Finite Group Databasebeta

← C11×#23509 #14600702

Subgroups — C11×#23509 #14600702

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C22×C11×#102C211yesmaximal, characteristic, complemented
6C11×#2317C211yesmaximal, characteristic, complemented
7C11×#2042C214yesmaximal, complemented
8C11×#2041C214yesmaximal, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535—24no—
16C2×C11×#127C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C11×#120—22no—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C11×#418—24no—
25C11×#417—24no—
26C11×#416—24no—
27C2×C11×#103C2212yescomplemented
28C2×C11×#103C2212yescomplemented
29C2×C11×#102—24no—
30C2×C11×#102C2214yes—
31C2×C11×#102C2214yes—
32C2×C11×#102C2212yescomplemented
33C2×C11×#102C2212yescomplemented
34C11×#389C2214yescomplemented
35C11×#385—22no—
36C11×#384—21no—
37C11×#382—21no—
38C11×#336C2214yescomplemented
39C25×C11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41D414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11D414yes—
57C22×D4×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C11×#127—24no—
71C11×#127—24no—
72C11×#124—24no—
73C11×#124—24no—
74C11×#121—28no—
75C11×#121—28no—
76C11×#120—216no—
77C11×#117—22no—
78C11×#117—22no—
79C11×#117—22no—
80C11×#117D414yescomplemented
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—24no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4D412yes—
93C2×C42×C11—21no—
94C2×C42×C11C2312yes—
95C11×#103—24no—
96C11×#103—24no—
97C11×#102—28no—
98C11×#102—24no—
99C11×#102—28no—
100C11×#102—24no—
101C11×#95—24no—
102#23509C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—24no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—82no—
109C24×C11—82no—
110C24×C11C2×D411yescharacteristic
111C11×#41—28no—
112C11×#41—28no—
113C11×#41—44no—
114C11×#41—44no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—24no—
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11—24no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11—44no—
142C2×D4×C11—42no—
143C2×D4×C11—84no—
144C2×D4×C11—84no—
145C2×D4×C11C2×D414yes—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—82no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C11×M16—44no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—44no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—84no—
180C11×C4⋊C4C2×D414yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—28no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C42×C11—24no—
186C42×C11—22no—
187C42×C11—22no—
188C2×#535C2×C1111yescharacteristic
189C2×#417C2×C1111yescharacteristic, complemented
190C2×#418C2×C1111yescharacteristic, complemented
191C2×#416C2×C1111yescharacteristic, complemented
192C22×#102C2×C1111yescharacteristic, complemented
193#2317C2×C1111yescharacteristic, complemented
194#2042C2×C1114yescomplemented
195#2041C2×C1114yescomplemented
196#1729C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—42no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—42no—
208C23×C11—44no—
209C23×C11—48no—
210C23×C11—84no—
211C23×C11—84no—
212C23×C11—88no—
213C23×C11—88no—
214C23×C11#12012yes—
215C23×C11#12112yes—
216C23×C11#12412yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—24no—
223D4×C11—22no—
224D4×C11—24no—
225D4×C11—22no—
226D4×C11—48no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—42no—
230D4×C11—41no—
231D4×C11—48no—
232D4×C11—88no—
233D4×C11—88no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—48no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—84no—
248C2×C4×C11#12012yes—
249C2×C4×C11#12114yes—
250C2×C4×C11#12114yes—
251C2×C4×C11#12112yes—
252C2×C4×C11#12314yes—
253C2×C4×C11#12314yes—
254C2×C4×C11#12412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C8×C11—42no—
262C8×C11—42no—
263C22×#41C22×C1111yescharacteristic
264C23×D4C22×C1111yescharacteristic
265C22×M16C22×C1111yescharacteristic
266C23×C8C22×C1111yescharacteristic
267#535—24no—
268#535—24no—
269C2×#127C22×C1112yes—
270C2×#124C22×C1112yes—
271C2×#121—21no—
272C2×#121—21no—
273C2×#120—22no—
274C2×#117C22×C1111yescharacteristic
275C2×#117C22×C1111yescharacteristic
276C22×C4⋊C4C22×C1111yescharacteristic
277#418—24no—
278#417—24no—
279#416—24no—
280C2×#103C22×C1112yescomplemented
281C2×#103C22×C1112yescomplemented
282C2×#102—24no—
283C2×#102C22×C1114yes—
284C2×#102C22×C1114yes—
285C2×#102C22×C1112yescomplemented
286C2×#102C22×C1112yescomplemented
287#389C22×C1114yescomplemented
288#385—22no—
289#384—21no—
290#382—21no—
291#336C22×C1114yescomplemented
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—816no—
303C22×C11—82no—
304C22×C11—84no—
305C22×C11—82no—
306C22×C11—84no—
307C22×C11#39414yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#12111yescharacteristic
310C22×C11C2×#12411yescharacteristic
311C22×C11#57612yes—
312C22×C11#57712yes—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11—82no—
318C4×C11#39414yes—
319C4×C11C2×#12111yescharacteristic
320C4×C11C2×#12111yescharacteristic
321C4×C11C2×#12311yescharacteristic
322C4×C11C2×#12311yescharacteristic
