Finite Group Databasebeta

← C11×#23593 #14600786

Subgroups — C11×#23593 #14600786

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3460C211yesmaximal, characteristic
2C4×C11×#137C212yesmaximal, complemented
3C11×#2326C211yesmaximal, characteristic, complemented
4C11×#2060C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic, complemented
6C11×#2037C212yesmaximal, complemented
7C11×#2028C211yesmaximal, characteristic, complemented
8C11×#2007C211yesmaximal, characteristic, complemented
9C11×#2004C212yesmaximal, complemented
10C11×#1759C212yesmaximal, 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×#385—22no—
41C11×#384C2211yescharacteristic
42C11×#376C2211yescharacteristic
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⋊C4—22no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11—22no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×#107—22no—
105C11×#106—22no—
106C11×#104—24no—
107C11×#104—24no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#100—24no—
113C11×#97—22no—
114C4×C8×C11—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—22no—
118#23593C1111yesmaximal, 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—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—82no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
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—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—82no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—82no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—21no—
187C42×C11—22no—
188C42×C11—42no—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C42×C11#4112yescomplemented
192#3460C2×C1111yescharacteristic
193C4×#137C2×C1112yescomplemented
194#2326C2×C1111yescharacteristic, complemented
195#2060C2×C1111yescharacteristic, complemented
196#2039C2×C1111yescharacteristic, complemented
197#2037C2×C1112yescomplemented
198#2028C2×C1111yescharacteristic, complemented
199#2007C2×C1111yescharacteristic, complemented
200#2004C2×C1112yescomplemented
201#1759C2×C1112yescomplemented
202C4×#100C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—24no—
211Q8×C11—22no—
212Q8×C11—22no—
213Q8×C11—42no—
214Q8×C11—82no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—84no—
222D4×C11—82no—
223D4×C11—84no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12012yes—
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4112yes—
254C2×C4×C11C2×#4111yescharacteristic
255C8×C11—24no—
256C8×C11—42no—
257C2×#137C22×C1112yes—
258#544C22×C1111yescharacteristic
259#542—22no—
260#540—22no—
261#538—22no—
262#537C22×C1111yescharacteristic
263#535C22×C1112yes—
264#532—22no—
265#529—22no—
266C2×#124C22×C1111yescharacteristic
267#525—22no—
268C4×#41C22×C1112yes—
269C2×C4×Q8C22×C1111yescharacteristic
270C2×C4×D4C22×C1111yescharacteristic
271#441—22no—
272#440—22no—
273C4×Q16—22no—
274C4×SD16—22no—
275#428C22×C1112yes—
276C2×#104C22×C1112yes—
277C2×#104C22×C1112yes—
278#419C22×C1112yes—
279#417C22×C1112yes—
280C2×#100C22×C1112yes—
281C4×M16C22×C1112yes—
282#391C22×C1111yescharacteristic
283#390C22×C1111yescharacteristic
284#388—22no—
285#385—22no—
286#384C22×C1111yescharacteristic
287#376C22×C1111yescharacteristic
288#343C22×C1111yescharacteristic
289#343C22×C1111yescharacteristic
290#339C22×C1112yes—
291#339C22×C1112yes—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—44no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—82no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#52511yescharacteristic
304C22×C11#53211yescharacteristic
305C4×C11—21no—
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—81no—
315C4×C11—81no—
316C4×C11#52512yes—
317C4×C11#53212yes—
318C2×#41—22no—
319C2×#41C23×C1112yes—
320C22×Q8C23×C1111yescharacteristic
321C22×D4C23×C1111yescharacteristic
322C23×C4D4×C1112yes—
323#137—24no—
324#137—24no—
325C2×Q16—22no—
326C2×SD16—22no—
327C2×M16C23×C1112yes—
328C2×M16C23×C1112yes—
329C4⋊Q8—22no—
330#127—22no—
331#126—24no—
332#125—22no—
