Finite Group Databasebeta

← C11×#23906 #14601099

Subgroups — C11×#23906 #14601099

Order 2816.

2502 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C211yesmaximal, characteristic, complemented
2C22×C11×#127C211yesmaximal, characteristic, complemented
3C2×C11×#453C212yesmaximal, complemented
4C11×#3003C212yesmaximal, complemented
5C11×#2002C214yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1887C212yesmaximal, complemented
8C11×#1783C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
10C23×D4×C11—22no—
11C23×D4×C11C2211yescharacteristic
12C23×D4×C11C2211yescharacteristic, complemented
13C2×C11×AGL(1,ℤ/8)C2214yescomplemented
14C11×#546—24no—
15D42×C11—24no—
16C11×#535C2212yescomplemented
17C11×#534—22no—
18C2×C11×#127—22no—
19C2×C11×#127—28no—
20C2×C11×#127C2212yes—
21C2×C11×#127C2212yescomplemented
22C11×#525C2212yes—
23C2×C11×#120—22no—
24C11×#518C2211yescharacteristic, complemented
25C22×C42×C11C2211yescharacteristic, complemented
26C11×#453—28no—
27C11×#450—24no—
28C11×#447—24no—
29C2×C11×#104C2214yescomplemented
30C11×#418C2214yescomplemented
31C2×C11×#100C2212yescomplemented
32C2×C11×#100C2212yescomplemented
33C11×#407C2212yescomplemented
34C11×#339C2214yescomplemented
35C25×C11—21no—
36C25×C11D412yes—
37C11×H(5,𝔽2)—24no—
38C11×H(5,𝔽2)—42no—
39C2×C11×#41—22no—
40C2×C11×#41C2312yes—
41C22×D4×C11—216no—
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11—24no—
45C22×D4×C11—24no—
46C22×D4×C11—24no—
47C22×D4×C11—24no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11—42no—
53C22×D4×C11—42no—
54C22×D4×C11—416no—
55C22×D4×C11D412yes—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C11×AGL(1,ℤ/8)—28no—
62C11×AGL(1,ℤ/8)—44no—
63C2×C11×SD16—24no—
64C2×C11×D8—24no—
65C2×C11×M16C2314yes—
66C11×#127—216no—
67C11×#127—24no—
68C11×#127—24no—
69C11×#127—22no—
70C11×#127—24no—
71C11×#127D418yescomplemented
72C11×#124—22no—
73C11×#123—24no—
74C11×#123—22no—
75C11×C22⋊Q8D414yescomplemented
76C11×#121—28no—
77C11×#121—24no—
78C11×#121D414yescomplemented
79C11×#120—28no—
80C11×#120—24no—
81C11×#120—22no—
82C11×#120—24no—
83C4×D4×C11—24no—
84C4×D4×C11—24no—
85C11×#117C2312yes—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11—21no—
89C2×C42×C11—24no—
90C2×C42×C11C2312yes—
91C11×#104—28no—
92C11×#102—28no—
93C11×#100—24no—
94C11×#100—42no—
95C11×C22⋊C8—24no—
96#23906C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11—24no—
98C24×C11—22no—
99C24×C11—24no—
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—42no—
103C24×C11—48no—
104C24×C11—42no—
105C24×C11—48no—
106C24×C11—42no—
107C24×C11C2×D411yescharacteristic
108C24×C11C2×D412yes—
109C24×C11C2×D412yes—
110C11×#41—24no—
111C11×#41—24no—
112C11×#41—48no—
113C2×Q8×C11C2×D412yescomplemented
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—216no—
117C2×D4×C11—24no—
118C2×D4×C11—24no—
119C2×D4×C11—216no—
120C2×D4×C11—22no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—416no—
132C2×D4×C11—416no—
133C2×D4×C11—42no—
134C2×D4×C11—416no—
135C2×D4×C11—416no—
136C2×D4×C11—464no—
137C2×D4×C11—42no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—42no—
142C2×D4×C11—88no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11C2×D412yescomplemented
145C2×D4×C11C2×D414yescomplemented
146C22×C4×C11—24no—
147C22×C4×C11—28no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2411yescharacteristic
157C11×SD16—48no—
158C11×D8—48no—
159C11×M16—24no—
160C11×M16—24no—
161C2×C8×C11—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4C2×D414yescomplemented
164C11×C22⋊C4—24no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—24no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11C2×D414yescomplemented
173#3484C2×C1111yescharacteristic, complemented
174C22×#127C2×C1111yescharacteristic, complemented
175C2×#453C2×C1112yescomplemented
176#3003C2×C1112yescomplemented
177#2002C2×C1114yescomplemented
178#1896C2×C1112yescomplemented
179#1887C2×C1112yescomplemented
180#1783C2×C1111yescharacteristic, complemented
