Finite Group Databasebeta

← C11×#18887 #14596080

Subgroups — C11×#18887 #14596080

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic
2C11×#3249C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C11×#3076C211yesmaximal, characteristic
5C11×#1653C212yesmaximal, complemented
6C11×#1652C212yesmaximal, complemented
7C11×#1638C212yesmaximal, complemented
8C11×#1636C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1481C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic
12C11×#557—21no—
13C11×#557C2212yes—
14C11×#556—21no—
15C11×#556C2212yes—
16C11×#552—22no—
17C11×#552—22no—
18C11×#541—22no—
19C11×#536—21no—
20C11×#533—21no—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C2×C11×C4⋊Q8C2211yescharacteristic
25C11×#519—21no—
26C4×C11×#41C2211yescharacteristic
27C11×#498C2212yes—
28C11×#487C2212yes—
29C11×#483—22no—
30C11×#479—21no—
31C11×#478—21no—
32C11×#477—21no—
33C11×#477C2211yescharacteristic
34C11×#477C2212yes—
35C11×#476C2211yescharacteristic
36C11×#475—22no—
37C11×#475C2211yescharacteristic
38C11×#474C2211yescharacteristic
39C11×#467—22no—
40C11×#462—21no—
41C11×#462C2212yes—
42C11×#431C2211yescharacteristic
43C11×#427—21no—
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—21no—
55C2×C11×Q16—22no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8D412yes—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×#126—24no—
68C11×#126—24no—
69C11×#125—22no—
70C11×#125—24no—
71C11×#125—22no—
72C11×#125—24no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#124—22no—
76C11×#123—24no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8D412yes—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2312yes—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11D411yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—24no—
102C11×#117—22no—
103C11×#117—21no—
104C11×#117—22no—
105C11×#117—21no—
106C11×#117—21no—
107C11×#117D411yescharacteristic
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D412yes—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—22no—
115C11×#106—24no—
116C11×#106—21no—
117C11×#106—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8C2312yes—
122C11×C4⋊C8C2311yescharacteristic
123C11×C4⋊C8C2311yescharacteristic
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—22no—
127C11×#103—22no—
128C11×#103—24no—
129C11×#102—21no—
130C11×#102—21no—
131C11×C22⋊C8—21no—
132C4×C8×C11C2312yes—
133#18887C1111yesmaximal, characteristic, direct product factor, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—42no—
142C2×Q8×C11—42no—
143C2×Q8×C11C2×D411yescharacteristic
144C2×Q8×C11C2×D412yes—
145C2×D4×C11—21no—
146C2×D4×C11C2×D411yescharacteristic
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C11×Q16—82no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—42no—
160C2×C8×C11—81no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4C2×D414yes—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—41no—
192C42×C11—24no—
193C42×C11—24no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—22no—
198C42×C11—41no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2411yescharacteristic
203#3509C2×C1111yescharacteristic
204#3249C2×C1111yescharacteristic, complemented
205#3229C2×C1111yescharacteristic, complemented
206#3076C2×C1111yescharacteristic
207#1653C2×C1112yescomplemented
208#1652C2×C1112yescomplemented
209#1638C2×C1112yescomplemented
210#1636C2×C1112yescomplemented
211C2×#332C2×C1111yescharacteristic, complemented
212#1481C2×C1111yescharacteristic, complemented
213#1477C2×C1111yescharacteristic
214C23×C11—21no—
215C23×C11#12011yescharacteristic
216Q8×C11—21no—
217Q8×C11—21no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—42no—
221Q8×C11—42no—
222Q8×C11—42no—
223Q8×C11—42no—
224Q8×C11—44no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—21no—
228D4×C11—21no—
229D4×C11—42no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#13512yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C8×C11—42no—
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—42no—
258#557—21no—
259#557C22×C1112yes—
260#556—21no—
261#556C22×C1112yes—
262#552—22no—
263#552—22no—
264#541—22no—
265#536—21no—
266#533—21no—
267#533—21no—
268#533C22×C1111yescharacteristic
269#533C22×C1111yescharacteristic
270C2×C4⋊Q8C22×C1111yescharacteristic
271#519—21no—
272C4×#41C22×C1111yescharacteristic
273#498C22×C1112yes—
274#487C22×C1112yes—
275#483—22no—
276#479—21no—
277#478—21no—
278#477—21no—
279#477C22×C1111yescharacteristic
280#477C22×C1112yes—
281#476C22×C1111yescharacteristic
282#475—22no—
283#475C22×C1111yescharacteristic
284#474C22×C1111yescharacteristic
285#467—22no—
286#462—21no—
287#462C22×C1112yes—
288#431C22×C1111yescharacteristic
289#427—21no—
290C2×C4⋊C8C22×C1111yescharacteristic
291C2×C4⋊C8C22×C1111yescharacteristic
