Finite Group Databasebeta

← C11×#22490 #14599683

Subgroups — C11×#22490 #14599683

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic
3C11×#2354C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1988C211yesmaximal, characteristic, complemented
6C11×#1892C212yesmaximal, complemented
7C11×#1873C212yesmaximal, complemented
8C11×#1825C212yesmaximal, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C4×C11×#103C211yesmaximal, characteristic, complemented
11C11×#1735C212yesmaximal, complemented
12C23×C8×C11C2212yes—
13C11×#556—24no—
14C11×#556C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2212yes—
23C2×C11×#117C2212yes—
24C8×D4×C11—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×C22⋊C8C2212yes—
30C2×C4×C8×C11C2211yescharacteristic
31C11×#390—21no—
32C11×#388—22no—
33C11×#384C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11C2312yes—
48C22×C8×C11—24no—
49C22×C8×C11—24no—
50C22×C8×C11—42no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8C2×C414yes—
56C11×#126—216no—
57C11×#124—28no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8C2×C418yes—
60C4×Q8×C11—28no—
61C4×Q8×C11—22no—
62C4×Q8×C11C2×C414yes—
63C4×D4×C11C2×C414yes—
64C4×D4×C11D414yes—
65C11×#117—24no—
66C11×#117—24no—
67C11×#117—42no—
68C11×#117C2×C418yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—22no—
86C2×C42×C11—21no—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C11×C4⋊C8—22no—
91C11×#103—22no—
92C11×#103—22no—
93C11×#103—42no—
94C11×C22⋊C8—24no—
95C4×C8×C11—22no—
96C11×#95—22no—
97C11×#95—21no—
98#22490C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11C2×D412yes—
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11C22×C412yes—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11C22⋊C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—48no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4C22⋊C414yes—
151C11×C4⋊C4C22×C412yes—
152C11×C4⋊C4C22×C414yes—
153C11×C4⋊C4#4112yes—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—82no—
158C11×C22⋊C4C22⋊C418yes—
159C42×C11—28no—
160C42×C11—24no—
161C42×C11—44no—
162C42×C11—42no—
163C42×C11C22×C412yes—
164C42×C11C2×D412yes—
165C2×#556C2×C1111yescharacteristic
166C2×C8×D4C2×C1111yescharacteristic
167#2354C2×C1111yescharacteristic
168#1990C2×C1111yescharacteristic, complemented
169#1988C2×C1111yescharacteristic, complemented
170#1892C2×C1112yescomplemented
171#1873C2×C1112yescomplemented
172#1825C2×C1112yescomplemented
173#1803C2×C1111yescharacteristic, complemented
174C4×#103C2×C1111yescharacteristic, complemented
175#1735C2×C1112yescomplemented
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11C2×C22⋊C414yes—
183C23×C11C22×D411yescharacteristic
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—41no—
187Q8×C11—41no—
188Q8×C11—48no—
189D4×C11—28no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11C2×C22⋊C414yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11#13512yes—
220C2×C4×C11#13512yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C8×C11—22no—
228C8×C11—42no—
229C8×C11—41no—
230C23×C8C22×C1112yes—
231#556—24no—
232#556C4×C1118yescomplemented
233C2×C4⋊Q8C22×C1111yescharacteristic
234C2×#126—22no—
235C2×#124—21no—
236C2×C22⋊Q8C22×C1112yes—
237C2×C4×Q8—21no—
238C2×C4×Q8C22×C1111yescharacteristic
239C2×C4×D4C22×C1111yescharacteristic
240C2×#117C22×C1112yes—
241C2×#117C22×C1112yes—
242C8×D4—24no—
243C2×C4⋊C8C22×C1111yescharacteristic
244C2×#103C22×C1111yescharacteristic
245C2×#103C22×C1111yescharacteristic
246C2×#103C22×C1112yes—
247C2×C22⋊C8C22×C1112yes—
248C2×C4×C8C22×C1111yescharacteristic
249#390—21no—
250#388—22no—
251#384C22×C1111yescharacteristic
252#380C22×C1112yes—
253C4×C4⋊C4—21no—
254C4×C4⋊C4C22×C1111yescharacteristic
255#340C22×C1112yes—
256#340C22×C1111yescharacteristic
257#340C22×C1112yes—
258#340C22×C1112yes—
259#340C22×C1112yes—
260#340C22×C1112yes—
261#340C22×C1111yescharacteristic
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—24no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11#54711yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13511yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—24no—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—81no—
283C4×C11—82no—
284C4×C11#41614yes—
285C4×C11C4×#4111yescharacteristic
286C4×C11#52011yescharacteristic
287C4×C11#54611yescharacteristic
288C4×C11#54711yescharacteristic
