Finite Group Databasebeta

← C11×#24269 #14601462

Subgroups — C11×#24269 #14601462

Order 2816.

1580 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C11×SD16C211yesmaximal, characteristic, complemented
2C2×C11×#468C212yesmaximal, complemented
3C2×C11×#435C211yesmaximal, characteristic, complemented
4C11×#2409C211yesmaximal, characteristic, complemented
5C11×#2408C211yesmaximal, characteristic
6C11×#2055C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1973C212yesmaximal, complemented
9C11×#1808C211yesmaximal, characteristic, complemented
10C11×#1787C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×SD16—28no—
15C22×C11×SD16—24no—
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×M16C2211yescharacteristic, complemented
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yescomplemented
21C2×C11×#121C2212yes—
22C2×C11×#120—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#468—28no—
25C11×#435—24no—
26C2×C11×#107C2212yescomplemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#103C2212yescomplemented
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic, complemented
34C2×C11×#97C2211yescharacteristic, complemented
35C11×#395—21no—
36C11×#394—21no—
37C11×#393—21no—
38C11×#392—21no—
39C11×#391C2212yescomplemented
40C11×#390C2212yes—
41C11×#386—21no—
42C11×#385—21no—
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#379—21no—
46C11×#340C2212yescomplemented
47C25×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—24no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2312yes—
54C22×D4×C11—24no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11—42no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2312yes—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C2×C11×SD16—232no—
66C2×C11×SD16—24no—
67C2×C11×SD16—24no—
68C2×C11×SD16—24no—
69C2×C11×SD16—24no—
70C2×C11×SD16—24no—
71C2×C11×SD16D418yescomplemented
72C2×C11×M16—22no—
73C2×C11×M16—24no—
74C22×C8×C11—24no—
75C22×C8×C11D414yescomplemented
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—42no—
82C11×#121—24no—
83C11×#121—42no—
84C11×#120—44no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#107—24no—
101C11×C4⋊C8—22no—
102C11×#103—24no—
103C11×#103—42no—
104C11×#102—24no—
105C11×#102—42no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—22no—
108C11×#97—22no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—22no—
112C11×#95—22no—
113#24269C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—22no—
115C24×C11—44no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—82no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C2×Q8×C11—22no—
123C2×Q8×C11—28no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11—44no—
131C2×Q8×C11—42no—
132C2×Q8×C11C2×D414yes—
133C2×D4×C11—28no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—48no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—82no—
149C2×D4×C11C2×D414yes—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—44no—
160C22×C4×C11—42no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C11×SD16—216no—
169C11×SD16—216no—
170C11×M16—44no—
171C2×C8×C11—28no—
172C2×C8×C11—22no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D414yes—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—44no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—44no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4—42no—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—82no—
194C42×C11—21no—
195C42×C11—21no—
196C23×SD16C2×C1111yescharacteristic, complemented
197C2×#468C2×C1112yescomplemented
198C2×#435C2×C1111yescharacteristic, complemented
199#2409C2×C1111yescharacteristic, complemented
200#2408C2×C1111yescharacteristic
201#2055C2×C1112yescomplemented
202#2000C2×C1112yescomplemented
203#1973C2×C1112yescomplemented
204#1808C2×C1111yescharacteristic, complemented
205#1787C2×C1111yescharacteristic, complemented
206#1786C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—48no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—88no—
223C23×C11—88no—
224C23×C11—84no—
225C23×C11—84no—
226C23×C11#12112yes—
227C23×C11AGL(1,ℤ/8)12yes—
