Finite Group Databasebeta

← C11×#24558 #14601751

Subgroups — C11×#24558 #14601751

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic, complemented
3C11×#2847C211yesmaximal, characteristic
4C2×C11×#380C211yesmaximal, characteristic, complemented
5C11×#2076C212yesmaximal, complemented
6C11×#2034C212yesmaximal, complemented
7C11×#1895C212yesmaximal, complemented
8C11×#1874C211yesmaximal, characteristic, complemented
9C11×#1853C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1809C212yesmaximal, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×M16C2212yes—
14C2×C11×#121C2211yescharacteristic
15C2×C11×#121C2211yescharacteristic
16C2×C11×#121C2211yescharacteristic
17C2×C11×#120—21no—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C11×#480—24no—
22C2×C11×#107C2212yescomplemented
23C2×C11×#106C2212yescomplemented
24C2×C11×#102C2212yescomplemented
25C2×C11×#102C2212yescomplemented
26C11×#407—24no—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2212yes—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#386—21no—
31C11×#386—21no—
32C11×#386—21no—
33C11×#380—21no—
34C11×#380—21no—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C2×C11×#95—21no—
41C11×#340C2212yescomplemented
42C11×#340C2212yescomplemented
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—24no—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11—42no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—24no—
63C2×C11×M16—24no—
64C2×C11×M16—42no—
65C22×C8×C11C2312yes—
66C22×C8×C11C2312yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—42no—
71C11×#120—44no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—42no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
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—21no—
90C2×C11×C22⋊C4—44no—
91C11×#107—24no—
92C11×#106—42no—
93C11×#102—24no—
94C11×#102—42no—
95C11×C22⋊C8—22no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8D414yescomplemented
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#24558C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—41no—
111C24×C11—41no—
112C24×C11C2×D411yescharacteristic
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
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—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—48no—
152C22×C4×C11—48no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4112yes—
164C22×C4×C11#4114yes—
165C22×C4×C11C2411yescharacteristic
166C11×M16—48no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—44no—
185C11×C22⋊C4—44no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C2×#480C2×C1111yescharacteristic, complemented
192C2×#407C2×C1111yescharacteristic, complemented
193#2847C2×C1111yescharacteristic
194C2×#380C2×C1111yescharacteristic, complemented
195#2076C2×C1112yescomplemented
196#2034C2×C1112yescomplemented
197#1895C2×C1112yescomplemented
198#1874C2×C1111yescharacteristic, complemented
199#1853C2×C1111yescharacteristic, complemented
200#1823C2×C1111yescharacteristic, complemented
201#1809C2×C1112yescomplemented
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—28no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11#12112yes—
233C23×C11#12312yes—
234C23×C11AGL(1,ℤ/8)12yes—
235C23×C11AGL(1,ℤ/8)12yes—
236C23×C11#13712yes—
237C23×C11C22×D411yescharacteristic
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—84no—
241D4×C11—84no—
242D4×C11—84no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—41no—
274C2×C4×C11—84no—
275C2×C4×C11—84no—
276C2×C4×C11#12112yes—
277C2×C4×C11#12312yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4112yes—
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)12yes—
282C8×C11—24no—
283C8×C11—42no—
284C24×C4C22×C1111yescharacteristic
285C22×M16C22×C1112yes—
286C2×#121C22×C1111yescharacteristic
287C2×#121C22×C1111yescharacteristic
288C2×#121C22×C1111yescharacteristic
289C2×#120—21no—
290C22×C4⋊C4C22×C1111yescharacteristic
291C22×C4⋊C4C22×C1111yescharacteristic
292C22×C22⋊C4—21no—
293#480—24no—
294C2×#107C22×C1112yescomplemented
295C2×#106C22×C1112yescomplemented
296C2×#102C22×C1112yescomplemented
297C2×#102C22×C1112yescomplemented
298#407—24no—
299C2×C22⋊C8C22×C1112yes—
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×C22⋊C8C22×C1111yescharacteristic
302#386—21no—
303#386—21no—
304#386—21no—
305#380—21no—
306#380—21no—
307#380C22×C1111yescharacteristic
308#380C22×C1112yes—
309#380C22×C1111yescharacteristic
310#380C22×C1112yes—
311#380C22×C1111yescharacteristic
312C2×#95—21no—
313#340C22×C1112yescomplemented
314#340C22×C1112yescomplemented
315#340C22×C1112yescomplemented
316#340C22×C1112yescomplemented
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—416no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11#46914yes—
346C22×C11C2×#12111yescharacteristic
347C22×C11C2×#12311yescharacteristic
348C22×C11#53411yescharacteristic
