Finite Group Databasebeta

← C11×#24190 #14601383

Subgroups — C11×#24190 #14601383

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
4C11×#2582C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1984C211yesmaximal, characteristic, complemented
8C11×#1957C211yesmaximal, characteristic
9C11×#1877C212yesmaximal, complemented
10C11×#1862C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C11×#559—24no—
15C11×#559—24no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#124C2212yes—
19C2×C11×#123—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2212yes—
25C11×#460—24no—
26C4×C11×Q16—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#398—22no—
37C11×#391—21no—
38C11×#391C2212yes—
39C11×#389—21no—
40C11×#389C2212yes—
41C11×#384C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C23×C4×C11—22no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—22no—
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#127—22no—
62C11×#127D414yes—
63C11×#124—28no—
64C11×#124—24no—
65C11×#124—24no—
66C11×#123—216no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11D414yes—
73C4×D4×C11—28no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C11×#107—22no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—22no—
97C11×#103—42no—
98C11×#102—24no—
99C11×#102—24no—
100C11×#102—42no—
101C4×C8×C11—22no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#24190C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
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—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C2×D412yes—
121C2×Q8×C11#4112yes—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11—81no—
132C2×D4×C11—81no—
133C2×D4×C11C2×D414yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—28no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—82no—
141C22×C4×C11—82no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C11×Q16—28no—
148C11×SD16—48no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11#4112yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4—82no—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—28no—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—42no—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C2×#559C2×C1111yescharacteristic
181C2×#460C2×C1111yescharacteristic
182C2×C4×Q16C2×C1111yescharacteristic, complemented
183#2582C2×C1111yescharacteristic, complemented
184#2042C2×C1112yescomplemented
185#2015C2×C1112yescomplemented
186#1984C2×C1111yescharacteristic, complemented
187#1957C2×C1111yescharacteristic
188#1877C2×C1112yescomplemented
189#1862C2×C1112yescomplemented
190#1803C2×C1111yescharacteristic, complemented
191C23×C11—24no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C22×D411yescharacteristic
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—22no—
202Q8×C11—22no—
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—44no—
208D4×C11—24no—
209D4×C11—24no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—48no—
213D4×C11—84no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—88no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12012yes—
240C2×C4×C11#13512yes—
241C2×C4×C11#13712yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C8×C11—22no—
249C8×C11—41no—
250C8×C11—42no—
251C22×Q16C22×C1111yescharacteristic
252C22×SD16C22×C1112yes—
253#559—24no—
254#559—24no—
255C2×#127C22×C1111yescharacteristic
256C2×#124—21no—
257C2×#124C22×C1112yes—
258C2×#123—22no—
259C2×C4×Q8C22×C1111yescharacteristic
260C2×C4×Q8C22×C1111yescharacteristic
261C2×C4×Q8C22×C1111yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C22×C1112yes—
264#460—24no—
265C4×Q16—24no—
266C2×#107C22×C1111yescharacteristic
267C2×C4⋊C8C22×C1111yescharacteristic
268C2×#103C22×C1111yescharacteristic
269C2×#103C22×C1111yescharacteristic
270C2×#103C22×C1112yes—
271C2×#102C22×C1112yes—
272C2×#102C22×C1112yes—
273C2×#102C22×C1112yes—
274C2×C4×C8C22×C1111yescharacteristic
275#398—22no—
276#391—21no—
277#391C22×C1112yes—
278#389—21no—
279#389C22×C1112yes—
280#384C22×C1111yescharacteristic
281#340C22×C1112yes—
282#336C22×C1112yes—
283#336C22×C1112yes—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11C2×#12011yescharacteristic
292C22×C11#54811yescharacteristic
293C22×C11#55011yescharacteristic
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×#13711yescharacteristic
296C22×C11#57611yescharacteristic
297C22×C11#57711yescharacteristic
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—82no—
305C4×C11—81no—
306C4×C11#45214yes—
