Finite Group Databasebeta

← C11×#20971 #14598164

Subgroups — C11×#20971 #14598164

Order 2816.

1986 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×M16C211yesmaximal, characteristic, complemented
2C2×C11×#525C211yesmaximal, characteristic
3C2×C11×#417C212yesmaximal, complemented
4C2×C11×#380C211yesmaximal, characteristic, complemented
5C11×#1895C212yesmaximal, complemented
6C11×#1894C212yesmaximal, complemented
7C11×#1893C212yesmaximal, complemented
8C11×#1892C212yesmaximal, complemented
9C11×#1736C212yesmaximal, complemented
10C22×C11×#41C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C22×C11×M16—24no—
13C22×C11×M16—28no—
14C22×C11×M16C2212yes—
15C22×C11×M16C2212yes—
16C23×C8×C11C2212yes—
17C11×#525—24no—
18C11×#525C418yescomplemented
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#120—21no—
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11—21no—
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29C22×C11×C22⋊C4—21no—
30C11×#417—28no—
31C2×C11×#103C2214yescomplemented
32C2×C11×#102C2214yescomplemented
33C11×#380—21no—
34C11×#380—21no—
35C11×#380C2212yes—
36C11×#380C2212yes—
37C2×C11×#95—21no—
38C11×#340C2214yescomplemented
39C11×#340C2214yescomplemented
40C25×C11D411yescharacteristic
41C2×C11×#41—22no—
42C2×C11×#41—24no—
43C2×C11×#41—24no—
44C2×C11×#41C2×C414yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C23×C4×C11C2×C414yes—
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D414yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—232no—
63C2×C11×M16—24no—
64C2×C11×M16—24no—
65C2×C11×M16—24no—
66C2×C11×M16—28no—
67C2×C11×M16D418yescomplemented
68C22×C8×C11—24no—
69C22×C8×C11—28no—
70C22×C8×C11C2314yes—
71C11×#123—28no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8C2×C414yescomplemented
75C11×C22⋊Q8C2×C414yescomplemented
76C11×#121—22no—
77C11×#121—22no—
78C11×#121C2×C414yescomplemented
79C11×#121C2×C414yescomplemented
80C11×#120—28no—
81C4×D4×C11—28no—
82C4×D4×C11—28no—
83C11×#117—22no—
84C11×#117C2×C414yes—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
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—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—44no—
101C2×C42×C11—21no—
102C11×#103—28no—
103C11×#102—28no—
104C11×#95—22no—
105C11×#95—22no—
106#20971C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—24no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—42no—
112C24×C11C22⋊C414yes—
113C24×C11C2×D411yescharacteristic
114C24×C11C2×D411yescharacteristic
115C24×C11C2×D411yescharacteristic
116C11×#41—216no—
117C11×#41—44no—
118C11×#41—44no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11C22×C412yes—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11C22×C412yes—
134C22×C4×C11—24no—
135C22×C4×C11—216no—
136C22×C4×C11—28no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—28no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11C22⋊C414yes—
154C22×C4×C11C22⋊C414yes—
155C22×C4×C11C22⋊C414yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11#4114yes—
167C22×C4×C11C2411yescharacteristic
168C11×M16—216no—
169C11×M16—216no—
170C2×C8×C11—216no—
171C2×C8×C11—24no—
172C2×C8×C11—24no—
173C2×C8×C11C2×D418yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—44no—
181C11×C4⋊C4C22×C412yes—
182C11×C4⋊C4C22×C412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C42×C11—24no—
191C23×M16C2×C1111yescharacteristic, complemented
192C2×#525C2×C1111yescharacteristic
193C2×#417C2×C1112yescomplemented
194C2×#380C2×C1111yescharacteristic, complemented
195#1895C2×C1112yescomplemented
196#1894C2×C1112yescomplemented
197#1893C2×C1112yescomplemented
198#1892C2×C1112yescomplemented
199#1736C2×C1112yescomplemented
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—22no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11C2×C22⋊C412yes—
220C23×C11C2×C22⋊C412yes—
221C23×C11C2×C22⋊C412yes—
222C23×C11#12114yes—
223C23×C11AGL(1,ℤ/8)12yes—
224C23×C11#13712yes—
