Finite Group Databasebeta

← C11×#24239 #14601432

Subgroups — C11×#24239 #14601432

Order 2816.

1490 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#448C212yesmaximal, complemented
4C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
5C11×#2537C211yesmaximal, characteristic
6C11×#2035C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic, complemented
10C11×#1803C211yesmaximal, characteristic, complemented
11C11×#1787C212yesmaximal, complemented
12C23×Q8×C11C2212yes—
13C22×C11×SD16C2212yes—
14C22×C11×SD16C2211yescharacteristic
15D4×Q8×C11—24no—
16D4×Q8×C11—24no—
17C2×C11×C4⋊Q8—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—22no—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121—21no—
22C2×C11×#121C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C11×#461—24no—
28C11×#448—28no—
29C4×C11×SD16—24no—
30C2×C11×#106C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#103C2212yes—
36C2×C11×#103C2212yes—
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2212yes—
39C2×C11×C22⋊C8C2212yes—
40C2×C4×C8×C11C2211yescharacteristic
41C11×#394—22no—
42C11×#384C2211yescharacteristic
43C11×#380—21no—
44C11×#380C2212yes—
45C11×#340C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—22no—
49C22×Q8×C11—24no—
50C22×Q8×C11—24no—
51C22×Q8×C11—42no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2312yes—
54C22×Q8×C11C2311yescharacteristic
55C22×D4×C11—22no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×SD16—42no—
66C2×C11×SD16D414yescomplemented
67C22×C8×C11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—28no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yescomplemented
73C11×C22⋊Q8—216no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×#121—24no—
77C11×#121—42no—
78C11×#121—44no—
79C4×Q8×C11—22no—
80C4×Q8×C11D414yescomplemented
81C4×D4×C11—28no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4D412yes—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C11×#106—22no—
104C11×C4⋊C8—22no—
105C11×#103—22no—
106C11×#103—24no—
107C11×#103—24no—
108C11×#103—24no—
109C11×#103—42no—
110C11×#102—22no—
111C11×C22⋊C8—24no—
112C11×C22⋊C8—42no—
113C4×C8×C11—22no—
114C11×#95—22no—
115#24239C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11C2×D412yes—
118C2×Q8×C11—28no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11—48no—
131C2×Q8×C11—48no—
132C2×Q8×C11—48no—
133C2×Q8×C11C2×D414yes—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11#4112yes—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—82no—
147C2×D4×C11SD1614yescomplemented
148C2×D4×C11C2×D412yes—
149C22×C4×C11—21no—
150C22×C4×C11—28no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—44no—
162C22×C4×C11—44no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C11×SD16—28no—
171C11×SD16—48no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—44no—
197C11×C22⋊C4—44no—
198C11×C22⋊C4—42no—
199C42×C11—24no—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202C2×D4×Q8C2×C1111yescharacteristic, complemented
203C2×#461C2×C1111yescharacteristic, complemented
204C2×#448C2×C1112yescomplemented
205C2×C4×SD16C2×C1111yescharacteristic, complemented
206#2537C2×C1111yescharacteristic
207#2035C2×C1112yescomplemented
208#2000C2×C1112yescomplemented
209#1956C2×C1111yescharacteristic, complemented
210#1954C2×C1111yescharacteristic, complemented
211#1803C2×C1111yescharacteristic, complemented
212#1787C2×C1112yescomplemented
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C2×SD1614yes—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—416no—
