Finite Group Databasebeta

← C11×#24237 #14601430

Subgroups — C11×#24237 #14601430

Order 2816.

1522 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#449C212yesmaximal, complemented
4C2×C4×C11×D8C211yesmaximal, characteristic, complemented
5C11×#2537C211yesmaximal, characteristic, complemented
6C11×#2036C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1956C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic, complemented
10C11×#1802C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×SD16C2212yes—
14C22×C11×D8C2211yescharacteristic
15C11×#547—24no—
16C11×#547—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—21no—
21C2×C11×#121—21no—
22C2×C11×#121C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4—21no—
27C11×#461—24no—
28C11×#449—28no—
29C4×C11×D8—24no—
30C2×C11×#107C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×C22⋊C8C2212yes—
40C2×C4×C8×C11C2211yescharacteristic
41C11×#394—22no—
42C11×#384C2211yescharacteristic
43C11×#380—21no—
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—22no—
60C23×C4×C11—21no—
61C23×C4×C11C2312yes—
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—42no—
65C2×C11×D8—22no—
66C2×C11×D8—22no—
67C2×C11×D8D414yescomplemented
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yescomplemented
73C11×#123—216no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×#121—28no—
77C11×#121—24no—
78C11×#121—42no—
79C11×#121—44no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11D414yescomplemented
86C2×C11×C4⋊C4—28no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
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—21no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4D412yes—
102C2×C42×C11C2311yescharacteristic
103C11×#107—22no—
104C11×C4⋊C8—22no—
105C11×#103—24no—
106C11×#103—24no—
107C11×#103—42no—
108C11×#102—22no—
109C11×#102—24no—
110C11×#102—22no—
111C11×C22⋊C8—24no—
112C11×C22⋊C8—42no—
113C4×C8×C11—22no—
114C11×#95—22no—
115#24237C1111yesmaximal, characteristic, direct product factor, Sylow
116C24×C11—21no—
117C24×C11—21no—
118C24×C11C2×D412yes—
119C11×#41—48no—
120C11×#41—48no—
121C11×#41—48no—
122C11×#41—48no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11C2×D414yes—
129C2×D4×C11—28no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—82no—
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C2×D4×C11#4112yes—
150C22×C4×C11—28no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C11×SD16—48no—
174C11×D8—28no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—22no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D412yes—
184C11×C4⋊C4—28no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—81no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—28no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—44no—
200C11×C22⋊C4—44no—
201C11×C22⋊C4—42no—
202C42×C11C2×D412yes—
203C42×C11C2×D412yes—
204C2×#547C2×C1111yescharacteristic, complemented
205C2×#461C2×C1111yescharacteristic, complemented
206C2×#449C2×C1112yescomplemented
207C2×C4×D8C2×C1111yescharacteristic, complemented
208#2537C2×C1111yescharacteristic, complemented
209#2036C2×C1112yescomplemented
210#2000C2×C1112yescomplemented
211#1956C2×C1111yescharacteristic, complemented
212#1954C2×C1111yescharacteristic, complemented
213#1802C2×C1111yescharacteristic, complemented
214#1788C2×C1112yescomplemented
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—42no—
240Q8×C11—42no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—416no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—44no—
