Finite Group Databasebeta

← C11×#24685 #14601878

Subgroups — C11×#24685 #14601878

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#479C211yesmaximal, characteristic, complemented
2C2×C4×C11×SD16C211yesmaximal, characteristic
3C11×#2566C211yesmaximal, characteristic
4C11×#2356C211yesmaximal, characteristic, complemented
5C11×#2074C211yesmaximal, characteristic, complemented
6C11×#2072C211yesmaximal, characteristic, complemented
7C11×#2055C211yesmaximal, characteristic
8C11×#2055C211yesmaximal, characteristic
9C11×#1991C211yesmaximal, characteristic, complemented
10C11×#1949C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C11×#1939C211yesmaximal, characteristic, complemented
13C11×#1926C211yesmaximal, characteristic
14C11×#1925C211yesmaximal, characteristic
15C11×#1804C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#479—24no—
21C4×C11×SD16—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—21no—
36C11×#396—21no—
37C11×#391C2211yescharacteristic
38C11×#391C2211yescharacteristic
39C11×#390C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#387—21no—
42C11×#387—21no—
43C11×#385—21no—
44C11×#385—21no—
45C11×#384C2211yescharacteristic
46C11×#383—21no—
47C11×#382C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C11×#376—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C2×C11×SD16—22no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#125—22no—
72C11×#125—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D414yes—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
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⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#106—22no—
103C11×#106—22no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8—22no—
106C11×C4⋊C8—22no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C4×C8×C11—22no—
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#24685C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11#4112yes—
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×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C11×SD16—28no—
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—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11#4112yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
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—41no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—81no—
193C11×C22⋊C4—81no—
194C42×C11—24no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—42no—
200C42×C11—42no—
201C42×C11C2×D412yes—
202C42×C11#4112yes—
203C2×#479C2×C1111yescharacteristic, complemented
204C2×C4×SD16C2×C1111yescharacteristic
205#2566C2×C1111yescharacteristic
206#2356C2×C1111yescharacteristic, complemented
207#2074C2×C1111yescharacteristic, complemented
208#2072C2×C1111yescharacteristic, complemented
209#2055C2×C1111yescharacteristic
210#2055C2×C1111yescharacteristic
211#1991C2×C1111yescharacteristic, complemented
212#1949C2×C1111yescharacteristic, complemented
213#1948C2×C1111yescharacteristic, complemented
214#1939C2×C1111yescharacteristic, complemented
215#1926C2×C1111yescharacteristic
216#1925C2×C1111yescharacteristic
217#1804C2×C1111yescharacteristic
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—41no—
233D4×C11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
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—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—41no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#13512yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C8×C11—22no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C22×SD16C22×C1111yescharacteristic
285C2×#125C22×C1111yescharacteristic
286C2×C4×Q8C22×C1111yescharacteristic
287C2×C4×D4C22×C1111yescharacteristic
288#479—24no—
289C4×SD16—24no—
290C2×#107C22×C1111yescharacteristic
291C2×#106C22×C1111yescharacteristic
292C2×#106C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×C4⋊C8C22×C1111yescharacteristic
295C2×C4⋊C8C22×C1111yescharacteristic
296C2×#103C22×C1111yescharacteristic
297C2×#103C22×C1111yescharacteristic
298C2×#103C22×C1111yescharacteristic
299C2×#102C22×C1111yescharacteristic
300C2×#102C22×C1111yescharacteristic
301C2×#102C22×C1111yescharacteristic
302C2×C4×C8C22×C1111yescharacteristic
303#396—21no—
304#396—21no—
305#391C22×C1111yescharacteristic
306#391C22×C1111yescharacteristic
307#390C22×C1111yescharacteristic
308#390C22×C1111yescharacteristic
309#387—21no—
310#387—21no—
311#385—21no—
312#385—21no—
