Finite Group Databasebeta

← C11×#11079 #14588272

Subgroups — C11×#11079 #14588272

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#104C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic
3C11×#2311C211yesmaximal, characteristic
4C2×C11×#382C211yesmaximal, characteristic, complemented
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C11×#1736C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C11×#104—22no—
16C2×C11×#104—22no—
17C2×C11×#104C414yescomplemented
18C11×#417—22no—
19C11×#417—22no—
20C2×C11×#103—21no—
21C2×C11×#102—21no—
22C11×#391—21no—
23C11×#390—21no—
24C11×#386—22no—
25C11×#382—22no—
26C11×#382—22no—
27C11×#380—22no—
28C2×C11×#95—22no—
29C11×#343—22no—
30C11×#340—22no—
31C11×#339—22no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41C2×C412yes—
43C2×C11×#41Q812yes—
44C22×Q8×C11D411yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2×C412yes—
63C2×C11×M16D412yes—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
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—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—24no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2×C412yes—
90C2×C42×C11D412yes—
91C2×C42×C11D412yes—
92C11×#104—28no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#95—28no—
96C11×#95—24no—
97#11079C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C2×D411yescharacteristic
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11C4⋊C412yes—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11C4⋊C412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×Q811yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16—41no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—84no—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—41no—
200C42×C11—41no—
201C42×C11C22⋊C414yescomplemented
202C22×#104C2×C1111yescharacteristic
203C2×#417C2×C1111yescharacteristic
204#2311C2×C1111yescharacteristic
205C2×#382C2×C1111yescharacteristic, complemented
206C2×#343C2×C1111yescharacteristic, complemented
207#1736C2×C1111yescharacteristic, complemented
208C2×#339C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11C4×D411yescharacteristic
217C23×C11#12011yescharacteristic
218C23×C11#12011yescharacteristic
219C23×C11#12111yescharacteristic
220C23×C11#12111yescharacteristic
221C23×C11C22⋊Q811yescharacteristic
222C23×C11#12411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—42no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—44no—
255C2×C4×C11—82no—
256C2×C4×C11—82no—
257C2×C4×C11—82no—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C4⋊C411yescharacteristic
260C2×C4×C11#11711yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11#12111yescharacteristic
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11C22⋊Q811yescharacteristic
272C2×C4×C11C22⋊Q811yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11#12311yescharacteristic
277C2×C4×C11#12311yescharacteristic
278C2×C4×C11#12311yescharacteristic
279C2×C4×C11#12311yescharacteristic
280C2×C4×C11#12311yescharacteristic
281C2×C4×C11#12411yescharacteristic
282C2×C4×C11#12411yescharacteristic
283C2×C4×C11#12611yescharacteristic
284C2×C4×C11#12611yescharacteristic
285C2×C4×C11#12711yescharacteristic
286C8×C11—42no—
287C8×C11—42no—
288C22×#41C22×C1111yescharacteristic
289C22×M16C22×C1111yescharacteristic
290C22×M16C22×C1111yescharacteristic
291C2×#117C22×C1111yescharacteristic
292C22×C4⋊C4C22×C1111yescharacteristic
293C22×C4⋊C4C22×C1111yescharacteristic
294C22×C42C22×C1111yescharacteristic
295C2×#104—22no—
296C2×#104—22no—
297C2×#104C4×C1114yescomplemented
298#417—22no—
299#417—22no—
300C2×#103—21no—
301C2×#102—21no—
302#391—21no—
303#390—21no—
304#386—22no—
305#382—22no—
306#382—22no—
307#380—22no—
308C2×#95—22no—
309#343—22no—
310#340—22no—
311#339—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11#38511yescharacteristic
326C22×C11#38611yescharacteristic
327C22×C11#38811yescharacteristic
328C22×C11#39211yescharacteristic
329C22×C11#39311yescharacteristic
330C22×C11#39411yescharacteristic
331C22×C11#39611yescharacteristic
332C22×C11#45412yes—
333C22×C11#45512yes—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11—82no—
337C4×C11—82no—
338C4×C11—82no—
339C4×C11#38011yescharacteristic
340C4×C11#38511yescharacteristic
341C4×C11#38811yescharacteristic
342C4×C11#39011yescharacteristic
343C4×C11#39411yescharacteristic
344C4×C11#39611yescharacteristic
345C4×C11#39711yescharacteristic
346C4×C11#39911yescharacteristic
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41C2×C4×C1112yes—
358C2×#41Q8×C1112yes—
359C22×Q8D4×C1111yescharacteristic
360C22×D4—21no—
