Finite Group Databasebeta

← C11×#19864 #14597057

Subgroups — C11×#19864 #14597057

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3360C211yesmaximal, characteristic, complemented
2C11×#3357C211yesmaximal, characteristic, complemented
3C11×#3341C211yesmaximal, characteristic
4C11×#3340C211yesmaximal, characteristic, complemented
5C11×#1723C211yesmaximal, characteristic, complemented
6C11×#1691C211yesmaximal, characteristic, complemented
7C11×#1683C211yesmaximal, characteristic, complemented
8C11×#1676C211yesmaximal, characteristic, complemented
9C11×#1675C211yesmaximal, characteristic, complemented
10C11×#1646C211yesmaximal, characteristic, complemented
11C11×#1638C211yesmaximal, characteristic, complemented
12C11×#1634C211yesmaximal, characteristic, complemented
13C11×#1632C211yesmaximal, characteristic, complemented
14C11×#1581C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#555C2211yescharacteristic
19C11×#554C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#498C2211yescharacteristic
23C11×#494C2211yescharacteristic
24C11×#488—21no—
25C11×#487C2211yescharacteristic
26C11×#487C2211yescharacteristic
27C11×#485—21no—
28C11×#485—21no—
29C11×#482—21no—
30C11×#482—21no—
31C11×#482—21no—
32C11×#480—21no—
33C11×#479—21no—
34C11×#477C2211yescharacteristic
35C11×#477C2211yescharacteristic
36C11×#476C2211yescharacteristic
37C11×#476C2211yescharacteristic
38C11×#476C2211yescharacteristic
39C11×#476C2211yescharacteristic
40C11×#474C2211yescharacteristic
41C11×#468—21no—
42C11×#466—21no—
43C11×#465—21no—
44C11×#463—21no—
45C11×#461C2211yescharacteristic
46C8×Q8×C11C2211yescharacteristic
47C4×C11×SD16—21no—
48C4×C11×SD16C2211yescharacteristic
49C4×C11×D8C2211yescharacteristic
50C11×#436C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C11×#428—21no—
54C11×#427—21no—
55C11×#427—21no—
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×Q16—41no—
68C2×C11×SD16—21no—
69C2×C11×SD16D411yescharacteristic
70C2×C11×D8D411yescharacteristic
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×C4⋊Q8C2311yescharacteristic
78C11×#126—41no—
79C11×#125—21no—
80C11×#124—21no—
81C11×#124—41no—
82C11×#124—41no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—41no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11C2311yescharacteristic
92C4×D4×C11—21no—
93C4×D4×C11C2311yescharacteristic
94C4×D4×C11C2311yescharacteristic
95C4×D4×C11C2311yescharacteristic
96C11×#117—21no—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117—21no—
100C11×#117—21no—
101C2×C11×C4⋊C4—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106—21no—
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—21no—
126C11×#103—21no—
127C11×#103—41no—
128C11×#103D411yescharacteristic
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—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19864C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—41no—
159C11×Q16—82no—
160C11×SD16—22no—
161C11×SD16—42no—
162C11×D8—41no—
163C11×M16—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C2×C8×C11—42no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C42×C11—21no—
202C42×C11—41no—
203C42×C11—41no—
204C42×C11—41no—
205C42×C11C2411yescharacteristic
206#3360C2×C1111yescharacteristic, complemented
207#3357C2×C1111yescharacteristic, complemented
208#3341C2×C1111yescharacteristic
209#3340C2×C1111yescharacteristic, complemented
210#1723C2×C1111yescharacteristic, complemented
211#1691C2×C1111yescharacteristic, complemented
212#1683C2×C1111yescharacteristic, complemented
213#1676C2×C1111yescharacteristic, complemented
214#1675C2×C1111yescharacteristic, complemented
215#1646C2×C1111yescharacteristic, complemented
216#1638C2×C1111yescharacteristic, complemented
217#1634C2×C1111yescharacteristic, complemented
218#1632C2×C1111yescharacteristic, complemented
219#1581C2×C1111yescharacteristic, complemented
220SD16⋊C8C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11—81no—
230Q8×C11—81no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—161no—
238D4×C11—161no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—161no—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11#13512yes—
267#556C22×C1111yescharacteristic
268#555C22×C1111yescharacteristic
269#555C22×C1111yescharacteristic
270#554C22×C1111yescharacteristic
271#500C22×C1111yescharacteristic
272#500C22×C1111yescharacteristic
273#498C22×C1111yescharacteristic
274#494C22×C1111yescharacteristic
275#488—21no—
276#487C22×C1111yescharacteristic
277#487C22×C1111yescharacteristic
278#485—21no—
279#485—21no—
280#482—21no—
281#482—21no—
282#482—21no—
283#480—21no—
284#479—21no—
285#477C22×C1111yescharacteristic
286#477C22×C1111yescharacteristic
287#476C22×C1111yescharacteristic
288#476C22×C1111yescharacteristic
289#476C22×C1111yescharacteristic
290#476C22×C1111yescharacteristic
291#474C22×C1111yescharacteristic
292#468—21no—
293#466—21no—
294#465—21no—
295#463—21no—
296#461C22×C1111yescharacteristic
297C8×Q8C22×C1111yescharacteristic
298C4×SD16—21no—
