Finite Group Databasebeta

← C11×#20964 #14598157

Subgroups — C11×#20964 #14598157

Order 2816.

1700 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C11×#3449C211yesmaximal, characteristic
3C2×C11×#413C211yesmaximal, characteristic, complemented
4C11×#2879C212yesmaximal, complemented
5C11×#1891C218yesmaximal, complemented
6C2×C11×#344C212yesmaximal, complemented
7C22×C11×#41C2211yescharacteristic
8C22×C11×#41C2211yescharacteristic
9C11×#568—22no—
10C11×#568—24no—
11C11×#568C2214yes—
12C2×C11×#131—24no—
13C22×C11×M16—22no—
14C22×C11×M16C2212yes—
15C22×C11×M16C2212yes—
16C11×#537—22no—
17C11×#536—21no—
18C11×#536C412yes—
19C11×#535—21no—
20C11×#535C412yes—
21C11×#534C414yes—
22C11×#532—22no—
23C11×#525—22no—
24C11×#525C2214yes—
25C2×C11×#117C2211yescharacteristic
26C11×#413—22no—
27C11×#413C2214yes—
28C2×C11×#101—21no—
29C2×C11×#100—21no—
30C11×#408—24no—
31C11×#408—24no—
32C11×#407C2218yescomplemented
33C11×#344C2218yescomplemented
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41C2×C412yes—
47C2×C11×#41D412yes—
48C2×C11×#41D412yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11C2×C411yescharacteristic
51C22×Q8×C11D411yescharacteristic
52C22×D4×C11C2×C412yes—
53C22×D4×C11C2×C412yes—
54C22×D4×C11C2×C411yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11D412yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C11×#131—216no—
60C11×#131—216no—
61C2×C11×M16—24no—
62C2×C11×M16—28no—
63C2×C11×M16—22no—
64C2×C11×M16—28no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16D414yescomplemented
74C2×C11×M16C2314yes—
75C2×C11×M16C2314yes—
76C22×C8×C11—24no—
77C22×C8×C11—22no—
78C22×C8×C11D414yescomplemented
79C11×C4⋊Q8—22no—
80C11×#127—22no—
81C11×#124—22no—
82C11×#124—22no—
83C11×#123—24no—
84C11×#123C2×C418yes—
85C11×C22⋊Q8—24no—
86C11×C22⋊Q8—24no—
87C11×#121—28no—
88C11×#121—24no—
89C11×#121—24no—
90C11×#120—24no—
91C11×#120C2×C418yes—
92C4×D4×C11—28no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117C2×C412yes—
96C11×#117C2312yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C22⋊C4C2×C412yes—
99C2×C42×C11—21no—
100C11×#101—24no—
101C11×#100—24no—
102C11×C22⋊C8—216no—
103#20964C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11C22⋊C412yes—
105C24×C11C22×C412yes—
106C24×C11C22×C411yescharacteristic
107C11×#41—24no—
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—24no—
115C11×#41—41no—
116C11×#41—42no—
117C11×#41—41no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—41no—
123C11×#41—41no—
124C11×#41—42no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C22⋊C412yes—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—28no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11C22⋊C414yes—
147C2×D4×C11C22⋊C412yes—
148C2×D4×C11C22×C414yes—
149C2×D4×C11C2×D412yes—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—24no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11C22⋊C414yes—
160C22×C4×C11C22⋊C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4112yes—
171C22×C4×C11#4112yes—
172C22×C4×C11C2411yescharacteristic
173C11×M16—216no—
174C11×M16—24no—
175C11×M16—24no—
176C11×M16—24no—
177C11×M16—24no—
178C11×M16—24no—
179C11×M16—24no—
180C11×M16—42no—
181C11×M16—42no—
182C2×C8×C11—216no—
183C2×C8×C11—24no—
184C2×C8×C11—24no—
185C2×C8×C11—24no—
186C2×C8×C11—42no—
187C2×C8×C11—42no—
188C2×C8×C11C2×D418yes—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—28no—
191C11×C4⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—28no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4C22×C414yes—
196C42×C11—22no—
197C42×C11—22no—
198C2×#568C2×C1111yescharacteristic, complemented
199#3449C2×C1111yescharacteristic
200C2×#413C2×C1111yescharacteristic, complemented
