Finite Group Databasebeta

← C11×#19800 #14596993

Subgroups — C11×#19800 #14596993

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3369C211yesmaximal, characteristic, complemented
2C11×#3362C211yesmaximal, characteristic, complemented
3C11×#3340C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1698C211yesmaximal, characteristic, complemented
7C11×#1683C211yesmaximal, characteristic, complemented
8C11×#1677C211yesmaximal, characteristic, complemented
9C11×#1672C211yesmaximal, characteristic, complemented
10C11×#1641C211yesmaximal, characteristic, complemented
11C11×#1634C211yesmaximal, characteristic, complemented
12C11×#1633C211yesmaximal, characteristic, complemented
13C11×#1628C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#556C2211yescharacteristic
18C11×#555C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#494C2211yescharacteristic
22C11×#489—21no—
23C11×#487C2211yescharacteristic
24C11×#486—21no—
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#485—21no—
29C11×#482—21no—
30C11×#482—21no—
31C11×#477C2211yescharacteristic
32C11×#477C2211yescharacteristic
33C11×#476—21no—
34C11×#476C2211yescharacteristic
35C11×#476C2211yescharacteristic
36C11×#475—21no—
37C11×#474C2211yescharacteristic
38C11×#466—21no—
39C11×#465—21no—
40C11×#464—21no—
41C11×#462C2211yescharacteristic
42C11×#460—21no—
43C11×#460C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#449—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#441—21no—
49C4×C11×SD16—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#427—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—
68C2×C11×Q16—21no—
69C2×C11×Q16—41no—
70C2×C11×SD16—21no—
71C2×C11×SD16D411yescharacteristic
72C2×C11×SD16D411yescharacteristic
73C2×C11×D8—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—41no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127—21no—
83C11×#127C2311yescharacteristic
84C11×#126—41no—
85C11×#124—21no—
86C11×#124—41no—
87C11×C22⋊Q8—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—41no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2311yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C11×#117—21no—
102C11×#117—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—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×#103D411yescharacteristic
124C11×#103D411yescharacteristic
125C11×#102—21no—
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—
139C11×#97—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19800C1111yesmaximal, 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×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11C2×D411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—41no—
164C11×Q16—42no—
165C11×Q16—82no—
166C11×SD16—22no—
167C11×SD16—41no—
168C11×SD16—42no—
169C11×D8—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—42no—
176C2×C8×C11—81no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—41no—
206C42×C11—41no—
207C42×C11—41no—
208C42×C11C2411yescharacteristic
209#3369C2×C1111yescharacteristic, complemented
210#3362C2×C1111yescharacteristic, complemented
211#3340C2×C1111yescharacteristic, complemented
212#3305C2×C1111yescharacteristic
213#1720C2×C1111yescharacteristic, complemented
214#1698C2×C1111yescharacteristic, complemented
215#1683C2×C1111yescharacteristic, complemented
216#1677C2×C1111yescharacteristic, complemented
217#1672C2×C1111yescharacteristic, complemented
218#1641C2×C1111yescharacteristic, complemented
219#1634C2×C1111yescharacteristic, complemented
220#1633C2×C1111yescharacteristic, complemented
221#1628C2×C1111yescharacteristic, complemented
222#1582C2×C1111yescharacteristic, complemented
223SD16⋊C8C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—41no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233Q8×C11—81no—
234Q8×C11—161no—
235Q8×C11#13512yes—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—82no—
245D4×C11—81no—
246D4×C11—161no—
247D4×C11—161no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—82no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274Q82C22×C1111yescharacteristic
275#556C22×C1111yescharacteristic
276#555C22×C1111yescharacteristic
277#550C22×C1111yescharacteristic
278#498C22×C1111yescharacteristic
279#494C22×C1111yescharacteristic
280#489—21no—
281#487C22×C1111yescharacteristic
282#486—21no—
283#486C22×C1111yescharacteristic
284#486C22×C1111yescharacteristic
285#486C22×C1111yescharacteristic
286#485—21no—
287#482—21no—
288#482—21no—
289#477C22×C1111yescharacteristic
290#477C22×C1111yescharacteristic
291#476—21no—
292#476C22×C1111yescharacteristic
293#476C22×C1111yescharacteristic
294#475—21no—
295#474C22×C1111yescharacteristic
296#466—21no—
297#465—21no—
298#464—21no—
299#462C22×C1111yescharacteristic
300#460—21no—
