Finite Group Databasebeta

← C11×#22572 #14599765

Subgroups — C11×#22572 #14599765

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#416C211yesmaximal, characteristic
2C11×#2346C211yesmaximal, characteristic, complemented
3C11×#2339C211yesmaximal, characteristic
4C11×#1933C212yesmaximal, complemented
5C11×#1927C212yesmaximal, complemented
6C11×#1864C212yesmaximal, complemented
7C11×#1825C211yesmaximal, characteristic, complemented
8C11×#1807C211yesmaximal, characteristic, complemented
9C11×#1788C211yesmaximal, characteristic
10C4×C11×#102C212yesmaximal, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C2×C11×#117C2211yescharacteristic
16C2×C11×#106C2212yes—
17C11×#416C418yescomplemented
18C2×C11×#103C2212yes—
19C2×C11×#103C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2212yes—
26C11×#391C2212yes—
27C11×#389C2212yes—
28C11×#388—22no—
29C11×#386—22no—
30C11×#382—21no—
31C11×#381—21no—
32C11×#380C2211yescharacteristic
33C11×#380C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C22⋊C4C2211yescharacteristic
36C11×#376—21no—
37C2×C11×#95—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#336C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11—42no—
53C22×C8×C11C2×C414yescomplemented
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C4×D4×C11—24no—
58C4×D4×C11—42no—
59C11×#117—22no—
60C11×#117C2×C414yescomplemented
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4D412yes—
71C2×C42×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C11×#106—42no—
75C11×#103—42no—
76C11×#103C2×C414yescomplemented
77C11×#103C2×C414yescomplemented
78C11×#102—24no—
79C11×#102C2×C414yes—
80C11×#102C2×C414yes—
81C11×C22⋊C8—22no—
82C4×C8×C11—42no—
83C11×#95—21no—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#22572C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C11×#41—28no—
95C11×#41—44no—
96C11×#41—48no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11C22×C412yes—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11#4114yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—44no—
116C22×C4×C11—44no—
117C22×C4×C11—44no—
118C22×C4×C11—82no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—44no—
131C2×C8×C11C22×C412yes—
132C2×C8×C11C22×C412yes—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—82no—
140C11×C4⋊C4C22×C412yes—
141C11×C4⋊C4C22×C412yes—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—81no—
146C11×C22⋊C4—81no—
147C42×C11—24no—
148C42×C11—22no—
149C42×C11—22no—
150C42×C11—44no—
151C2×#416C2×C1111yescharacteristic
152#2346C2×C1111yescharacteristic, complemented
153#2339C2×C1111yescharacteristic
154#1933C2×C1112yescomplemented
155#1927C2×C1112yescomplemented
156#1864C2×C1112yescomplemented
157#1825C2×C1111yescharacteristic, complemented
158#1807C2×C1111yescharacteristic, complemented
159#1788C2×C1111yescharacteristic
160C4×#102C2×C1112yescomplemented
161C8×C22⋊C4C2×C1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—24no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—42no—
176D4×C11—22no—
177D4×C11—24no—
178D4×C11—48no—
179D4×C11#11714yes—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—48no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—88no—
204C2×C4×C11C4×D412yes—
205C2×C4×C11#13514yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C2×#4112yes—
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)12yes—
210C8×C11—22no—
211C8×C11—22no—
212C8×C11—42no—
213C22×#41C22×C1111yescharacteristic
214C23×C8C22×C1111yescharacteristic
215C2×C4×D4C22×C1112yes—
216C2×#117C22×C1111yescharacteristic
217C2×#106C22×C1112yes—
218#416C4×C1118yescomplemented
219C2×#103C22×C1112yes—
220C2×#103C22×C1111yescharacteristic
221C2×#103C22×C1111yescharacteristic
222C2×#102C22×C1112yes—
223C2×#102C22×C1111yescharacteristic
224C2×#102C22×C1111yescharacteristic
225C2×C22⋊C8C22×C1111yescharacteristic
226C2×C4×C8C22×C1112yes—
227#391C22×C1112yes—
228#389C22×C1112yes—
229#388—22no—
230#386—22no—
231#382—21no—
232#381—21no—
233#380C22×C1111yescharacteristic
234#380C22×C1111yescharacteristic
235C4×C4⋊C4C22×C1112yes—
236C4×C22⋊C4C22×C1111yescharacteristic
237#376—21no—
238C2×#95—21no—
239#340C22×C1112yes—
240#340C22×C1112yes—
241#340C22×C1112yes—
242#336C22×C1112yes—
243C22×C11—22no—
244C22×C11—24no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—44no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—44no—
253C22×C11C2×C4×D411yescharacteristic
254C22×C11#54612yes—
255C22×C11C2×#13512yes—
256C22×C11#57711yescharacteristic
257C22×C11#57711yescharacteristic
258C4×C11—22no—
259C4×C11—24no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11—82no—
