Finite Group Databasebeta

← C11×#24653 #14601846

Subgroups — C11×#24653 #14601846

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#460C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic, complemented
3C11×#2856C211yesmaximal, characteristic
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1982C211yesmaximal, characteristic, complemented
8C11×#1968C212yesmaximal, complemented
9C11×#1948C211yesmaximal, characteristic, complemented
10C11×#1934C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C11×#121—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#460—24no—
21C11×#431—24no—
22C2×C11×#106C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2212yes—
31C11×#391C2211yescharacteristic
32C11×#390—21no—
33C11×#390—21no—
34C11×#390C2212yes—
35C11×#389C2211yescharacteristic
36C11×#387—21no—
37C11×#385—21no—
38C11×#384C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×SD16—24no—
54C2×C11×SD16—24no—
55C2×C11×SD16—42no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2312yes—
58C11×#127—22no—
59C11×#127—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×#121—42no—
63C11×#121—42no—
64C11×#121—44no—
65C11×#121—44no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11D411yescharacteristic
87C2×C42×C11D411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C11×#106—42no—
91C11×C4⋊C8—22no—
92C11×C4⋊C8D414yescomplemented
93C11×#103—42no—
94C11×#102—24no—
95C11×#102—24no—
96C11×#102—42no—
97C11×C22⋊C8—24no—
98C4×C8×C11—24no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#24653C1111yesmaximal, characteristic, direct product factor, Sylow
105C24×C11—22no—
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11#4112yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—41no—
144C22×C4×C11SD1614yescomplemented
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×SD16—48no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C2×D414yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4#4112yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—44no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—42no—
181C42×C11—42no—
182C42×C11C2×D412yes—
183C42×C11#4112yes—
184C2×#460C2×C1111yescharacteristic, complemented
185C2×#431C2×C1111yescharacteristic, complemented
186#2856C2×C1111yescharacteristic
187C4×C22⋊Q8C2×C1111yescharacteristic, complemented
188#2034C2×C1112yescomplemented
189#2000C2×C1112yescomplemented
190#1982C2×C1111yescharacteristic, complemented
191#1968C2×C1112yescomplemented
192#1948C2×C1111yescharacteristic, complemented
193#1934C2×C1112yescomplemented
194#1803C2×C1111yescharacteristic, complemented
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C2×SD1612yes—
209C23×C11C22×D411yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—84no—
219D4×C11—88no—
220D4×C11—84no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—28no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#12112yes—
252C2×C4×C11#12112yes—
253C2×C4×C11C2×SD1612yes—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11#13512yes—
256C2×C4×C11AGL(1,ℤ/8)12yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C8×C11—24no—
264C8×C11—42no—
265C22×SD16C22×C1112yes—
266C2×#127C22×C1111yescharacteristic
267C2×C22⋊Q8C22×C1111yescharacteristic
268C2×#121—21no—
269C2×#121—21no—
270C2×#121C22×C1112yes—
271C2×C4×Q8C22×C1111yescharacteristic
272C22×C42C22×C1111yescharacteristic
273#460—24no—
274#431—24no—
275C2×#106C22×C1112yes—
276C2×C4⋊C8C22×C1111yescharacteristic
277C2×C4⋊C8C22×C1111yescharacteristic
278C2×#103C22×C1112yes—
279C2×#102C22×C1112yes—
280C2×#102C22×C1112yes—
281C2×#102C22×C1112yes—
282C2×C22⋊C8C22×C1112yes—
283C2×C4×C8C22×C1112yes—
284#391C22×C1111yescharacteristic
285#390—21no—
286#390—21no—
287#390C22×C1112yes—
288#389C22×C1111yescharacteristic
289#387—21no—
290#385—21no—
291#384C22×C1111yescharacteristic
292#380C22×C1111yescharacteristic
293C4×C4⋊C4—21no—
294C4×C4⋊C4C22×C1111yescharacteristic
295C4×C22⋊C4—21no—
296#340C22×C1112yes—
297#340C22×C1112yes—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11C2×#12111yescharacteristic
313C22×C11#52511yescharacteristic
314C22×C11#53511yescharacteristic
315C22×C11C22×SD1611yescharacteristic
316C22×C11C2×#13511yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57511yescharacteristic
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—42no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—82no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11#46514yes—
329C4×C11#54611yescharacteristic
330C4×C11#55011yescharacteristic
331C4×C11#55311yescharacteristic
