Finite Group Databasebeta

← C11×#19828 #14597021

Subgroups — C11×#19828 #14597021

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C11×SD16C211yesmaximal, characteristic, complemented
2C11×#3362C211yesmaximal, characteristic, complemented
3C11×#3329C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1697C211yesmaximal, characteristic, complemented
7C11×#1684C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1671C211yesmaximal, characteristic, complemented
10C11×#1642C211yesmaximal, characteristic, complemented
11C11×#1634C211yesmaximal, characteristic, complemented
12C11×#1633C211yesmaximal, characteristic, complemented
13C11×#1627C211yesmaximal, characteristic, complemented
14C11×#1583C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#550C2211yescharacteristic
19D4×Q8×C11C2211yescharacteristic
20C11×#498—21no—
21C11×#498C2211yescharacteristic
22C11×#494C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#486—21no—
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#485—21no—
29C11×#482—21no—
30C11×#477C2211yescharacteristic
31C11×#477C2211yescharacteristic
32C11×#476—21no—
33C11×#476—21no—
34C11×#476C2211yescharacteristic
35C11×#476C2211yescharacteristic
36C11×#475—21no—
37C11×#475C2211yescharacteristic
38C11×#468—21no—
39C11×#466—21no—
40C11×#461C2211yescharacteristic
41C11×#460—21no—
42C11×#460C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#449—21no—
45C11×#448—21no—
46C8×Q8×C11C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C4×C11×SD16—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C11×#436C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#419—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C2×C11×Q16—41no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16D411yescharacteristic
73C2×C11×SD16D411yescharacteristic
74C2×C11×D8—21no—
75C2×C11×M16—21no—
76C22×C8×C11—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8—21no—
80C11×C4⋊Q8—41no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127—21no—
85C11×#127C2311yescharacteristic
86C11×#124—41no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—41no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C11×#117—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
110C11×#106D411yescharacteristic
111C11×#106D411yescharacteristic
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×#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—41no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19828C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—41no—
152C2×Q8×C11—42no—
153C2×Q8×C11—81no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C11×Q16—82no—
169C11×SD16—22no—
170C11×SD16—22no—
171C11×SD16—42no—
172C11×SD16—81no—
173C11×D8—81no—
174C11×M16—81no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—81no—
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—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—41no—
209C42×C11—41no—
210C42×C11C2411yescharacteristic
211Q8×SD16C2×C1111yescharacteristic, complemented
212#3362C2×C1111yescharacteristic, complemented
213#3329C2×C1111yescharacteristic, complemented
214#3305C2×C1111yescharacteristic
215#1720C2×C1111yescharacteristic, complemented
216#1697C2×C1111yescharacteristic, complemented
217#1684C2×C1111yescharacteristic, complemented
218#1678C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1642C2×C1111yescharacteristic, complemented
221#1634C2×C1111yescharacteristic, complemented
222#1633C2×C1111yescharacteristic, complemented
223#1627C2×C1111yescharacteristic, complemented
224#1583C2×C1111yescharacteristic, complemented
225SD16⋊C8C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—41no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—82no—
234Q8×C11—81no—
235Q8×C11—81no—
236Q8×C11—161no—
237Q8×C11#13512yes—
238Q8×C11#13712yes—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—82no—
248D4×C11—81no—
249D4×C11—161no—
250D4×C11—161no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—82no—
265C2×C4×C11—82no—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278Q82C22×C1111yescharacteristic
279#555C22×C1111yescharacteristic
280#550C22×C1111yescharacteristic
281D4×Q8C22×C1111yescharacteristic
282#498—21no—
283#498C22×C1111yescharacteristic
284#494C22×C1111yescharacteristic
285#487C22×C1111yescharacteristic
286#486—21no—
287#486C22×C1111yescharacteristic
288#486C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#485—21no—
291#482—21no—
292#477C22×C1111yescharacteristic
293#477C22×C1111yescharacteristic
294#476—21no—
295#476—21no—
296#476C22×C1111yescharacteristic
297#476C22×C1111yescharacteristic
298#475—21no—
299#475C22×C1111yescharacteristic
300#468—21no—
301#466—21no—
302#461C22×C1111yescharacteristic
303#460—21no—
304#460C22×C1111yescharacteristic
305#459C22×C1111yescharacteristic
306#449—21no—
307#448—21no—
308C8×Q8C22×C1111yescharacteristic
309C8×Q8C22×C1111yescharacteristic
310C4×SD16—21no—
311C4×SD16—21no—
