Finite Group Databasebeta

← C11×#11069 #14588262

Subgroups — C11×#11069 #14588262

Order 2816.

2538 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2315C211yesmaximal, characteristic, complemented
2C2×C11×#379C212yesmaximal
3C2×C11×#379C211yesmaximal, characteristic
4C2×C11×#342C212yesmaximal, complemented
5C2×C11×#342C211yesmaximal, characteristic, complemented
6C26×C11C2211yescharacteristic
7C22×C11×C22⋊C4—24no—
8C22×C11×C22⋊C4—22no—
9C22×C11×C22⋊C4C2212yes—
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C11×#385—24no—
14C11×#380—22no—
15C11×#379—24no—
16C11×#379—24no—
17C11×#379—22no—
18C11×#379C414yescomplemented
19C11×#342—22no—
20C11×#342—24no—
21C25×C11—21no—
22C25×C11—22no—
23C25×C11—21no—
24C25×C11—22no—
25C25×C11—22no—
26C25×C11—21no—
27C25×C11—21no—
28C25×C11—22no—
29C25×C11—48no—
30C25×C11C2×C412yes—
31C25×C11D412yes—
32C25×C11Q812yes—
33C25×C11C2311yescharacteristic
34C23×C4×C11—21no—
35C23×C4×C11—22no—
36C23×C4×C11D414yes—
37C23×C4×C11D412yes—
38C2×C11×C4⋊C4—24no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—216no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—28no—
57C2×C11×C22⋊C4—48no—
58C2×C11×C22⋊C4—416no—
59C2×C11×C22⋊C4C2×C412yes—
60C2×C11×C22⋊C4C2×C412yes—
61C2×C11×C22⋊C4D414yes—
62C2×C11×C22⋊C4D412yes—
63C11×#95—24no—
64#11069C1111yesmaximal, characteristic, direct product factor, Sylow
65C24×C11—28no—
66C24×C11—216no—
67C24×C11—22no—
68C24×C11—24no—
69C24×C11—24no—
70C24×C11—22no—
71C24×C11—22no—
72C24×C11—24no—
73C24×C11—22no—
74C24×C11—24no—
75C24×C11—22no—
76C24×C11—22no—
77C24×C11—24no—
78C24×C11—24no—
79C24×C11—48no—
80C24×C11—48no—
81C24×C11—48no—
82C24×C11—44no—
83C24×C11—44no—
84C24×C11—48no—
85C24×C11—48no—
86C24×C11—416no—
87C24×C11—416no—
88C24×C11—48no—
89C24×C11—48no—
90C24×C11—416no—
91C24×C11—41no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11—41no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—41no—
99C24×C11—42no—
100C24×C11—41no—
101C24×C11C4⋊C414yescomplemented
102C24×C11C22×C411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D412yes—
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C24×C11C2×D412yes—
108C24×C11C2×Q811yescharacteristic
109C24×C11#4111yescharacteristic
110C24×C11#4111yescharacteristic
111C24×C11#4112yes—
112C24×C11#4112yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—44no—
121C22×C4×C11—48no—
122C22×C4×C11—44no—
123C22×C4×C11—48no—
124C22×C4×C11—42no—
125C22×C4×C11—41no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11C22⋊C414yescomplemented
129C11×C4⋊C4—84no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—416no—
136C11×C22⋊C4—432no—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—42no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—42no—
144#2315C2×C1111yescharacteristic, complemented
145C2×#379C2×C1112yes—
146C2×#379C2×C1111yescharacteristic
147C2×#342C2×C1112yescomplemented
148C2×#342C2×C1111yescharacteristic, complemented
149C23×C11—24no—
150C23×C11—28no—
151C23×C11—28no—
152C23×C11—216no—
153C23×C11—216no—
154C23×C11—28no—
155C23×C11—28no—
156C23×C11—216no—
157C23×C11—24no—
158C23×C11—28no—
159C23×C11—48no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—44no—
164C23×C11—42no—
165C23×C11—44no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—416no—
171C23×C11—48no—
172C23×C11—48no—
173C23×C11—48no—
174C23×C11—416no—
175C23×C11—48no—
176C23×C11—44no—
177C23×C11—48no—
178C23×C11—416no—
179C23×C11—44no—
180C23×C11—48no—
181C23×C11—48no—
182C23×C11—416no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11—416no—
186C23×C11—416no—
187C23×C11—416no—
188C23×C11—416no—
189C23×C11—416no—
190C23×C11—42no—
