Finite Group Databasebeta

← C11×#19865 #14597058

Subgroups — C11×#19865 #14597058

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3380C211yesmaximal, characteristic
2C11×#3360C211yesmaximal, characteristic
3C11×#3356C211yesmaximal, characteristic, complemented
4C11×#3338C211yesmaximal, characteristic, complemented
5C11×#1723C211yesmaximal, characteristic, complemented
6C11×#1695C211yesmaximal, characteristic, complemented
7C11×#1684C211yesmaximal, characteristic, complemented
8C11×#1676C211yesmaximal, characteristic, complemented
9C11×#1671C211yesmaximal, characteristic, complemented
10C11×#1643C211yesmaximal, characteristic, complemented
11C11×#1638C211yesmaximal, characteristic, complemented
12C11×#1632C211yesmaximal, characteristic, complemented
13C11×#1632C211yesmaximal, characteristic, complemented
14C11×#1581C211yesmaximal, characteristic
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#554C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#499—21no—
23C11×#498C2211yescharacteristic
24C11×#494C2211yescharacteristic
25C11×#488—21no—
26C11×#487C2211yescharacteristic
27C11×#487C2211yescharacteristic
28C11×#485—21no—
29C11×#484—21no—
30C11×#484—21no—
31C11×#483—21no—
32C11×#479—21no—
33C11×#478—21no—
34C11×#478—21no—
35C11×#477C2211yescharacteristic
36C11×#477C2211yescharacteristic
37C11×#477C2211yescharacteristic
38C11×#476C2211yescharacteristic
39C11×#476C2211yescharacteristic
40C11×#476C2211yescharacteristic
41C11×#475C2211yescharacteristic
42C11×#470—21no—
43C11×#467—21no—
44C11×#463—21no—
45C11×#461C2211yescharacteristic
46C8×Q8×C11C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C4×C11×Q16C2211yescharacteristic
49C4×C11×SD16—21no—
50C4×C11×D8—21no—
51C4×C11×D8C2211yescharacteristic
52C11×#436C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C11×#428—21no—
55C2×C11×#107—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×Q16—41no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8D411yescharacteristic
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#126—41no—
78C11×#125—21no—
79C11×#125—21no—
80C11×#125—21no—
81C11×#124—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—41no—
87C11×C22⋊Q8—41no—
88C11×C22⋊Q8—41no—
89C4×Q8×C11—21no—
90C4×Q8×C11C2311yescharacteristic
91C4×Q8×C11C2311yescharacteristic
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11C2311yescharacteristic
96C4×D4×C11C2311yescharacteristic
97C11×#117—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C11×#107—21no—
102C11×#107—21no—
103C11×#107—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107D411yescharacteristic
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106—21no—
112C11×#106—21no—
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×#103—21no—
129C11×#103—41no—
130C11×#103D411yescharacteristic
131C11×#103D411yescharacteristic
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19865C1111yesmaximal, 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×Q8×C11C2×D411yescharacteristic
151C2×D4×C11C2×D411yescharacteristic
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C11×Q16—22no—
159C11×Q16—82no—
160C11×SD16—42no—
161C11×D8—22no—
162C11×M16—42no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—42no—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
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—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
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—21no—
203C42×C11—41no—
204C42×C11C2411yescharacteristic
205#3380C2×C1111yescharacteristic
206#3360C2×C1111yescharacteristic
207#3356C2×C1111yescharacteristic, complemented
208#3338C2×C1111yescharacteristic, complemented
209#1723C2×C1111yescharacteristic, complemented
210#1695C2×C1111yescharacteristic, complemented
211#1684C2×C1111yescharacteristic, complemented
212#1676C2×C1111yescharacteristic, complemented
213#1671C2×C1111yescharacteristic, complemented
214#1643C2×C1111yescharacteristic, complemented
215#1638C2×C1111yescharacteristic, complemented
216#1632C2×C1111yescharacteristic, complemented
217#1632C2×C1111yescharacteristic, complemented
218#1581C2×C1111yescharacteristic
219#1579C2×C1111yescharacteristic, complemented
220C23×C11—21no—
221C23×C11—21no—
222Q8×C11—21no—
223Q8×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#13712yes—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—161no—
250C2×C4×C11—161no—
251C2×C4×C11—161no—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—41no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11#13512yes—
264#556C22×C1111yescharacteristic
265#554C22×C1111yescharacteristic
266#554C22×C1111yescharacteristic
267#554C22×C1111yescharacteristic
268#500C22×C1111yescharacteristic
269#500C22×C1111yescharacteristic
270#499—21no—
271#498C22×C1111yescharacteristic
272#494C22×C1111yescharacteristic
273#488—21no—
274#487C22×C1111yescharacteristic
275#487C22×C1111yescharacteristic
276#485—21no—
277#484—21no—
278#484—21no—
279#483—21no—
280#479—21no—
281#478—21no—
282#478—21no—
283#477C22×C1111yescharacteristic
284#477C22×C1111yescharacteristic
285#477C22×C1111yescharacteristic
