Finite Group Databasebeta

← C11×#24690 #14601883

Subgroups — C11×#24690 #14601883

Order 2816.

808 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×#478C211yesmaximal, characteristic
2C2×C11×#440C211yesmaximal, characteristic
3C11×#2565C211yesmaximal, characteristic, complemented
4C11×#2354C211yesmaximal, characteristic
5C11×#2073C211yesmaximal, characteristic
6C11×#2071C211yesmaximal, characteristic
7C11×#2055C211yesmaximal, characteristic
8C11×#2055C211yesmaximal, characteristic
9C11×#1992C211yesmaximal, characteristic, complemented
10C11×#1949C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C11×#1940C211yesmaximal, characteristic, complemented
13C11×#1928C211yesmaximal, characteristic, complemented
14C11×#1927C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C11×#478—24no—
22C11×#440—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C11×#398—21no—
37C11×#398—21no—
38C11×#391C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#390C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#388—21no—
43C11×#388—21no—
44C11×#387—21no—
45C11×#387—21no—
46C11×#384C2211yescharacteristic
47C11×#384C2211yescharacteristic
48C11×#382C2211yescharacteristic
49C11×#380—21no—
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
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×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D414yes—
77C11×#117—44no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×#107—22no—
105C11×#107—22no—
106C11×#106—22no—
107C11×C4⋊C8—22no—
108C11×C4⋊C8—22no—
109C11×C4⋊C8—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#102—22no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#97—22no—
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×#95D411yescharacteristic
126C11×#95D411yescharacteristic
127#24690C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C11×SD16—28no—
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—21no—
170C2×C8×C11#4112yes—
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—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—81no—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—81no—
196C11×C22⋊C4—81no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—42no—
202C42×C11—42no—
203C42×C11—42no—
204C42×C11C2×D412yes—
205C42×C11#4112yes—
206C2×#478C2×C1111yescharacteristic
207C2×#440C2×C1111yescharacteristic
208#2565C2×C1111yescharacteristic, complemented
209#2354C2×C1111yescharacteristic
210#2073C2×C1111yescharacteristic
211#2071C2×C1111yescharacteristic
212#2055C2×C1111yescharacteristic
213#2055C2×C1111yescharacteristic
214#1992C2×C1111yescharacteristic, complemented
215#1949C2×C1111yescharacteristic, complemented
216#1947C2×C1111yescharacteristic, complemented
217#1940C2×C1111yescharacteristic, complemented
218#1928C2×C1111yescharacteristic, complemented
219#1927C2×C1111yescharacteristic, complemented
220#1803C2×C1111yescharacteristic, complemented
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—41no—
236D4×C11—41no—
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—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—48no—
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#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11AGL(1,ℤ/8)12yes—
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—41no—
285C8×C11—41no—
286C8×C11—41no—
287C22×SD16C22×C1111yescharacteristic
288C2×#125C22×C1111yescharacteristic
289C2×C4×Q8C22×C1111yescharacteristic
290C2×C4×D4C22×C1111yescharacteristic
291C2×#117—21no—
292#478—24no—
293#440—24no—
294C2×#107C22×C1111yescharacteristic
295C2×#107C22×C1111yescharacteristic
296C2×#106C22×C1111yescharacteristic
297C2×C4⋊C8C22×C1111yescharacteristic
298C2×C4⋊C8C22×C1111yescharacteristic
299C2×C4⋊C8C22×C1111yescharacteristic
300C2×#103C22×C1111yescharacteristic
301C2×#103C22×C1111yescharacteristic
302C2×#103C22×C1111yescharacteristic
303C2×#102C22×C1111yescharacteristic
304C2×#102C22×C1111yescharacteristic
305C2×#102C22×C1111yescharacteristic
306C2×#97C22×C1111yescharacteristic
307#398—21no—
308#398—21no—
309#391C22×C1111yescharacteristic
310#391C22×C1111yescharacteristic
311#390C22×C1111yescharacteristic
312#390C22×C1111yescharacteristic
313#388—21no—
314#388—21no—
315#387—21no—
316#387—21no—
317#384C22×C1111yescharacteristic
318#384C22×C1111yescharacteristic
319#382C22×C1111yescharacteristic
