Finite Group Databasebeta

← C11×#24216 #14601409

Subgroups — C11×#24216 #14601409

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic
2C2×C11×#464C212yesmaximal, complemented
3C2×C11×#452C212yesmaximal, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2043C211yesmaximal, characteristic, complemented
6C11×#2041C211yesmaximal, characteristic, complemented
7C11×#2016C211yesmaximal, characteristic, complemented
8C11×#2014C211yesmaximal, characteristic, complemented
9C11×#1983C212yesmaximal, complemented
10C11×#1797C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C11×#532—28no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121—21no—
21C2×C11×#121—21no—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11—21no—
25C22×C42×C11C2211yescharacteristic
26C11×#464—28no—
27C11×#452—28no—
28C2×C11×C4⋊C8C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
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×#336C2211yescharacteristic
45C11×#336C2211yescharacteristic
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×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2312yes—
58C23×C4×C11—22no—
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×Q16—24no—
63C2×C11×Q16—24no—
64C2×C11×Q16—42no—
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×C4⋊Q8—24no—
71C11×#127—24no—
72C11×#124—24no—
73C11×#124D418yes—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8D414yescomplemented
76C11×#121—28no—
77C11×#121—28no—
78C4×Q8×C11—24no—
79C4×D4×C11—28no—
80C4×D4×C11—28no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11—24no—
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—24no—
101C11×#103—24no—
102C11×#103—24no—
103C11×#103—42no—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—42no—
107C11×C22⋊C8—24no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113#24216C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—22no—
115C24×C11C2×D411yescharacteristic
116C11×#41—48no—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
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×Q8×C11C2×D412yes—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—28no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—28no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—44no—
160C22×C4×C11—44no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C11×Q16—48no—
170C11×SD16—48no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—42no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—42no—
194C42×C11—42no—
195C42×C11C2×D414yes—
196C2×#532C2×C1111yescharacteristic
197C2×#464C2×C1112yescomplemented
198C2×#452C2×C1112yescomplemented
199C4×C22⋊Q8C2×C1111yescharacteristic, complemented
200#2043C2×C1111yescharacteristic, complemented
201#2041C2×C1111yescharacteristic, complemented
202#2016C2×C1111yescharacteristic, complemented
203#2014C2×C1111yescharacteristic, complemented
204#1983C2×C1112yescomplemented
205#1797C2×C1111yescharacteristic, complemented
206#1788C2×C1112yescomplemented
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—24no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11#12112yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—24no—
225Q8×C11—42no—
226Q8×C11—42no—
227Q8×C11—42no—
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—48no—
231D4×C11—48no—
232D4×C11—416no—
233D4×C11—42no—
234D4×C11—42no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—416no—
253C2×C4×C11—41no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—41no—
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#12012yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#12112yes—
268C2×C4×C11#13512yes—
269C2×C4×C11#13712yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D412yes—
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)12yes—
274C8×C11—42no—
275C8×C11—42no—
276C22×#41C22×C1112yes—
277C22×Q16C22×C1112yes—
278C22×SD16C22×C1112yes—
279#532—28no—
280C2×C4⋊Q8C22×C1111yescharacteristic
281C2×#127C22×C1111yescharacteristic
282C2×#124C22×C1112yes—
283C2×C22⋊Q8C22×C1111yescharacteristic
284C2×#121—21no—
285C2×#121—21no—
286C2×C4×Q8C22×C1111yescharacteristic
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C22×C42C22×C1111yescharacteristic
290#464—28no—
291#452—28no—
292C2×C4⋊C8C22×C1112yes—
293C2×#103C22×C1112yes—
294C2×#103C22×C1112yes—
295C2×#103C22×C1112yes—
296C2×#102C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×C22⋊C8C22×C1112yes—
300#391C22×C1111yescharacteristic
301#389C22×C1111yescharacteristic
302#387—21no—
303#385—21no—
304#380C22×C1111yescharacteristic
305C4×C4⋊C4—21no—
306C4×C4⋊C4C22×C1111yescharacteristic
307C4×C22⋊C4—21no—
308#336C22×C1111yescharacteristic
