Finite Group Databasebeta

← C11×#24000 #14601193

Subgroups — C11×#24000 #14601193

Order 2816.

1170 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×#3510C211yesmaximal, characteristic, complemented
2C11×#3019C211yesmaximal, characteristic
3C2×C11×#455C211yesmaximal, characteristic, complemented
4C11×#2883C211yesmaximal, characteristic, complemented
5C11×#2031C212yesmaximal, complemented
6C11×#2009C212yesmaximal, complemented
7C11×#1911C211yesmaximal, characteristic, complemented
8C11×#1906C212yesmaximal, complemented
9C11×#1905C212yesmaximal, complemented
10C11×#1885C211yesmaximal, characteristic, complemented
11C11×#1829C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C11×#575C2212yes—
14C2×C11×#137C2212yes—
15C11×#559—22no—
16C11×#556—22no—
17C11×#551—24no—
18C11×#542—22no—
19C11×#536C2211yescharacteristic, complemented
20C11×#535C2211yescharacteristic
21C11×#533C2211yescharacteristic, complemented
22C11×#529—22no—
23C2×C11×#124C2211yescharacteristic
24C11×#519C2211yescharacteristic, complemented
25C11×#518C2211yescharacteristic
26C11×#518C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic, complemented
28C11×#455—22no—
29C11×#455—22no—
30C11×#455—22no—
31C11×#453—22no—
32C11×#421C2212yes—
33C11×#421C2212yescomplemented
34C2×C11×#104C2212yes—
35C11×#419C2212yescomplemented
36C2×C11×#100C2211yescharacteristic
37C2×C11×#100C2211yescharacteristic
38C11×#410C2212yes—
39C11×#410C2212yes—
40C2×C11×#99—24no—
41C11×#344C2212yescomplemented
42C11×#344C2212yescomplemented
43C11×#339C2212yescomplemented
44C11×H(3,ℤ/4)C2212yescomplemented
45C11×H(5,𝔽2)—22no—
46C11×H(5,𝔽2)—22no—
47C11×H(5,𝔽2)—42no—
48C2×C11×#41—22no—
49C2×C11×#41C2311yescharacteristic
50C2×C11×#41C2312yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11C2311yescharacteristic
55C11×#137—24no—
56C11×#137—22no—
57C11×#137—22no—
58C11×#137—42no—
59C11×AGL(1,ℤ/8)—22no—
60C11×AGL(1,ℤ/8)—22no—
61C11×#135—42no—
62C2×C11×Q16—22no—
63C2×C11×SD16—22no—
64C2×C11×M16C2312yes—
65C2×C11×M16C2312yes—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×#127D412yes—
69C11×#126—24no—
70C11×#126—24no—
71C11×#125—21no—
72C11×#124—24no—
73C11×#124—22no—
74C11×#124—21no—
75C11×#124D412yes—
76C11×#124D412yes—
77C11×#124D412yes—
78C11×#123—24no—
79C11×#123—24no—
80C11×#123—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×#121—22no—
85C11×#120—22no—
86C4×Q8×C11—21no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×D4×C11—24no—
91C4×D4×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—42no—
96C11×#117—24no—
97C11×#117—22no—
98C11×#117—21no—
99C11×#117C2312yes—
100C11×#117C2311yescharacteristic
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4D414yes—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—22no—
110C11×#104—24no—
111C11×#104—42no—
112C11×#103—42no—
113C11×#100—22no—
114C11×#100—22no—
115C11×#99—24no—
116C11×#99—24no—
117#24000C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—22no—
119C24×C11C2×D412yes—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D411yescharacteristic
134C2×Q8×C11#4112yes—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C2×D4×C11C2×D411yescharacteristic
146C2×D4×C11C2×D412yes—
147C2×D4×C11C2×D412yes—
148C2×D4×C11#4112yes—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—42no—
157C22×C4×C11C2411yescharacteristic
158C11×Q16—44no—
159C11×Q16—42no—
160C11×SD16—44no—
161C11×SD16—42no—
162C11×SD16—42no—
163C11×D8—42no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4C2×D412yes—
190C11×C22⋊C4C2×D412yes—
191C42×C11—22no—
192C42×C11—24no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—22no—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D412yes—
200#3510C2×C1111yescharacteristic, complemented