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—48no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—416no—
195C23×C11—416no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—44no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—48no—
202C23×C11—84no—
203C23×C11—88no—
204C23×C11—88no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11#12012yes—
209C23×C11#12014yes—
210C23×C11C22×D411yescharacteristic
211Q8×C11—24no—
212D4×C11—28no—
213D4×C11—24no—
214D4×C11—28no—
215D4×C11—48no—
216D4×C11—432no—
217D4×C11—432no—
218D4×C11—48no—
219D4×C11—48no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—48no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—88no—
226C2×C4×C11—216no—
227C2×C4×C11—28no—
228C2×C4×C11—21no—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—84no—
237C2×C4×C11#12012yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C8×C11—44no—
242C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
243C23×D4—22no—
244C23×D4C22×C1111yescharacteristic
245C23×D4C22×C1111yescharacteristic, complemented
246C2×AGL(1,ℤ/8)C22×C1114yescomplemented
247#546—24no—
248D42—24no—
249#535C22×C1112yescomplemented
250#534—22no—
251C2×#127—22no—
252C2×#127—28no—
253C2×#127C22×C1112yes—
254C2×#127C22×C1112yescomplemented
255#525C22×C1112yes—
256C2×#120—22no—
257#518C22×C1111yescharacteristic, complemented
258C22×C42C22×C1111yescharacteristic, complemented
259#453—28no—
260#450—24no—
261#447—24no—
262C2×#104C22×C1114yescomplemented
263#418C22×C1114yescomplemented
264C2×#100C22×C1112yescomplemented
265C2×#100C22×C1112yescomplemented
266#407C22×C1112yescomplemented
267#339C22×C1114yescomplemented
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—24no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—48no—
277C22×C11—44no—
278C22×C11—42no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—82no—
284C22×C11—816no—
285C22×C11—82no—
286C22×C11—84no—
287C22×C11—816no—
288C22×C11—84no—
289C22×C11—164no—
290C22×C11#45314yescomplemented
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×#12011yescharacteristic
293C22×C11#53411yescharacteristic
294C4×C11—28no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11D4214yes—
299C25—21no—
300C25D4×C1112yes—
301H(5,𝔽2)—24no—
302H(5,𝔽2)—42no—
303C2×#41—22no—
304C2×#41C23×C1112yes—
305C22×D4—216no—
306C22×D4—22no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—416no—
319C22×D4D4×C1112yes—
320C22×D4C23×C1111yescharacteristic
321C22×D4C23×C1112yes—
322C22×D4C23×C1111yescharacteristic
323C23×C4—21no—
324C23×C4C23×C1111yescharacteristic
325AGL(1,ℤ/8)—28no—
326AGL(1,ℤ/8)—44no—
327C2×SD16—24no—
328C2×D8—24no—
329C2×M16C23×C1114yes—
330#127—216no—
331#127—24no—
332#127—24no—
333#127—22no—
334#127—24no—
335#127D4×C1118yescomplemented
336#124—22no—
337#123—24no—
338#123—22no—
339C22⋊Q8D4×C1114yescomplemented
340#121—28no—
341#121—24no—
342#121D4×C1114yescomplemented
343#120—28no—
344#120—24no—
345#120—22no—
346#120—24no—
347C4×D4—24no—
348C4×D4—24no—
349#117C23×C1112yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C42—21no—
353C2×C42—24no—
354C2×C42C23×C1112yes—
355#104—28no—
356#102—28no—
357#100—24no—
358#100—42no—
359C22⋊C8—24no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—24no—
363C2×C11—44no—
364C2×C11—82no—
365C2×C11—84no—
366C2×C11—82no—
367C2×C11#240311yescharacteristic
368C2×C11C2×#45312yes—
369C24—24no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—24no—
374C24—42no—
375C24—48no—
376C24—42no—
377C24—48no—
378C24—42no—
379C24C2×D4×C1111yescharacteristic
380C24C2×D4×C1112yes—
381C24C2×D4×C1112yes—
382#41—24no—
383#41—24no—
384#41—48no—
385C2×Q8C2×D4×C1112yescomplemented
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—216no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—216no—
392C2×D4—22no—
393C2×D4—28no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—416no—
404C2×D4—416no—
405C2×D4—42no—
406C2×D4—416no—
407C2×D4—416no—
408C2×D4—464no—
409C2×D4—42no—
410C2×D4—48no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—88no—
415C2×D4C2×D4×C1114yes—
