Finite Group Databasebeta

← C11×#23589 #14600782

Subgroups — C11×#23589 #14600782

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic
2C4×C11×#137C212yesmaximal, complemented
3C4×C11×#124C211yesmaximal, characteristic, complemented
4C11×#2061C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#2028C211yesmaximal, characteristic, complemented
8C11×#2007C211yesmaximal, characteristic, complemented
9C11×#2004C212yesmaximal, complemented
10C4×C11×#104C212yesmaximal, complemented
11C4×C11×#100C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#540—22no—
16C11×#538—22no—
17C11×#537C2211yescharacteristic
18C11×#535C2212yes—
19C11×#532—22no—
20C11×#529—22no—
21C2×C11×#124C2211yescharacteristic
22C11×#525—22no—
23C4×C11×#41C2212yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#441—22no—
27C11×#440—22no—
28C4×C11×Q16—22no—
29C4×C11×SD16—22no—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#419C2212yes—
34C11×#417C2212yes—
35C2×C11×#100C2212yes—
36C4×C11×M16C2212yes—
37C11×#391C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C4×C11×C22⋊C4—22no—
42C43×C11C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41C2312yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11D412yes—
52C11×#137—24no—
53C11×#137—24no—
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C2×C11×M16C2312yes—
57C2×C11×M16C2312yes—
58C11×C4⋊Q8—22no—
59C11×#127—22no—
60C11×#126—24no—
61C11×#125—22no—
62C11×#124—24no—
63C11×#124—22no—
64C11×#124—22no—
65C11×#124—22no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×#121—22no—
72C11×#121—24no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#120—24no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11D412yes—
81C4×Q8×C11D412yes—
82C4×D4×C11—24no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11D412yes—
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117C2312yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—22no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#106—22no—
107C11×#104—24no—
108C11×#104—24no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×#102—22no—
113C11×#100—24no—
114C11×#97—22no—
115C4×C8×C11—22no—
116C11×#95—22no—
117C11×#95—22no—
118#23589C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11C2×D412yes—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—84no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11C2×D412yes—
130C2×Q8×C11#4112yescomplemented
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—44no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C11×Q16—28no—
155C11×SD16—28no—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16#4114yescomplemented
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—44no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—21no—
185C42×C11—22no—
186C42×C11—42no—
187C42×C11—42no—
188C42×C11—41no—
189C42×C11—41no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192C42×C11#4112yescomplemented
193#3460C2×C1111yescharacteristic
194C4×#137C2×C1112yescomplemented
195C4×#124C2×C1111yescharacteristic, complemented
196#2061C2×C1111yescharacteristic, complemented
197#2040C2×C1111yescharacteristic, complemented
198#2037C2×C1112yescomplemented
199#2028C2×C1111yescharacteristic, complemented
200#2007C2×C1111yescharacteristic, complemented
201#2004C2×C1112yescomplemented
202C4×#104C2×C1112yescomplemented
203C4×#100C2×C1111yescharacteristic, complemented
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C22×D411yescharacteristic
211Q8×C11—24no—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—42no—
215Q8×C11—82no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—84no—
223D4×C11—82no—
224D4×C11—84no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—82no—
248C2×C4×C11—82no—
249C2×C4×C11#12012yes—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11C22×D412yes—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11C2×#4111yescharacteristic
256C8×C11—24no—
257C8×C11—42no—
258C2×#137C22×C1112yes—
259#544C22×C1111yescharacteristic
260#542—22no—
261#540—22no—
262#538—22no—
263#537C22×C1111yescharacteristic
264#535C22×C1112yes—
265#532—22no—
266#529—22no—
267C2×#124C22×C1111yescharacteristic
268#525—22no—
269C4×#41C22×C1112yes—
270C2×C4×Q8C22×C1111yescharacteristic
271C2×C4×D4C22×C1111yescharacteristic
272#441—22no—
273#440—22no—
274C4×Q16—22no—
275C4×SD16—22no—
276#428C22×C1112yes—
277C2×#104C22×C1112yes—
278C2×#104C22×C1112yes—
279#419C22×C1112yes—
280#417C22×C1112yes—
281C2×#100C22×C1112yes—
282C4×M16C22×C1112yes—
283#391C22×C1111yescharacteristic
284#390C22×C1111yescharacteristic
285#388—22no—
286#382C22×C1111yescharacteristic
287C4×C22⋊C4—22no—
288C43C22×C1111yescharacteristic
289#343C22×C1111yescharacteristic
290#343C22×C1111yescharacteristic
291#339C22×C1112yes—
292#339C22×C1112yes—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—82no—
303C22×C11C2×#12011yescharacteristic
