Finite Group Databasebeta

← C11×#24751 #14601944

Subgroups — C11×#24751 #14601944

Order 2816.

1076 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×#465C212yesmaximal
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
4C11×#2857C211yesmaximal, characteristic, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C11×#2066C212yesmaximal, complemented
7C11×#2055C212yesmaximal, complemented
8C11×#1981C211yesmaximal, characteristic, complemented
9C11×#1948C211yesmaximal, characteristic, complemented
10C11×#1892C212yesmaximal, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2212yes—
13C23×C8×C11C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C22⋊Q8C2212yes—
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#465—28no—
21C11×#461—24no—
22C2×C11×#106C2212yes—
23C2×C11×C4⋊C8—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#102C2212yes—
31C11×#391C2212yes—
32C11×#390C2211yescharacteristic
33C11×#389—21no—
34C11×#389—21no—
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#386—21no—
38C11×#384C2211yescharacteristic
39C11×#380—21no—
40C11×#380—21no—
41C11×#380C2211yescharacteristic
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11C2312yes—
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C2×C11×SD16—24no—
54C2×C11×SD16—24no—
55C2×C11×SD16—42no—
56C22×C8×C11—24no—
57C22×C8×C11—24no—
58C22×C8×C11—42no—
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C11×#121—22no—
66C11×#121D414yes—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—44no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
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×#106—24no—
94C11×C4⋊C8—24no—
95C11×C4⋊C8—22no—
96C11×C4⋊C8D414yescomplemented
97C11×#103—24no—
98C11×#103—24no—
99C11×#103—42no—
100C11×#102—24no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—22no—
105C11×#95—22no—
106#24751C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D411yescharacteristic
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×D4×C11—24no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11C2×D412yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—41no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11SD1614yescomplemented
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C11×SD16—48no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—48no—
157C2×C8×C11C2×D414yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—44no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—42no—
183C42×C11C2×D412yes—
184C42×C11#4112yes—
185C2×#465C2×C1112yes—
186C2×#461C2×C1111yescharacteristic, complemented
187C22×C4⋊C8C2×C1111yescharacteristic, complemented
188#2857C2×C1111yescharacteristic, complemented
189C4×#121C2×C1111yescharacteristic
190#2066C2×C1112yescomplemented
191#2055C2×C1112yescomplemented
192#1981C2×C1111yescharacteristic, complemented
193#1948C2×C1111yescharacteristic, complemented
194#1892C2×C1112yescomplemented
195#1802C2×C1111yescharacteristic, complemented
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11#12112yes—
208C23×C11C2×SD1612yes—
209C23×C11#13712yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—42no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—48no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—28no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—84no—
251C2×C4×C11#12112yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#12112yes—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11C2×SD1612yes—
256C2×C4×C11#13512yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C8×C11—24no—
264C8×C11—42no—
265C22×SD16C22×C1112yes—
266C23×C8C22×C1112yes—
267C2×C4⋊Q8C22×C1111yescharacteristic
268C2×C22⋊Q8C22×C1112yes—
269C2×#121C22×C1111yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4C22×C1111yescharacteristic
272C22×C42C22×C1111yescharacteristic
273#465—28no—
274#461—24no—
275C2×#106C22×C1112yes—
276C2×C4⋊C8—24no—
277C2×C4⋊C8C22×C1112yes—
278C2×C4⋊C8C22×C1111yescharacteristic
279C2×C4⋊C8C22×C1111yescharacteristic
280C2×#103C22×C1112yes—
281C2×#103C22×C1112yes—
282C2×#103C22×C1112yes—
283C2×#102C22×C1112yes—
284#391C22×C1112yes—
285#390C22×C1111yescharacteristic
286#389—21no—
287#389—21no—
288#389C22×C1111yescharacteristic
289#388—21no—
290#386—21no—
291#384C22×C1111yescharacteristic
292#380—21no—
293#380—21no—
294#380C22×C1111yescharacteristic
295C4×C4⋊C4C22×C1111yescharacteristic
296C4×C22⋊C4—21no—
297#340C22×C1112yes—
298#340C22×C1112yes—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11#46114yescomplemented
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12111yescharacteristic
315C22×C11#53711yescharacteristic
316C22×C11C22×SD1611yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×#13711yescharacteristic
319C22×C11#57511yescharacteristic
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—41no—
325C4×C11—82no—
326C4×C11—81no—
327C4×C11—82no—
328C4×C11—81no—
329C4×C11#46514yescomplemented
330C4×C11D4211yescharacteristic
