Finite Group Databasebeta

← C11×#19854 #14597047

Subgroups — C11×#19854 #14597047

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3397C211yesmaximal, characteristic, complemented
2C11×#3341C211yesmaximal, characteristic, complemented
3C11×#3340C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic, complemented
5C11×#1714C211yesmaximal, characteristic, complemented
6C11×#1696C211yesmaximal, characteristic, complemented
7C11×#1677C211yesmaximal, characteristic, complemented
8C11×#1671C211yesmaximal, characteristic, complemented
9C11×#1665C211yesmaximal, characteristic, complemented
10C11×#1646C211yesmaximal, characteristic, complemented
11C11×#1638C211yesmaximal, characteristic, complemented
12C11×#1631C211yesmaximal, characteristic, complemented
13C11×#1624C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#555C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#498C2211yescharacteristic
22C11×#496—21no—
23C11×#492C2211yescharacteristic
24C11×#492C2211yescharacteristic
25C11×#487C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#485—21no—
28C11×#482—21no—
29C11×#482—21no—
30C11×#482—21no—
31C11×#482—21no—
32C11×#477C2211yescharacteristic
33C11×#477C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#476C2211yescharacteristic
36C11×#474C2211yescharacteristic
37C11×#466—21no—
38C11×#466—21no—
39C11×#465—21no—
40C11×#463—21no—
41C11×#461C2211yescharacteristic
42C11×#460—21no—
43C11×#459C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#449—21no—
46C11×#446C2211yescharacteristic
47C11×#440—21no—
48C4×C11×SD16C2211yescharacteristic
49C4×C11×D8C2211yescharacteristic
50C8×D4×C11C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C11×#427—21no—
54C11×#427—21no—
55C11×#416—21no—
56C11×#334C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×SD16—41no—
72C2×C11×SD16D411yescharacteristic
73C2×C11×D8—21no—
74C2×C11×D8—21no—
75C2×C11×D8D411yescharacteristic
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127—21no—
83C11×#127C2311yescharacteristic
84C11×#126—41no—
85C11×#124—21no—
86C11×#124—41no—
87C11×#124—41no—
88C11×C22⋊Q8—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—41no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—21no—
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C11×#117—21no—
103C11×#117—21no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107D411yescharacteristic
112C11×#106—21no—
113C11×#106—21no—
114C11×#106—21no—
115C11×#106—21no—
116C11×#106D411yescharacteristic
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—41no—
126C11×#103D411yescharacteristic
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102D411yescharacteristic
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×#97—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19854C1111yesmaximal, 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×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11C2×D411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C11×SD16—41no—
166C11×SD16—42no—
167C11×SD16—81no—
168C11×SD16—81no—
169C11×SD16—82no—
170C11×D8—22no—
171C11×D8—81no—
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—42no—
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—41no—
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—21no—
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—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C42×C11—21no—
208C42×C11—41no—
209C42×C11—41no—
210C42×C11—41no—
211C42×C11C2411yescharacteristic
212#3397C2×C1111yescharacteristic, complemented
213#3341C2×C1111yescharacteristic, complemented
214#3340C2×C1111yescharacteristic, complemented
215#3305C2×C1111yescharacteristic, complemented
216#1714C2×C1111yescharacteristic, complemented
217#1696C2×C1111yescharacteristic, complemented
218#1677C2×C1111yescharacteristic, complemented
219#1671C2×C1111yescharacteristic, complemented
220#1665C2×C1111yescharacteristic, complemented
221#1646C2×C1111yescharacteristic, complemented
222#1638C2×C1111yescharacteristic, complemented
223#1631C2×C1111yescharacteristic, complemented
224#1624C2×C1111yescharacteristic, complemented
225#1582C2×C1111yescharacteristic, complemented
226#1580C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—81no—
236Q8×C11—81no—
237D4×C11—21no—
238D4×C11—21no—
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—81no—
248D4×C11—82no—
249D4×C11—161no—
250D4×C11—161no—
251D4×C11—161no—
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—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#555C22×C1111yescharacteristic
281#555C22×C1111yescharacteristic
282#550C22×C1111yescharacteristic
283#500C22×C1111yescharacteristic
284#498C22×C1111yescharacteristic
285#496—21no—
286#492C22×C1111yescharacteristic
287#492C22×C1111yescharacteristic
288#487C22×C1111yescharacteristic
289#486C22×C1111yescharacteristic
290#485—21no—
291#482—21no—
292#482—21no—
293#482—21no—
294#482—21no—
295#477C22×C1111yescharacteristic
296#477C22×C1111yescharacteristic
297#476C22×C1111yescharacteristic
298#476C22×C1111yescharacteristic
299#474C22×C1111yescharacteristic
