Finite Group Databasebeta

← C11×#24133 #14601326

Subgroups — C11×#24133 #14601326

Order 2816.

1140 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#555C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic, complemented
4C11×#2536C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#2000C212yesmaximal, complemented
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1955C211yesmaximal, characteristic, complemented
9C11×#1873C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C11×#555—24no—
14C11×#555—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124—22no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117—21no—
24C2×C11×#117C2212yes—
25C11×#475—24no—
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×#97C2211yescharacteristic
37C11×#398—21no—
38C11×#394—21no—
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2312yes—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yes—
60C11×#124—216no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—42no—
63C11×#121—28no—
64C11×#121—24no—
65C11×#121—24no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11D414yes—
72C11×#117—28no—
73C11×#117—24no—
74C11×#117—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#107—22no—
93C11×#106—24no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—24no—
97C11×#102—22no—
98C11×#102—42no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—42no—
101C11×#97—22no—
102C11×#95—22no—
103C11×#95—21no—
104C11×#95—21no—
105#24133C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
107C24×C11C2×D412yes—
108C2×Q8×C11—24no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—82no—
115C2×Q8×C11#4112yes—
116C2×D4×C11—28no—
117C2×D4×C11—22no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—42no—
124C2×D4×C11—82no—
125C2×D4×C11—82no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—44no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C11×SD16—28no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C2×D414yes—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—44no—
172C42×C11—28no—
173C42×C11—42no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176C2×#555C2×C1111yescharacteristic
177C2×#475C2×C1111yescharacteristic, complemented
178C2×#440C2×C1111yescharacteristic, complemented
179#2536C2×C1111yescharacteristic, complemented
180#2034C2×C1112yescomplemented
181#2000C2×C1112yescomplemented
182#1993C2×C1111yescharacteristic, complemented
183#1955C2×C1111yescharacteristic, complemented
184#1873C2×C1112yescomplemented
185#1854C2×C1112yescomplemented
186#1804C2×C1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11C22×D411yescharacteristic
200Q8×C11—22no—
201Q8×C11—22no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—84no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—44no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—88no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—48no—
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—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C8×C11—22no—
243C8×C11—41no—
244C8×C11—42no—
245C22×SD16C22×C1111yescharacteristic
246#555—24no—
247#555—24no—
248C2×C4⋊Q8C22×C1111yescharacteristic
249C2×#124—22no—
250C2×C22⋊Q8C22×C1112yes—
251C2×#121—21no—
252C2×#121C22×C1112yes—
253C2×C4×Q8C22×C1111yescharacteristic
254C2×C4×D4C22×C1111yescharacteristic
255C2×C4×D4C22×C1111yescharacteristic
256C2×#117—21no—
257C2×#117C22×C1112yes—
258#475—24no—
259#440—24no—
260C2×#107C22×C1111yescharacteristic
261C2×#106C22×C1112yes—
262C2×C4⋊C8C22×C1111yescharacteristic
263C2×#103C22×C1112yes—
264C2×#103C22×C1111yescharacteristic
265C2×#102C22×C1111yescharacteristic
266C2×#102C22×C1112yes—
267C2×C22⋊C8C22×C1112yes—
268C2×C22⋊C8C22×C1112yes—
269C2×#97C22×C1111yescharacteristic
270#398—21no—
271#394—21no—
272#388—22no—
273#382C22×C1111yescharacteristic
274#380C22×C1112yes—
275#340C22×C1112yes—
276#340C22×C1112yes—
277#340C22×C1112yes—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11C2×#12011yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11#54711yescharacteristic
293C22×C11#57512yes—
294C22×C11#57712yes—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—44no—
301C4×C11—81no—
302C4×C11—82no—
303C4×C11#52511yescharacteristic
304C4×C11#53711yescharacteristic
