Finite Group Databasebeta

← C11×#24123 #14601316

Subgroups — C11×#24123 #14601316

Order 2816.

1090 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×#556C211yesmaximal, characteristic
2C2×C11×#475C211yesmaximal, characteristic, complemented
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2538C211yesmaximal, characteristic
5C11×#2035C212yesmaximal, complemented
6C11×#2001C212yesmaximal, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1954C211yesmaximal, characteristic
9C11×#1873C212yesmaximal, complemented
10C11×#1854C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C11×#556—24no—
14C11×#556—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2212yes—
25C11×#475—24no—
26C4×C11×Q16—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C11×#396—22no—
38C11×#390—21no—
39C11×#389—21no—
40C11×#384C2211yescharacteristic
41C11×#380C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11C2312yes—
50C2×C11×Q16—22no—
51C2×C11×Q16—22no—
52C2×C11×Q16—22no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yes—
58C11×#126—216no—
59C11×#124—28no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—42no—
64C4×Q8×C11—28no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11D414yes—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C11×#117—24no—
72C11×#117—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11—22no—
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C11×#107—22no—
95C11×#106—24no—
96C11×C4⋊C8—22no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#103—24no—
100C11×#103—42no—
101C11×C22⋊C8—24no—
102C11×C22⋊C8—42no—
103C4×C8×C11—22no—
104C11×#95—22no—
105#24123C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C2×D412yes—
107C2×Q8×C11—24no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11#4112yes—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C11×Q16—28no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—44no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—82no—
172C42×C11—28no—
173C42×C11—24no—
174C42×C11—42no—
175C42×C11C2×D412yes—
176C42×C11C2×D412yes—
177C2×#556C2×C1111yescharacteristic
178C2×#475C2×C1111yescharacteristic, complemented
179C2×C4×Q16C2×C1111yescharacteristic, complemented
180#2538C2×C1111yescharacteristic
181#2035C2×C1112yescomplemented
182#2001C2×C1112yescomplemented
183#1990C2×C1111yescharacteristic, complemented
184#1954C2×C1111yescharacteristic
185#1873C2×C1112yescomplemented
186#1854C2×C1112yescomplemented
187#1803C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11C22×D411yescharacteristic
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—41no—
204Q8×C11—48no—
205D4×C11—44no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11#12012yes—
234C2×C4×C11#12012yes—
235C2×C4×C11#13512yes—
236C2×C4×C11#13712yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C8×C11—22no—
244C8×C11—41no—
245C8×C11—42no—
246C22×Q16C22×C1111yescharacteristic
247#556—24no—
248#556—24no—
249C2×C4⋊Q8C22×C1111yescharacteristic
250C2×#126—22no—
251C2×#124—21no—
252C2×C22⋊Q8C22×C1112yes—
253C2×C22⋊Q8C22×C1112yes—
254C2×C4×Q8—21no—
255C2×C4×Q8C22×C1111yescharacteristic
256C2×C4×Q8C22×C1111yescharacteristic
257C2×C4×D4C22×C1111yescharacteristic
258C2×#117C22×C1112yes—
259#475—24no—
260C4×Q16—24no—
261C2×#107C22×C1111yescharacteristic
262C2×#106C22×C1112yes—
263C2×C4⋊C8C22×C1111yescharacteristic
264C2×#103C22×C1112yes—
265C2×#103C22×C1111yescharacteristic
266C2×#103C22×C1111yescharacteristic
267C2×#103C22×C1112yes—
268C2×C22⋊C8C22×C1112yes—
269C2×C22⋊C8C22×C1112yes—
270C2×C4×C8C22×C1111yescharacteristic
271#396—22no—
272#390—21no—
273#389—21no—
274#384C22×C1111yescharacteristic
275#380C22×C1112yes—
276#340C22×C1112yes—
277#340C22×C1112yes—
278#340C22×C1112yes—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11C2×#12011yescharacteristic
287C22×C11#54611yescharacteristic
288C22×C11#54711yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C22×C11#57711yescharacteristic
292C22×C11#57811yescharacteristic
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—81no—
300C4×C11—82no—
301C4×C11#45214yes—
302C4×C11#52511yescharacteristic
303C4×C11#53711yescharacteristic
304C4×C11#54811yescharacteristic
305C4×C11#55011yescharacteristic
