Finite Group Databasebeta

← C11×#24611 #14601804

Subgroups — C11×#24611 #14601804

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic
3C11×#2855C211yesmaximal, characteristic
4C11×#2296C211yesmaximal, characteristic
5C11×#2088C211yesmaximal, characteristic, complemented
6C11×#2087C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#1944C211yesmaximal, characteristic, complemented
10C11×#1943C211yesmaximal, characteristic, complemented
11C11×#1935C211yesmaximal, characteristic, complemented
12C11×#1935C211yesmaximal, characteristic, complemented
13C11×#1873C211yesmaximal, characteristic
14C11×#1854C211yesmaximal, characteristic
15C11×#1825C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#485—24no—
21C11×#432—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#391C2211yescharacteristic
38C11×#389C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#387—21no—
45C11×#387—21no—
46C11×#385—21no—
47C11×#385—21no—
48C11×#385—21no—
49C11×#381—21no—
50C11×#380C2211yescharacteristic
51C4×C11×C4⋊C4—21no—
52C4×C11×C4⋊C4—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—22no—
94C2×C42×C11—21no—
95C2×C42×C11—22no—
96C2×C42×C11—21no—
97C2×C42×C11D411yescharacteristic
98C2×C42×C11D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#107—22no—
103C11×#106—22no—
104C11×#106—22no—
105C11×C4⋊C8—22no—
106C11×C4⋊C8—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8D414yes—
113C11×#97—22no—
114C11×#97—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126#24611C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D412yes—
171C2×C8×C11C2×D412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4#4112yes—
192C11×C4⋊C4#4112yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—42no—
196C11×C22⋊C4—42no—
197C42×C11—24no—
198C42×C11—22no—
199C42×C11—22no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—42no—
205C2×#485C2×C1111yescharacteristic
206C2×#432C2×C1111yescharacteristic
207#2855C2×C1111yescharacteristic
208#2296C2×C1111yescharacteristic
209#2088C2×C1111yescharacteristic, complemented
210#2087C2×C1111yescharacteristic, complemented
211#2068C2×C1111yescharacteristic, complemented
212#2066C2×C1111yescharacteristic, complemented
213#1944C2×C1111yescharacteristic, complemented
214#1943C2×C1111yescharacteristic, complemented
215#1935C2×C1111yescharacteristic, complemented
216#1935C2×C1111yescharacteristic, complemented
217#1873C2×C1111yescharacteristic
218#1854C2×C1111yescharacteristic
219#1825C2×C1111yescharacteristic
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11#12112yes—
227C23×C11C22×D411yescharacteristic
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11#12112yes—
276C2×C4×C11#13712yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C8×C11—22no—
284C8×C11—22no—
285C8×C11—41no—
286C8×C11—41no—
287C2×C22⋊Q8C22×C1111yescharacteristic
288C2×#117C22×C1111yescharacteristic
289C2×#117C22×C1111yescharacteristic
290C22×C42C22×C1111yescharacteristic
291#485—24no—
292#432—24no—
293C2×#107C22×C1111yescharacteristic
294C2×#107C22×C1111yescharacteristic
295C2×#106C22×C1111yescharacteristic
296C2×#106C22×C1111yescharacteristic
297C2×C4⋊C8C22×C1111yescharacteristic
298C2×C4⋊C8C22×C1111yescharacteristic
299C2×#103C22×C1111yescharacteristic
300C2×#103C22×C1111yescharacteristic
301C2×#103C22×C1111yescharacteristic
302C2×#103C22×C1111yescharacteristic
303C2×C22⋊C8C22×C1111yescharacteristic
304C2×C22⋊C8C22×C1111yescharacteristic
305C2×#97C22×C1111yescharacteristic
306C2×#97C22×C1111yescharacteristic
307#391C22×C1111yescharacteristic
308#391C22×C1111yescharacteristic
309#389C22×C1111yescharacteristic
310#389C22×C1111yescharacteristic
311#389C22×C1111yescharacteristic
312#389C22×C1111yescharacteristic
313#389C22×C1111yescharacteristic
314#389C22×C1111yescharacteristic
315#387—21no—
316#387—21no—
317#385—21no—
318#385—21no—
319#385—21no—