201#2879C2×C1112yescomplemented
202#1891C2×C1118yescomplemented
203C2×#344C2×C1112yescomplemented
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—81no—
209C23×C11—82no—
210C23×C11—82no—
211C23×C11C2×C22⋊C414yes—
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11C2×C22⋊C411yescharacteristic
214C23×C11C4×D412yes—
215C23×C11C4×D412yes—
216C23×C11C23×C411yescharacteristic
217Q8×C11—24no—
218Q8×C11—24no—
219Q8×C11—41no—
220Q8×C11—41no—
221Q8×C11—42no—
222D4×C11—28no—
223D4×C11—28no—
224D4×C11—24no—
225D4×C11—24no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—44no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11—42no—
232D4×C11—88no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11C2×C22⋊C414yes—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C4×D412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12012yes—
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12112yes—
255C2×C4×C11#12112yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12312yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4112yes—
265C8×C11—28no—
266C8×C11—44no—
267C22×#41C22×C1111yescharacteristic
268C22×#41C22×C1111yescharacteristic
269#568—22no—
270#568—24no—
271#568C22×C1114yes—
272C2×#131—24no—
273C22×M16—22no—
274C22×M16C22×C1112yes—
275C22×M16C22×C1112yes—
276#537—22no—
277#536—21no—
278#536C4×C1112yes—
279#535—21no—
280#535C4×C1112yes—
281#534C4×C1114yes—
282#532—22no—
283#525—22no—
284#525C22×C1114yes—
285C2×#117C22×C1111yescharacteristic
286#413—22no—
287#413C22×C1114yes—
288C2×#101—21no—
289C2×#100—21no—
290#408—24no—
291#408—24no—
292#407C22×C1118yescomplemented
293#344C22×C1118yescomplemented
294C22×C11—24no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—48no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11#38611yescharacteristic
307C22×C11#38611yescharacteristic
308C22×C11#38612yes—
309C22×C11C22×C22⋊C411yescharacteristic
310C22×C11C2×C4×D412yes—
311C4×C11—24no—
312C4×C11—44no—
313C4×C11—42no—
314C4×C11#38611yescharacteristic
315C4×C11#38611yescharacteristic
316C4×C11#38612yes—
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12112yes—
319C4×C11C2×#12311yescharacteristic
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C2×C4×C1112yes—
333C2×#41D4×C1112yes—
334C2×#41D4×C1112yes—
335C2×#41C23×C1112yes—
336C22×Q8C2×C4×C1111yescharacteristic
337C22×Q8D4×C1111yescharacteristic
338C22×D4C2×C4×C1112yes—
339C22×D4C2×C4×C1112yes—
340C22×D4C2×C4×C1111yescharacteristic
341C22×D4D4×C1111yescharacteristic
342C23×C4D4×C1112yes—
343C23×C4C23×C1112yes—
344C23×C4C23×C1111yescharacteristic
345#131—216no—
346#131—216no—
347C2×M16—24no—
348C2×M16—28no—
349C2×M16—22no—
350C2×M16—28no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16D4×C1114yescomplemented
360C2×M16C23×C1114yes—
361C2×M16C23×C1114yes—
362C22×C8—24no—
363C22×C8—22no—
364C22×C8D4×C1114yescomplemented
365C4⋊Q8—22no—
366#127—22no—
367#124—22no—
368#124—22no—
369#123—24no—
370#123C2×C4×C1118yes—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373#121—28no—
374#121—24no—
375#121—24no—
376#120—24no—
377#120C2×C4×C1118yes—
378C4×D4—28no—
379#117—21no—
380#117—21no—
381#117C2×C4×C1112yes—
382#117C23×C1112yes—
383C2×C4⋊C4—21no—
384C2×C22⋊C4C2×C4×C1112yes—
385C2×C42—21no—
386#101—24no—
387#100—24no—
388C22⋊C8—216no—
389C2×C11—21no—
390C2×C11—22no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—22no—
394C2×C11—44no—
395C2×C11—82no—
396C2×C11C2×#38611yescharacteristic
397C24C11×C22⋊C412yes—
398C24C22×C4×C1112yes—
399C24C22×C4×C1111yescharacteristic
400#41—24no—
401#41—24no—
402#41—24no—
403#41—24no—
404#41—24no—
405#41—24no—
406#41—24no—
407#41—24no—
408#41—41no—
409#41—42no—
