Finite Group Databasebeta

← C11×#24251 #14601444

Subgroups — C11×#24251 #14601444

Order 2816.

1456 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#448C212yesmaximal, complemented
4C2×C11×#440C211yesmaximal, characteristic, complemented
5C11×#2535C211yesmaximal, characteristic
6C11×#2036C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1805C211yesmaximal, characteristic, complemented
11C11×#1787C212yesmaximal, complemented
12C23×Q8×C11C2212yes—
13C22×C11×SD16C2212yes—
14C22×C11×SD16C2211yescharacteristic
15D4×Q8×C11—24no—
16D4×Q8×C11—24no—
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#461—24no—
27C11×#448—28no—
28C11×#440—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#102C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#397—21no—
41C11×#392—21no—
42C11×#386—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—24no—
50C22×Q8×C11—24no—
51C22×Q8×C11—42no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2312yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—22no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—42no—
66C2×C11×SD16D414yescomplemented
67C22×C8×C11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—28no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yescomplemented
73C11×C22⋊Q8—216no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×#121—24no—
77C11×#121—42no—
78C4×Q8×C11—22no—
79C4×Q8×C11D414yescomplemented
80C4×D4×C11—28no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×C4⋊C8—22no—
102C11×#103—22no—
103C11×#103—24no—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—42no—
107C11×#102—22no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24251C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11C2×D412yes—
117C2×Q8×C11—28no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—44no—
127C2×Q8×C11—44no—
128C2×Q8×C11—48no—
129C2×Q8×C11—48no—
130C2×Q8×C11—48no—
131C2×Q8×C11—48no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11#4112yes—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—82no—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—21no—
148C22×C4×C11—28no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—44no—
160C22×C4×C11—44no—
161C22×C4×C11—42no—
162C22×C4×C11—82no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C11×SD16—28no—
168C11×SD16—48no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—82no—
194C42×C11—24no—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C2×D4×Q8C2×C1111yescharacteristic, complemented
198C2×#461C2×C1111yescharacteristic, complemented
199C2×#448C2×C1112yescomplemented
200C2×#440C2×C1111yescharacteristic, complemented
201#2535C2×C1111yescharacteristic
202#2036C2×C1112yescomplemented
203#2000C2×C1112yescomplemented
204#1960C2×C1111yescharacteristic, complemented
205#1955C2×C1111yescharacteristic, complemented
206#1805C2×C1111yescharacteristic, complemented
207#1787C2×C1112yescomplemented
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11#13714yes—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—416no—
227Q8×C11—42no—
228Q8×C11—42no—
229Q8×C11#12114yes—
230D4×C11—28no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—88no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—416no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—84no—
260C2×C4×C11#12012yes—
261C2×C4×C11#12012yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C8×C11—22no—
269C8×C11—41no—
270C8×C11—42no—
271C23×Q8C22×C1112yes—
272C22×SD16C22×C1112yes—
273C22×SD16C22×C1111yescharacteristic
274D4×Q8—24no—
275D4×Q8—24no—
276C2×C4⋊Q8—21no—
277C2×C4⋊Q8C22×C1111yescharacteristic
278C2×C22⋊Q8—22no—
279C2×C22⋊Q8C22×C1112yes—
280C2×#121C22×C1112yes—
281C2×C4×Q8C22×C1111yescharacteristic
282C2×C4×D4—21no—
283C2×C4×D4C22×C1111yescharacteristic
284C2×C4×D4C22×C1111yescharacteristic
285#461—24no—
286#448—28no—
287#440—24no—
288C2×#107C22×C1111yescharacteristic
289C2×C4⋊C8C22×C1111yescharacteristic
290C2×#103C22×C1112yes—
291C2×#103C22×C1111yescharacteristic
292C2×#103C22×C1112yes—
293C2×#103C22×C1112yes—
294C2×#103C22×C1112yes—
295C2×#102C22×C1111yescharacteristic
296C2×C22⋊C8C22×C1112yes—
297C2×C22⋊C8C22×C1112yes—
298C2×#97C22×C1111yescharacteristic
299#397—21no—
300#392—21no—
301#386—22no—
302#382C22×C1111yescharacteristic
303#380C22×C1112yes—
304#340C22×C1112yes—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—82no—
317C22×C11C2×#12011yescharacteristic
318C22×C11D4211yescharacteristic
319C22×C11#54611yescharacteristic
320C22×C11C2×#13712yes—
321C22×C11#57712yes—
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—82no—
330C4×C11C2×#12111yescharacteristic
331C4×C11#53511yescharacteristic
332C4×C11D4211yescharacteristic
