Finite Group Databasebeta

← C11×#24010 #14601203

Subgroups — C11×#24010 #14601203

Order 2816.

1428 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×C11×#485C212yesmaximal, complemented
3C11×#2280C211yesmaximal, characteristic
4C11×#2036C212yesmaximal, complemented
5C11×#2035C212yesmaximal, complemented
6C11×#1873C212yesmaximal, complemented
7C11×#1853C211yesmaximal, characteristic, complemented
8C11×#1852C211yesmaximal, characteristic, complemented
9C11×#1787C211yesmaximal, characteristic, complemented
10C11×#1787C211yesmaximal, characteristic, complemented
11C11×#1779C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8—28no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4—21no—
24C11×#485—28no—
25C2×C11×#107C2212yescomplemented
26C2×C11×#106C2212yescomplemented
27C2×C11×#103C2212yescomplemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#103C2212yescomplemented
31C2×C11×C22⋊C8C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2212yes—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C11×#379—21no—
41C4×C11×C22⋊C4—21no—
42C4×C11×C22⋊C4—21no—
43C11×#340C2212yescomplemented
44C11×#340C2212yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11—24no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11—24no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—42no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C11×C22⋊Q8—28no—
67C11×C22⋊Q8—28no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8D418yes—
72C11×#117—24no—
73C11×#117—42no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—21no—
94C2×C42×C11—21no—
95C11×#107—24no—
96C11×#106—24no—
97C11×#103—24no—
98C11×#103—24no—
99C11×#103—42no—
100C11×#103—42no—
101C11×C22⋊C8—24no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—22no—
104C11×C22⋊C8—42no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109#24010C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—41no—
116C24×C11—41no—
117C24×C11C2×D411yescharacteristic
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—48no—
127C2×Q8×C11—48no—
128C2×Q8×C11—42no—
129C2×Q8×C11—42no—
130C2×Q8×C11C2×D414yes—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C2×D414yes—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C42×C11—42no—
194C42×C11—42no—
195C22×C22⋊Q8C2×C1111yescharacteristic
196C2×#485C2×C1112yescomplemented
197#2280C2×C1111yescharacteristic
198#2036C2×C1112yescomplemented
199#2035C2×C1112yescomplemented
200#1873C2×C1112yescomplemented
201#1853C2×C1111yescharacteristic, complemented
202#1852C2×C1111yescharacteristic, complemented
203#1787C2×C1111yescharacteristic, complemented
204#1787C2×C1111yescharacteristic, complemented
205#1779C2×C1111yescharacteristic
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—28no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11#12012yes—
230C23×C11#12312yes—
231C23×C11#13512yes—
232C23×C11#13712yes—
233C23×C11#13712yes—
234C23×C11C22×D411yescharacteristic
235Q8×C11—24no—
236Q8×C11—24no—
237Q8×C11—48no—
238Q8×C11—42no—
239Q8×C11—42no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—48no—
257C2×C4×C11—48no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
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#12012yes—
277C2×C4×C11#12312yes—
278C2×C4×C11C22×D412yes—
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)12yes—
282C8×C11—42no—
283C8×C11—42no—
284C23×Q8C22×C1111yescharacteristic
285C24×C4C22×C1111yescharacteristic
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8—21no—
288C2×C22⋊Q8—28no—
289C2×C22⋊Q8C22×C1112yes—
290C2×C22⋊Q8C22×C1112yes—
291C2×#117C22×C1111yescharacteristic
292C2×#117C22×C1111yescharacteristic
293C22×C4⋊C4—21no—
294C22×C4⋊C4C22×C1111yescharacteristic
295C22×C22⋊C4—21no—
296#485—28no—
297C2×#107C22×C1112yescomplemented
298C2×#106C22×C1112yescomplemented
299C2×#103C22×C1112yescomplemented
300C2×#103C22×C1112yescomplemented
301C2×#103C22×C1112yescomplemented
302C2×#103C22×C1112yescomplemented
303C2×C22⋊C8C22×C1112yes—
304C2×C22⋊C8C22×C1111yescharacteristic
305C2×C22⋊C8C22×C1111yescharacteristic
306C2×C22⋊C8C22×C1112yes—
307#381—21no—
308#380C22×C1111yescharacteristic
309#380C22×C1111yescharacteristic
310#380C22×C1111yescharacteristic
311#380C22×C1111yescharacteristic
312#379—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315#340C22×C1112yescomplemented
316#340C22×C1112yescomplemented
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—416no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11#48514yescomplemented
339C22×C11C2×#12011yescharacteristic
340C22×C11C2×#12311yescharacteristic
341C22×C11#53411yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—44no—
