Finite Group Databasebeta

← C11×#19833 #14597026

Subgroups — C11×#19833 #14597026

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3392C211yesmaximal, characteristic, complemented
2C11×#3365C211yesmaximal, characteristic, complemented
3C11×#3361C211yesmaximal, characteristic, complemented
4C11×#3333C211yesmaximal, characteristic, complemented
5C11×#1717C211yesmaximal, characteristic, complemented
6C11×#1701C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic, complemented
10C11×#1643C211yesmaximal, characteristic, complemented
11C11×#1636C211yesmaximal, characteristic, complemented
12C11×#1621C211yesmaximal, characteristic
13C11×#1620C211yesmaximal, characteristic, complemented
14C11×#1583C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#557C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#492—21no—
22C11×#492C2211yescharacteristic
23C11×#488—21no—
24C11×#488—21no—
25C11×#487C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#480—21no—
30C11×#478—21no—
31C11×#478—21no—
32C11×#477C2211yescharacteristic
33C11×#477C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#468—21no—
36C11×#464—21no—
37C11×#463—21no—
38C11×#461—21no—
39C11×#461C2211yescharacteristic
40C11×#460—21no—
41C11×#460C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#460C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#452—21no—
46C8×Q8×C11C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C4×C11×Q16C2211yescharacteristic
50C4×C11×SD16—21no—
51C4×C11×SD16—21no—
52C4×C11×SD16C2211yescharacteristic
53C4×C11×D8—21no—
54C11×#436C2211yescharacteristic
55C11×#417—21no—
56C11×#334C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16D411yescharacteristic
76C2×C11×D8—21no—
77C2×C11×D8—41no—
78C2×C11×M16—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127—21no—
83C11×#127C2311yescharacteristic
84C11×#127C2311yescharacteristic
85C11×#125—21no—
86C11×#125—21no—
87C11×#125—41no—
88C11×#124—21no—
89C11×#124—21no—
90C11×#123—41no—
91C11×C22⋊Q8—21no—
92C11×C22⋊Q8—41no—
93C11×#121—21no—
94C11×#121—41no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2311yescharacteristic
98C4×Q8×C11C2311yescharacteristic
99C4×Q8×C11C2311yescharacteristic
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11C2311yescharacteristic
105C2×C11×C4⋊C4—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107D411yescharacteristic
109C11×#106—21no—
110C11×#106D411yescharacteristic
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—41no—
123C11×#103D411yescharacteristic
124C11×#103D411yescharacteristic
125C11×#103D411yescharacteristic
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19833C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×Q8×C11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11C2×D411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C11×Q16—22no—
166C11×SD16—41no—
167C11×SD16—42no—
168C11×SD16—42no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×D8—42no—
174C11×D8—82no—
175C11×M16—81no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—41no—
211C42×C11C2411yescharacteristic
212#3392C2×C1111yescharacteristic, complemented
213#3365C2×C1111yescharacteristic, complemented
214#3361C2×C1111yescharacteristic, complemented
215#3333C2×C1111yescharacteristic, complemented
216#1717C2×C1111yescharacteristic, complemented
217#1701C2×C1111yescharacteristic, complemented
218#1678C2×C1111yescharacteristic, complemented
219#1678C2×C1111yescharacteristic, complemented
220#1666C2×C1111yescharacteristic, complemented
221#1643C2×C1111yescharacteristic, complemented
222#1636C2×C1111yescharacteristic, complemented
223#1621C2×C1111yescharacteristic
224#1620C2×C1111yescharacteristic, complemented
225#1583C2×C1111yescharacteristic, complemented
226#1579C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—41no—
229C23×C11—41no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—81no—
238Q8×C11#13512yes—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—82no—
250D4×C11—81no—
251D4×C11—81no—
252D4×C11—161no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—82no—
265C2×C4×C11—161no—
266C2×C4×C11—161no—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279#559C22×C1111yescharacteristic
280#557C22×C1111yescharacteristic
281#554C22×C1111yescharacteristic
282#550C22×C1111yescharacteristic
283#493C22×C1111yescharacteristic
284#492—21no—
285#492C22×C1111yescharacteristic
286#488—21no—
287#488—21no—
288#487C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#486C22×C1111yescharacteristic
291#486C22×C1111yescharacteristic
292#480—21no—
293#478—21no—
294#478—21no—
295#477C22×C1111yescharacteristic
296#477C22×C1111yescharacteristic
297#475C22×C1111yescharacteristic
298#468—21no—
299#464—21no—
300#463—21no—
301#461—21no—
302#461C22×C1111yescharacteristic
303#460—21no—
304#460C22×C1111yescharacteristic
