Finite Group Databasebeta

← C11×#18296 #14595489

Subgroups — C11×#18296 #14595489

Order 2816.

1162 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×#538C211yesmaximal, characteristic, complemented
2C11×#3187C211yesmaximal, characteristic, complemented
3C11×#3186C211yesmaximal, characteristic, complemented
4C11×#2617C211yesmaximal, characteristic, complemented
5C11×#1612C214yesmaximal, complemented
6C11×#1600C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic, complemented
9C2×C11×#323C211yesmaximal, characteristic, complemented
10C11×#538—22no—
11C11×#538—22no—
12C11×#538—22no—
13C11×#538C2214yes—
14C2×C11×#126—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#120—21no—
22C2×C11×#120—21no—
23C2×C4×D4×C11—21no—
24C22×C11×C22⋊C4C2211yescharacteristic
25C11×#483C2212yescomplemented
26C11×#481—21no—
27C11×#480—21no—
28C11×#480C2212yescomplemented
29C11×#466—22no—
30C11×#465—22no—
31C11×#450C2212yescomplemented
32C11×#448—21no—
33C11×#447—21no—
34C11×#447C2212yescomplemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#397C2212yescomplemented
38C11×#394—22no—
39C11×#392C2212yescomplemented
40C11×#386—21no—
41C11×#380C2211yescharacteristic
42C11×#328C2214yescomplemented
43C11×#327C2214yescomplemented
44C11×#323C2214yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic, complemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11D411yescharacteristic, complemented
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C2×C11×SD16—22no—
58C2×C11×D8—22no—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C11×#126—24no—
62C11×#126—24no—
63C11×#124—24no—
64C11×#124—24no—
65C11×#123—24no—
66C11×#123—24no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8D412yescomplemented
70C11×C22⋊Q8C2312yes—
71C11×#121—24no—
72C11×#121—24no—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121D412yescomplemented
80C11×#121C2312yes—
81C11×#120—24no—
82C11×#120—24no—
83C11×#120—44no—
84C4×D4×C11—24no—
85C4×D4×C11—24no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic, complemented
90C2×C11×C4⋊C4D411yescharacteristic, complemented
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D412yes—
106C2×C11×C22⋊C4C2312yes—
107C2×C42×C11—21no—
108C11×#107—22no—
109C11×#106—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116C11×C22⋊C8C2312yes—
117C11×C22⋊C8C2312yes—
118C11×#95—22no—
119C11×#95C2312yes—
120#18296C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—21no—
127C24×C11—81no—
128C24×C11—81no—
129C24×C11C2×D412yes—
130C24×C11C2×D411yescharacteristic
131C2×Q8×C11—21no—
132C2×Q8×C11—81no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—44no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—81no—
149C2×D4×C11—81no—
150C2×D4×C11—82no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11—82no—
154C2×D4×C11C2×D412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—81no—
164C22×C4×C11—81no—
165C22×C4×C11—82no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C11×SD16—82no—
174C11×D8—82no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—81no—
178C2×C8×C11—81no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—44no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—82no—
205C42×C11—24no—
206C2×#538C2×C1111yescharacteristic, complemented
207#3187C2×C1111yescharacteristic, complemented
208#3186C2×C1111yescharacteristic, complemented
209#2617C2×C1111yescharacteristic, complemented
210#1612C2×C1114yescomplemented
211#1600C2×C1114yescomplemented
212#1520C2×C1111yescharacteristic, complemented
213#1519C2×C1111yescharacteristic, complemented
214C2×#323C2×C1111yescharacteristic, complemented
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—81no—
236C23×C11—81no—
237C23×C11—84no—
238C23×C11—84no—
239C23×C11#12011yescharacteristic
240C23×C11#12011yescharacteristic
241C23×C11#13512yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11C22×D411yescharacteristic
244Q8×C11—42no—
245Q8×C11—81no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—44no—
252D4×C11—81no—
253D4×C11—84no—
254D4×C11—84no—
255D4×C11—88no—
256D4×C11—82no—
257D4×C11—82no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
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—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—41no—
279C2×C4×C11—81no—
280C2×C4×C11—84no—
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C8×C11—42no—
286C8×C11—42no—
287#538—22no—
288#538—22no—
289#538—22no—
290#538C22×C1114yes—
291C2×#126—21no—
292C2×#124—21no—
293C2×#123—21no—
294C2×C22⋊Q8C22×C1111yescharacteristic
295C2×#121—21no—
296C2×#121C22×C1111yescharacteristic
297C2×#121C22×C1111yescharacteristic
298C2×#120—21no—
299C2×#120—21no—
300C2×C4×D4—21no—
301C22×C22⋊C4C22×C1111yescharacteristic
302#483C22×C1112yescomplemented
303#481—21no—
304#480—21no—
305#480C22×C1112yescomplemented
306#466—22no—
307#465—22no—
308#450C22×C1112yescomplemented
309#448—21no—
310#447—21no—
311#447C22×C1112yescomplemented
312C2×C22⋊C8C22×C1111yescharacteristic
313C2×C22⋊C8C22×C1111yescharacteristic
314#397C22×C1112yescomplemented
315#394—22no—
316#392C22×C1112yescomplemented
317#386—21no—
318#380C22×C1111yescharacteristic
319#328C22×C1114yescomplemented
320#327C22×C1114yescomplemented
321#323C22×C1114yescomplemented
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—82no—
338C22×C11—84no—