333#124—24no—
334#124—22no—
335#124—22no—
336#124—22no—
337#123—24no—
338#123—24no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342#121—22no—
343#121—24no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348#120—24no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8D4×C1112yes—
352C4×Q8D4×C1112yes—
353C4×D4—24no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4D4×C1112yes—
359C4×D4D4×C1112yes—
360#117—22no—
361#117—22no—
362#117C23×C1112yes—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
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×C42C23×C1111yescharacteristic
373C2×C42C23×C1111yescharacteristic
374C2×C42C23×C1111yescharacteristic
375#107—22no—
376#106—22no—
377#104—24no—
378#104—24no—
379#103—22no—
380#103—22no—
381#103—22no—
382#102—22no—
383#100—24no—
384#97—22no—
385C4×C8—22no—
386#95—21no—
387#95—21no—
388#95—22no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—82no—
392C2×C11—82no—
393C2×C11#238811yescharacteristic
394C2×C11#301911yescharacteristic
395C2×C11#302211yescharacteristic
396C24C2×D4×C1112yes—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—84no—
402C2×Q8—22no—
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8C2×D4×C1112yes—
407C2×Q8C11×#4112yescomplemented
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4C2×D4×C1112yes—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—82no—
427C22×C4C2×D4×C1112yes—
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C24×C1111yescharacteristic
431Q16—28no—
432SD16—28no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16C11×#4114yescomplemented
437C2×C8—22no—
438C2×C8—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—82no—
449C4⋊C4C2×D4×C1112yes—
450C4⋊C4C2×D4×C1112yes—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—82no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42—21no—
464C42—22no—
465C42—42no—
466C42C2×D4×C1112yes—
467C42C2×D4×C1112yes—
468C42C11×#4112yescomplemented
469C11#2359311yescharacteristic, direct product factor, Sylow
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—42no—
475C23—42no—
476C23C22×D4×C1111yescharacteristic
477Q8—24no—
478Q8—22no—
479Q8—22no—
480Q8—42no—
481Q8—82no—
482D4—22no—
483D4—22no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—84no—
489D4—82no—
490D4—84no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4C11×#12011yescharacteristic
516C2×C4C11×#12012yes—
517C2×C4C11×#12011yescharacteristic
518C2×C4C22×D4×C1112yes—
519C2×C4C2×C11×#4111yescharacteristic
520C2×C4C2×C11×#4112yes—
521C2×C4C2×C11×#4111yescharacteristic
522C8—24no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—82no—
534C22C2×C11×#12011yescharacteristic
535C22C11×#52511yescharacteristic
536C22C11×#53211yescharacteristic
537C4—21no—
538C4—21no—
539C4—22no—
540C4—42no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—81no—
548C4C11×#52512yes—
549C4C11×#53212yes—
550C2—21no—
551C2—21no—
552C2—82no—
553C2—82no—
554C2C11×#238811yescharacteristic
555C2C11×#301911yescharacteristic
556C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#137C2semidirect
3. C11×#2326C2semidirect
4. C11×#2060C2semidirect
5. C11×#2039C2semidirect
6. C11×#2037C2semidirect
7. C11×#2028C2semidirect
8. C11×#2007C2semidirect
9. C11×#2004C2semidirect
10. C11×#1759C2semidirect
11. C4×C11×#100C2semidirect
118. #23593C11direct (N × H)
130. C2×Q8×C11#41semidirect
159. C11×M16#41semidirect
191. C42×C11#41semidirect
193. C4×#137C2×C11semidirect
194. #2326C2×C11semidirect
195. #2060C2×C11semidirect
196. #2039C2×C11semidirect
197. #2037C2×C11semidirect
198. #2028C2×C11semidirect
199. #2007C2×C11semidirect
200. #2004C2×C11semidirect
201. #1759C2×C11semidirect
202. C4×#100C2×C11semidirect
407. C2×Q8C11×#41semidirect
436. M16C11×#41semidirect
468. C42C11×#41semidirect
469. C11#23593direct (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
C11×#23262
C11×#20602
C11×#20392
C11×#20372
C11×#20282
C11×#20072
C11×#20042
C11×#17592
C4×C11×#1002
#2359311