Finite Group Databasebeta

← C11×#21291 #14598484

Subgroups — C11×#21291 #14598484

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#440C211yesmaximal, characteristic
2C11×#2320C211yesmaximal, characteristic, complemented
3C11×#2319C211yesmaximal, characteristic
4C11×#1973C211yesmaximal, characteristic
5C11×#1968C211yesmaximal, characteristic
6C11×#1943C211yesmaximal, characteristic, complemented
7C11×#1942C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic
9C11×#1935C211yesmaximal, characteristic, complemented
10C11×#1934C211yesmaximal, characteristic
11C11×#1933C211yesmaximal, characteristic, complemented
12C11×#1776C211yesmaximal, characteristic, complemented
13C4×C11×#103C211yesmaximal, characteristic, complemented
14C4×C11×#102C211yesmaximal, characteristic
15C11×#1726C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#440C418yescomplemented
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×C11×#97C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C2×C4×C8×C11C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#387—21no—
46C11×#387—21no—
47C11×#383—21no—
48C11×#382—21no—
49C11×#381—21no—
50C11×#380—21no—
51C4×C11×C4⋊C4C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#376C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16C2×C414yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11C2×C414yes—
72C4×D4×C11—22no—
73C4×D4×C11C2×C414yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C11×#107—22no—
97C11×#107C2×C414yes—
98C11×#106—22no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103C2×C414yes—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102C2×C414yes—
105C11×#97—22no—
106C11×#97—22no—
107C11×#97C2×C414yes—
108C4×C8×C11—22no—
109C4×C8×C11—22no—
110C4×C8×C11—22no—
111C11×#95—21no—
112C11×#95—21no—
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×#95D411yescharacteristic
122C11×#95D411yescharacteristic
123C11×#95D411yescharacteristic
124C11×#95D411yescharacteristic
125#21291C1111yesmaximal, characteristic, direct product factor, Sylow
126C24×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C22×C412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—81no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C11×SD16—28no—
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×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11#4112yes—
166C2×C8×C11#4112yes—
167C2×C8×C11#4112yes—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—24no—
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—21no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C22×C412yes—
185C11×C4⋊C4C22×C412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—81no—
188C11×C22⋊C4—81no—
189C11×C22⋊C4—81no—
190C11×C22⋊C4—81no—
191C42×C11—24no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—81no—
197C42×C11—81no—
198C42×C11C22×C412yes—
199C42×C11#4112yes—
200C2×#440C2×C1111yescharacteristic
201#2320C2×C1111yescharacteristic, complemented
202#2319C2×C1111yescharacteristic
203#1973C2×C1111yescharacteristic
204#1968C2×C1111yescharacteristic
205#1943C2×C1111yescharacteristic, complemented
206#1942C2×C1111yescharacteristic, complemented
207#1936C2×C1111yescharacteristic
208#1935C2×C1111yescharacteristic, complemented
209#1934C2×C1111yescharacteristic
210#1933C2×C1111yescharacteristic, complemented
211#1776C2×C1111yescharacteristic, complemented
212C4×#103C2×C1111yescharacteristic, complemented
213C4×#102C2×C1111yescharacteristic
214#1726C2×C1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—41no—
230D4×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
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—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
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—84no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C4×D412yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—22no—
280C8×C11#11714yes—
281C22×SD16C22×C1111yescharacteristic
282C2×C4×Q8C22×C1111yescharacteristic
283C2×C4×D4C22×C1111yescharacteristic
284#440C4×C1118yescomplemented
285C2×#107C22×C1111yescharacteristic
286C2×#107C22×C1111yescharacteristic
287C2×#106C22×C1111yescharacteristic
288C2×#103C22×C1111yescharacteristic
289C2×#103C22×C1111yescharacteristic
290C2×#103C22×C1111yescharacteristic
291C2×#102C22×C1111yescharacteristic
292C2×#102C22×C1111yescharacteristic
293C2×#102C22×C1111yescharacteristic
294C2×#97C22×C1111yescharacteristic
295C2×#97C22×C1111yescharacteristic
296C2×#97C22×C1111yescharacteristic
297C2×C4×C8C22×C1111yescharacteristic
298C2×C4×C8C22×C1111yescharacteristic
299C2×C4×C8C22×C1111yescharacteristic
300#391C22×C1111yescharacteristic
301#391C22×C1111yescharacteristic
302#390C22×C1111yescharacteristic
303#390C22×C1111yescharacteristic
304#389C22×C1111yescharacteristic
305#389C22×C1111yescharacteristic
306#389C22×C1111yescharacteristic
307#389C22×C1111yescharacteristic
308#388—21no—
309#388—21no—