286#476C22×C1111yescharacteristic
287#476C22×C1111yescharacteristic
288#476C22×C1111yescharacteristic
289#475C22×C1111yescharacteristic
290#470—21no—
291#467—21no—
292#463—21no—
293#461C22×C1111yescharacteristic
294C8×Q8C22×C1111yescharacteristic
295C8×Q8C22×C1111yescharacteristic
296C4×Q16C22×C1111yescharacteristic
297C4×SD16—21no—
298C4×D8—21no—
299C4×D8C22×C1111yescharacteristic
300#436C22×C1111yescharacteristic
301C8×D4C22×C1111yescharacteristic
302#428—21no—
303C2×#107—21no—
304#335C22×C1111yescharacteristic
305#334C22×C1111yescharacteristic
306#333C22×C1111yescharacteristic
307#333C22×C1111yescharacteristic
308#333C22×C1111yescharacteristic
309#332C22×C1111yescharacteristic
310Q8⋊C8C22×C1111yescharacteristic
311Q8⋊C8C22×C1111yescharacteristic
312D4⋊C8C22×C1111yescharacteristic
313D4⋊C8C22×C1111yescharacteristic
314#322C22×C1111yescharacteristic
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11D4211yescharacteristic
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11C2×#13511yescharacteristic
334C4×C11C2×#13711yescharacteristic
335C4×C11#57811yescharacteristic
336C4×C11#57811yescharacteristic
337C2×Q16—41no—
338C2×Q16D4×C1111yescharacteristic
339C2×SD16—21no—
340C2×D8D4×C1111yescharacteristic
341C2×M16—21no—
342C22×C8—21no—
343C4⋊Q8C23×C1111yescharacteristic
344C4⋊Q8C23×C1111yescharacteristic
345C4⋊Q8C23×C1111yescharacteristic
346C4⋊Q8C23×C1111yescharacteristic
347#126—41no—
348#125—21no—
349#125—21no—
350#125—21no—
351#124—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—41no—
357C22⋊Q8—41no—
358C22⋊Q8—41no—
359C4×Q8—21no—
360C4×Q8C23×C1111yescharacteristic
361C4×Q8C23×C1111yescharacteristic
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C23×C1111yescharacteristic
366C4×D4C23×C1111yescharacteristic
367#117—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107D4×C1111yescharacteristic
379#107D4×C1111yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8C23×C1111yescharacteristic
389C4⋊C8C23×C1111yescharacteristic
390C4⋊C8C23×C1111yescharacteristic
391C4⋊C8C23×C1111yescharacteristic
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—41no—
400#103D4×C1111yescharacteristic
401#103D4×C1111yescharacteristic
402#102—21no—
403#102—21no—
404#102—21no—
405#102D4×C1111yescharacteristic
406#102D4×C1111yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8C23×C1111yescharacteristic
412C4×C8C23×C1111yescharacteristic
413C4×C8C23×C1111yescharacteristic
414C2×C11—42no—
415C2×C11—81no—
416C2×C11#327011yescharacteristic
417C2×C11#328311yescharacteristic
418C2×C11#328811yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8C2×D4×C1111yescharacteristic
424C2×Q8C2×D4×C1111yescharacteristic
425C2×D4C2×D4×C1111yescharacteristic
426C2×D4C2×D4×C1111yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432Q16—22no—
433Q16—82no—
434SD16—42no—
435D8—22no—
436M16—42no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—42no—
443C2×C8C2×D4×C1111yescharacteristic
444C2×C8C2×D4×C1111yescharacteristic
445C2×C8C2×D4×C1111yescharacteristic
446C2×C8C2×D4×C1111yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C1111yescharacteristic
465C4⋊C4C2×D4×C1111yescharacteristic
466C4⋊C4C2×D4×C1111yescharacteristic
467C4⋊C4C2×D4×C1111yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42C24×C1111yescharacteristic
479C11#1986511yescharacteristic, direct product factor, Sylow
480C23—21no—
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491D4—21no—
492D4—21no—
493D4—21no—
494D4C11×#13712yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—161no—
510C2×C4—161no—
511C2×C4—161no—
512C2×C4C22×D4×C1111yescharacteristic
513C2×C4C22×D4×C1111yescharacteristic
514C2×C4C11×H(5,𝔽2)11yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8C11×#13512yes—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D42×C1111yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4C2×C11×#13511yescharacteristic
543C4C2×C11×#13711yescharacteristic
544C4C11×#57811yescharacteristic
545C4C11×#57811yescharacteristic
546C2—42no—
547C2—81no—
548C2C11×#327011yescharacteristic
549C2C11×#328311yescharacteristic
550C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×D8D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C11×#3356C2semidirect
4. C11×#3338C2semidirect
5. C11×#1723C2semidirect
6. C11×#1695C2semidirect
7. C11×#1684C2semidirect
8. C11×#1676C2semidirect
9. C11×#1671C2semidirect
10. C11×#1643C2semidirect
11. C11×#1638C2semidirect
12. C11×#1632C2semidirect
13. C11×#1632C2semidirect
15. C11×#1579C2semidirect
144. #19865C11direct (N × H)
207. #3356C2×C11semidirect
208. #3338C2×C11semidirect
209. #1723C2×C11semidirect
210. #1695C2×C11semidirect
211. #1684C2×C11semidirect
212. #1676C2×C11semidirect
213. #1671C2×C11semidirect
214. #1643C2×C11semidirect
215. #1638C2×C11semidirect
216. #1632C2×C11semidirect
217. #1632C2×C11semidirect
219. #1579C2×C11semidirect
479. C11#19865direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33802
C11×#33602
C11×#33562
C11×#33382
C11×#17232
C11×#16952
C11×#16842
C11×#16762
C11×#16712
C11×#16432
C11×#16382
C11×#16322
C11×#15812
C11×#15792
#1986511