305#460C22×C1111yescharacteristic
306#460C22×C1111yescharacteristic
307#459C22×C1111yescharacteristic
308#452—21no—
309C8×Q8C22×C1111yescharacteristic
310C8×Q8C22×C1111yescharacteristic
311C8×Q8C22×C1111yescharacteristic
312C4×Q16C22×C1111yescharacteristic
313C4×SD16—21no—
314C4×SD16—21no—
315C4×SD16C22×C1111yescharacteristic
316C4×D8—21no—
317#436C22×C1111yescharacteristic
318#417—21no—
319#334C22×C1111yescharacteristic
320#334C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#331C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325Q8⋊C8C22×C1111yescharacteristic
326Q8⋊C8C22×C1111yescharacteristic
327Q8⋊C8C22×C1111yescharacteristic
328D4⋊C8C22×C1111yescharacteristic
329#322C22×C1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11D4211yescharacteristic
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×#13511yescharacteristic
351C4×C11#57511yescharacteristic
352C4×C11#57711yescharacteristic
353C4×C11#57711yescharacteristic
354C2×#41—21no—
355C2×Q16D4×C1111yescharacteristic
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C1111yescharacteristic
363C2×D8—21no—
364C2×D8—41no—
365C2×M16—21no—
366C4⋊Q8—21no—
367C4⋊Q8C23×C1111yescharacteristic
368C4⋊Q8C23×C1111yescharacteristic
369#127—21no—
370#127C23×C1111yescharacteristic
371#127C23×C1111yescharacteristic
372#125—21no—
373#125—21no—
374#125—41no—
375#124—21no—
376#124—21no—
377#123—41no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380#121—21no—
381#121—41no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C1111yescharacteristic
385C4×Q8C23×C1111yescharacteristic
386C4×Q8C23×C1111yescharacteristic
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C1111yescharacteristic
392C2×C4⋊C4—21no—
393#107—21no—
394#107—21no—
395#107D4×C1111yescharacteristic
396#106—21no—
397#106D4×C1111yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404C4⋊C8C23×C1111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—41no—
410#103D4×C1111yescharacteristic
411#103D4×C1111yescharacteristic
412#103D4×C1111yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C1111yescharacteristic
424C22⋊C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C4×C8C23×C1111yescharacteristic
431C2×C11—81no—
432C2×C11—161no—
433C2×C11—161no—
434C2×C11#327111yescharacteristic
435C2×C11#328211yescharacteristic
436C2×C11#328811yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×D4×C1111yescharacteristic
442C2×Q8C2×D4×C1111yescharacteristic
443C2×Q8C2×D4×C1111yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×D4×C1111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—22no—
458SD16—41no—
459SD16—42no—
460SD16—42no—
461SD16—81no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465D8—42no—
466D8—82no—
467M16—81no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C2×C8C2×D4×C1111yescharacteristic
476C2×C8C2×D4×C1111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C24×C1111yescharacteristic
504C11#1983311yescharacteristic, direct product factor, Sylow
505C23—21no—
506C23—41no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—41no—
514Q8—41no—
515Q8—81no—
516Q8C11×#13512yes—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4—81no—
529D4—81no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—161no—
544C2×C4—161no—
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C11×H(5,𝔽2)11yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C1111yescharacteristic
567C4—22no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4C2×C11×#13511yescharacteristic
578C4C11×#57511yescharacteristic
579C4C11×#57711yescharacteristic
580C4C11×#57711yescharacteristic
581C2—81no—
582C2—161no—
583C2—161no—
584C2C11×#327111yescharacteristic
585C2C11×#328211yescharacteristic
586C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#1621C2
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×#3392C2semidirect
2. C11×#3365C2semidirect
3. C11×#3361C2semidirect
4. C11×#3333C2semidirect
5. C11×#1717C2semidirect
6. C11×#1701C2semidirect
7. C11×#1678C2semidirect
8. C11×#1678C2semidirect
9. C11×#1666C2semidirect
10. C11×#1643C2semidirect
11. C11×#1636C2semidirect
13. C11×#1620C2semidirect
14. C11×#1583C2semidirect
15. C11×#1579C2semidirect
144. #19833C11direct (N × H)
212. #3392C2×C11semidirect
213. #3365C2×C11semidirect
214. #3361C2×C11semidirect
215. #3333C2×C11semidirect
216. #1717C2×C11semidirect
217. #1701C2×C11semidirect
218. #1678C2×C11semidirect
219. #1678C2×C11semidirect
220. #1666C2×C11semidirect
221. #1643C2×C11semidirect
222. #1636C2×C11semidirect
224. #1620C2×C11semidirect
225. #1583C2×C11semidirect
226. #1579C2×C11semidirect
504. C11#19833direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33922
C11×#33652
C11×#33612
C11×#33332
C11×#17172
C11×#17012
C11×#16782
C11×#16662
C11×#16432
C11×#16362
C11×#16212
C11×#16202
C11×#15832
C11×#15792
#1983311