Finite Group Databasebeta

← C11×#11276 #14588469

Subgroups — C11×#11276 #14588469

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2317C211yesmaximal, characteristic
2C2×C11×#343C211yesmaximal, characteristic
3C11×#1736C211yesmaximal, characteristic
4C11×#1736C211yesmaximal, characteristic
5C2×C11×#339C211yesmaximal, characteristic
6C2×C11×#339C211yesmaximal, characteristic
7C11×C4⋊#95C211yesmaximal, characteristic
8C22×C11×M16C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C11×#389—21no—
16C11×#389—21no—
17C11×#385—22no—
18C11×#384—21no—
19C11×#382—21no—
20C2×C11×#95—22no—
21C11×#343—22no—
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—21no—
25C11×#340—21no—
26C11×#339—22no—
27C11×#339C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11—21no—
30C23×C4×C11D412yes—
31C23×C4×C11C2311yescharacteristic
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C2×C11×M16—21no—
39C2×C11×M16—21no—
40C2×C11×M16—21no—
41C2×C11×M16—21no—
42C2×C11×M16C2×C412yes—
43C2×C11×M16D412yes—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C11×#117—21no—
47C11×#117—21no—
48C11×#117—21no—
49C11×#117—21no—
50C11×#117—21no—
51C11×#117—21no—
52C11×#117C2×C412yes—
53C11×#117Q812yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4Q812yes—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2×C412yes—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—44no—
85#11276C1111yesmaximal, characteristic, direct product factor, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×Q811yescharacteristic
113C22×C4×C11C2×Q811yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C11×M16—22no—
123C11×M16—22no—
124C11×M16—22no—
125C11×M16—22no—
126C11×M16—41no—
127C11×M16—41no—
128C11×M16—41no—
129C11×M16—41no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—41no—
133C2×C8×C11—41no—
134C2×C8×C11—41no—
135C2×C8×C11—41no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—82no—
151C11×C4⋊C4—82no—
152C11×C4⋊C4C4⋊C412yes—
153C11×C4⋊C4C4⋊C412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—41no—
163C42×C11—41no—
164C42×C11—41no—
165C42×C11—41no—
166#2317C2×C1111yescharacteristic
167C2×#343C2×C1111yescharacteristic
168#1736C2×C1111yescharacteristic
169#1736C2×C1111yescharacteristic
170C2×#339C2×C1111yescharacteristic
171C2×#339C2×C1111yescharacteristic
172C4⋊#95C2×C1111yescharacteristic
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11C4×D411yescharacteristic
178C23×C11#12011yescharacteristic
179C23×C11#12111yescharacteristic
180C23×C11C22⋊Q811yescharacteristic
181C23×C11C22⋊Q811yescharacteristic
182C23×C11#12311yescharacteristic
183C23×C11#12411yescharacteristic
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—44no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11—81no—
211C2×C4×C11—81no—
212C2×C4×C11—82no—
213C2×C4×C11C2×C4⋊C411yescharacteristic
214C2×C4×C11#11711yescharacteristic
215C2×C4×C11#11711yescharacteristic
216C2×C4×C11C4×D411yescharacteristic
217C2×C4×C11C4×D411yescharacteristic
218C2×C4×C11C4×Q811yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11C22⋊Q811yescharacteristic
222C2×C4×C11C22⋊Q811yescharacteristic
223C2×C4×C11C22⋊Q811yescharacteristic
224C2×C4×C11#12311yescharacteristic
225C2×C4×C11#12311yescharacteristic
226C2×C4×C11#12311yescharacteristic
227C2×C4×C11#12311yescharacteristic
228C2×C4×C11#12411yescharacteristic
229C2×C4×C11#12411yescharacteristic
230C2×C4×C11#12411yescharacteristic
231C2×C4×C11#12511yescharacteristic
232C2×C4×C11#12511yescharacteristic
233C2×C4×C11#12511yescharacteristic
234C2×C4×C11#12511yescharacteristic
235C2×C4×C11#12511yescharacteristic
236C2×C4×C11#12611yescharacteristic
237C2×C4×C11#12611yescharacteristic
238C2×C4×C11#12611yescharacteristic
239C2×C4×C11#12611yescharacteristic
240C2×C4×C11C4⋊Q811yescharacteristic
241C8×C11—42no—
242C8×C11—42no—
243C22×M16C22×C1111yescharacteristic
244C22×M16C22×C1111yescharacteristic
245C2×#117C22×C1111yescharacteristic
246C2×#117C22×C1111yescharacteristic
247C22×C4⋊C4C22×C1111yescharacteristic
248C22×C4⋊C4C22×C1111yescharacteristic
249C22×C42C22×C1111yescharacteristic
250#389—21no—
251#389—21no—
252#385—22no—
253#384—21no—
254#382—21no—
255C2×#95—22no—
256#343—22no—
257#340—21no—
258#340—21no—
259#340—21no—
260#340—21no—
261#339—22no—
262#339C4×C1114yescomplemented
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11#38511yescharacteristic
276C22×C11#38711yescharacteristic
277C22×C11#38811yescharacteristic
278C22×C11#39311yescharacteristic
279C22×C11#39411yescharacteristic
280C22×C11#39811yescharacteristic
281C22×C11#40011yescharacteristic
282C22×C11#45311yescharacteristic
283C22×C11#45411yescharacteristic
284C22×C11#45511yescharacteristic
285C22×C11#45611yescharacteristic
286C4×C11—44no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11—81no—
291C4×C11—82no—
