Finite Group Databasebeta

← C11×#19087 #14596280

Subgroups — C11×#19087 #14596280

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3558C211yesmaximal, characteristic
2C11×#3240C211yesmaximal, characteristic, complemented
3C11×#3216C211yesmaximal, characteristic, complemented
4C11×#3215C211yesmaximal, characteristic, complemented
5C11×#1661C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1659C212yesmaximal, complemented
8C11×#1659C212yesmaximal, 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×#533C2211yescharacteristic, complemented
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C11×#501C2211yescharacteristic, complemented
29C11×#501C2211yescharacteristic, complemented
30C11×#497C2212yescomplemented
31C11×#497C2212yescomplemented
32C11×#489C2211yescharacteristic, complemented
33C11×#489C2211yescharacteristic, complemented
34C11×#489C2212yescomplemented
35C11×#489C2212yescomplemented
36C11×#485—21no—
37C11×#482—21no—
38C11×#479—21no—
39C11×#478—21no—
40C11×#464—22no—
41C11×#462—21no—
42C11×#460—21no—
43C11×#452—22no—
44C11×#451—21no—
45C11×#450—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×#41D412yes—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11D411yescharacteristic
61C2×C11×Q16—22no—
62C2×C11×Q16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×C4⋊Q8C2311yescharacteristic
68C11×#127—21no—
69C11×#127D411yescharacteristic
70C11×#126—22no—
71C11×#126—21no—
72C11×#125—21no—
73C11×#125C2311yescharacteristic
74C11×#124—21no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124—21no—
79C11×#124—21no—
80C11×#124D412yes—
81C11×#124C2311yescharacteristic
82C11×#124C2312yes—
83C11×#124C2312yes—
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—21no—
87C11×#123—22no—
88C11×#123—22no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8D411yescharacteristic
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—21no—
99C11×#121—22no—
100C11×#121—22no—
101C11×#121—21no—
102C11×#121—21no—
103C11×#121D411yescharacteristic
104C11×#120—22no—
105C11×#120—22no—
106C11×#120—22no—
107C11×#120—22no—
108C11×#120—22no—
109C4×Q8×C11—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11D411yescharacteristic
113C4×D4×C11—22no—
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11D411yescharacteristic
120C11×#117—21no—
121C11×#117—21no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C42×C11C2311yescharacteristic
126C11×#107—21no—
127C11×#107—21no—
128C11×#106—21no—
129C11×#106—21no—
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×#97C2311yescharacteristic
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2312yes—
148#19087C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—22no—
150C24×C11—21no—
151C11×#41—82no—
152C11×#41—82no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—81no—
157C2×Q8×C11C2×D411yescharacteristic
158C2×Q8×C11C2×D412yes—
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×D411yescharacteristic
174C2×D4×C11C2×D412yes—
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—82no—
185C11×Q16—82no—
186C11×SD16—82no—
187C11×SD16—82no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
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—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—41no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11—41no—
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2411yescharacteristic
232#3558C2×C1111yescharacteristic
233#3240C2×C1111yescharacteristic, complemented
234#3216C2×C1111yescharacteristic, complemented
235#3215C2×C1111yescharacteristic, complemented
236#1661C2×C1112yescomplemented
237#1661C2×C1112yescomplemented
238#1659C2×C1112yescomplemented
239#1659C2×C1112yescomplemented
240#1536C2×C1111yescharacteristic, complemented