299C4×SD16C22×C1111yescharacteristic
300C4×D8C22×C1111yescharacteristic
301#436C22×C1111yescharacteristic
302C8×D4C22×C1111yescharacteristic
303C8×D4C22×C1111yescharacteristic
304#428—21no—
305#427—21no—
306#427—21no—
307#335C22×C1111yescharacteristic
308#335C22×C1111yescharacteristic
309#333C22×C1111yescharacteristic
310#333C22×C1111yescharacteristic
311#333C22×C1111yescharacteristic
312#332C22×C1111yescharacteristic
313Q8⋊C8C22×C1111yescharacteristic
314D4⋊C8C22×C1111yescharacteristic
315D4⋊C8C22×C1111yescharacteristic
316D4⋊C8C22×C1111yescharacteristic
317#322C22×C1111yescharacteristic
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11D4211yescharacteristic
328C4×C11—21no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11C2×#13511yescharacteristic
339C4×C11#57511yescharacteristic
340C4×C11#57811yescharacteristic
341C4×C11#57811yescharacteristic
342C2×Q16—41no—
343C2×SD16—21no—
344C2×SD16D4×C1111yescharacteristic
345C2×D8D4×C1111yescharacteristic
346C2×M16—21no—
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8C23×C1111yescharacteristic
350C4⋊Q8C23×C1111yescharacteristic
351C4⋊Q8C23×C1111yescharacteristic
352C4⋊Q8C23×C1111yescharacteristic
353#126—41no—
354#125—21no—
355#124—21no—
356#124—41no—
357#124—41no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365C4×Q8—21no—
366C4×Q8C23×C1111yescharacteristic
367C4×D4—21no—
368C4×D4C23×C1111yescharacteristic
369C4×D4C23×C1111yescharacteristic
370C4×D4C23×C1111yescharacteristic
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376C2×C4⋊C4—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107D4×C1111yescharacteristic
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C1111yescharacteristic
392C4⋊C8—21no—
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396C4⋊C8C23×C1111yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—41no—
403#103D4×C1111yescharacteristic
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102D4×C1111yescharacteristic
410#102D4×C1111yescharacteristic
411#102D4×C1111yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C4×C8—21no—
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C4×C8C23×C1111yescharacteristic
419C2×C11—81no—
420C2×C11—81no—
421C2×C11—81no—
422C2×C11#326911yescharacteristic
423C2×C11#328311yescharacteristic
424C2×C11#328811yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×D4×C1111yescharacteristic
430C2×D4—41no—
431C2×D4—41no—
432C2×D4C2×D4×C1111yescharacteristic
433C2×D4C2×D4×C1111yescharacteristic
434C2×D4C2×D4×C1111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439Q16—82no—
440SD16—22no—
441SD16—42no—
442D8—41no—
443M16—42no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8C2×D4×C1111yescharacteristic
452C2×C8C2×D4×C1111yescharacteristic
453C2×C8C2×D4×C1111yescharacteristic
454C2×C8C2×D4×C1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C1111yescharacteristic
468C4⋊C4C2×D4×C1111yescharacteristic
469C4⋊C4C2×D4×C1111yescharacteristic
470C4⋊C4C2×D4×C1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42C24×C1111yescharacteristic
486C11#1986411yescharacteristic, direct product factor, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—81no—
497D4—21no—
498D4—21no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503D4—161no—
504D4—161no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—161no—
521C2×C4C22×D4×C1111yescharacteristic
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C11×H(5,𝔽2)11yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8C11×#13512yes—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22D42×C1111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4C2×C11×#13511yescharacteristic
554C4C11×#57511yescharacteristic
555C4C11×#57811yescharacteristic
556C4C11×#57811yescharacteristic
557C2—81no—
558C2—81no—
559C2—81no—
560C2C11×#326911yescharacteristic
561C2C11×#328311yescharacteristic
562C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3341C2
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×#3360C2semidirect
2. C11×#3357C2semidirect
4. C11×#3340C2semidirect
5. C11×#1723C2semidirect
6. C11×#1691C2semidirect
7. C11×#1683C2semidirect
8. C11×#1676C2semidirect
9. C11×#1675C2semidirect
10. C11×#1646C2semidirect
11. C11×#1638C2semidirect
12. C11×#1634C2semidirect
13. C11×#1632C2semidirect
14. C11×#1581C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19864C11direct (N × H)
206. #3360C2×C11semidirect
207. #3357C2×C11semidirect
209. #3340C2×C11semidirect
210. #1723C2×C11semidirect
211. #1691C2×C11semidirect
212. #1683C2×C11semidirect
213. #1676C2×C11semidirect
214. #1675C2×C11semidirect
215. #1646C2×C11semidirect
216. #1638C2×C11semidirect
217. #1634C2×C11semidirect
218. #1632C2×C11semidirect
219. #1581C2×C11semidirect
220. SD16⋊C8C2×C11semidirect
486. C11#19864direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33602
C11×#33572
C11×#33412
C11×#33402
C11×#17232
C11×#16912
C11×#16832
C11×#16762
C11×#16752
C11×#16462
C11×#16382
C11×#16342
C11×#16322
C11×#15812
C11×SD16⋊C82
#1986411