228C23×C11#13712yes—
229C23×C11C22×D411yescharacteristic
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—48no—
233Q8×C11—42no—
234Q8×C11—42no—
235D4×C11—24no—
236D4×C11—24no—
237D4×C11—48no—
238D4×C11—44no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—88no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—48no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11#12112yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D412yes—
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)12yes—
271C8×C11—22no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11#12014yescomplemented
275C23×Q8C22×C1111yescharacteristic
276C23×D4C22×C1111yescharacteristic
277C22×SD16—28no—
278C22×SD16—24no—
279C22×SD16C22×C1112yes—
280C22×SD16C22×C1112yes—
281C22×M16C22×C1111yescharacteristic, complemented
282C23×C8C22×C1111yescharacteristic
283C2×C22⋊Q8C22×C1112yescomplemented
284C2×#121C22×C1112yes—
285C2×#120—21no—
286C2×C4×D4C22×C1111yescharacteristic
287#468—28no—
288#435—24no—
289C2×#107C22×C1112yescomplemented
290C2×C4⋊C8C22×C1111yescharacteristic, complemented
291C2×#103C22×C1112yescomplemented
292C2×#103C22×C1112yescomplemented
293C2×#102C22×C1112yes—
294C2×#102C22×C1112yes—
295C2×C22⋊C8C22×C1111yescharacteristic
296C2×C22⋊C8C22×C1111yescharacteristic, complemented
297C2×#97C22×C1111yescharacteristic, complemented
298#395—21no—
299#394—21no—
300#393—21no—
301#392—21no—
302#391C22×C1112yescomplemented
303#390C22×C1112yes—
304#386—21no—
305#385—21no—
306#380C22×C1111yescharacteristic
307#380C22×C1111yescharacteristic
308#379—21no—
309#340C22×C1112yescomplemented
310C22×C11—22no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—22no—
314C22×C11—41no—
315C22×C11—44no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—816no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11#46814yescomplemented
328C22×C11C2×#12111yescharacteristic
329C22×C11D4212yes—
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11C2×#13711yescharacteristic
332C22×C11#57712yes—
333C4×C11—22no—
334C4×C11—41no—
335C4×C11—44no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—82no—
339C4×C11—82no—
340C4×C11C2×#12011yescharacteristic
341C4×C11#53511yescharacteristic
342C4×C11#54612yes—
343C25—21no—
344C22×Q8—21no—
345C22×Q8—24no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—42no—
349C22×Q8C23×C1112yes—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—42no—
356C22×D4D4×C1111yescharacteristic
357C22×D4C23×C1112yes—
358C23×C4—21no—
359C23×C4C23×C1111yescharacteristic
360C23×C4C23×C1111yescharacteristic
361C2×SD16—232no—
362C2×SD16—24no—
363C2×SD16—24no—
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—24no—
367C2×SD16D4×C1118yescomplemented
368C2×M16—22no—
369C2×M16—24no—
370C22×C8—24no—
371C22×C8D4×C1114yescomplemented
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1111yescharacteristic
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376C22⋊Q8—24no—
377C22⋊Q8—42no—
378#121—24no—
379#121—42no—
380#120—44no—
381C4×D4—22no—
382C4×D4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4D4×C1111yescharacteristic
385C2×C4⋊C4C23×C1112yes—
386C2×C4⋊C4C23×C1112yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4D4×C1111yescharacteristic
394C2×C22⋊C4D4×C1111yescharacteristic
395C2×C42C23×C1111yescharacteristic
396#107—24no—
397C4⋊C8—22no—
398#103—24no—
399#103—42no—
400#102—24no—
401#102—42no—
402C22⋊C8—22no—
403C22⋊C8—22no—
404#97—22no—
405#95—21no—
406#95—21no—
407#95—22no—
408#95—22no—
409C2×C11—24no—
410C2×C11—81no—
411C2×C11—84no—
412C2×C11#240811yescharacteristic
413C2×C11C2×#46811yescharacteristic
414C2×C11#305711yescharacteristic
415C2×C11#326512yes—
416C2×C11#326612yes—
417C24—22no—
418C24—44no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—82no—
423C24C2×D4×C1111yescharacteristic
424C24C2×D4×C1111yescharacteristic
425C2×Q8—22no—
426C2×Q8—28no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—44no—
432C2×Q8—48no—
433C2×Q8—44no—
434C2×Q8—42no—
435C2×Q8C2×D4×C1114yes—
436C2×D4—28no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—48no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4—82no—
