Finite Group Databasebeta

← C11×#11120 #14588313

Subgroups — C11×#11120 #14588313

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 626 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
3C2×C11×#417C211yesmaximal, characteristic
4C2×C11×#413C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C2×C11×#343C211yesmaximal, characteristic, complemented
7C11×#1736C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C11×#421—22no—
19C11×#421C414yescomplemented
20C2×C11×#104—22no—
21C11×#417—22no—
22C11×#417—22no—
23C2×C11×#103—21no—
24C2×C11×#102—21no—
25C11×#413—22no—
26C11×#413—22no—
27C2×C11×#101—21no—
28C2×C11×#100—21no—
29C11×#344—22no—
30C11×#343—22no—
31C11×#340—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×C11C2311yescharacteristic
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×M16—21no—
68C2×C11×M16C2×C412yes—
69C2×C11×M16D412yes—
70C2×C11×M16D412yes—
71C2×C11×M16D412yes—
72C2×C11×M16D412yes—
73C2×C11×M16D412yes—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117C2×C412yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4D412yes—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C11×#108—28no—
92C11×#104—28no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#101—24no—
96C11×#100—24no—
97#11120C1111yesmaximal, 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×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—82no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×Q811yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16—41no—
172C11×M16—41no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16C22⋊C414yes—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C2×C8×C11—41no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—41no—
196C42×C11—22no—
197C42×C11—41no—
198C2×#430C2×C1111yescharacteristic, complemented
199C2×#421C2×C1111yescharacteristic
200C2×#417C2×C1111yescharacteristic
201C2×#413C2×C1111yescharacteristic
202C2×#344C2×C1111yescharacteristic, complemented
203C2×#343C2×C1111yescharacteristic, complemented
204#1736C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11C4×D411yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11C22⋊Q811yescharacteristic
215C23×C11#12311yescharacteristic
216C23×C11#12411yescharacteristic
217C23×C11#12411yescharacteristic
218C23×C11#12611yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—81no—
241C2×C4×C11—81no—
242C2×C4×C11—82no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C4⋊C411yescharacteristic
247C2×C4×C11#11711yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11#12311yescharacteristic
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12311yescharacteristic
269C2×C4×C11#12311yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12611yescharacteristic
272C2×C4×C11#12711yescharacteristic
273C8×C11—24no—
274C8×C11—42no—
275C8×C11—42no—
276C8×C11—42no—
277C22×#41C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C22×M16C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C22×C4⋊C4C22×C1111yescharacteristic
284#430—22no—
285#430—22no—
286C2×#108—22no—
287#421—22no—
288#421C4×C1114yescomplemented
289C2×#104—22no—
290#417—22no—
291#417—22no—
292C2×#103—21no—
293C2×#102—21no—
294#413—22no—
295#413—22no—
296C2×#101—21no—
297C2×#100—21no—
298#344—22no—
299#343—22no—
300#340—22no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11—42no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11#38511yescharacteristic
317C22×C11#38811yescharacteristic
318C22×C11#39011yescharacteristic
319C22×C11#39311yescharacteristic
320C22×C11#39411yescharacteristic
321C22×C11#39611yescharacteristic
322C22×C11#39711yescharacteristic
323C4×C11—42no—
324C4×C11—82no—
325C4×C11—82no—
326C4×C11#38011yescharacteristic
327C4×C11#38511yescharacteristic
328C4×C11#38611yescharacteristic
329C4×C11#38811yescharacteristic
330C4×C11#39211yescharacteristic
331C4×C11#39411yescharacteristic
332C4×C11#39611yescharacteristic
333C4×C11#39911yescharacteristic
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41C2×C4×C1112yes—
345C2×#41Q8×C1112yes—
346C22×Q8D4×C1111yescharacteristic
347C22×D4—21no—
