1904311yescharacteristic, direct product factor, Sylow
557C23—22no—
558C23—21no—
559C23—22no—
560C23—42no—
561C23—81no—
562C23—81no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23C11×#12011yescharacteristic
567Q8—41no—
568Q8—42no—
569Q8—42no—
570Q8—42no—
571Q8—41no—
572Q8—42no—
573Q8—41no—
574D4—41no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—44no—
581D4—81no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—82no—
599C2×C4—81no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4C11×#12011yescharacteristic
603C2×C4C11×#12011yescharacteristic
604C2×C4C11×#12011yescharacteristic
605C2×C4C22×D4×C1111yescharacteristic
606C2×C4C22×D4×C1111yescharacteristic
607C2×C4C22×D4×C1111yescharacteristic
608C8—22no—
609C8—42no—
610C8—41no—
611C8—42no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—42no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—162no—
624C22—164no—
625C22C11×#45512yes—
626C22C2×C11×#12011yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—42no—
638C4—81no—
639C4—81no—
640C2—22no—
641C2—82no—
642C2—81no—
643C2—82no—
644C2C2×C11×#45511yescharacteristic
645C2C11×#301811yescharacteristic
646C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3558C2
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
2. C11×#3215C2semidirect
3. C11×#3181C2semidirect
4. C11×#3135C2semidirect
5. C11×#1662C2semidirect
6. C11×#1661C2semidirect
7. C11×#1659C2semidirect
8. C11×#1659C2semidirect
9. C11×#1532C2semidirect
10. C11×#1530C2semidirect
11. C2×C11×#329C2semidirect
24. C11×#533C22semidirect
28. C11×#501C22semidirect
29. C11×#497C22semidirect
30. C11×#497C22semidirect
32. C11×#491C22semidirect
34. C11×#489C22semidirect
35. C11×#489C22semidirect
36. C11×#489C22semidirect
37. C11×#489C22semidirect
45. 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
148. #19043C11direct (N × H)
235. #3215C2×C11semidirect
236. #3181C2×C11semidirect
237. #3135C2×C11semidirect
238. #1662C2×C11semidirect
239. #1661C2×C11semidirect
240. #1659C2×C11semidirect
241. #1659C2×C11semidirect
242. #1532C2×C11semidirect
243. #1530C2×C11semidirect
244. C2×#329C2×C11semidirect
312. #533C22×C11semidirect
316. #501C22×C11semidirect
317. #497C22×C11semidirect
318. #497C22×C11semidirect
320. #491C22×C11semidirect
322. #489C22×C11semidirect
323. #489C22×C11semidirect
324. #489C22×C11semidirect
325. #489C22×C11semidirect
333. #432C22×C11semidirect
335. C2×#97C22×C11semidirect
336. C2×#97C22×C11semidirect
337. #330C22×C11semidirect
338. #329C22×C11semidirect
339. #329C22×C11semidirect
340. #329C22×C11semidirect
341. #329C22×C11semidirect
342. #329C22×C11semidirect
556. C11#19043direct (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×#32152
C11×#31812
C11×#31352
C11×#16622
C11×#16612
C11×#16592
C11×#15322
C11×#15302
C2×C11×#3292
#1904311