Finite Group Databasebeta

← C11×#24850 #14602043

Subgroups — C11×#24850 #14602043

Order 2816.

788 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#479C211yesmaximal, characteristic, complemented
2C2×C11×#424C211yesmaximal, characteristic
3C11×#2629C211yesmaximal, characteristic
4C11×#2323C211yesmaximal, characteristic
5C11×#2088C211yesmaximal, characteristic, complemented
6C11×#2086C211yesmaximal, characteristic, complemented
7C11×#2068C211yesmaximal, characteristic, complemented
8C11×#2068C211yesmaximal, characteristic, complemented
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1947C211yesmaximal, characteristic, complemented
11C11×#1894C211yesmaximal, characteristic
12C11×#1892C211yesmaximal, characteristic
13C11×#1809C211yesmaximal, characteristic
14C11×#1808C211yesmaximal, characteristic
15C11×#1803C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#479—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C11×#424—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C11×#398—21no—
37C11×#398—21no—
38C11×#396—21no—
39C11×#396—21no—
40C11×#391C2211yescharacteristic
41C11×#389—21no—
42C11×#389C2211yescharacteristic
43C11×#389C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#388—21no—
46C11×#388—21no—
47C11×#387—21no—
48C11×#384C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C11×#380C2211yescharacteristic
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—41no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#125—22no—
74C11×#125—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8Q814yes—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C11×#117—22no—
80C11×#117—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C11×#107—22no—
110C11×#107—41no—
111C11×#107—41no—
112C11×#106—22no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8D414yes—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—41no—
120C11×#103—41no—
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130#24850C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11C2×D411yescharacteristic
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×Q812yes—
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×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×Q812yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C11×M16—44no—
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—44no—
170C2×C8×C11C2×D412yes—
171C2×C8×C11C2×D412yes—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
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—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—81no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4—81no—
194C11×C4⋊C4—81no—
195C11×C4⋊C4—81no—
196C11×C4⋊C4C2×Q812yes—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—81no—
201C11×C22⋊C4—81no—
202C11×C22⋊C4—81no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—42no—
206C42×C11—81no—
207C42×C11C2×D412yes—
208C42×C11#4112yes—
209C2×#479C2×C1111yescharacteristic, complemented
210C2×#424C2×C1111yescharacteristic
211#2629C2×C1111yescharacteristic
212#2323C2×C1111yescharacteristic
213#2088C2×C1111yescharacteristic, complemented
214#2086C2×C1111yescharacteristic, complemented
215#2068C2×C1111yescharacteristic, complemented
216#2068C2×C1111yescharacteristic, complemented
217#1989C2×C1111yescharacteristic, complemented
218#1947C2×C1111yescharacteristic, complemented
219#1894C2×C1111yescharacteristic
220#1892C2×C1111yescharacteristic
221#1809C2×C1111yescharacteristic
222#1808C2×C1111yescharacteristic
223#1803C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11C22⋊Q812yes—
231C23×C11C22×D411yescharacteristic
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
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—41no—
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11C22⋊Q812yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C8×C11—22no—
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
289C22×M16C22×C1111yescharacteristic
290C23×C8C22×C1111yescharacteristic
291C2×#125C22×C1111yescharacteristic
292C2×C22⋊Q8C22×C1111yescharacteristic
293C2×C4×Q8C22×C1111yescharacteristic
294C2×#117C22×C1111yescharacteristic
295#479—24no—
296C2×#107C22×C1111yescharacteristic
297C2×#107C22×C1111yescharacteristic
298C2×#107C22×C1111yescharacteristic
299C2×#106C22×C1111yescharacteristic
300#424—24no—
301C2×C4⋊C8C22×C1111yescharacteristic
302C2×C4⋊C8C22×C1111yescharacteristic
303C2×C4⋊C8C22×C1111yescharacteristic
304C2×C4⋊C8C22×C1111yescharacteristic
305C2×#103C22×C1111yescharacteristic
306C2×#103C22×C1111yescharacteristic
307C2×#103C22×C1111yescharacteristic
308C2×#103C22×C1111yescharacteristic
309#398—21no—
310#398—21no—
311#396—21no—
312#396—21no—
313#391C22×C1111yescharacteristic
314#389—21no—
315#389C22×C1111yescharacteristic
316#389C22×C1111yescharacteristic
