Finite Group Databasebeta

← C11×#20960 #14598153

Subgroups — C11×#20960 #14598153

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C2×C11×#518C211yesmaximal, characteristic, complemented
3C22×C11×#99C211yesmaximal, characteristic, complemented
4C11×#2308C212yesmaximal, complemented
5C11×#1890C214yesmaximal, complemented
6C11×#1889C214yesmaximal, complemented
7C2×C11×#342C212yesmaximal, complemented
8C23×D4×C11C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C11×#534—24no—
11C11×#534C418yescomplemented
12C2×C11×#123—21no—
13C2×C11×#123C2212yes—
14C2×C11×#121—22no—
15C2×C11×#120—21no—
16C2×C11×#120C2212yes—
17C11×#518—22no—
18C11×#518—24no—
19C11×#518C2214yes—
20C2×C4×D4×C11—24no—
21C2×C11×#117—21no—
22C22×C11×C22⋊C4—21no—
23C22×C11×C22⋊C4C2212yes—
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×C11×#99—24no—
27C2×C11×#99C2214yes—
28C11×#386—24no—
29C11×#386—24no—
30C11×#381C2214yescomplemented
31C11×#379C2214yescomplemented
32C11×#342C2218yescomplemented
33C25×C11D411yescharacteristic
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—24no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—24no—
45C22×D4×C11—22no—
46C22×D4×C11C2×C414yes—
47C22×D4×C11C2×C414yescomplemented
48C22×D4×C11D414yes—
49C22×D4×C11D412yes—
50C22×D4×C11C2312yes—
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D414yescomplemented
56C23×C4×C11C2311yescharacteristic
57C11×#123—24no—
58C11×#123—28no—
59C11×#123C2×C418yescomplemented
60C11×#121—216no—
61C11×#120—28no—
62C11×#120—24no—
63C11×#120C2×C418yescomplemented
64C4×D4×C11—216no—
65C4×D4×C11—216no—
66C11×#117—24no—
67C11×#117—24no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4C2×C414yescomplemented
86C2×C11×C22⋊C4D414yescomplemented
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11—22no—
91C11×#99—28no—
92C11×#95—28no—
93#20960C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—22no—
101C24×C11—82no—
102C24×C11—82no—
103C24×C11—82no—
104C24×C11C22⋊C414yescomplemented
105C24×C11C22×C412yes—
106C24×C11C22×C412yescomplemented
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D412yes—
111C24×C11C2×D412yes—
112C24×C11C2×D412yes—
113C24×C11#4114yes—
114C24×C11C2411yescharacteristic
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11—41no—
129C2×D4×C11—42no—
130C2×D4×C11—41no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—84no—
136C2×D4×C11C22⋊C418yescomplemented
137C2×D4×C11C22×C414yes—
138C2×D4×C11C2×D414yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—44no—
153C22×C4×C11—84no—
154C22×C4×C11—84no—
155C22×C4×C11—82no—
156C22×C4×C11—84no—
157C22×C4×C11C22⋊C414yescomplemented
158C22×C4×C11C22×C412yescomplemented
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D418yes—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—28no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—88no—
176C11×C22⋊C4C22×C414yescomplemented
177C42×C11—28no—
178C2×#534C2×C1111yescharacteristic
179C2×#518C2×C1111yescharacteristic, complemented
180C22×#99C2×C1111yescharacteristic, complemented
181#2308C2×C1112yescomplemented
182#1890C2×C1114yescomplemented
183#1889C2×C1114yescomplemented
184C2×#342C2×C1112yescomplemented
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—48no—
199C23×C11—44no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—82no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11—82no—
211C23×C11—84no—
212C23×C11C2×C22⋊C414yes—
213C23×C11C2×C22⋊C412yes—
214C23×C11C2×C22⋊C412yes—
215C23×C11C4×D414yes—
216C23×C11C4×D414yes—
217C23×C11#12011yescharacteristic
218C23×C11#12012yes—
219C23×C11#12011yescharacteristic
220C23×C11#12114yes—
221C23×C11#12114yes—
222C23×C11#12312yes—
223C23×C11#12312yes—
224C23×C11C23×C411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D412yes—