201#3019C2×C1111yescharacteristic
202C2×#455C2×C1111yescharacteristic, complemented
203#2883C2×C1111yescharacteristic, complemented
204#2031C2×C1112yescomplemented
205#2009C2×C1112yescomplemented
206#1911C2×C1111yescharacteristic, complemented
207#1906C2×C1112yescomplemented
208#1905C2×C1112yescomplemented
209#1885C2×C1111yescharacteristic, complemented
210#1829C2×C1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—44no—
216C23×C11—82no—
217C23×C11—162no—
218C23×C11#12014yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—24no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—42no—
225Q8×C11—82no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—48no—
232D4×C11—42no—
233D4×C11—41no—
234D4×C11—42no—
235D4×C11—41no—
236D4×C11—84no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—44no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—82no—
253C2×C4×C11—84no—
254C2×C4×C11—81no—
255C2×C4×C11—162no—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4112yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C8×C11—42no—
261C8×C11—42no—
262C2×H(5,𝔽2)C22×C1111yescharacteristic
263#575C22×C1112yes—
264C2×#137C22×C1112yes—
265#559—22no—
266#556—22no—
267#551—24no—
268#542—22no—
269#536C22×C1111yescharacteristic, complemented
270#535C22×C1111yescharacteristic
271#533C22×C1111yescharacteristic, complemented
272#529—22no—
273C2×#124C22×C1111yescharacteristic
274#519C22×C1111yescharacteristic, complemented
275#518C22×C1111yescharacteristic
276#518C22×C1111yescharacteristic
277C4×#41C22×C1111yescharacteristic, complemented
278#455—22no—
279#455—22no—
280#455—22no—
281#453—22no—
282#421C22×C1112yes—
283#421C22×C1112yescomplemented
284C2×#104C22×C1112yes—
285#419C22×C1112yescomplemented
286C2×#100C22×C1111yescharacteristic
287C2×#100C22×C1111yescharacteristic
288#410C22×C1112yes—
289#410C22×C1112yes—
290C2×#99—24no—
291#344C22×C1112yescomplemented
292#344C22×C1112yescomplemented
293#339C22×C1112yescomplemented
294H(3,ℤ/4)C22×C1112yescomplemented
295C22×C11—24no—
296C22×C11—41no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—41no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—164no—
305C22×C11C2×#12011yescharacteristic
306C22×C11#52511yescharacteristic
307C22×C11#53511yescharacteristic
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—42no—
311C4×C11—41no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11#54612yes—
318C4×C11#54612yes—
319H(5,𝔽2)—22no—
320H(5,𝔽2)—22no—
321H(5,𝔽2)—42no—
322C2×#41—22no—
323C2×#41C23×C1111yescharacteristic
324C2×#41C23×C1112yes—
325C22×Q8C23×C1111yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4C23×C1111yescharacteristic
329#137—24no—
330#137—22no—
331#137—22no—
332#137—42no—
333AGL(1,ℤ/8)—22no—
334AGL(1,ℤ/8)—22no—
335#135—42no—
336C2×Q16—22no—
337C2×SD16—22no—
338C2×M16C23×C1112yes—
339C2×M16C23×C1112yes—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342#127D4×C1112yes—
343#126—24no—
344#126—24no—
345#125—21no—
346#124—24no—
347#124—22no—
348#124—21no—
349#124D4×C1112yes—
350#124D4×C1112yes—
351#124D4×C1112yes—
352#123—24no—
353#123—24no—
354#123—22no—
355C22⋊Q8—24no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358#121—22no—
359#120—22no—
360C4×Q8—21no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—24no—
365C4×D4—21no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—42no—
370#117—24no—
371#117—22no—
372#117—21no—
373#117C23×C1112yes—
374#117C23×C1111yescharacteristic
375#117C23×C1111yescharacteristic
376#117C23×C1111yescharacteristic
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4D4×C1114yes—
380C2×C42—21no—
381C2×C42C23×C1111yescharacteristic
382#104—22no—
383#104—22no—
384#104—24no—
385#104—42no—
386#103—42no—
387#100—22no—
388#100—22no—