452C2×D4C2×D4×C1114yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—42no—
464C22×C4C2×D4×C1111yescharacteristic
465C22×C4C2×D4×C1111yescharacteristic
466C22×C4C2×D4×C1111yescharacteristic
467C22×C4C2×D4×C1111yescharacteristic
468C22×C4C2×D4×C1112yes—
469C22×C4C11×#4112yes—
470C22×C4C24×C1111yescharacteristic
471SD16—216no—
472SD16—216no—
473M16—44no—
474C2×C8—22no—
475C2×C8—28no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8C2×D4×C1112yes—
481C2×C8C2×D4×C1112yes—
482C2×C8C2×D4×C1114yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—44no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—44no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—82no—
497C42—21no—
498C42—21no—
499C11#2426911yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—22no—
502C23—21no—
503C23—22no—
504C23—24no—
505C23—21no—
506C23—21no—
507C23—22no—
508C23—48no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—88no—
516C23—88no—
517C23—84no—
518C23—84no—
519C23C11×#12112yes—
520C23C11×AGL(1,ℤ/8)12yes—
521C23C11×#13712yes—
522C23C22×D4×C1111yescharacteristic
523Q8—24no—
524Q8—24no—
525Q8—48no—
526Q8—42no—
527Q8—42no—
528D4—24no—
529D4—24no—
530D4—48no—
531D4—44no—
532D4—42no—
533D4—42no—
534D4—88no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—48no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4C11×#12112yes—
560C2×C4C22×D4×C1111yescharacteristic
561C2×C4C22×D4×C1112yes—
562C2×C4C2×C11×#4111yescharacteristic
563C2×C4C11×H(5,𝔽2)12yes—
564C8—22no—
565C8—41no—
566C8—41no—
567C8C11×#12014yescomplemented
568C22—22no—
569C22—24no—
570C22—24no—
571C22—22no—
572C22—41no—
573C22—44no—
574C22—42no—
575C22—44no—
576C22—42no—
577C22—44no—
578C22—41no—
579C22—41no—
580C22—816no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22C11×#46814yescomplemented
586C22C2×C11×#12111yescharacteristic
587C22D42×C1112yes—
588C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
589C22C2×C11×#13711yescharacteristic
590C22C11×#57712yes—
591C4—22no—
592C4—41no—
593C4—44no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4—82no—
598C4C2×C11×#12011yescharacteristic
599C4C11×#53511yescharacteristic
600C4C11×#54612yes—
601C2—24no—
602C2—81no—
603C2—84no—
604C2C11×#240811yescharacteristic
605C2C2×C11×#46811yescharacteristic
606C2C11×#305711yescharacteristic
607C2C11×#326512yes—
608C2C11×#326612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2408C2
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. C23×C11×SD16C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#435C2semidirect
4. C11×#2409C2semidirect
6. C11×#2055C2semidirect
7. C11×#2000C2semidirect
8. C11×#1973C2semidirect
9. C11×#1808C2semidirect
10. C11×#1787C2semidirect
11. C11×#1786C2semidirect
18. C22×C11×M16C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
26. C2×C11×#107C22semidirect
27. C2×C11×C4⋊C8C22semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
33. C2×C11×C22⋊C8C22semidirect
34. C2×C11×#97C22semidirect
39. C11×#391C22semidirect
46. C11×#340C22semidirect
71. C2×C11×SD16D4semidirect
75. C22×C8×C11D4semidirect
113. #24269C11direct (N × H)
196. C23×SD16C2×C11semidirect
197. C2×#468C2×C11semidirect
198. C2×#435C2×C11semidirect
199. #2409C2×C11semidirect
201. #2055C2×C11semidirect
202. #2000C2×C11semidirect
203. #1973C2×C11semidirect
204. #1808C2×C11semidirect
205. #1787C2×C11semidirect
206. #1786C2×C11semidirect
274. C8×C11#120semidirect
281. C22×M16C22×C11semidirect
283. C2×C22⋊Q8C22×C11semidirect
289. C2×#107C22×C11semidirect
290. C2×C4⋊C8C22×C11semidirect
291. C2×#103C22×C11semidirect
292. C2×#103C22×C11semidirect
296. C2×C22⋊C8C22×C11semidirect
297. C2×#97C22×C11semidirect
302. #391C22×C11semidirect
309. #340C22×C11semidirect
327. C22×C11#468semidirect
367. C2×SD16D4×C11semidirect
371. C22×C8D4×C11semidirect
499. C11#24269direct (N × H)
567. C8C11×#120semidirect
585. C22C11×#468semidirect

Maximal subgroups

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

subgroupindex
C23×C11×SD162
C2×C11×#4682
C2×C11×#4352
C11×#24092
C11×#24082
C11×#20552
C11×#20002
C11×#19732
C11×#18082
C11×#17872
C11×#17862
#2426911