Finite Group Databasebeta

← C11×#24119 #14601312

Subgroups — C11×#24119 #14601312

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2537C211yesmaximal, characteristic
5C11×#2036C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1954C211yesmaximal, characteristic, complemented
9C11×#1875C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C11×#556—24no—
14C11×#556—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2212yes—
26C11×#474—24no—
27C4×C11×SD16—24no—
28C2×C11×#107C2212yes—
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C11×#394—22no—
39C11×#384C2211yescharacteristic
40C11×#380—21no—
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2312yes—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yescomplemented
60C11×#126—216no—
61C11×#124—28no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C11×#121—24no—
65C11×#121—42no—
66C11×#121—44no—
67C4×Q8×C11—28no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yescomplemented
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C11×#117—24no—
75C11×#117—24no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4D412yes—
92C2×C42×C11—22no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C11×#107—24no—
96C11×#106—22no—
97C11×C4⋊C8—22no—
98C11×#103—22no—
99C11×#103—42no—
100C11×#102—22no—
101C11×#102—24no—
102C11×C22⋊C8—24no—
103C11×C22⋊C8—42no—
104C4×C8×C11—22no—
105C11×#95—22no—
106#24119C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—82no—
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×SD16—28no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11#4112yes—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—81no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—44no—
177C11×C22⋊C4—42no—
178C42×C11—28no—
179C42×C11—24no—
180C42×C11C2×D412yes—
181C42×C11C2×D412yes—
182C2×#556C2×C1111yescharacteristic, complemented
183C2×#474C2×C1111yescharacteristic, complemented
184C2×C4×SD16C2×C1111yescharacteristic, complemented
185#2537C2×C1111yescharacteristic
186#2036C2×C1112yescomplemented
187#2000C2×C1112yescomplemented
188#1990C2×C1111yescharacteristic, complemented
189#1954C2×C1111yescharacteristic, complemented
190#1875C2×C1112yescomplemented
191#1854C2×C1112yescomplemented
192#1803C2×C1111yescharacteristic, complemented
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C22×D411yescharacteristic
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—41no—
211Q8×C11—41no—
212Q8×C11—48no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—44no—
218D4×C11—88no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—84no—
244C2×C4×C11#12012yes—
245C2×C4×C11#12012yes—
246C2×C4×C11#13512yes—
247C2×C4×C11AGL(1,ℤ/8)12yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C8×C11—22no—
255C8×C11—41no—
256C8×C11—42no—
257C22×SD16C22×C1111yescharacteristic
258#556—24no—
259#556—24no—
260C2×C4⋊Q8C22×C1111yescharacteristic
261C2×#126—22no—
262C2×#124—21no—
263C2×C22⋊Q8C22×C1112yes—
264C2×#121—21no—
265C2×#121C22×C1112yes—
266C2×C4×Q8—21no—
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269C2×C4×D4C22×C1111yescharacteristic
270C2×#117C22×C1112yes—
271#474—24no—
272C4×SD16—24no—
273C2×#107C22×C1112yes—
274C2×#106C22×C1111yescharacteristic
275C2×C4⋊C8C22×C1111yescharacteristic
276C2×#103C22×C1111yescharacteristic
277C2×#103C22×C1112yes—
278C2×#102C22×C1111yescharacteristic
279C2×#102C22×C1112yes—
280C2×C22⋊C8C22×C1112yes—
281C2×C22⋊C8C22×C1112yes—
282C2×C4×C8C22×C1111yescharacteristic
283#394—22no—
284#384C22×C1111yescharacteristic
285#380—21no—
286#380C22×C1112yes—
287#340C22×C1112yes—
288#340C22×C1112yes—
289#340C22×C1112yes—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11C2×#12011yescharacteristic
305C22×C11#54611yescharacteristic
306C22×C11#54711yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C11#57711yescharacteristic
310C22×C11#57811yescharacteristic
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—81no—
317C4×C11—82no—
318C4×C11#44914yes—
319C4×C11#52511yescharacteristic
320C4×C11#53711yescharacteristic
321C4×C11#54811yescharacteristic
322C4×C11#55011yescharacteristic
323C22×Q8—21no—
324C22×Q8C23×C1111yescharacteristic
325C22×D4—22no—
326C22×D4D4×C1111yescharacteristic
327C22×D4C23×C1111yescharacteristic
328C23×C4—21no—