348C22×D4D4×C1111yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C23×C4C23×C1111yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16C2×C4×C1112yes—
371C2×M16D4×C1112yes—
372C2×M16D4×C1112yes—
373C2×M16D4×C1112yes—
374C2×M16D4×C1112yes—
375C2×M16D4×C1112yes—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117C2×C4×C1112yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4D4×C1112yes—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393#108—28no—
394#104—28no—
395#103—24no—
396#102—24no—
397#101—24no—
398#100—24no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—82no—
406C2×C11#143911yescharacteristic
407C2×C11#204811yescharacteristic
408C2×C11#204911yescharacteristic
409C24—21no—
410C24C11×#4111yescharacteristic
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C11×C4⋊C412yes—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4C11×C4⋊C412yes—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—82no—
457C22×C4C22×C4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×Q8×C1111yescharacteristic
466C22×C4C11×#4111yescharacteristic
467C22×C4C11×#4111yescharacteristic
468C22×C4C11×#4111yescharacteristic
469C22×C4C11×#4111yescharacteristic
470C22×C4C11×#4111yescharacteristic
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16C11×C22⋊C414yes—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C42—22no—
508C42—41no—
509C11#1112011yescharacteristic, direct product factor, Sylow
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—81no—
516C23—81no—
517C23C4×D4×C1111yescharacteristic
518C23C11×#12111yescharacteristic
519C23C11×C22⋊Q811yescharacteristic
520C23C11×#12311yescharacteristic
521C23C11×#12411yescharacteristic
522C23C11×#12411yescharacteristic
523C23C11×#12611yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—41no—
535D4—41no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4C2×C11×C22⋊C411yescharacteristic
551C2×C4C2×C11×C4⋊C411yescharacteristic
552C2×C4C11×#11711yescharacteristic
553C2×C4C4×D4×C1111yescharacteristic
554C2×C4C4×D4×C1111yescharacteristic
555C2×C4C4×D4×C1111yescharacteristic
556C2×C4C11×#12011yescharacteristic
557C2×C4C11×#12011yescharacteristic
558C2×C4C11×#12011yescharacteristic
559C2×C4C11×#12111yescharacteristic
560C2×C4C11×#12111yescharacteristic
561C2×C4C11×#12111yescharacteristic
562C2×C4C11×#12111yescharacteristic
563C2×C4C11×#12111yescharacteristic
564C2×C4C11×#12111yescharacteristic
565C2×C4C11×#12111yescharacteristic
566C2×C4C11×C22⋊Q811yescharacteristic
567C2×C4C11×C22⋊Q811yescharacteristic
568C2×C4C11×C22⋊Q811yescharacteristic
569C2×C4C11×C22⋊Q811yescharacteristic
570C2×C4C11×C22⋊Q811yescharacteristic
571C2×C4C11×#12311yescharacteristic
572C2×C4C11×#12311yescharacteristic
573C2×C4C11×#12311yescharacteristic
574C2×C4C11×#12311yescharacteristic
575C2×C4C11×#12411yescharacteristic
576C2×C4C11×#12611yescharacteristic
577C2×C4C11×#12711yescharacteristic
578C8—24no—
579C8—42no—
580C8—42no—
581C8—42no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—81no—
596C22—81no—
597C22C11×#38511yescharacteristic
598C22C11×#38811yescharacteristic
599C22C11×#39011yescharacteristic
600C22C11×#39311yescharacteristic
601C22C11×#39411yescharacteristic
602C22C11×#39611yescharacteristic
603C22C11×#39711yescharacteristic
604C4—42no—
605C4—82no—
606C4—82no—
607C4C11×#38011yescharacteristic
608C4C11×#38511yescharacteristic
609C4C11×#38611yescharacteristic
610C4C11×#38811yescharacteristic
611C4C11×#39211yescharacteristic
612C4C11×#39411yescharacteristic
613C4C11×#39611yescharacteristic
614C4C11×#39911yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—82no—
622C2C11×#143911yescharacteristic
623C2C11×#204811yescharacteristic
624C2C11×#204911yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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. C2×C11×#343C2semidirect
7. C11×#1736C2semidirect
19. C11×#421C4semidirect
97. #11120C11direct (N × H)
198. C2×#430C2×C11semidirect
202. C2×#344C2×C11semidirect
203. C2×#343C2×C11semidirect
204. #1736C2×C11semidirect
288. #421C4×C11semidirect
509. C11#11120direct (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
C2×C11×#4172
C2×C11×#4132
C2×C11×#3442
C2×C11×#3432
C11×#17362
#1112011