Finite Group Databasebeta

← C11×#23966 #14601159

Subgroups — C11×#23966 #14601159

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#552C211yesmaximal, characteristic, complemented
2C2×C11×#450C211yesmaximal, characteristic, complemented
3C22×C11×#102C211yesmaximal, characteristic, complemented
4C11×#2408C211yesmaximal, characteristic
5C11×#2025C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1880C212yesmaximal, complemented
9C11×#1875C212yesmaximal, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C23×C8×C11C2211yescharacteristic
15C11×#552—24no—
16C11×#552—24no—
17C2×C11×#126—21no—
18C2×C11×#125—21no—
19C2×C11×#125C2211yescharacteristic, complemented
20C2×C11×#123—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121C2212yes—
24C2×C11×#120—21no—
25C2×C4×Q8×C11C2211yescharacteristic, complemented
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic, complemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C11×#450—24no—
31C2×C11×#103C2212yescomplemented
32C2×C11×#102—24no—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yescomplemented
38C11×#394—21no—
39C11×#392—21no—
40C11×#390C2212yes—
41C11×#380C2211yescharacteristic
42C11×#379—21no—
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C11×#340C2212yescomplemented
46C11×#336C2212yescomplemented
47C25×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—42no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2312yes—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16—42no—
63C22×C8×C11—22no—
64C22×C8×C11—42no—
65C22×C8×C11C2312yes—
66C22×C8×C11C2312yes—
67C11×#126—28no—
68C11×#125—28no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#123—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8D414yescomplemented
76C11×#121—24no—
77C11×#121—42no—
78C11×#120—44no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C11×#117—28no—
84C11×#117—22no—
85C11×#117—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D414yescomplemented
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C11×#103—42no—
112C11×#102—24no—
113C11×#102—24no—
114C11×#102—24no—
115C11×C22⋊C8—22no—
116C11×C22⋊C8—42no—
117C11×#95—21no—
118#23966C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—82no—
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D412yes—
131C2×D4×C11—28no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—48no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—42no—
146C2×D4×C11—82no—
147C2×D4×C11#4114yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C11×SD16—48no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—44no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D412yes—
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—44no—
198C11×C22⋊C4—44no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—82no—
201C42×C11—24no—
202C42×C11—24no—
203C42×C11—21no—
204C42×C11—21no—
205C2×#552C2×C1111yescharacteristic, complemented
206C2×#450C2×C1111yescharacteristic, complemented
207C22×#102C2×C1111yescharacteristic, complemented
208#2408C2×C1111yescharacteristic
209#2025C2×C1112yescomplemented
210#2000C2×C1112yescomplemented
211#1892C2×C1111yescharacteristic, complemented
212#1880C2×C1112yescomplemented
213#1875C2×C1112yescomplemented
214#1869C2×C1111yescharacteristic, complemented
215#1823C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—48no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—88no—
232C23×C11—88no—
233C23×C11—84no—
234C23×C11—84no—
235C23×C11#12012yes—
236C23×C11#13512yes—
237C23×C11AGL(1,ℤ/8)12yes—
238C23×C11C22×D411yescharacteristic
239Q8×C11—24no—
240Q8×C11—41no—
241Q8×C11—41no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—48no—
245D4×C11—44no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—88no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—48no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11#12012yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4112yes—
281C2×C4×C11H(5,𝔽2)12yes—
282C8×C11—42no—
283C8×C11—42no—
284C23×D4C22×C1111yescharacteristic
285C22×SD16C22×C1112yes—
286C23×C8C22×C1111yescharacteristic
287#552—24no—
288#552—24no—
289C2×#126—21no—
290C2×#125—21no—
291C2×#125C22×C1111yescharacteristic, complemented
292C2×#123—21no—
293C2×C22⋊Q8C22×C1111yescharacteristic
294C2×C22⋊Q8C22×C1111yescharacteristic, complemented
295C2×#121C22×C1112yes—
296C2×#120—21no—
297C2×C4×Q8C22×C1111yescharacteristic, complemented
298C2×C4×D4C22×C1111yescharacteristic
299C2×#117—21no—
300C2×#117C22×C1111yescharacteristic, complemented
301C22×C4⋊C4C22×C1111yescharacteristic
302#450—24no—
303C2×#103C22×C1112yescomplemented
304C2×#102—24no—
305C2×#102C22×C1112yes—
306C2×#102C22×C1112yes—
307C2×#102C22×C1112yes—
308C2×C22⋊C8C22×C1111yescharacteristic
309C2×C22⋊C8C22×C1112yescomplemented
310#394—21no—
311#392—21no—
312#390C22×C1112yes—
313#380C22×C1111yescharacteristic
314#379—21no—
315#340C22×C1112yescomplemented
316#340C22×C1112yescomplemented
317#340C22×C1112yescomplemented
318#336C22×C1112yescomplemented
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—41no—
324C22×C11—44no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—42no—
328C22×C11—44no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—816no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11#44914yes—
337C22×C11C2×#12011yescharacteristic
338C22×C11#54612yes—
339C22×C11C2×#13511yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11#57712yes—