389#99—24no—
390#99—24no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—44no—
395C2×C11—81no—
396C2×C11—82no—
397C2×C11#240411yescharacteristic
398C24—22no—
399C24C2×D4×C1112yes—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—44no—
407#41—44no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8C2×D4×C1112yes—
413C2×Q8C2×D4×C1111yescharacteristic
414C2×Q8C11×#4112yes—
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—24no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4C2×D4×C1111yescharacteristic
426C2×D4C2×D4×C1112yes—
427C2×D4C2×D4×C1112yes—
428C2×D4C11×#4112yes—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4C24×C1111yescharacteristic
438Q16—44no—
439Q16—42no—
440SD16—44no—
441SD16—42no—
442SD16—42no—
443D8—42no—
444M16—22no—
445M16—22no—
446M16—22no—
447M16—22no—
448C2×C8—22no—
449C2×C8—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—21no—
467C22⋊C4—22no—
468C22⋊C4—42no—
469C22⋊C4C2×D4×C1112yes—
470C22⋊C4C2×D4×C1112yes—
471C42—22no—
472C42—24no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—22no—
477C42C2×D4×C1111yescharacteristic
478C42C2×D4×C1111yescharacteristic
479C42C2×D4×C1112yes—
480C11#2400011yescharacteristic, direct product factor, Sylow
481C23—22no—
482C23—22no—
483C23—21no—
484C23—22no—
485C23—44no—
486C23—82no—
487C23—162no—
488C23C11×#12014yes—
489C23C22×D4×C1111yescharacteristic
490Q8—24no—
491Q8—22no—
492Q8—22no—
493Q8—22no—
494Q8—42no—
495Q8—82no—
496D4—24no—
497D4—24no—
498D4—22no—
499D4—22no—
500D4—22no—
501D4—48no—
502D4—42no—
503D4—41no—
504D4—42no—
505D4—41no—
506D4—84no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—44no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—84no—
524C2×C4—81no—
525C2×C4—162no—
526C2×C4C22×D4×C1111yescharacteristic
527C2×C4C22×D4×C1111yescharacteristic
528C2×C4C2×C11×#4112yes—
529C2×C4C11×H(5,𝔽2)12yes—
530C8—42no—
531C8—42no—
532C22—24no—
533C22—41no—
534C22—44no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—164no—
542C22C2×C11×#12011yescharacteristic
543C22C11×#52511yescharacteristic
544C22C11×#53511yescharacteristic
545C4—42no—
546C4—41no—
547C4—42no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—82no—
554C4C11×#54612yes—
555C4C11×#54612yes—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—44no—
560C2—81no—
561C2—82no—
562C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3019C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3510C2semidirect
3. C2×C11×#455C2semidirect
4. C11×#2883C2semidirect
5. C11×#2031C2semidirect
6. C11×#2009C2semidirect
7. C11×#1911C2semidirect
8. C11×#1906C2semidirect
9. C11×#1905C2semidirect
10. C11×#1885C2semidirect
11. C11×#1829C2semidirect
19. C11×#536C22semidirect
21. C11×#533C22semidirect
24. C11×#519C22semidirect
27. C4×C11×#41C22semidirect
33. C11×#421C22semidirect
35. C11×#419C22semidirect
41. C11×#344C22semidirect
42. C11×#344C22semidirect
43. C11×#339C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
117. #24000C11direct (N × H)
200. #3510C2×C11semidirect
202. C2×#455C2×C11semidirect
203. #2883C2×C11semidirect
204. #2031C2×C11semidirect
205. #2009C2×C11semidirect
206. #1911C2×C11semidirect
207. #1906C2×C11semidirect
208. #1905C2×C11semidirect
209. #1885C2×C11semidirect
210. #1829C2×C11semidirect
269. #536C22×C11semidirect
271. #533C22×C11semidirect
274. #519C22×C11semidirect
277. C4×#41C22×C11semidirect
283. #421C22×C11semidirect
285. #419C22×C11semidirect
291. #344C22×C11semidirect
292. #344C22×C11semidirect
293. #339C22×C11semidirect
294. H(3,ℤ/4)C22×C11semidirect
480. C11#24000direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35102
C11×#30192
C2×C11×#4552
C11×#28832
C11×#20312
C11×#20092
C11×#19112
C11×#19062
C11×#19052
C11×#18852
C11×#18292
#2400011