Finite Group Databasebeta

← C11×#11125 #14588318

Subgroups — C11×#11125 #14588318

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#108C211yesmaximal, characteristic, complemented
2C22×C11×#104C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C2×C11×#408C211yesmaximal, characteristic
5C2×C11×#339C211yesmaximal, characteristic, complemented
6C11×#1729C211yesmaximal, characteristic, complemented
7C2×C11×#336C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C11×#108—22no—
16C2×C11×#108—22no—
17C2×C11×#108—22no—
18C2×C11×#104—22no—
19C2×C11×#104—22no—
20C2×C11×#104—22no—
21C11×#416—22no—
22C11×#416—22no—
23C2×C11×#103C411yescharacteristic, complemented
24C2×C11×#103C411yescharacteristic, complemented
25C2×C11×#102C411yescharacteristic, complemented
26C2×C11×#102C411yescharacteristic, complemented
27C11×#408—22no—
28C11×#408—22no—
29C2×C11×C22⋊C8—22no—
30C11×#339—22no—
31C11×#336—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×C11—21no—
50C23×C4×C11C2311yescharacteristic
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×M16D412yes—
62C2×C11×M16D412yes—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11C2×C411yescharacteristic
76C22×C8×C11C2×C411yescharacteristic
77C22×C8×C11D412yes—
78C22×C8×C11D412yes—
79C22×C8×C11D412yes—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11D412yes—
94C11×#108—28no—
95C11×#104—28no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×C22⋊C8—28no—
101#11125C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11#4111yescharacteristic
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—24no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×Q811yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—41no—
171C11×M16—41no—
172C11×M16—41no—
173C11×M16—41no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—41no—
188C2×C8×C11—41no—
189C2×C8×C11—41no—
190C2×C8×C11—41no—
191C2×C8×C11—41no—
192C2×C8×C11—41no—
193C2×C8×C11—41no—
194C2×C8×C11—41no—
195C2×C8×C11C22⋊C412yes—
196C2×C8×C11C22⋊C412yes—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—41no—
206C42×C11—41no—
207C42×C11—41no—
208C42×C11—41no—
209C22×#108C2×C1111yescharacteristic, complemented
210C22×#104C2×C1111yescharacteristic
211C2×#416C2×C1111yescharacteristic
212C2×#408C2×C1111yescharacteristic
213C2×#339C2×C1111yescharacteristic, complemented
214#1729C2×C1111yescharacteristic, complemented
215C2×#336C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C4×D411yescharacteristic
224C23×C11#12111yescharacteristic
225C23×C11C22⋊Q811yescharacteristic
226C23×C11#12311yescharacteristic
227C23×C11#12411yescharacteristic
228C23×C11#12411yescharacteristic
229C23×C11#12611yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
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—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
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#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11#12111yescharacteristic
274C2×C4×C11C22⋊Q811yescharacteristic
275C2×C4×C11C22⋊Q811yescharacteristic
276C2×C4×C11C22⋊Q811yescharacteristic
277C2×C4×C11C22⋊Q811yescharacteristic
278C2×C4×C11C22⋊Q811yescharacteristic
279C2×C4×C11#12311yescharacteristic
280C2×C4×C11#12311yescharacteristic
281C2×C4×C11#12311yescharacteristic
282C2×C4×C11#12311yescharacteristic
283C2×C4×C11#12411yescharacteristic
284C2×C4×C11#12611yescharacteristic
285C2×C4×C11#12711yescharacteristic
286C8×C11—22no—
287C8×C11—22no—
288C8×C11—42no—
289C8×C11—42no—
290C8×C11—42no—
291C22×#41C22×C1111yescharacteristic
292C22×M16C22×C1111yescharacteristic
293C22×M16C22×C1111yescharacteristic
294C23×C8C22×C1111yescharacteristic
295C23×C8C22×C1111yescharacteristic
296C2×#117C22×C1111yescharacteristic
297C22×C42C22×C1111yescharacteristic
298C2×#108—22no—
299C2×#108—22no—
300C2×#108—22no—
301C2×#104—22no—
302C2×#104—22no—
303C2×#104—22no—
304#416—22no—
305#416—22no—
306C2×#103C4×C1111yescharacteristic, complemented
307C2×#103C4×C1111yescharacteristic, complemented
308C2×#102C4×C1111yescharacteristic, complemented
309C2×#102C4×C1111yescharacteristic, complemented
310#408—22no—
311#408—22no—
312C2×C22⋊C8—22no—
313#339—22no—
314#336—22no—
315#336—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—82no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11#38511yescharacteristic
330C22×C11#38811yescharacteristic
331C22×C11#39011yescharacteristic
332C22×C11#39311yescharacteristic
333C22×C11#39411yescharacteristic
334C22×C11#39611yescharacteristic
335C22×C11#39711yescharacteristic
336C22×C11#44312yes—
337C22×C11#44412yes—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#38011yescharacteristic
343C4×C11#38511yescharacteristic
344C4×C11#38611yescharacteristic
345C4×C11#38811yescharacteristic
346C4×C11#39211yescharacteristic
347C4×C11#39411yescharacteristic
348C4×C11#39611yescharacteristic
349C4×C11#39911yescharacteristic
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41D4×C1112yes—
361C2×#41Q8×C1112yes—
