Finite Group Databasebeta

← C11×#23948 #14601141

Subgroups — C11×#23948 #14601141

Order 2816.

1474 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic, complemented
2C11×#3003C212yesmaximal, complemented
3C2×C11×#390C211yesmaximal, characteristic, complemented
4C11×#2027C212yesmaximal, complemented
5C11×#2006C212yesmaximal, complemented
6C11×#1896C212yesmaximal, complemented
7C11×#1883C214yesmaximal, complemented
8C11×#1821C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C2×C11×AGL(1,ℤ/8)C2214yes—
11C11×#554—22no—
12C11×#553—22no—
13C11×#552—22no—
14C11×#547—22no—
15C11×#544C2211yescharacteristic, complemented
16C11×#539—22no—
17C11×#537C2211yescharacteristic, complemented
18C11×#525—22no—
19C11×#525C2212yes—
20C11×#520C2212yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4—22no—
23C22×C42×C11C2211yescharacteristic
24C11×#450—22no—
25C11×#450—22no—
26C11×#447—22no—
27C11×#447—22no—
28C2×C11×#104C2214yescomplemented
29C11×#418C2214yes—
30C11×#407C2212yes—
31C11×#390—22no—
32C11×#390C2212yes—
33C11×#390C2212yes—
34C11×#343C2212yescomplemented
35C11×#343C2212yescomplemented
36C11×#339C2214yescomplemented
37C25×C11—21no—
38C2×C11×#41—22no—
39C2×C11×#41C2312yes—
40C22×D4×C11—24no—
41C22×D4×C11—21no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—42no—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11D412yes—
48C23×C4×C11C2311yescharacteristic
49C11×AGL(1,ℤ/8)—28no—
50C11×AGL(1,ℤ/8)—44no—
51C2×C11×SD16—24no—
52C2×C11×D8—24no—
53C2×C11×M16C2314yes—
54C11×C4⋊Q8—22no—
55C11×#126—24no—
56C11×#125—24no—
57C11×#125—22no—
58C11×#123—24no—
59C11×#123—24no—
60C11×#123—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8D412yes—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121D412yes—
71C11×#121D412yes—
72C11×#120—22no—
73C4×Q8×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—22no—
76C4×D4×C11—24no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C11×#117—22no—
80C11×#117—22no—
81C11×#117C2312yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—48no—
91C2×C42×C11—21no—
92C2×C42×C11—42no—
93C2×C42×C11C2312yes—
94C11×#104—44no—
95C11×#102—24no—
96C11×#102—24no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99#23948C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—24no—
101C24×C11—22no—
102C24×C11—44no—
103C24×C11—42no—
104C24×C11—44no—
105C24×C11—41no—
106C24×C11—41no—
107C24×C11C2×D411yescharacteristic
108C11×#41—24no—
109C11×#41—24no—
110C11×#41—84no—
111C2×Q8×C11—22no—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—48no—
122C2×D4×C11—48no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11C2×D412yes—
126C2×D4×C11#4114yescomplemented
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—44no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C11×SD16—48no—
145C11×D8—48no—
146C11×M16—24no—
147C11×M16—24no—
148C2×C8×C11—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D412yes—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—48no—
168C11×C22⋊C4—48no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—24no—
172C42×C11—42no—
173#3492C2×C1111yescharacteristic, complemented
174#3003C2×C1112yescomplemented
175C2×#390C2×C1111yescharacteristic, complemented
176#2027C2×C1112yescomplemented
177#2006C2×C1112yescomplemented
178#1896C2×C1112yescomplemented
179#1883C2×C1114yescomplemented
180#1821C2×C1111yescharacteristic, complemented
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11—416no—
191C23×C11—44no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—88no—
195C23×C11—82no—
196C23×C11—82no—
197C23×C11—82no—
198C23×C11—82no—
199C23×C11#12011yescharacteristic
200C23×C11#12011yescharacteristic
201C23×C11C22×D411yescharacteristic
202Q8×C11—24no—
203Q8×C11—82no—
204D4×C11—24no—
205D4×C11—28no—
206D4×C11—48no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—44no—
211D4×C11—44no—
212D4×C11—82no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—82no—
231C2×C4×C11—84no—
232C2×C4×C11#12012yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C8×C11—44no—
237C23×D4C22×C1111yescharacteristic
238C2×AGL(1,ℤ/8)C22×C1114yes—
239#554—22no—
240#553—22no—
241#552—22no—
242#547—22no—
243#544C22×C1111yescharacteristic, complemented
244#539—22no—
245#537C22×C1111yescharacteristic, complemented
246#525—22no—
247#525C22×C1112yes—
248#520C22×C1112yescomplemented
249C22×C4⋊C4C22×C1111yescharacteristic
250C22×C22⋊C4—22no—
251C22×C42C22×C1111yescharacteristic
252#450—22no—
253#450—22no—
254#447—22no—
255#447—22no—
256C2×#104C22×C1114yescomplemented
257#418C22×C1114yes—
258#407C22×C1112yes—
259#390—22no—
260#390C22×C1112yes—
261#390C22×C1112yes—
262#343C22×C1112yescomplemented
263#343C22×C1112yescomplemented
264#339C22×C1114yescomplemented
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—48no—
274C22×C11—42no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—84no—
279C22×C11—88no—
