Finite Group Databasebeta

← C11×#24527 #14601720

Subgroups — C11×#24527 #14601720

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#450C211yesmaximal, characteristic
2C22×C11×#102C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic, complemented
4D4×C11×C22⋊C4C211yesmaximal, characteristic
5C11×#2073C212yesmaximal, complemented
6C11×#2055C212yesmaximal, complemented
7C11×#1892C211yesmaximal, characteristic, complemented
8C11×#1877C212yesmaximal, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1823C211yesmaximal, characteristic, complemented
11C11×#1804C212yesmaximal, complemented
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C22×C11×SD16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×D4×C11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C11×#450—24no—
21C2×C11×C4⋊C8C2212yescomplemented
22C2×C11×#103C2212yescomplemented
23C2×C11×#102—24no—
24C2×C11×#102C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#400—22no—
30C11×#391C2212yescomplemented
31C11×#390C2212yes—
32C11×#386—22no—
33C11×#382C2212yescomplemented
34C11×#381—21no—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C11×#379—21no—
38C4×C11×C22⋊C4C2211yescharacteristic
39C11×#340C2212yescomplemented
40C11×#340C2212yescomplemented
41C11×#340C2212yescomplemented
42C11×#336C2212yescomplemented
43C25×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—24no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11D414yes—
50C22×D4×C11C2311yescharacteristic
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—24no—
58C2×C11×SD16—42no—
59C22×C8×C11—22no—
60C22×C8×C11—42no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2312yes—
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×D4×C11—24no—
67C4×D4×C11—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2312yes—
84C11×C4⋊C8—42no—
85C11×#103—42no—
86C11×#102—24no—
87C11×#102—24no—
88C11×#102—22no—
89C11×#102—22no—
90C11×C22⋊C8—22no—
91C11×#95—21no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95D412yes—
97#24527C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—24no—
101C24×C11—44no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—82no—
105C24×C11C2×D411yescharacteristic
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×D4×C11—28no—
111C2×D4×C11—24no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—44no—
118C2×D4×C11—48no—
119C2×D4×C11—44no—
120C2×D4×C11C2×D412yes—
121C2×D4×C11C2×D412yes—
122C2×D4×C11#4114yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—44no—
130C22×C4×C11—44no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—82no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C11×SD16—44no—
142C11×SD16—44no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—44no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—44no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—82no—
166C42×C11—22no—
167C42×C11—22no—
168C2×#450C2×C1111yescharacteristic
169C22×#102C2×C1111yescharacteristic
170#2503C2×C1111yescharacteristic, complemented
171D4×C22⋊C4C2×C1111yescharacteristic
172#2073C2×C1112yescomplemented
173#2055C2×C1112yescomplemented
174#1892C2×C1111yescharacteristic, complemented
175#1877C2×C1112yescomplemented
176#1850C2×C1111yescharacteristic, complemented
177#1823C2×C1111yescharacteristic, complemented
178#1804C2×C1112yescomplemented
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11—48no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—48no—
193C23×C11—84no—
194C23×C11—88no—
195C23×C11—88no—
196C23×C11#12112yes—
197C23×C11#13512yes—
198C23×C11AGL(1,ℤ/8)12yes—
199C23×C11C22×D411yescharacteristic
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—42no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—24no—
207D4×C11—48no—
208D4×C11—42no—
209D4×C11#12314yes—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—88no—
231C2×C4×C11—84no—
232C2×C4×C11#12112yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4112yes—
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C8×C11—41no—
238C8×C11—42no—
239C8×C11—41no—
240C23×D4C22×C1111yescharacteristic
241C22×SD16C22×C1111yescharacteristic
242C22×SD16C22×C1111yescharacteristic
243C23×C8C22×C1111yescharacteristic
244C2×C22⋊Q8C22×C1111yescharacteristic
245C2×C4×D4C22×C1112yes—
246C22×C4⋊C4C22×C1111yescharacteristic
247C22×C22⋊C4—21no—
248#450—24no—
249C2×C4⋊C8C22×C1112yescomplemented
250C2×#103C22×C1112yescomplemented
251C2×#102—24no—
252C2×#102C22×C1112yes—
253C2×#102C22×C1111yescharacteristic
254C2×#102C22×C1112yes—
255C2×#102C22×C1111yescharacteristic
256C2×C22⋊C8C22×C1111yescharacteristic
257#400—22no—
258#391C22×C1112yescomplemented
259#390C22×C1112yes—
260#386—22no—
261#382C22×C1112yescomplemented
262#381—21no—
263#381—21no—
264#380C22×C1111yescharacteristic
265#379—21no—
266C4×C22⋊C4C22×C1111yescharacteristic
267#340C22×C1112yescomplemented
268#340C22×C1112yescomplemented
269#340C22×C1112yescomplemented
270#336C22×C1112yescomplemented
271C22×C11—22no—
272C22×C11—24no—
273C22×C11—22no—
274C22×C11—24no—
275C22×C11—24no—
276C22×C11—42no—
277C22×C11—44no—
