Finite Group Databasebeta

← C11×#19873 #14597066

Subgroups — C11×#19873 #14597066

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3400C211yesmaximal, characteristic
2C11×#3395C211yesmaximal, characteristic, complemented
3C11×#3383C211yesmaximal, characteristic, complemented
4C11×#3365C211yesmaximal, characteristic
5C11×#1722C211yesmaximal, characteristic
6C11×#1690C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic
8C11×#1674C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic
10C11×#1648C211yesmaximal, characteristic, complemented
11C11×#1648C211yesmaximal, 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×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#499—21no—
23C11×#497—21no—
24C11×#494—21no—
25C11×#494C2211yescharacteristic
26C11×#492C2211yescharacteristic
27C11×#488—21no—
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#479—21no—
31C11×#479—21no—
32C11×#478—21no—
33C11×#475C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#475C2211yescharacteristic
36C11×#464—21no—
37C11×#464—21no—
38C11×#462—21no—
39C11×#462—21no—
40C11×#462C2211yescharacteristic
41C11×#462C2211yescharacteristic
42C11×#462C2211yescharacteristic
43C11×#461—21no—
44C11×#460C2211yescharacteristic
45C11×#460C2211yescharacteristic
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#440—21no—
51C4×C11×Q16—21no—
52C4×C11×Q16—21no—
53C4×C11×Q16C2211yescharacteristic
54C4×C11×Q16C2211yescharacteristic
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—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127C2311yescharacteristic
85C11×#125—21no—
86C11×#125—21no—
87C11×#125—21no—
88C11×#125—41no—
89C11×#125—41no—
90C11×#125—41no—
91C11×#124—21no—
92C11×#124—21no—
93C11×#123—41no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11C2311yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107—41no—
109C11×#107D411yescharacteristic
110C11×#107D411yescharacteristic
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8—21no—
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×#103—21no—
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#103D411yescharacteristic
129C11×#103D411yescharacteristic
130C11×#103D411yescharacteristic
131C11×#103D411yescharacteristic
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#19873C1111yesmaximal, 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—22no—
158C11×Q16—42no—
159C11×Q16—81no—
160C11×Q16—81no—
161C11×Q16—81no—
162C11×Q16—81no—
163C11×SD16—42no—
164C11×SD16—42no—
165C11×SD16—81no—
166C11×SD16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
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—21no—
185C11×C4⋊C4—21no—
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⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—41no—
207C42×C11—41no—
208C42×C11—41no—
209C42×C11C2411yescharacteristic
210#3400C2×C1111yescharacteristic
211#3395C2×C1111yescharacteristic, complemented
212#3383C2×C1111yescharacteristic, complemented
213#3365C2×C1111yescharacteristic
214#1722C2×C1111yescharacteristic
215#1690C2×C1111yescharacteristic, complemented
216#1682C2×C1111yescharacteristic
217#1674C2×C1111yescharacteristic, complemented
218#1666C2×C1111yescharacteristic
219#1648C2×C1111yescharacteristic, complemented
220#1648C2×C1111yescharacteristic, complemented
221#1640C2×C1111yescharacteristic
222#1626C2×C1111yescharacteristic
223#1584C2×C1111yescharacteristic, complemented
224#1579C2×C1111yescharacteristic, complemented
225C23×C11—41no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11#13712yes—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—81no—
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—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—161no—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11#13512yes—
269#559C22×C1111yescharacteristic
270#557C22×C1111yescharacteristic
271#557C22×C1111yescharacteristic
272#557C22×C1111yescharacteristic
273#500C22×C1111yescharacteristic
274#500C22×C1111yescharacteristic
275#499—21no—
276#497—21no—
277#494—21no—
278#494C22×C1111yescharacteristic
279#492C22×C1111yescharacteristic
280#488—21no—
281#486C22×C1111yescharacteristic
282#486C22×C1111yescharacteristic
283#479—21no—
284#479—21no—
285#478—21no—
286#475C22×C1111yescharacteristic
287#475C22×C1111yescharacteristic
288#475C22×C1111yescharacteristic
289#464—21no—
290#464—21no—
291#462—21no—
292#462—21no—
293#462C22×C1111yescharacteristic
294#462C22×C1111yescharacteristic
295#462C22×C1111yescharacteristic
296#461—21no—
297#460C22×C1111yescharacteristic
298#460C22×C1111yescharacteristic
