Finite Group Databasebeta

← C11×#8415 #14585608

Subgroups — C11×#8415 #14585608

Order 2816.

704 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×#3515C211yesmaximal, characteristic
2C11×#1759C211yesmaximal, characteristic, complemented
3C11×#1529C211yesmaximal, characteristic, complemented
4C11×#1506C211yesmaximal, characteristic, complemented
5C11×#1500C211yesmaximal, characteristic, complemented
6C11×#1488C211yesmaximal, characteristic, complemented
7C11×#1485C211yesmaximal, characteristic, complemented
8C11×#557C411yescharacteristic, complemented
9C11×#554C411yescharacteristic, complemented
10C11×#554C411yescharacteristic, complemented
11C11×#553—21no—
12C11×#552—21no—
13C11×#552—22no—
14C11×#552—21no—
15C11×#547—21no—
16C11×#547C411yescharacteristic, complemented
17C11×#541—21no—
18C11×#539—22no—
19C11×#533C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2211yescharacteristic
22C2×C11×#125—21no—
23C11×#520—21no—
24C4×C11×#41C2211yescharacteristic
25C11×#432C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×#104—21no—
28C4×C11×M16C2211yescharacteristic
29C11×#376C2211yescharacteristic
30C11×#339—21no—
31C11×#330—21no—
32C11×#329—21no—
33C11×#328—21no—
34C11×#328—22no—
35C11×#327—21no—
36C11×Q8⋊C8—22no—
37C11×Q8⋊C8—21no—
38C11×D4⋊C8—21no—
39C2×C11×#41—21no—
40C2×C11×#41D411yescharacteristic
41C2×C11×M16—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#126—22no—
46C11×#126—22no—
47C11×#126—22no—
48C11×#126—21no—
49C11×#125—22no—
50C11×#125—22no—
51C11×#125—22no—
52C11×#125—21no—
53C11×#125—21no—
54C11×#125—22no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125D411yescharacteristic
58C11×#124D411yescharacteristic
59C11×#123—22no—
60C11×#123—22no—
61C11×#123—22no—
62C11×#123—21no—
63C11×#123—22no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8D411yescharacteristic
71C11×C22⋊Q8D412yes—
72C11×#121—22no—
73C11×#121—21no—
74C11×#121D411yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×Q8×C11D412yes—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11C2×C411yescharacteristic
90C4×D4×C11C2×C411yescharacteristic
91C4×D4×C11D411yescharacteristic
92C11×#117—22no—
93C11×#117—22no—
94C11×#117—21no—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117D411yescharacteristic
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×#104—24no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112C11×#97—21no—
113C4×C8×C11—21no—
114C4×C8×C11—21no—
115C11×#95—21no—
116C11×#95—21no—
117#8415C1111yesmaximal, characteristic, direct product factor, Sylow
118C11×#41—22no—
119C11×#41—41no—
120C11×#41—42no—
121C11×#41—42no—
122C2×Q8×C11—21no—
123C2×Q8×C11C22⋊C411yescharacteristic
124C2×Q8×C11C22⋊C411yescharacteristic
125C2×Q8×C11C22⋊C412yes—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22⋊C411yescharacteristic
130C2×D4×C11C22⋊C411yescharacteristic
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—41no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C11×M16—22no—
143C11×M16—41no—
144C2×C8×C11—41no—
145C2×C8×C11—41no—
146C2×C8×C11—41no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22⋊C411yescharacteristic
167C11×C4⋊C4C22⋊C411yescharacteristic
168C11×C4⋊C4C22⋊C411yescharacteristic
169C11×C4⋊C4C22⋊C411yescharacteristic
170C11×C4⋊C4C22⋊C412yes—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C42×C11—22no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11—41no—
191C42×C11C22×C411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195#3515C2×C1111yescharacteristic
196#1759C2×C1111yescharacteristic, complemented
197#1529C2×C1111yescharacteristic, complemented
198#1506C2×C1111yescharacteristic, complemented
199#1500C2×C1111yescharacteristic, complemented
200#1488C2×C1111yescharacteristic, complemented
201#1485C2×C1111yescharacteristic, complemented
202C23×C11—21no—
203C23×C11—21no—
204C23×C11#12011yescharacteristic
205Q8×C11—21no—
206Q8×C11—21no—
207Q8×C11—42no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—21no—
212D4×C11—41no—
213D4×C11—42no—
214D4×C11—44no—
215D4×C11—81no—
216D4×C11#10412yes—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—81no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11—81no—
239C2×C4×C11—81no—
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11C2×C22⋊C411yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C8×C11—42no—
247C8×C11—81no—
248C8×C11—81no—
249#557C4×C1111yescharacteristic, complemented
250#554C4×C1111yescharacteristic, complemented
251#554C4×C1111yescharacteristic, complemented
252#553—21no—
253#552—21no—
254#552—22no—
255#552—21no—
256#547—21no—
257#547C4×C1111yescharacteristic, complemented
258#541—21no—
259#539—22no—
260#533C22×C1111yescharacteristic
261#529—21no—
262#529C22×C1111yescharacteristic
263C2×#125—21no—
264#520—21no—
265C4×#41C22×C1111yescharacteristic
266#432C22×C1111yescharacteristic
267#431C22×C1111yescharacteristic
268C2×#104—21no—
269C4×M16C22×C1111yescharacteristic
