Finite Group Databasebeta

← C11×#24154 #14601347

Subgroups — C11×#24154 #14601347

Order 2816.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1988C211yesmaximal, characteristic, complemented
8C11×#1982C211yesmaximal, characteristic, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1864C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×SD16C2212yes—
14C11×#532—24no—
15C11×#532—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C2×C11×#124—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2212yes—
25C22×C42×C11C2211yescharacteristic
26C11×#475—24no—
27C11×#460—24no—
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C11×#391C2211yescharacteristic
37C11×#389C2211yescharacteristic
38C11×#387—21no—
39C11×#385—21no—
40C11×#380C2211yescharacteristic
41C4×C11×C4⋊C4—21no—
42C4×C11×C4⋊C4C2211yescharacteristic
43C4×C11×C22⋊C4—21no—
44C11×#340C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—28no—
48C2×C11×#41—44no—
49C2×C11×#41—44no—
50C22×Q8×C11—21no—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11C2312yes—
56C23×C4×C11—22no—
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16—42no—
63C22×C8×C11C2312yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8D414yes—
67C11×#127—22no—
68C11×#127D414yes—
69C11×#124—28no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×#121—28no—
73C11×#121—24no—
74C11×#121—24no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×D4×C11—28no—
78C4×D4×C11—24no—
79C4×D4×C11—24no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#106—24no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—22no—
103C11×#103—24no—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—42no—
107C11×C22⋊C8—42no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113#24154C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—22no—
115C24×C11C2×D411yescharacteristic
116C11×#41—432no—
117C2×Q8×C11—24no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11#4112yescomplemented
126C2×D4×C11—28no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—28no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—44no—
159C22×C4×C11—44no—
160C22×C4×C11SD1614yescomplemented
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C11×SD16—48no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4C2×D414yes—
185C11×C4⋊C4#4112yescomplemented
186C11×C22⋊C4—28no—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195C42×C11—42no—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C2×#532C2×C1111yescharacteristic
199C2×#475C2×C1111yescharacteristic, complemented
200C2×#460C2×C1111yescharacteristic, complemented
201C4×C22⋊Q8C2×C1111yescharacteristic, complemented
202#2034C2×C1112yescomplemented
203#2000C2×C1112yescomplemented
204#1988C2×C1111yescharacteristic, complemented
205#1982C2×C1111yescharacteristic, complemented
206#1877C2×C1112yescomplemented
207#1864C2×C1112yescomplemented
208#1797C2×C1111yescharacteristic, complemented
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—24no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11C2×SD1612yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—48no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—48no—
232D4×C11—416no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—48no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—28no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—44no—
251C2×C4×C11—416no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#12012yes—
269C2×C4×C11#12012yes—
270C2×C4×C11C2×SD1612yes—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11AGL(1,ℤ/8)12yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C8×C11—42no—
280C8×C11—42no—
281C22×#41—21no—
282C22×SD16C22×C1112yes—
283#532—24no—
284#532—24no—
285C2×C4⋊Q8C22×C1111yescharacteristic
286C2×#127C22×C1111yescharacteristic
287C2×#124—21no—
288C2×C22⋊Q8C22×C1111yescharacteristic
289C2×#121—21no—
290C2×#121C22×C1112yes—
291C2×C4×Q8C22×C1111yescharacteristic
292C2×C4×D4—21no—
293C2×C4×D4C22×C1112yes—
294C22×C42C22×C1111yescharacteristic
295#475—24no—
296#460—24no—
297C2×#106C22×C1112yes—
298C2×C4⋊C8C22×C1111yescharacteristic
299C2×C4⋊C8C22×C1111yescharacteristic
300C2×#103C22×C1112yes—
301C2×#102C22×C1112yes—
302C2×#102C22×C1112yes—
303C2×#102C22×C1112yes—
304C2×C22⋊C8C22×C1112yes—
305#391C22×C1111yescharacteristic
306#389C22×C1111yescharacteristic
307#387—21no—
308#385—21no—
309#380C22×C1111yescharacteristic
310C4×C4⋊C4—21no—
311C4×C4⋊C4C22×C1111yescharacteristic
312C4×C22⋊C4—21no—
313#340C22×C1112yes—
314#340C22×C1112yes—
315#336C22×C1112yes—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11C2×#12011yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#53711yescharacteristic
333C22×C11C22×SD1611yescharacteristic
334C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—44no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11#45014yes—
347C4×C11#54611yescharacteristic