299#446C22×C1111yescharacteristic
300C8×Q8C22×C1111yescharacteristic
301C8×Q8C22×C1111yescharacteristic
302C8×Q8C22×C1111yescharacteristic
303#440—21no—
304C4×Q16—21no—
305C4×Q16—21no—
306C4×Q16C22×C1111yescharacteristic
307C4×Q16C22×C1111yescharacteristic
308C4×SD16—21no—
309#335C22×C1111yescharacteristic
310#334C22×C1111yescharacteristic
311#332C22×C1111yescharacteristic
312#332C22×C1111yescharacteristic
313#332C22×C1111yescharacteristic
314#331C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316Q8⋊C8C22×C1111yescharacteristic
317Q8⋊C8C22×C1111yescharacteristic
318Q8⋊C8C22×C1111yescharacteristic
319#322C22×C1111yescharacteristic
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11D4211yescharacteristic
324C4×C11—22no—
325C4×C11—21no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#13511yescharacteristic
337C4×C11C2×#13711yescharacteristic
338C4×C11#57611yescharacteristic
339C4×C11#57811yescharacteristic
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16D4×C1111yescharacteristic
346C2×Q16D4×C1111yescharacteristic
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C1111yescharacteristic
355C4⋊Q8C23×C1111yescharacteristic
356C4⋊Q8C23×C1111yescharacteristic
357#127C23×C1111yescharacteristic
358#125—21no—
359#125—21no—
360#125—21no—
361#125—41no—
362#125—41no—
363#125—41no—
364#124—21no—
365#124—21no—
366#123—41no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C1111yescharacteristic
374C4×Q8C23×C1111yescharacteristic
375C4×Q8C23×C1111yescharacteristic
376C4×Q8C23×C1111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379#107—21no—
380#107—21no—
381#107—41no—
382#107D4×C1111yescharacteristic
383#107D4×C1111yescharacteristic
384#106—21no—
385#106—21no—
386#106—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103D4×C1111yescharacteristic
402#103D4×C1111yescharacteristic
403#103D4×C1111yescharacteristic
404#103D4×C1111yescharacteristic
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—41no—
410#97—21no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C1111yescharacteristic
415C4×C8C23×C1111yescharacteristic
416C4×C8C23×C1111yescharacteristic
417C2×C11—161no—
418C2×C11#327011yescharacteristic
419C2×C11#328711yescharacteristic
420C2×C11#328911yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D4×C1111yescharacteristic
425C2×Q8C2×D4×C1111yescharacteristic
426C2×Q8C2×D4×C1111yescharacteristic
427C2×Q8C2×D4×C1111yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C22×C4—41no—
432Q16—22no—
433Q16—22no—
434Q16—42no—
435Q16—81no—
436Q16—81no—
437Q16—81no—
438Q16—81no—
439SD16—42no—
440SD16—42no—
441SD16—81no—
442SD16—81no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8C2×D4×C1111yescharacteristic
449C2×C8C2×D4×C1111yescharacteristic
450C2×C8C2×D4×C1111yescharacteristic
451C2×C8C2×D4×C1111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C1111yescharacteristic
472C4⋊C4C2×D4×C1111yescharacteristic
473C4⋊C4C2×D4×C1111yescharacteristic
474C4⋊C4C2×D4×C1111yescharacteristic
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C1111yescharacteristic
486C11#1987311yescharacteristic, direct product factor, Sylow
487C23—41no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8C11×#13712yes—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—161no—
519C2×C4C22×D4×C1111yescharacteristic
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C11×H(5,𝔽2)11yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8C11×#13512yes—
531C22—81no—
532C22—81no—
533C22—81no—
534C22D42×C1111yescharacteristic
535C4—22no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4C2×C11×#13511yescharacteristic
548C4C2×C11×#13711yescharacteristic
549C4C11×#57611yescharacteristic
550C4C11×#57811yescharacteristic
551C2—161no—
552C2C11×#327011yescharacteristic
553C2C11×#328711yescharacteristic
554C2C11×#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
2. C11×#3395C2semidirect
3. C11×#3383C2semidirect
6. C11×#1690C2semidirect
8. C11×#1674C2semidirect
10. C11×#1648C2semidirect
11. C11×#1648C2semidirect
14. C11×#1584C2semidirect
15. C11×#1579C2semidirect
144. #19873C11direct (N × H)
211. #3395C2×C11semidirect
212. #3383C2×C11semidirect
215. #1690C2×C11semidirect
217. #1674C2×C11semidirect
219. #1648C2×C11semidirect
220. #1648C2×C11semidirect
223. #1584C2×C11semidirect
224. #1579C2×C11semidirect
486. C11#19873direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34002
C11×#33952
C11×#33832
C11×#33652
C11×#17222
C11×#16902
C11×#16822
C11×#16742
C11×#16662
C11×#16482
C11×#16402
C11×#16262
C11×#15842
C11×#15792
#1987311