Finite Group Databasebeta

← C11×#24651 #14601844

Subgroups — C11×#24651 #14601844

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#461C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2857C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic
5C11×#2035C212yesmaximal, complemented
6C11×#2000C212yesmaximal
7C11×#1981C211yesmaximal, characteristic, complemented
8C11×#1968C212yesmaximal, complemented
9C11×#1948C211yesmaximal, characteristic, complemented
10C11×#1933C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#121C2211yescharacteristic
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C11×#461—24no—
20C11×#431—24no—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C4×C8×C11C2212yes—
30C11×#391C2212yes—
31C11×#390C2211yescharacteristic
32C11×#389—21no—
33C11×#389—21no—
34C11×#389C2211yescharacteristic
35C11×#388—21no—
36C11×#386—21no—
37C11×#384C2211yescharacteristic
38C11×#380—21no—
39C11×#380—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11C2312yes—
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C2×C11×SD16—24no—
53C2×C11×SD16—24no—
54C2×C11×SD16—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C22⋊Q8—42no—
60C11×C22⋊Q8—42no—
61C11×#121—22no—
62C11×#121—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—44no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11D411yescharacteristic
86C2×C42×C11D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C11×#106—42no—
90C11×C4⋊C8—22no—
91C11×C4⋊C8D414yescomplemented
92C11×#103—24no—
93C11×#103—24no—
94C11×#103—42no—
95C11×#102—42no—
96C11×C22⋊C8—24no—
97C4×C8×C11—24no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—22no—
102C11×#95—22no—
103#24651C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—21no—
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11#4112yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11SD1614yescomplemented
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×SD16—48no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11C2×D414yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4#4112yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179C42×C11C2×D412yes—
180C42×C11#4112yes—
181C2×#461C2×C1111yescharacteristic, complemented
182C2×#431C2×C1111yescharacteristic, complemented
183#2857C2×C1111yescharacteristic, complemented
184C4×#121C2×C1111yescharacteristic
185#2035C2×C1112yescomplemented
186#2000C2×C1112yes—
187#1981C2×C1111yescharacteristic, complemented
188#1968C2×C1112yescomplemented
189#1948C2×C1111yescharacteristic, complemented
190#1933C2×C1112yescomplemented
191#1802C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11C2×SD1612yes—
206C23×C11C22×D411yescharacteristic
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—42no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—48no—
214D4×C11—41no—
215D4×C11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—28no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—44no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—84no—
247C2×C4×C11#12112yes—
248C2×C4×C11#12112yes—
249C2×C4×C11C2×SD1612yes—
250C2×C4×C11C2×SD1612yes—
251C2×C4×C11#13512yes—
252C2×C4×C11#13712yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C8×C11—24no—
260C8×C11—42no—
261C22×SD16C22×C1112yes—
262C2×C4⋊Q8C22×C1111yescharacteristic
263C2×C22⋊Q8C22×C1112yes—
264C2×#121C22×C1111yescharacteristic
265C2×C4×D4—21no—
266C2×C4×D4C22×C1111yescharacteristic
267C22×C42C22×C1111yescharacteristic
268#461—24no—
269#431—24no—
270C2×#106C22×C1112yes—
271C2×C4⋊C8C22×C1111yescharacteristic
272C2×C4⋊C8C22×C1111yescharacteristic
273C2×#103C22×C1112yes—
274C2×#103C22×C1112yes—
275C2×#103C22×C1112yes—
276C2×#102C22×C1112yes—
277C2×C22⋊C8C22×C1112yes—
278C2×C4×C8C22×C1112yes—
279#391C22×C1112yes—
280#390C22×C1111yescharacteristic
281#389—21no—
282#389—21no—
283#389C22×C1111yescharacteristic
284#388—21no—
285#386—21no—
286#384C22×C1111yescharacteristic
287#380—21no—
288#380—21no—
289#380C22×C1111yescharacteristic
290C4×C4⋊C4C22×C1111yescharacteristic
291C4×C22⋊C4—21no—
292#340C22×C1112yes—
293#340C22×C1112yes—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11C2×#12111yescharacteristic
309C22×C11#52511yescharacteristic
310C22×C11#53511yescharacteristic
311C22×C11C22×SD1611yescharacteristic
312C22×C11C2×#13511yescharacteristic
313C22×C11C2×#13711yescharacteristic
314C22×C11#57511yescharacteristic
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—41no—
320C4×C11—82no—
321C4×C11—81no—
322C4×C11—82no—
323C4×C11—81no—
324C4×C11#46514yes—