350C4×C11—44no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11#54612yes—
356C4×C11#54612yes—
357C25D4×C1111yescharacteristic
358C22×Q8—24no—
359C22×Q8—21no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—42no—
363C22×Q8C23×C1112yes—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—42no—
370C23×C4D4×C1111yescharacteristic
371C23×C4D4×C1111yescharacteristic
372C23×C4D4×C1111yescharacteristic
373C23×C4C23×C1111yescharacteristic
374C23×C4C23×C1111yescharacteristic
375C23×C4C23×C1111yescharacteristic
376C22×C8C23×C1112yes—
377C22×C8C23×C1112yes—
378C22⋊Q8—28no—
379C22⋊Q8—28no—
380C22⋊Q8—24no—
381C22⋊Q8—24no—
382C22⋊Q8—24no—
383C22⋊Q8D4×C1118yes—
384#117—24no—
385#117—42no—
386C2×C4⋊C4—28no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C4⋊C4C23×C1112yes—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C42—21no—
406C2×C42—21no—
407#107—24no—
408#106—24no—
409#103—24no—
410#103—24no—
411#103—42no—
412#103—42no—
413C22⋊C8—24no—
414C22⋊C8—22no—
415C22⋊C8—22no—
416C22⋊C8—42no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C2×C11—24no—
422C2×C11—42no—
423C2×C11—42no—
424C2×C11#240511yescharacteristic
425C2×C11#300211yescharacteristic
426C2×C11#300411yescharacteristic
427C2×C11C2×#48511yescharacteristic
428C2×C11#309511yescharacteristic
429C2×C11#319011yescharacteristic
430C2×C11#319611yescharacteristic
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—41no—
437C24—41no—
438C24C2×D4×C1111yescharacteristic
439C24C2×D4×C1111yescharacteristic
440C24C2×D4×C1111yescharacteristic
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—48no—
448C2×Q8—48no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8C2×D4×C1114yes—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1114yes—
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C11×#4112yes—
489C22×C4C11×#4112yes—
490C22×C4C24×C1111yescharacteristic
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C4⋊C4—24no—
498C4⋊C4—28no—
499C4⋊C4—28no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4C2×D4×C1114yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C42—42no—
515C42—42no—
516C11#2401011yescharacteristic, direct product factor, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—28no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—44no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23C11×#12012yes—
541C23C11×#12312yes—
542C23C11×#13512yes—
543C23C11×#13712yes—
544C23C11×#13712yes—
545C23C22×D4×C1111yescharacteristic
546Q8—24no—
547Q8—24no—
548Q8—48no—
549Q8—42no—
550Q8—42no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4C11×#12012yes—
588C2×C4C11×#12312yes—
589C2×C4C22×D4×C1112yes—
590C2×C4C2×C11×#4111yescharacteristic
591C2×C4C2×C11×#4111yescharacteristic
592C2×C4C11×H(5,𝔽2)12yes—
593C8—42no—
594C8—42no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—416no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C11×#48514yescomplemented
617C22C2×C11×#12011yescharacteristic
618C22C2×C11×#12311yescharacteristic
619C22C11×#53411yescharacteristic
620C22C2×C11×#13511yescharacteristic
621C22C2×C11×#13711yescharacteristic
622C22C2×C11×#13711yescharacteristic
623C22C11×#57511yescharacteristic
624C4—22no—
625C4—22no—
626C4—41no—
627C4—44no—
628C4—44no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4C11×#54612yes—
634C4C11×#54612yes—
635C2—24no—
636C2—42no—
637C2—42no—
638C2C11×#240511yescharacteristic
639C2C11×#300211yescharacteristic
640C2C11×#300411yescharacteristic
641C2C2×C11×#48511yescharacteristic
642C2C11×#309511yescharacteristic
643C2C11×#319011yescharacteristic
644C2C11×#319611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#485C2semidirect
4. C11×#2036C2semidirect
5. C11×#2035C2semidirect
6. C11×#1873C2semidirect
7. C11×#1853C2semidirect
8. C11×#1852C2semidirect
9. C11×#1787C2semidirect
10. C11×#1787C2semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#106C22semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
43. C11×#340C22semidirect
44. C11×#340C22semidirect
109. #24010C11direct (N × H)
196. C2×#485C2×C11semidirect
198. #2036C2×C11semidirect
199. #2035C2×C11semidirect
200. #1873C2×C11semidirect
201. #1853C2×C11semidirect
202. #1852C2×C11semidirect
203. #1787C2×C11semidirect
204. #1787C2×C11semidirect
297. C2×#107C22×C11semidirect
298. C2×#106C22×C11semidirect
299. C2×#103C22×C11semidirect
300. C2×#103C22×C11semidirect
301. C2×#103C22×C11semidirect
302. C2×#103C22×C11semidirect
315. #340C22×C11semidirect
316. #340C22×C11semidirect
338. C22×C11#485semidirect
516. C11#24010direct (N × H)
616. C22C11×#485semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C2×C11×#4852
C11×#22802
C11×#20362
C11×#20352
C11×#18732
C11×#18532
C11×#18522
C11×#17872
C11×#17792
#2401011