339C22×C11—84no—
340C22×C11—84no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#44912yes—
347C22×C11#44912yes—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11—82no—
360C4×C11—81no—
361C25D4×C1111yescharacteristic
362C22×Q8D4×C1111yescharacteristic, complemented
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—22no—
368C22×D4D4×C1111yescharacteristic, complemented
369C22×D4C23×C1111yescharacteristic
370C23×C4—21no—
371C23×C4D4×C1111yescharacteristic
372C23×C4C23×C1111yescharacteristic
373C2×SD16—22no—
374C2×D8—22no—
375C22×C8—21no—
376C22×C8—21no—
377#126—24no—
378#126—24no—
379#124—24no—
380#124—24no—
381#123—24no—
382#123—24no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8D4×C1112yescomplemented
386C22⋊Q8C23×C1112yes—
387#121—24no—
388#121—24no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121D4×C1112yescomplemented
396#121C23×C1112yes—
397#120—24no—
398#120—24no—
399#120—44no—
400C4×D4—24no—
401C4×D4—24no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4D4×C1111yescharacteristic, complemented
406C2×C4⋊C4D4×C1111yescharacteristic, complemented
407C2×C4⋊C4C23×C1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4D4×C1112yes—
422C2×C22⋊C4C23×C1112yes—
423C2×C42—21no—
424#107—22no—
425#106—22no—
426#103—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8C23×C1112yes—
433C22⋊C8C23×C1112yes—
434#95—22no—
435#95C23×C1112yes—
436C2×C11—21no—
437C2×C11—21no—
438C2×C11—22no—
439C2×C11—22no—
440C2×C11—82no—
441C2×C11—82no—
442C2×C11—161no—
443C2×C11C2×#44911yescharacteristic
444C2×C11#301911yescharacteristic
445C2×C11#302611yescharacteristic
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—81no—
453C24—81no—
454C24C2×D4×C1112yes—
455C24C2×D4×C1111yescharacteristic
456C2×Q8—21no—
457C2×Q8—81no—
458C2×Q8C2×D4×C1112yes—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—44no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—82no—
476C2×D4—82no—
477C2×D4—82no—
478C2×D4—82no—
479C2×D4C2×D4×C1112yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—82no—
491C22×C4C2×D4×C1112yes—
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C24×C1111yescharacteristic
498SD16—82no—
499D8—82no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—81no—
503C2×C8—81no—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—81no—
512C4⋊C4C2×D4×C1112yes—
513C4⋊C4C2×D4×C1112yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—44no—
526C22⋊C4—42no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—82no—
530C42—24no—
531C11#1829611yescharacteristic, direct product factor, Sylow
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—81no—
553C23—81no—
554C23—84no—
555C23—84no—
556C23C11×#12011yescharacteristic
557C23C11×#12011yescharacteristic
558C23C11×#13512yes—
559C23C11×AGL(1,ℤ/8)12yes—
560C23C22×D4×C1111yescharacteristic
561Q8—42no—
562Q8—81no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—44no—
569D4—81no—
570D4—84no—
571D4—84no—
572D4—88no—
573D4—82no—
574D4—82no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—81no—
597C2×C4—84no—
598C2×C4C11×#12011yescharacteristic
599C2×C4C11×#12011yescharacteristic
600C2×C4C22×D4×C1111yescharacteristic
601C2×C4C22×D4×C1111yescharacteristic
602C8—42no—
603C8—42no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—82no—
620C22—84no—
621C22—84no—
622C22—84no—
623C22—82no—
624C22—82no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22C11×#44912yes—
629C22C11×#44912yes—
630C22C2×C11×#12011yescharacteristic
631C22C2×C11×#13511yescharacteristic
632C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—82no—
642C4—81no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—22no—
647C2—82no—
648C2—82no—
649C2—161no—
650C2C2×C11×#44911yescharacteristic
651C2C11×#301911yescharacteristic
652C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#538C2semidirect
2. C11×#3187C2semidirect
3. C11×#3186C2semidirect
4. C11×#2617C2semidirect
5. C11×#1612C2semidirect
6. C11×#1600C2semidirect
7. C11×#1520C2semidirect
8. C11×#1519C2semidirect
9. C2×C11×#323C2semidirect
25. C11×#483C22semidirect
28. C11×#480C22semidirect
31. C11×#450C22semidirect
34. C11×#447C22semidirect
37. C11×#397C22semidirect
39. C11×#392C22semidirect
42. C11×#328C22semidirect
43. C11×#327C22semidirect
44. C11×#323C22semidirect
46. C22×Q8×C11D4semidirect
52. C22×D4×C11D4semidirect
69. C11×C22⋊Q8D4semidirect
79. C11×#121D4semidirect
89. C2×C11×C4⋊C4D4semidirect
90. C2×C11×C4⋊C4D4semidirect
120. #18296C11direct (N × H)
206. C2×#538C2×C11semidirect
207. #3187C2×C11semidirect
208. #3186C2×C11semidirect
209. #2617C2×C11semidirect
210. #1612C2×C11semidirect
211. #1600C2×C11semidirect
212. #1520C2×C11semidirect
213. #1519C2×C11semidirect
214. C2×#323C2×C11semidirect
302. #483C22×C11semidirect
305. #480C22×C11semidirect
308. #450C22×C11semidirect
311. #447C22×C11semidirect
314. #397C22×C11semidirect
316. #392C22×C11semidirect
319. #328C22×C11semidirect
320. #327C22×C11semidirect
321. #323C22×C11semidirect
362. C22×Q8D4×C11semidirect
368. C22×D4D4×C11semidirect
385. C22⋊Q8D4×C11semidirect
395. #121D4×C11semidirect
405. C2×C4⋊C4D4×C11semidirect
406. C2×C4⋊C4D4×C11semidirect
531. C11#18296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5382
C11×#31872
C11×#31862
C11×#26172
C11×#16122
C11×#16002
C11×#15202
C11×#15192
C2×C11×#3232
#1829611