362C22×Q8C2×C4×C1111yescharacteristic
363C22×D4—21no—
364C22×D4C2×C4×C1111yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4C23×C1111yescharacteristic
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×M16—21no—
378C2×M16D4×C1112yes—
379C2×M16D4×C1112yes—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8C2×C4×C1111yescharacteristic
393C22×C8C2×C4×C1111yescharacteristic
394C22×C8D4×C1112yes—
395C22×C8D4×C1112yes—
396C22×C8D4×C1112yes—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401C2×C4⋊C4C2×C4×C1111yescharacteristic
402C2×C4⋊C4C2×C4×C1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42D4×C1112yes—
411#108—28no—
412#104—28no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417C22⋊C8—28no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—82no—
423C2×C11#143911yescharacteristic
424C2×C11#186612yes—
425C2×C11#192912yes—
426C2×C11#197411yescharacteristic
427C2×C11#197511yescharacteristic
428C24—21no—
429C24C11×#4111yescharacteristic
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—22no—
437#41—22no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445#41—41no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C11×C4⋊C412yes—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C11×C4⋊C412yes—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4C22×C4×C1111yescharacteristic
479C22×C4C2×D4×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
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8C11×C22⋊C412yes—
522C2×C8C11×C22⋊C412yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C42—22no—
530C42—22no—
531C42—41no—
532C42—41no—
533C42—41no—
534C42—41no—
535C11#1112511yescharacteristic, direct product factor, Sylow
536C23—22no—
537C23—22no—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23C4×D4×C1111yescharacteristic
544C23C11×#12111yescharacteristic
545C23C11×C22⋊Q811yescharacteristic
546C23C11×#12311yescharacteristic
547C23C11×#12411yescharacteristic
548C23C11×#12411yescharacteristic
549C23C11×#12611yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—41no—
553Q8—41no—
554D4—22no—
555D4—22no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—41no—
561D4—41no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4C2×C11×C22⋊C411yescharacteristic
579C2×C4C2×C11×C4⋊C411yescharacteristic
580C2×C4C11×#11711yescharacteristic
581C2×C4C4×D4×C1111yescharacteristic
582C2×C4C4×D4×C1111yescharacteristic
583C2×C4C4×D4×C1111yescharacteristic
584C2×C4C11×#12011yescharacteristic
585C2×C4C11×#12011yescharacteristic
586C2×C4C11×#12011yescharacteristic
587C2×C4C11×#12111yescharacteristic
588C2×C4C11×#12111yescharacteristic
589C2×C4C11×#12111yescharacteristic
590C2×C4C11×#12111yescharacteristic
591C2×C4C11×#12111yescharacteristic
592C2×C4C11×#12111yescharacteristic
593C2×C4C11×#12111yescharacteristic
594C2×C4C11×C22⋊Q811yescharacteristic
595C2×C4C11×C22⋊Q811yescharacteristic
596C2×C4C11×C22⋊Q811yescharacteristic
597C2×C4C11×C22⋊Q811yescharacteristic
598C2×C4C11×C22⋊Q811yescharacteristic
599C2×C4C11×#12311yescharacteristic
600C2×C4C11×#12311yescharacteristic
601C2×C4C11×#12311yescharacteristic
602C2×C4C11×#12311yescharacteristic
603C2×C4C11×#12411yescharacteristic
604C2×C4C11×#12611yescharacteristic
605C2×C4C11×#12711yescharacteristic
606C8—22no—
607C8—22no—
608C8—42no—
609C8—42no—
610C8—42no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—44no—
620C22—42no—
621C22—82no—
622C22—81no—
623C22—81no—
624C22C11×#38511yescharacteristic
625C22C11×#38811yescharacteristic
626C22C11×#39011yescharacteristic
627C22C11×#39311yescharacteristic
628C22C11×#39411yescharacteristic
629C22C11×#39611yescharacteristic
630C22C11×#39711yescharacteristic
631C22C11×#44312yes—
632C22C11×#44412yes—
633C4—44no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4C11×#38011yescharacteristic
638C4C11×#38511yescharacteristic
639C4C11×#38611yescharacteristic
640C4C11×#38811yescharacteristic
641C4C11×#39211yescharacteristic
642C4C11×#39411yescharacteristic
643C4C11×#39611yescharacteristic
644C4C11×#39911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—82no—
650C2C11×#143911yescharacteristic
651C2C11×#186612yes—
652C2C11×#192912yes—
653C2C11×#197411yescharacteristic
654C2C11×#197511yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC23×C11C4×D4
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#108C2semidirect
5. C2×C11×#339C2semidirect
6. C11×#1729C2semidirect
7. C2×C11×#336C2semidirect
23. C2×C11×#103C4semidirect
24. C2×C11×#103C4semidirect
25. C2×C11×#102C4semidirect
26. C2×C11×#102C4semidirect
101. #11125C11direct (N × H)
209. C22×#108C2×C11semidirect
213. C2×#339C2×C11semidirect
214. #1729C2×C11semidirect
215. C2×#336C2×C11semidirect
306. C2×#103C4×C11semidirect
307. C2×#103C4×C11semidirect
308. C2×#102C4×C11semidirect
309. C2×#102C4×C11semidirect
535. C11#11125direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1082
C22×C11×#1042
C2×C11×#4162
C2×C11×#4082
C2×C11×#3392
C11×#17292
C2×C11×#3362
#1112511