Finite Group Databasebeta

← C11×#24492 #14601685

Subgroups — C11×#24492 #14601685

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#482C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic, complemented
3C11×#2433C211yesmaximal, characteristic
4C11×#2347C211yesmaximal, characteristic, complemented
5C11×#2067C212yesmaximal, complemented
6C11×#2041C212yesmaximal, complemented
7C11×#1982C212yesmaximal, complemented
8C11×#1926C212yesmaximal, complemented
9C11×#1895C211yesmaximal, characteristic, complemented
10C11×#1851C211yesmaximal, characteristic, complemented
11C11×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#127C2212yes—
15C2×C11×#121C2211yescharacteristic
16C2×C11×#120—22no—
17C2×C11×#117C2211yescharacteristic
18C11×#482—24no—
19C2×C11×#107C2211yescharacteristic, complemented
20C2×C11×#106C2211yescharacteristic, complemented
21C2×C11×C4⋊C8C2212yescomplemented
22C11×#418—24no—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×#102C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic, complemented
29C2×C11×#102C2212yescomplemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C11×#392—21no—
32C11×#392—21no—
33C11×#390C2212yes—
34C11×#389C2212yescomplemented
35C11×#388—22no—
36C11×#383—21no—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yescomplemented
40C4×C11×C22⋊C4C2211yescharacteristic
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×D4×C11—24no—
45C22×D4×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—42no—
52C22×D4×C11C2311yescharacteristic
53C22×D4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C2×C11×M16—22no—
56C2×C11×M16—42no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C11×#127—24no—
61C11×#127—42no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#120—48no—
65C11×#117—22no—
66C11×#117D414yescomplemented
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2312yes—
81C11×#107—22no—
82C11×#106—22no—
83C11×C4⋊C8—42no—
84C11×#102—24no—
85C11×#102—24no—
86C11×#102—24no—
87C11×#102—22no—
88C11×#102—22no—
89C11×#102—42no—
90C11×#102—42no—
91C11×C22⋊C8—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95D411yescharacteristic
96C11×#95D411yescharacteristic
97#24492C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—22no—
99C24×C11—21no—
100C24×C11—44no—
101C24×C11—44no—
102C24×C11—42no—
103C24×C11—81no—
104C24×C11—81no—
105C24×C11C2×D411yescharacteristic
106C2×D4×C11—28no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—48no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—44no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11#4114yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C11×M16—44no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—44no—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—81no—
164C42×C11—24no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—82no—
168C2×#482C2×C1111yescharacteristic, complemented
169C2×#418C2×C1111yescharacteristic, complemented
170#2433C2×C1111yescharacteristic
171#2347C2×C1111yescharacteristic, complemented
172#2067C2×C1112yescomplemented
173#2041C2×C1112yescomplemented
174#1982C2×C1112yescomplemented
175#1926C2×C1112yescomplemented
176#1895C2×C1111yescharacteristic, complemented
177#1851C2×C1111yescharacteristic, complemented
178#1786C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—24no—
184C23×C11—48no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—84no—
197C23×C11—84no—
198C23×C11—88no—
199C23×C11—88no—
200C23×C11#12112yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—24no—
203D4×C11—24no—
204D4×C11—48no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—41no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—88no—
211D4×C11—88no—
212D4×C11—84no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11#12112yes—
233C2×C4×C11AGL(1,ℤ/8)14yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4112yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)12yes—
238C8×C11—41no—
239C8×C11—41no—
240C8×C11—42no—
241C23×D4C22×C1111yescharacteristic
242C22×M16C22×C1111yescharacteristic
243C2×#127C22×C1112yes—
244C2×#121C22×C1111yescharacteristic
245C2×#120—22no—
246C2×#117C22×C1111yescharacteristic
247#482—24no—
248C2×#107C22×C1111yescharacteristic, complemented
249C2×#106C22×C1111yescharacteristic, complemented
250C2×C4⋊C8C22×C1112yescomplemented
251#418—24no—
252C2×#102C22×C1112yes—
253C2×#102C22×C1112yes—
254C2×#102C22×C1112yes—
255C2×#102C22×C1112yes—
256C2×#102C22×C1111yescharacteristic, complemented
257C2×#102C22×C1111yescharacteristic, complemented
258C2×#102C22×C1112yescomplemented
259C2×C22⋊C8C22×C1111yescharacteristic
260#392—21no—
261#392—21no—
262#390C22×C1112yes—
263#389C22×C1112yescomplemented
264#388—22no—
265#383—21no—
266#380C22×C1111yescharacteristic
267C4×C4⋊C4—21no—
268C4×C4⋊C4C22×C1112yescomplemented
269C4×C22⋊C4C22×C1111yescharacteristic
270#340C22×C1112yescomplemented
271#336C22×C1112yescomplemented
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—44no—