300#466—21no—
301#466—21no—
302#465—21no—
303#463—21no—
304#461C22×C1111yescharacteristic
305#460—21no—
306#459C22×C1111yescharacteristic
307#459C22×C1111yescharacteristic
308#449—21no—
309#446C22×C1111yescharacteristic
310#440—21no—
311C4×SD16C22×C1111yescharacteristic
312C4×D8C22×C1111yescharacteristic
313C8×D4C22×C1111yescharacteristic
314C8×D4C22×C1111yescharacteristic
315C8×D4C22×C1111yescharacteristic
316#427—21no—
317#427—21no—
318#416—21no—
319#334C22×C1111yescharacteristic
320#334C22×C1111yescharacteristic
321#333C22×C1111yescharacteristic
322#333C22×C1111yescharacteristic
323#332C22×C1111yescharacteristic
324#331C22×C1111yescharacteristic
325Q8⋊C8C22×C1111yescharacteristic
326D4⋊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—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11D4211yescharacteristic
343C4×C11—21no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×#13511yescharacteristic
353C4×C11#57511yescharacteristic
354C4×C11#57711yescharacteristic
355C4×C11#57711yescharacteristic
356C2×#41—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—41no—
361C2×SD16D4×C1111yescharacteristic
362C2×D8—21no—
363C2×D8—21no—
364C2×D8D4×C1111yescharacteristic
365C22×C8—21no—
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#124—21no—
375#124—41no—
376#124—41no—
377C22⋊Q8—21no—
378#121—21no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8C23×C1111yescharacteristic
386C4×D4—21no—
387C4×D4C23×C1111yescharacteristic
388C4×D4C23×C1111yescharacteristic
389C4×D4C23×C1111yescharacteristic
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107D4×C1111yescharacteristic
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106D4×C1111yescharacteristic
406C4⋊C8—21no—
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410C4⋊C8C23×C1111yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C1111yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102D4×C1111yescharacteristic
424#102D4×C1111yescharacteristic
425#102D4×C1111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97—21no—
430C4×C8C23×C1111yescharacteristic
431C4×C8C23×C1111yescharacteristic
432C4×C8C23×C1111yescharacteristic
433C2×C11—81no—
434C2×C11—81no—
435C2×C11—81no—
436C2×C11—161no—
437C2×C11#326711yescharacteristic
438C2×C11#328411yescharacteristic
439C2×C11#328811yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×D4×C1111yescharacteristic
454C2×D4C2×D4×C1111yescharacteristic
455C2×D4C2×D4×C1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460SD16—41no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464SD16—82no—
465D8—22no—
466D8—81no—
467D8—81no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—42no—
474C2×C8—42no—
475C2×C8—81no—
476C2×C8C2×D4×C1111yescharacteristic
477C2×C8C2×D4×C1111yescharacteristic
478C2×C8C2×D4×C1111yescharacteristic
479C2×C8C2×D4×C1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C1111yescharacteristic
489C4⋊C4C2×D4×C1111yescharacteristic
490C4⋊C4C2×D4×C1111yescharacteristic
491C4⋊C4C2×D4×C1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—41no—
504C42—41no—
505C42—41no—
506C42C24×C1111yescharacteristic
507C11#1985411yescharacteristic, direct product factor, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—81no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531D4—161no—
532D4—161no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4C22×D4×C1111yescharacteristic
549C2×C4C22×D4×C1111yescharacteristic
550C2×C4C11×H(5,𝔽2)11yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8C11×#13512yes—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C1111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4C2×C11×#13511yescharacteristic
583C4C11×#57511yescharacteristic
584C4C11×#57711yescharacteristic
585C4C11×#57711yescharacteristic
586C2—81no—
587C2—81no—
588C2—81no—
589C2—161no—
590C2C11×#326711yescharacteristic
591C2C11×#328411yescharacteristic
592C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
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×#3397C2semidirect
2. C11×#3341C2semidirect
3. C11×#3340C2semidirect
4. C11×#3305C2semidirect
5. C11×#1714C2semidirect
6. C11×#1696C2semidirect
7. C11×#1677C2semidirect
8. C11×#1671C2semidirect
9. C11×#1665C2semidirect
10. C11×#1646C2semidirect
11. C11×#1638C2semidirect
12. C11×#1631C2semidirect
13. C11×#1624C2semidirect
14. C11×#1582C2semidirect
15. C11×#1580C2semidirect
144. #19854C11direct (N × H)
212. #3397C2×C11semidirect
213. #3341C2×C11semidirect
214. #3340C2×C11semidirect
215. #3305C2×C11semidirect
216. #1714C2×C11semidirect
217. #1696C2×C11semidirect
218. #1677C2×C11semidirect
219. #1671C2×C11semidirect
220. #1665C2×C11semidirect
221. #1646C2×C11semidirect
222. #1638C2×C11semidirect
223. #1631C2×C11semidirect
224. #1624C2×C11semidirect
225. #1582C2×C11semidirect
226. #1580C2×C11semidirect
507. C11#19854direct (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×#33412
C11×#33402
C11×#33052
C11×#17142
C11×#16962
C11×#16772
C11×#16712
C11×#16652
C11×#16462
C11×#16382
C11×#16312
C11×#16242
C11×#15822
C11×#15802
#1985411