331C4×C11#54711yescharacteristic
332C4×C11#54811yescharacteristic
333C4×C11#55311yescharacteristic
334C22×Q8C23×C1112yes—
335C22×D4—21no—
336C22×D4C23×C1111yescharacteristic
337C23×C4—21no—
338C23×C4D4×C1111yescharacteristic
339C23×C4D4×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—42no—
344C22×C8—24no—
345C22×C8—24no—
346C22×C8—42no—
347C22×C8C23×C1112yes—
348C22×C8C23×C1112yes—
349C4⋊Q8—22no—
350C4⋊Q8—22no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353#121—22no—
354#121D4×C1114yes—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—44no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C4⋊C4C23×C1112yes—
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C4⋊C4C23×C1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—21no—
377C2×C42D4×C1111yescharacteristic
378C2×C42D4×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380C2×C42C23×C1111yescharacteristic
381#106—24no—
382C4⋊C8—24no—
383C4⋊C8—22no—
384C4⋊C8D4×C1114yescomplemented
385#103—24no—
386#103—24no—
387#103—42no—
388#102—24no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—22no—
393#95—22no—
394C2×C11—24no—
395C2×C11—82no—
396C2×C11#241611yescharacteristic
397C2×C11C2×#46111yescharacteristic
398C2×C11#303511yescharacteristic
399C2×C11C2×#46511yescharacteristic
400C2×C11#305611yescharacteristic
401C2×C11#324611yescharacteristic
402C2×C11#324811yescharacteristic
403C24—21no—
404C24C2×D4×C1111yescharacteristic
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4C2×D4×C1112yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4C11×SD1614yescomplemented
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1112yes—
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×D4×C1111yescharacteristic
444C22×C4C11×#4112yes—
445C22×C4C24×C1111yescharacteristic
446SD16—48no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—48no—
453C2×C8C2×D4×C1114yes—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—44no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4C2×D4×C1112yes—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—44no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C42—22no—
475C42—22no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42C2×D4×C1112yes—
480C42C11×#4112yes—
481C11#2475111yescharacteristic, direct product factor, Sylow
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C11×#12112yes—
494C23C2×C11×SD1612yes—
495C23C11×#13712yes—
496C23C22×D4×C1111yescharacteristic
497Q8—42no—
498Q8—42no—
499Q8—42no—
500Q8—42no—
501D4—22no—
502D4—22no—
503D4—48no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—28no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—84no—
537C2×C4C11×#12112yes—
538C2×C4C11×#12112yes—
539C2×C4C11×#12112yes—
540C2×C4C2×C11×SD1612yes—
541C2×C4C2×C11×SD1612yes—
542C2×C4C11×#13512yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C2×C11×#4111yescharacteristic
546C2×C4C2×C11×#4111yescharacteristic
547C2×C4C11×H(5,𝔽2)11yescharacteristic
548C2×C4C11×2−1+411yescharacteristic
549C8—24no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C11×#46114yescomplemented
565C22C2×C11×#12111yescharacteristic
566C22C2×C11×#12111yescharacteristic
567C22C11×#53711yescharacteristic
568C22C22×C11×SD1611yescharacteristic
569C22C2×C11×#13511yescharacteristic
570C22C2×C11×#13711yescharacteristic
571C22C11×#57511yescharacteristic
572C4—22no—
573C4—22no—
574C4—22no—
575C4—42no—
576C4—41no—
577C4—82no—
578C4—81no—
579C4—82no—
580C4—81no—
581C4C11×#46514yescomplemented
582C4D42×C1111yescharacteristic
583C4C11×#54711yescharacteristic
584C4C11×#54811yescharacteristic
585C4C11×#55311yescharacteristic
586C2—24no—
587C2—82no—
588C2C11×#241611yescharacteristic
589C2C2×C11×#46111yescharacteristic
590C2C11×#303511yescharacteristic
591C2C2×C11×#46511yescharacteristic
592C2C11×#305611yescharacteristic
593C2C11×#324611yescharacteristic
594C2C11×#324811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
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
2. C2×C11×#461C2semidirect
3. C22×C11×C4⋊C8C2semidirect
4. C11×#2857C2semidirect
6. C11×#2066C2semidirect
7. C11×#2055C2semidirect
8. C11×#1981C2semidirect
9. C11×#1948C2semidirect
10. C11×#1892C2semidirect
11. C11×#1802C2semidirect
96. C11×C4⋊C8D4semidirect
106. #24751C11direct (N × H)
141. C22×C4×C11SD16semidirect
186. C2×#461C2×C11semidirect
187. C22×C4⋊C8C2×C11semidirect
188. #2857C2×C11semidirect
190. #2066C2×C11semidirect
191. #2055C2×C11semidirect
192. #1981C2×C11semidirect
193. #1948C2×C11semidirect
194. #1892C2×C11semidirect
195. #1802C2×C11semidirect
312. C22×C11#461semidirect
329. C4×C11#465semidirect
384. C4⋊C8D4×C11semidirect
437. C22×C4C11×SD16semidirect
481. C11#24751direct (N × H)
564. C22C11×#461semidirect
581. C4C11×#465semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C2×C11×#4612
C22×C11×C4⋊C82
C11×#28572
C4×C11×#1212
C11×#20662
C11×#20552
C11×#19812
C11×#19482
C11×#18922
C11×#18022
#2475111