270#376C22×C1111yescharacteristic
271#339—21no—
272#330—21no—
273#329—21no—
274#328—21no—
275#328—22no—
276#327—21no—
277Q8⋊C8—22no—
278Q8⋊C8—21no—
279D4⋊C8—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11#37911yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—42no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11—41no—
301C4×C11—41no—
302C4×C11—42no—
303C4×C11—82no—
304C4×C11C2×#10411yescharacteristic
305C4×C11#42111yescharacteristic
306C2×#41—21no—
307C2×#41D4×C1111yescharacteristic
308C2×M16—21no—
309C4⋊Q8—21no—
310C4⋊Q8C2×C4×C1111yescharacteristic
311C4⋊Q8C2×C4×C1111yescharacteristic
312#126—22no—
313#126—22no—
314#126—22no—
315#126—21no—
316#125—22no—
317#125—22no—
318#125—22no—
319#125—21no—
320#125—21no—
321#125—22no—
322#125—21no—
323#125—21no—
324#125D4×C1111yescharacteristic
325#124D4×C1111yescharacteristic
326#123—22no—
327#123—22no—
328#123—22no—
329#123—21no—
330#123—22no—
331C22⋊Q8—21no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8D4×C1111yescharacteristic
338C22⋊Q8D4×C1112yes—
339#121—22no—
340#121—21no—
341#121D4×C1111yescharacteristic
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2×C4×C1111yescharacteristic
346C4×Q8C2×C4×C1111yescharacteristic
347C4×Q8D4×C1111yescharacteristic
348C4×Q8D4×C1112yes—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4C2×C4×C1111yescharacteristic
357C4×D4C2×C4×C1111yescharacteristic
358C4×D4D4×C1111yescharacteristic
359#117—22no—
360#117—22no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117D4×C1111yescharacteristic
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42C23×C1111yescharacteristic
373C4⋊C8—21no—
374C4⋊C8—21no—
375#104—24no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378#97—21no—
379#97—21no—
380C4×C8—21no—
381C4×C8—21no—
382#95—21no—
383#95—21no—
384C2×C11—41no—
385C2×C11—42no—
386C2×C11—81no—
387C2×C11#178911yescharacteristic
388C2×C11#179411yescharacteristic
389C2×C11#179611yescharacteristic
390#41—22no—
391#41—41no—
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8C11×C22⋊C411yescharacteristic
396C2×Q8C11×C22⋊C411yescharacteristic
397C2×Q8C11×C22⋊C412yes—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4C11×C22⋊C411yescharacteristic
402C2×D4C11×C22⋊C411yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—41no—
411C22×C4C2×D4×C1111yescharacteristic
412C22×C4C2×D4×C1111yescharacteristic
413C22×C4C2×D4×C1111yescharacteristic
414M16—22no—
415M16—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4C11×C22⋊C411yescharacteristic
439C4⋊C4C11×C22⋊C411yescharacteristic
440C4⋊C4C11×C22⋊C411yescharacteristic
441C4⋊C4C11×C22⋊C411yescharacteristic
442C4⋊C4C11×C22⋊C412yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C42—22no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—22no—
461C42—22no—
462C42—41no—
463C42C22×C4×C1111yescharacteristic
464C42C2×D4×C1111yescharacteristic
465C42C2×D4×C1111yescharacteristic
466C42C2×D4×C1111yescharacteristic
467C11#841511yescharacteristic, direct product factor, Sylow
468C23—21no—
469C23—21no—
470C23C11×#12011yescharacteristic
471Q8—21no—
472Q8—21no—
473Q8—42no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477D4—21no—
478D4—41no—
479D4—42no—
480D4—44no—
481D4—81no—
482D4C11×#10412yes—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—81no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4C2×C11×C22⋊C411yescharacteristic
507C2×C4C2×C11×C22⋊C411yescharacteristic
508C2×C4C2×C11×C22⋊C411yescharacteristic
509C2×C4C11×#12011yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12011yescharacteristic
512C8—42no—
513C8—81no—
514C8—81no—
515C22—21no—
516C22—22no—
517C22—21no—
518C22—21no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22C11×#37911yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—42no—
533C4—41no—
534C4—41no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—82no—
539C4C2×C11×#10411yescharacteristic
540C4C11×#42111yescharacteristic
541C2—41no—
542C2—42no—
543C2—81no—
544C2C11×#178911yescharacteristic
545C2C11×#179411yescharacteristic
546C2C11×#179611yescharacteristic
subgroupG/H
center, socleC22×C11#379
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3515C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1759C2semidirect
3. C11×#1529C2semidirect
4. C11×#1506C2semidirect
5. C11×#1500C2semidirect
6. C11×#1488C2semidirect
7. C11×#1485C2semidirect
8. C11×#557C4semidirect
9. C11×#554C4semidirect
10. C11×#554C4semidirect
16. C11×#547C4semidirect
117. #8415C11direct (N × H)
196. #1759C2×C11semidirect
197. #1529C2×C11semidirect
198. #1506C2×C11semidirect
199. #1500C2×C11semidirect
200. #1488C2×C11semidirect
201. #1485C2×C11semidirect
249. #557C4×C11semidirect
250. #554C4×C11semidirect
251. #554C4×C11semidirect
257. #547C4×C11semidirect
467. C11#8415direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35152
C11×#17592
C11×#15292
C11×#15062
C11×#15002
C11×#14882
C11×#14852
#841511