Finite Group Databasebeta

← C11×#24650 #14601843

Subgroups — C11×#24650 #14601843

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2856C211yesmaximal, characteristic, complemented
4C4×C11×#121C211yesmaximal, characteristic, complemented
5C11×#2033C212yesmaximal, complemented
6C11×#1999C212yesmaximal, complemented
7C11×#1982C211yesmaximal, characteristic, complemented
8C11×#1970C212yesmaximal, complemented
9C11×#1947C211yesmaximal, characteristic, complemented
10C11×#1934C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#121—21no—
15C2×C11×#121—21no—
16C2×C11×#121C2211yescharacteristic
17C2×C11×#121C2212yes—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C11×#459—24no—
22C11×#431—24no—
23C2×C11×#107C2212yes—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C4×C8×C11C2212yes—
32C11×#390—21no—
33C11×#390—21no—
34C11×#390C2212yes—
35C11×#390C2211yescharacteristic
36C11×#389C2211yescharacteristic
37C11×#388—21no—
38C11×#386—21no—
39C11×#384C2211yescharacteristic
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×D8—24no—
56C2×C11×D8—24no—
57C2×C11×D8—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C11×#127—22no—
61C11×#127—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—42no—
65C11×#121—42no—
66C11×#121—44no—
67C11×#121—44no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—44no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C11×#107—42no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8D414yescomplemented
96C11×#102—24no—
97C11×#102—24no—
98C11×#102—42no—
99C11×#102—42no—
100C11×C22⋊C8—24no—
101C4×C8×C11—24no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105#24650C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11—22no—
108C24×C11C2×D411yescharacteristic
109C2×D4×C11—24no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11#4112yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
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—22no—
147C22×C4×C11—41no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11D814yescomplemented
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C11×D8—48no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11C2×D414yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—44no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C42×C11C2×D412yes—
190C42×C11#4112yes—
191C2×#459C2×C1111yescharacteristic, complemented
192C2×#431C2×C1111yescharacteristic, complemented
193#2856C2×C1111yescharacteristic, complemented
194C4×#121C2×C1111yescharacteristic, complemented
195#2033C2×C1112yescomplemented
196#1999C2×C1112yescomplemented
197#1982C2×C1111yescharacteristic, complemented
198#1970C2×C1112yescomplemented
199#1947C2×C1111yescharacteristic, complemented
200#1934C2×C1112yescomplemented
201#1802C2×C1111yescharacteristic, complemented
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11C2×D812yes—
223C23×C11C22×D411yescharacteristic
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—48no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—41no—
232D4×C11—42no—
233D4×C11—84no—
234D4×C11—88no—
235D4×C11—84no—
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—28no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—44no—
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—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—84no—
264C2×C4×C11#12112yes—
265C2×C4×C11#12112yes—
266C2×C4×C11C2×D812yes—
267C2×C4×C11C2×D812yes—
268C2×C4×C11#13512yes—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C8×C11—24no—
277C8×C11—42no—
278C22×D8C22×C1112yes—
279C2×#127C22×C1111yescharacteristic
280C2×#121—21no—
281C2×#121—21no—
282C2×#121C22×C1111yescharacteristic
283C2×#121C22×C1112yes—
284C2×C4×D4—21no—
285C2×C4×D4C22×C1111yescharacteristic
286C22×C42C22×C1111yescharacteristic
287#459—24no—
288#431—24no—
289C2×#107C22×C1112yes—
290C2×C4⋊C8C22×C1111yescharacteristic
291C2×C4⋊C8C22×C1111yescharacteristic
292C2×#102C22×C1112yes—
293C2×#102C22×C1112yes—
294C2×#102C22×C1112yes—
295C2×#102C22×C1112yes—
296C2×C22⋊C8C22×C1112yes—
297C2×C4×C8C22×C1112yes—
298#390—21no—
299#390—21no—
300#390C22×C1112yes—
301#390C22×C1111yescharacteristic
302#389C22×C1111yescharacteristic
303#388—21no—
304#386—21no—
305#384C22×C1111yescharacteristic
306#380C22×C1111yescharacteristic
307C4×C4⋊C4C22×C1111yescharacteristic
308C4×C22⋊C4—21no—
309#340C22×C1112yes—
310#340C22×C1112yes—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11C2×#12111yescharacteristic
333C22×C11#52511yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11C22×D811yescharacteristic
336C22×C11C2×#13511yescharacteristic
337C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C11#57511yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—82no—
