Finite Group Databasebeta

← C11×#19849 #14597042

Subgroups — C11×#19849 #14597042

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3395C211yesmaximal, characteristic, complemented
2C11×#3374C211yesmaximal, characteristic, complemented
3C11×#3365C211yesmaximal, characteristic
4C11×#3365C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic
6C11×#1702C211yesmaximal, characteristic
7C11×#1682C211yesmaximal, characteristic
8C11×#1680C211yesmaximal, characteristic, complemented
9C11×#1670C211yesmaximal, characteristic, complemented
10C11×#1653C211yesmaximal, characteristic, complemented
11C11×#1653C211yesmaximal, characteristic, complemented
12C11×#1640C211yesmaximal, characteristic
13C11×#1626C211yesmaximal, characteristic
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#557C2211yescharacteristic
18C11×#557C2211yescharacteristic
19C11×#557C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#494—21no—
22C11×#494C2211yescharacteristic
23C11×#491—21no—
24C11×#488—21no—
25C11×#488—21no—
26C11×#487C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#479—21no—
31C11×#478—21no—
32C11×#478—21no—
33C11×#475C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#475C2211yescharacteristic
36C11×#464—21no—
37C11×#464—21no—
38C11×#462—21no—
39C11×#462—21no—
40C11×#462—21no—
41C11×#462C2211yescharacteristic
42C11×#462C2211yescharacteristic
43C11×#462C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#460C2211yescharacteristic
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#441—21no—
51C4×C11×Q16—21no—
52C4×C11×Q16C2211yescharacteristic
53C4×C11×Q16C2211yescharacteristic
54C4×C11×SD16—21no—
55C4×C11×SD16—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16—21no—
72C2×C11×Q16D411yescharacteristic
73C2×C11×Q16D411yescharacteristic
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127C2311yescharacteristic
83C11×#125—21no—
84C11×#125—21no—
85C11×#125—21no—
86C11×#125—41no—
87C11×#125—41no—
88C11×#125—41no—
89C11×#124—21no—
90C11×#124—21no—
91C11×#123—41no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11C2311yescharacteristic
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2311yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C11×#107D411yescharacteristic
105C11×#107D411yescharacteristic
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—41no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103D411yescharacteristic
127C11×#103D411yescharacteristic
128C11×#103D411yescharacteristic
129C11×#103D411yescharacteristic
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—41no—
137C11×#97—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19849C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C22×C4×C11—41no—
156C11×Q16—22no—
157C11×Q16—41no—
158C11×Q16—42no—
159C11×Q16—42no—
160C11×Q16—81no—
161C11×Q16—81no—
162C11×Q16—81no—
163C11×SD16—42no—
164C11×SD16—42no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—41no—
205C42×C11—41no—
206C42×C11—41no—
207C42×C11C2411yescharacteristic
208#3395C2×C1111yescharacteristic, complemented
209#3374C2×C1111yescharacteristic, complemented
210#3365C2×C1111yescharacteristic
211#3365C2×C1111yescharacteristic
212#1720C2×C1111yescharacteristic
213#1702C2×C1111yescharacteristic
214#1682C2×C1111yescharacteristic
215#1680C2×C1111yescharacteristic, complemented
216#1670C2×C1111yescharacteristic, complemented
217#1653C2×C1111yescharacteristic, complemented
218#1653C2×C1111yescharacteristic, complemented
219#1640C2×C1111yescharacteristic
220#1626C2×C1111yescharacteristic
221#1584C2×C1111yescharacteristic, complemented
222#1579C2×C1111yescharacteristic, complemented
223C23×C11—41no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11#13512yes—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—81no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—161no—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267#559C22×C1111yescharacteristic
268#557C22×C1111yescharacteristic
269#557C22×C1111yescharacteristic
270#557C22×C1111yescharacteristic
271#498C22×C1111yescharacteristic
272#494—21no—
273#494C22×C1111yescharacteristic
274#491—21no—
275#488—21no—
276#488—21no—
277#487C22×C1111yescharacteristic
278#486C22×C1111yescharacteristic
279#486C22×C1111yescharacteristic
280#486C22×C1111yescharacteristic
281#479—21no—
282#478—21no—
283#478—21no—
284#475C22×C1111yescharacteristic
285#475C22×C1111yescharacteristic
286#475C22×C1111yescharacteristic
287#464—21no—
288#464—21no—
289#462—21no—
290#462—21no—
291#462—21no—
292#462C22×C1111yescharacteristic
293#462C22×C1111yescharacteristic
294#462C22×C1111yescharacteristic
295#460C22×C1111yescharacteristic
296#460C22×C1111yescharacteristic