307C4×C11#52511yescharacteristic
308C4×C11#53711yescharacteristic
309C4×C11#54611yescharacteristic
310C4×C11#54711yescharacteristic
311C22×Q8D4×C1111yescharacteristic
312C22×Q8C23×C1111yescharacteristic
313C22×Q8C23×C1111yescharacteristic
314C22×D4—21no—
315C22×D4—21no—
316C22×D4C23×C1112yes—
317C23×C4—22no—
318C2×Q16—22no—
319C2×Q16—22no—
320C2×Q16—22no—
321C2×SD16—24no—
322C2×SD16—24no—
323C2×SD16—42no—
324C22×C8C23×C1112yes—
325C22×C8C23×C1111yescharacteristic
326C22×C8C23×C1111yescharacteristic
327#127—22no—
328#127D4×C1114yes—
329#124—28no—
330#124—24no—
331#124—24no—
332#123—216no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8D4×C1114yes—
339C4×D4—28no—
340C4×D4—24no—
341C4×D4—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4D4×C1111yescharacteristic
348C2×C4⋊C4D4×C1112yes—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C4⋊C4C23×C1112yes—
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42C23×C1112yes—
358C2×C42C23×C1111yescharacteristic
359#107—22no—
360C4⋊C8—22no—
361#103—22no—
362#103—22no—
363#103—42no—
364#102—24no—
365#102—24no—
366#102—42no—
367C4×C8—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371C2×C11—84no—
372C2×C11#240711yescharacteristic
373C2×C11C2×#45211yescharacteristic
374C2×C11#301211yescharacteristic
375C2×C11#336511yescharacteristic
376C2×C11#337511yescharacteristic
377C2×C11#339611yescharacteristic
378C2×C11#340011yescharacteristic
379C24—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C2×D4×C1112yes—
394C2×Q8C11×#4112yes—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4C2×D4×C1114yes—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—28no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4C2×D4×C1112yes—
416C22×C4C2×D4×C1112yes—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C24×C1111yescharacteristic
420Q16—28no—
421SD16—48no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—21no—
428C2×C8—22no—
429C2×C8—21no—
430C2×C8C11×#4112yes—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4—81no—
442C4⋊C4—82no—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—28no—
445C22⋊C4—28no—
446C22⋊C4—28no—
447C42—24no—
448C42—22no—
449C42—22no—
450C42—42no—
451C42C2×D4×C1112yes—
452C42C2×D4×C1112yes—
453C11#2419011yescharacteristic, direct product factor, Sylow
454C23—24no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22×D4×C1111yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—22no—
465Q8—22no—
466Q8—41no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—44no—
471D4—24no—
472D4—24no—
473D4—42no—
474D4—42no—
475D4—48no—
476D4—84no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—88no—
501C2×C4C11×#12012yes—
502C2×C4C11×#12012yes—
503C2×C4C11×#13512yes—
504C2×C4C11×#13712yes—
505C2×C4C22×D4×C1111yescharacteristic
506C2×C4C22×D4×C1111yescharacteristic
507C2×C4C2×C11×#4111yescharacteristic
508C2×C4C2×C11×#4111yescharacteristic
509C2×C4C11×H(5,𝔽2)11yescharacteristic
510C2×C4C11×2−1+411yescharacteristic
511C8—22no—
512C8—41no—
513C8—42no—
514C22—44no—
515C22—44no—
516C22—44no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22C2×C11×#12011yescharacteristic
522C22C11×#54811yescharacteristic
523C22C11×#55011yescharacteristic
524C22C2×C11×#13511yescharacteristic
525C22C2×C11×#13711yescharacteristic
526C22C11×#57611yescharacteristic
527C22C11×#57711yescharacteristic
528C4—22no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—81no—
535C4—82no—
536C4C11×#45214yes—
537C4C11×#52511yescharacteristic
538C4C11×#53711yescharacteristic
539C4C11×#54611yescharacteristic
540C4C11×#54711yescharacteristic
541C2—84no—
542C2C11×#240711yescharacteristic
543C2C2×C11×#45211yescharacteristic
544C2C11×#301211yescharacteristic
545C2C11×#336511yescharacteristic
546C2C11×#337511yescharacteristic
547C2C11×#339611yescharacteristic
548C2C11×#340011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×Q16C2semidirect
4. C11×#2582C2semidirect
5. C11×#2042C2semidirect
6. C11×#2015C2semidirect
7. C11×#1984C2semidirect
9. C11×#1877C2semidirect
10. C11×#1862C2semidirect
11. C11×#1803C2semidirect
105. #24190C11direct (N × H)
182. C2×C4×Q16C2×C11semidirect
183. #2582C2×C11semidirect
184. #2042C2×C11semidirect
185. #2015C2×C11semidirect
186. #1984C2×C11semidirect
188. #1877C2×C11semidirect
189. #1862C2×C11semidirect
190. #1803C2×C11semidirect
453. C11#24190direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C2×C11×#4602
C2×C4×C11×Q162
C11×#25822
C11×#20422
C11×#20152
C11×#19842
C11×#19572
C11×#18772
C11×#18622
C11×#18032
#2419011