241#1535C2×C1111yescharacteristic, complemented
242#1533C2×C1111yescharacteristic, complemented
243C23×C11—21no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—81no—
248C23×C11—81no—
249C23×C11—82no—
250C23×C11—82no—
251C23×C11—82no—
252C23×C11#12011yescharacteristic
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—41no—
256Q8×C11—42no—
257Q8×C11—41no—
258Q8×C11—42no—
259Q8×C11—41no—
260D4×C11—42no—
261D4×C11—42no—
262D4×C11—41no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—44no—
267D4×C11—81no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—82no—
271D4×C11—82no—
272D4×C11—82no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—82no—
285C2×C4×C11—81no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C8×C11—41no—
295C8×C11—41no—
296C8×C11—42no—
297C8×C11—42no—
298#562C22×C1112yes—
299H(3,𝔽4)C22×C1112yes—
300#559—21no—
301#548—21no—
302#546—22no—
303#546—21no—
304D42—21no—
305#542—21no—
306#538—22no—
307#538—21no—
308#535—21no—
309#534—21no—
310#533C22×C1111yescharacteristic, complemented
311#532C22×C1111yescharacteristic
312#529C22×C1111yescharacteristic
313C2×#124C22×C1111yescharacteristic
314#501C22×C1111yescharacteristic, complemented
315#501C22×C1111yescharacteristic, complemented
316#497C22×C1112yescomplemented
317#497C22×C1112yescomplemented
318#489C22×C1111yescharacteristic, complemented
319#489C22×C1111yescharacteristic, complemented
320#489C22×C1112yescomplemented
321#489C22×C1112yescomplemented
322#485—21no—
323#482—21no—
324#479—21no—
325#478—21no—
326#464—22no—
327#462—21no—
328#460—21no—
329#452—22no—
330#451—21no—
331#450—21no—
332#432C22×C1111yescharacteristic, complemented
333#432C22×C1111yescharacteristic, complemented
334#432C22×C1111yescharacteristic, complemented
335#330C22×C1112yescomplemented
336#329C22×C1112yescomplemented
337#329C22×C1112yescomplemented
338#329C22×C1112yescomplemented
339#329C22×C1112yescomplemented
340#329C22×C1112yescomplemented
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—41no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—162no—
354C22×C11—164no—
355C22×C11C2×#12011yescharacteristic
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C2×#41—21no—
370C2×#41D4×C1112yes—
371C22×Q8D4×C1111yescharacteristic
372C22×D4—22no—
373C22×D4—21no—
374C22×D4D4×C1111yescharacteristic
375C2×Q16—22no—
376C2×Q16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C4⋊Q8D4×C1111yescharacteristic
380C4⋊Q8C23×C1111yescharacteristic
381C4⋊Q8C23×C1111yescharacteristic
382#127—21no—
383#127D4×C1111yescharacteristic
384#126—22no—
385#126—21no—
386#125—21no—
387#125C23×C1111yescharacteristic
388#124—21no—
389#124—22no—
390#124—22no—
391#124—22no—
392#124—21no—
393#124—21no—
394#124D4×C1112yes—
395#124C23×C1112yes—
396#124C23×C1111yescharacteristic
397#124C23×C1112yes—
398#123—22no—
399#123—22no—
400#123—21no—
401#123—22no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8D4×C1111yescharacteristic
409#121—22no—
410#121—22no—
411#121—22no—
412#121—21no—
413#121—22no—
414#121—22no—
415#121—21no—
416#121—21no—
417#121D4×C1111yescharacteristic
418#120—22no—
419#120—22no—
420#120—22no—
421#120—22no—
422#120—22no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8D4×C1111yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4D4×C1111yescharacteristic
434#117—21no—
435#117—21no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42C23×C1111yescharacteristic
440#107—21no—
441#107—21no—
442#106—21no—
443#106—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447#103—22no—
448#103—22no—
449#103—21no—
450#103—21no—
451#102—22no—
452#102—22no—
453#102—21no—
454#102—21no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458#97C23×C1111yescharacteristic