332C4×C11#55511yescharacteristic
333C22×Q8C23×C1111yescharacteristic
334C22×D4—22no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C23×C1112yes—
338C23×C4D4×C1111yescharacteristic
339C23×C4D4×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—42no—
344C22×C8C23×C1112yes—
345C22×C8C23×C1112yes—
346#127—22no—
347#127—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350#121—42no—
351#121—42no—
352#121—44no—
353#121—44no—
354C4×Q8—22no—
355C4×Q8—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1112yes—
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42D4×C1111yescharacteristic
375C2×C42D4×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377C2×C42C23×C1111yescharacteristic
378#106—42no—
379C4⋊C8—22no—
380C4⋊C8D4×C1114yescomplemented
381#103—42no—
382#102—24no—
383#102—24no—
384#102—42no—
385C22⋊C8—24no—
386C4×C8—24no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392C2×C11—42no—
393C2×C11—162no—
394C2×C11#241411yescharacteristic
395C2×C11C2×#46511yescharacteristic
396C2×C11#305511yescharacteristic
397C2×C11#310311yescharacteristic
398C2×C11#310611yescharacteristic
399C2×C11#320811yescharacteristic
400C2×C11#321211yescharacteristic
401C24—22no—
402C24C2×D4×C1111yescharacteristic
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C11×#4112yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4C11×SD1614yescomplemented
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C2×D4×C1111yescharacteristic
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C24×C1111yescharacteristic
447SD16—48no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8C2×D4×C1114yes—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4C11×#4112yes—
467C22⋊C4—24no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—44no—
471C22⋊C4—44no—
472C42—22no—
473C42—22no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—42no—
478C42C2×D4×C1112yes—
479C42C11×#4112yes—
480C11#2465311yescharacteristic, direct product factor, Sylow
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23C2×C11×SD1612yes—
495C23C22×D4×C1111yescharacteristic
496Q8—22no—
497Q8—22no—
498Q8—41no—
499Q8—41no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—42no—
504D4—84no—
505D4—88no—
506D4—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—28no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—44no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4C11×#12112yes—
538C2×C4C11×#12112yes—
539C2×C4C2×C11×SD1612yes—
540C2×C4C2×C11×SD1612yes—
541C2×C4C11×#13512yes—
542C2×C4C11×AGL(1,ℤ/8)12yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C2×C11×#4111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C11×H(5,𝔽2)11yescharacteristic
548C2×C4C11×H(5,𝔽2)11yescharacteristic
549C8—24no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22C2×C11×#12111yescharacteristic
566C22C11×#52511yescharacteristic
567C22C11×#53511yescharacteristic
568C22C22×C11×SD1611yescharacteristic
569C22C2×C11×#13511yescharacteristic
570C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
571C22C11×#57511yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—41no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—81no—
580C4—81no—
581C4C11×#46514yes—
582C4C11×#54611yescharacteristic
583C4C11×#55011yescharacteristic
584C4C11×#55311yescharacteristic
585C4C11×#55511yescharacteristic
586C2—42no—
587C2—162no—
588C2C11×#241411yescharacteristic
589C2C2×C11×#46511yescharacteristic
590C2C11×#305511yescharacteristic
591C2C11×#310311yescharacteristic
592C2C11×#310611yescharacteristic
593C2C11×#320811yescharacteristic
594C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2856C2
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×#460C2semidirect
2. C2×C11×#431C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2034C2semidirect
6. C11×#2000C2semidirect
7. C11×#1982C2semidirect
8. C11×#1968C2semidirect
9. C11×#1948C2semidirect
10. C11×#1934C2semidirect
11. C11×#1803C2semidirect
92. C11×C4⋊C8D4semidirect
104. #24653C11direct (N × H)
144. C22×C4×C11SD16semidirect
184. C2×#460C2×C11semidirect
185. C2×#431C2×C11semidirect
187. C4×C22⋊Q8C2×C11semidirect
188. #2034C2×C11semidirect
189. #2000C2×C11semidirect
190. #1982C2×C11semidirect
191. #1968C2×C11semidirect
192. #1948C2×C11semidirect
193. #1934C2×C11semidirect
194. #1803C2×C11semidirect
380. C4⋊C8D4×C11semidirect
440. C22×C4C11×SD16semidirect
480. C11#24653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4602
C2×C11×#4312
C11×#28562
C4×C11×C22⋊Q82
C11×#20342
C11×#20002
C11×#19822
C11×#19682
C11×#19482
C11×#19342
C11×#18032
#2465311