342C4×C11—22no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—82no—
351C4×C11#52511yescharacteristic
352C4×C11#53511yescharacteristic
353C4×C11#54612yes—
354C25—21no—
355C22×Q8C23×C1111yescharacteristic
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—42no—
362C22×D4D4×C1111yescharacteristic
363C22×D4C23×C1112yes—
364C23×C4—21no—
365C23×C4C23×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C2×SD16—24no—
368C2×SD16—24no—
369C2×SD16—42no—
370C22×C8—22no—
371C22×C8—42no—
372C22×C8C23×C1112yes—
373C22×C8C23×C1112yes—
374#126—28no—
375#125—28no—
376#125—22no—
377#125—22no—
378#123—28no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8D4×C1114yescomplemented
383#121—24no—
384#121—42no—
385#120—44no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×D4—22no—
389C4×D4—22no—
390#117—28no—
391#117—22no—
392#117—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C1111yescharacteristic
401C2×C4⋊C4D4×C1114yescomplemented
402C2×C4⋊C4C23×C1112yes—
403C2×C4⋊C4C23×C1111yescharacteristic
404C2×C4⋊C4C23×C1111yescharacteristic
405C2×C4⋊C4C23×C1111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4D4×C1111yescharacteristic
414C2×C22⋊C4D4×C1111yescharacteristic
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C23×C1111yescharacteristic
418#103—42no—
419#102—24no—
420#102—24no—
421#102—24no—
422C22⋊C8—22no—
423C22⋊C8—42no—
424#95—21no—
425C2×C11—24no—
426C2×C11—81no—
427C2×C11—84no—
428C2×C11#240411yescharacteristic
429C2×C11C2×#44911yescharacteristic
430C2×C11#301011yescharacteristic
431C2×C11#329612yes—
432C2×C11#331012yes—
433C24—22no—
434C24—44no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—82no—
439C24C2×D4×C1111yescharacteristic
440C24C2×D4×C1111yescharacteristic
441C2×Q8—21no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8C2×D4×C1112yes—
445C2×D4—28no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—42no—
460C2×D4—82no—
461C2×D4C11×#4114yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1112yes—
481C22×C4C2×D4×C1112yes—
482C22×C4C24×C1111yescharacteristic
483SD16—48no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—44no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4C2×D4×C1112yes—
504C4⋊C4C2×D4×C1112yes—
505C4⋊C4C2×D4×C1112yes—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—44no—
512C22⋊C4—44no—
513C22⋊C4—42no—
514C22⋊C4—82no—
515C42—24no—
516C42—24no—
517C42—21no—
518C42—21no—
519C11#2396611yescharacteristic, direct product factor, Sylow
520C23—22no—
521C23—22no—
522C23—21no—
523C23—24no—
524C23—22no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—48no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—88no—
536C23—88no—
537C23—84no—
538C23—84no—
539C23C11×#12012yes—
540C23C11×#13512yes—
541C23C11×AGL(1,ℤ/8)12yes—
542C23C22×D4×C1111yescharacteristic
543Q8—24no—
544Q8—41no—
545Q8—41no—
546D4—24no—
547D4—24no—
548D4—48no—
549D4—44no—
550D4—42no—
551D4—42no—
552D4—88no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4C11×#12012yes—
582C2×C4C22×D4×C1111yescharacteristic
583C2×C4C22×D4×C1111yescharacteristic
584C2×C4C2×C11×#4112yes—
585C2×C4C11×H(5,𝔽2)12yes—
586C8—42no—
587C8—42no—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—24no—
592C22—41no—
593C22—44no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—44no—
598C22—42no—
599C22—44no—
600C22—816no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22C11×#44914yes—
606C22C2×C11×#12011yescharacteristic
607C22C11×#54612yes—
608C22C2×C11×#13511yescharacteristic
609C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
610C22C11×#57712yes—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—42no—
619C4—82no—
620C4C11×#52511yescharacteristic
621C4C11×#53511yescharacteristic
622C4C11×#54612yes—
623C2—24no—
624C2—81no—
625C2—84no—
626C2C11×#240411yescharacteristic
627C2C2×C11×#44911yescharacteristic
628C2C11×#301011yescharacteristic
629C2C11×#329612yes—
630C2C11×#331012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2408C2
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×#552C2semidirect
2. C2×C11×#450C2semidirect
3. C22×C11×#102C2semidirect
5. C11×#2025C2semidirect
6. C11×#2000C2semidirect
7. C11×#1892C2semidirect
8. C11×#1880C2semidirect
9. C11×#1875C2semidirect
10. C11×#1869C2semidirect
11. C11×#1823C2semidirect
19. C2×C11×#125C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
25. C2×C4×Q8×C11C22semidirect
28. C2×C11×#117C22semidirect
31. C2×C11×#103C22semidirect
37. C2×C11×C22⋊C8C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
45. C11×#340C22semidirect
46. C11×#336C22semidirect
75. C11×C22⋊Q8D4semidirect
94. C2×C11×C4⋊C4D4semidirect
118. #23966C11direct (N × H)
205. C2×#552C2×C11semidirect
206. C2×#450C2×C11semidirect
207. C22×#102C2×C11semidirect
209. #2025C2×C11semidirect
210. #2000C2×C11semidirect
211. #1892C2×C11semidirect
212. #1880C2×C11semidirect
213. #1875C2×C11semidirect
214. #1869C2×C11semidirect
215. #1823C2×C11semidirect
291. C2×#125C22×C11semidirect
294. C2×C22⋊Q8C22×C11semidirect
297. C2×C4×Q8C22×C11semidirect
300. C2×#117C22×C11semidirect
303. C2×#103C22×C11semidirect
309. C2×C22⋊C8C22×C11semidirect
315. #340C22×C11semidirect
316. #340C22×C11semidirect
317. #340C22×C11semidirect
318. #336C22×C11semidirect
382. C22⋊Q8D4×C11semidirect
401. C2×C4⋊C4D4×C11semidirect
519. C11#23966direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5522
C2×C11×#4502
C22×C11×#1022
C11×#24082
C11×#20252
C11×#20002
C11×#18922
C11×#18802
C11×#18752
C11×#18692
C11×#18232
#2396611