225C23×C11C22×D411yescharacteristic
226Q8×C11—24no—
227Q8×C11—41no—
228Q8×C11—41no—
229D4×C11—24no—
230D4×C11—48no—
231D4×C11—48no—
232D4×C11—48no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—28no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—28no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—48no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—88no—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C4×D418yes—
262C2×C4×C11#12014yes—
263C2×C4×C11#12114yes—
264C2×C4×C11#12314yes—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4112yes—
269C8×C11—28no—
270C22×#41C22×C1111yescharacteristic
271C24×C4C22×C1111yescharacteristic
272C22×M16—24no—
273C22×M16—28no—
274C22×M16C22×C1112yes—
275C22×M16C22×C1112yes—
276C23×C8C22×C1112yes—
277#525—24no—
278#525C4×C1118yescomplemented
279C2×#123—21no—
280C2×C22⋊Q8C22×C1111yescharacteristic
281C2×C22⋊Q8C22×C1111yescharacteristic
282C2×#121C22×C1111yescharacteristic
283C2×#121C22×C1111yescharacteristic
284C2×#120—21no—
285C2×C4×D4—21no—
286C2×C4×D4—21no—
287C2×#117C22×C1111yescharacteristic
288C22×C4⋊C4C22×C1112yes—
289C22×C22⋊C4—21no—
290#417—28no—
291C2×#103C22×C1114yescomplemented
292C2×#102C22×C1114yescomplemented
293#380—21no—
294#380—21no—
295#380C22×C1112yes—
296#380C22×C1112yes—
297C2×#95—21no—
298#340C22×C1114yescomplemented
299#340C22×C1114yescomplemented
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—416no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11#38614yes—
320C22×C11#41714yescomplemented
321C22×C11C22×C22⋊C411yescharacteristic
322C22×C11C2×#12112yes—
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C11C2×#13711yescharacteristic
325C22×C11#57512yes—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—84no—
332C4×C11#38614yes—
333C4×C11C2×C4×D412yes—
334C4×C11C2×#12011yescharacteristic
335C4×C11C2×#12311yescharacteristic
336C25D4×C1111yescharacteristic
337C2×#41—22no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41C2×C4×C1114yes—
341C22×Q8C23×C1111yescharacteristic
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4C23×C1111yescharacteristic
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—21no—
349C23×C4—22no—
350C23×C4C2×C4×C1114yes—
351C23×C4D4×C1111yescharacteristic
352C23×C4D4×C1111yescharacteristic
353C23×C4D4×C1111yescharacteristic
354C23×C4D4×C1114yes—
355C23×C4C23×C1111yescharacteristic
356C23×C4C23×C1111yescharacteristic
357C23×C4C23×C1111yescharacteristic
358C2×M16—232no—
359C2×M16—24no—
360C2×M16—24no—
361C2×M16—24no—
362C2×M16—28no—
363C2×M16D4×C1118yescomplemented
364C22×C8—24no—
365C22×C8—28no—
366C22×C8C23×C1114yes—
367#123—28no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8C2×C4×C1114yescomplemented
371C22⋊Q8C2×C4×C1114yescomplemented
372#121—22no—
373#121—22no—
374#121C2×C4×C1114yescomplemented
375#121C2×C4×C1114yescomplemented
376#120—28no—
377C4×D4—28no—
378C4×D4—28no—
379#117—22no—
380#117C2×C4×C1114yes—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4C23×C1114yes—
387C2×C4⋊C4C23×C1111yescharacteristic
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—44no—
397C2×C42—21no—
398#103—28no—
399#102—28no—
400#95—22no—
401#95—22no—
402C2×C11—24no—
403C2×C11—24no—
404C2×C11—42no—
405C2×C11—82no—
406C2×C11C2×#38611yescharacteristic
407C2×C11C2×#41711yescharacteristic
408C2×C11#289611yescharacteristic
409C2×C11#305512yes—
410C2×C11#305612yes—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—42no—
416C24C11×C22⋊C414yes—
417C24C2×D4×C1111yescharacteristic
418C24C2×D4×C1111yescharacteristic
419C24C2×D4×C1111yescharacteristic
420#41—216no—
421#41—44no—
422#41—44no—
423C2×Q8—21no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8C22×C4×C1112yes—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4C22×C4×C1112yes—
438C22×C4—24no—
439C22×C4—216no—
440C22×C4—28no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—28no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4C11×C22⋊C414yes—