325C4×C11#54611yescharacteristic
326C4×C11#55011yescharacteristic
327C4×C11#55311yescharacteristic
328C4×C11#55511yescharacteristic
329C22×Q8C23×C1112yes—
330C22×D4—21no—
331C22×D4C23×C1111yescharacteristic
332C23×C4—21no—
333C23×C4D4×C1111yescharacteristic
334C23×C4D4×C1111yescharacteristic
335C23×C4C23×C1111yescharacteristic
336C2×SD16—24no—
337C2×SD16—24no—
338C2×SD16—42no—
339C22×C8C23×C1112yes—
340C22×C8C23×C1112yes—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345#121—22no—
346#121—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—44no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1111yescharacteristic
359C2×C4⋊C4C23×C1111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—21no—
369C2×C42D4×C1111yescharacteristic
370C2×C42D4×C1111yescharacteristic
371C2×C42C23×C1111yescharacteristic
372C2×C42C23×C1111yescharacteristic
373#106—42no—
374C4⋊C8—22no—
375C4⋊C8D4×C1114yescomplemented
376#103—24no—
377#103—24no—
378#103—42no—
379#102—42no—
380C22⋊C8—24no—
381C4×C8—24no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—22no—
386#95—22no—
387C2×C11—42no—
388C2×C11—82no—
389C2×C11#241411yescharacteristic
390C2×C11C2×#46511yescharacteristic
391C2×C11#305611yescharacteristic
392C2×C11#310111yescharacteristic
393C2×C11#310711yescharacteristic
394C2×C11#320611yescharacteristic
395C2×C11#321211yescharacteristic
396C24—21no—
397C24C2×D4×C1111yescharacteristic
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4C11×#4112yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—41no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4C11×SD1614yescomplemented
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439SD16—48no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8C2×D4×C1114yes—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—44no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4C11×#4112yes—
460C22⋊C4—24no—
461C22⋊C4—44no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—42no—
465C22⋊C4—42no—
466C42—22no—
467C42—22no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42C2×D4×C1112yes—
472C42C11×#4112yes—
473C11#2465111yescharacteristic, direct product factor, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23C2×C11×SD1612yes—
488C23C22×D4×C1111yescharacteristic
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—48no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—28no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—44no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—84no—
529C2×C4C11×#12112yes—
530C2×C4C11×#12112yes—
531C2×C4C2×C11×SD1612yes—
532C2×C4C2×C11×SD1612yes—
533C2×C4C11×#13512yes—
534C2×C4C11×#13712yes—
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C2×C4C2×C11×#4111yescharacteristic
538C2×C4C2×C11×#4111yescharacteristic
539C2×C4C11×H(5,𝔽2)11yescharacteristic
540C2×C4C11×H(5,𝔽2)11yescharacteristic
541C8—24no—
542C8—42no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×C11×#12111yescharacteristic
558C22C11×#52511yescharacteristic
559C22C11×#53511yescharacteristic
560C22C22×C11×SD1611yescharacteristic
561C22C2×C11×#13511yescharacteristic
562C22C2×C11×#13711yescharacteristic
563C22C11×#57511yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—82no—
570C4—81no—
571C4—82no—
572C4—81no—
573C4C11×#46514yes—
574C4C11×#54611yescharacteristic
575C4C11×#55011yescharacteristic
576C4C11×#55311yescharacteristic
577C4C11×#55511yescharacteristic
578C2—42no—
579C2—82no—
580C2C11×#241411yescharacteristic
581C2C2×C11×#46511yescharacteristic
582C2C11×#305611yescharacteristic
583C2C11×#310111yescharacteristic
584C2C11×#310711yescharacteristic
585C2C11×#320611yescharacteristic
586C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C11×#461C2semidirect
2. C2×C11×#431C2semidirect
3. C11×#2857C2semidirect
5. C11×#2035C2semidirect
7. C11×#1981C2semidirect
8. C11×#1968C2semidirect
9. C11×#1948C2semidirect
10. C11×#1933C2semidirect
11. C11×#1802C2semidirect
91. C11×C4⋊C8D4semidirect
103. #24651C11direct (N × H)
140. C22×C4×C11SD16semidirect
181. C2×#461C2×C11semidirect
182. C2×#431C2×C11semidirect
183. #2857C2×C11semidirect
185. #2035C2×C11semidirect
187. #1981C2×C11semidirect
188. #1968C2×C11semidirect
189. #1948C2×C11semidirect
190. #1933C2×C11semidirect
191. #1802C2×C11semidirect
375. C4⋊C8D4×C11semidirect
432. C22×C4C11×SD16semidirect
473. C11#24651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4612
C2×C11×#4312
C11×#28572
C4×C11×#1212
C11×#20352
C11×#20002
C11×#19812
C11×#19682
C11×#19482
C11×#19332
C11×#18022
#2465111