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57511yescharacteristic
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—82no—
359C4×C11—82no—
360C4×C11—81no—
361C4×C11#54612yes—
362C4×C11#55112yes—
363C25D4×C1111yescharacteristic
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4C23×C1111yescharacteristic
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—42no—
374C23×C4D4×C1111yescharacteristic
375C23×C4D4×C1111yescharacteristic
376C23×C4D4×C1111yescharacteristic
377C23×C4C23×C1111yescharacteristic
378C23×C4C23×C1111yescharacteristic
379C23×C4C23×C1111yescharacteristic
380C2×M16—24no—
381C2×M16—24no—
382C2×M16—42no—
383C22×C8C23×C1112yes—
384C22×C8C23×C1112yes—
385#121—22no—
386#121—22no—
387#121—24no—
388#121—42no—
389#120—44no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4C23×C1112yes—
396C2×C4⋊C4C23×C1112yes—
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—44no—
409#107—24no—
410#106—42no—
411#102—24no—
412#102—42no—
413C22⋊C8—22no—
414C22⋊C8—24no—
415C22⋊C8D4×C1114yescomplemented
416#95—22no—
417#95—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421C2×C11—24no—
422C2×C11—42no—
423C2×C11—42no—
424C2×C11—161no—
425C2×C11#241211yescharacteristic
426C2×C11C2×#46911yescharacteristic
427C2×C11#305611yescharacteristic
428C2×C11#309211yescharacteristic
429C2×C11#309411yescharacteristic
430C2×C11#319311yescharacteristic
431C2×C11#319411yescharacteristic
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—41no—
439C24—41no—
440C24C2×D4×C1111yescharacteristic
441C24C2×D4×C1111yescharacteristic
442C24C2×D4×C1111yescharacteristic
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1112yes—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C11×#4112yes—
492C22×C4C11×#4114yes—
493C22×C4C24×C1111yescharacteristic
494M16—48no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8C2×D4×C1114yes—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—44no—
513C22⋊C4—44no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C11#2455811yescharacteristic, direct product factor, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—28no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23C11×#12112yes—
551C23C11×#12312yes—
552C23C11×AGL(1,ℤ/8)12yes—
553C23C11×AGL(1,ℤ/8)12yes—
554C23C11×#13712yes—
555C23C22×D4×C1111yescharacteristic
556D4—42no—
557D4—42no—
558D4—84no—
559D4—84no—
560D4—84no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4C11×#12112yes—
595C2×C4C11×#12312yes—
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C2×C11×#4112yes—
598C2×C4C2×C11×#4111yescharacteristic
599C2×C4C11×H(5,𝔽2)12yes—
600C8—24no—
601C8—42no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—416no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22C11×#46914yes—
631C22C2×C11×#12111yescharacteristic
632C22C2×C11×#12311yescharacteristic
633C22C11×#53411yescharacteristic
634C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
635C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
636C22C2×C11×#13711yescharacteristic
637C22C11×#57511yescharacteristic
638C4—22no—
639C4—22no—
640C4—41no—
641C4—81no—
642C4—82no—
643C4—82no—
644C4—81no—
645C4—81no—
646C4C11×#54612yes—
647C4C11×#55112yes—
648C2—24no—
649C2—42no—
650C2—42no—
651C2—161no—
652C2C11×#241211yescharacteristic
653C2C2×C11×#46911yescharacteristic
654C2C11×#305611yescharacteristic
655C2C11×#309211yescharacteristic
656C2C11×#309411yescharacteristic
657C2C11×#319311yescharacteristic
658C2C11×#319411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2847C2
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×#480C2semidirect
2. C2×C11×#407C2semidirect
4. C2×C11×#380C2semidirect
5. C11×#2076C2semidirect
6. C11×#2034C2semidirect
7. C11×#1895C2semidirect
8. C11×#1874C2semidirect
9. C11×#1853C2semidirect
10. C11×#1823C2semidirect
11. C11×#1809C2semidirect
22. C2×C11×#107C22semidirect
23. C2×C11×#106C22semidirect
24. C2×C11×#102C22semidirect
25. C2×C11×#102C22semidirect
41. C11×#340C22semidirect
42. C11×#340C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
97. C11×C22⋊C8D4semidirect
103. #24558C11direct (N × H)
191. C2×#480C2×C11semidirect
192. C2×#407C2×C11semidirect
194. C2×#380C2×C11semidirect
195. #2076C2×C11semidirect
196. #2034C2×C11semidirect
197. #1895C2×C11semidirect
198. #1874C2×C11semidirect
199. #1853C2×C11semidirect
200. #1823C2×C11semidirect
201. #1809C2×C11semidirect
294. C2×#107C22×C11semidirect
295. C2×#106C22×C11semidirect
296. C2×#102C22×C11semidirect
297. C2×#102C22×C11semidirect
313. #340C22×C11semidirect
314. #340C22×C11semidirect
315. #340C22×C11semidirect
316. #340C22×C11semidirect
415. C22⋊C8D4×C11semidirect
519. C11#24558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C2×C11×#4072
C11×#28472
C2×C11×#3802
C11×#20762
C11×#20342
C11×#18952
C11×#18742
C11×#18532
C11×#18232
C11×#18092
#2455811