234Q8×C11—42no—
235Q8×C11—42no—
236Q8×C11#12114yescomplemented
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—28no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—88no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—416no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—84no—
269C2×C4×C11#12012yes—
270C2×C4×C11#12012yes—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11#13712yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C8×C11—22no—
280C8×C11—41no—
281C8×C11—42no—
282C23×Q8C22×C1112yes—
283C22×SD16C22×C1112yes—
284C22×SD16C22×C1111yescharacteristic
285D4×Q8—24no—
286D4×Q8—24no—
287C2×C4⋊Q8—21no—
288C2×C4⋊Q8C22×C1111yescharacteristic
289C2×C22⋊Q8—22no—
290C2×C22⋊Q8C22×C1112yes—
291C2×#121—21no—
292C2×#121C22×C1112yes—
293C2×C4×Q8C22×C1111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C22×C1111yescharacteristic
296C2×C4×D4C22×C1111yescharacteristic
297#461—24no—
298#448—28no—
299C4×SD16—24no—
300C2×#106C22×C1111yescharacteristic
301C2×C4⋊C8C22×C1111yescharacteristic
302C2×#103C22×C1112yes—
303C2×#103C22×C1111yescharacteristic
304C2×#103C22×C1112yes—
305C2×#103C22×C1112yes—
306C2×#103C22×C1112yes—
307C2×#102C22×C1111yescharacteristic
308C2×C22⋊C8C22×C1112yes—
309C2×C22⋊C8C22×C1112yes—
310C2×C4×C8C22×C1111yescharacteristic
311#394—22no—
312#384C22×C1111yescharacteristic
313#380—21no—
314#380C22×C1112yes—
315#340C22×C1112yes—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11C2×#12011yescharacteristic
331C22×C11D4211yescharacteristic
332C22×C11#54611yescharacteristic
333C22×C11C22×SD1611yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57811yescharacteristic
337C4×C11—24no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—82no—
344C4×C11#44814yescomplemented
345C4×C11C2×#12111yescharacteristic
346C4×C11#53511yescharacteristic
347C4×C11D4211yescharacteristic
348C4×C11#54611yescharacteristic
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—22no—
352C22×Q8—24no—
353C22×Q8—24no—
354C22×Q8—42no—
355C22×Q8—42no—
356C22×Q8C23×C1112yes—
357C22×Q8C23×C1111yescharacteristic
358C22×D4—22no—
359C22×D4D4×C1111yescharacteristic
360C22×D4C23×C1111yescharacteristic
361C23×C4—22no—
362C23×C4—21no—
363C23×C4C23×C1112yes—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—42no—
369C2×SD16D4×C1114yescomplemented
370C22×C8C23×C1112yes—
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373C4⋊Q8—28no—
374C4⋊Q8—22no—
375C4⋊Q8D4×C1114yescomplemented
376C22⋊Q8—216no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379#121—24no—
380#121—42no—
381#121—44no—
382C4×Q8—22no—
383C4×Q8D4×C1114yescomplemented
384C4×D4—28no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C1111yescharacteristic
396C2×C4⋊C4C23×C1111yescharacteristic
397C2×C4⋊C4C23×C1112yes—
398C2×C4⋊C4C23×C1111yescharacteristic
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4D4×C1112yes—
404C2×C42—21no—
405C2×C42C23×C1111yescharacteristic
406#106—22no—
407C4⋊C8—22no—
408#103—22no—
409#103—24no—
410#103—24no—
411#103—24no—
412#103—42no—
413#102—22no—
414C22⋊C8—24no—
415C22⋊C8—42no—
416C4×C8—22no—
417#95—22no—
418C2×C11—44no—
419C2×C11—82no—
420C2×C11#240811yescharacteristic
421C2×C11C2×#44811yescharacteristic
422C2×C11#301311yescharacteristic
423C2×C11#327611yescharacteristic
424C2×C11D4×SD1611yescharacteristic
425C2×C11#329811yescharacteristic
426C2×C11#332911yescharacteristic
427C24—21no—
428C24C2×D4×C1112yes—
429C2×Q8—28no—
430C2×Q8—21no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8C2×D4×C1114yes—