410#41—41no—
411#41—42no—
412#41—42no—
413#41—42no—
414#41—42no—
415#41—41no—
416#41—41no—
417#41—42no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8C11×C22⋊C412yes—
425C2×Q8C2×D4×C1112yes—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4C11×C22⋊C414yes—
440C2×D4C11×C22⋊C412yes—
441C2×D4C22×C4×C1114yes—
442C2×D4C2×D4×C1112yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4C11×C22⋊C414yes—
453C22×C4C11×C22⋊C412yes—
454C22×C4C22×C4×C1112yes—
455C22×C4C22×C4×C1111yescharacteristic
456C22×C4C2×D4×C1114yes—
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1112yes—
462C22×C4C2×D4×C1112yes—
463C22×C4C11×#4112yes—
464C22×C4C11×#4112yes—
465C22×C4C24×C1111yescharacteristic
466M16—216no—
467M16—24no—
468M16—24no—
469M16—24no—
470M16—24no—
471M16—24no—
472M16—24no—
473M16—42no—
474M16—42no—
475C2×C8—216no—
476C2×C8—24no—
477C2×C8—24no—
478C2×C8—24no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8C2×D4×C1118yes—
482C4⋊C4—22no—
483C4⋊C4—28no—
484C4⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—28no—
487C22⋊C4—28no—
488C22⋊C4C22×C4×C1114yes—
489C42—22no—
490C42—22no—
491C11#2096411yescharacteristic, direct product factor, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—81no—
497C23—82no—
498C23—82no—
499C23C2×C11×C22⋊C414yes—
500C23C2×C11×C22⋊C411yescharacteristic
501C23C2×C11×C22⋊C411yescharacteristic
502C23C4×D4×C1112yes—
503C23C4×D4×C1112yes—
504C23C23×C4×C1111yescharacteristic
505Q8—24no—
506Q8—24no—
507Q8—41no—
508Q8—41no—
509Q8—42no—
510D4—28no—
511D4—28no—
512D4—24no—
513D4—24no—
514D4—42no—
515D4—42no—
516D4—44no—
517D4—41no—
518D4—41no—
519D4—42no—
520D4—88no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—82no—
534C2×C4C2×C11×C22⋊C414yes—
535C2×C4C2×C11×C22⋊C411yescharacteristic
536C2×C4C2×C11×C22⋊C411yescharacteristic
537C2×C4C4×D4×C1112yes—
538C2×C4C4×D4×C1112yes—
539C2×C4C11×#12011yescharacteristic
540C2×C4C11×#12012yes—
541C2×C4C11×#12011yescharacteristic
542C2×C4C11×#12112yes—
543C2×C4C11×#12112yes—
544C2×C4C11×#12112yes—
545C2×C4C11×#12112yes—
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12311yescharacteristic
548C2×C4C11×#12312yes—
549C2×C4C22×D4×C1112yes—
550C2×C4C22×D4×C1111yescharacteristic
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C2×C11×#4112yes—
553C8—28no—
554C8—44no—
555C22—24no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—48no—
565C22—42no—
566C22—82no—
567C22C11×#38611yescharacteristic
568C22C11×#38611yescharacteristic
569C22C11×#38612yes—
570C22C22×C11×C22⋊C411yescharacteristic
571C22C2×C4×D4×C1112yes—
572C4—24no—
573C4—44no—
574C4—42no—
575C4C11×#38611yescharacteristic
576C4C11×#38611yescharacteristic
577C4C11×#38612yes—
578C4C2×C11×#12011yescharacteristic
579C4C2×C11×#12112yes—
580C4C2×C11×#12311yescharacteristic
581C2—21no—
582C2—22no—
583C2—21no—
584C2—21no—
585C2—22no—
586C2—44no—
587C2—82no—
588C2C2×C11×#38611yescharacteristic
subgroupG/H
centerC4×C11C2×#120
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#386
prime radicalC11×#3449C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
3. C2×C11×#413C2semidirect
4. C11×#2879C2semidirect
5. C11×#1891C2semidirect
6. C2×C11×#344C2semidirect
32. C11×#407C22semidirect
33. C11×#344C22semidirect
73. C2×C11×M16D4semidirect
78. C22×C8×C11D4semidirect
103. #20964C11direct (N × H)
198. C2×#568C2×C11semidirect
200. C2×#413C2×C11semidirect
201. #2879C2×C11semidirect
202. #1891C2×C11semidirect
203. C2×#344C2×C11semidirect
292. #407C22×C11semidirect
293. #344C22×C11semidirect
359. C2×M16D4×C11semidirect
364. C22×C8D4×C11semidirect
491. C11#20964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C11×#34492
C2×C11×#4132
C11×#28792
C11×#18912
C2×C11×#3442
#2096411