280C22×C11—816no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11C2×#12111yescharacteristic
291C22×C11#54612yes—
292C22×C11C2×AGL(1,ℤ/8)12yes—
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C4×C11—22no—
296C4×C11—24no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—81no—
301C4×C11—82no—
302C4×C11#52511yescharacteristic
303C4×C11#53511yescharacteristic
304C4×C11#55112yes—
305C25—21no—
306C22×D4—24no—
307C22×D4—21no—
308C22×D4—22no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—42no—
314C22×D4C23×C1111yescharacteristic
315C22×D4C23×C1112yes—
316C23×C4C23×C1111yescharacteristic
317C2×M16—22no—
318C2×M16—42no—
319C22×C8C23×C1112yes—
320C22×C8C23×C1111yescharacteristic
321C22×C8C23×C1111yescharacteristic
322#127—24no—
323#127—42no—
324#121—22no—
325#121—22no—
326#120—48no—
327#117—22no—
328#117D4×C1114yescomplemented
329C2×C4⋊C4—22no—
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4D4×C1112yes—
340C2×C42—21no—
341C2×C42—22no—
342C2×C42C23×C1112yes—
343#107—22no—
344#106—22no—
345C4⋊C8—42no—
346#102—24no—
347#102—24no—
348#102—24no—
349#102—22no—
350#102—22no—
351#102—42no—
352#102—42no—
353C22⋊C8—22no—
354#95—21no—
355#95—22no—
356#95—22no—
357#95D4×C1111yescharacteristic
358#95D4×C1111yescharacteristic
359C2×C11—42no—
360C2×C11—84no—
361C2×C11—161no—
362C2×C11#241111yescharacteristic
363C2×C11#303811yescharacteristic
364C2×C11#304511yescharacteristic
365C2×C11#331812yes—
366C2×C11#332412yes—
367C24—22no—
368C24—21no—
369C24—44no—
370C24—44no—
371C24—42no—
372C24—81no—
373C24—81no—
374C24C2×D4×C1111yescharacteristic
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—48no—
386C2×D4—44no—
387C2×D4—44no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—44no—
395C2×D4—82no—
396C2×D4—82no—
397C2×D4C11×#4114yes—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C2×D4×C1112yes—
407C22×C4C2×D4×C1112yes—
408C22×C4C11×#4112yes—
409C22×C4C24×C1111yescharacteristic
410M16—44no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—44no—
425C4⋊C4C2×D4×C1112yes—
426C4⋊C4C2×D4×C1112yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—44no—
430C22⋊C4—42no—
431C22⋊C4—44no—
432C22⋊C4—81no—
433C42—24no—
434C42—22no—
435C42—22no—
436C42—82no—
437C11#2449211yescharacteristic, direct product factor, Sylow
438C23—22no—
439C23—22no—
440C23—21no—
441C23—21no—
442C23—24no—
443C23—48no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23—84no—
456C23—84no—
457C23—88no—
458C23—88no—
459C23C11×#12112yes—
460C23C22×D4×C1111yescharacteristic
461D4—24no—
462D4—24no—
463D4—48no—
464D4—41no—
465D4—42no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—88no—
470D4—88no—
471D4—84no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4C11×#12112yes—
492C2×C4C11×AGL(1,ℤ/8)14yes—
493C2×C4C22×D4×C1111yescharacteristic
494C2×C4C2×C11×#4112yes—
495C2×C4C2×C11×#4111yescharacteristic
496C2×C4C11×H(5,𝔽2)12yes—
497C8—41no—
498C8—42no—
499C8—41no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—816no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—82no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22C2×C11×#12111yescharacteristic
519C22C11×#54612yes—
520C22C2×C11×AGL(1,ℤ/8)12yes—
521C22C11×#57611yescharacteristic
522C22C11×#57711yescharacteristic
523C4—22no—
524C4—24no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—82no—
530C4C11×#52511yescharacteristic
531C4C11×#53511yescharacteristic
532C4C11×#55112yes—
533C2—42no—
534C2—84no—
535C2—161no—
536C2C11×#241111yescharacteristic
537C2C11×#303811yescharacteristic
538C2C11×#304511yescharacteristic
539C2C11×#331812yes—
540C2C11×#332412yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#482C2semidirect
2. C2×C11×#418C2semidirect
4. C11×#2347C2semidirect
5. C11×#2067C2semidirect
6. C11×#2041C2semidirect
7. C11×#1982C2semidirect
8. C11×#1926C2semidirect
9. C11×#1895C2semidirect
10. C11×#1851C2semidirect
11. C11×#1786C2semidirect
19. C2×C11×#107C22semidirect
20. C2×C11×#106C22semidirect
21. C2×C11×C4⋊C8C22semidirect
27. C2×C11×#102C22semidirect
28. C2×C11×#102C22semidirect
29. C2×C11×#102C22semidirect
34. C11×#389C22semidirect
39. C4×C11×C4⋊C4C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
66. C11×#117D4semidirect
97. #24492C11direct (N × H)
168. C2×#482C2×C11semidirect
169. C2×#418C2×C11semidirect
171. #2347C2×C11semidirect
172. #2067C2×C11semidirect
173. #2041C2×C11semidirect
174. #1982C2×C11semidirect
175. #1926C2×C11semidirect
176. #1895C2×C11semidirect
177. #1851C2×C11semidirect
178. #1786C2×C11semidirect
248. C2×#107C22×C11semidirect
249. C2×#106C22×C11semidirect
250. C2×C4⋊C8C22×C11semidirect
256. C2×#102C22×C11semidirect
257. C2×#102C22×C11semidirect
258. C2×#102C22×C11semidirect
263. #389C22×C11semidirect
268. C4×C4⋊C4C22×C11semidirect
270. #340C22×C11semidirect
271. #336C22×C11semidirect
328. #117D4×C11semidirect
437. C11#24492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4822
C2×C11×#4182
C11×#24332
C11×#23472
C11×#20672
C11×#20412
C11×#19822
C11×#19262
C11×#18952
C11×#18512
C11×#17862
#2449211