Finite Group Databasebeta

← C11×#24018 #14601211

Subgroups — C11×#24018 #14601211

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3484C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C2×C11×#390C211yesmaximal, characteristic, complemented
4C11×#2037C214yesmaximal, complemented
5C11×#1896C212yesmaximal, complemented
6C11×#1856C212yesmaximal, complemented
7C11×#1792C212yesmaximal, complemented
8C11×#1783C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C11×#546—22no—
12C11×#546—22no—
13D42×C11—22no—
14D42×C11—22no—
15C11×#535C2212yes—
16C11×#534—22no—
17C11×#525C2212yes—
18C2×C11×#120—22no—
19C11×#518C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21C22×C11×C22⋊C4—22no—
22C22×C42×C11C2211yescharacteristic, complemented
23C11×#484—22no—
24C11×#483—22no—
25C11×#481—22no—
26C11×#480—22no—
27C11×#428C2214yescomplemented
28C2×C11×#104C2214yescomplemented
29C11×#417C2214yescomplemented
30C2×C11×#100C2212yes—
31C2×C11×#100C2212yescomplemented
32C11×#407C2212yescomplemented
33C11×#390—22no—
34C11×#390C2212yes—
35C11×#390C2212yescomplemented
36C11×#339C2214yescomplemented
37C25×C11D412yes—
38C11×H(5,𝔽2)—24no—
39C11×H(5,𝔽2)—42no—
40C2×C11×#41—22no—
41C2×C11×#41C2312yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—42no—
50C22×D4×C11D412yes—
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C2×C11×M16C2314yes—
57C11×#127—22no—
58C11×#124—22no—
59C11×#123—24no—
60C11×#123—22no—
61C11×C22⋊Q8D412yes—
62C11×C22⋊Q8D412yes—
63C11×#121—24no—
64C11×#121—24no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121D412yes—
68C11×#121D412yes—
69C11×#120—24no—
70C11×#120—24no—
71C11×#120—24no—
72C11×#120—22no—
73C11×#120—24no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C11×#117C2312yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—48no—
89C2×C42×C11—21no—
90C2×C42×C11—42no—
91C2×C42×C11C2312yes—
92C11×#107—24no—
93C11×#106—24no—
94C11×#104—44no—
95C11×#103—24no—
96C11×#102—24no—
97C11×#100—24no—
98C11×#100—42no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—22no—
101#24018C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—42no—
107C24×C11—44no—
108C24×C11—44no—
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D412yes—
111C24×C11C2×D412yes—
112C11×#41—24no—
113C11×#41—24no—
114C11×#41—48no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—24no—
120C2×D4×C11—22no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—48no—
130C2×D4×C11—48no—
131C2×D4×C11—42no—
132C2×D4×C11—48no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—84no—
136C2×D4×C11—84no—
137C2×D4×C11C2×D412yes—
138C2×D4×C11#4114yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—44no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×M16—24no—
158C11×M16—24no—
159C2×C8×C11—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—48no—
175C11×C22⋊C4—48no—
176C42×C11—22no—
177C42×C11—24no—
178C42×C11—42no—
179#3484C2×C1111yescharacteristic
180#3092C2×C1112yescomplemented
181C2×#390C2×C1111yescharacteristic, complemented
182#2037C2×C1114yescomplemented
183#1896C2×C1112yescomplemented
184#1856C2×C1112yescomplemented
185#1792C2×C1112yescomplemented
186#1783C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—416no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—82no—
208C23×C11—82no—
209C23×C11—88no—
210C23×C11—82no—
211C23×C11—82no—
212C23×C11#12011yescharacteristic
213C23×C11#12011yescharacteristic
214C23×C11#12314yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—24no—
217D4×C11—28no—
218D4×C11—24no—
219D4×C11—48no—
220D4×C11—48no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—44no—
226D4×C11—84no—
227D4×C11—84no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—48no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11—42no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11#12012yes—
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C8×C11—44no—
252C2×H(5,𝔽2)C22×C1111yescharacteristic
253C23×D4C22×C1111yescharacteristic
254#546—22no—
255#546—22no—
256D42—22no—
257D42—22no—
258#535C22×C1112yes—
259#534—22no—
260#525C22×C1112yes—
261C2×#120—22no—
262#518C22×C1111yescharacteristic
263C22×C4⋊C4C22×C1111yescharacteristic, complemented
264C22×C22⋊C4—22no—
265C22×C42C22×C1111yescharacteristic, complemented
266#484—22no—
267#483—22no—
268#481—22no—
269#480—22no—
270#428C22×C1114yescomplemented
271C2×#104C22×C1114yescomplemented
272#417C22×C1114yescomplemented
273C2×#100C22×C1112yes—
274C2×#100C22×C1112yescomplemented
275#407C22×C1112yescomplemented
276#390—22no—
277#390C22×C1112yes—
278#390C22×C1112yescomplemented
279#339C22×C1114yescomplemented
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—24no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—82no—
300C22×C11—88no—
301C22×C11—88no—
302C22×C11—82no—
303C22×C11—164no—
304C22×C11#45312yes—
305C22×C11#45512yes—
