Finite Group Databasebeta

← C11×#11217 #14588410

Subgroups — C11×#11217 #14588410

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#428C211yesmaximal, characteristic
2C11×#2317C211yesmaximal, characteristic
3C2×C11×#343C211yesmaximal, 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×#428—22no—
16C11×#428C414yescomplemented
17C2×C11×#107—21no—
18C2×C11×#106—21no—
19C11×#389—21no—
20C11×#389—21no—
21C11×#385—22no—
22C11×#384—21no—
23C11×#382—21no—
24C2×C11×#95—22no—
25C11×#343—22no—
26C11×#340—21no—
27C11×#340—21no—
28C11×#339—22no—
29C11×#339—22no—
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11D412yes—
33C23×C4×C11C2311yescharacteristic
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—
44C2×C11×M16Q812yes—
45C2×C11×M16Q812yes—
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C11×#117—21no—
49C11×#117—21no—
50C11×#117—21no—
51C11×#117—21no—
52C11×#117—21no—
53C11×#117—21no—
54C11×#117C2×C412yes—
55C11×#117D412yes—
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—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4C2×C412yes—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11Q812yes—
84C11×#107—24no—
85C11×#106—24no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—44no—
89#11217C1111yesmaximal, characteristic, direct product factor, Sylow
90C24×C11C2×D411yescharacteristic
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×Q811yescharacteristic
118C22×C4×C11C2×Q811yescharacteristic
119C22×C4×C11C2×Q811yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C11×M16—22no—
127C11×M16—22no—
128C11×M16—22no—
129C11×M16—22no—
130C11×M16—22no—
131C11×M16—41no—
132C11×M16—41no—
133C11×M16C4⋊C414yescomplemented
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—41no—
139C2×C8×C11—41no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—82no—
155C11×C4⋊C4—82no—
156C11×C4⋊C4C22⋊C412yes—
157C11×C4⋊C4C22⋊C412yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C42×C11—22no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—41no—
167C42×C11—41no—
168C42×C11—41no—
169C42×C11—41no—
170C2×#428C2×C1111yescharacteristic
171#2317C2×C1111yescharacteristic
172C2×#343C2×C1111yescharacteristic
173#1736C2×C1111yescharacteristic
174C2×#339C2×C1111yescharacteristic
175C2×#339C2×C1111yescharacteristic
176C4⋊#95C2×C1111yescharacteristic
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11C4×D411yescharacteristic
182C23×C11#12011yescharacteristic
183C23×C11#12111yescharacteristic
184C23×C11#12111yescharacteristic
185C23×C11C22⋊Q811yescharacteristic
186C23×C11#12311yescharacteristic
187C23×C11C4⋊Q811yescharacteristic
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—82no—
214C2×C4×C11—81no—
215C2×C4×C11—81no—
216C2×C4×C11—82no—
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C4⋊C411yescharacteristic
219C2×C4×C11#11711yescharacteristic
220C2×C4×C11C4×D411yescharacteristic
221C2×C4×C11C4×Q811yescharacteristic
222C2×C4×C11C4×Q811yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11C22⋊Q811yescharacteristic
228C2×C4×C11C22⋊Q811yescharacteristic
229C2×C4×C11C22⋊Q811yescharacteristic
230C2×C4×C11C22⋊Q811yescharacteristic
231C2×C4×C11C22⋊Q811yescharacteristic
232C2×C4×C11C22⋊Q811yescharacteristic
233C2×C4×C11C22⋊Q811yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12411yescharacteristic
237C2×C4×C11#12511yescharacteristic
238C2×C4×C11#12511yescharacteristic
239C2×C4×C11#12511yescharacteristic
240C2×C4×C11#12511yescharacteristic
241C2×C4×C11#12611yescharacteristic
242C2×C4×C11#12611yescharacteristic
243C2×C4×C11C4⋊Q811yescharacteristic
244C2×C4×C11C4⋊Q811yescharacteristic
245C8×C11—24no—
246C8×C11—42no—
247C22×M16C22×C1111yescharacteristic
248C22×M16C22×C1111yescharacteristic
249C2×#117C22×C1111yescharacteristic
250C2×#117C22×C1111yescharacteristic
251C22×C4⋊C4C22×C1111yescharacteristic
252C22×C4⋊C4C22×C1111yescharacteristic
253C22×C42C22×C1111yescharacteristic
254#428—22no—
255#428C4×C1114yescomplemented
256C2×#107—21no—
257C2×#106—21no—
258#389—21no—
259#389—21no—
260#385—22no—
261#384—21no—
262#382—21no—
263C2×#95—22no—
264#343—22no—
265#340—21no—
266#340—21no—
267#339—22no—
268#339—22no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11#38611yescharacteristic
282C22×C11#38711yescharacteristic
283C22×C11#38911yescharacteristic
284C22×C11#39411yescharacteristic
285C22×C11#39511yescharacteristic
286C22×C11#39611yescharacteristic
287C22×C11#39811yescharacteristic
288C22×C11#45311yescharacteristic
289C22×C11#45411yescharacteristic
290C22×C11#45511yescharacteristic
291C22×C11#45611yescharacteristic
292C4×C11—44no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11—81no—
299C4×C11#38011yescharacteristic
300C4×C11#38711yescharacteristic
301C4×C11#38911yescharacteristic
302C4×C11#39111yescharacteristic
303C4×C11#39611yescharacteristic
304C4×C11#39811yescharacteristic
305C4×C11#39811yescharacteristic
306C4×C11#40011yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4D4×C1112yes—