227C23×C11C22×D411yescharacteristic
228C23×C11C2×#4112yes—
229D4×C11—28no—
230D4×C11—28no—
231D4×C11—216no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—48no—
235D4×C11—88no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—48no—
245C2×C4×C11—44no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—48no—
250C2×C4×C11—48no—
251C2×C4×C11—44no—
252C2×C4×C11—84no—
253C2×C4×C11—84no—
254C2×C4×C11—88no—
255C2×C4×C11—88no—
256C2×C4×C11C2×C22⋊C414yes—
257C23×D4C22×C1111yescharacteristic
258C23×D4C22×C1111yescharacteristic
259#534—24no—
260#534C4×C1118yescomplemented
261C2×#123—21no—
262C2×#123C22×C1112yes—
263C2×#121—22no—
264C2×#120—21no—
265C2×#120C22×C1112yes—
266#518—22no—
267#518—24no—
268#518C22×C1114yes—
269C2×C4×D4—24no—
270C2×#117—21no—
271C22×C22⋊C4—21no—
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1112yes—
274C22×C22⋊C4C22×C1111yescharacteristic
275C2×#99—24no—
276C2×#99C22×C1114yes—
277#386—24no—
278#386—24no—
279#381C22×C1114yescomplemented
280#379C22×C1114yescomplemented
281#342C22×C1118yescomplemented
282C22×C11—22no—
283C22×C11—24no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—22no—
287C22×C11—24no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—42no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—44no—
302C22×C11—48no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—84no—
307C22×C11—84no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11#38612yes—
311C22×C11#38612yes—
312C22×C11#38614yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C22×C11C2×C4×D412yes—
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12112yes—
317C22×C11C2×#12311yescharacteristic
318C4×C11—24no—
319C4×C11—44no—
320C4×C11—48no—
321C4×C11—42no—
322C4×C11—84no—
323C25D4×C1111yescharacteristic
324C25C23×C1111yescharacteristic
325C25C23×C1111yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—24no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4C2×C4×C1114yes—
337C22×D4C2×C4×C1114yescomplemented
338C22×D4D4×C1114yes—
339C22×D4D4×C1112yes—
340C22×D4C23×C1112yes—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4D4×C1111yescharacteristic
345C23×C4D4×C1114yescomplemented
346C23×C4C23×C1111yescharacteristic
347#123—24no—
348#123—28no—
349#123C2×C4×C1118yescomplemented
350#121—216no—
351#120—28no—
352#120—24no—
353#120C2×C4×C1118yescomplemented
354C4×D4—216no—
355C4×D4—216no—
356#117—24no—
357#117—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4C2×C4×C1114yescomplemented
376C2×C22⋊C4D4×C1114yescomplemented
377C2×C22⋊C4C23×C1114yes—
378C2×C22⋊C4C23×C1114yes—
379C2×C22⋊C4C23×C1112yes—
380C2×C42—22no—
381#99—28no—
382#95—28no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11—22no—
386C2×C11—22no—
387C2×C11—21no—
388C2×C11—22no—
389C2×C11—24no—
390C2×C11—44no—
391C2×C11—82no—
392C2×C11C2×#38611yescharacteristic
393C2×C11#302612yes—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—82no—
402C24—82no—
403C24—82no—
404C24C11×C22⋊C414yescomplemented
405C24C22×C4×C1112yes—
406C24C22×C4×C1112yescomplemented
407C24C2×D4×C1112yes—
408C24C2×D4×C1111yescharacteristic
409C24C2×D4×C1111yescharacteristic
410C24C2×D4×C1112yes—
411C24C2×D4×C1112yes—
412C24C2×D4×C1112yes—
413C24C11×#4114yes—
414C24C24×C1111yescharacteristic
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—24no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—28no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4—41no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—84no—
436C2×D4C11×C22⋊C418yescomplemented
437C2×D4C22×C4×C1114yes—
438C2×D4C2×D4×C1114yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—84no—
454C22×C4—84no—
455C22×C4—82no—
456C22×C4—84no—
