Finite Group Databasebeta

← C11×#18902 #14596095

Subgroups — C11×#18902 #14596095

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3226C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic, complemented
4C2×C11×#461C211yesmaximal, characteristic, complemented
5C11×#1647C214yesmaximal, complemented
6C11×#1639C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C22×C11×SD16—21no—
12C11×#547—21no—
13C11×#547C2212yes—
14C11×#546—22no—
15C11×#546—22no—
16D42×C11—21no—
17D42×C11C2212yes—
18C11×#537—21no—
19C11×#534—22no—
20C11×#532C2211yescharacteristic
21C11×#532C2211yescharacteristic
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121—22no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#500—21no—
26C11×#500C2212yescomplemented
27C11×#486—21no—
28C11×#486C2212yescomplemented
29C11×#480—22no—
30C11×#480—22no—
31C11×#474—22no—
32C11×#474C2214yescomplemented
33C11×#461—22no—
34C11×#461C2214yescomplemented
35C11×#431C2211yescharacteristic, complemented
36C11×#431C2211yescharacteristic, complemented
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×#103—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×D4⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C11×H(5,𝔽2)—44no—
44C11×H(5,𝔽2)—44no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×Q8×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C2×C11×SD16—24no—
57C2×C11×SD16—44no—
58C22×C8×C11—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2312yes—
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#124—21no—
68C11×#124—21no—
69C11×#123—24no—
70C11×#123—24no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121D412yes—
82C11×#121D412yes—
83C11×#120—24no—
84C11×#120—24no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D412yes—
90C4×D4×C11D412yes—
91C4×D4×C11C2312yes—
92C4×D4×C11C2312yes—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107—24no—
101C11×#107—24no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C11×#103—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2312yes—
113#18902C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—21no—
115C24×C11—24no—
116C11×#41—44no—
117C11×#41—48no—
118C11×#41—44no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—41no—
127C2×Q8×C11—42no—
128C2×Q8×C11—42no—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—44no—
141C2×D4×C11—48no—
142C2×D4×C11—416no—
143C2×D4×C11—44no—
144C2×D4×C11—84no—
145C2×D4×C11D814yes—
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—41no—
156C22×C4×C11—82no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C11×SD16—48no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—42no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2411yescharacteristic
188#3496C2×C1111yescharacteristic
189#3226C2×C1111yescharacteristic, complemented
190#3226C2×C1111yescharacteristic, complemented
191C2×#461C2×C1111yescharacteristic, complemented
192#1647C2×C1114yescomplemented
193#1639C2×C1114yescomplemented
194#1540C2×C1111yescharacteristic, complemented
195#1480C2×C1111yescharacteristic, complemented
196#1478C2×C1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—48no—
202C23×C11—81no—
203C23×C11—81no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11#12011yescharacteristic
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—82no—
213D4×C11—22no—
214D4×C11—24no—
215D4×C11—24no—
216D4×C11—42no—
217D4×C11—48no—
218D4×C11—48no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—81no—
226D4×C11—84no—
227D4×C11C2×D814yes—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—48no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—82no—
240C2×C4×C11—81no—
241C2×C4×C11—82no—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11C2×D812yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C8×C11—42no—
251C8×C11—42no—
252C8×C11—42no—
253C2×H(5,𝔽2)—21no—
254C22×SD16—21no—
255#547—21no—
256#547C22×C1112yes—
257#546—22no—
258#546—22no—
259D42—21no—
260D42C22×C1112yes—
261#537—21no—
262#534—22no—
263#532C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265C2×C4⋊Q8C22×C1111yescharacteristic, complemented
266C2×#121—22no—
267C2×C4×D4C22×C1111yescharacteristic
268#500—21no—
269#500C22×C1112yescomplemented
270#486—21no—
271#486C22×C1112yescomplemented
272#480—22no—
273#480—22no—
274#474—22no—
275#474C22×C1114yescomplemented
276#461—22no—
277#461C22×C1114yescomplemented
278#431C22×C1111yescharacteristic, complemented
279#431C22×C1111yescharacteristic, complemented
280C2×C4⋊C8C22×C1111yescharacteristic, complemented
281C2×#103—21no—
282#332C22×C1112yescomplemented
283#331C22×C1112yescomplemented
284D4⋊C8C22×C1114yescomplemented
285D4⋊C8C22×C1114yescomplemented
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—24no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—84no—
298C22×C11—168no—
299C22×C11#44712yes—
300C22×C11C2×#12011yescharacteristic
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11#44712yes—
309C4×C11C22×D811yescharacteristic
310C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
