Finite Group Databasebeta

← C11×#24423 #14601616

Subgroups — C11×#24423 #14601616

Order 2816.

1284 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×#3586C211yesmaximal, characteristic
2C11×#3069C212yesmaximal, complemented
3C11×#3022C211yesmaximal, characteristic, complemented
4C11×#3011C211yesmaximal, characteristic, complemented
5C11×#2889C211yesmaximal, characteristic, complemented
6C11×#2049C212yesmaximal, complemented
7C11×#2020C212yesmaximal, complemented
8C11×#1915C211yesmaximal, characteristic, complemented
9C11×#1881C212yesmaximal, complemented
10C11×#1858C211yesmaximal, characteristic, complemented
11C11×#1791C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13C2×C11×2−1+4C2211yescharacteristic
14C11×#578—24no—
15C11×#577—24no—
16C11×#575—22no—
17C11×#575C2212yes—
18C2×C11×#137—22no—
19C2×C11×#137C2212yes—
20C2×C11×#137C2212yes—
21C2×C11×#137C2211yescharacteristic, complemented
22C22×C11×Q16C2211yescharacteristic, complemented
23C11×#568C2211yescharacteristic
24C11×#568C2212yescomplemented
25C11×#536C2211yescharacteristic
26C11×#473—24no—
27C11×#471—24no—
28C11×#456—22no—
29C11×#455—22no—
30C11×#452—22no—
31C11×#451—22no—
32C11×#430C2212yescomplemented
33C11×#421C2212yes—
34C11×#419C2211yescharacteristic, complemented
35C11×#416C2211yescharacteristic, complemented
36C11×#413—22no—
37C11×#413C2211yescharacteristic
38C11×#413C2212yes—
39C11×#413C2211yescharacteristic
40C2×C11×#101—22no—
41C2×C11×#101C2212yescomplemented
42C2×C11×#101C2212yescomplemented
43C11×#408C2211yescharacteristic
44C11×#408C2212yes—
45C11×#344C2212yescomplemented
46C11×#341C2212yescomplemented
47C11×2−1+4—24no—
48C11×2−1+4—22no—
49C11×2−1+4—21no—
50C11×2−1+4—42no—
51C11×H(5,𝔽2)—22no—
52C11×H(5,𝔽2)—22no—
53C11×H(5,𝔽2)—21no—
54C2×C11×#41—21no—
55C2×C11×#41—22no—
56C2×C11×#41—22no—
57C2×C11×#41—42no—
58C2×C11×#41D412yes—
59C2×C11×#41C2312yes—
60C2×C11×#41C2311yescharacteristic
61C2×C11×#41C2311yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11D412yes—
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C11×#137—28no—
67C11×#137—24no—
68C11×#137—22no—
69C11×#137—24no—
70C11×#137—24no—
71C11×#137—24no—
72C11×#137—24no—
73C11×#137—42no—
74C11×#137D414yes—
75C11×AGL(1,ℤ/8)—24no—
76C11×AGL(1,ℤ/8)—22no—
77C11×AGL(1,ℤ/8)D414yes—
78C11×#135—28no—
79C11×#135—24no—
80C2×C11×Q16—24no—
81C2×C11×Q16—22no—
82C2×C11×Q16—22no—
83C2×C11×Q16—22no—
84C2×C11×Q16—21no—
85C2×C11×Q16—42no—
86C2×C11×SD16—24no—
87C2×C11×SD16—22no—
88C2×C11×SD16—22no—
89C2×C11×SD16—21no—
90C11×#131—24no—
91C11×#131—24no—
92C11×#131—42no—
93C2×C11×M16—22no—
94C2×C11×M16—24no—
95C2×C11×M16C2312yes—
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2312yes—
98C2×C11×M16C2312yes—
99C22×C8×C11C2311yescharacteristic
100C11×C4⋊Q8—21no—
101C11×#124—21no—
102C11×#123—22no—
103C11×C22⋊Q8—22no—
104C11×#117C2311yescharacteristic
105C11×#108—24no—
106C11×#104—24no—
107C11×#103—21no—
108C11×#103—22no—
109C11×#102—21no—
110C11×#101—21no—
111C11×#101—22no—
112C11×#101—24no—
113C11×#101—24no—
114C11×#101D412yes—
115C11×#100—21no—
116C11×#100—22no—
117C11×#100D412yes—
118C11×C22⋊C8—22no—
119C11×C22⋊C8—42no—
120#24423C1111yesmaximal, characteristic, direct product factor, Sylow
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—24no—
125C11×#41—24no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—42no—
131C11×#41—44no—
132C11×#41—44no—
133C11×#41—42no—
134C11×#41—48no—
135C11×#41—42no—
136C11×#41—42no—
137C11×#41—42no—
138C11×#41C2×D414yes—
139C2×Q8×C11—22no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—42no—
152C2×Q8×C11C2×D412yes—
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—42no—
161C2×D4×C11—44no—
162C2×D4×C11—42no—
163C2×D4×C11C2×D412yes—
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11#4112yes—
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—42no—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C11×Q16—28no—
177C11×Q16—24no—
178C11×Q16—44no—
179C11×Q16—44no—
180C11×Q16—42no—
181C11×SD16—28no—
182C11×SD16—24no—
183C11×SD16—24no—
184C11×SD16—44no—
185C11×SD16—42no—