297#446C22×C1111yescharacteristic
298C8×Q8C22×C1111yescharacteristic
299C8×Q8C22×C1111yescharacteristic
300C8×Q8C22×C1111yescharacteristic
301#441—21no—
302C4×Q16—21no—
303C4×Q16C22×C1111yescharacteristic
304C4×Q16C22×C1111yescharacteristic
305C4×SD16—21no—
306C4×SD16—21no—
307#335C22×C1111yescharacteristic
308#334C22×C1111yescharacteristic
309#332C22×C1111yescharacteristic
310#332C22×C1111yescharacteristic
311#332C22×C1111yescharacteristic
312#331C22×C1111yescharacteristic
313Q8⋊C8C22×C1111yescharacteristic
314Q8⋊C8C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316Q8⋊C8C22×C1111yescharacteristic
317#322C22×C1111yescharacteristic
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11D4211yescharacteristic
322C4×C11—22no—
323C4×C11—21no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C2×#13511yescharacteristic
335C4×C11#57511yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16D4×C1111yescharacteristic
344C2×Q16D4×C1111yescharacteristic
345C2×SD16—21no—
346C2×SD16—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C1111yescharacteristic
351C4⋊Q8C23×C1111yescharacteristic
352C4⋊Q8C23×C1111yescharacteristic
353#127C23×C1111yescharacteristic
354#125—21no—
355#125—21no—
356#125—21no—
357#125—41no—
358#125—41no—
359#125—41no—
360#124—21no—
361#124—21no—
362#123—41no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C1111yescharacteristic
370C4×Q8C23×C1111yescharacteristic
371C4×Q8C23×C1111yescharacteristic
372C4×Q8C23×C1111yescharacteristic
373C4×D4—21no—
374C4×D4—21no—
375#107D4×C1111yescharacteristic
376#107D4×C1111yescharacteristic
377#106—21no—
378#106—21no—
379#106—21no—
380#106—41no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8C23×C1111yescharacteristic
386C4⋊C8C23×C1111yescharacteristic
387C4⋊C8C23×C1111yescharacteristic
388C4⋊C8C23×C1111yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103D4×C1111yescharacteristic
398#103D4×C1111yescharacteristic
399#103D4×C1111yescharacteristic
400#103D4×C1111yescharacteristic
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405#102—21no—
406#102—21no—
407#102—41no—
408#97—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8C23×C1111yescharacteristic
413C4×C8C23×C1111yescharacteristic
414C4×C8C23×C1111yescharacteristic
415C2×C11—161no—
416C2×C11#327111yescharacteristic
417C2×C11#328511yescharacteristic
418C2×C11#328911yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C2×D4×C1111yescharacteristic
423C2×Q8C2×D4×C1111yescharacteristic
424C2×Q8C2×D4×C1111yescharacteristic
425C2×Q8C2×D4×C1111yescharacteristic
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C22×C4—41no—
430Q16—22no—
431Q16—41no—
432Q16—42no—
433Q16—42no—
434Q16—81no—
435Q16—81no—
436Q16—81no—
437SD16—42no—
438SD16—42no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C2×D4×C1111yescharacteristic
445C2×C8C2×D4×C1111yescharacteristic
446C2×C8C2×D4×C1111yescharacteristic
447C2×C8C2×D4×C1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C1111yescharacteristic
468C4⋊C4C2×D4×C1111yescharacteristic
469C4⋊C4C2×D4×C1111yescharacteristic
470C4⋊C4C2×D4×C1111yescharacteristic
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42—41no—
481C42C24×C1111yescharacteristic
482C11#1984911yescharacteristic, direct product factor, Sylow
483C23—41no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8C11×#13512yes—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—81no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—161no—
515C2×C4C22×D4×C1111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C11×H(5,𝔽2)11yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22D42×C1111yescharacteristic
531C4—22no—
532C4—21no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×C11×#13511yescharacteristic
544C4C11×#57511yescharacteristic
545C4C11×#57711yescharacteristic
546C4C11×#57811yescharacteristic
547C2—161no—
548C2C11×#327111yescharacteristic
549C2C11×#328511yescharacteristic
550C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#127C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3395C2semidirect
2. C11×#3374C2semidirect
8. C11×#1680C2semidirect
9. C11×#1670C2semidirect
10. C11×#1653C2semidirect
11. C11×#1653C2semidirect
14. C11×#1584C2semidirect
15. C11×#1579C2semidirect
144. #19849C11direct (N × H)
208. #3395C2×C11semidirect
209. #3374C2×C11semidirect
215. #1680C2×C11semidirect
216. #1670C2×C11semidirect
217. #1653C2×C11semidirect
218. #1653C2×C11semidirect
221. #1584C2×C11semidirect
222. #1579C2×C11semidirect
482. C11#19849direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33952
C11×#33742
C11×#33652
C11×#17202
C11×#17022
C11×#16822
C11×#16802
C11×#16702
C11×#16532
C11×#16402
C11×#16262
C11×#15842
C11×#15792
#1984911