250D4×C11—88no—
251D4×C11#12114yescomplemented
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—416no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—48no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—84no—
276C2×C4×C11#12012yes—
277C2×C4×C11#12012yes—
278C2×C4×C11#13512yes—
279C2×C4×C11AGL(1,ℤ/8)12yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—42no—
289C22×#41C22×C1112yes—
290C22×SD16C22×C1112yes—
291C22×D8C22×C1111yescharacteristic
292#547—24no—
293#547—24no—
294C2×C4⋊Q8C22×C1111yescharacteristic
295C2×#123—22no—
296C2×C22⋊Q8C22×C1112yes—
297C2×#121—21no—
298C2×#121—21no—
299C2×#121C22×C1112yes—
300C2×C4×D4C22×C1111yescharacteristic
301C2×C4×D4C22×C1111yescharacteristic
302C2×C4×D4C22×C1111yescharacteristic
303C22×C4⋊C4—21no—
304#461—24no—
305#449—28no—
306C4×D8—24no—
307C2×#107C22×C1111yescharacteristic
308C2×C4⋊C8C22×C1111yescharacteristic
309C2×#103C22×C1112yes—
310C2×#103C22×C1112yes—
311C2×#103C22×C1112yes—
312C2×#102C22×C1112yes—
313C2×#102C22×C1111yescharacteristic
314C2×#102C22×C1111yescharacteristic
315C2×C22⋊C8C22×C1112yes—
316C2×C22⋊C8C22×C1112yes—
317C2×C4×C8C22×C1111yescharacteristic
318#394—22no—
319#384C22×C1111yescharacteristic
320#380—21no—
321#380C22×C1112yes—
322#340C22×C1112yes—
323C22×C11—24no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11C2×#12011yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—82no—
357C4×C11#44914yescomplemented
358C4×C11C2×#12111yescharacteristic
359C4×C11#53511yescharacteristic
360C4×C11D4211yescharacteristic
361C4×C11#54611yescharacteristic
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—24no—
366C2×#41—42no—
367C2×#41—42no—
368C22×Q8C23×C1112yes—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4D4×C1111yescharacteristic
372C22×D4C23×C1111yescharacteristic
373C22×D4C23×C1111yescharacteristic
374C23×C4—21no—
375C23×C4—22no—
376C23×C4—21no—
377C23×C4C23×C1112yes—
378C2×SD16—24no—
379C2×SD16—24no—
380C2×SD16—42no—
381C2×D8—22no—
382C2×D8—22no—
383C2×D8D4×C1114yescomplemented
384C22×C8C23×C1112yes—
385C22×C8C23×C1111yescharacteristic
386C22×C8C23×C1111yescharacteristic
387C4⋊Q8—22no—
388C4⋊Q8D4×C1114yescomplemented
389#123—216no—
390C22⋊Q8—24no—
391C22⋊Q8—24no—
392#121—28no—
393#121—24no—
394#121—42no—
395#121—44no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4D4×C1114yescomplemented
402C2×C4⋊C4—28no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4D4×C1111yescharacteristic
409C2×C4⋊C4C23×C1111yescharacteristic
410C2×C4⋊C4C23×C1112yes—
411C2×C4⋊C4C23×C1111yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4D4×C1112yes—
418C2×C42C23×C1111yescharacteristic
419#107—22no—
420C4⋊C8—22no—
421#103—24no—
422#103—24no—
423#103—42no—
424#102—22no—
425#102—24no—
426#102—22no—
427C22⋊C8—24no—
428C22⋊C8—42no—
429C4×C8—22no—
430#95—22no—
431C2×C11—44no—
432C2×C11—82no—
433C2×C11—82no—
434C2×C11#240811yescharacteristic
435C2×C11C2×#44911yescharacteristic
436C2×C11#301311yescharacteristic
437C2×C11#327211yescharacteristic
438C2×C11#328311yescharacteristic
439C2×C11#330311yescharacteristic
440C2×C11#333011yescharacteristic
441C24—21no—
442C24—21no—
443C24C2×D4×C1112yes—
444#41—48no—
445#41—48no—
446#41—48no—
447#41—48no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8C2×D4×C1114yes—
454C2×D4—28no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—82no—
471C2×D4C2×D4×C1112yes—
472C2×D4C2×D4×C1112yes—
473C2×D4C2×D4×C1112yes—
474C2×D4C11×#4112yes—