191C23×C11—44no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—44no—
196C23×C11—44no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—48no—
200C23×C11C2×C22⋊C411yescharacteristic
201C23×C11C2×C4⋊C411yescharacteristic
202C23×C11#11711yescharacteristic
203C23×C11C4×D412yes—
204C23×C11C4×D412yes—
205C23×C11#12012yes—
206C23×C11#12011yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11#12112yes—
209C23×C11#12112yes—
210C23×C11#12111yescharacteristic
211C23×C11#12112yes—
212C23×C11C22⋊Q811yescharacteristic
213C23×C11C22⋊Q812yes—
214C23×C11C22⋊Q811yescharacteristic
215C23×C11C22⋊Q812yes—
216C23×C11#12311yescharacteristic
217C23×C11#12312yes—
218C23×C11#12312yes—
219C23×C11#12412yes—
220C23×C11#12411yescharacteristic
221C23×C11#12612yes—
222C23×C11#12711yescharacteristic
223C2×C4×C11—24no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—48no—
233C2×C4×C11—82no—
234C2×C4×C11—84no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11—84no—
238C2×C4×C11—84no—
239C26C22×C1111yescharacteristic
240C22×C22⋊C4—24no—
241C22×C22⋊C4—22no—
242C22×C22⋊C4C22×C1112yes—
243C22×C22⋊C4C22×C1111yescharacteristic
244C22×C22⋊C4C22×C1112yes—
245C22×C22⋊C4C22×C1111yescharacteristic
246#385—24no—
247#380—22no—
248#379—24no—
249#379—24no—
250#379—22no—
251#379C4×C1114yescomplemented
252#342—22no—
253#342—24no—
254C22×C11—22no—
255C22×C11—24no—
256C22×C11—22no—
257C22×C11—24no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—22no—
265C22×C11—24no—
266C22×C11—28no—
267C22×C11—216no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—48no—
279C22×C11—416no—
280C22×C11—44no—
281C22×C11—48no—
282C22×C11—416no—
283C22×C11—416no—
284C22×C11—48no—
285C22×C11—48no—
286C22×C11—48no—
287C22×C11—44no—
288C22×C11—48no—
289C22×C11—48no—
290C22×C11#38011yescharacteristic
291C22×C11#38512yes—
292C22×C11#38611yescharacteristic
293C22×C11#38812yes—
294C22×C11#39011yescharacteristic
295C22×C11#39211yescharacteristic
296C22×C11#39311yescharacteristic
297C22×C11#39412yes—
298C22×C11#39612yes—
299C22×C11#39711yescharacteristic
300C22×C11#39911yescharacteristic
301C22×C11B(4,𝔽2)14yes—
302C4×C11—44no—
303C4×C11—82no—
304C4×C11—84no—
305C4×C11—84no—
306C25—21no—
307C25—22no—
308C25—21no—
309C25—22no—
310C25—22no—
311C25—21no—
312C25—21no—
313C25—22no—
314C25—48no—
315C25C2×C4×C1112yes—
316C25D4×C1112yes—
317C25Q8×C1112yes—
318C25C23×C1111yescharacteristic
319C23×C4—21no—
320C23×C4—22no—
321C23×C4D4×C1114yes—
322C23×C4D4×C1112yes—
323C2×C4⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—216no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—48no—
343C2×C22⋊C4—416no—
344C2×C22⋊C4C2×C4×C1112yes—
345C2×C22⋊C4C2×C4×C1112yes—
346C2×C22⋊C4D4×C1114yes—
347C2×C22⋊C4D4×C1112yes—
348#95—24no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—21no—
352C2×C11—22no—
353C2×C11—22no—
354C2×C11—22no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—48no—
358C2×C11#143911yescharacteristic
359C2×C11#188912yes—
360C2×C11#202112yes—
361C2×C11#202912yes—
362C24—28no—
363C24—216no—
364C24—22no—
365C24—24no—
366C24—24no—
367C24—22no—
368C24—22no—
369C24—24no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—24no—
376C24—48no—
377C24—48no—
378C24—48no—
379C24—44no—
380C24—44no—
381C24—48no—
382C24—48no—
383C24—416no—
384C24—416no—
385C24—48no—
386C24—48no—
387C24—416no—
388C24—41no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—41no—
393C24—42no—
394C24—42no—
395C24—41no—
396C24—42no—
397C24—41no—
398C24C11×C4⋊C414yescomplemented
399C24C22×C4×C1111yescharacteristic
400C24C2×D4×C1111yescharacteristic
401C24C2×D4×C1112yes—
402C24C2×D4×C1111yescharacteristic