459#97C23×C1111yescharacteristic
460#97C23×C1112yes—
461#97C23×C1112yes—
462C2×C11—41no—
463C2×C11—82no—
464C2×C11—81no—
465C2×C11—82no—
466C2×C11#301911yescharacteristic
467C2×C11#301911yescharacteristic
468C2×C11#302211yescharacteristic
469C24—22no—
470C24—21no—
471#41—82no—
472#41—82no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—81no—
477C2×Q8C2×D4×C1111yescharacteristic
478C2×Q8C2×D4×C1112yes—
479C2×Q8C2×D4×C1112yes—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—81no—
491C2×D4—82no—
492C2×D4—84no—
493C2×D4C2×D4×C1111yescharacteristic
494C2×D4C2×D4×C1112yes—
495C2×D4C2×D4×C1112yes—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1111yescharacteristic
503C22×C4C2×D4×C1111yescharacteristic
504Q16—82no—
505Q16—82no—
506SD16—82no—
507SD16—82no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4C2×D4×C1111yescharacteristic
527C4⋊C4C2×D4×C1111yescharacteristic
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—41no—
545C42—22no—
546C42—21no—
547C42—41no—
548C42C2×D4×C1111yescharacteristic
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C24×C1111yescharacteristic
552C11#1908711yescharacteristic, direct product factor, Sylow
553C23—21no—
554C23—22no—
555C23—22no—
556C23—42no—
557C23—81no—
558C23—81no—
559C23—82no—
560C23—82no—
561C23—82no—
562C23C11×#12011yescharacteristic
563Q8—42no—
564Q8—42no—
565Q8—41no—
566Q8—42no—
567Q8—41no—
568Q8—42no—
569Q8—41no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—44no—
577D4—81no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—82no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4C11×#12011yescharacteristic
599C2×C4C11×#12011yescharacteristic
600C2×C4C11×#12011yescharacteristic
601C2×C4C22×D4×C1111yescharacteristic
602C2×C4C22×D4×C1111yescharacteristic
603C2×C4C22×D4×C1111yescharacteristic
604C8—42no—
605C8—42no—
606C8—41no—
607C8—41no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—42no—
620C22—162no—
621C22—164no—
622C22C2×C11×#12011yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—42no—
633C4—41no—
634C4—81no—
635C4—81no—
636C2—41no—
637C2—81no—
638C2—82no—
639C2—82no—
640C2C11×#301911yescharacteristic
641C2C11×#301911yescharacteristic
642C2C11×#302211yescharacteristic
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×#3240C2semidirect
3. C11×#3216C2semidirect
4. C11×#3215C2semidirect
5. C11×#1661C2semidirect
6. C11×#1661C2semidirect
7. C11×#1659C2semidirect
8. C11×#1659C2semidirect
9. C11×#1536C2semidirect
10. C11×#1535C2semidirect
11. C11×#1533C2semidirect
24. C11×#533C22semidirect
28. C11×#501C22semidirect
29. C11×#501C22semidirect
30. C11×#497C22semidirect
31. C11×#497C22semidirect
32. C11×#489C22semidirect
33. C11×#489C22semidirect
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. #19087C11direct (N × H)
233. #3240C2×C11semidirect
234. #3216C2×C11semidirect
235. #3215C2×C11semidirect
236. #1661C2×C11semidirect
237. #1661C2×C11semidirect
238. #1659C2×C11semidirect
239. #1659C2×C11semidirect
240. #1536C2×C11semidirect
241. #1535C2×C11semidirect
242. #1533C2×C11semidirect
310. #533C22×C11semidirect
314. #501C22×C11semidirect
315. #501C22×C11semidirect
316. #497C22×C11semidirect
317. #497C22×C11semidirect
318. #489C22×C11semidirect
319. #489C22×C11semidirect
320. #489C22×C11semidirect
321. #489C22×C11semidirect
332. #432C22×C11semidirect
333. #432C22×C11semidirect
334. #432C22×C11semidirect
335. #330C22×C11semidirect
336. #329C22×C11semidirect
337. #329C22×C11semidirect
338. #329C22×C11semidirect
339. #329C22×C11semidirect
340. #329C22×C11semidirect
552. C11#19087direct (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×#32402
C11×#32162
C11×#32152
C11×#16612
C11×#16592
C11×#15362
C11×#15352
C11×#15332
#1908711