Finite Group Databasebeta

← C11×#11126 #14588319

Subgroups — C11×#11126 #14588319

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#427C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C2×C11×#410C211yesmaximal, characteristic
5C11×#1740C211yesmaximal, characteristic, complemented
6C11×#1733C211yesmaximal, characteristic, complemented
7C11×#1729C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#427—22no—
16C11×#427—22no—
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C11×#421—22no—
20C11×#421—22no—
21C2×C11×#104—22no—
22C11×#416—22no—
23C11×#416—21no—
24C11×#416—21no—
25C2×C11×#103C412yescomplemented
26C2×C11×#102C412yescomplemented
27C11×#410—22no—
28C11×#410—22no—
29C2×C11×#99—22no—
30C11×#342—22no—
31C11×#339—22no—
32C11×#336—22no—
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×#41—21no—
43C2×C11×#41D412yes—
44C2×C11×#41Q812yes—
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16D412yes—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C22×C8×C11C2×C412yes—
62C22×C8×C11D412yes—
63C22×C8×C11D411yescharacteristic
64C22×C8×C11D411yescharacteristic
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D412yes—
80C11×#117D412yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2×C412yes—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C11×#107—24no—
94C11×#106—24no—
95C11×#104—28no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#99—28no—
101#11126C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11C2×D411yescharacteristic
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11C4⋊C412yes—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11C4⋊C412yes—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×Q811yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—41no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11C22⋊C412yes—
179C2×C8×C11C22⋊C412yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—41no—
199C42×C11—41no—
200C42×C11—41no—
201C42×C11—41no—
202C42×C11—41no—
203C42×C11—41no—
204C2×#427C2×C1111yescharacteristic, complemented
205C2×#421C2×C1111yescharacteristic
206C2×#416C2×C1111yescharacteristic
207C2×#410C2×C1111yescharacteristic
208#1740C2×C1111yescharacteristic, complemented
209#1733C2×C1111yescharacteristic, complemented
210#1729C2×C1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—82no—
216C23×C11C4×D411yescharacteristic
217C23×C11#12011yescharacteristic
218C23×C11#12111yescharacteristic
219C23×C11#12111yescharacteristic
220C23×C11C22⋊Q811yescharacteristic
221C23×C11#12311yescharacteristic
222C23×C11#12711yescharacteristic
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—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—82no—
248C2×C4×C11—82no—
249C2×C4×C11—82no—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C4⋊C411yescharacteristic
252C2×C4×C11#11711yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11#12111yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11C22⋊Q811yescharacteristic
267C2×C4×C11C22⋊Q811yescharacteristic
268C2×C4×C11C22⋊Q811yescharacteristic
269C2×C4×C11#12311yescharacteristic
270C2×C4×C11#12311yescharacteristic
271C2×C4×C11#12311yescharacteristic
272C2×C4×C11#12311yescharacteristic
273C2×C4×C11#12411yescharacteristic
274C2×C4×C11#12411yescharacteristic
275C2×C4×C11#12411yescharacteristic
276C2×C4×C11#12611yescharacteristic
277C2×C4×C11#12611yescharacteristic
278C8×C11—22no—
279C8×C11—22no—
280C8×C11—42no—
281C22×#41C22×C1111yescharacteristic
282C22×M16C22×C1111yescharacteristic
283C23×C8C22×C1111yescharacteristic
284C2×#117C22×C1111yescharacteristic
285C2×#117C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287C2×#117C22×C1111yescharacteristic
288#427—22no—
289#427—22no—
290C2×#107—21no—
291C2×#106—21no—
292#421—22no—
293#421—22no—
294C2×#104—22no—
295#416—22no—
296#416—21no—
297#416—21no—
298C2×#103C4×C1112yescomplemented
299C2×#102C4×C1112yescomplemented
300#410—22no—
301#410—22no—
302C2×#99—22no—
303#342—22no—
304#339—22no—
305#336—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11#38511yescharacteristic
318C22×C11#38811yescharacteristic
319C22×C11#39011yescharacteristic
320C22×C11#39211yescharacteristic
321C22×C11#39411yescharacteristic
322C22×C11#39611yescharacteristic
323C22×C11#39911yescharacteristic
324C4×C11—42no—
325C4×C11—82no—
326C4×C11—82no—
327C4×C11—82no—
328C4×C11—82no—
329C4×C11#38011yescharacteristic
330C4×C11#38511yescharacteristic
331C4×C11#38611yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#39311yescharacteristic
334C4×C11#39411yescharacteristic
335C4×C11#39611yescharacteristic
336C4×C11#39711yescharacteristic
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41D4×C1112yes—
