Finite Group Databasebeta

← C11×#11116 #14588309

Subgroups — C11×#11116 #14588309

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C11×#2896C211yesmaximal, characteristic
4C2×C11×#413C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1742C211yesmaximal, characteristic, complemented
7C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C11×#421—22no—
19C11×#421—22no—
20C2×C11×#104C414yescomplemented
21C11×#419—21no—
22C11×#418—21no—
23C11×#417—22no—
24C11×#416—22no—
25C11×#413—22no—
26C11×#413—22no—
27C2×C11×#101—21no—
28C2×C11×#100—21no—
29C11×#344—22no—
30C11×#343—22no—
31C11×H(3,ℤ/4)—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×C11C2311yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
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×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16C2×C412yes—
68C2×C11×M16D412yes—
69C2×C11×M16D412yes—
70C2×C11×M16D412yes—
71C2×C11×M16D412yes—
72C2×C11×M16D412yes—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117D412yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2×C412yes—
91C11×#108—28no—
92C11×#104—28no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#101—24no—
96C11×#100—24no—
97#11116C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11#4111yescharacteristic
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—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q811yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16—41no—
172C11×M16C22⋊C414yes—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—41no—
197C2×#430C2×C1111yescharacteristic, complemented
198C2×#421C2×C1111yescharacteristic
199#2896C2×C1111yescharacteristic
200C2×#413C2×C1111yescharacteristic
201C2×#344C2×C1111yescharacteristic, complemented
202#1742C2×C1111yescharacteristic, complemented
203C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—81no—
208C23×C11—82no—
209C23×C11C4×D411yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11C22⋊Q811yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12411yescharacteristic
215C23×C11#12611yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—41no—
227D4×C11—41no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—82no—
238C2×C4×C11—82no—
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C4⋊C411yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C2×C4×C11#12311yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12611yescharacteristic
266C2×C4×C11#12711yescharacteristic
267C8×C11—24no—
268C8×C11—42no—
269C8×C11—42no—
270C8×C11—42no—
271C22×#41C22×C1111yescharacteristic
272C22×M16C22×C1111yescharacteristic
273C22×M16C22×C1111yescharacteristic
274C22×M16C22×C1111yescharacteristic
275C22×M16C22×C1111yescharacteristic
276C2×#117C22×C1111yescharacteristic
277C2×#117C22×C1111yescharacteristic
278#430—22no—
279#430—22no—
280C2×#108—22no—
281#421—22no—
282#421—22no—
283C2×#104C4×C1114yescomplemented
284#419—21no—
285#418—21no—
286#417—22no—
287#416—22no—
288#413—22no—
289#413—22no—
290C2×#101—21no—
291C2×#100—21no—
292#344—22no—
293#343—22no—
294H(3,ℤ/4)—22no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11#38511yescharacteristic
307C22×C11#38811yescharacteristic
308C22×C11#39011yescharacteristic
309C22×C11#39311yescharacteristic
310C22×C11#39411yescharacteristic
311C22×C11#39611yescharacteristic
312C22×C11#39711yescharacteristic
313C4×C11—42no—
314C4×C11—82no—
315C4×C11—82no—
316C4×C11#38011yescharacteristic
317C4×C11#38511yescharacteristic
318C4×C11#38611yescharacteristic
319C4×C11#38811yescharacteristic
320C4×C11#39211yescharacteristic
321C4×C11#39411yescharacteristic
322C4×C11#39611yescharacteristic
323C4×C11#39911yescharacteristic
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41C2×C4×C1112yes—
335C2×#41Q8×C1112yes—
336C22×Q8D4×C1111yescharacteristic
337C22×D4—21no—
338C22×D4D4×C1111yescharacteristic
339C23×C4—21no—
340C23×C4C23×C1111yescharacteristic
