Finite Group Databasebeta

← C11×#14641 #14591834

Subgroups — C11×#14641 #14591834

Order 2816.

1486 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×#394C211yesmaximal, characteristic
2C11×#1445C211yesmaximal, characteristic, complemented
3C11×#1442C212yesmaximal, complemented
4C11×#1440C212yesmaximal, complemented
5C11×#1439C212yesmaximal, complemented
6C11×#1439C212yesmaximal, complemented
7C11×#1438C212yesmaximal
8C11×#1437C212yesmaximal, complemented
9C11×#1436C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C11×#394C418yescomplemented
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C25×C11C2312yes—
33C22×D4×C11—42no—
34C22×D4×C11—42no—
35C22×D4×C11—41no—
36C22×D4×C11—41no—
37C22×D4×C11C2×C414yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4—41no—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—42no—
50C2×C11×C4⋊C4—42no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C22⋊C4—24no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—42no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4—42no—
63C2×C11×C22⋊C4—42no—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4C2×C418yes—
69C2×C11×C22⋊C4C2×C418yes—
70C2×C42×C11—42no—
71C2×C42×C11—41no—
72C11×#95—24no—
73C11×#95—42no—
74C11×#95—42no—
75C11×#95—42no—
76C11×#95—42no—
77C11×#95—42no—
78C11×#95—41no—
79C11×#95—41no—
80C11×#95—41no—
81C11×#95—42no—
82C11×#95C2×C414yes—
83#14641C1111yesmaximal, characteristic, direct product factor, Sylow
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C22×C414yes—
99C24×C11C2411yescharacteristic
100C2×D4×C11—44no—
101C2×D4×C11—48no—
102C2×D4×C11—48no—
103C2×D4×C11—44no—
104C2×D4×C11—44no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
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—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11#4114yes—
155C11×C4⋊C4—44no—
156C11×C4⋊C4—48no—
157C11×C22⋊C4—48no—
158C11×C22⋊C4—48no—
159C11×C22⋊C4—48no—
160C11×C22⋊C4—48no—
161C11×C22⋊C4—48no—
162C11×C22⋊C4—48no—
163C42×C11—44no—
164C2×#394C2×C1111yescharacteristic
165#1445C2×C1111yescharacteristic, complemented
166#1442C2×C1112yescomplemented
167#1440C2×C1112yescomplemented
168#1439C2×C1112yescomplemented
169#1439C2×C1112yescomplemented
170#1438C2×C1112yes—
171#1437C2×C1112yescomplemented
172#1436C2×C1111yescharacteristic, complemented
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C23×C411yescharacteristic
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)11yescharacteristic
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)11yescharacteristic
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)12yes—
216C23×C112−1+412yes—
217D4×C11—416no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
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—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C23×D4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1112yes—
270C22×C4⋊C4C22×C1111yescharacteristic
271C22×C22⋊C4C22×C1112yes—
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1112yes—
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1112yes—
276C22×C22⋊C4C22×C1112yes—
277C22×C42C22×C1111yescharacteristic
278#394C4×C1118yescomplemented
279C2×#95C22×C1112yes—
280C2×#95C22×C1112yes—
281C2×#95C22×C1111yescharacteristic
282C2×#95C22×C1112yes—
283C2×#95C22×C1112yes—
284C2×#95C22×C1112yes—
285C2×#95C22×C1112yes—
286C2×#95C22×C1111yescharacteristic
287C2×#95C22×C1112yes—
288C2×#95C22×C1111yescharacteristic
289C2×#95C22×C1111yescharacteristic
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11C4×#4111yescharacteristic
306C22×C11#51811yescharacteristic
307C22×C11#51811yescharacteristic
308C22×C11#51812yes—
309C22×C11#52012yes—
310C22×C11#53812yes—
311C22×C11#53812yes—
312C22×C11#53912yes—
313C22×C11#54012yes—
314C22×C11#54012yes—
315C22×C11#54212yes—
316C22×C11#56012yes—
317C22×C11#56012yes—