317#389C22×C1111yescharacteristic
318#388—21no—
319#388—21no—
320#387—21no—
321#384C22×C1111yescharacteristic
322#380C22×C1111yescharacteristic
323#380C22×C1111yescharacteristic
324#380C22×C1111yescharacteristic
325C4×C4⋊C4C22×C1111yescharacteristic
326#340C22×C1111yescharacteristic
327#340C22×C1111yescharacteristic
328#340C22×C1111yescharacteristic
329#340C22×C1111yescharacteristic
330#340C22×C1111yescharacteristic
331#340C22×C1111yescharacteristic
332#340C22×C1111yescharacteristic
333#340C22×C1111yescharacteristic
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×#12111yescharacteristic
342C22×C11C2×C22⋊Q811yescharacteristic
343C22×C11#53711yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57811yescharacteristic
347C22×C11#57811yescharacteristic
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11#54611yescharacteristic
362C4×C11D4×Q811yescharacteristic
363C4×C11#55211yescharacteristic
364C4×C11#55411yescharacteristic
365C22×Q8C23×C1111yescharacteristic
366C23×C4C23×C1111yescharacteristic
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—41no—
370C22×C8—22no—
371C22×C8—22no—
372C22×C8—41no—
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C22×C8C23×C1111yescharacteristic
377#125—22no—
378#125—22no—
379C22⋊Q8—22no—
380C22⋊Q8Q8×C1114yes—
381C4×Q8—22no—
382C4×Q8—22no—
383#117—22no—
384#117—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C1111yescharacteristic
395C2×C4⋊C4D4×C1111yescharacteristic
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C4⋊C4C23×C1111yescharacteristic
401C2×C4⋊C4C23×C1111yescharacteristic
402C2×C4⋊C4C23×C1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4D4×C1111yescharacteristic
408C2×C22⋊C4D4×C1111yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C1111yescharacteristic
412C2×C42C23×C1111yescharacteristic
413#107—22no—
414#107—41no—
415#107—41no—
416#106—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8D4×C1114yes—
421#103—22no—
422#103—22no—
423#103—41no—
424#103—41no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434C2×C11—42no—
435C2×C11#241711yescharacteristic
436C2×C11#306111yescharacteristic
437C2×C11#306311yescharacteristic
438C2×C11#308211yescharacteristic
439C2×C11#308311yescharacteristic
440C2×C11#325711yescharacteristic
441C2×C11#326111yescharacteristic
442C24C2×D4×C1111yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×Q8×C1112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×Q8×C1112yes—
467C22×C4C11×#4112yes—
468C22×C4C24×C1111yescharacteristic
469M16—44no—
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×C8—21no—
480C2×C8—44no—
481C2×C8C2×D4×C1112yes—
482C2×C8C2×D4×C1112yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4C2×Q8×C1112yes—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—81no—
518C42C2×D4×C1112yes—
519C42C11×#4112yes—
520C11#2485011yescharacteristic, direct product factor, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C11×C22⋊Q812yes—
528C23C22×D4×C1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
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×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4C11×#12112yes—
574C2×C4C11×#12112yes—
575C2×C4C11×C22⋊Q812yes—
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C22×Q8×C1111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C2×C4C11×2−1+411yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×C11×#12111yescharacteristic
594C22C2×C11×C22⋊Q811yescharacteristic
595C22C11×#53711yescharacteristic
596C22C11×#57611yescharacteristic
597C22C11×#57711yescharacteristic
598C22C11×#57811yescharacteristic
599C22C11×#57811yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—42no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C11×#54611yescharacteristic
614C4D4×Q8×C1111yescharacteristic
615C4C11×#55211yescharacteristic
616C4C11×#55411yescharacteristic
617C2—42no—
618C2C11×#241711yescharacteristic
619C2C11×#306111yescharacteristic
620C2C11×#306311yescharacteristic
621C2C11×#308211yescharacteristic
622C2C11×#308311yescharacteristic
623C2C11×#325711yescharacteristic
624C2C11×#326111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#479C2semidirect
5. C11×#2088C2semidirect
6. C11×#2086C2semidirect
7. C11×#2068C2semidirect
8. C11×#2068C2semidirect
9. C11×#1989C2semidirect
10. C11×#1947C2semidirect
15. C11×#1803C2semidirect
130. #24850C11direct (N × H)
209. C2×#479C2×C11semidirect
213. #2088C2×C11semidirect
214. #2086C2×C11semidirect
215. #2068C2×C11semidirect
216. #2068C2×C11semidirect
217. #1989C2×C11semidirect
218. #1947C2×C11semidirect
223. #1803C2×C11semidirect
520. C11#24850direct (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×C11×#4242
C11×#26292
C11×#23232
C11×#20882
C11×#20862
C11×#20682
C11×#19892
C11×#19472
C11×#18942
C11×#18922
C11×#18092
C11×#18082
C11×#18032
#2485011