Finite Group Databasebeta

← C11×#19870 #14597063

Subgroups — C11×#19870 #14597063

Order 2816.

604 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×#3397C211yesmaximal, characteristic
2C11×#3393C211yesmaximal, characteristic, complemented
3C11×#3342C211yesmaximal, characteristic, complemented
4C11×#3304C211yesmaximal, characteristic, complemented
5C11×#1722C211yesmaximal, characteristic, complemented
6C11×#1690C211yesmaximal, characteristic, complemented
7C11×#1681C211yesmaximal, characteristic, complemented
8C11×#1673C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic, complemented
10C11×#1650C211yesmaximal, characteristic, complemented
11C11×#1650C211yesmaximal, characteristic, complemented
12C11×#1642C211yesmaximal, characteristic, complemented
13C11×#1628C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#556C2211yescharacteristic
18C11×#556C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#496—21no—
23C11×#495—21no—
24C11×#494C2211yescharacteristic
25C11×#492C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#485—21no—
29C11×#485—21no—
30C11×#482—21no—
31C11×#475C2211yescharacteristic
32C11×#475C2211yescharacteristic
33C11×#475C2211yescharacteristic
34C11×#467—21no—
35C11×#465—21no—
36C11×#464—21no—
37C11×#464—21no—
38C11×#463—21no—
39C11×#461C2211yescharacteristic
40C11×#461C2211yescharacteristic
41C11×#461C2211yescharacteristic
42C11×#460—21no—
43C11×#460C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#440—21no—
49C4×C11×Q16—21no—
50C4×C11×Q16C2211yescharacteristic
51C4×C11×D8C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#427—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#332C2211yescharacteristic
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—21no—
70C2×C11×Q16D411yescharacteristic
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×D8—21no—
78C2×C11×D8D411yescharacteristic
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127—21no—
85C11×#127C2311yescharacteristic
86C11×#126—41no—
87C11×#126—41no—
88C11×#126—41no—
89C11×#124—21no—
90C11×#124—21no—
91C11×#124—21no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×#121—21no—
96C11×#121—41no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11C2311yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×D4×C11—21no—
103C4×D4×C11C2311yescharacteristic
104C4×D4×C11C2311yescharacteristic
105C11×#117—21no—
106C11×#117—21no—
107C11×#117—21no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—41no—
111C11×#107D411yescharacteristic
112C11×#107D411yescharacteristic
113C11×#106—21no—
114C11×#106—21no—
115C11×#106—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×#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#19870C1111yesmaximal, 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×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C11×Q16—41no—
163C11×Q16—42no—
164C11×Q16—81no—
165C11×SD16—42no—
166C11×SD16—81no—
167C11×SD16—81no—
168C11×SD16—81no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×D8—22no—
172C11×D8—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—42no—
179C2×C8×C11—81no—
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
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—21no—
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—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—41no—
211C42×C11—41no—
212C42×C11—41no—
213C42×C11C2411yescharacteristic
214#3397C2×C1111yescharacteristic
215#3393C2×C1111yescharacteristic, complemented
216#3342C2×C1111yescharacteristic, complemented
217#3304C2×C1111yescharacteristic, complemented
218#1722C2×C1111yescharacteristic, complemented
219#1690C2×C1111yescharacteristic, complemented
220#1681C2×C1111yescharacteristic, complemented
221#1673C2×C1111yescharacteristic, complemented
222#1666C2×C1111yescharacteristic, complemented
223#1650C2×C1111yescharacteristic, complemented
224#1650C2×C1111yescharacteristic, complemented
225#1642C2×C1111yescharacteristic, complemented
226#1628C2×C1111yescharacteristic, complemented
227#1584C2×C1111yescharacteristic, complemented
228#1580C2×C1111yescharacteristic, complemented
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—41no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—81no—
251D4×C11—82no—
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—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—82no—
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—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11#13512yes—
279#556C22×C1111yescharacteristic
280#556C22×C1111yescharacteristic
281#556C22×C1111yescharacteristic
282#550C22×C1111yescharacteristic
283#500C22×C1111yescharacteristic
284#500C22×C1111yescharacteristic
285#496—21no—
286#495—21no—
287#494C22×C1111yescharacteristic
288#492C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#486C22×C1111yescharacteristic
291#485—21no—
292#485—21no—
293#482—21no—
294#475C22×C1111yescharacteristic