186C11×D8—24no—
187C11×M16—24no—
188C11×M16—22no—
189C11×M16—22no—
190C11×M16—22no—
191C11×M16—22no—
192C11×M16—22no—
193C11×M16—44no—
194C11×M16C2×D414yes—
195C11×M16C2×D414yes—
196C2×C8×C11—24no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11—44no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—42no—
208C42×C11—21no—
209#3586C2×C1111yescharacteristic
210#3069C2×C1112yescomplemented
211#3022C2×C1111yescharacteristic, complemented
212#3011C2×C1111yescharacteristic, complemented
213#2889C2×C1111yescharacteristic, complemented
214#2049C2×C1112yescomplemented
215#2020C2×C1112yescomplemented
216#1915C2×C1111yescharacteristic, complemented
217#1881C2×C1112yescomplemented
218#1858C2×C1111yescharacteristic, complemented
219#1791C2×C1111yescharacteristic, complemented
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11#12112yes—
224C23×C11C2×#4111yescharacteristic
225Q8×C11—21no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—44no—
232Q8×C11—42no—
233Q8×C11—42no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—42no—
237Q8×C11#12012yes—
238D4×C11—24no—
239D4×C11—24no—
240D4×C11—22no—
241D4×C11—21no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—42no—
245D4×C11—44no—
246D4×C11—44no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11#12012yes—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—44no—
257C2×C4×C11—44no—
258C2×C4×C11—44no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11#12112yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11H(5,𝔽2)12yes—
271C8×C11—24no—
272C8×C11—24no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—42no—
276#585C22×C1111yescharacteristic
277C2×2−1+4C22×C1111yescharacteristic
278#578—24no—
279#577—24no—
280#575—22no—
281#575C22×C1112yes—
282C2×#137—22no—
283C2×#137C22×C1112yes—
284C2×#137C22×C1112yes—
285C2×#137C22×C1111yescharacteristic, complemented
286C22×Q16C22×C1111yescharacteristic, complemented
287#568C22×C1111yescharacteristic
288#568C22×C1112yescomplemented
289#536C22×C1111yescharacteristic
290#473—24no—
291#471—24no—
292#456—22no—
293#455—22no—
294#452—22no—
295#451—22no—
296#430C22×C1112yescomplemented
297#421C22×C1112yes—
298#419C22×C1111yescharacteristic, complemented
299#416C22×C1111yescharacteristic, complemented
300#413—22no—
301#413C22×C1112yes—
302#413C22×C1111yescharacteristic
303#413C22×C1111yescharacteristic
304C2×#101—22no—
305C2×#101C22×C1112yescomplemented
306C2×#101C22×C1112yescomplemented
307#408C22×C1111yescharacteristic
308#408C22×C1112yes—
309#344C22×C1112yescomplemented
310#341C22×C1112yescomplemented
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—82no—
318C22×C11—162no—
319C22×C11C2×#12111yescharacteristic
320C22×C11#54612yes—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11C2×#12011yescharacteristic
328C4×C11#53411yescharacteristic
329C4×C11D4212yes—
3302−1+4—24no—
3312−1+4—22no—
3322−1+4—21no—
3332−1+4—42no—
334H(5,𝔽2)—22no—
335H(5,𝔽2)—22no—
336H(5,𝔽2)—21no—
337C2×#41—21no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—42no—
341C2×#41D4×C1112yes—
342C2×#41C23×C1112yes—
343C2×#41C23×C1111yescharacteristic
344C2×#41C23×C1111yescharacteristic
345C22×Q8—21no—
346C22×Q8D4×C1112yes—
347C22×Q8C23×C1111yescharacteristic
348C22×Q8C23×C1111yescharacteristic
349#137—28no—
350#137—24no—
351#137—22no—
352#137—24no—
353#137—24no—
354#137—24no—
355#137—24no—
356#137—42no—
357#137D4×C1114yes—
358AGL(1,ℤ/8)—24no—
359AGL(1,ℤ/8)—22no—
360AGL(1,ℤ/8)D4×C1114yes—
361#135—28no—
362#135—24no—
363C2×Q16—24no—
364C2×Q16—22no—
365C2×Q16—22no—
366C2×Q16—22no—
367C2×Q16—21no—
368C2×Q16—42no—
369C2×SD16—24no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16—21no—
373#131—24no—
374#131—24no—
375#131—42no—
376C2×M16—22no—
377C2×M16—24no—
378C2×M16C23×C1112yes—
379C2×M16C23×C1111yescharacteristic
380C2×M16C23×C1112yes—
381C2×M16C23×C1112yes—
382C22×C8C23×C1111yescharacteristic
383C4⋊Q8—21no—
384#124—21no—
385#123—22no—
386C22⋊Q8—22no—
387#117C23×C1111yescharacteristic
388#108—24no—
389#104—24no—
390#103—21no—
391#103—22no—
392#102—21no—
393#101—21no—