416C2×D4C2×D4×C1112yescomplemented
417C2×D4C2×D4×C1114yescomplemented
418C22×C4—24no—
419C22×C4—28no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1114yes—
428C22×C4C24×C1111yescharacteristic
429SD16—48no—
430D8—48no—
431M16—24no—
432M16—24no—
433C2×C8—24no—
434C4⋊C4—24no—
435C4⋊C4C2×D4×C1114yescomplemented
436C22⋊C4—24no—
437C22⋊C4—28no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—24no—
441C42—24no—
442C42—22no—
443C42—22no—
444C42C2×D4×C1114yescomplemented
445C11#2390611yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—21no—
448C23—24no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—24no—
455C23—22no—
456C23—48no—
457C23—44no—
458C23—44no—
459C23—416no—
460C23—416no—
461C23—48no—
462C23—48no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—48no—
467C23—84no—
468C23—88no—
469C23—88no—
470C23—84no—
471C23—84no—
472C23—84no—
473C23C11×#12012yes—
474C23C11×#12014yes—
475C23C22×D4×C1111yescharacteristic
476Q8—24no—
477D4—28no—
478D4—24no—
479D4—28no—
480D4—48no—
481D4—432no—
482D4—432no—
483D4—48no—
484D4—48no—
485D4—42no—
486D4—42no—
487D4—48no—
488D4—44no—
489D4—44no—
490D4—88no—
491C2×C4—216no—
492C2×C4—28no—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—28no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—84no—
502C2×C4C11×#12012yes—
503C2×C4C22×D4×C1112yes—
504C2×C4C22×D4×C1112yes—
505C2×C4C11×H(5,𝔽2)12yes—
506C8—44no—
507C22—24no—
508C22—24no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—24no—
513C22—44no—
514C22—44no—
515C22—48no—
516C22—44no—
517C22—42no—
518C22—44no—
519C22—42no—
520C22—44no—
521C22—44no—
522C22—82no—
523C22—816no—
524C22—82no—
525C22—84no—
526C22—816no—
527C22—84no—
528C22—164no—
529C22C11×#45314yescomplemented
530C22C2×C11×#12011yescharacteristic
531C22C2×C11×#12011yescharacteristic
532C22C11×#53411yescharacteristic
533C4—28no—
534C4—22no—
535C4—42no—
536C4—44no—
537C4D42×C1114yes—
538C2—21no—
539C2—21no—
540C2—24no—
541C2—44no—
542C2—82no—
543C2—84no—
544C2—82no—
545C2C11×#240311yescharacteristic
546C2C2×C11×#45312yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3484C2semidirect
2. C22×C11×#127C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#3003C2semidirect
5. C11×#2002C2semidirect
6. C11×#1896C2semidirect
7. C11×#1887C2semidirect
8. C11×#1783C2semidirect
9. C2×C11×H(5,𝔽2)C22semidirect
12. C23×D4×C11C22semidirect
13. C2×C11×AGL(1,ℤ/8)C22semidirect
16. C11×#535C22semidirect
21. C2×C11×#127C22semidirect
24. C11×#518C22semidirect
25. C22×C42×C11C22semidirect
29. C2×C11×#104C22semidirect
30. C11×#418C22semidirect
31. C2×C11×#100C22semidirect
32. C2×C11×#100C22semidirect
33. C11×#407C22semidirect
34. C11×#339C22semidirect
71. C11×#127D4semidirect
75. C11×C22⋊Q8D4semidirect
78. C11×#121D4semidirect
96. #23906C11direct (N × H)
113. C2×Q8×C11C2×D4semidirect
144. C2×D4×C11C2×D4semidirect
145. C2×D4×C11C2×D4semidirect
163. C11×C4⋊C4C2×D4semidirect
172. C42×C11C2×D4semidirect
173. #3484C2×C11semidirect
174. C22×#127C2×C11semidirect
175. C2×#453C2×C11semidirect
176. #3003C2×C11semidirect
177. #2002C2×C11semidirect
178. #1896C2×C11semidirect
179. #1887C2×C11semidirect
180. #1783C2×C11semidirect
242. C2×H(5,𝔽2)C22×C11semidirect
245. C23×D4C22×C11semidirect
246. C2×AGL(1,ℤ/8)C22×C11semidirect
249. #535C22×C11semidirect
254. C2×#127C22×C11semidirect
257. #518C22×C11semidirect
258. C22×C42C22×C11semidirect
262. C2×#104C22×C11semidirect
263. #418C22×C11semidirect
264. C2×#100C22×C11semidirect
265. C2×#100C22×C11semidirect
266. #407C22×C11semidirect
267. #339C22×C11semidirect
290. C22×C11#453semidirect
335. #127D4×C11semidirect
339. C22⋊Q8D4×C11semidirect
342. #121D4×C11semidirect
385. C2×Q8C2×D4×C11semidirect
416. C2×D4C2×D4×C11semidirect
417. C2×D4C2×D4×C11semidirect
435. C4⋊C4C2×D4×C11semidirect
444. C42C2×D4×C11semidirect
445. C11#23906direct (N × H)
529. C22C11×#453semidirect

Maximal subgroups

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

subgroupindex
C11×#34842
C22×C11×#1272
C2×C11×#4532
C11×#30032
C11×#20022
C11×#18962
C11×#18872
C11×#17832
#2390611