Finite Group Databasebeta

← C11×#19090 #14596283

Subgroups — C11×#19090 #14596283

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3561C211yesmaximal, characteristic, complemented
2C11×#3235C211yesmaximal, characteristic, complemented
3C11×#3219C211yesmaximal, characteristic, complemented
4C11×#3213C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1657C212yesmaximal, complemented
8C11×#1656C212yesmaximal, complemented
9C11×#1537C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1533C211yesmaximal, characteristic, complemented
12C11×#563C2212yes—
13C11×#562C2212yes—
14C11×#556—21no—
15C11×#551—22no—
16D4×Q8×C11—21no—
17C11×#548—21no—
18C11×#546—21no—
19C11×#543—21no—
20C11×#542—21no—
21C11×#542—22no—
22C11×#538—21no—
23C11×#536—21no—
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C11×#501C2212yescomplemented
29C11×#497C2211yescharacteristic, complemented
30C11×#496C2212yes—
31C11×#496C2211yescharacteristic, complemented
32C11×#491C2211yescharacteristic, complemented
33C11×#490C2212yescomplemented
34C11×#490C2211yescharacteristic, complemented
35C11×#489C2212yes—
36C11×#482—22no—
37C11×#476—21no—
38C11×#474—21no—
39C11×#464—21no—
40C11×#463—22no—
41C11×#463—21no—
42C11×#452—21no—
43C11×#449—21no—
44C11×#448—21no—
45C11×#447—21no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yescomplemented
50C11×#330C2212yescomplemented
51C11×#330C2212yescomplemented
52C11×#329C2212yes—
53C11×#329C2212yes—
54C11×#329C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11D411yescharacteristic
59C22×D4×C11D411yescharacteristic
60C2×C11×Q16—21no—
61C2×C11×SD16—22no—
62C2×C11×SD16—21no—
63C2×C11×SD16—21no—
64C2×C11×D8—22no—
65C2×C11×D8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8D411yescharacteristic
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#127C2311yescharacteristic
72C11×#126—22no—
73C11×#126—22no—
74C11×#126—22no—
75C11×#126—21no—
76C11×#125C2311yescharacteristic
77C11×#125C2312yes—
78C11×#124—21no—
79C11×#124—22no—
80C11×#124—22no—
81C11×#124—21no—
82C11×#124—21no—
83C11×#124—21no—
84C11×#124D412yes—
85C11×#124C2312yes—
86C11×#124C2311yescharacteristic
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—21no—
90C11×#123—22no—
91C11×#123—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8—21no—
100C11×C22⋊Q8—22no—
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8D411yescharacteristic
103C11×#121—21no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121D411yescharacteristic
109C11×#120—22no—
110C4×Q8×C11—21no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11D411yescharacteristic
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—22no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11D411yescharacteristic
121C11×#117—22no—
122C11×#117—21no—
123C11×#117D412yes—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C42×C11C2311yescharacteristic
128C11×#107—22no—
129C11×#106—22no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—22no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#102—22no—
137C11×#102—21no—
138C11×#102—21no—
139C11×#102—22no—
140C11×#102—22no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2312yes—
145C11×#97C2312yes—
146C11×#97C2311yescharacteristic
147C11×#97C2311yescharacteristic
148#19090C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C11×#41—81no—
151C11×#41—81no—
152C11×#41—82no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—82no—
159C2×Q8×C11—81no—
160C2×Q8×C11C2×D412yes—
161C2×Q8×C11C2×D411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—41no—
170C2×D4×C11—81no—
171C2×D4×C11C2×D412yes—
172C2×D4×C11C2×D411yescharacteristic
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—41no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C11×Q16—81no—
183C11×SD16—81no—
184C11×SD16—82no—
185C11×SD16—81no—
186C11×D8—81no—
187C11×D8—82no—
188C2×C8×C11—22no—
189C2×C8×C11—21no—
190C2×C8×C11—22no—