320#380—21no—
321C4×C4⋊C4C22×C1111yescharacteristic
322C4×C4⋊C4C22×C1111yescharacteristic
323C4×C4⋊C4C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325#340C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#336C22×C1111yescharacteristic
331#336C22×C1111yescharacteristic
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11C2×#12111yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11#54811yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57711yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#52511yescharacteristic
360C4×C11#53611yescharacteristic
361C4×C11#55211yescharacteristic
362C4×C11#55611yescharacteristic
363C22×Q8C23×C1111yescharacteristic
364C22×D4C23×C1111yescharacteristic
365C23×C4—21no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C22×C8C23×C1111yescharacteristic
370C22×C8C23×C1111yescharacteristic
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373#125—22no—
374#125—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×D4—22no—
378C4×D4D4×C1114yes—
379#117—44no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4D4×C1111yescharacteristic
388C2×C4⋊C4D4×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C23×C1111yescharacteristic
404C2×C42C23×C1111yescharacteristic
405C2×C42C23×C1111yescharacteristic
406#107—22no—
407#107—22no—
408#106—22no—
409C4⋊C8—22no—
410C4⋊C8—22no—
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—22no—
415#102—22no—
416#102—22no—
417#102—22no—
418#97—22no—
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#95D4×C1111yescharacteristic
428#95D4×C1111yescharacteristic
429C2×C11—82no—
430C2×C11#241511yescharacteristic
431C2×C11#303611yescharacteristic
432C2×C11#304611yescharacteristic
433C2×C11#334311yescharacteristic
434C2×C11#334811yescharacteristic
435C2×C11#336811yescharacteristic
436C2×C11#337711yescharacteristic
437C24—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C11×#4112yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×D4×C1112yes—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C24×C1111yescharacteristic
467SD16—28no—
468C2×C8—21no—
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×C8C11×#4112yes—
480C4⋊C4—22no—
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—41no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—81no—
500C4⋊C4C2×D4×C1112yes—
501C22⋊C4—24no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—42no—
512C42—42no—
513C42C2×D4×C1112yes—
514C42C11×#4112yes—
515C11#2469011yescharacteristic, direct product factor, Sylow
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×D4×C1111yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—48no—
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×C4C11×#12112yes—
570C2×C4C11×#12112yes—
571C2×C4C11×AGL(1,ℤ/8)12yes—
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—41no—
580C8—41no—
581C8—41no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C2×C11×#12111yescharacteristic
590C22C11×#54711yescharacteristic
591C22C11×#54811yescharacteristic
592C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
593C22C11×#57511yescharacteristic
594C22C11×#57711yescharacteristic
595C22C11×#57811yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4C11×#52511yescharacteristic
610C4C11×#53611yescharacteristic
611C4C11×#55211yescharacteristic
612C4C11×#55611yescharacteristic
613C2—82no—
614C2C11×#241511yescharacteristic
615C2C11×#303611yescharacteristic
616C2C11×#304611yescharacteristic
617C2C11×#334311yescharacteristic
618C2C11×#334811yescharacteristic
619C2C11×#336811yescharacteristic
620C2C11×#337711yescharacteristic
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
3. C11×#2565C2semidirect
9. C11×#1992C2semidirect
10. C11×#1949C2semidirect
11. C11×#1947C2semidirect
12. C11×#1940C2semidirect
13. C11×#1928C2semidirect
14. C11×#1927C2semidirect
15. C11×#1803C2semidirect
127. #24690C11direct (N × H)
208. #2565C2×C11semidirect
214. #1992C2×C11semidirect
215. #1949C2×C11semidirect
216. #1947C2×C11semidirect
217. #1940C2×C11semidirect
218. #1928C2×C11semidirect
219. #1927C2×C11semidirect
220. #1803C2×C11semidirect
515. C11#24690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4782
C2×C11×#4402
C11×#25652
C11×#23542
C11×#20732
C11×#20712
C11×#20552
C11×#19922
C11×#19492
C11×#19472
C11×#19402
C11×#19282
C11×#19272
C11×#18032
#2469011