394#101—22no—
395#101—24no—
396#101—24no—
397#101D4×C1112yes—
398#100—21no—
399#100—22no—
400#100D4×C1112yes—
401C22⋊C8—22no—
402C22⋊C8—42no—
403C2×C11—21no—
404C2×C11—22no—
405C2×C11—42no—
406C2×C11—42no—
407C2×C11—82no—
408C2×C11#241011yescharacteristic
409#41—22no—
410#41—22no—
411#41—22no—
412#41—24no—
413#41—24no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—42no—
419#41—44no—
420#41—44no—
421#41—42no—
422#41—48no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41C2×D4×C1114yes—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—42no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8C2×D4×C1112yes—
441C2×Q8C2×D4×C1112yes—
442C2×Q8C2×D4×C1111yescharacteristic
443C2×Q8C2×D4×C1111yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—42no—
451C2×D4C2×D4×C1112yes—
452C2×D4C2×D4×C1111yescharacteristic
453C2×D4C2×D4×C1111yescharacteristic
454C2×D4C11×#4112yes—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—42no—
462C22×C4C2×D4×C1112yes—
463C22×C4C24×C1111yescharacteristic
464Q16—28no—
465Q16—24no—
466Q16—44no—
467Q16—44no—
468Q16—42no—
469SD16—28no—
470SD16—24no—
471SD16—24no—
472SD16—44no—
473SD16—42no—
474D8—24no—
475M16—24no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—44no—
482M16C2×D4×C1114yes—
483M16C2×D4×C1114yes—
484C2×C8—24no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—44no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C22⋊C4—21no—
495C22⋊C4—42no—
496C42—21no—
497C11#2442311yescharacteristic, direct product factor, Sylow
498C23—21no—
499C23—22no—
500C23—42no—
501C23C11×#12112yes—
502C23C2×C11×#4111yescharacteristic
503Q8—21no—
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8—22no—
508Q8—22no—
509Q8—44no—
510Q8—42no—
511Q8—42no—
512Q8—41no—
513Q8—41no—
514Q8—42no—
515Q8C11×#12012yes—
516D4—24no—
517D4—24no—
518D4—22no—
519D4—21no—
520D4—22no—
521D4—22no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—42no—
526D4—42no—
527D4C11×#12012yes—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4C11×#12112yes—
545C2×C4C22×D4×C1111yescharacteristic
546C2×C4C22×D4×C1112yes—
547C2×C4C22×D4×C1111yescharacteristic
548C2×C4C11×H(5,𝔽2)12yes—
549C8—24no—
550C8—24no—
551C8—41no—
552C8—41no—
553C8—42no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—82no—
561C22—162no—
562C22C2×C11×#12111yescharacteristic
563C22C11×#54612yes—
564C4—22no—
565C4—22no—
566C4—42no—
567C4—42no—
568C4—81no—
569C4—81no—
570C4C2×C11×#12011yescharacteristic
571C4C11×#53411yescharacteristic
572C4D42×C1112yes—
573C2—21no—
574C2—22no—
575C2—42no—
576C2—42no—
577C2—82no—
578C2C11×#241011yescharacteristic
subgroupG/H
center, socleC2×C11#2410
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3586C2
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
2. C11×#3069C2semidirect
3. C11×#3022C2semidirect
4. C11×#3011C2semidirect
5. C11×#2889C2semidirect
6. C11×#2049C2semidirect
7. C11×#2020C2semidirect
8. C11×#1915C2semidirect
9. C11×#1881C2semidirect
10. C11×#1858C2semidirect
11. C11×#1791C2semidirect
21. C2×C11×#137C22semidirect
22. C22×C11×Q16C22semidirect
24. C11×#568C22semidirect
32. C11×#430C22semidirect
34. C11×#419C22semidirect
35. C11×#416C22semidirect
41. C2×C11×#101C22semidirect
42. C2×C11×#101C22semidirect
45. C11×#344C22semidirect
46. C11×#341C22semidirect
120. #24423C11direct (N × H)
210. #3069C2×C11semidirect
211. #3022C2×C11semidirect
212. #3011C2×C11semidirect
213. #2889C2×C11semidirect
214. #2049C2×C11semidirect
215. #2020C2×C11semidirect
216. #1915C2×C11semidirect
217. #1881C2×C11semidirect
218. #1858C2×C11semidirect
219. #1791C2×C11semidirect
285. C2×#137C22×C11semidirect
286. C22×Q16C22×C11semidirect
288. #568C22×C11semidirect
296. #430C22×C11semidirect
298. #419C22×C11semidirect
299. #416C22×C11semidirect
305. C2×#101C22×C11semidirect
306. C2×#101C22×C11semidirect
309. #344C22×C11semidirect
310. #341C22×C11semidirect
497. C11#24423direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35862
C11×#30692
C11×#30222
C11×#30112
C11×#28892
C11×#20492
C11×#20202
C11×#19152
C11×#18812
C11×#18582
C11×#17912
#2442311