312C4×SD16C22×C1111yescharacteristic
313C4×SD16C22×C1111yescharacteristic
314#436C22×C1111yescharacteristic
315C8×D4C22×C1111yescharacteristic
316#419—21no—
317#416—21no—
318#335C22×C1111yescharacteristic
319#334C22×C1111yescharacteristic
320#333C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#331C22×C1111yescharacteristic
324Q8⋊C8C22×C1111yescharacteristic
325Q8⋊C8C22×C1111yescharacteristic
326D4⋊C8C22×C1111yescharacteristic
327D4⋊C8C22×C1111yescharacteristic
328#322C22×C1111yescharacteristic
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11D4211yescharacteristic
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×#13511yescharacteristic
350C4×C11C2×#13711yescharacteristic
351C4×C11#57711yescharacteristic
352C4×C11#57711yescharacteristic
353C2×#41—21no—
354C22×Q8—21no—
355C2×Q16—41no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16D4×C1111yescharacteristic
359C2×SD16D4×C1111yescharacteristic
360C2×D8—21no—
361C2×M16—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—41no—
367C4⋊Q8C23×C1111yescharacteristic
368C4⋊Q8C23×C1111yescharacteristic
369C4⋊Q8C23×C1111yescharacteristic
370#127—21no—
371#127C23×C1111yescharacteristic
372#124—41no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375#121—21no—
376#121—21no—
377#121—21no—
378#121—41no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C1111yescharacteristic
382C4×Q8C23×C1111yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C1111yescharacteristic
386C4×D4C23×C1111yescharacteristic
387#117—21no—
388#117—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106D4×C1111yescharacteristic
397#106D4×C1111yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C1111yescharacteristic
401C4⋊C8C23×C1111yescharacteristic
402C4⋊C8C23×C1111yescharacteristic
403C4⋊C8C23×C1111yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103D4×C1111yescharacteristic
411#103D4×C1111yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—41no—
421#102D4×C1111yescharacteristic
422#102D4×C1111yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C1111yescharacteristic
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C2×C11—81no—
431C2×C11—81no—
432C2×C11—161no—
433C2×C11#326611yescharacteristic
434C2×C11#328211yescharacteristic
435C2×C11#328811yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C1111yescharacteristic
446C2×Q8C2×D4×C1111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C1111yescharacteristic
454C2×D4C2×D4×C1111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—82no—
460SD16—22no—
461SD16—22no—
462SD16—42no—
463SD16—81no—
464D8—81no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8C2×D4×C1111yescharacteristic
473C2×C8C2×D4×C1111yescharacteristic
474C2×C8C2×D4×C1111yescharacteristic
475C2×C8C2×D4×C1111yescharacteristic
476C4⋊C4—21no—
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⋊C4C2×D4×C1111yescharacteristic
488C4⋊C4C2×D4×C1111yescharacteristic
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C24×C1111yescharacteristic
502C11#1982811yescharacteristic, direct product factor, Sylow
503C23—21no—
504C23—21no—
505C23—41no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—82no—
511Q8—81no—
512Q8—81no—
513Q8—161no—
514Q8C11×#13512yes—
515Q8C11×#13712yes—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—82no—
525D4—81no—
526D4—161no—
527D4—161no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C11×H(5,𝔽2)11yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22D42×C1111yescharacteristic
565C4—22no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×C11×#13511yescharacteristic
576C4C2×C11×#13711yescharacteristic
577C4C11×#57711yescharacteristic
578C4C11×#57711yescharacteristic
579C2—81no—
580C2—81no—
581C2—161no—
582C2C11×#326611yescharacteristic
583C2C11×#328211yescharacteristic
584C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3305C2
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. Q8×C11×SD16C2semidirect
2. C11×#3362C2semidirect
3. C11×#3329C2semidirect
5. C11×#1720C2semidirect
6. C11×#1697C2semidirect
7. C11×#1684C2semidirect
8. C11×#1678C2semidirect
9. C11×#1671C2semidirect
10. C11×#1642C2semidirect
11. C11×#1634C2semidirect
12. C11×#1633C2semidirect
13. C11×#1627C2semidirect
14. C11×#1583C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19828C11direct (N × H)
211. Q8×SD16C2×C11semidirect
212. #3362C2×C11semidirect
213. #3329C2×C11semidirect
215. #1720C2×C11semidirect
216. #1697C2×C11semidirect
217. #1684C2×C11semidirect
218. #1678C2×C11semidirect
219. #1671C2×C11semidirect
220. #1642C2×C11semidirect
221. #1634C2×C11semidirect
222. #1633C2×C11semidirect
223. #1627C2×C11semidirect
224. #1583C2×C11semidirect
225. SD16⋊C8C2×C11semidirect
502. C11#19828direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×C11×SD162
C11×#33622
C11×#33292
C11×#33052
C11×#17202
C11×#16972
C11×#16842
C11×#16782
C11×#16712
C11×#16422
C11×#16342
C11×#16332
C11×#16272
C11×#15832
C11×SD16⋊C82
#1982811