191C2×C8×C11—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
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—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D412yes—
209C11×C4⋊C4C2×D412yes—
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—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—21no—
224C11×C22⋊C4—21no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—41no—
227C42×C11—22no—
228C42×C11—22no—
229C42×C11—21no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2411yescharacteristic
234#3561C2×C1111yescharacteristic, complemented
235#3235C2×C1111yescharacteristic, complemented
236#3219C2×C1111yescharacteristic, complemented
237#3213C2×C1111yescharacteristic, complemented
238#1664C2×C1112yescomplemented
239#1661C2×C1112yescomplemented
240#1657C2×C1112yescomplemented
241#1656C2×C1112yescomplemented
242#1537C2×C1111yescharacteristic, complemented
243#1535C2×C1111yescharacteristic, complemented
244#1533C2×C1111yescharacteristic, complemented
245C23×C11—22no—
246C23×C11—21no—
247C23×C11—42no—
248C23×C11—41no—
249C23×C11—81no—
250C23×C11—81no—
251C23×C11#12011yescharacteristic
252Q8×C11—41no—
253Q8×C11—42no—
254Q8×C11—42no—
255Q8×C11—42no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—81no—
259Q8×C11—82no—
260D4×C11—41no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—82no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—41no—
282C2×C4×C11—82no—
283C2×C4×C11—81no—
284C2×C4×C11—82no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C8×C11—42no—
294C8×C11—42no—
295C8×C11—41no—
296C8×C11—41no—
297#563C22×C1112yes—
298#562C22×C1112yes—
299#556—21no—
300#551—22no—
301D4×Q8—21no—
302#548—21no—
303#546—21no—
304#543—21no—
305#542—21no—
306#542—22no—
307#538—21no—
308#536—21no—
309#533C22×C1111yescharacteristic
310#532C22×C1111yescharacteristic
311#529C22×C1111yescharacteristic
312C2×#124C22×C1111yescharacteristic
313#501C22×C1112yescomplemented
314#497C22×C1111yescharacteristic, complemented
315#496C22×C1112yes—
316#496C22×C1111yescharacteristic, complemented
317#491C22×C1111yescharacteristic, complemented
318#490C22×C1112yescomplemented
319#490C22×C1111yescharacteristic, complemented
320#489C22×C1112yes—
321#482—22no—
322#476—21no—
323#474—21no—
324#464—21no—
325#463—22no—
326#463—21no—
327#452—21no—
328#449—21no—
329#448—21no—
330#447—21no—
331#432C22×C1111yescharacteristic
332#432C22×C1111yescharacteristic
333#432C22×C1111yescharacteristic
334#330C22×C1112yescomplemented
335#330C22×C1112yescomplemented
336#330C22×C1112yescomplemented
337#329C22×C1112yes—
338#329C22×C1112yes—
339#329C22×C1112yescomplemented
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—41no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—41no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—162no—
353C22×C11C2×#12011yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—81no—
367C2×#41—21no—
368C2×#41—21no—
369C22×Q8—21no—
370C22×Q8D4×C1111yescharacteristic
371C22×D4D4×C1111yescharacteristic
372C2×Q16—21no—
373C2×SD16—22no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×D8—22no—
377C2×D8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—22no—
380C4⋊Q8D4×C1111yescharacteristic
381C4⋊Q8D4×C1111yescharacteristic
382C4⋊Q8C23×C1111yescharacteristic
383#127C23×C1111yescharacteristic
384#126—22no—
385#126—22no—
386#126—22no—
387#126—21no—
388#125C23×C1111yescharacteristic
389#125C23×C1112yes—
390#124—21no—
391#124—22no—
392#124—22no—
393#124—21no—
394#124—21no—
395#124—21no—
396#124D4×C1112yes—
397#124C23×C1112yes—
398#124C23×C1111yescharacteristic
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8D4×C1111yescharacteristic
415#121—21no—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121D4×C1111yescharacteristic
421#120—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8D4×C1111yescharacteristic
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4D4×C1111yescharacteristic
433#117—22no—
434#117—21no—