292C4×C11—81no—
293C4×C11#38211yescharacteristic
294C4×C11#38711yescharacteristic
295C4×C11#38811yescharacteristic
296C4×C11#38911yescharacteristic
297C4×C11#39711yescharacteristic
298C4×C11#39811yescharacteristic
299C4×C11#40011yescharacteristic
300C4×C11#40011yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4D4×C1112yes—
304C23×C4C23×C1111yescharacteristic
305C2×M16—21no—
306C2×M16—21no—
307C2×M16—21no—
308C2×M16—21no—
309C2×M16—21no—
310C2×M16—21no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16C2×C4×C1112yes—
316C2×M16D4×C1112yes—
317C22×C8—21no—
318C22×C8—21no—
319#117—21no—
320#117—21no—
321#117—21no—
322#117—21no—
323#117—21no—
324#117—21no—
325#117C2×C4×C1112yes—
326#117Q8×C1112yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C4⋊C4D4×C1111yescharacteristic
343C2×C4⋊C4D4×C1111yescharacteristic
344C2×C4⋊C4Q8×C1112yes—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C2×C4×C1112yes—
355#95—22no—
356#95—22no—
357#95—44no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11#144211yescharacteristic
363C2×C11#185911yescharacteristic
364C2×C11#186011yescharacteristic
365C2×C11#202711yescharacteristic
366C2×C11#202811yescharacteristic
367C2×C11#203711yescharacteristic
368C2×C11#203811yescharacteristic
369C24C2×D4×C1111yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4C22×C4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×Q8×C1111yescharacteristic
396C22×C4C2×Q8×C1111yescharacteristic
397C22×C4C11×#4111yescharacteristic
398C22×C4C11×#4111yescharacteristic
399C22×C4C11×#4111yescharacteristic
400C22×C4C11×#4111yescharacteristic
401C22×C4C11×#4111yescharacteristic
402C22×C4C11×#4111yescharacteristic
403C22×C4C11×#4111yescharacteristic
404C22×C4C11×#4111yescharacteristic
405M16—22no—
406M16—22no—
407M16—22no—
408M16—22no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—82no—
434C4⋊C4—82no—
435C4⋊C4C11×C4⋊C412yes—
436C4⋊C4C11×C4⋊C412yes—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—41no—
446C42—41no—
447C42—41no—
448C42—41no—
449C11#1127611yescharacteristic, direct product factor, Sylow
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23C4×D4×C1111yescharacteristic
455C23C11×#12011yescharacteristic
456C23C11×#12111yescharacteristic
457C23C11×C22⋊Q811yescharacteristic
458C23C11×C22⋊Q811yescharacteristic
459C23C11×#12311yescharacteristic
460C23C11×#12411yescharacteristic
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4C2×C11×C4⋊C411yescharacteristic
491C2×C4C11×#11711yescharacteristic
492C2×C4C11×#11711yescharacteristic
493C2×C4C4×D4×C1111yescharacteristic
494C2×C4C4×D4×C1111yescharacteristic
495C2×C4C4×Q8×C1111yescharacteristic
496C2×C4C11×#12111yescharacteristic
497C2×C4C11×#12111yescharacteristic
498C2×C4C11×C22⋊Q811yescharacteristic
499C2×C4C11×C22⋊Q811yescharacteristic
500C2×C4C11×C22⋊Q811yescharacteristic
501C2×C4C11×#12311yescharacteristic
502C2×C4C11×#12311yescharacteristic
503C2×C4C11×#12311yescharacteristic
504C2×C4C11×#12311yescharacteristic
505C2×C4C11×#12411yescharacteristic
506C2×C4C11×#12411yescharacteristic
507C2×C4C11×#12411yescharacteristic
508C2×C4C11×#12511yescharacteristic
509C2×C4C11×#12511yescharacteristic
510C2×C4C11×#12511yescharacteristic
511C2×C4C11×#12511yescharacteristic
512C2×C4C11×#12511yescharacteristic
513C2×C4C11×#12611yescharacteristic
514C2×C4C11×#12611yescharacteristic
515C2×C4C11×#12611yescharacteristic
516C2×C4C11×#12611yescharacteristic
517C2×C4C11×C4⋊Q811yescharacteristic
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22C11×#38511yescharacteristic
533C22C11×#38711yescharacteristic
534C22C11×#38811yescharacteristic
535C22C11×#39311yescharacteristic
536C22C11×#39411yescharacteristic
537C22C11×#39811yescharacteristic
538C22C11×#40011yescharacteristic
539C22C11×#45311yescharacteristic
540C22C11×#45411yescharacteristic
541C22C11×#45511yescharacteristic
542C22C11×#45611yescharacteristic
543C4—44no—
544C4—42no—
545C4—42no—
546C4—82no—
547C4—82no—
548C4—81no—
549C4—81no—
550C4C11×#38211yescharacteristic
551C4C11×#38711yescharacteristic
552C4C11×#38811yescharacteristic
553C4C11×#38911yescharacteristic
554C4C11×#39711yescharacteristic
555C4C11×#39811yescharacteristic
556C4C11×#40011yescharacteristic
557C4C11×#40011yescharacteristic
558C2—21no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2C11×#144211yescharacteristic
563C2C11×#185911yescharacteristic
564C2C11×#186011yescharacteristic
565C2C11×#202711yescharacteristic
566C2C11×#202811yescharacteristic
567C2C11×#203711yescharacteristic
568C2C11×#203811yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
27. C11×#339C4semidirect
85. #11276C11direct (N × H)
262. #339C4×C11semidirect
449. C11#11276direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23172
C2×C11×#3432
C11×#17362
C2×C11×#3392
C11×C4⋊#952
#1127611