445C2×Q8C2×D4×C1112yes—
446C2×Q8C2×D4×C1112yes—
447C2×Q8C11×#4112yes—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—82no—
458C2×D4C11×SD1614yescomplemented
459C2×D4C2×D4×C1112yes—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4C2×D4×C1112yes—
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C24×C1111yescharacteristic
481SD16—28no—
482SD16—48no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—21no—
489C2×C8—22no—
490C2×C8—21no—
491C2×C8C2×D4×C1112yes—
492C4⋊C4—28no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4C2×D4×C1112yes—
505C22⋊C4—28no—
506C22⋊C4—24no—
507C22⋊C4—44no—
508C22⋊C4—44no—
509C22⋊C4—42no—
510C42—24no—
511C42C2×D4×C1112yes—
512C42C2×D4×C1112yes—
513C11#2423911yescharacteristic, direct product factor, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C2×C11×SD1614yes—
528C23C22×D4×C1111yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—24no—
533Q8—24no—
534Q8—416no—
535Q8—42no—
536Q8—42no—
537Q8C11×#12114yescomplemented
538D4—22no—
539D4—22no—
540D4—28no—
541D4—41no—
542D4—41no—
543D4—88no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—416no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—84no—
570C2×C4C11×#12012yes—
571C2×C4C11×#12012yes—
572C2×C4C2×C11×SD1612yes—
573C2×C4C11×#13712yes—
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C22×D4×C1111yescharacteristic
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C11×H(5,𝔽2)11yescharacteristic
579C2×C4C11×H(5,𝔽2)11yescharacteristic
580C8—22no—
581C8—41no—
582C8—42no—
583C22—24no—
584C22—24no—
585C22—24no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22C2×C11×#12011yescharacteristic
598C22D42×C1111yescharacteristic
599C22C11×#54611yescharacteristic
600C22C22×C11×SD1611yescharacteristic
601C22C2×C11×#13711yescharacteristic
602C22C11×#57711yescharacteristic
603C22C11×#57811yescharacteristic
604C4—24no—
605C4—22no—
606C4—42no—
607C4—44no—
608C4—42no—
609C4—81no—
610C4—82no—
611C4C11×#44814yescomplemented
612C4C2×C11×#12111yescharacteristic
613C4C11×#53511yescharacteristic
614C4D42×C1111yescharacteristic
615C4C11×#54611yescharacteristic
616C2—44no—
617C2—82no—
618C2C11×#240811yescharacteristic
619C2C2×C11×#44811yescharacteristic
620C2C11×#301311yescharacteristic
621C2C11×#327611yescharacteristic
622C2D4×C11×SD1611yescharacteristic
623C2C11×#329811yescharacteristic
624C2C11×#332911yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C11C2semidirect
2. C2×C11×#461C2semidirect
3. C2×C11×#448C2semidirect
4. C2×C4×C11×SD16C2semidirect
6. C11×#2035C2semidirect
7. C11×#2000C2semidirect
8. C11×#1956C2semidirect
9. C11×#1954C2semidirect
10. C11×#1803C2semidirect
11. C11×#1787C2semidirect
66. C2×C11×SD16D4semidirect
72. C11×C4⋊Q8D4semidirect
80. C4×Q8×C11D4semidirect
115. #24239C11direct (N × H)
147. C2×D4×C11SD16semidirect
202. C2×D4×Q8C2×C11semidirect
203. C2×#461C2×C11semidirect
204. C2×#448C2×C11semidirect
205. C2×C4×SD16C2×C11semidirect
207. #2035C2×C11semidirect
208. #2000C2×C11semidirect
209. #1956C2×C11semidirect
210. #1954C2×C11semidirect
211. #1803C2×C11semidirect
212. #1787C2×C11semidirect
236. Q8×C11#121semidirect
344. C4×C11#448semidirect
369. C2×SD16D4×C11semidirect
375. C4⋊Q8D4×C11semidirect
383. C4×Q8D4×C11semidirect
458. C2×D4C11×SD16semidirect
513. C11#24239direct (N × H)
537. Q8C11×#121semidirect
611. C4C11×#448semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C112
C2×C11×#4612
C2×C11×#4482
C2×C4×C11×SD162
C11×#25372
C11×#20352
C11×#20002
C11×#19562
C11×#19542
C11×#18032
C11×#17872
#2423911