306C22×Q8—21no—
307C22×Q8C23×C1111yescharacteristic
308C22×Q8C23×C1111yescharacteristic
309C22×D4D4×C1111yescharacteristic
310C23×C4C23×C1112yes—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—22no—
314C22×C8C23×C1111yescharacteristic
315C22×C8C23×C1112yes—
316C22×C8C23×C1111yescharacteristic
317C4⋊Q8—22no—
318C4⋊Q8D4×C1114yes—
319#126—216no—
320#124—28no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—42no—
325C4×Q8—28no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8D4×C1114yes—
330C4×D4—22no—
331C4×D4—22no—
332#117—24no—
333#117—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4D4×C1111yescharacteristic
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1111yescharacteristic
345C2×C4⋊C4C23×C1112yes—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4D4×C1112yes—
351C2×C42—22no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42C23×C1111yescharacteristic
355#107—22no—
356#106—24no—
357C4⋊C8—22no—
358#103—22no—
359#103—22no—
360#103—24no—
361#103—42no—
362C22⋊C8—24no—
363C22⋊C8—42no—
364C4×C8—22no—
365#95—22no—
366C2×C11—82no—
367C2×C11#240711yescharacteristic
368C2×C11C2×#45211yescharacteristic
369C2×C11#301311yescharacteristic
370C2×C11#330411yescharacteristic
371C2×C11#332811yescharacteristic
372C2×C11#334211yescharacteristic
373C2×C11#335611yescharacteristic
374C24C2×D4×C1112yes—
375C2×Q8—24no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8C2×D4×C1112yes—
389C2×Q8C11×#4112yes—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4C2×D4×C1112yes—
406C22×C4C2×D4×C1111yescharacteristic
407C22×C4C2×D4×C1111yescharacteristic
408C22×C4C24×C1111yescharacteristic
409Q16—28no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8C11×#4112yes—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—44no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C4⋊C4—81no—
433C4⋊C4C2×D4×C1114yes—
434C4⋊C4C2×D4×C1112yes—
435C22⋊C4—28no—
436C22⋊C4—28no—
437C22⋊C4—24no—
438C22⋊C4—44no—
439C22⋊C4—82no—
440C42—28no—
441C42—24no—
442C42—42no—
443C42C2×D4×C1112yes—
444C42C2×D4×C1112yes—
445C11#2412311yescharacteristic, direct product factor, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23C22×D4×C1111yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—22no—
457Q8—22no—
458Q8—41no—
459Q8—41no—
460Q8—41no—
461Q8—41no—
462Q8—48no—
463D4—44no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4C11×#12012yes—
492C2×C4C11×#12012yes—
493C2×C4C11×#13512yes—
494C2×C4C11×#13712yes—
495C2×C4C22×D4×C1111yescharacteristic
496C2×C4C22×D4×C1111yescharacteristic
497C2×C4C2×C11×#4111yescharacteristic
498C2×C4C2×C11×#4111yescharacteristic
499C2×C4C11×H(5,𝔽2)11yescharacteristic
500C2×C4C11×2−1+411yescharacteristic
501C8—22no—
502C8—41no—
503C8—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22C2×C11×#12011yescharacteristic
512C22C11×#54611yescharacteristic
513C22C11×#54711yescharacteristic
514C22C2×C11×#13511yescharacteristic
515C22C2×C11×#13711yescharacteristic
516C22C11×#57711yescharacteristic
517C22C11×#57811yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—81no—
525C4—82no—
526C4C11×#45214yes—
527C4C11×#52511yescharacteristic
528C4C11×#53711yescharacteristic
529C4C11×#54811yescharacteristic
530C4C11×#55011yescharacteristic
531C2—82no—
532C2C11×#240711yescharacteristic
533C2C2×C11×#45211yescharacteristic
534C2C11×#301311yescharacteristic
535C2C11×#330411yescharacteristic
536C2C11×#332811yescharacteristic
537C2C11×#334211yescharacteristic
538C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
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×C4×C11×Q16C2semidirect
5. C11×#2035C2semidirect
6. C11×#2001C2semidirect
7. C11×#1990C2semidirect
9. C11×#1873C2semidirect
10. C11×#1854C2semidirect
11. C11×#1803C2semidirect
105. #24123C11direct (N × H)
178. C2×#475C2×C11semidirect
179. C2×C4×Q16C2×C11semidirect
181. #2035C2×C11semidirect
182. #2001C2×C11semidirect
183. #1990C2×C11semidirect
185. #1873C2×C11semidirect
186. #1854C2×C11semidirect
187. #1803C2×C11semidirect
445. C11#24123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4752
C2×C4×C11×Q162
C11×#25382
C11×#20352
C11×#20012
C11×#19902
C11×#19542
C11×#18732
C11×#18542
C11×#18032
#2412311