Finite Group Databasebeta

← C11×#24551 #14601744

Subgroups — C11×#24551 #14601744

Order 2816.

1188 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#483C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C11×#2848C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic
5C11×#2077C212yesmaximal, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#1892C212yesmaximal, complemented
8C11×#1872C211yesmaximal, characteristic, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1807C212yesmaximal, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C8×C11C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C11×#483—24no—
21C2×C11×#106C2212yescomplemented
22C2×C11×#106C2212yescomplemented
23C2×C11×#103C2212yescomplemented
24C2×C11×#103C2212yescomplemented
25C2×C11×C22⋊C8—24no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#385—21no—
30C11×#385—21no—
31C11×#385—21no—
32C11×#380—21no—
33C11×#380—21no—
34C11×#380C2212yes—
35C11×#380C2212yes—
36C11×#380C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#379—21no—
40C2×C11×#95—21no—
41C11×#340C2212yescomplemented
42C11×#340C2212yescomplemented
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—24no—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—42no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C8×C11—24no—
60C22×C8×C11—24no—
61C22×C8×C11—42no—
62C22×C8×C11C2312yes—
63C22×C8×C11C2312yes—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—42no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—44no—
90C11×#106—24no—
91C11×#106—42no—
92C11×#103—24no—
93C11×#103—42no—
94C11×C22⋊C8—22no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8D414yes—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102#24551C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—41no—
108C24×C11—41no—
109C24×C11SD1614yes—
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—48no—
142C22×C4×C11—48no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4114yes—
155C22×C4×C11C2411yescharacteristic
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—48no—
162C2×C8×C11C2×D414yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—42no—
184C2×#483C2×C1111yescharacteristic, complemented
185C22×C22⋊C8C2×C1111yescharacteristic
186#2848C2×C1111yescharacteristic
187C2×#380C2×C1111yescharacteristic
188#2077C2×C1112yescomplemented
189#2035C2×C1112yescomplemented
190#1892C2×C1112yescomplemented
191#1872C2×C1111yescharacteristic, complemented
192#1853C2×C1111yescharacteristic, complemented
193#1823C2×C1111yescharacteristic, complemented
194#1807C2×C1112yescomplemented
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11#12112yes—
217C23×C11#12312yes—
218C23×C11C2×SD1612yes—
219C23×C11C2×SD1612yes—
220C23×C11C2×SD1612yes—
221C23×C11#13512yes—
222C23×C11#13712yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—42no—
225Q8×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—84no—
261C2×C4×C11—84no—
262C2×C4×C11#12112yes—
263C2×C4×C11#12312yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)12yes—
268C8×C11—24no—
269C8×C11—42no—
270C24×C4C22×C1111yescharacteristic
271C23×C8C22×C1112yes—
272C2×C22⋊Q8C22×C1111yescharacteristic
273C2×C22⋊Q8C22×C1111yescharacteristic
274C2×C22⋊Q8C22×C1111yescharacteristic
275C22×C4⋊C4C22×C1111yescharacteristic
276C22×C4⋊C4C22×C1111yescharacteristic
277C22×C22⋊C4—21no—
278#483—24no—
279C2×#106C22×C1112yescomplemented
280C2×#106C22×C1112yescomplemented
281C2×#103C22×C1112yescomplemented
282C2×#103C22×C1112yescomplemented
283C2×C22⋊C8—24no—
284C2×C22⋊C8C22×C1112yes—
285C2×C22⋊C8C22×C1111yescharacteristic
286C2×C22⋊C8C22×C1111yescharacteristic
287#385—21no—
288#385—21no—
289#385—21no—
290#380—21no—
291#380—21no—
292#380C22×C1111yescharacteristic
293#380C22×C1112yes—
294#380C22×C1111yescharacteristic
295#380C22×C1112yes—
296#380C22×C1111yescharacteristic
297#379—21no—
298C2×#95—21no—
299#340C22×C1112yescomplemented
300#340C22×C1112yescomplemented
301#340C22×C1112yescomplemented
302#340C22×C1112yescomplemented
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—416no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11#46514yes—
324C22×C11#48314yescomplemented
325C22×C11C2×#12111yescharacteristic
326C22×C11C2×#12311yescharacteristic
327C22×C11#53411yescharacteristic
328C22×C11C22×SD1611yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11C2×#13711yescharacteristic
331C22×C11#57511yescharacteristic
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11—81no—
339C4×C11—82no—
340C4×C11—81no—
341C4×C11#54612yes—
342C4×C11#55112yes—