333C4×C11#54611yescharacteristic
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8C23×C1112yes—
342C22×Q8C23×C1111yescharacteristic
343C22×D4—22no—
344C22×D4D4×C1111yescharacteristic
345C22×D4C23×C1111yescharacteristic
346C23×C4—22no—
347C23×C4—21no—
348C23×C4C23×C1112yes—
349C2×SD16—22no—
350C2×SD16—22no—
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—42no—
354C2×SD16D4×C1114yescomplemented
355C22×C8C23×C1112yes—
356C22×C8C23×C1111yescharacteristic
357C22×C8C23×C1111yescharacteristic
358C4⋊Q8—28no—
359C4⋊Q8—22no—
360C4⋊Q8D4×C1114yescomplemented
361C22⋊Q8—216no—
362C22⋊Q8—24no—
363C22⋊Q8—24no—
364#121—24no—
365#121—42no—
366C4×Q8—22no—
367C4×Q8D4×C1114yescomplemented
368C4×D4—28no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4D4×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1112yes—
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4D4×C1112yes—
386C2×C42—21no—
387C2×C42C23×C1111yescharacteristic
388#107—22no—
389C4⋊C8—22no—
390#103—22no—
391#103—24no—
392#103—24no—
393#103—24no—
394#103—42no—
395#102—22no—
396C22⋊C8—24no—
397C22⋊C8—42no—
398#97—22no—
399#95—22no—
400#95—21no—
401#95—21no—
402C2×C11—44no—
403C2×C11—82no—
404C2×C11#240811yescharacteristic
405C2×C11#300411yescharacteristic
406C2×C11#301011yescharacteristic
407C2×C11#326612yes—
408C2×C11#332012yes—
409C24—21no—
410C24C2×D4×C1112yes—
411C2×Q8—28no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—44no—
421C2×Q8—44no—
422C2×Q8—48no—
423C2×Q8—48no—
424C2×Q8—48no—
425C2×Q8—48no—
426C2×Q8C2×D4×C1114yes—
427C2×Q8C2×D4×C1112yes—
428C2×Q8C2×D4×C1112yes—
429C2×Q8C11×#4112yes—
430C2×D4—24no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—82no—
440C2×D4C2×D4×C1112yes—
441C22×C4—21no—
442C22×C4—28no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—42no—
456C22×C4—82no—
457C22×C4C2×D4×C1112yes—
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C24×C1111yescharacteristic
461SD16—28no—
462SD16—48no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—21no—
469C2×C8—22no—
470C2×C8—21no—
471C2×C8C2×D4×C1112yes—
472C4⋊C4—28no—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4C2×D4×C1112yes—
483C22⋊C4—28no—
484C22⋊C4—24no—
485C22⋊C4—44no—
486C22⋊C4—42no—
487C22⋊C4—82no—
488C42—24no—
489C42C2×D4×C1112yes—
490C42C2×D4×C1112yes—
491C11#2425111yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—42no—
503C23C11×#13714yes—
504C23C22×D4×C1111yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—22no—
508Q8—24no—
509Q8—24no—
510Q8—416no—
511Q8—42no—
512Q8—42no—
513Q8C11×#12114yes—
514D4—28no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—88no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—416no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—84no—
544C2×C4C11×#12012yes—
545C2×C4C11×#12012yes—
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C22×D4×C1111yescharacteristic
549C2×C4C2×C11×#4111yescharacteristic
550C2×C4C11×H(5,𝔽2)11yescharacteristic
551C2×C4C11×H(5,𝔽2)11yescharacteristic
552C8—22no—
553C8—41no—
554C8—42no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—81no—
565C22—81no—
566C22—82no—
567C22C2×C11×#12011yescharacteristic
568C22D42×C1111yescharacteristic
569C22C11×#54611yescharacteristic
570C22C2×C11×#13712yes—
571C22C11×#57712yes—
572C4—24no—
573C4—22no—
574C4—22no—
575C4—42no—
576C4—44no—
577C4—42no—
578C4—81no—
579C4—82no—
580C4C2×C11×#12111yescharacteristic
581C4C11×#53511yescharacteristic
582C4D42×C1111yescharacteristic
583C4C11×#54611yescharacteristic
584C2—44no—
585C2—82no—
586C2C11×#240811yescharacteristic
587C2C11×#300411yescharacteristic
588C2C11×#301011yescharacteristic
589C2C11×#326612yes—
590C2C11×#332012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2535C2
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×D4×Q8×C11C2semidirect
2. C2×C11×#461C2semidirect
3. C2×C11×#448C2semidirect
4. C2×C11×#440C2semidirect
6. C11×#2036C2semidirect
7. C11×#2000C2semidirect
8. C11×#1960C2semidirect
9. C11×#1955C2semidirect
10. C11×#1805C2semidirect
11. C11×#1787C2semidirect
66. C2×C11×SD16D4semidirect
72. C11×C4⋊Q8D4semidirect
79. C4×Q8×C11D4semidirect
114. #24251C11direct (N × H)
197. C2×D4×Q8C2×C11semidirect
198. C2×#461C2×C11semidirect
199. C2×#448C2×C11semidirect
200. C2×#440C2×C11semidirect
202. #2036C2×C11semidirect
203. #2000C2×C11semidirect
204. #1960C2×C11semidirect
205. #1955C2×C11semidirect
206. #1805C2×C11semidirect
207. #1787C2×C11semidirect
354. C2×SD16D4×C11semidirect
360. C4⋊Q8D4×C11semidirect
367. C4×Q8D4×C11semidirect
491. C11#24251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4612
C2×C11×#4482
C2×C11×#4402
C11×#25352
C11×#20362
C11×#20002
C11×#19602
C11×#19552
C11×#18052
C11×#17872
#2425111