Finite Group Databasebeta

← C11×#22403 #14599596

Subgroups — C11×#22403 #14599596

Order 2816.

1512 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#435C212yesmaximal, complemented
3C2×C11×#408C212yesmaximal, complemented
4C11×#1955C212yesmaximal, complemented
5C11×#1870C212yesmaximal, complemented
6C11×#1869C212yesmaximal, complemented
7C11×#1797C211yesmaximal, characteristic, complemented
8C11×#1780C212yesmaximal, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C22×C11×#41C2212yes—
11C22×C11×M16C2212yes—
12C23×C8×C11C2212yes—
13C11×#532—28no—
14C2×C11×C4⋊Q8C411yescharacteristic
15C2×C11×#127C411yescharacteristic
16C2×C11×#124C412yes—
17C2×C11×#121C411yescharacteristic
18C2×C11×#121C411yescharacteristic
19C2×C11×#121C412yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#435—28no—
25C2×C11×C4⋊C8C2212yes—
26C11×#408—28no—
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×#97C2212yes—
37C11×#336C2211yescharacteristic
38C11×#336C2212yes—
39C11×#336C2211yescharacteristic
40C2×C11×#41—24no—
41C2×C11×#41—24no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41—42no—
46C22×Q8×C11C2×C412yes—
47C22×D4×C11C2×C412yes—
48C22×D4×C11C2×C412yes—
49C22×D4×C11C2×C412yes—
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C411yescharacteristic
52C22×D4×C11C2×C411yescharacteristic
53C23×C4×C11C2×C411yescharacteristic
54C23×C4×C11C2×C411yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C2×C11×M16—24no—
59C2×C11×M16—24no—
60C2×C11×M16—42no—
61C22×C8×C11—24no—
62C22×C8×C11—24no—
63C22×C8×C11—42no—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C11×C4⋊Q8—24no—
69C11×#127—24no—
70C11×#124—28no—
71C11×#121—24no—
72C11×#121—24no—
73C11×#121—28no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C4×D4×C11D418yes—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C412yes—
82C2×C11×C22⋊C4C2×C412yes—
83C2×C11×C22⋊C4C2×C412yes—
84C2×C11×C22⋊C4C2×C412yes—
85C2×C42×C11—24no—
86C2×C42×C11C2×C411yescharacteristic
87C2×C42×C11C2×C411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C11×C4⋊C8—24no—
91C11×C22⋊C8—24no—
92C11×C22⋊C8—24no—
93C11×C22⋊C8—24no—
94C11×C22⋊C8—22no—
95C11×C22⋊C8—24no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—42no—
98C11×C22⋊C8—42no—
99C11×C22⋊C8D414yescomplemented
100C11×#97—24no—
101#22403C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11C22×C412yes—
103C24×C11C22×C412yes—
104C24×C11C22×C411yescharacteristic
105C11×#41—48no—
106C11×#41—48no—
107C11×#41—48no—
108C11×#41—48no—
109C2×Q8×C11—24no—
110C2×Q8×C11—24no—
111C2×Q8×C11—42no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—24no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C22⋊C414yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
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—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C412yes—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C11×M16—48no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—48no—
173C2×C8×C11C2×D414yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C22⋊C414yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4C22⋊C418yes—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11C2×D414yes—
185C2×#532C2×C1111yescharacteristic
186C2×#435C2×C1112yescomplemented
187C2×#408C2×C1112yescomplemented
188#1955C2×C1112yescomplemented
189#1870C2×C1112yescomplemented