475C22×C4—28no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4C2×D4×C1112yes—
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C24×C1111yescharacteristic
498SD16—48no—
499D8—28no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—21no—
506C2×C8—22no—
507C2×C8—21no—
508C2×C8C2×D4×C1112yes—
509C4⋊C4—28no—
510C4⋊C4—22no—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—42no—
519C4⋊C4—81no—
520C4⋊C4C2×D4×C1112yes—
521C22⋊C4—28no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—44no—
525C22⋊C4—44no—
526C22⋊C4—42no—
527C42C2×D4×C1112yes—
528C42C2×D4×C1112yes—
529C11#2423711yescharacteristic, direct product factor, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23C22×D4×C1111yescharacteristic
552Q8—24no—
553Q8—24no—
554Q8—42no—
555Q8—42no—
556D4—22no—
557D4—22no—
558D4—22no—
559D4—22no—
560D4—22no—
561D4—416no—
562D4—41no—
563D4—41no—
564D4—44no—
565D4—88no—
566D4C11×#12114yescomplemented
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—416no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—48no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—84no—
591C2×C4C11×#12012yes—
592C2×C4C11×#12012yes—
593C2×C4C11×#13512yes—
594C2×C4C11×AGL(1,ℤ/8)12yes—
595C2×C4C22×D4×C1111yescharacteristic
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C22×D4×C1111yescharacteristic
598C2×C4C2×C11×#4111yescharacteristic
599C2×C4C11×H(5,𝔽2)11yescharacteristic
600C2×C4C11×H(5,𝔽2)11yescharacteristic
601C8—22no—
602C8—41no—
603C8—42no—
604C22—24no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C2×C11×#12011yescharacteristic
626C22D42×C1111yescharacteristic
627C22C11×#54611yescharacteristic
628C22C2×C11×#13511yescharacteristic
629C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
630C22C11×#57711yescharacteristic
631C22C11×#57811yescharacteristic
632C4—22no—
633C4—42no—
634C4—44no—
635C4—42no—
636C4—81no—
637C4—82no—
638C4C11×#44914yescomplemented
639C4C2×C11×#12111yescharacteristic
640C4C11×#53511yescharacteristic
641C4D42×C1111yescharacteristic
642C4C11×#54611yescharacteristic
643C2—44no—
644C2—82no—
645C2—82no—
646C2C11×#240811yescharacteristic
647C2C2×C11×#44911yescharacteristic
648C2C11×#301311yescharacteristic
649C2C11×#327211yescharacteristic
650C2C11×#328311yescharacteristic
651C2C11×#330311yescharacteristic
652C2C11×#333011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
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×C11×#547C2semidirect
2. C2×C11×#461C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C4×C11×D8C2semidirect
5. C11×#2537C2semidirect
6. C11×#2036C2semidirect
7. C11×#2000C2semidirect
8. C11×#1956C2semidirect
9. C11×#1954C2semidirect
10. C11×#1802C2semidirect
11. C11×#1788C2semidirect
67. C2×C11×D8D4semidirect
72. C11×C4⋊Q8D4semidirect
85. C4×D4×C11D4semidirect
115. #24237C11direct (N × H)
204. C2×#547C2×C11semidirect
205. C2×#461C2×C11semidirect
206. C2×#449C2×C11semidirect
207. C2×C4×D8C2×C11semidirect
208. #2537C2×C11semidirect
209. #2036C2×C11semidirect
210. #2000C2×C11semidirect
211. #1956C2×C11semidirect
212. #1954C2×C11semidirect
213. #1802C2×C11semidirect
214. #1788C2×C11semidirect
251. D4×C11#121semidirect
357. C4×C11#449semidirect
383. C2×D8D4×C11semidirect
388. C4⋊Q8D4×C11semidirect
401. C4×D4D4×C11semidirect
529. C11#24237direct (N × H)
566. D4C11×#121semidirect
638. C4C11×#449semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4612
C2×C11×#4492
C2×C4×C11×D82
C11×#25372
C11×#20362
C11×#20002
C11×#19562
C11×#19542
C11×#18022
C11×#17882
#2423711