Finite Group Databasebeta

← C11×#19840 #14597033

Subgroups — C11×#19840 #14597033

Order 2816.

600 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×#3366C211yesmaximal, characteristic
2C11×#3360C211yesmaximal, characteristic, complemented
3C11×#3338C211yesmaximal, characteristic, complemented
4C11×#3304C211yesmaximal, characteristic, complemented
5C11×#1719C211yesmaximal, characteristic, complemented
6C11×#1704C211yesmaximal, characteristic, complemented
7C11×#1681C211yesmaximal, characteristic, complemented
8C11×#1678C211yesmaximal, characteristic, complemented
9C11×#1675C211yesmaximal, characteristic, complemented
10C11×#1643C211yesmaximal, characteristic, complemented
11C11×#1638C211yesmaximal, characteristic, complemented
12C11×#1631C211yesmaximal, characteristic, complemented
13C11×#1622C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#490—21no—
23C11×#488—21no—
24C11×#487C2211yescharacteristic
25C11×#487C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#484—21no—
29C11×#484—21no—
30C11×#482—21no—
31C11×#479—21no—
32C11×#478—21no—
33C11×#477C2211yescharacteristic
34C11×#477C2211yescharacteristic
35C11×#476C2211yescharacteristic
36C11×#476C2211yescharacteristic
37C11×#475C2211yescharacteristic
38C11×#467—21no—
39C11×#465—21no—
40C11×#463—21no—
41C11×#461C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#459—21no—
44C11×#459C2211yescharacteristic
45C11×#452—21no—
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C11×#442—21no—
49C4×C11×Q16C2211yescharacteristic
50C4×C11×SD16—21no—
51C4×C11×D8C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C2×C11×#107—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×Q16D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—41no—
72C2×C11×D8—21no—
73C2×C11×D8D411yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×C4⋊Q8C2311yescharacteristic
78C11×C4⋊Q8C2311yescharacteristic
79C11×#127—21no—
80C11×#127C2311yescharacteristic
81C11×#126—41no—
82C11×#125—21no—
83C11×#125—21no—
84C11×#124—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×C22⋊Q8—41no—
90C11×#121—21no—
91C11×#121—41no—
92C4×Q8×C11—21no—
93C4×Q8×C11C2311yescharacteristic
94C4×Q8×C11C2311yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107D411yescharacteristic
108C11×#107D411yescharacteristic
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—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—21no—
123C11×#103—21no—
124C11×#103—41no—
125C11×#103D411yescharacteristic
126C11×#103D411yescharacteristic
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×#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#19840C1111yesmaximal, 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—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C11×Q16—41no—
165C11×SD16—42no—
166C11×SD16—81no—
167C11×SD16—82no—
168C11×D8—22no—
169C11×D8—42no—
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⋊C4—41no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—41no—
208C42×C11C2411yescharacteristic
209#3366C2×C1111yescharacteristic
210#3360C2×C1111yescharacteristic, complemented
211#3338C2×C1111yescharacteristic, complemented
212#3304C2×C1111yescharacteristic, complemented
213#1719C2×C1111yescharacteristic, complemented
214#1704C2×C1111yescharacteristic, complemented
215#1681C2×C1111yescharacteristic, complemented
216#1678C2×C1111yescharacteristic, complemented
217#1675C2×C1111yescharacteristic, complemented
218#1643C2×C1111yescharacteristic, complemented
219#1638C2×C1111yescharacteristic, complemented
220#1631C2×C1111yescharacteristic, complemented
221#1622C2×C1111yescharacteristic, complemented
222#1584C2×C1111yescharacteristic, complemented
223#1580C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—41no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—81no—
234Q8×C11—81no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—81no—
243D4×C11—82no—
244D4×C11—161no—
245D4×C11#13512yes—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—82no—
260C2×C4×C11—161no—
261C2×C4×C11—161no—
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—
274#556C22×C1111yescharacteristic
275#554C22×C1111yescharacteristic
276#554C22×C1111yescharacteristic
277#550C22×C1111yescharacteristic
278#500C22×C1111yescharacteristic
279#492C22×C1111yescharacteristic
280#490—21no—
281#488—21no—
282#487C22×C1111yescharacteristic
283#487C22×C1111yescharacteristic