190#1869C2×C1112yescomplemented
191#1797C2×C1111yescharacteristic, complemented
192#1780C2×C1112yescomplemented
193#1749C2×C1111yescharacteristic, complemented
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11C2×C22⋊C414yes—
214C23×C11C4×D412yes—
215C23×C11C23×C411yescharacteristic
216Q8×C11—48no—
217D4×C11—44no—
218D4×C11—48no—
219D4×C11—48no—
220D4×C11—48no—
221D4×C11—44no—
222D4×C11—48no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C414yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11#13112yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C8×C11—24no—
261C8×C11—42no—
262C8×C11—42no—
263C8×C11—42no—
264C22×#41C22×C1112yes—
265C22×M16C22×C1112yes—
266C23×C8C22×C1112yes—
267#532—28no—
268C2×C4⋊Q8C4×C1111yescharacteristic
269C2×#127C4×C1111yescharacteristic
270C2×#124C4×C1112yes—
271C2×#121C4×C1111yescharacteristic
272C2×#121C4×C1111yescharacteristic
273C2×#121C4×C1112yes—
274C2×C4×D4C22×C1112yes—
275C2×C4×D4C22×C1111yescharacteristic
276C2×C4×D4C22×C1111yescharacteristic
277C22×C42C22×C1111yescharacteristic
278#435—28no—
279C2×C4⋊C8C22×C1112yes—
280#408—28no—
281C2×C22⋊C8C22×C1112yes—
282C2×C22⋊C8C22×C1112yes—
283C2×C22⋊C8C22×C1112yes—
284C2×C22⋊C8C22×C1112yes—
285C2×C22⋊C8C22×C1112yes—
286C2×C22⋊C8C22×C1111yescharacteristic
287C2×C22⋊C8C22×C1112yes—
288C2×C22⋊C8C22×C1112yes—
289C2×C22⋊C8C22×C1111yescharacteristic
290C2×#97C22×C1112yes—
291#336C22×C1111yescharacteristic
292#336C22×C1111yescharacteristic
293#336C22×C1112yes—
294C22×C11—22no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#51811yescharacteristic
318C22×C11C2×#13111yescharacteristic
319C22×C11#56811yescharacteristic
320C22×C11#56811yescharacteristic
321C22×C11#56811yescharacteristic
322C4×C11—24no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—41no—
329C4×C11D4212yes—
330C4×C11#54612yes—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—42no—
336C2×#41—42no—
337C22×Q8C2×C4×C1112yes—
338C22×D4C2×C4×C1112yes—
339C22×D4C2×C4×C1112yes—
340C22×D4C2×C4×C1112yes—
341C22×D4C2×C4×C1112yes—
342C22×D4C2×C4×C1111yescharacteristic
343C22×D4C2×C4×C1111yescharacteristic
344C23×C4C2×C4×C1111yescharacteristic
345C23×C4C2×C4×C1111yescharacteristic
346C23×C4C23×C1112yes—
347C23×C4C23×C1112yes—
348C23×C4C23×C1111yescharacteristic
349C2×M16—24no—
350C2×M16—24no—
351C2×M16—42no—
352C22×C8—24no—
353C22×C8—24no—
354C22×C8—42no—
355C22×C8C23×C1112yes—
356C22×C8C23×C1112yes—
357C22×C8C23×C1112yes—
358C22×C8C23×C1112yes—
359C4⋊Q8—24no—
360#127—24no—
361#124—28no—
362#121—24no—
363#121—24no—
364#121—28no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4D4×C1118yes—
369C2×C4⋊C4C2×C4×C1111yescharacteristic
370C2×C4⋊C4C2×C4×C1112yes—
371C2×C4⋊C4C2×C4×C1111yescharacteristic
372C2×C22⋊C4C2×C4×C1112yes—
373C2×C22⋊C4C2×C4×C1112yes—
374C2×C22⋊C4C2×C4×C1112yes—
375C2×C22⋊C4C2×C4×C1112yes—
376C2×C42—24no—
377C2×C42C2×C4×C1111yescharacteristic
378C2×C42C2×C4×C1111yescharacteristic
379C2×C42C23×C1111yescharacteristic
380C2×C42C23×C1111yescharacteristic
381C4⋊C8—24no—
382C22⋊C8—24no—
383C22⋊C8—24no—
384C22⋊C8—24no—
385C22⋊C8—22no—
386C22⋊C8—24no—
387C22⋊C8—24no—
388C22⋊C8—42no—
389C22⋊C8—42no—
390C22⋊C8D4×C1114yescomplemented
391#97—24no—
392C2×C11—42no—
393C2×C11—44no—
394C2×C11—82no—
395C2×C11D4×C22⋊C411yescharacteristic
396C2×C11#287911yescharacteristic
397C2×C11#288011yescharacteristic
398C2×C11#293211yescharacteristic