318C22×C11#56012yes—
319C22×C11#56011yescharacteristic
320C22×C11H(3,𝔽4)11yescharacteristic
321C22×C11H(3,𝔽4)11yescharacteristic
322C22×C11#56212yes—
323C22×C11#56212yes—
324C22×C11#56212yes—
325C22×C11#56311yescharacteristic
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—44no—
331C4×C11—82no—
332C4×C11—82no—
333C4×C11—82no—
334C25C23×C1112yes—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4C2×C4×C1114yes—
340C23×C4C23×C1112yes—
341C23×C4C23×C1112yes—
342C23×C4C23×C1112yes—
343C23×C4C23×C1111yescharacteristic
344C23×C4C23×C1112yes—
345C23×C4C23×C1111yescharacteristic
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1112yes—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4C2×C4×C1114yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4C2×C4×C1118yes—
371C2×C22⋊C4C2×C4×C1118yes—
372C2×C42—42no—
373C2×C42—41no—
374#95—24no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—41no—
381#95—41no—
382#95—41no—
383#95—42no—
384#95C2×C4×C1114yes—
385C2×C11—84no—
386C2×C11#233311yescharacteristic
387C2×C11#233512yes—
388C2×C11#237511yescharacteristic
389C2×C11#237712yes—
390C2×C11#237911yescharacteristic
391C2×C11#282412yes—
392C2×C11#282812yes—
393C2×C11#282912yes—
394C2×C11#283712yes—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24C22×C4×C1114yes—
410C24C24×C1111yescharacteristic
411C2×D4—44no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—44no—
415C2×D4—44no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4C22×C4×C1114yes—
462C22×C4C22×C4×C1112yes—
463C22×C4C22×C4×C1112yes—
464C22×C4C22×C4×C1112yes—
465C22×C4C11×#4114yes—
466C4⋊C4—44no—
467C4⋊C4—48no—
468C22⋊C4—48no—
469C22⋊C4—48no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—48no—
473C22⋊C4—48no—
474C42—44no—
475C11#1464111yescharacteristic, direct product factor, Sylow
476C23—24no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23C23×C4×C1111yescharacteristic
512C23C2×C11×#4112yes—
513C23C11×H(5,𝔽2)11yescharacteristic
514C23C11×H(5,𝔽2)12yes—
515C23C11×H(5,𝔽2)12yes—
516C23C11×H(5,𝔽2)11yescharacteristic
517C23C11×H(5,𝔽2)12yes—
518C23C11×H(5,𝔽2)12yes—
519C23C11×2−1+412yes—
520D4—416no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C22—44no—
572C22—44no—
573C22—44no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22C4×C11×#4111yescharacteristic
587C22C11×#51811yescharacteristic
588C22C11×#51811yescharacteristic
589C22C11×#51812yes—
590C22C11×#52012yes—
591C22C11×#53812yes—
592C22C11×#53812yes—
593C22C11×#53912yes—
594C22C11×#54012yes—
595C22C11×#54012yes—
596C22C11×#54212yes—
597C22C11×#56012yes—
598C22C11×#56012yes—
599C22C11×#56012yes—
600C22C11×#56011yescharacteristic
601C22C11×H(3,𝔽4)11yescharacteristic
602C22C11×H(3,𝔽4)11yescharacteristic
603C22C11×#56212yes—
604C22C11×#56212yes—
605C22C11×#56212yes—
606C22C11×#56311yescharacteristic
607C4—44no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—44no—
612C4—82no—
613C4—82no—
614C4—82no—
615C2—84no—
616C2C11×#233311yescharacteristic
617C2C11×#233512yes—
618C2C11×#237511yescharacteristic
619C2C11×#237712yes—
620C2C11×#237911yescharacteristic
621C2C11×#282412yes—
622C2C11×#282812yes—
623C2C11×#282912yes—
624C2C11×#283712yes—
subgroupG/H
center, socleC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1445C2semidirect
3. C11×#1442C2semidirect
4. C11×#1440C2semidirect
5. C11×#1439C2semidirect
6. C11×#1439C2semidirect
8. C11×#1437C2semidirect
9. C11×#1436C2semidirect
20. C11×#394C4semidirect
83. #14641C11direct (N × H)
165. #1445C2×C11semidirect
166. #1442C2×C11semidirect
167. #1440C2×C11semidirect
168. #1439C2×C11semidirect
169. #1439C2×C11semidirect
171. #1437C2×C11semidirect
172. #1436C2×C11semidirect
278. #394C4×C11semidirect
475. C11#14641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3942
C11×#14452
C11×#14422
C11×#14402
C11×#14392
C11×#14382
C11×#14372
C11×#14362
#1464111