304C22×C11#52511yescharacteristic
305C22×C11#53211yescharacteristic
306C4×C11—21no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—42no—
315C4×C11—81no—
316C4×C11#45512yes—
317C4×C11#52512yes—
318C4×C11#53212yes—
319C2×#41—22no—
320C2×#41C23×C1112yes—
321C22×Q8C23×C1111yescharacteristic
322C22×D4C23×C1111yescharacteristic
323C23×C4D4×C1112yes—
324#137—24no—
325#137—24no—
326C2×Q16—22no—
327C2×SD16—22no—
328C2×M16C23×C1112yes—
329C2×M16C23×C1112yes—
330C4⋊Q8—22no—
331#127—22no—
332#126—24no—
333#125—22no—
334#124—24no—
335#124—22no—
336#124—22no—
337#124—22no—
338#123—24no—
339#123—24no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343#121—22no—
344#121—24no—
345#121—22no—
346#121—22no—
347#121—22no—
348#121—22no—
349#120—24no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8D4×C1112yes—
353C4×Q8D4×C1112yes—
354C4×D4—24no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4D4×C1112yes—
360C4×D4D4×C1112yes—
361#117—22no—
362#117—22no—
363#117C23×C1112yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C23×C1111yescharacteristic
366C2×C4⋊C4C23×C1111yescharacteristic
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4D4×C1112yes—
370C2×C42—22no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376C2×C42C23×C1111yescharacteristic
377#107—22no—
378#106—22no—
379#104—24no—
380#104—24no—
381#103—22no—
382#103—22no—
383#103—22no—
384#102—22no—
385#100—24no—
386#97—22no—
387C4×C8—22no—
388#95—22no—
389#95—22no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11—82no—
393C2×C11—82no—
394C2×C11#238811yescharacteristic
395C2×C11C2×#45511yescharacteristic
396C2×C11#301811yescharacteristic
397C24C2×D4×C1112yes—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—84no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8C2×D4×C1112yes—
408C2×Q8C11×#4112yescomplemented
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×D4×C1112yes—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—44no—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1112yes—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C24×C1111yescharacteristic
432Q16—28no—
433SD16—28no—
434M16—22no—
435M16—22no—
436M16—22no—
437M16C11×#4114yescomplemented
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—24no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4C2×D4×C1112yes—
449C4⋊C4C2×D4×C1112yes—
450C22⋊C4—28no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—24no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—44no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42—21no—
463C42—22no—
464C42—42no—
465C42—42no—
466C42—41no—
467C42—41no—
468C42C2×D4×C1112yes—
469C42C2×D4×C1112yes—
470C42C11×#4112yescomplemented
471C11#2358911yescharacteristic, direct product factor, Sylow
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—42no—
477C23—42no—
478C23C22×D4×C1111yescharacteristic
479Q8—24no—
480Q8—22no—
481Q8—22no—
482Q8—42no—
483Q8—82no—
484D4—22no—
485D4—22no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—84no—
491D4—82no—
492D4—84no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4C11×#12012yes—
518C2×C4C11×#12011yescharacteristic
519C2×C4C11×#12011yescharacteristic
520C2×C4C22×D4×C1112yes—
521C2×C4C2×C11×#4111yescharacteristic
522C2×C4C2×C11×#4112yes—
523C2×C4C2×C11×#4111yescharacteristic
524C8—24no—
525C8—42no—
526C22—21no—
527C22—21no—
528C22—44no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—82no—
536C22C2×C11×#12011yescharacteristic
537C22C11×#52511yescharacteristic
538C22C11×#53211yescharacteristic
539C4—21no—
540C4—22no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—81no—
549C4C11×#45512yes—
550C4C11×#52512yes—
551C4C11×#53212yes—
552C2—21no—
553C2—21no—
554C2—82no—
555C2—82no—
556C2C11×#238811yescharacteristic
557C2C2×C11×#45511yescharacteristic
558C2C11×#301811yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×#120
prime radicalC11×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#137C2semidirect
3. C4×C11×#124C2semidirect
4. C11×#2061C2semidirect
5. C11×#2040C2semidirect
6. C11×#2037C2semidirect
7. C11×#2028C2semidirect
8. C11×#2007C2semidirect
9. C11×#2004C2semidirect
10. C4×C11×#104C2semidirect
11. C4×C11×#100C2semidirect
118. #23589C11direct (N × H)
130. C2×Q8×C11#41semidirect
159. C11×M16#41semidirect
192. C42×C11#41semidirect
194. C4×#137C2×C11semidirect
195. C4×#124C2×C11semidirect
196. #2061C2×C11semidirect
197. #2040C2×C11semidirect
198. #2037C2×C11semidirect
199. #2028C2×C11semidirect
200. #2007C2×C11semidirect
201. #2004C2×C11semidirect
202. C4×#104C2×C11semidirect
203. C4×#100C2×C11semidirect
408. C2×Q8C11×#41semidirect
437. M16C11×#41semidirect
470. C42C11×#41semidirect
471. C11#23589direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34602
C4×C11×#1372
C4×C11×#1242
C11×#20612
C11×#20402
C11×#20372
C11×#20282
C11×#20072
C11×#20042
C4×C11×#1042
C4×C11×#1002
#2358911