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16C2×C4×C1112yes—
360C2×M16D4×C1112yes—
361C2×M16D4×C1112yes—
362C2×M16D4×C1112yes—
363C2×M16D4×C1112yes—
364C2×M16D4×C1112yes—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117D4×C1112yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42C2×C4×C1112yes—
383#108—28no—
384#104—28no—
385#103—24no—
386#102—24no—
387#101—24no—
388#100—24no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—82no—
397C2×C11#143911yescharacteristic
398C24—21no—
399C24C11×#4111yescharacteristic
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8C11×C4⋊C412yes—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4C11×C4⋊C412yes—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C22×C4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×Q8×C1111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453C22×C4C11×#4111yescharacteristic
454C22×C4C11×#4111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456C22×C4C11×#4111yescharacteristic
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16C11×C22⋊C414yes—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—41no—
497C11#1111611yescharacteristic, direct product factor, Sylow
498C23—22no—
499C23—41no—
500C23—41no—
501C23—81no—
502C23—82no—
503C23C4×D4×C1111yescharacteristic
504C23C11×#12111yescharacteristic
505C23C11×C22⋊Q811yescharacteristic
506C23C11×#12311yescharacteristic
507C23C11×#12411yescharacteristic
508C23C11×#12411yescharacteristic
509C23C11×#12611yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—41no—
521D4—41no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4C2×C11×C22⋊C411yescharacteristic
534C2×C4C2×C11×C4⋊C411yescharacteristic
535C2×C4C11×#11711yescharacteristic
536C2×C4C4×D4×C1111yescharacteristic
537C2×C4C4×D4×C1111yescharacteristic
538C2×C4C4×D4×C1111yescharacteristic
539C2×C4C11×#12011yescharacteristic
540C2×C4C11×#12011yescharacteristic
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12111yescharacteristic
543C2×C4C11×#12111yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12111yescharacteristic
546C2×C4C11×#12111yescharacteristic
547C2×C4C11×#12111yescharacteristic
548C2×C4C11×#12111yescharacteristic
549C2×C4C11×C22⋊Q811yescharacteristic
550C2×C4C11×C22⋊Q811yescharacteristic
551C2×C4C11×C22⋊Q811yescharacteristic
552C2×C4C11×C22⋊Q811yescharacteristic
553C2×C4C11×C22⋊Q811yescharacteristic
554C2×C4C11×#12311yescharacteristic
555C2×C4C11×#12311yescharacteristic
556C2×C4C11×#12311yescharacteristic
557C2×C4C11×#12311yescharacteristic
558C2×C4C11×#12411yescharacteristic
559C2×C4C11×#12611yescharacteristic
560C2×C4C11×#12711yescharacteristic
561C8—24no—
562C8—42no—
563C8—42no—
564C8—42no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22C11×#38511yescharacteristic
577C22C11×#38811yescharacteristic
578C22C11×#39011yescharacteristic
579C22C11×#39311yescharacteristic
580C22C11×#39411yescharacteristic
581C22C11×#39611yescharacteristic
582C22C11×#39711yescharacteristic
583C4—42no—
584C4—82no—
585C4—82no—
586C4C11×#38011yescharacteristic
587C4C11×#38511yescharacteristic
588C4C11×#38611yescharacteristic
589C4C11×#38811yescharacteristic
590C4C11×#39211yescharacteristic
591C4C11×#39411yescharacteristic
592C4C11×#39611yescharacteristic
593C4C11×#39911yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—82no—
602C2C11×#143911yescharacteristic
subgroupG/H
centerC4×C11#388
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1439
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1742C2semidirect
7. C2×C11×H(3,ℤ/4)C2semidirect
20. C2×C11×#104C4semidirect
97. #11116C11direct (N × H)
197. C2×#430C2×C11semidirect
201. C2×#344C2×C11semidirect
202. #1742C2×C11semidirect
203. C2×H(3,ℤ/4)C2×C11semidirect
283. C2×#104C4×C11semidirect
497. C11#11116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#4212
C11×#28962
C2×C11×#4132
C2×C11×#3442
C11×#17422
C2×C11×H(3,ℤ/4)2
#1111611