346C4×C11—81no—
347C4×C11#46614yes—
348C4×C11#54611yescharacteristic
349C4×C11#55011yescharacteristic
350C4×C11#55311yescharacteristic
351C4×C11#55511yescharacteristic
352C22×D4—21no—
353C22×D4—22no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4C23×C1112yes—
357C22×D4C23×C1111yescharacteristic
358C23×C4—21no—
359C23×C4D4×C1111yescharacteristic
360C23×C4D4×C1111yescharacteristic
361C23×C4C23×C1111yescharacteristic
362C2×D8—24no—
363C2×D8—24no—
364C2×D8—42no—
365C22×C8C23×C1112yes—
366C22×C8C23×C1112yes—
367#127—22no—
368#127—22no—
369#121—22no—
370#121—22no—
371#121—42no—
372#121—42no—
373#121—44no—
374#121—44no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—44no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4C23×C1111yescharacteristic
382C2×C4⋊C4C23×C1112yes—
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—21no—
396C2×C42D4×C1111yescharacteristic
397C2×C42D4×C1111yescharacteristic
398C2×C42C23×C1111yescharacteristic
399C2×C42C23×C1111yescharacteristic
400#107—42no—
401C4⋊C8—22no—
402C4⋊C8D4×C1114yescomplemented
403#102—24no—
404#102—24no—
405#102—42no—
406#102—42no—
407C22⋊C8—24no—
408C4×C8—24no—
409#95—21no—
410#95—21no—
411#95—21no—
412C2×C11—42no—
413C2×C11—82no—
414C2×C11—162no—
415C2×C11#241411yescharacteristic
416C2×C11C2×#46611yescharacteristic
417C2×C11#305511yescharacteristic
418C2×C11#310011yescharacteristic
419C2×C11#310611yescharacteristic
420C2×C11#320511yescharacteristic
421C2×C11#321211yescharacteristic
422C24—21no—
423C24—22no—
424C24C2×D4×C1111yescharacteristic
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4C11×#4112yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4C11×D814yescomplemented
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C24×C1111yescharacteristic
474D8—48no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8C2×D4×C1114yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4C11×#4112yes—
492C22⋊C4—24no—
493C22⋊C4—44no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—44no—
498C22⋊C4—44no—
499C22⋊C4—42no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42C2×D4×C1112yes—
506C42C11×#4112yes—
507C11#2465011yescharacteristic, direct product factor, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C2×C11×D812yes—
529C23C22×D4×C1111yescharacteristic
530D4—22no—
531D4—22no—
532D4—48no—
533D4—42no—
534D4—41no—
535D4—42no—
536D4—42no—
537D4—41no—
538D4—42no—
539D4—84no—
540D4—88no—
541D4—84no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—28no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—84no—
570C2×C4C11×#12112yes—
571C2×C4C11×#12112yes—
572C2×C4C2×C11×D812yes—
573C2×C4C2×C11×D812yes—
574C2×C4C11×#13512yes—
575C2×C4C11×AGL(1,ℤ/8)12yes—
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C2×C11×#4111yescharacteristic
580C2×C4C11×H(5,𝔽2)11yescharacteristic
581C2×C4C11×H(5,𝔽2)11yescharacteristic
582C8—24no—
583C8—42no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22C2×C11×#12111yescharacteristic
606C22C11×#52511yescharacteristic
607C22C11×#53511yescharacteristic
608C22C22×C11×D811yescharacteristic
609C22C2×C11×#13511yescharacteristic
610C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
611C22C11×#57511yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—41no—
616C4—42no—
617C4—82no—
618C4—81no—
619C4—81no—
620C4C11×#46614yes—
621C4C11×#54611yescharacteristic
622C4C11×#55011yescharacteristic
623C4C11×#55311yescharacteristic
624C4C11×#55511yescharacteristic
625C2—42no—
626C2—82no—
627C2—162no—
628C2C11×#241411yescharacteristic
629C2C2×C11×#46611yescharacteristic
630C2C11×#305511yescharacteristic
631C2C11×#310011yescharacteristic
632C2C11×#310611yescharacteristic
633C2C11×#320511yescharacteristic
634C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#459C2semidirect
2. C2×C11×#431C2semidirect
3. C11×#2856C2semidirect
4. C4×C11×#121C2semidirect
5. C11×#2033C2semidirect
6. C11×#1999C2semidirect
7. C11×#1982C2semidirect
8. C11×#1970C2semidirect
9. C11×#1947C2semidirect
10. C11×#1934C2semidirect
11. C11×#1802C2semidirect
95. C11×C4⋊C8D4semidirect
105. #24650C11direct (N × H)
151. C22×C4×C11D8semidirect
191. C2×#459C2×C11semidirect
192. C2×#431C2×C11semidirect
193. #2856C2×C11semidirect
194. C4×#121C2×C11semidirect
195. #2033C2×C11semidirect
196. #1999C2×C11semidirect
197. #1982C2×C11semidirect
198. #1970C2×C11semidirect
199. #1947C2×C11semidirect
200. #1934C2×C11semidirect
201. #1802C2×C11semidirect
402. C4⋊C8D4×C11semidirect
467. C22×C4C11×D8semidirect
507. C11#24650direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4312
C11×#28562
C4×C11×#1212
C11×#20332
C11×#19992
C11×#19822
C11×#19702
C11×#19472
C11×#19342
C11×#18022
#2465011