Finite Group Databasebeta

← C11×#24586 #14601779

Subgroups — C11×#24586 #14601779

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic
2C2×C11×#427C211yesmaximal, characteristic
3C11×#2499C211yesmaximal, characteristic
4C11×#2346C211yesmaximal, characteristic
5C11×#2085C211yesmaximal, characteristic, complemented
6C11×#2084C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2066C211yesmaximal, characteristic, complemented
9C11×#1949C211yesmaximal, characteristic, complemented
10C11×#1947C211yesmaximal, characteristic, complemented
11C11×#1928C211yesmaximal, characteristic, complemented
12C11×#1927C211yesmaximal, characteristic, complemented
13C11×#1892C211yesmaximal, characteristic
14C11×#1850C211yesmaximal, characteristic
15C11×#1825C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C11×#485—24no—
21C11×#427—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#397—21no—
36C11×#397—21no—
37C11×#391C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388—21no—
42C11×#388—21no—
43C11×#387—21no—
44C11×#387—21no—
45C11×#384C2211yescharacteristic
46C11×#382—21no—
47C11×#382C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C11×#376—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×#117—22no—
73C11×#117—22no—
74C11×#117—22no—
75C11×#117D414yes—
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⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#107—22no—
101C11×#107—22no—
102C11×#107—22no—
103C11×#106—22no—
104C11×#106—22no—
105C11×#106—22no—
106C11×C4⋊C8—22no—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×C22⋊C8—22no—
113C11×#95—21no—
114C11×#95—21no—
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×#95D411yescharacteristic
125C11×#95D411yescharacteristic
126#24586C1111yesmaximal, 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—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C2×C8×C11—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11#4112yes—
166C2×C8×C11#4112yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
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—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—81no—
192C42×C11—24no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—42no—
198C42×C11—42no—
199C42×C11—42no—
200C2×#485C2×C1111yescharacteristic
201C2×#427C2×C1111yescharacteristic
202#2499C2×C1111yescharacteristic
203#2346C2×C1111yescharacteristic
204#2085C2×C1111yescharacteristic, complemented
205#2084C2×C1111yescharacteristic, complemented
206#2068C2×C1111yescharacteristic, complemented
207#2066C2×C1111yescharacteristic, complemented
208#1949C2×C1111yescharacteristic, complemented
209#1947C2×C1111yescharacteristic, complemented
210#1928C2×C1111yescharacteristic, complemented
211#1927C2×C1111yescharacteristic, complemented
212#1892C2×C1111yescharacteristic
213#1850C2×C1111yescharacteristic
214#1825C2×C1111yescharacteristic
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11#12112yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
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#12112yes—
269C2×C4×C11#13512yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C8×C11—22no—
277C8×C11—22no—
278C8×C11—41no—
279C8×C11—41no—
280C23×C8C22×C1111yescharacteristic
281C2×C22⋊Q8C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C2×#117C22×C1111yescharacteristic
284#485—24no—
285#427—24no—
286C2×#107C22×C1111yescharacteristic
287C2×#107C22×C1111yescharacteristic
288C2×#107C22×C1111yescharacteristic
289C2×#106C22×C1111yescharacteristic
290C2×#106C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×C4⋊C8C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×#103C22×C1111yescharacteristic
295C2×#103C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299#397—21no—
300#397—21no—
301#391C22×C1111yescharacteristic
302#391C22×C1111yescharacteristic
303#389C22×C1111yescharacteristic
304#389C22×C1111yescharacteristic
305#388—21no—
306#388—21no—
307#387—21no—
308#387—21no—
309#384C22×C1111yescharacteristic
310#382—21no—
311#382C22×C1111yescharacteristic
312#380C22×C1111yescharacteristic
313C4×C4⋊C4C22×C1111yescharacteristic