323C25—21no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41D4×C1114yes—
330C22×Q8C23×C1111yescharacteristic
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4D4×C1114yes—
341C22×D4C23×C1112yes—
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4C23×C1111yescharacteristic
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8C23×C1112yes—
353C22×C8C23×C1112yes—
354#127—24no—
355#127—24no—
356#124—24no—
357#124—24no—
358#121—28no—
359#121—28no—
360#120—216no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117D4×C1114yescomplemented
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4D4×C1111yescharacteristic
370C2×C4⋊C4D4×C1111yescharacteristic
371C2×C4⋊C4C23×C1112yes—
372C2×C4⋊C4C23×C1112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4D4×C1112yes—
377C2×C42—21no—
378C2×C42C23×C1112yes—
379#103—24no—
380#103—24no—
381#102—28no—
382#102—24no—
383#102—28no—
384#102—24no—
385#95—24no—
386C2×C11—24no—
387C2×C11—82no—
388C2×C11—84no—
389C2×C11C2×#39411yescharacteristic
390C2×C11#300811yescharacteristic
391C2×C11#300911yescharacteristic
392C2×C11#304512yes—
393C2×C11#313612yes—
394C24—22no—
395C24—21no—
396C24—24no—
397C24—42no—
398C24—42no—
399C24—82no—
400C24—82no—
401C24C2×D4×C1111yescharacteristic
402#41—28no—
403#41—28no—
404#41—44no—
405#41—44no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C2×D4×C1112yes—
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—24no—
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—84no—
435C2×D4—84no—
436C2×D4C2×D4×C1114yes—
437C2×D4C2×D4×C1112yes—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—82no—
446C22×C4C2×D4×C1112yes—
447C22×C4C2×D4×C1112yes—
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1112yes—
450C22×C4C2×D4×C1112yes—
451C22×C4C2×D4×C1112yes—
452C22×C4C11×#4112yes—
453C22×C4C11×#4112yes—
454C22×C4C11×#4112yes—
455C22×C4C24×C1111yescharacteristic
456M16—44no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—44no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C4⋊C4—84no—
471C4⋊C4C2×D4×C1114yes—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C42—24no—
477C42—22no—
478C42—22no—
479C11#2350911yescharacteristic, direct product factor, Sylow
480C23—22no—
481C23—22no—
482C23—24no—
483C23—22no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—48no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—44no—
493C23—84no—
494C23—84no—
495C23—88no—
496C23—88no—
497C23C11×#12012yes—
498C23C11×#12112yes—
499C23C11×#12412yes—
500C23C22×D4×C1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505D4—24no—
506D4—22no—
507D4—24no—
508D4—22no—
509D4—48no—
510D4—42no—
511D4—41no—
512D4—42no—
513D4—41no—
514D4—48no—
515D4—88no—
516D4—88no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—84no—
531C2×C4C11×#12012yes—
532C2×C4C11×#12114yes—
533C2×C4C11×#12114yes—
534C2×C4C11×#12112yes—
535C2×C4C11×#12314yes—
536C2×C4C11×#12314yes—
537C2×C4C11×#12412yes—
538C2×C4C22×D4×C1111yescharacteristic
539C2×C4C22×D4×C1111yescharacteristic
540C2×C4C22×D4×C1111yescharacteristic
541C2×C4C2×C11×#4111yescharacteristic
542C2×C4C2×C11×#4111yescharacteristic
543C2×C4C2×C11×#4111yescharacteristic
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—24no—
549C22—24no—
550C22—42no—
551C22—44no—
552C22—42no—
553C22—44no—
554C22—42no—
555C22—44no—
556C22—816no—
557C22—84no—
558C22—82no—
559C22—84no—
560C22—82no—
561C22C11×#39414yes—
562C22C2×C11×#12011yescharacteristic
563C22C2×C11×#12111yescharacteristic
564C22C2×C11×#12411yescharacteristic
565C22C11×#57612yes—
566C22C11×#57712yes—
567C4—42no—
568C4—42no—
569C4—42no—
570C4—44no—
571C4—82no—
572C4C11×#39414yes—
573C4C2×C11×#12111yescharacteristic
574C4C2×C11×#12111yescharacteristic
575C4C2×C11×#12311yescharacteristic
576C4C2×C11×#12311yescharacteristic
577C2—24no—
578C2—84no—
579C2—82no—
580C2C2×C11×#39411yescharacteristic
581C2C11×#300811yescharacteristic
582C2C11×#300911yescharacteristic
583C2C11×#304512yes—
584C2C11×#313612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#417C2semidirect
3. C2×C11×#418C2semidirect
4. C2×C11×#416C2semidirect
5. C22×C11×#102C2semidirect
6. C11×#2317C2semidirect
7. C11×#2042C2semidirect
8. C11×#2041C2semidirect
9. C11×#1729C2semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#103C22semidirect
32. C2×C11×#102C22semidirect
33. C2×C11×#102C22semidirect
34. C11×#389C22semidirect
38. C11×#336C22semidirect
80. C11×#117D4semidirect
102. #23509C11direct (N × H)
189. C2×#417C2×C11semidirect
190. C2×#418C2×C11semidirect
191. C2×#416C2×C11semidirect
192. C22×#102C2×C11semidirect
193. #2317C2×C11semidirect
194. #2042C2×C11semidirect
195. #2041C2×C11semidirect
196. #1729C2×C11semidirect
280. C2×#103C22×C11semidirect
281. C2×#103C22×C11semidirect
285. C2×#102C22×C11semidirect
286. C2×#102C22×C11semidirect
287. #389C22×C11semidirect
291. #336C22×C11semidirect
364. #117D4×C11semidirect
479. C11#23509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4172
C2×C11×#4182
C2×C11×#4162
C22×C11×#1022
C11×#23172
C11×#20422
C11×#20412
C11×#17292
#2350911