310#387—21no—
311#387—21no—
312#383—21no—
313#382—21no—
314#381—21no—
315#380—21no—
316C4×C4⋊C4C22×C1111yescharacteristic
317C4×C4⋊C4C22×C1111yescharacteristic
318#376C22×C1111yescharacteristic
319#340C22×C1111yescharacteristic
320#340C22×C1111yescharacteristic
321#340C22×C1111yescharacteristic
322#340C22×C1111yescharacteristic
323#340C22×C1111yescharacteristic
324#340C22×C1111yescharacteristic
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#53211yescharacteristic
334C22×C11#53211yescharacteristic
335C22×C11#57611yescharacteristic
336C22×C11#57711yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×#11711yescharacteristic
353C4×C11C4×#4111yescharacteristic
354C4×C11#52911yescharacteristic
355C4×C11#52911yescharacteristic
356C22×Q8C23×C1111yescharacteristic
357C22×D4C23×C1111yescharacteristic
358C23×C4—21no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16C2×C4×C1114yes—
362C22×C8C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366C4×Q8—22no—
367C4×Q8C2×C4×C1114yes—
368C4×D4—22no—
369C4×D4C2×C4×C1114yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1111yescharacteristic
377C2×C4⋊C4C23×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C4⋊C4C23×C1111yescharacteristic
380C2×C4⋊C4C23×C1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C1111yescharacteristic
390C2×C42C23×C1111yescharacteristic
391C2×C42C23×C1111yescharacteristic
392#107—22no—
393#107C2×C4×C1114yes—
394#106—22no—
395#103—22no—
396#103—22no—
397#103C2×C4×C1114yes—
398#102—22no—
399#102—22no—
400#102C2×C4×C1114yes—
401#97—22no—
402#97—22no—
403#97C2×C4×C1114yes—
404C4×C8—22no—
405C4×C8—22no—
406C4×C8—22no—
407#95—21no—
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#95D4×C1111yescharacteristic
418#95D4×C1111yescharacteristic
419#95D4×C1111yescharacteristic
420#95D4×C1111yescharacteristic
421C2×C11—82no—
422C2×C11#229311yescharacteristic
423C2×C11#294611yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11#317411yescharacteristic
426C2×C11#317511yescharacteristic
427C2×C11#317811yescharacteristic
428C2×C11#317911yescharacteristic
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×C4×C1112yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×C4×C1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C24×C1111yescharacteristic
459SD16—28no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8C22×C4×C1112yes—
467C2×C8C22×C4×C1112yes—
468C2×C8C11×#4112yes—
469C2×C8C11×#4112yes—
470C2×C8C11×#4112yes—
471C2×C8C11×#4112yes—
472C4⋊C4—24no—
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—21no—
482C4⋊C4—21no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4C22×C4×C1112yes—
488C4⋊C4C22×C4×C1112yes—
489C22⋊C4—24no—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C42—24no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—81no—
501C42C22×C4×C1112yes—
502C42C11×#4112yes—
503C11#2129111yescharacteristic, direct product factor, Sylow
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C1111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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×C4—41no—
557C2×C4—84no—
558C2×C4C4×D4×C1112yes—
559C2×C4C4×D4×C1112yes—
560C2×C4C23×C4×C1111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C2×C4C2×C11×#4111yescharacteristic
563C2×C4C2×C11×#4111yescharacteristic
564C2×C4C2×C11×#4111yescharacteristic
565C2×C4C2×C11×#4111yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8C11×#11714yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×D4×C1111yescharacteristic
578C22C11×#53211yescharacteristic
579C22C11×#53211yescharacteristic
580C22C11×#57611yescharacteristic
581C22C11×#57711yescharacteristic
582C22C11×#57711yescharacteristic
583C22C11×#57811yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×C11×#11711yescharacteristic
598C4C4×C11×#4111yescharacteristic
599C4C11×#52911yescharacteristic
600C4C11×#52911yescharacteristic
601C2—82no—
602C2C11×#229311yescharacteristic
603C2C11×#294611yescharacteristic
604C2C11×#294711yescharacteristic
605C2C11×#317411yescharacteristic
606C2C11×#317511yescharacteristic
607C2C11×#317811yescharacteristic
608C2C11×#317911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2320C2semidirect
6. C11×#1943C2semidirect
7. C11×#1942C2semidirect
9. C11×#1935C2semidirect
11. C11×#1933C2semidirect
12. C11×#1776C2semidirect
13. C4×C11×#103C2semidirect
15. C11×#1726C2semidirect
19. C11×#440C4semidirect
125. #21291C11direct (N × H)
201. #2320C2×C11semidirect
205. #1943C2×C11semidirect
206. #1942C2×C11semidirect
208. #1935C2×C11semidirect
210. #1933C2×C11semidirect
211. #1776C2×C11semidirect
212. C4×#103C2×C11semidirect
214. #1726C2×C11semidirect
284. #440C4×C11semidirect
503. C11#21291direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4402
C11×#23202
C11×#23192
C11×#19732
C11×#19682
C11×#19432
C11×#19422
C11×#19362
C11×#19352
C11×#19342
C11×#19332
C11×#17762
C4×C11×#1032
C4×C11×#1022
C11×#17262
#2129111