314C4×C4⋊C4C22×C1111yescharacteristic
315C4×C22⋊C4C22×C1111yescharacteristic
316#376—21no—
317#340C22×C1111yescharacteristic
318#340C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#336C22×C1111yescharacteristic
324#336C22×C1111yescharacteristic
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×#12111yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#52511yescharacteristic
353C4×C11#53611yescharacteristic
354C4×C11#55211yescharacteristic
355C4×C11#55211yescharacteristic
356C22×Q8C23×C1111yescharacteristic
357C23×C4C23×C1111yescharacteristic
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8C23×C1111yescharacteristic
362C22×C8C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367#117—22no—
368#117—22no—
369#117—22no—
370#117D4×C1114yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4D4×C1111yescharacteristic
388C2×C22⋊C4D4×C1111yescharacteristic
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C1111yescharacteristic
394C2×C42C23×C1111yescharacteristic
395#107—22no—
396#107—22no—
397#107—22no—
398#106—22no—
399#106—22no—
400#106—22no—
401C4⋊C8—22no—
402C4⋊C8—22no—
403#103—22no—
404#103—22no—
405#103—22no—
406#103—22no—
407C22⋊C8—22no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95D4×C1111yescharacteristic
420#95D4×C1111yescharacteristic
421C2×C11—42no—
422C2×C11#241311yescharacteristic
423C2×C11#303511yescharacteristic
424C2×C11#304611yescharacteristic
425C2×C11#333611yescharacteristic
426C2×C11#334011yescharacteristic
427C2×C11#334811yescharacteristic
428C2×C11#334911yescharacteristic
429C24C2×D4×C1111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450C22×C4C2×D4×C1111yescharacteristic
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1112yes—
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C11×#4112yes—
455C22×C4C24×C1111yescharacteristic
456C2×C8—28no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C11×#4112yes—
468C2×C8C11×#4112yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4C2×D4×C1112yes—
487C4⋊C4C2×D4×C1112yes—
488C22⋊C4—24no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—81no—
494C42—24no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—42no—
501C42—42no—
502C11#2458611yescharacteristic, direct product factor, Sylow
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23C11×#12112yes—
510C23C22×D4×C1111yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
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×C4C11×#12112yes—
557C2×C4C11×#13512yes—
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C2×C11×#4111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C2×C4C11×2−1+411yescharacteristic
563C2×C4C11×2−1+411yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×C11×#12111yescharacteristic
576C22C11×#54711yescharacteristic
577C22C11×#54711yescharacteristic
578C22C2×C11×#13511yescharacteristic
579C22C11×#57511yescharacteristic
580C22C11×#57711yescharacteristic
581C22C11×#57811yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C11×#52511yescharacteristic
596C4C11×#53611yescharacteristic
597C4C11×#55211yescharacteristic
598C4C11×#55211yescharacteristic
599C2—42no—
600C2C11×#241311yescharacteristic
601C2C11×#303511yescharacteristic
602C2C11×#304611yescharacteristic
603C2C11×#333611yescharacteristic
604C2C11×#334011yescharacteristic
605C2C11×#334811yescharacteristic
606C2C11×#334911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
5. C11×#2085C2semidirect
6. C11×#2084C2semidirect
7. C11×#2068C2semidirect
8. C11×#2066C2semidirect
9. C11×#1949C2semidirect
10. C11×#1947C2semidirect
11. C11×#1928C2semidirect
12. C11×#1927C2semidirect
126. #24586C11direct (N × H)
204. #2085C2×C11semidirect
205. #2084C2×C11semidirect
206. #2068C2×C11semidirect
207. #2066C2×C11semidirect
208. #1949C2×C11semidirect
209. #1947C2×C11semidirect
210. #1928C2×C11semidirect
211. #1927C2×C11semidirect
502. C11#24586direct (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×#4272
C11×#24992
C11×#23462
C11×#20852
C11×#20842
C11×#20682
C11×#20662
C11×#19492
C11×#19472
C11×#19282
C11×#19272
C11×#18922
C11×#18502
C11×#18252
#2458611