280C22×C11—88no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11#45312yes—
284C22×C11#45412yes—
285C22×C11C2×#12011yescharacteristic
286C22×C11#52511yescharacteristic
287C22×C11#53511yescharacteristic
288C4×C11—22no—
289C4×C11—44no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11#54614yes—
296C25—21no—
297C2×#41—22no—
298C2×#41C23×C1112yes—
299C22×D4—24no—
300C22×D4—21no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—42no—
304C22×D4C23×C1112yes—
305C23×C4—21no—
306C23×C4D4×C1112yes—
307C23×C4C23×C1111yescharacteristic
308AGL(1,ℤ/8)—28no—
309AGL(1,ℤ/8)—44no—
310C2×SD16—24no—
311C2×D8—24no—
312C2×M16C23×C1114yes—
313C4⋊Q8—22no—
314#126—24no—
315#125—24no—
316#125—22no—
317#123—24no—
318#123—24no—
319#123—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8D4×C1112yes—
325C22⋊Q8D4×C1112yes—
326#121—22no—
327#121—22no—
328#121—22no—
329#121D4×C1112yes—
330#121D4×C1112yes—
331#120—22no—
332C4×Q8—22no—
333C4×D4—24no—
334C4×D4—22no—
335C4×D4—24no—
336C4×D4—22no—
337C4×D4—22no—
338#117—22no—
339#117—22no—
340#117C23×C1112yes—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4D4×C1112yes—
345C2×C4⋊C4C23×C1111yescharacteristic
346C2×C4⋊C4C23×C1111yescharacteristic
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—48no—
350C2×C42—21no—
351C2×C42—42no—
352C2×C42C23×C1112yes—
353#104—44no—
354#102—24no—
355#102—24no—
356C22⋊C8—22no—
357C22⋊C8—22no—
358C2×C11—21no—
359C2×C11—21no—
360C2×C11—22no—
361C2×C11—22no—
362C2×C11—82no—
363C2×C11—84no—
364C2×C11#240411yescharacteristic
365C2×C11C2×#45311yescharacteristic
366C2×C11C2×#45411yescharacteristic
367C24—24no—
368C24—22no—
369C24—44no—
370C24—42no—
371C24—44no—
372C24—41no—
373C24—41no—
374C24C2×D4×C1111yescharacteristic
375#41—24no—
376#41—24no—
377#41—84no—
378C2×Q8—22no—
379C2×Q8C2×D4×C1112yes—
380C2×D4—24no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—48no—
389C2×D4—48no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4C2×D4×C1112yes—
393C2×D4C11×#4114yescomplemented
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—44no—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1112yes—
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1112yes—
410C22×C4C24×C1111yescharacteristic
411SD16—48no—
412D8—48no—
413M16—24no—
414M16—24no—
415C2×C8—24no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4C2×D4×C1112yes—
426C4⋊C4C2×D4×C1112yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—48no—
435C22⋊C4—48no—
436C42—24no—
437C42—22no—
438C42—24no—
439C42—42no—
440C11#2394811yescharacteristic, direct product factor, Sylow
441C23—21no—
442C23—21no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—24no—
447C23—44no—
448C23—44no—
449C23—44no—
450C23—416no—
451C23—44no—
452C23—42no—
453C23—42no—
454C23—88no—
455C23—82no—
456C23—82no—
457C23—82no—
458C23—82no—
459C23C11×#12011yescharacteristic
460C23C11×#12011yescharacteristic
461C23C22×D4×C1111yescharacteristic
462Q8—24no—
463Q8—82no—
464D4—24no—
465D4—28no—
466D4—48no—
467D4—42no—
468D4—42no—
469D4—44no—
470D4—44no—
471D4—44no—
472D4—82no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—82no—
491C2×C4—84no—
492C2×C4C11×#12012yes—
493C2×C4C22×D4×C1112yes—
494C2×C4C2×C11×#4112yes—
495C2×C4C11×H(5,𝔽2)12yes—
496C8—44no—
497C22—24no—
498C22—24no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—48no—
506C22—42no—
507C22—44no—
508C22—42no—
509C22—42no—
510C22—84no—
511C22—88no—
512C22—88no—
513C22—82no—
514C22—82no—
515C22C11×#45312yes—
516C22C11×#45412yes—
517C22C2×C11×#12011yescharacteristic
518C22C11×#52511yescharacteristic
519C22C11×#53511yescharacteristic
520C4—22no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4C11×#54614yes—
528C2—21no—
529C2—21no—
530C2—22no—
531C2—22no—
532C2—84no—
533C2—82no—
534C2C11×#240411yescharacteristic
535C2C2×C11×#45311yescharacteristic
536C2C2×C11×#45411yescharacteristic
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×#3492C2semidirect
2. C11×#3003C2semidirect
3. C2×C11×#390C2semidirect
4. C11×#2027C2semidirect
5. C11×#2006C2semidirect
6. C11×#1896C2semidirect
7. C11×#1883C2semidirect
8. C11×#1821C2semidirect
15. C11×#544C22semidirect
17. C11×#537C22semidirect
20. C11×#520C22semidirect
28. C2×C11×#104C22semidirect
34. C11×#343C22semidirect
35. C11×#343C22semidirect
36. C11×#339C22semidirect
99. #23948C11direct (N × H)
126. C2×D4×C11#41semidirect
173. #3492C2×C11semidirect
174. #3003C2×C11semidirect
175. C2×#390C2×C11semidirect
176. #2027C2×C11semidirect
177. #2006C2×C11semidirect
178. #1896C2×C11semidirect
179. #1883C2×C11semidirect
180. #1821C2×C11semidirect
243. #544C22×C11semidirect
245. #537C22×C11semidirect
248. #520C22×C11semidirect
256. C2×#104C22×C11semidirect
262. #343C22×C11semidirect
263. #343C22×C11semidirect
264. #339C22×C11semidirect
393. C2×D4C11×#41semidirect
440. C11#23948direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30032
C2×C11×#3902
C11×#20272
C11×#20062
C11×#18962
C11×#18832
C11×#18212
#2394811