310C23×C4C23×C1111yescharacteristic
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16—21no—
316C2×M16—21no—
317C2×M16—21no—
318C2×M16—21no—
319C2×M16C2×C4×C1112yes—
320C2×M16D4×C1112yes—
321C2×M16Q8×C1112yes—
322C2×M16Q8×C1112yes—
323C22×C8—21no—
324C22×C8—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117C2×C4×C1112yes—
332#117D4×C1112yes—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4C2×C4×C1112yes—
347C2×C4⋊C4D4×C1111yescharacteristic
348C2×C4⋊C4D4×C1111yescharacteristic
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4D4×C1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42Q8×C1112yes—
361#107—24no—
362#106—24no—
363#95—22no—
364#95—22no—
365#95—44no—
366C2×C11—21no—
367C2×C11—21no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11#144111yescharacteristic
371C2×C11#188211yescharacteristic
372C2×C11#188311yescharacteristic
373C2×C11#203711yescharacteristic
374C2×C11#203811yescharacteristic
375C2×C11#206011yescharacteristic
376C2×C11#206111yescharacteristic
377C24C2×D4×C1111yescharacteristic
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4C22×C4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×Q8×C1111yescharacteristic
405C22×C4C2×Q8×C1111yescharacteristic
406C22×C4C2×Q8×C1111yescharacteristic
407C22×C4C11×#4111yescharacteristic
408C22×C4C11×#4111yescharacteristic
409C22×C4C11×#4111yescharacteristic
410C22×C4C11×#4111yescharacteristic
411C22×C4C11×#4111yescharacteristic
412C22×C4C11×#4111yescharacteristic
413M16—22no—
414M16—22no—
415M16—22no—
416M16—22no—
417M16—22no—
418M16—41no—
419M16—41no—
420M16C11×C4⋊C414yescomplemented
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—41no—
426C2×C8—41no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—82no—
442C4⋊C4—82no—
443C4⋊C4C11×C22⋊C412yes—
444C4⋊C4C11×C22⋊C412yes—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C42—22no—
450C42—22no—
451C42—22no—
452C42—22no—
453C42—41no—
454C42—41no—
455C42—41no—
456C42—41no—
457C11#1121711yescharacteristic, direct product factor, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23C4×D4×C1111yescharacteristic
463C23C11×#12011yescharacteristic
464C23C11×#12111yescharacteristic
465C23C11×#12111yescharacteristic
466C23C11×C22⋊Q811yescharacteristic
467C23C11×#12311yescharacteristic
468C23C11×C4⋊Q811yescharacteristic
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—82no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4C2×C11×C22⋊C411yescharacteristic
499C2×C4C2×C11×C4⋊C411yescharacteristic
500C2×C4C11×#11711yescharacteristic
501C2×C4C4×D4×C1111yescharacteristic
502C2×C4C4×Q8×C1111yescharacteristic
503C2×C4C4×Q8×C1111yescharacteristic
504C2×C4C11×#12111yescharacteristic
505C2×C4C11×#12111yescharacteristic
506C2×C4C11×#12111yescharacteristic
507C2×C4C11×#12111yescharacteristic
508C2×C4C11×C22⋊Q811yescharacteristic
509C2×C4C11×C22⋊Q811yescharacteristic
510C2×C4C11×C22⋊Q811yescharacteristic
511C2×C4C11×C22⋊Q811yescharacteristic
512C2×C4C11×C22⋊Q811yescharacteristic
513C2×C4C11×C22⋊Q811yescharacteristic
514C2×C4C11×C22⋊Q811yescharacteristic
515C2×C4C11×#12311yescharacteristic
516C2×C4C11×#12311yescharacteristic
517C2×C4C11×#12411yescharacteristic
518C2×C4C11×#12511yescharacteristic
519C2×C4C11×#12511yescharacteristic
520C2×C4C11×#12511yescharacteristic
521C2×C4C11×#12511yescharacteristic
522C2×C4C11×#12611yescharacteristic
523C2×C4C11×#12611yescharacteristic
524C2×C4C11×C4⋊Q811yescharacteristic
525C2×C4C11×C4⋊Q811yescharacteristic
526C8—24no—
527C8—42no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22C11×#38611yescharacteristic
541C22C11×#38711yescharacteristic
542C22C11×#38911yescharacteristic
543C22C11×#39411yescharacteristic
544C22C11×#39511yescharacteristic
545C22C11×#39611yescharacteristic
546C22C11×#39811yescharacteristic
547C22C11×#45311yescharacteristic
548C22C11×#45411yescharacteristic
549C22C11×#45511yescharacteristic
550C22C11×#45611yescharacteristic
551C4—44no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—82no—
556C4—81no—
557C4—81no—
558C4C11×#38011yescharacteristic
559C4C11×#38711yescharacteristic
560C4C11×#38911yescharacteristic
561C4C11×#39111yescharacteristic
562C4C11×#39611yescharacteristic
563C4C11×#39811yescharacteristic
564C4C11×#39811yescharacteristic
565C4C11×#40011yescharacteristic
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2C11×#144111yescharacteristic
571C2C11×#188211yescharacteristic
572C2C11×#188311yescharacteristic
573C2C11×#203711yescharacteristic
574C2C11×#203811yescharacteristic
575C2C11×#206011yescharacteristic
576C2C11×#206111yescharacteristic
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
16. C11×#428C4semidirect
89. #11217C11direct (N × H)
133. C11×M16C4⋊C4semidirect
255. #428C4×C11semidirect
420. M16C11×C4⋊C4semidirect
457. C11#11217direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4282
C11×#23172
C2×C11×#3432
C11×#17362
C2×C11×#3392
C11×C4⋊#952
#1121711