361C22×D4D4×C1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4D4×C1112yes—
366C23×C4C23×C1111yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16C2×C4×C1112yes—
378C2×M16D4×C1112yes—
379C22×C8—21no—
380C22×C8—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C1112yes—
397C2×C4⋊C4D4×C1112yes—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—24no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C2×C4×C1112yes—
405C2×C42D4×C1112yes—
406C2×C42D4×C1112yes—
407#104—28no—
408#103—24no—
409#102—24no—
410#95—28no—
411#95—24no—
412C2×C11—21no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—82no—
417C2×C11#143911yescharacteristic
418C2×C11#186012yes—
419C2×C11#200311yescharacteristic
420C2×C11#200411yescharacteristic
421C2×C11#204012yes—
422C24—21no—
423C24C2×D4×C1111yescharacteristic
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C11×C4⋊C412yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C11×C4⋊C412yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4C22×C4×C1111yescharacteristic
480C22×C4C2×D4×C1111yescharacteristic
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×Q8×C1111yescharacteristic
487C22×C4C11×#4111yescharacteristic
488C22×C4C11×#4111yescharacteristic
489C22×C4C11×#4111yescharacteristic
490C22×C4C11×#4111yescharacteristic
491C22×C4C11×#4111yescharacteristic
492C22×C4C11×#4111yescharacteristic
493M16—22no—
494M16—22no—
495M16—22no—
496M16—22no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—84no—
520C42—22no—
521C42—22no—
522C42—22no—
523C42—41no—
524C42—41no—
525C42C11×C22⋊C414yescomplemented
526C11#1107911yescharacteristic, direct product factor, Sylow
527C23—22no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23C4×D4×C1111yescharacteristic
535C23C11×#12011yescharacteristic
536C23C11×#12011yescharacteristic
537C23C11×#12111yescharacteristic
538C23C11×#12111yescharacteristic
539C23C11×C22⋊Q811yescharacteristic
540C23C11×#12411yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545D4—22no—
546D4—22no—
547D4—42no—
548D4—42no—
549D4—42no—
550D4—42no—
551D4—41no—
552D4—41no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4C2×C11×C22⋊C411yescharacteristic
577C2×C4C2×C11×C4⋊C411yescharacteristic
578C2×C4C11×#11711yescharacteristic
579C2×C4C4×D4×C1111yescharacteristic
580C2×C4C4×D4×C1111yescharacteristic
581C2×C4C4×D4×C1111yescharacteristic
582C2×C4C11×#12011yescharacteristic
583C2×C4C11×#12111yescharacteristic
584C2×C4C11×#12111yescharacteristic
585C2×C4C11×#12111yescharacteristic
586C2×C4C11×#12111yescharacteristic
587C2×C4C11×#12111yescharacteristic
588C2×C4C11×#12111yescharacteristic
589C2×C4C11×C22⋊Q811yescharacteristic
590C2×C4C11×C22⋊Q811yescharacteristic
591C2×C4C11×C22⋊Q811yescharacteristic
592C2×C4C11×C22⋊Q811yescharacteristic
593C2×C4C11×C22⋊Q811yescharacteristic
594C2×C4C11×#12311yescharacteristic
595C2×C4C11×#12311yescharacteristic
596C2×C4C11×#12311yescharacteristic
597C2×C4C11×#12311yescharacteristic
598C2×C4C11×#12311yescharacteristic
599C2×C4C11×#12411yescharacteristic
600C2×C4C11×#12411yescharacteristic
601C2×C4C11×#12611yescharacteristic
602C2×C4C11×#12611yescharacteristic
603C2×C4C11×#12711yescharacteristic
604C8—42no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—42no—
615C22—44no—
616C22—81no—
617C22—81no—
618C22—82no—
619C22C11×#38511yescharacteristic
620C22C11×#38611yescharacteristic
621C22C11×#38811yescharacteristic
622C22C11×#39211yescharacteristic
623C22C11×#39311yescharacteristic
624C22C11×#39411yescharacteristic
625C22C11×#39611yescharacteristic
626C22C11×#45412yes—
627C22C11×#45512yes—
628C4—44no—
629C4—42no—
630C4—82no—
631C4—82no—
632C4—82no—
633C4C11×#38011yescharacteristic
634C4C11×#38511yescharacteristic
635C4C11×#38811yescharacteristic
636C4C11×#39011yescharacteristic
637C4C11×#39411yescharacteristic
638C4C11×#39611yescharacteristic
639C4C11×#39711yescharacteristic
640C4C11×#39911yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—82no—
646C2C11×#143911yescharacteristic
647C2C11×#186012yes—
648C2C11×#200311yescharacteristic
649C2C11×#200411yescharacteristic
650C2C11×#204012yes—
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C11×#382C2semidirect
5. C2×C11×#343C2semidirect
6. C11×#1736C2semidirect
7. C2×C11×#339C2semidirect
17. C2×C11×#104C4semidirect
97. #11079C11direct (N × H)
201. C42×C11C22⋊C4semidirect
205. C2×#382C2×C11semidirect
206. C2×#343C2×C11semidirect
207. #1736C2×C11semidirect
208. C2×#339C2×C11semidirect
297. C2×#104C4×C11semidirect
525. C42C11×C22⋊C4semidirect
526. C11#11079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1042
C2×C11×#4172
C11×#23112
C2×C11×#3822
C2×C11×#3432
C11×#17362
C2×C11×#3392
#1107911