284#486C22×C1111yescharacteristic
285#486C22×C1111yescharacteristic
286#484—21no—
287#484—21no—
288#482—21no—
289#479—21no—
290#478—21no—
291#477C22×C1111yescharacteristic
292#477C22×C1111yescharacteristic
293#476C22×C1111yescharacteristic
294#476C22×C1111yescharacteristic
295#475C22×C1111yescharacteristic
296#467—21no—
297#465—21no—
298#463—21no—
299#461C22×C1111yescharacteristic
300#460C22×C1111yescharacteristic
301#459—21no—
302#459C22×C1111yescharacteristic
303#452—21no—
304#446C22×C1111yescharacteristic
305C8×Q8C22×C1111yescharacteristic
306#442—21no—
307C4×Q16C22×C1111yescharacteristic
308C4×SD16—21no—
309C4×D8C22×C1111yescharacteristic
310C8×D4C22×C1111yescharacteristic
311C8×D4C22×C1111yescharacteristic
312C2×#107—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—22no—
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—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×C11#57511yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57811yescharacteristic
349C2×#41—21no—
350C2×Q16D4×C1111yescharacteristic
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—41no—
354C2×D8—21no—
355C2×D8D4×C1111yescharacteristic
356C22×C8—21no—
357C22×C8—21no—
358C4⋊Q8C23×C1111yescharacteristic
359C4⋊Q8C23×C1111yescharacteristic
360C4⋊Q8C23×C1111yescharacteristic
361#127—21no—
362#127C23×C1111yescharacteristic
363#126—41no—
364#125—21no—
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—41no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8C23×C1111yescharacteristic
376C4×Q8C23×C1111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C23×C1111yescharacteristic
381C4×D4C23×C1111yescharacteristic
382#117—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107D4×C1111yescharacteristic
390#107D4×C1111yescharacteristic
391#106—21no—
392#106—21no—
393#106—21no—
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#103—21no—
406#103—41no—
407#103D4×C1111yescharacteristic
408#103D4×C1111yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
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—42no—
427C2×C11—81no—
428C2×C11—161no—
429C2×C11#326711yescharacteristic
430C2×C11#328511yescharacteristic
431C2×C11#328811yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
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
445C2×D4C2×D4×C1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451Q16—41no—
452SD16—42no—
453SD16—81no—
454SD16—82no—
455D8—22no—
456D8—42no—
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⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C1111yescharacteristic
482C4⋊C4C2×D4×C1111yescharacteristic
483C4⋊C4C2×D4×C1111yescharacteristic
484C4⋊C4C2×D4×C1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42C24×C1111yescharacteristic
496C11#1984011yescharacteristic, direct product factor, Sylow
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517D4—161no—
518D4C11×#13512yes—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—161no—
534C2×C4—161no—
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—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C1111yescharacteristic
557C4—21no—
558C4—41no—
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—42no—
572C2—81no—
573C2—161no—
574C2C11×#326711yescharacteristic
575C2C11×#328511yescharacteristic
576C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3366C2
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×#3360C2semidirect
3. C11×#3338C2semidirect
4. C11×#3304C2semidirect
5. C11×#1719C2semidirect
6. C11×#1704C2semidirect
7. C11×#1681C2semidirect
8. C11×#1678C2semidirect
9. C11×#1675C2semidirect
10. C11×#1643C2semidirect
11. C11×#1638C2semidirect
12. C11×#1631C2semidirect
13. C11×#1622C2semidirect
14. C11×#1584C2semidirect
15. C11×#1580C2semidirect
144. #19840C11direct (N × H)
210. #3360C2×C11semidirect
211. #3338C2×C11semidirect
212. #3304C2×C11semidirect
213. #1719C2×C11semidirect
214. #1704C2×C11semidirect
215. #1681C2×C11semidirect
216. #1678C2×C11semidirect
217. #1675C2×C11semidirect
218. #1643C2×C11semidirect
219. #1638C2×C11semidirect
220. #1631C2×C11semidirect
221. #1622C2×C11semidirect
222. #1584C2×C11semidirect
223. #1580C2×C11semidirect
496. C11#19840direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33662
C11×#33602
C11×#33382
C11×#33042
C11×#17192
C11×#17042
C11×#16812
C11×#16782
C11×#16752
C11×#16432
C11×#16382
C11×#16312
C11×#16222
C11×#15842
C11×#15802
#1984011