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12311yescharacteristic
308C22×C11#53411yescharacteristic
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—82no—
315C4×C11#54614yes—
316C25D4×C1112yes—
317H(5,𝔽2)—24no—
318H(5,𝔽2)—42no—
319C2×#41—22no—
320C2×#41C23×C1112yes—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—24no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—42no—
329C22×D4D4×C1112yes—
330C22×D4C23×C1111yescharacteristic
331C22×D4C23×C1111yescharacteristic
332C23×C4—21no—
333C23×C4—21no—
334C23×C4C23×C1111yescharacteristic
335C2×M16C23×C1114yes—
336#127—22no—
337#124—22no—
338#123—24no—
339#123—22no—
340C22⋊Q8D4×C1112yes—
341C22⋊Q8D4×C1112yes—
342#121—24no—
343#121—24no—
344#121—22no—
345#121—22no—
346#121D4×C1112yes—
347#121D4×C1112yes—
348#120—24no—
349#120—24no—
350#120—24no—
351#120—22no—
352#120—24no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357#117C23×C1112yes—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C23×C1112yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—48no—
368C2×C42—21no—
369C2×C42—42no—
370C2×C42C23×C1112yes—
371#107—24no—
372#106—24no—
373#104—44no—
374#103—24no—
375#102—24no—
376#100—24no—
377#100—42no—
378C22⋊C8—22no—
379C22⋊C8—22no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—22no—
383C2×C11—22no—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11—82no—
387C2×C11#240511yescharacteristic
388C2×C11C2×#45311yescharacteristic
389C2×C11C2×#45511yescharacteristic
390C24—22no—
391C24—24no—
392C24—22no—
393C24—22no—
394C24—42no—
395C24—44no—
396C24—44no—
397C24C2×D4×C1111yescharacteristic
398C24C2×D4×C1112yes—
399C24C2×D4×C1112yes—
400#41—24no—
401#41—24no—
402#41—48no—
403C2×Q8C2×D4×C1112yes—
404C2×D4—24no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—22no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—42no—
420C2×D4—48no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—84no—
424C2×D4—84no—
425C2×D4C2×D4×C1112yes—
426C2×D4C11×#4114yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1112yes—
443C22×C4C2×D4×C1112yes—
444C22×C4C24×C1111yescharacteristic
445M16—24no—
446M16—24no—
447C2×C8—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4—42no—
452C4⋊C4C2×D4×C1112yes—
453C4⋊C4C2×D4×C1112yes—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—48no—
463C22⋊C4—48no—
464C42—22no—
465C42—24no—
466C42—42no—
467C11#2401811yescharacteristic, direct product factor, Sylow
468C23—21no—
469C23—21no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—44no—
479C23—44no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—416no—
485C23—44no—
486C23—44no—
487C23—44no—
488C23—82no—
489C23—82no—
490C23—88no—
491C23—82no—
492C23—82no—
493C23C11×#12011yescharacteristic
494C23C11×#12011yescharacteristic
495C23C11×#12314yes—
496C23C22×D4×C1111yescharacteristic
497Q8—24no—
498D4—28no—
499D4—24no—
500D4—48no—
501D4—48no—
502D4—42no—
503D4—42no—
504D4—44no—
505D4—44no—
506D4—44no—
507D4—84no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4C11×#12012yes—
529C2×C4C22×D4×C1112yes—
530C2×C4C2×C11×#4112yes—
531C2×C4C11×H(5,𝔽2)12yes—
532C8—44no—
533C22—24no—
534C22—24no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—24no—
542C22—44no—
543C22—44no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—88no—
554C22—88no—
555C22—82no—
556C22—164no—
557C22C11×#45312yes—
558C22C11×#45512yes—
559C22C2×C11×#12011yescharacteristic
560C22C2×C11×#12311yescharacteristic
561C22C11×#53411yescharacteristic
562C4—22no—
563C4—44no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4C11×#54614yes—
569C2—21no—
570C2—21no—
571C2—22no—
572C2—22no—
573C2—44no—
574C2—82no—
575C2—82no—
576C2C11×#240511yescharacteristic
577C2C2×C11×#45311yescharacteristic
578C2C2×C11×#45511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3484C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C2×C11×#390C2semidirect
4. C11×#2037C2semidirect
5. C11×#1896C2semidirect
6. C11×#1856C2semidirect
7. C11×#1792C2semidirect
8. C11×#1783C2semidirect
20. C22×C11×C4⋊C4C22semidirect
22. C22×C42×C11C22semidirect
27. C11×#428C22semidirect
28. C2×C11×#104C22semidirect
29. C11×#417C22semidirect
31. C2×C11×#100C22semidirect
32. C11×#407C22semidirect
35. C11×#390C22semidirect
36. C11×#339C22semidirect
101. #24018C11direct (N × H)
180. #3092C2×C11semidirect
181. C2×#390C2×C11semidirect
182. #2037C2×C11semidirect
183. #1896C2×C11semidirect
184. #1856C2×C11semidirect
185. #1792C2×C11semidirect
186. #1783C2×C11semidirect
263. C22×C4⋊C4C22×C11semidirect
265. C22×C42C22×C11semidirect
270. #428C22×C11semidirect
271. C2×#104C22×C11semidirect
272. #417C22×C11semidirect
274. C2×#100C22×C11semidirect
275. #407C22×C11semidirect
278. #390C22×C11semidirect
279. #339C22×C11semidirect
467. C11#24018direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34842
C11×#30922
C2×C11×#3902
C11×#20372
C11×#18962
C11×#18562
C11×#17922
C11×#17832
#2401811