Finite Group Databasebeta

← C11×#19869 #14597062

Subgroups — C11×#19869 #14597062

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3398C211yesmaximal, characteristic, complemented
2C11×#3392C211yesmaximal, characteristic
3C11×#3383C211yesmaximal, characteristic, complemented
4C11×#3304C211yesmaximal, characteristic
5C11×#1722C211yesmaximal, characteristic, complemented
6C11×#1686C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic, complemented
8C11×#1673C211yesmaximal, characteristic, complemented
9C11×#1670C211yesmaximal, characteristic, complemented
10C11×#1650C211yesmaximal, characteristic, complemented
11C11×#1648C211yesmaximal, characteristic, complemented
12C11×#1642C211yesmaximal, characteristic
13C11×#1626C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic
17C11×#557C2211yescharacteristic
18C11×#556C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#499—21no—
23C11×#497—21no—
24C11×#494C2211yescharacteristic
25C11×#492—21no—
26C11×#492C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#482—21no—
30C11×#479—21no—
31C11×#479—21no—
32C11×#475C2211yescharacteristic
33C11×#475C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#465—21no—
36C11×#464—21no—
37C11×#462—21no—
38C11×#462C2211yescharacteristic
39C11×#461—21no—
40C11×#461C2211yescharacteristic
41C11×#461C2211yescharacteristic
42C11×#460—21no—
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C11×#441—21no—
50C4×C11×Q16—21no—
51C4×C11×Q16C2211yescharacteristic
52C4×C11×SD16—21no—
53C4×C11×SD16C2211yescharacteristic
54C8×D4×C11C2211yescharacteristic
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—21no—
71C2×C11×Q16D411yescharacteristic
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×SD16D411yescharacteristic
79C22×C8×C11—21no—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×#127—21no—
86C11×#127C2311yescharacteristic
87C11×#126—41no—
88C11×#125—21no—
89C11×#125—21no—
90C11×#125—41no—
91C11×#125—41no—
92C11×#124—21no—
93C11×C22⋊Q8—21no—
94C11×#121—21no—
95C11×#121—41no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11C2311yescharacteristic
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×D4×C11—21no—
105C4×D4×C11C2311yescharacteristic
106C11×#117—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107—41no—
110C11×#107D411yescharacteristic
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×#106D411yescharacteristic
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×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—41no—
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19869C1111yesmaximal, 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×C11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C11×Q16—22no—
162C11×Q16—42no—
163C11×Q16—81no—
164C11×Q16—81no—
165C11×SD16—22no—
166C11×SD16—42no—
167C11×SD16—81no—
168C11×SD16—81no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×SD16—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—81no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
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—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4—41no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C22⋊C4—21no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—41no—
210C42×C11—41no—
211C42×C11—41no—
212C42×C11C2411yescharacteristic
213#3398C2×C1111yescharacteristic, complemented
214#3392C2×C1111yescharacteristic
215#3383C2×C1111yescharacteristic, complemented
216#3304C2×C1111yescharacteristic
217#1722C2×C1111yescharacteristic, complemented
218#1686C2×C1111yescharacteristic, complemented
219#1682C2×C1111yescharacteristic, complemented
220#1673C2×C1111yescharacteristic, complemented
221#1670C2×C1111yescharacteristic, complemented
222#1650C2×C1111yescharacteristic, complemented
223#1648C2×C1111yescharacteristic, complemented
224#1642C2×C1111yescharacteristic
225#1626C2×C1111yescharacteristic, complemented
226#1584C2×C1111yescharacteristic, complemented
227SD16⋊C8C2×C1111yescharacteristic, complemented
228C23×C11—21no—
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—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11#13712yes—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—82no—
249D4×C11—81no—
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—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—82no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11#13512yes—
276#557C22×C1111yescharacteristic
277#557C22×C1111yescharacteristic
278#556C22×C1111yescharacteristic
279#550C22×C1111yescharacteristic
280#500C22×C1111yescharacteristic
281#500C22×C1111yescharacteristic
282#499—21no—
283#497—21no—
284#494C22×C1111yescharacteristic
285#492—21no—
286#492C22×C1111yescharacteristic
287#486C22×C1111yescharacteristic
288#486C22×C1111yescharacteristic
289#482—21no—
290#479—21no—
291#479—21no—
292#475C22×C1111yescharacteristic
293#475C22×C1111yescharacteristic
294#475C22×C1111yescharacteristic
295#465—21no—
296#464—21no—
297#462—21no—
298#462C22×C1111yescharacteristic