343C25D4×C1111yescharacteristic
344C22×Q8C23×C1111yescharacteristic
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—24no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—42no—
351C23×C4D4×C1111yescharacteristic
352C23×C4D4×C1111yescharacteristic
353C23×C4D4×C1111yescharacteristic
354C23×C4C23×C1111yescharacteristic
355C23×C4C23×C1111yescharacteristic
356C23×C4C23×C1111yescharacteristic
357C22×C8—24no—
358C22×C8—24no—
359C22×C8—42no—
360C22×C8C23×C1112yes—
361C22×C8C23×C1112yes—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—24no—
365C22⋊Q8—42no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4C23×C1112yes—
375C2×C4⋊C4C23×C1112yes—
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—44no—
388#106—24no—
389#106—42no—
390#103—24no—
391#103—42no—
392C22⋊C8—22no—
393C22⋊C8—24no—
394C22⋊C8D4×C1114yes—
395#95—22no—
396#95—22no—
397#95—21no—
398#95—21no—
399#95—21no—
400C2×C11—24no—
401C2×C11—24no—
402C2×C11—42no—
403C2×C11#241211yescharacteristic
404C2×C11C2×#46511yescharacteristic
405C2×C11#305611yescharacteristic
406C2×C11C2×#48311yescharacteristic
407C2×C11#309111yescharacteristic
408C2×C11#318711yescharacteristic
409C2×C11#319011yescharacteristic
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—41no—
415C24—41no—
416C24C11×SD1614yes—
417C24C2×D4×C1111yescharacteristic
418C24C2×D4×C1111yescharacteristic
419C24C2×D4×C1111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—22no—
423C2×Q8—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—48no—
449C22×C4—48no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1112yes—
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C11×#4112yes—
461C22×C4C11×#4114yes—
462C22×C4C24×C1111yescharacteristic
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—48no—
469C2×C8C2×D4×C1114yes—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—44no—
488C22⋊C4—44no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C11#2455111yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—28no—
507C23—28no—
508C23—44no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23C11×#12112yes—
514C23C11×#12312yes—
515C23C2×C11×SD1612yes—
516C23C2×C11×SD1612yes—
517C23C2×C11×SD1612yes—
518C23C11×#13512yes—
519C23C11×#13712yes—
520C23C22×D4×C1111yescharacteristic
521Q8—42no—
522Q8—42no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4C11×#12112yes—
560C2×C4C11×#12312yes—
561C2×C4C22×D4×C1111yescharacteristic
562C2×C4C2×C11×#4112yes—
563C2×C4C2×C11×#4111yescharacteristic
564C2×C4C11×H(5,𝔽2)12yes—
565C8—24no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—416no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C11×#46514yes—
588C22C11×#48314yescomplemented
589C22C2×C11×#12111yescharacteristic
590C22C2×C11×#12311yescharacteristic
591C22C11×#53411yescharacteristic
592C22C22×C11×SD1611yescharacteristic
593C22C2×C11×#13511yescharacteristic
594C22C2×C11×#13711yescharacteristic
595C22C11×#57511yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—81no—
600C4—82no—
601C4—81no—
602C4—82no—
603C4—81no—
604C4—81no—
605C4C11×#54612yes—
606C4C11×#55112yes—
607C2—24no—
608C2—24no—
609C2—42no—
610C2C11×#241211yescharacteristic
611C2C2×C11×#46511yescharacteristic
612C2C11×#305611yescharacteristic
613C2C2×C11×#48311yescharacteristic
614C2C11×#309111yescharacteristic
615C2C11×#318711yescharacteristic
616C2C11×#319011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#483C2semidirect
5. C11×#2077C2semidirect
6. C11×#2035C2semidirect
7. C11×#1892C2semidirect
8. C11×#1872C2semidirect
9. C11×#1853C2semidirect
10. C11×#1823C2semidirect
11. C11×#1807C2semidirect
21. C2×C11×#106C22semidirect
22. C2×C11×#106C22semidirect
23. C2×C11×#103C22semidirect
24. C2×C11×#103C22semidirect
41. C11×#340C22semidirect
42. C11×#340C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
102. #24551C11direct (N × H)
184. C2×#483C2×C11semidirect
188. #2077C2×C11semidirect
189. #2035C2×C11semidirect
190. #1892C2×C11semidirect
191. #1872C2×C11semidirect
192. #1853C2×C11semidirect
193. #1823C2×C11semidirect
194. #1807C2×C11semidirect
279. C2×#106C22×C11semidirect
280. C2×#106C22×C11semidirect
281. C2×#103C22×C11semidirect
282. C2×#103C22×C11semidirect
299. #340C22×C11semidirect
300. #340C22×C11semidirect
301. #340C22×C11semidirect
302. #340C22×C11semidirect
324. C22×C11#483semidirect
491. C11#24551direct (N × H)
588. C22C11×#483semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4832
C22×C11×C22⋊C82
C11×#28482
C2×C11×#3802
C11×#20772
C11×#20352
C11×#18922
C11×#18722
C11×#18532
C11×#18232
C11×#18072
#2455111