301#460C22×C1111yescharacteristic
302#459C22×C1111yescharacteristic
303#449—21no—
304#446C22×C1111yescharacteristic
305C8×Q8C22×C1111yescharacteristic
306#441—21no—
307C4×SD16—21no—
308C4×SD16C22×C1111yescharacteristic
309C4×SD16C22×C1111yescharacteristic
310C8×D4C22×C1111yescharacteristic
311C8×D4C22×C1111yescharacteristic
312#427—21no—
313#416—21no—
314#335C22×C1111yescharacteristic
315#334C22×C1111yescharacteristic
316#333C22×C1111yescharacteristic
317#333C22×C1111yescharacteristic
318#332C22×C1111yescharacteristic
319#331C22×C1111yescharacteristic
320Q8⋊C8C22×C1111yescharacteristic
321Q8⋊C8C22×C1111yescharacteristic
322D4⋊C8C22×C1111yescharacteristic
323D4⋊C8C22×C1111yescharacteristic
324#322C22×C1111yescharacteristic
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11D4211yescharacteristic
335C4×C11—22no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57811yescharacteristic
349C2×#41—21no—
350C2×Q16—21no—
351C2×Q16—41no—
352C2×SD16—21no—
353C2×SD16D4×C1111yescharacteristic
354C2×SD16D4×C1111yescharacteristic
355C2×D8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—41no—
361C4⋊Q8C23×C1111yescharacteristic
362C4⋊Q8C23×C1111yescharacteristic
363C4⋊Q8C23×C1111yescharacteristic
364#127—21no—
365#127C23×C1111yescharacteristic
366#126—41no—
367#124—21no—
368#124—41no—
369C22⋊Q8—21no—
370#121—21no—
371#121—21no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8C23×C1111yescharacteristic
378C4×Q8C23×C1111yescharacteristic
379C4×D4—21no—
380C4×D4C23×C1111yescharacteristic
381C4×D4C23×C1111yescharacteristic
382#117—21no—
383#117—21no—
384#117—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106D4×C1111yescharacteristic
393#106D4×C1111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399C4⋊C8C23×C1111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103D4×C1111yescharacteristic
406#103D4×C1111yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—41no—
417#102D4×C1111yescharacteristic
418#102D4×C1111yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8C23×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C2×C11—81no—
427C2×C11—81no—
428C2×C11—161no—
429C2×C11#326911yescharacteristic
430C2×C11#328211yescharacteristic
431C2×C11#328811yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—41no—
438C2×Q8C2×D4×C1111yescharacteristic
439C2×Q8C2×D4×C1111yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C2×D4×C1111yescharacteristic
447C2×D4C2×D4×C1111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451Q16—42no—
452Q16—82no—
453SD16—22no—
454SD16—41no—
455SD16—42no—
456D8—81no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—81no—
464C2×C8C2×D4×C1111yescharacteristic
465C2×C8C2×D4×C1111yescharacteristic
466C2×C8C2×D4×C1111yescharacteristic
467C2×C8C2×D4×C1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C1111yescharacteristic
480C4⋊C4C2×D4×C1111yescharacteristic
481C4⋊C4C2×D4×C1111yescharacteristic
482C4⋊C4C2×D4×C1111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42C24×C1111yescharacteristic
496C11#1980011yescharacteristic, direct product factor, Sylow
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—81no—
507Q8—161no—
508Q8C11×#13512yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—41no—
517D4—82no—
518D4—81no—
519D4—161no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C11×H(5,𝔽2)11yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C1111yescharacteristic
557C4—22no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×C11×#13511yescharacteristic
568C4C11×#57511yescharacteristic
569C4C11×#57711yescharacteristic
570C4C11×#57811yescharacteristic
571C2—81no—
572C2—81no—
573C2—161no—
574C2C11×#326911yescharacteristic
575C2C11×#328211yescharacteristic
576C2C11×#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. C11×#3369C2semidirect
2. C11×#3362C2semidirect
3. C11×#3340C2semidirect
5. C11×#1720C2semidirect
6. C11×#1698C2semidirect
7. C11×#1683C2semidirect
8. C11×#1677C2semidirect
9. C11×#1672C2semidirect
10. C11×#1641C2semidirect
11. C11×#1634C2semidirect
12. C11×#1633C2semidirect
13. C11×#1628C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19800C11direct (N × H)
209. #3369C2×C11semidirect
210. #3362C2×C11semidirect
211. #3340C2×C11semidirect
213. #1720C2×C11semidirect
214. #1698C2×C11semidirect
215. #1683C2×C11semidirect
216. #1677C2×C11semidirect
217. #1672C2×C11semidirect
218. #1641C2×C11semidirect
219. #1634C2×C11semidirect
220. #1633C2×C11semidirect
221. #1628C2×C11semidirect
222. #1582C2×C11semidirect
223. SD16⋊C8C2×C11semidirect
496. C11#19800direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33692
C11×#33622
C11×#33402
C11×#33052
C11×#17202
C11×#16982
C11×#16832
C11×#16772
C11×#16722
C11×#16412
C11×#16342
C11×#16332
C11×#16282
C11×#15822
C11×SD16⋊C82
#1980011