278C22×C11—42no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—816no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11#46314yes—
287C22×C11C2×#12111yescharacteristic
288C22×C11#54612yes—
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C11#57712yes—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—81no—
296C4×C11—82no—
297C4×C11—81no—
298C4×C11—82no—
299C4×C11C2×#12311yescharacteristic
300C4×C11#53411yescharacteristic
301C4×C11#55112yes—
302C25—21no—
303C22×Q8C23×C1111yescharacteristic
304C22×D4—24no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—42no—
308C22×D4D4×C1114yes—
309C22×D4C23×C1111yescharacteristic
310C22×D4C23×C1111yescharacteristic
311C23×C4—21no—
312C23×C4—22no—
313C23×C4C23×C1111yescharacteristic
314C2×SD16—22no—
315C2×SD16—22no—
316C2×SD16—24no—
317C2×SD16—42no—
318C22×C8—22no—
319C22×C8—42no—
320C22×C8C23×C1112yes—
321C22×C8C23×C1111yescharacteristic
322C22×C8C23×C1111yescharacteristic
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C4×D4—24no—
326C4×D4—42no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4D4×C1111yescharacteristic
341C2×C22⋊C4D4×C1111yescharacteristic
342C2×C42C23×C1112yes—
343C4⋊C8—42no—
344#103—42no—
345#102—24no—
346#102—24no—
347#102—22no—
348#102—22no—
349C22⋊C8—22no—
350#95—21no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95D4×C1112yes—
356C2×C11—24no—
357C2×C11—44no—
358C2×C11—82no—
359C2×C11#241211yescharacteristic
360C2×C11C2×#46311yescharacteristic
361C2×C11#304211yescharacteristic
362C2×C11#329612yes—
363C2×C11#331012yes—
364C24—21no—
365C24—21no—
366C24—24no—
367C24—44no—
368C24—42no—
369C24—42no—
370C24—82no—
371C24C2×D4×C1111yescharacteristic
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×D4—28no—
377C2×D4—24no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—44no—
384C2×D4—48no—
385C2×D4—44no—
386C2×D4C2×D4×C1112yes—
387C2×D4C2×D4×C1112yes—
388C2×D4C11×#4114yes—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—82no—
401C22×C4C2×D4×C1112yes—
402C22×C4C2×D4×C1112yes—
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1112yes—
405C22×C4C11×#4112yes—
406C22×C4C24×C1111yescharacteristic
407SD16—44no—
408SD16—44no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—44no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—44no—
428C22⋊C4—44no—
429C22⋊C4—42no—
430C22⋊C4—42no—
431C22⋊C4—82no—
432C42—22no—
433C42—22no—
434C11#2452711yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—48no—
441C23—41no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—41no—
446C23—41no—
447C23—42no—
448C23—48no—
449C23—84no—
450C23—88no—
451C23—88no—
452C23C11×#12112yes—
453C23C11×#13512yes—
454C23C11×AGL(1,ℤ/8)12yes—
455C23C22×D4×C1111yescharacteristic
456Q8—41no—
457Q8—41no—
458Q8—42no—
459D4—22no—
460D4—22no—
461D4—22no—
462D4—24no—
463D4—48no—
464D4—42no—
465D4C11×#12314yes—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—88no—
487C2×C4—84no—
488C2×C4C11×#12112yes—
489C2×C4C22×D4×C1111yescharacteristic
490C2×C4C2×C11×#4112yes—
491C2×C4C2×C11×#4111yescharacteristic
492C2×C4C11×H(5,𝔽2)12yes—
493C8—41no—
494C8—42no—
495C8—41no—
496C22—22no—
497C22—24no—
498C22—22no—
499C22—24no—
500C22—24no—
501C22—42no—
502C22—44no—
503C22—42no—
504C22—44no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—816no—
509C22—82no—
510C22—82no—
511C22C11×#46314yes—
512C22C2×C11×#12111yescharacteristic
513C22C11×#54612yes—
514C22C2×C11×#13511yescharacteristic
515C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
516C22C11×#57712yes—
517C4—22no—
518C4—42no—
519C4—42no—
520C4—81no—
521C4—82no—
522C4—81no—
523C4—82no—
524C4C2×C11×#12311yescharacteristic
525C4C11×#53411yescharacteristic
526C4C11×#55112yes—
527C2—24no—
528C2—44no—
529C2—82no—
530C2C11×#241211yescharacteristic
531C2C2×C11×#46311yescharacteristic
532C2C11×#304211yescharacteristic
533C2C11×#329612yes—
534C2C11×#331012yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC23×D4×C11C22
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
3. C11×#2503C2semidirect
5. C11×#2073C2semidirect
6. C11×#2055C2semidirect
7. C11×#1892C2semidirect
8. C11×#1877C2semidirect
9. C11×#1850C2semidirect
10. C11×#1823C2semidirect
11. C11×#1804C2semidirect
21. C2×C11×C4⋊C8C22semidirect
22. C2×C11×#103C22semidirect
30. C11×#391C22semidirect
33. C11×#382C22semidirect
39. C11×#340C22semidirect
40. C11×#340C22semidirect
41. C11×#340C22semidirect
42. C11×#336C22semidirect
97. #24527C11direct (N × H)
170. #2503C2×C11semidirect
172. #2073C2×C11semidirect
173. #2055C2×C11semidirect
174. #1892C2×C11semidirect
175. #1877C2×C11semidirect
176. #1850C2×C11semidirect
177. #1823C2×C11semidirect
178. #1804C2×C11semidirect
249. C2×C4⋊C8C22×C11semidirect
250. C2×#103C22×C11semidirect
258. #391C22×C11semidirect
261. #382C22×C11semidirect
267. #340C22×C11semidirect
268. #340C22×C11semidirect
269. #340C22×C11semidirect
270. #336C22×C11semidirect
434. C11#24527direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4502
C22×C11×#1022
C11×#25032
D4×C11×C22⋊C42
C11×#20732
C11×#20552
C11×#18922
C11×#18772
C11×#18502
C11×#18232
C11×#18042
#2452711