399C2×C11#293511yescharacteristic
400C2×C11#298011yescharacteristic
401C2×C11#298111yescharacteristic
402C24C22×C4×C1112yes—
403C24C22×C4×C1112yes—
404C24C22×C4×C1111yescharacteristic
405#41—48no—
406#41—48no—
407#41—48no—
408#41—48no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—42no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4C11×C22⋊C414yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4C22×C4×C1111yescharacteristic
449C22×C4C22×C4×C1112yes—
450C22×C4C22×C4×C1111yescharacteristic
451C22×C4C22×C4×C1111yescharacteristic
452C22×C4C22×C4×C1112yes—
453C22×C4C22×C4×C1111yescharacteristic
454C22×C4C22×C4×C1111yescharacteristic
455C22×C4C2×D4×C1114yes—
456C22×C4C2×D4×C1114yes—
457C22×C4C2×D4×C1112yes—
458C22×C4C11×#4112yes—
459C22×C4C24×C1111yescharacteristic
460M16—48no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—48no—
473C2×C8C2×D4×C1114yes—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4C11×C22⋊C414yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4C11×C22⋊C418yes—
481C42—22no—
482C42—22no—
483C42—22no—
484C42C2×D4×C1114yes—
485C11#2240311yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23—22no—
488C23—21no—
489C23—22no—
490C23—21no—
491C23—22no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23C2×C11×C22⋊C414yes—
506C23C4×D4×C1112yes—
507C23C23×C4×C1111yescharacteristic
508Q8—48no—
509D4—44no—
510D4—48no—
511D4—48no—
512D4—48no—
513D4—44no—
514D4—48no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4C2×C11×C22⋊C412yes—
544C2×C4C2×C11×C22⋊C412yes—
545C2×C4C2×C11×C22⋊C414yes—
546C2×C4C4×D4×C1112yes—
547C2×C4C11×#13112yes—
548C2×C4C22×D4×C1111yescharacteristic
549C2×C4C22×D4×C1112yes—
550C2×C4C2×C11×#4111yescharacteristic
551C2×C4C11×H(5,𝔽2)12yes—
552C8—24no—
553C8—42no—
554C8—42no—
555C8—42no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—42no—
563C22—42no—
564C22—41no—
565C22—42no—
566C22—41no—
567C22—42no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22C22×C11×C22⋊C411yescharacteristic
578C22C2×C4×D4×C1111yescharacteristic
579C22C11×#51811yescharacteristic
580C22C2×C11×#13111yescharacteristic
581C22C11×#56811yescharacteristic
582C22C11×#56811yescharacteristic
583C22C11×#56811yescharacteristic
584C4—24no—
585C4—22no—
586C4—22no—
587C4—22no—
588C4—22no—
589C4—42no—
590C4—41no—
591C4D42×C1112yes—
592C4C11×#54612yes—
593C2—42no—
594C2—44no—
595C2—82no—
596C2D4×C11×C22⋊C411yescharacteristic
597C2C11×#287911yescharacteristic
598C2C11×#288011yescharacteristic
599C2C11×#293211yescharacteristic
600C2C11×#293511yescharacteristic
601C2C11×#298011yescharacteristic
602C2C11×#298111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#532C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. C2×C11×#408C2semidirect
4. C11×#1955C2semidirect
5. C11×#1870C2semidirect
6. C11×#1869C2semidirect
7. C11×#1797C2semidirect
8. C11×#1780C2semidirect
9. C11×#1749C2semidirect
99. C11×C22⋊C8D4semidirect
101. #22403C11direct (N × H)
186. C2×#435C2×C11semidirect
187. C2×#408C2×C11semidirect
188. #1955C2×C11semidirect
189. #1870C2×C11semidirect
190. #1869C2×C11semidirect
191. #1797C2×C11semidirect
192. #1780C2×C11semidirect
193. #1749C2×C11semidirect
390. C22⋊C8D4×C11semidirect
485. C11#22403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4352
C2×C11×#4082
C11×#19552
C11×#18702
C11×#18692
C11×#17972
C11×#17802
C11×#17492
#2240311