458C22×C4C11×C22⋊C414yes—
459C22×C4C11×C22⋊C414yes—
460C22×C4C22×C4×C1112yes—
461C22×C4C22×C4×C1112yes—
462C22×C4C22×C4×C1112yes—
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1112yes—
466C22×C4C2×D4×C1112yes—
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1114yes—
470C22×C4C11×#4114yes—
471C22×C4C24×C1111yescharacteristic
472M16—216no—
473M16—216no—
474C2×C8—216no—
475C2×C8—24no—
476C2×C8—24no—
477C2×C8C2×D4×C1118yes—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—44no—
485C4⋊C4C22×C4×C1112yes—
486C4⋊C4C22×C4×C1112yes—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C42—24no—
495C11#2097111yescharacteristic, direct product factor, Sylow
496C23—22no—
497C23—21no—
498C23—21no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—28no—
503C23—28no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—22no—
508C23—44no—
509C23—48no—
510C23—48no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23C2×C11×C22⋊C412yes—
516C23C2×C11×C22⋊C412yes—
517C23C2×C11×C22⋊C412yes—
518C23C11×#12114yes—
519C23C11×AGL(1,ℤ/8)12yes—
520C23C11×#13712yes—
521C23C22×D4×C1111yescharacteristic
522Q8—24no—
523Q8—41no—
524Q8—41no—
525D4—24no—
526D4—48no—
527D4—48no—
528D4—48no—
529D4—41no—
530D4—41no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—28no—
539C2×C4—28no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—48no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—88no—
554C2×C4C2×C11×C22⋊C412yes—
555C2×C4C2×C11×C22⋊C412yes—
556C2×C4C2×C11×C22⋊C412yes—
557C2×C4C4×D4×C1118yes—
558C2×C4C11×#12014yes—
559C2×C4C11×#12114yes—
560C2×C4C11×#12314yes—
561C2×C4C23×C4×C1111yescharacteristic
562C2×C4C22×D4×C1112yes—
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C2×C11×#4112yes—
565C8—28no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—24no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—416no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—82no—
584C22—82no—
585C22C11×#38614yes—
586C22C11×#41714yescomplemented
587C22C22×C11×C22⋊C411yescharacteristic
588C22C2×C11×#12112yes—
589C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
590C22C2×C11×#13711yescharacteristic
591C22C11×#57512yes—
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—84no—
598C4C11×#38614yes—
599C4C2×C4×D4×C1112yes—
600C4C2×C11×#12011yescharacteristic
601C4C2×C11×#12311yescharacteristic
602C2—24no—
603C2—24no—
604C2—42no—
605C2—82no—
606C2C2×C11×#38611yescharacteristic
607C2C2×C11×#41711yescharacteristic
608C2C11×#289611yescharacteristic
609C2C11×#305512yes—
610C2C11×#305612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C11×M16C2semidirect
3. C2×C11×#417C2semidirect
4. C2×C11×#380C2semidirect
5. C11×#1895C2semidirect
6. C11×#1894C2semidirect
7. C11×#1893C2semidirect
8. C11×#1892C2semidirect
9. C11×#1736C2semidirect
18. C11×#525C4semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#102C22semidirect
38. C11×#340C22semidirect
39. C11×#340C22semidirect
67. C2×C11×M16D4semidirect
74. C11×C22⋊Q8C2×C4semidirect
75. C11×C22⋊Q8C2×C4semidirect
78. C11×#121C2×C4semidirect
79. C11×#121C2×C4semidirect
106. #20971C11direct (N × H)
191. C23×M16C2×C11semidirect
193. C2×#417C2×C11semidirect
194. C2×#380C2×C11semidirect
195. #1895C2×C11semidirect
196. #1894C2×C11semidirect
197. #1893C2×C11semidirect
198. #1892C2×C11semidirect
199. #1736C2×C11semidirect
278. #525C4×C11semidirect
291. C2×#103C22×C11semidirect
292. C2×#102C22×C11semidirect
298. #340C22×C11semidirect
299. #340C22×C11semidirect
320. C22×C11#417semidirect
363. C2×M16D4×C11semidirect
370. C22⋊Q8C2×C4×C11semidirect
371. C22⋊Q8C2×C4×C11semidirect
374. #121C2×C4×C11semidirect
375. #121C2×C4×C11semidirect
495. C11#20971direct (N × H)
586. C22C11×#417semidirect

Maximal subgroups

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

subgroupindex
C23×C11×M162
C2×C11×#5252
C2×C11×#4172
C2×C11×#3802
C11×#18952
C11×#18942
C11×#18932
C11×#18922
C11×#17362
#2097111