309#336C22×C1111yescharacteristic
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C22×C11#53511yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11D4212yes—
342C4×C11#54612yes—
343C2×#41—24no—
344C2×#41—24no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—42no—
348C2×#41—42no—
349C22×Q8C23×C1111yescharacteristic
350C22×Q8C23×C1112yes—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4C23×C1112yes—
355C23×C4—22no—
356C23×C4D4×C1111yescharacteristic
357C23×C4D4×C1111yescharacteristic
358C23×C4C23×C1111yescharacteristic
359C2×Q16—24no—
360C2×Q16—24no—
361C2×Q16—42no—
362C2×SD16—24no—
363C2×SD16—24no—
364C2×SD16—42no—
365C22×C8C23×C1112yes—
366C22×C8C23×C1112yes—
367C4⋊Q8—24no—
368#127—24no—
369#124—24no—
370#124D4×C1118yes—
371C22⋊Q8—22no—
372C22⋊Q8D4×C1114yescomplemented
373#121—28no—
374#121—28no—
375C4×Q8—24no—
376C4×D4—28no—
377C4×D4—28no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C23×C1111yescharacteristic
384C2×C4⋊C4C23×C1111yescharacteristic
385C2×C4⋊C4C23×C1111yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42D4×C1111yescharacteristic
394C2×C42D4×C1111yescharacteristic
395C2×C42C23×C1111yescharacteristic
396C2×C42C23×C1111yescharacteristic
397C4⋊C8—24no—
398#103—24no—
399#103—24no—
400#103—42no—
401#102—24no—
402#102—24no—
403#102—42no—
404C22⋊C8—24no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410C2×C11—42no—
411C2×C11—84no—
412C2×C11#240811yescharacteristic
413C2×C11#300211yescharacteristic
414C2×C11#300711yescharacteristic
415C2×C11#303511yescharacteristic
416C2×C11#303711yescharacteristic
417C2×C11#321011yescharacteristic
418C2×C11#321911yescharacteristic
419C24—22no—
420C24C2×D4×C1111yescharacteristic
421#41—48no—
422#41—48no—
423#41—48no—
424#41—48no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8C2×D4×C1114yes—
434C2×Q8C2×D4×C1112yes—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4C2×D4×C1114yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1111yescharacteristic
469C22×C4C2×D4×C1112yes—
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C11×#4112yes—
473C22×C4C24×C1111yescharacteristic
474Q16—48no—
475SD16—48no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4C2×D4×C1112yes—
491C22⋊C4—24no—
492C22⋊C4—28no—
493C22⋊C4—28no—
494C22⋊C4—42no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—42no—
499C42—42no—
500C42C2×D4×C1114yes—
501C11#2421611yescharacteristic, direct product factor, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23C11×#12112yes—
516C23C22×D4×C1111yescharacteristic
517Q8—24no—
518Q8—24no—
519Q8—24no—
520Q8—42no—
521Q8—42no—
522Q8—42no—
523D4—24no—
524D4—24no—
525D4—48no—
526D4—48no—
527D4—416no—
528D4—42no—
529D4—42no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—416no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4C11×#12012yes—
561C2×C4C11×#12012yes—
562C2×C4C11×#12112yes—
563C2×C4C11×#13512yes—
564C2×C4C11×#13712yes—
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1112yes—
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C11×H(5,𝔽2)12yes—
569C8—42no—
570C8—42no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22C2×C11×#12011yescharacteristic
586C22C2×C11×#12111yescharacteristic
587C22C11×#53511yescharacteristic
588C22C2×C11×#13511yescharacteristic
589C22C2×C11×#13711yescharacteristic
590C22C11×#57511yescharacteristic
591C22C11×#57511yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—22no—
597C4—44no—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4D42×C1112yes—
603C4C11×#54612yes—
604C2—42no—
605C2—84no—
606C2C11×#240811yescharacteristic
607C2C11×#300211yescharacteristic
608C2C11×#300711yescharacteristic
609C2C11×#303511yescharacteristic
610C2C11×#303711yescharacteristic
611C2C11×#321011yescharacteristic
612C2C11×#321911yescharacteristic
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×#464C2semidirect
3. C2×C11×#452C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2043C2semidirect
6. C11×#2041C2semidirect
7. C11×#2016C2semidirect
8. C11×#2014C2semidirect
9. C11×#1983C2semidirect
10. C11×#1797C2semidirect
11. C11×#1788C2semidirect
75. C11×C22⋊Q8D4semidirect
113. #24216C11direct (N × H)
197. C2×#464C2×C11semidirect
198. C2×#452C2×C11semidirect
199. C4×C22⋊Q8C2×C11semidirect
200. #2043C2×C11semidirect
201. #2041C2×C11semidirect
202. #2016C2×C11semidirect
203. #2014C2×C11semidirect
204. #1983C2×C11semidirect
205. #1797C2×C11semidirect
206. #1788C2×C11semidirect
372. C22⋊Q8D4×C11semidirect
501. C11#24216direct (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×#4642
C2×C11×#4522
C4×C11×C22⋊Q82
C11×#20432
C11×#20412
C11×#20162
C11×#20142
C11×#19832
C11×#17972
C11×#17882
#2421611