403C24C2×D4×C1111yescharacteristic
404C24C2×D4×C1112yes—
405C24C2×Q8×C1111yescharacteristic
406C24C11×#4111yescharacteristic
407C24C11×#4111yescharacteristic
408C24C11×#4112yes—
409C24C11×#4112yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—44no—
418C22×C4—48no—
419C22×C4—44no—
420C22×C4—48no—
421C22×C4—42no—
422C22×C4—41no—
423C22×C4—42no—
424C22×C4—41no—
425C22×C4C11×C22⋊C414yescomplemented
426C4⋊C4—84no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—416no—
433C22⋊C4—432no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C11#1106911yescharacteristic, direct product factor, Sylow
442C23—24no—
443C23—28no—
444C23—28no—
445C23—216no—
446C23—216no—
447C23—28no—
448C23—28no—
449C23—216no—
450C23—24no—
451C23—28no—
452C23—48no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—44no—
457C23—42no—
458C23—44no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—44no—
463C23—416no—
464C23—48no—
465C23—48no—
466C23—48no—
467C23—416no—
468C23—48no—
469C23—44no—
470C23—48no—
471C23—416no—
472C23—44no—
473C23—48no—
474C23—48no—
475C23—416no—
476C23—48no—
477C23—48no—
478C23—416no—
479C23—416no—
480C23—416no—
481C23—416no—
482C23—416no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—44no—
490C23—42no—
491C23—42no—
492C23—48no—
493C23C2×C11×C22⋊C411yescharacteristic
494C23C2×C11×C4⋊C411yescharacteristic
495C23C11×#11711yescharacteristic
496C23C4×D4×C1112yes—
497C23C4×D4×C1112yes—
498C23C11×#12012yes—
499C23C11×#12011yescharacteristic
500C23C11×#12111yescharacteristic
501C23C11×#12112yes—
502C23C11×#12112yes—
503C23C11×#12111yescharacteristic
504C23C11×#12112yes—
505C23C11×C22⋊Q811yescharacteristic
506C23C11×C22⋊Q812yes—
507C23C11×C22⋊Q811yescharacteristic
508C23C11×C22⋊Q812yes—
509C23C11×#12311yescharacteristic
510C23C11×#12312yes—
511C23C11×#12312yes—
512C23C11×#12412yes—
513C23C11×#12411yescharacteristic
514C23C11×#12612yes—
515C23C11×#12711yescharacteristic
516C2×C4—24no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—48no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—82no—
527C2×C4—84no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C22—22no—
533C22—24no—
534C22—22no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—28no—
545C22—216no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—48no—
557C22—416no—
558C22—44no—
559C22—48no—
560C22—416no—
561C22—416no—
562C22—48no—
563C22—48no—
564C22—48no—
565C22—44no—
566C22—48no—
567C22—48no—
568C22C11×#38011yescharacteristic
569C22C11×#38512yes—
570C22C11×#38611yescharacteristic
571C22C11×#38812yes—
572C22C11×#39011yescharacteristic
573C22C11×#39211yescharacteristic
574C22C11×#39311yescharacteristic
575C22C11×#39412yes—
576C22C11×#39612yes—
577C22C11×#39711yescharacteristic
578C22C11×#39911yescharacteristic
579C22C11×B(4,𝔽2)14yes—
580C4—44no—
581C4—82no—
582C4—84no—
583C4—84no—
584C2—21no—
585C2—22no—
586C2—21no—
587C2—22no—
588C2—22no—
589C2—22no—
590C2—21no—
591C2—21no—
592C2—48no—
593C2C11×#143911yescharacteristic
594C2C11×#188912yes—
595C2C11×#202112yes—
596C2C11×#202912yes—
subgroupG/H
center, socleC23×C11#120
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC26×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2315C2semidirect
4. C2×C11×#342C2semidirect
5. C2×C11×#342C2semidirect
18. C11×#379C4semidirect
64. #11069C11direct (N × H)
101. C24×C11C4⋊C4semidirect
128. C22×C4×C11C22⋊C4semidirect
144. #2315C2×C11semidirect
147. C2×#342C2×C11semidirect
148. C2×#342C2×C11semidirect
251. #379C4×C11semidirect
398. C24C11×C4⋊C4semidirect
425. C22×C4C11×C22⋊C4semidirect
441. C11#11069direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C2×C11×#3792
C2×C11×#3422
#1106911