348C2×#41Q8×C1112yes—
349C22×Q8C2×C4×C1111yescharacteristic
350C22×D4—21no—
351C22×D4C2×C4×C1111yescharacteristic
352C23×C4—21no—
353C23×C4C23×C1111yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16D4×C1112yes—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8C2×C4×C1112yes—
366C22×C8D4×C1112yes—
367C22×C8D4×C1111yescharacteristic
368C22×C8D4×C1111yescharacteristic
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117D4×C1112yes—
384#117D4×C1112yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4C2×C4×C1112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4D4×C1112yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397#107—24no—
398#106—24no—
399#104—28no—
400#103—22no—
401#103—22no—
402#102—22no—
403#102—22no—
404#99—28no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—21no—
411C2×C11—82no—
412C2×C11#143911yescharacteristic
413C2×C11#197612yes—
414C24—21no—
415C24C2×D4×C1111yescharacteristic
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C11×C4⋊C412yes—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4C11×C4⋊C412yes—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4C22×C4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×Q8×C1111yescharacteristic
469C22×C4C11×#4111yescharacteristic
470C22×C4C11×#4111yescharacteristic
471C22×C4C11×#4111yescharacteristic
472C22×C4C11×#4111yescharacteristic
473C22×C4C11×#4111yescharacteristic
474C22×C4C11×#4111yescharacteristic
475M16—22no—
476M16—22no—
477M16—41no—
478M16—41no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—22no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8C11×C22⋊C412yes—
491C2×C8C11×C22⋊C412yes—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—22no—
509C42—22no—
510C42—41no—
511C42—41no—
512C42—41no—
513C42—41no—
514C42—41no—
515C42—41no—
516C11#1112611yescharacteristic, direct product factor, Sylow
517C23—22no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—82no—
522C23C4×D4×C1111yescharacteristic
523C23C11×#12011yescharacteristic
524C23C11×#12111yescharacteristic
525C23C11×#12111yescharacteristic
526C23C11×C22⋊Q811yescharacteristic
527C23C11×#12311yescharacteristic
528C23C11×#12711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C2×C11×C22⋊C411yescharacteristic
557C2×C4C2×C11×C4⋊C411yescharacteristic
558C2×C4C11×#11711yescharacteristic
559C2×C4C4×D4×C1111yescharacteristic
560C2×C4C4×D4×C1111yescharacteristic
561C2×C4C4×D4×C1111yescharacteristic
562C2×C4C11×#12011yescharacteristic
563C2×C4C11×#12011yescharacteristic
564C2×C4C11×#12111yescharacteristic
565C2×C4C11×#12111yescharacteristic
566C2×C4C11×#12111yescharacteristic
567C2×C4C11×#12111yescharacteristic
568C2×C4C11×#12111yescharacteristic
569C2×C4C11×#12111yescharacteristic
570C2×C4C11×C22⋊Q811yescharacteristic
571C2×C4C11×C22⋊Q811yescharacteristic
572C2×C4C11×C22⋊Q811yescharacteristic
573C2×C4C11×C22⋊Q811yescharacteristic
574C2×C4C11×C22⋊Q811yescharacteristic
575C2×C4C11×#12311yescharacteristic
576C2×C4C11×#12311yescharacteristic
577C2×C4C11×#12311yescharacteristic
578C2×C4C11×#12311yescharacteristic
579C2×C4C11×#12411yescharacteristic
580C2×C4C11×#12411yescharacteristic
581C2×C4C11×#12411yescharacteristic
582C2×C4C11×#12611yescharacteristic
583C2×C4C11×#12611yescharacteristic
584C8—22no—
585C8—22no—
586C8—42no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22C11×#38511yescharacteristic
599C22C11×#38811yescharacteristic
600C22C11×#39011yescharacteristic
601C22C11×#39211yescharacteristic
602C22C11×#39411yescharacteristic
603C22C11×#39611yescharacteristic
604C22C11×#39911yescharacteristic
605C4—42no—
606C4—82no—
607C4—82no—
608C4—82no—
609C4—82no—
610C4C11×#38011yescharacteristic
611C4C11×#38511yescharacteristic
612C4C11×#38611yescharacteristic
613C4C11×#38811yescharacteristic
614C4C11×#39311yescharacteristic
615C4C11×#39411yescharacteristic
616C4C11×#39611yescharacteristic
617C4C11×#39711yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—82no—
625C2C11×#143911yescharacteristic
626C2C11×#197612yes—
subgroupG/H
centerC2×C4×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#390
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#427C2semidirect
5. C11×#1740C2semidirect
6. C11×#1733C2semidirect
7. C11×#1729C2semidirect
25. C2×C11×#103C4semidirect
26. C2×C11×#102C4semidirect
101. #11126C11direct (N × H)
204. C2×#427C2×C11semidirect
208. #1740C2×C11semidirect
209. #1733C2×C11semidirect
210. #1729C2×C11semidirect
298. C2×#103C4×C11semidirect
299. C2×#102C4×C11semidirect
516. C11#11126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4272
C2×C11×#4212
C2×C11×#4162
C2×C11×#4102
C11×#17402
C11×#17332
C11×#17292
#1112611