320#381—21no—
321#380C22×C1111yescharacteristic
322C4×C4⋊C4—21no—
323C4×C4⋊C4—21no—
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#340C22×C1111yescharacteristic
331#340C22×C1111yescharacteristic
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×#12111yescharacteristic
340C22×C11#52511yescharacteristic
341C22×C11#53611yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#54711yescharacteristic
360C4×C11#54711yescharacteristic
361C4×C11#55211yescharacteristic
362C4×C11#55211yescharacteristic
363C22×Q8C23×C1111yescharacteristic
364C23×C4D4×C1111yescharacteristic
365C23×C4D4×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1111yescharacteristic
369C22×C8C23×C1111yescharacteristic
370C22×C8C23×C1111yescharacteristic
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373#117—22no—
374#117—22no—
375#117—22no—
376#117—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—21no—
399C2×C42D4×C1111yescharacteristic
400C2×C42D4×C1111yescharacteristic
401C2×C42C23×C1111yescharacteristic
402C2×C42C23×C1111yescharacteristic
403#107—22no—
404#107—22no—
405#106—22no—
406#106—22no—
407C4⋊C8—22no—
408C4⋊C8—22no—
409#103—22no—
410#103—22no—
411#103—22no—
412#103—22no—
413C22⋊C8—22no—
414C22⋊C8D4×C1114yes—
415#97—22no—
416#97—22no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428C2×C11—42no—
429C2×C11#241311yescharacteristic
430C2×C11#305411yescharacteristic
431C2×C11#305611yescharacteristic
432C2×C11#311111yescharacteristic
433C2×C11#311611yescharacteristic
434C2×C11#323711yescharacteristic
435C2×C11#324011yescharacteristic
436C24C2×D4×C1111yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C11×#4112yes—
468C22×C4C24×C1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8C2×D4×C1112yes—
480C2×C8C2×D4×C1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4C11×#4112yes—
501C4⋊C4C11×#4112yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C42—24no—
507C42—22no—
508C42—22no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—42no—
514C11#2461111yescharacteristic, direct product factor, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C11×#12112yes—
522C23C22×D4×C1111yescharacteristic
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4C11×#12112yes—
571C2×C4C11×#13712yes—
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C2×C11×#4111yescharacteristic
574C2×C4C2×C11×#4111yescharacteristic
575C2×C4C2×C11×#4111yescharacteristic
576C2×C4C11×2−1+411yescharacteristic
577C2×C4C11×2−1+411yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×C11×#12111yescharacteristic
590C22C11×#52511yescharacteristic
591C22C11×#53611yescharacteristic
592C22C2×C11×#13711yescharacteristic
593C22C11×#57511yescharacteristic
594C22C11×#57511yescharacteristic
595C22C11×#57511yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4C11×#54711yescharacteristic
610C4C11×#54711yescharacteristic
611C4C11×#55211yescharacteristic
612C4C11×#55211yescharacteristic
613C2—42no—
614C2C11×#241311yescharacteristic
615C2C11×#305411yescharacteristic
616C2C11×#305611yescharacteristic
617C2C11×#311111yescharacteristic
618C2C11×#311611yescharacteristic
619C2C11×#323711yescharacteristic
620C2C11×#324011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2088C2semidirect
6. C11×#2087C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#1944C2semidirect
10. C11×#1943C2semidirect
11. C11×#1935C2semidirect
12. C11×#1935C2semidirect
126. #24611C11direct (N × H)
209. #2088C2×C11semidirect
210. #2087C2×C11semidirect
211. #2068C2×C11semidirect
212. #2066C2×C11semidirect
213. #1944C2×C11semidirect
214. #1943C2×C11semidirect
215. #1935C2×C11semidirect
216. #1935C2×C11semidirect
514. C11#24611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4322
C11×#28552
C11×#22962
C11×#20882
C11×#20872
C11×#20682
C11×#20662
C11×#19442
C11×#19432
C11×#19352
C11×#18732
C11×#18542
C11×#18252
#2461111