313#384C22×C1111yescharacteristic
314#383—21no—
315#382C22×C1111yescharacteristic
316#382C22×C1111yescharacteristic
317C4×C4⋊C4C22×C1111yescharacteristic
318C4×C4⋊C4C22×C1111yescharacteristic
319C4×C4⋊C4C22×C1111yescharacteristic
320#376—21no—
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328#336C22×C1111yescharacteristic
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11C2×#12111yescharacteristic
337C22×C11#54711yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11C2×#13511yescharacteristic
340C22×C11#57511yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57711yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11#52511yescharacteristic
357C4×C11#53611yescharacteristic
358C4×C11#55211yescharacteristic
359C4×C11#55611yescharacteristic
360C22×Q8C23×C1111yescharacteristic
361C22×D4C23×C1111yescharacteristic
362C23×C4—21no—
363C2×SD16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C22×C8C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1111yescharacteristic
369C22×C8C23×C1111yescharacteristic
370#125—22no—
371#125—22no—
372C4×Q8—22no—
373C4×Q8D4×C1114yes—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C1111yescharacteristic
382C2×C4⋊C4D4×C1111yescharacteristic
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399C2×C42C23×C1111yescharacteristic
400#107—22no—
401#106—22no—
402#106—22no—
403C4⋊C8—22no—
404C4⋊C8—22no—
405C4⋊C8—22no—
406#103—22no—
407#103—22no—
408#103—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412C4×C8—22no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95D4×C1111yescharacteristic
424#95D4×C1111yescharacteristic
425C2×C11—82no—
426C2×C11#241511yescharacteristic
427C2×C11#303511yescharacteristic
428C2×C11#304311yescharacteristic
429C2×C11#333711yescharacteristic
430C2×C11#335111yescharacteristic
431C2×C11#336011yescharacteristic
432C2×C11#337611yescharacteristic
433C24—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×D4×C1112yes—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C11×#4112yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C24×C1111yescharacteristic
463SD16—28no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C11×#4112yes—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
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—41no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4C2×D4×C1112yes—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—42no—
507C42C2×D4×C1112yes—
508C42C11×#4112yes—
509C11#2468511yescharacteristic, direct product factor, Sylow
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×D4×C1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
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×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4C11×#12112yes—
564C2×C4C11×#12112yes—
565C2×C4C11×#13512yes—
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C2×C4C2×C11×#4111yescharacteristic
570C2×C4C11×2−1+411yescharacteristic
571C2×C4C11×2−1+411yescharacteristic
572C8—22no—
573C8—41no—
574C8—41no—
575C8—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×C11×#12111yescharacteristic
584C22C11×#54711yescharacteristic
585C22C11×#54811yescharacteristic
586C22C2×C11×#13511yescharacteristic
587C22C11×#57511yescharacteristic
588C22C11×#57711yescharacteristic
589C22C11×#57711yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C11×#52511yescharacteristic
604C4C11×#53611yescharacteristic
605C4C11×#55211yescharacteristic
606C4C11×#55611yescharacteristic
607C2—82no—
608C2C11×#241511yescharacteristic
609C2C11×#303511yescharacteristic
610C2C11×#304311yescharacteristic
611C2C11×#333711yescharacteristic
612C2C11×#335111yescharacteristic
613C2C11×#336011yescharacteristic
614C2C11×#337611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#479C2semidirect
4. C11×#2356C2semidirect
5. C11×#2074C2semidirect
6. C11×#2072C2semidirect
9. C11×#1991C2semidirect
10. C11×#1949C2semidirect
11. C11×#1948C2semidirect
12. C11×#1939C2semidirect
126. #24685C11direct (N × H)
203. C2×#479C2×C11semidirect
206. #2356C2×C11semidirect
207. #2074C2×C11semidirect
208. #2072C2×C11semidirect
211. #1991C2×C11semidirect
212. #1949C2×C11semidirect
213. #1948C2×C11semidirect
214. #1939C2×C11semidirect
509. C11#24685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4792
C2×C4×C11×SD162
C11×#25662
C11×#23562
C11×#20742
C11×#20722
C11×#20552
C11×#19912
C11×#19492
C11×#19482
C11×#19392
C11×#19262
C11×#19252
C11×#18042
#2468511