311C4×C11#57712yes—
312H(5,𝔽2)—44no—
313H(5,𝔽2)—44no—
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—21no—
317C2×#41—21no—
318C22×Q8—21no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4D4×C1111yescharacteristic
324C23×C4—21no—
325C2×SD16—24no—
326C2×SD16—44no—
327C22×C8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8D4×C1111yescharacteristic
332C4⋊Q8C23×C1112yes—
333C4⋊Q8C23×C1111yescharacteristic
334#127D4×C1111yescharacteristic
335#127C23×C1111yescharacteristic
336#124—21no—
337#124—21no—
338#123—24no—
339#123—24no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342#121—24no—
343#121—24no—
344#121—22no—
345#121—22no—
346#121—21no—
347#121—21no—
348#121—22no—
349#121—22no—
350#121D4×C1112yes—
351#121D4×C1112yes—
352#120—24no—
353#120—24no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4D4×C1112yes—
359C4×D4D4×C1112yes—
360C4×D4C23×C1112yes—
361C4×D4C23×C1112yes—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C1111yescharacteristic
366C2×C22⋊C4—24no—
367C2×C22⋊C4—21no—
368C2×C42C23×C1111yescharacteristic
369#107—24no—
370#107—24no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8C23×C1112yes—
374C4⋊C8C23×C1112yes—
375#103—24no—
376#102—24no—
377#102—24no—
378C22⋊C8—21no—
379C22⋊C8—21no—
380C4×C8—21no—
381C4×C8C23×C1112yes—
382C2×C11—22no—
383C2×C11—44no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11C2×#44711yescharacteristic
387C2×C11#300911yescharacteristic
388C2×C11#302211yescharacteristic
389C24—21no—
390C24—24no—
391#41—44no—
392#41—48no—
393#41—44no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—41no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—24no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—44no—
416C2×D4—48no—
417C2×D4—416no—
418C2×D4—44no—
419C2×D4—84no—
420C2×D4C11×D814yes—
421C2×D4C2×D4×C1112yes—
422C2×D4C2×D4×C1112yes—
423C2×D4C2×D4×C1112yes—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4—82no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435SD16—48no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—42no—
440C4⋊C4—24no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4C2×D4×C1112yes—
449C4⋊C4C2×D4×C1112yes—
450C4⋊C4C2×D4×C1112yes—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C42C2×D4×C1111yescharacteristic
460C42C2×D4×C1111yescharacteristic
461C42C2×D4×C1111yescharacteristic
462C42C24×C1111yescharacteristic
463C11#1890211yescharacteristic, direct product factor, Sylow
464C23—22no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—48no—
469C23—81no—
470C23—81no—
471C23—84no—
472C23—84no—
473C23C11×#12011yescharacteristic
474Q8—41no—
475Q8—41no—
476Q8—42no—
477Q8—42no—
478Q8—42no—
479Q8—82no—
480D4—22no—
481D4—24no—
482D4—24no—
483D4—42no—
484D4—48no—
485D4—48no—
486D4—44no—
487D4—44no—
488D4—41no—
489D4—41no—
490D4—42no—
491D4—42no—
492D4—81no—
493D4—84no—
494D4C2×C11×D814yes—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—82no—
509C2×C4C11×#12011yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12011yescharacteristic
512C2×C4C2×C11×D812yes—
513C2×C4C11×AGL(1,ℤ/8)12yes—
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C8—42no—
518C8—42no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—24no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—84no—
532C22—168no—
533C22C11×#44712yes—
534C22C2×C11×#12011yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—82no—
542C4C11×#44712yes—
543C4C22×C11×D811yescharacteristic
544C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
545C4C11×#57712yes—
546C2—22no—
547C2—44no—
548C2—82no—
549C2—82no—
550C2C2×C11×#44711yescharacteristic
551C2C11×#300911yescharacteristic
552C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3496C2
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×#3226C2semidirect
3. C11×#3226C2semidirect
4. C2×C11×#461C2semidirect
5. C11×#1647C2semidirect
6. C11×#1639C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1478C2semidirect
22. C2×C11×C4⋊Q8C22semidirect
26. C11×#500C22semidirect
28. C11×#486C22semidirect
32. C11×#474C22semidirect
34. C11×#461C22semidirect
35. C11×#431C22semidirect
36. C11×#431C22semidirect
37. C2×C11×C4⋊C8C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×D4⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
113. #18902C11direct (N × H)
189. #3226C2×C11semidirect
190. #3226C2×C11semidirect
191. C2×#461C2×C11semidirect
192. #1647C2×C11semidirect
193. #1639C2×C11semidirect
194. #1540C2×C11semidirect
195. #1480C2×C11semidirect
196. #1478C2×C11semidirect
265. C2×C4⋊Q8C22×C11semidirect
269. #500C22×C11semidirect
271. #486C22×C11semidirect
275. #474C22×C11semidirect
277. #461C22×C11semidirect
278. #431C22×C11semidirect
279. #431C22×C11semidirect
280. C2×C4⋊C8C22×C11semidirect
282. #332C22×C11semidirect
283. #331C22×C11semidirect
284. D4⋊C8C22×C11semidirect
285. D4⋊C8C22×C11semidirect
463. C11#18902direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#32262
C2×C11×#4612
C11×#16472
C11×#16392
C11×#15402
C11×#14802
C11×#14782
#1890211