299#461—21no—
300#461C22×C1111yescharacteristic
301#461C22×C1111yescharacteristic
302#460—21no—
303#460C22×C1111yescharacteristic
304#460C22×C1111yescharacteristic
305#452—21no—
306#446C22×C1111yescharacteristic
307C8×Q8C22×C1111yescharacteristic
308C8×Q8C22×C1111yescharacteristic
309#441—21no—
310C4×Q16—21no—
311C4×Q16C22×C1111yescharacteristic
312C4×SD16—21no—
313C4×SD16C22×C1111yescharacteristic
314C8×D4C22×C1111yescharacteristic
315#416—21no—
316#335C22×C1111yescharacteristic
317#335C22×C1111yescharacteristic
318#332C22×C1111yescharacteristic
319#332C22×C1111yescharacteristic
320#332C22×C1111yescharacteristic
321#331C22×C1111yescharacteristic
322Q8⋊C8C22×C1111yescharacteristic
323Q8⋊C8C22×C1111yescharacteristic
324Q8⋊C8C22×C1111yescharacteristic
325D4⋊C8C22×C1111yescharacteristic
326#322C22×C1111yescharacteristic
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11D4211yescharacteristic
334C4×C11—22no—
335C4×C11—21no—
336C4×C11—41no—
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×C11C2×#13711yescharacteristic
347C4×C11#57611yescharacteristic
348C4×C11#57711yescharacteristic
349C2×#41—21no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16D4×C1111yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16D4×C1111yescharacteristic
361C22×C8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8C23×C1111yescharacteristic
365C4⋊Q8C23×C1111yescharacteristic
366C4⋊Q8C23×C1111yescharacteristic
367#127—21no—
368#127C23×C1111yescharacteristic
369#126—41no—
370#125—21no—
371#125—21no—
372#125—41no—
373#125—41no—
374#124—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—41no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C23×C1111yescharacteristic
384C4×Q8C23×C1111yescharacteristic
385C4×Q8C23×C1111yescharacteristic
386C4×D4—21no—
387C4×D4C23×C1111yescharacteristic
388#117—21no—
389#107—21no—
390#107—21no—
391#107—41no—
392#107D4×C1111yescharacteristic
393#106—21no—
394#106—21no—
395#106—21no—
396#106D4×C1111yescharacteristic
397C4⋊C8—21no—
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#103D4×C1111yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—41no—
418#102D4×C1111yescharacteristic
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8C23×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C2×C11—81no—
427C2×C11—161no—
428C2×C11#326611yescharacteristic
429C2×C11#328711yescharacteristic
430C2×C11#328911yescharacteristic
431#41—42no—
432#41—81no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×D4×C1111yescharacteristic
437C2×Q8C2×D4×C1111yescharacteristic
438C2×Q8C2×D4×C1111yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4C2×D4×C1111yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447Q16—22no—
448Q16—42no—
449Q16—81no—
450Q16—81no—
451SD16—22no—
452SD16—42no—
453SD16—81no—
454SD16—81no—
455SD16—81no—
456SD16—81no—
457SD16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
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—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C1111yescharacteristic
485C4⋊C4C2×D4×C1111yescharacteristic
486C4⋊C4C2×D4×C1111yescharacteristic
487C4⋊C4C2×D4×C1111yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42C24×C1111yescharacteristic
499C11#1986911yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—41no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8C11×#13712yes—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—81no—
522D4—161no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4C22×D4×C1111yescharacteristic
537C2×C4C22×D4×C1111yescharacteristic
538C2×C4C11×H(5,𝔽2)11yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8C11×#13512yes—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22D42×C1111yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×C11×#13511yescharacteristic
567C4C2×C11×#13711yescharacteristic
568C4C11×#57611yescharacteristic
569C4C11×#57711yescharacteristic
570C2—81no—
571C2—161no—
572C2C11×#326611yescharacteristic
573C2C11×#328711yescharacteristic
574C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#550C22
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×#3398C2semidirect
3. C11×#3383C2semidirect
5. C11×#1722C2semidirect
6. C11×#1686C2semidirect
7. C11×#1682C2semidirect
8. C11×#1673C2semidirect
9. C11×#1670C2semidirect
10. C11×#1650C2semidirect
11. C11×#1648C2semidirect
13. C11×#1626C2semidirect
14. C11×#1584C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19869C11direct (N × H)
213. #3398C2×C11semidirect
215. #3383C2×C11semidirect
217. #1722C2×C11semidirect
218. #1686C2×C11semidirect
219. #1682C2×C11semidirect
220. #1673C2×C11semidirect
221. #1670C2×C11semidirect
222. #1650C2×C11semidirect
223. #1648C2×C11semidirect
225. #1626C2×C11semidirect
226. #1584C2×C11semidirect
227. SD16⋊C8C2×C11semidirect
499. C11#19869direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33982
C11×#33922
C11×#33832
C11×#33042
C11×#17222
C11×#16862
C11×#16822
C11×#16732
C11×#16702
C11×#16502
C11×#16482
C11×#16422
C11×#16262
C11×#15842
C11×SD16⋊C82
#1986911