305C4×C11#54811yescharacteristic
306C4×C11#55011yescharacteristic
307C22×Q8—21no—
308C22×Q8C23×C1111yescharacteristic
309C22×D4—22no—
310C22×D4D4×C1111yescharacteristic
311C22×D4C23×C1111yescharacteristic
312C23×C4—21no—
313C23×C4C23×C1112yes—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×SD16—22no—
317C22×C8C23×C1111yescharacteristic
318C22×C8C23×C1112yes—
319C22×C8C23×C1111yescharacteristic
320C4⋊Q8—22no—
321C4⋊Q8D4×C1114yes—
322#124—216no—
323C22⋊Q8—24no—
324C22⋊Q8—42no—
325#121—28no—
326#121—24no—
327#121—24no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4D4×C1114yes—
334#117—28no—
335#117—24no—
336#117—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4D4×C1111yescharacteristic
341C2×C4⋊C4C23×C1111yescharacteristic
342C2×C4⋊C4C23×C1112yes—
343C2×C4⋊C4C23×C1111yescharacteristic
344C2×C4⋊C4C23×C1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4D4×C1112yes—
351C2×C42—22no—
352C2×C42—21no—
353C2×C42C23×C1111yescharacteristic
354#107—22no—
355#106—24no—
356C4⋊C8—22no—
357#103—22no—
358#103—24no—
359#102—22no—
360#102—42no—
361C22⋊C8—24no—
362C22⋊C8—42no—
363#97—22no—
364#95—22no—
365#95—21no—
366#95—21no—
367C2×C11—82no—
368C2×C11—82no—
369C2×C11#240711yescharacteristic
370C2×C11#300511yescharacteristic
371C2×C11#300911yescharacteristic
372C2×C11#332112yes—
373C2×C11#334812yes—
374C24—21no—
375C24C2×D4×C1112yes—
376C2×Q8—24no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—82no—
383C2×Q8C11×#4112yes—
384C2×D4—28no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—82no—
393C2×D4—82no—
394C2×D4C2×D4×C1112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—44no—
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C24×C1111yescharacteristic
412SD16—28no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8C11×#4112yes—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—44no—
431C4⋊C4—42no—
432C4⋊C4C2×D4×C1114yes—
433C4⋊C4C2×D4×C1112yes—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—44no—
439C22⋊C4—44no—
440C42—28no—
441C42—42no—
442C42C2×D4×C1112yes—
443C42C2×D4×C1112yes—
444C11#2413311yescharacteristic, direct product factor, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23C22×D4×C1111yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—41no—
461Q8—41no—
462Q8—84no—
463D4—22no—
464D4—22no—
465D4—44no—
466D4—41no—
467D4—41no—
468D4—88no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—48no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4C11×#12012yes—
493C2×C4C11×#12012yes—
494C2×C4C22×D4×C1111yescharacteristic
495C2×C4C22×D4×C1111yescharacteristic
496C2×C4C2×C11×#4111yescharacteristic
497C2×C4C2×C11×#4111yescharacteristic
498C2×C4C11×H(5,𝔽2)11yescharacteristic
499C2×C4C11×2−1+411yescharacteristic
500C8—22no—
501C8—41no—
502C8—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—82no—
514C22—82no—
515C22C2×C11×#12011yescharacteristic
516C22C11×#54611yescharacteristic
517C22C11×#54711yescharacteristic
518C22C11×#57512yes—
519C22C11×#57712yes—
520C4—22no—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—44no—
526C4—81no—
527C4—82no—
528C4C11×#52511yescharacteristic
529C4C11×#53711yescharacteristic
530C4C11×#54811yescharacteristic
531C4C11×#55011yescharacteristic
532C2—82no—
533C2—82no—
534C2C11×#240711yescharacteristic
535C2C11×#300511yescharacteristic
536C2C11×#300911yescharacteristic
537C2C11×#332112yes—
538C2C11×#334812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#555C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#475C2semidirect
3. C2×C11×#440C2semidirect
4. C11×#2536C2semidirect
5. C11×#2034C2semidirect
6. C11×#2000C2semidirect
7. C11×#1993C2semidirect
8. C11×#1955C2semidirect
9. C11×#1873C2semidirect
10. C11×#1854C2semidirect
11. C11×#1804C2semidirect
105. #24133C11direct (N × H)
177. C2×#475C2×C11semidirect
178. C2×#440C2×C11semidirect
179. #2536C2×C11semidirect
180. #2034C2×C11semidirect
181. #2000C2×C11semidirect
182. #1993C2×C11semidirect
183. #1955C2×C11semidirect
184. #1873C2×C11semidirect
185. #1854C2×C11semidirect
186. #1804C2×C11semidirect
444. C11#24133direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5552
C2×C11×#4752
C2×C11×#4402
C11×#25362
C11×#20342
C11×#20002
C11×#19932
C11×#19552
C11×#18732
C11×#18542
C11×#18042
#2413311