435#117D4×C1112yes—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42C23×C1111yescharacteristic
440#107—22no—
441#106—22no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445#103—22no—
446#103—21no—
447#103—21no—
448#102—22no—
449#102—21no—
450#102—21no—
451#102—22no—
452#102—22no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456#97C23×C1112yes—
457#97C23×C1111yescharacteristic
458#97C23×C1111yescharacteristic
459#97C23×C1112yes—
460C2×C11—41no—
461C2×C11—81no—
462C2×C11—82no—
463C2×C11—161no—
464C2×C11#301911yescharacteristic
465C2×C11#302011yescharacteristic
466C2×C11#302111yescharacteristic
467C24—21no—
468#41—81no—
469#41—81no—
470#41—82no—
471C2×Q8—22no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—82no—
477C2×Q8—81no—
478C2×Q8C2×D4×C1112yes—
479C2×Q8C2×D4×C1111yescharacteristic
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—41no—
488C2×D4—81no—
489C2×D4C2×D4×C1112yes—
490C2×D4C2×D4×C1111yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500Q16—81no—
501SD16—82no—
502SD16—81no—
503SD16—81no—
504D8—81no—
505D8—82no—
506C2×C8—22no—
507C2×C8—21no—
508C2×C8—22no—
509C2×C8—21no—
510C4⋊C4—22no—
511C4⋊C4—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—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4C2×D4×C1111yescharacteristic
525C4⋊C4C2×D4×C1111yescharacteristic
526C4⋊C4C2×D4×C1112yes—
527C4⋊C4C2×D4×C1112yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42C2×D4×C1111yescharacteristic
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C24×C1111yescharacteristic
552C11#1909011yescharacteristic, direct product factor, Sylow
553C23—22no—
554C23—21no—
555C23—42no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23C11×#12011yescharacteristic
560Q8—41no—
561Q8—42no—
562Q8—42no—
563Q8—42no—
564Q8—41no—
565Q8—41no—
566Q8—81no—
567Q8—82no—
568D4—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—42no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—82no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4C11×#12011yescharacteristic
596C2×C4C11×#12011yescharacteristic
597C2×C4C11×#12011yescharacteristic
598C2×C4C22×D4×C1111yescharacteristic
599C2×C4C22×D4×C1111yescharacteristic
600C2×C4C22×D4×C1111yescharacteristic
601C8—42no—
602C8—41no—
603C8—41no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—162no—
618C22C2×C11×#12011yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—81no—
632C2—41no—
633C2—82no—
634C2—81no—
635C2—161no—
636C2C11×#301911yescharacteristic
637C2C11×#302011yescharacteristic
638C2C11×#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×#3561C2semidirect
2. C11×#3235C2semidirect
3. C11×#3219C2semidirect
4. C11×#3213C2semidirect
5. C11×#1664C2semidirect
6. C11×#1661C2semidirect
7. C11×#1657C2semidirect
8. C11×#1656C2semidirect
9. C11×#1537C2semidirect
10. C11×#1535C2semidirect
11. C11×#1533C2semidirect
28. C11×#501C22semidirect
29. C11×#497C22semidirect
31. C11×#496C22semidirect
32. C11×#491C22semidirect
33. C11×#490C22semidirect
34. C11×#490C22semidirect
49. C11×#330C22semidirect
50. C11×#330C22semidirect
51. C11×#330C22semidirect
54. C11×#329C22semidirect
148. #19090C11direct (N × H)
234. #3561C2×C11semidirect
235. #3235C2×C11semidirect
236. #3219C2×C11semidirect
237. #3213C2×C11semidirect
238. #1664C2×C11semidirect
239. #1661C2×C11semidirect
240. #1657C2×C11semidirect
241. #1656C2×C11semidirect
242. #1537C2×C11semidirect
243. #1535C2×C11semidirect
244. #1533C2×C11semidirect
313. #501C22×C11semidirect
314. #497C22×C11semidirect
316. #496C22×C11semidirect
317. #491C22×C11semidirect
318. #490C22×C11semidirect
319. #490C22×C11semidirect
334. #330C22×C11semidirect
335. #330C22×C11semidirect
336. #330C22×C11semidirect
339. #329C22×C11semidirect
552. C11#19090direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35612
C11×#32352
C11×#32192
C11×#32132
C11×#16642
C11×#16612
C11×#16572
C11×#16562
C11×#15372
C11×#15352
C11×#15332
#1909011