266C4×C11C2×#11711yescharacteristic
267C4×C11#51811yescharacteristic
268C4×C11#55112yes—
269C2×#41—22no—
270C2×#41—24no—
271C2×#41—42no—
272C2×#41C2×C4×C1114yes—
273C22×Q8C23×C1111yescharacteristic
274C22×D4—21no—
275C22×D4C23×C1111yescharacteristic
276C23×C4—21no—
277C23×C4—22no—
278C23×C4C23×C1111yescharacteristic
279C22×C8—42no—
280C22×C8C2×C4×C1114yescomplemented
281C22×C8C23×C1112yes—
282C22×C8C23×C1111yescharacteristic
283C22×C8C23×C1111yescharacteristic
284C4×D4—24no—
285C4×D4—42no—
286#117—22no—
287#117C2×C4×C1114yescomplemented
288C2×C4⋊C4—22no—
289C2×C4⋊C4C23×C1112yes—
290C2×C4⋊C4C23×C1112yes—
291C2×C4⋊C4C23×C1111yescharacteristic
292C2×C4⋊C4C23×C1111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4D4×C1112yes—
298C2×C42—21no—
299C2×C42—22no—
300C2×C42C23×C1112yes—
301#106—42no—
302#103—42no—
303#103C2×C4×C1114yescomplemented
304#103C2×C4×C1114yescomplemented
305#102—24no—
306#102C2×C4×C1114yes—
307#102C2×C4×C1114yes—
308C22⋊C8—22no—
309C4×C8—42no—
310#95—21no—
311#95—22no—
312#95—21no—
313#95—22no—
314#95—22no—
315#95—22no—
316#95D4×C1111yescharacteristic
317#95D4×C1111yescharacteristic
318C2×C11—42no—
319C2×C11—44no—
320C2×C11#234211yescharacteristic
321C2×C11C4×#13511yescharacteristic
322C2×C11#295211yescharacteristic
323C2×C11#329612yes—
324C2×C11#330312yes—
325C24—21no—
326C24C2×D4×C1111yescharacteristic
327#41—28no—
328#41—44no—
329#41—48no—
330C2×Q8—21no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8C22×C4×C1112yes—
334C2×D4—24no—
335C2×D4—21no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C22×C4×C1112yes—
339C2×D4C11×#4114yes—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—82no—
352C22×C4C22×C4×C1112yes—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1111yescharacteristic
355C22×C4C2×D4×C1112yes—
356C22×C4C11×#4112yes—
357C22×C4C24×C1111yescharacteristic
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—44no—
364C2×C8C22×C4×C1112yes—
365C2×C8C22×C4×C1112yes—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—82no—
373C4⋊C4C22×C4×C1112yes—
374C4⋊C4C22×C4×C1112yes—
375C22⋊C4—24no—
376C22⋊C4—24no—
377C22⋊C4—44no—
378C22⋊C4—81no—
379C22⋊C4—81no—
380C42—24no—
381C42—22no—
382C42—22no—
383C42—44no—
384C11#2257211yescharacteristic, direct product factor, Sylow
385C23—22no—
386C23—24no—
387C23—22no—
388C23—22no—
389C23—21no—
390C23—21no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23C4×D4×C1112yes—
395C23C22×D4×C1111yescharacteristic
396Q8—22no—
397Q8—22no—
398Q8—42no—
399D4—22no—
400D4—24no—
401D4—48no—
402D4C11×#11714yes—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—48no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—88no—
427C2×C4C4×D4×C1112yes—
428C2×C4C11×#13514yes—
429C2×C4C23×C4×C1111yescharacteristic
430C2×C4C2×C11×#4112yes—
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C11×H(5,𝔽2)12yes—
433C8—22no—
434C8—22no—
435C8—42no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—24no—
440C22—42no—
441C22—42no—
442C22—44no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22C2×C4×D4×C1111yescharacteristic
447C22C11×#54612yes—
448C22C2×C11×#13512yes—
449C22C11×#57711yescharacteristic
450C22C11×#57711yescharacteristic
451C4—24no—
452C4—22no—
453C4—42no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—82no—
458C4—82no—
459C4C2×C11×#11711yescharacteristic
460C4C11×#51811yescharacteristic
461C4C11×#55112yes—
462C2—42no—
463C2—44no—
464C2C11×#234211yescharacteristic
465C2C4×C11×#13511yescharacteristic
466C2C11×#295211yescharacteristic
467C2C11×#329612yes—
468C2C11×#330312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×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
2. C11×#2346C2semidirect
4. C11×#1933C2semidirect
5. C11×#1927C2semidirect
6. C11×#1864C2semidirect
7. C11×#1825C2semidirect
8. C11×#1807C2semidirect
10. C4×C11×#102C2semidirect
11. C8×C11×C22⋊C4C2semidirect
17. C11×#416C4semidirect
53. C22×C8×C11C2×C4semidirect
60. C11×#117C2×C4semidirect
76. C11×#103C2×C4semidirect
77. C11×#103C2×C4semidirect
91. #22572C11direct (N × H)
152. #2346C2×C11semidirect
154. #1933C2×C11semidirect
155. #1927C2×C11semidirect
156. #1864C2×C11semidirect
157. #1825C2×C11semidirect
158. #1807C2×C11semidirect
160. C4×#102C2×C11semidirect
161. C8×C22⋊C4C2×C11semidirect
218. #416C4×C11semidirect
280. C22×C8C2×C4×C11semidirect
287. #117C2×C4×C11semidirect
303. #103C2×C4×C11semidirect
304. #103C2×C4×C11semidirect
384. C11#22572direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4162
C11×#23462
C11×#23392
C11×#19332
C11×#19272
C11×#18642
C11×#18252
C11×#18072
C11×#17882
C4×C11×#1022
C8×C11×C22⋊C42
#2257211