295#475C22×C1111yescharacteristic
296#475C22×C1111yescharacteristic
297#467—21no—
298#465—21no—
299#464—21no—
300#464—21no—
301#463—21no—
302#461C22×C1111yescharacteristic
303#461C22×C1111yescharacteristic
304#461C22×C1111yescharacteristic
305#460—21no—
306#460C22×C1111yescharacteristic
307#459C22×C1111yescharacteristic
308#452—21no—
309#446C22×C1111yescharacteristic
310C8×Q8C22×C1111yescharacteristic
311#440—21no—
312C4×Q16—21no—
313C4×Q16C22×C1111yescharacteristic
314C4×D8C22×C1111yescharacteristic
315C8×D4C22×C1111yescharacteristic
316C8×D4C22×C1111yescharacteristic
317#427—21no—
318#416—21no—
319#335C22×C1111yescharacteristic
320#334C22×C1111yescharacteristic
321#332C22×C1111yescharacteristic
322#332C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325Q8⋊C8C22×C1111yescharacteristic
326Q8⋊C8C22×C1111yescharacteristic
327D4⋊C8C22×C1111yescharacteristic
328D4⋊C8C22×C1111yescharacteristic
329#322C22×C1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11D4211yescharacteristic
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×#13511yescharacteristic
351C4×C11#57511yescharacteristic
352C4×C11#57611yescharacteristic
353C4×C11#57711yescharacteristic
354C2×#41—21no—
355C2×Q16—21no—
356C2×Q16—21no—
357C2×Q16D4×C1111yescharacteristic
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×D8—21no—
365C2×D8D4×C1111yescharacteristic
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C1111yescharacteristic
369C4⋊Q8C23×C1111yescharacteristic
370C4⋊Q8C23×C1111yescharacteristic
371#127—21no—
372#127C23×C1111yescharacteristic
373#126—41no—
374#126—41no—
375#126—41no—
376#124—21no—
377#124—21no—
378#124—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C23×C1111yescharacteristic
388C4×Q8C23×C1111yescharacteristic
389C4×D4—21no—
390C4×D4C23×C1111yescharacteristic
391C4×D4C23×C1111yescharacteristic
392#117—21no—
393#117—21no—
394#117—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#107D4×C1111yescharacteristic
399#107D4×C1111yescharacteristic
400#106—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C1111yescharacteristic
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103D4×C1111yescharacteristic
416#103D4×C1111yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C1111yescharacteristic
423#102D4×C1111yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427C4×C8—21no—
428C4×C8C23×C1111yescharacteristic
429C4×C8C23×C1111yescharacteristic
430C4×C8C23×C1111yescharacteristic
431C2×C11—81no—
432C2×C11—81no—
433C2×C11—161no—
434C2×C11#326711yescharacteristic
435C2×C11#328711yescharacteristic
436C2×C11#328911yescharacteristic
437#41—42no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C1111yescharacteristic
443C2×Q8C2×D4×C1111yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4C2×D4×C1111yescharacteristic
450C2×D4C2×D4×C1111yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454Q16—41no—
455Q16—42no—
456Q16—81no—
457SD16—42no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461SD16—81no—
462SD16—81no—
463D8—22no—
464D8—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—42no—
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—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42—41no—
504C42—41no—
505C42C24×C1111yescharacteristic
506C11#1987011yescharacteristic, direct product factor, Sylow
507C23—21no—
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1111yescharacteristic
547C2×C4C11×H(5,𝔽2)11yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8C11×#13512yes—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C1111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×C11×#13511yescharacteristic
578C4C11×#57511yescharacteristic
579C4C11×#57611yescharacteristic
580C4C11×#57711yescharacteristic
581C2—81no—
582C2—81no—
583C2—161no—
584C2C11×#326711yescharacteristic
585C2C11×#328711yescharacteristic
586C2C11×#328911yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3397C2
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×#3393C2semidirect
3. C11×#3342C2semidirect
4. C11×#3304C2semidirect
5. C11×#1722C2semidirect
6. C11×#1690C2semidirect
7. C11×#1681C2semidirect
8. C11×#1673C2semidirect
9. C11×#1666C2semidirect
10. C11×#1650C2semidirect
11. C11×#1650C2semidirect
12. C11×#1642C2semidirect
13. C11×#1628C2semidirect
14. C11×#1584C2semidirect
15. C11×#1580C2semidirect
144. #19870C11direct (N × H)
215. #3393C2×C11semidirect
216. #3342C2×C11semidirect
217. #3304C2×C11semidirect
218. #1722C2×C11semidirect
219. #1690C2×C11semidirect
220. #1681C2×C11semidirect
221. #1673C2×C11semidirect
222. #1666C2×C11semidirect
223. #1650C2×C11semidirect
224. #1650C2×C11semidirect
225. #1642C2×C11semidirect
226. #1628C2×C11semidirect
227. #1584C2×C11semidirect
228. #1580C2×C11semidirect
506. C11#19870direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33972
C11×#33932
C11×#33422
C11×#33042
C11×#17222
C11×#16902
C11×#16812
C11×#16732
C11×#16662
C11×#16502
C11×#16422
C11×#16282
C11×#15842
C11×#15802
#1987011