348C4×C11#54711yescharacteristic
349C4×C11#54811yescharacteristic
350C4×C11#55011yescharacteristic
351C2×#41—28no—
352C2×#41—44no—
353C2×#41—44no—
354C22×Q8—21no—
355C22×Q8C23×C1111yescharacteristic
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C23×C1112yes—
360C23×C4—22no—
361C23×C4D4×C1111yescharacteristic
362C23×C4D4×C1111yescharacteristic
363C23×C4C23×C1111yescharacteristic
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—42no—
367C22×C8C23×C1112yes—
368C22×C8C23×C1112yes—
369C4⋊Q8—22no—
370C4⋊Q8D4×C1114yes—
371#127—22no—
372#127D4×C1114yes—
373#124—28no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#121—28no—
377#121—24no—
378#121—24no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×D4—28no—
382C4×D4—24no—
383C4×D4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1112yes—
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42D4×C1111yescharacteristic
401C2×C42D4×C1111yescharacteristic
402C2×C42C23×C1111yescharacteristic
403C2×C42C23×C1111yescharacteristic
404#106—24no—
405C4⋊C8—22no—
406C4⋊C8—22no—
407#103—24no—
408#102—24no—
409#102—24no—
410#102—42no—
411C22⋊C8—42no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417C2×C11—42no—
418C2×C11—84no—
419C2×C11#240711yescharacteristic
420C2×C11C2×#45011yescharacteristic
421C2×C11#300511yescharacteristic
422C2×C11#310311yescharacteristic
423C2×C11#311511yescharacteristic
424C2×C11#324611yescharacteristic
425C2×C11#325111yescharacteristic
426C24—22no—
427C24C2×D4×C1111yescharacteristic
428#41—432no—
429C2×Q8—24no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8C11×#4112yescomplemented
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4C2×D4×C1114yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—28no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4C11×SD1614yescomplemented
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C24×C1111yescharacteristic
479SD16—48no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—24no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4C2×D4×C1114yes—
497C4⋊C4C11×#4112yescomplemented
498C22⋊C4—28no—
499C22⋊C4—28no—
500C22⋊C4—24no—
501C22⋊C4—42no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—42no—
508C42C2×D4×C1112yes—
509C42C2×D4×C1112yes—
510C11#2415411yescharacteristic, direct product factor, Sylow
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C2×C11×SD1612yes—
525C23C22×D4×C1111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—48no—
531D4—24no—
532D4—24no—
533D4—48no—
534D4—416no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—44no—
553C2×C4—416no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4C11×#12012yes—
571C2×C4C11×#12012yes—
572C2×C4C2×C11×SD1612yes—
573C2×C4C2×C11×SD1612yes—
574C2×C4C11×AGL(1,ℤ/8)12yes—
575C2×C4C22×D4×C1111yescharacteristic
576C2×C4C22×D4×C1111yescharacteristic
577C2×C4C2×C11×#4111yescharacteristic
578C2×C4C2×C11×#4111yescharacteristic
579C2×C4C11×H(5,𝔽2)11yescharacteristic
580C2×C4C11×2−1+411yescharacteristic
581C8—42no—
582C8—42no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×C11×#12011yescharacteristic
598C22C11×#52511yescharacteristic
599C22C11×#53711yescharacteristic
600C22C22×C11×SD1611yescharacteristic
601C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
602C22C11×#57511yescharacteristic
603C22C11×#57511yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—42no—
608C4—44no—
609C4—41no—
610C4—42no—
611C4—81no—
612C4—81no—
613C4C11×#45014yes—
614C4C11×#54611yescharacteristic
615C4C11×#54711yescharacteristic
616C4C11×#54811yescharacteristic
617C4C11×#55011yescharacteristic
618C2—42no—
619C2—84no—
620C2C11×#240711yescharacteristic
621C2C2×C11×#45011yescharacteristic
622C2C11×#300511yescharacteristic
623C2C11×#310311yescharacteristic
624C2C11×#311511yescharacteristic
625C2C11×#324611yescharacteristic
626C2C11×#325111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#532C2
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×#475C2semidirect
3. C2×C11×#460C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2034C2semidirect
6. C11×#2000C2semidirect
7. C11×#1988C2semidirect
8. C11×#1982C2semidirect
9. C11×#1877C2semidirect
10. C11×#1864C2semidirect
11. C11×#1797C2semidirect
113. #24154C11direct (N × H)
125. C2×Q8×C11#41semidirect
160. C22×C4×C11SD16semidirect
185. C11×C4⋊C4#41semidirect
199. C2×#475C2×C11semidirect
200. C2×#460C2×C11semidirect
201. C4×C22⋊Q8C2×C11semidirect
202. #2034C2×C11semidirect
203. #2000C2×C11semidirect
204. #1988C2×C11semidirect
205. #1982C2×C11semidirect
206. #1877C2×C11semidirect
207. #1864C2×C11semidirect
208. #1797C2×C11semidirect
437. C2×Q8C11×#41semidirect
472. C22×C4C11×SD16semidirect
497. C4⋊C4C11×#41semidirect
510. C11#24154direct (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×#4752
C2×C11×#4602
C4×C11×C22⋊Q82
C11×#20342
C11×#20002
C11×#19882
C11×#19822
C11×#18772
C11×#18642
C11×#17972
#2415411