292#416—21no—
293#332C22×C1112yes—
294#332C22×C1112yes—
295Q8⋊C8C22×C1112yes—
296Q8⋊C8C22×C1112yes—
297Q8⋊C8C22×C1112yes—
298D4⋊C8C22×C1112yes—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11#45212yes—
305C22×C11C2×#12011yescharacteristic
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—41no—
310C4×C11—44no—
311C4×C11—41no—
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11#45212yes—
318C4×C11C2×#13511yescharacteristic
319C4×C11C2×#13711yescharacteristic
320C4×C11#57711yescharacteristic
321C4×C11#57811yescharacteristic
322C2×#41D4×C1111yescharacteristic
323C22×Q8—21no—
324C2×Q16—22no—
325C22×C8—21no—
326C22×C8—21no—
327C4⋊Q8—22no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8D4×C1111yescharacteristic
331C4⋊Q8D4×C1112yes—
332C4⋊Q8D4×C1111yescharacteristic
333C4⋊Q8C23×C1111yescharacteristic
334C4⋊Q8C23×C1111yescharacteristic
335C4⋊Q8C23×C1112yes—
336#126—24no—
337#126—24no—
338#125—22no—
339#125—24no—
340#125—22no—
341#125—24no—
342#125—21no—
343#125—21no—
344#124—22no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8D4×C1112yes—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8D4×C1111yescharacteristic
364C4×Q8C23×C1111yescharacteristic
365C4×Q8C23×C1112yes—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4D4×C1111yescharacteristic
369C4×D4C23×C1111yescharacteristic
370#117—24no—
371#117—22no—
372#117—21no—
373#117—22no—
374#117—21no—
375#117—21no—
376#117D4×C1111yescharacteristic
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C1112yes—
379C2×C42—21no—
380C2×C42C23×C1111yescharacteristic
381#107—21no—
382#107—21no—
383#107—22no—
384#106—21no—
385#106—21no—
386#106—24no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8C23×C1112yes—
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393#103—21no—
394#103—21no—
395#103—22no—
396#103—22no—
397#103—24no—
398#102—21no—
399#102—21no—
400C22⋊C8—21no—
401C4×C8C23×C1112yes—
402C2×C11—22no—
403C2×C11—81no—
404C2×C11C2×#45211yescharacteristic
405C2×C11#301311yescharacteristic
406C2×C11#302011yescharacteristic
407#41—22no—
408#41—22no—
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8C2×D4×C1111yescharacteristic
417C2×Q8C2×D4×C1112yes—
418C2×D4—21no—
419C2×D4C2×D4×C1111yescharacteristic
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427Q16—82no—
428C2×C8—22no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—42no—
433C2×C8—81no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4C2×D4×C1114yes—
455C4⋊C4C2×D4×C1112yes—
456C4⋊C4C2×D4×C1111yescharacteristic
457C4⋊C4C2×D4×C1111yescharacteristic
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—21no—
461C22⋊C4—22no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—41no—
465C42—24no—
466C42—24no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—22no—
471C42—41no—
472C42C2×D4×C1111yescharacteristic
473C42C2×D4×C1111yescharacteristic
474C42C2×D4×C1111yescharacteristic
475C42C24×C1111yescharacteristic
476C11#1888711yescharacteristic, direct product factor, Sylow
477C23—21no—
478C23C11×#12011yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—22no—
482Q8—22no—
483Q8—42no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—44no—
488Q8—41no—
489Q8—41no—
490D4—21no—
491D4—21no—
492D4—42no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4C11×#12011yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12011yescharacteristic
512C2×C4C11×#13512yes—
513C2×C4C11×#13712yes—
514C2×C4C22×D4×C1111yescharacteristic
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C8—42no—
518C8—41no—
519C8—41no—
520C8—42no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C11×#45212yes—
527C22C2×C11×#12011yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—44no—
533C4—41no—
534C4—42no—
535C4—41no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4C11×#45212yes—
540C4C2×C11×#13511yescharacteristic
541C4C2×C11×#13711yescharacteristic
542C4C11×#57711yescharacteristic
543C4C11×#57811yescharacteristic
544C2—22no—
545C2—81no—
546C2C2×C11×#45211yescharacteristic
547C2C11×#301311yescharacteristic
548C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#41D4
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×#3249C2semidirect
3. C11×#3229C2semidirect
5. C11×#1653C2semidirect
6. C11×#1652C2semidirect
7. C11×#1638C2semidirect
8. C11×#1636C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1481C2semidirect
133. #18887C11direct (N × H)
204. #3249C2×C11semidirect
205. #3229C2×C11semidirect
207. #1653C2×C11semidirect
208. #1652C2×C11semidirect
209. #1638C2×C11semidirect
210. #1636C2×C11semidirect
211. C2×#332C2×C11semidirect
212. #1481C2×C11semidirect
476. C11#18887direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#32492
C11×#32292
C11×#30762
C11×#16532
C11×#16522
C11×#16382
C11×#16362
C2×C11×#3322
C11×#14812
C11×#14772
#1888711