457C22×C4C11×C22⋊C414yescomplemented
458C22×C4C22×C4×C1112yescomplemented
459C22×C4C2×D4×C1112yes—
460C22×C4C2×D4×C1118yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—24no—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—28no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—44no—
475C22⋊C4—88no—
476C22⋊C4C22×C4×C1114yescomplemented
477C42—28no—
478C11#2096011yescharacteristic, direct product factor, Sylow
479C23—22no—
480C23—24no—
481C23—24no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—44no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23—84no—
502C23—84no—
503C23—84no—
504C23—82no—
505C23—84no—
506C23C2×C11×C22⋊C414yes—
507C23C2×C11×C22⋊C412yes—
508C23C2×C11×C22⋊C412yes—
509C23C4×D4×C1114yes—
510C23C4×D4×C1114yes—
511C23C11×#12011yescharacteristic
512C23C11×#12012yes—
513C23C11×#12011yescharacteristic
514C23C11×#12114yes—
515C23C11×#12114yes—
516C23C11×#12312yes—
517C23C11×#12312yes—
518C23C23×C4×C1111yescharacteristic
519C23C22×D4×C1111yescharacteristic
520C23C22×D4×C1112yes—
521C23C22×D4×C1111yescharacteristic
522C23C2×C11×#4112yes—
523D4—28no—
524D4—28no—
525D4—216no—
526D4—44no—
527D4—44no—
528D4—48no—
529D4—88no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—28no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—48no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4—88no—
549C2×C4—88no—
550C2×C4C2×C11×C22⋊C414yes—
551C22—22no—
552C22—24no—
553C22—22no—
554C22—24no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—42no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—48no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—84no—
576C22—84no—
577C22—82no—
578C22—82no—
579C22C11×#38612yes—
580C22C11×#38612yes—
581C22C11×#38614yes—
582C22C22×C11×C22⋊C411yescharacteristic
583C22C2×C4×D4×C1112yes—
584C22C2×C11×#12011yescharacteristic
585C22C2×C11×#12112yes—
586C22C2×C11×#12311yescharacteristic
587C4—24no—
588C4—44no—
589C4—48no—
590C4—42no—
591C4—84no—
592C2—21no—
593C2—22no—
594C2—22no—
595C2—22no—
596C2—21no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—82no—
601C2C2×C11×#38611yescharacteristic
602C2C11×#302612yes—
subgroupG/H
center, socleC22×C11C2×#120
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#534C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#518C2semidirect
3. C22×C11×#99C2semidirect
4. C11×#2308C2semidirect
5. C11×#1890C2semidirect
6. C11×#1889C2semidirect
7. C2×C11×#342C2semidirect
11. C11×#534C4semidirect
30. C11×#381C22semidirect
31. C11×#379C22semidirect
32. C11×#342C22semidirect
47. C22×D4×C11C2×C4semidirect
55. C23×C4×C11D4semidirect
59. C11×#123C2×C4semidirect
63. C11×#120C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
86. C2×C11×C22⋊C4D4semidirect
93. #20960C11direct (N × H)
104. C24×C11C22⋊C4semidirect
106. C24×C11C22×C4semidirect
136. C2×D4×C11C22⋊C4semidirect
157. C22×C4×C11C22⋊C4semidirect
158. C22×C4×C11C22×C4semidirect
176. C11×C22⋊C4C22×C4semidirect
179. C2×#518C2×C11semidirect
180. C22×#99C2×C11semidirect
181. #2308C2×C11semidirect
182. #1890C2×C11semidirect
183. #1889C2×C11semidirect
184. C2×#342C2×C11semidirect
260. #534C4×C11semidirect
279. #381C22×C11semidirect
280. #379C22×C11semidirect
281. #342C22×C11semidirect
337. C22×D4C2×C4×C11semidirect
345. C23×C4D4×C11semidirect
349. #123C2×C4×C11semidirect
353. #120C2×C4×C11semidirect
375. C2×C22⋊C4C2×C4×C11semidirect
376. C2×C22⋊C4D4×C11semidirect
404. C24C11×C22⋊C4semidirect
406. C24C22×C4×C11semidirect
436. C2×D4C11×C22⋊C4semidirect
457. C22×C4C11×C22⋊C4semidirect
458. C22×C4C22×C4×C11semidirect
476. C22⋊C4C22×C4×C11semidirect
478. C11#20960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C2×C11×#5182
C22×C11×#992
C11×#23082
C11×#18902
C11×#18892
C2×C11×#3422
#2096011