329C23×C4C23×C1112yes—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—22no—
333C22×C8C23×C1111yescharacteristic
334C22×C8C23×C1112yes—
335C22×C8C23×C1111yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8D4×C1114yescomplemented
338#126—216no—
339#124—28no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342#121—24no—
343#121—42no—
344#121—44no—
345C4×Q8—28no—
346C4×Q8—22no—
347C4×Q8D4×C1114yescomplemented
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—24no—
353#117—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4D4×C1111yescharacteristic
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4D4×C1112yes—
370C2×C42—22no—
371C2×C42—21no—
372C2×C42C23×C1111yescharacteristic
373#107—24no—
374#106—22no—
375C4⋊C8—22no—
376#103—22no—
377#103—42no—
378#102—22no—
379#102—24no—
380C22⋊C8—24no—
381C22⋊C8—42no—
382C4×C8—22no—
383#95—22no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11#240711yescharacteristic
387C2×C11C2×#44911yescharacteristic
388C2×C11#301311yescharacteristic
389C2×C11#330211yescharacteristic
390C2×C11#332411yescharacteristic
391C2×C11#334011yescharacteristic
392C2×C11#335311yescharacteristic
393C24—21no—
394C24C2×D4×C1112yes—
395C2×Q8—24no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8C2×D4×C1112yes—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—82no—
415C2×D4C11×#4112yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C1112yes—
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C24×C1111yescharacteristic
434SD16—28no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—21no—
441C2×C8—22no—
442C2×C8—21no—
443C2×C8C11×#4112yes—
444C4⋊C4—28no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4C2×D4×C1112yes—
457C4⋊C4C2×D4×C1114yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—24no—
461C22⋊C4—44no—
462C22⋊C4—44no—
463C22⋊C4—42no—
464C42—28no—
465C42—24no—
466C42C2×D4×C1112yes—
467C42C2×D4×C1112yes—
468C11#2411911yescharacteristic, direct product factor, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23C22×D4×C1111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—48no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—44no—
494D4—88no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—84no—
520C2×C4C11×#12012yes—
521C2×C4C11×#12012yes—
522C2×C4C11×#13512yes—
523C2×C4C11×AGL(1,ℤ/8)12yes—
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C22×D4×C1111yescharacteristic
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C2×C11×#4111yescharacteristic
528C2×C4C11×H(5,𝔽2)11yescharacteristic
529C2×C4C11×2−1+411yescharacteristic
530C8—22no—
531C8—41no—
532C8—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C2×C11×#12011yescharacteristic
548C22C11×#54611yescharacteristic
549C22C11×#54711yescharacteristic
550C22C2×C11×#13511yescharacteristic
551C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
552C22C11×#57711yescharacteristic
553C22C11×#57811yescharacteristic
554C4—22no—
555C4—42no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—81no—
560C4—82no—
561C4C11×#44914yes—
562C4C11×#52511yescharacteristic
563C4C11×#53711yescharacteristic
564C4C11×#54811yescharacteristic
565C4C11×#55011yescharacteristic
566C2—82no—
567C2—82no—
568C2C11×#240711yescharacteristic
569C2C2×C11×#44911yescharacteristic
570C2C11×#301311yescharacteristic
571C2C11×#330211yescharacteristic
572C2C11×#332411yescharacteristic
573C2C11×#334011yescharacteristic
574C2C11×#335311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#556C2semidirect
2. C2×C11×#474C2semidirect
3. C2×C4×C11×SD16C2semidirect
5. C11×#2036C2semidirect
6. C11×#2000C2semidirect
7. C11×#1990C2semidirect
8. C11×#1954C2semidirect
9. C11×#1875C2semidirect
10. C11×#1854C2semidirect
11. C11×#1803C2semidirect
59. C11×C4⋊Q8D4semidirect
69. C4×Q8×C11D4semidirect
106. #24119C11direct (N × H)
182. C2×#556C2×C11semidirect
183. C2×#474C2×C11semidirect
184. C2×C4×SD16C2×C11semidirect
186. #2036C2×C11semidirect
187. #2000C2×C11semidirect
188. #1990C2×C11semidirect
189. #1954C2×C11semidirect
190. #1875C2×C11semidirect
191. #1854C2×C11semidirect
192. #1803C2×C11semidirect
337. C4⋊Q8D4×C11semidirect
347. C4×Q8D4×C11semidirect
468. C11#24119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4742
C2×C4×C11×SD162
C11×#25372
C11×#20362
C11×#20002
C11×#19902
C11×#19542
C11×#18752
C11×#18542
C11×#18032
#2411911