289C22×Q8—21no—
290C22×Q8C23×C1111yescharacteristic
291C22×D4D4×C1111yescharacteristic
292C23×C4C23×C1112yes—
293C22×C8—24no—
294C22×C8—24no—
295C22×C8—42no—
296C22×C8C23×C1112yes—
297C22×C8C23×C1111yescharacteristic
298C22×C8C23×C1111yescharacteristic
299C4⋊Q8—22no—
300C4⋊Q8C2×C4×C1114yes—
301#126—216no—
302#124—28no—
303C22⋊Q8—24no—
304C22⋊Q8C2×C4×C1118yes—
305C4×Q8—28no—
306C4×Q8—22no—
307C4×Q8C2×C4×C1114yes—
308C4×D4C2×C4×C1114yes—
309C4×D4D4×C1114yes—
310#117—24no—
311#117—24no—
312#117—42no—
313#117C2×C4×C1118yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1111yescharacteristic
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4D4×C1112yes—
330C2×C42—22no—
331C2×C42—21no—
332C2×C42—22no—
333C2×C42—21no—
334C2×C42C23×C1111yescharacteristic
335C4⋊C8—22no—
336#103—22no—
337#103—22no—
338#103—42no—
339C22⋊C8—24no—
340C4×C8—22no—
341#95—22no—
342#95—21no—
343C2×C11—44no—
344C2×C11#233911yescharacteristic
345C2×C11C2×#41611yescharacteristic
346C2×C11#289811yescharacteristic
347C2×C11#330211yescharacteristic
348C2×C11#330411yescharacteristic
349C2×C11#334011yescharacteristic
350C2×C11#334211yescharacteristic
351C24C2×D4×C1112yes—
352C2×Q8—24no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8C22×C4×C1112yes—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4C11×C22⋊C414yes—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4C22×C4×C1114yes—
375C22×C4C2×D4×C1112yes—
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1114yes—
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C24×C1111yescharacteristic
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—48no—
389C2×C8C11×#4112yes—
390C4⋊C4—28no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—42no—
401C4⋊C4—81no—
402C4⋊C4C11×C22⋊C414yes—
403C4⋊C4C22×C4×C1112yes—
404C4⋊C4C22×C4×C1114yes—
405C4⋊C4C11×#4112yes—
406C22⋊C4—28no—
407C22⋊C4—28no—
408C22⋊C4—44no—
409C22⋊C4—82no—
410C22⋊C4C11×C22⋊C418yes—
411C42—28no—
412C42—24no—
413C42—44no—
414C42—42no—
415C42C22×C4×C1112yes—
416C42C2×D4×C1112yes—
417C11#2249011yescharacteristic, direct product factor, Sylow
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23C2×C11×C22⋊C414yes—
425C23C22×D4×C1111yescharacteristic
426Q8—22no—
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—48no—
431D4—28no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4C2×C11×C22⋊C414yes—
459C2×C4C2×C11×C22⋊C412yes—
460C2×C4C2×C11×C22⋊C412yes—
461C2×C4C11×#13512yes—
462C2×C4C11×#13512yes—
463C2×C4C23×C4×C1111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C2×C11×#4111yescharacteristic
466C2×C4C2×C11×#4111yescharacteristic
467C2×C4C11×H(5,𝔽2)11yescharacteristic
468C2×C4C11×2−1+411yescharacteristic
469C8—22no—
470C8—42no—
471C8—41no—
472C22—24no—
473C22—24no—
474C22—24no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22C22×C11×C22⋊C411yescharacteristic
480C22C11×#54611yescharacteristic
481C22C11×#54711yescharacteristic
482C22C2×C11×#13511yescharacteristic
483C22C2×C11×#13511yescharacteristic
484C22C11×#57711yescharacteristic
485C22C11×#57811yescharacteristic
486C4—22no—
487C4—24no—
488C4—44no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—82no—
493C4—81no—
494C4C11×#41614yes—
495C4C4×C11×#4111yescharacteristic
496C4C11×#52011yescharacteristic
497C4C11×#54611yescharacteristic
498C4C11×#54711yescharacteristic
499C2—44no—
500C2C11×#233911yescharacteristic
501C2C2×C11×#41611yescharacteristic
502C2C11×#289811yescharacteristic
503C2C11×#330211yescharacteristic
504C2C11×#330411yescharacteristic
505C2C11×#334011yescharacteristic
506C2C11×#334211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×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
4. C11×#1990C2semidirect
5. C11×#1988C2semidirect
6. C11×#1892C2semidirect
7. C11×#1873C2semidirect
8. C11×#1825C2semidirect
9. C11×#1803C2semidirect
10. C4×C11×#103C2semidirect
11. C11×#1735C2semidirect
14. C11×#556C4semidirect
98. #22490C11direct (N × H)
168. #1990C2×C11semidirect
169. #1988C2×C11semidirect
170. #1892C2×C11semidirect
171. #1873C2×C11semidirect
172. #1825C2×C11semidirect
173. #1803C2×C11semidirect
174. C4×#103C2×C11semidirect
175. #1735C2×C11semidirect
232. #556C4×C11semidirect
417. C11#22490direct (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×C8×D4×C112
C11×#23542
C11×#19902
C11×#19882
C11×#18922
C11×#18732
C11×#18252
C11×#18032
C4×C11×#1032
C11×#17352
#2249011