Finite Group Databasebeta

← C11×#22541 #14599734

Subgroups — C11×#22541 #14599734

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
3C11×#2355C211yesmaximal, characteristic, complemented
4C11×#1983C212yesmaximal
5C11×#1981C211yesmaximal, characteristic, complemented
6C11×#1958C212yesmaximal
7C11×#1956C211yesmaximal, characteristic, complemented
8C11×#1805C212yesmaximal, complemented
9C11×#1802C211yesmaximal, characteristic
10C4×C11×#103C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic
12C11×#556—24no—
13C11×#556C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C8×Q8×C11—24no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C2×C4×C8×C11C2212yes—
34C11×#391—21no—
35C11×#387—22no—
36C11×#384C2211yescharacteristic
37C11×#382C2212yes—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C4⋊C4C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#340C2212yes—
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C11×#126—216no—
54C11×#124—24no—
55C11×#124C2×C418yes—
56C11×C22⋊Q8—28no—
57C4×Q8×C11—24no—
58C4×Q8×C11C2×C418yes—
59C4×Q8×C11C2×C414yes—
60C4×Q8×C11D414yes—
61C4×D4×C11—22no—
62C4×D4×C11C2×C414yes—
63C11×#117—28no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11—22no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2312yes—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—24no—
85C11×#103—24no—
86C11×#103—24no—
87C11×#103—42no—
88C11×#103—42no—
89C11×#102—22no—
90C11×#102—22no—
91C11×#102—42no—
92C4×C8×C11—22no—
93C4×C8×C11—24no—
94C11×#95—22no—
95C11×#95—21no—
96C11×#95—22no—
97C11×#95—22no—
98#22541C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22⋊C414yes—
108C2×Q8×C11C22×C414yes—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
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—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11#4112yes—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—81no—
148C11×C4⋊C4C22⋊C414yes—
149C11×C4⋊C4C22⋊C418yes—
150C11×C4⋊C4C22×C412yes—
151C11×C4⋊C4#4112yes—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—28no—
155C42×C11—28no—
156C42×C11—42no—
157C42×C11—82no—
158C42×C11C22×C412yes—
159C42×C11C22×C414yes—
160C42×C11C2×D412yes—
161C42×C11C2×D414yes—
162C2×#556C2×C1111yescharacteristic
163C2×C8×Q8C2×C1111yescharacteristic, complemented
164#2355C2×C1111yescharacteristic, complemented
165#1983C2×C1112yes—
166#1981C2×C1111yescharacteristic, complemented
167#1958C2×C1112yes—
168#1956C2×C1111yescharacteristic, complemented
169#1805C2×C1112yescomplemented
170#1802C2×C1111yescharacteristic
171C4×#103C2×C1112yescomplemented
172C4×#102C2×C1111yescharacteristic
173C23×C11—22no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11C22×D411yescharacteristic
181Q8×C11—28no—
182Q8×C11—24no—
183Q8×C11—24no—
184Q8×C11—42no—
185Q8×C11—42no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11—41no—
189D4×C11—41no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—48no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11C2×C22⋊C414yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C414yes—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11#13512yes—
217C2×C4×C11#13512yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C8×C11—22no—
225C8×C11—41no—
226C8×C11—42no—
227#556—24no—
228#556C4×C1118yescomplemented
229C2×C4⋊Q8C22×C1111yescharacteristic
230C2×#126—22no—
231C2×#124C22×C1112yes—
232C2×C22⋊Q8—21no—
233C2×C4×Q8C22×C1112yes—
234C2×C4×Q8C22×C1111yescharacteristic
235C2×C4×D4C22×C1111yescharacteristic
236C2×#117—21no—
237C8×Q8—24no—
238C2×C4⋊C8C22×C1111yescharacteristic
239C2×C4⋊C8C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#103C22×C1112yes—
242C2×#103C22×C1112yes—
243C2×#103C22×C1112yes—
244C2×#102C22×C1111yescharacteristic
245C2×#102C22×C1111yescharacteristic
246C2×#102C22×C1112yes—
247C2×C4×C8C22×C1111yescharacteristic
248C2×C4×C8C22×C1112yes—
249#391—21no—
250#387—22no—
251#384C22×C1111yescharacteristic
252#382C22×C1112yes—
253C4×C4⋊C4—21no—
254C4×C4⋊C4C22×C1111yescharacteristic
255C4×C4⋊C4C22×C1112yes—
256#340C22×C1112yes—
257#340C22×C1111yescharacteristic
258#340C22×C1111yescharacteristic
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54811yescharacteristic
268C22×C11#55011yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C4×C11—24no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—42no—
277C4×C11—44no—
278C4×C11—42no—
279C4×C11—81no—
280C4×C11—82no—
281C4×C11#41614yes—
282C4×C11C4×#4111yescharacteristic
283C4×C11#52011yescharacteristic
284C4×C11#54811yescharacteristic
285C4×C11#55011yescharacteristic
286C22×Q8D4×C1111yescharacteristic
287C22×Q8C23×C1112yes—
288C22×D4C23×C1111yescharacteristic
289C23×C4—21no—
290C22×C8C23×C1111yescharacteristic
291C22×C8C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C4⋊Q8—22no—
294C4⋊Q8C2×C4×C1114yes—
295#126—216no—
296#124—24no—
297#124C2×C4×C1118yes—
298C22⋊Q8—28no—
299C4×Q8—24no—
300C4×Q8C2×C4×C1118yes—
301C4×Q8C2×C4×C1114yes—
302C4×Q8D4×C1114yes—
303C4×D4—22no—
304C4×D4C2×C4×C1114yes—
305#117—28no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C4⋊C4D4×C1112yes—
313C2×C4⋊C4C23×C1111yescharacteristic
314C2×C4⋊C4C23×C1112yes—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C22⋊C4—22no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42—22no—
323C2×C42C23×C1111yescharacteristic
324C2×C42C23×C1112yes—
325C4⋊C8—22no—
326C4⋊C8—24no—
327#103—24no—
328#103—24no—
329#103—42no—
330#103—42no—
331#102—22no—
332#102—22no—
333#102—42no—
334C4×C8—22no—
335C4×C8—24no—
336#95—22no—
337#95—21no—
338#95—22no—
339#95—22no—
340C2×C11—82no—
341C2×C11#234111yescharacteristic
342C2×C11C2×#41611yescharacteristic
343C2×C11#289811yescharacteristic
344C2×C11#336011yescharacteristic
345C2×C11#336411yescharacteristic
346C2×C11#339311yescharacteristic
347C2×C11#339411yescharacteristic
348C24—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8C11×C22⋊C414yes—
357C2×Q8C22×C4×C1114yes—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4C22×C4×C1112yes—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4C2×D4×C1112yes—
373C22×C4C2×D4×C1112yes—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C24×C1111yescharacteristic
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8C11×#4112yes—
386C4⋊C4—24no—
387C4⋊C4—28no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—42no—
396C4⋊C4—81no—
397C4⋊C4C11×C22⋊C414yes—
398C4⋊C4C11×C22⋊C418yes—
399C4⋊C4C22×C4×C1112yes—
400C4⋊C4C11×#4112yes—
401C22⋊C4—28no—
402C22⋊C4—24no—
403C22⋊C4—28no—
404C42—28no—
405C42—42no—
406C42—82no—
407C42C22×C4×C1112yes—
408C42C22×C4×C1114yes—
409C42C2×D4×C1112yes—
410C42C2×D4×C1114yes—
411C11#2254111yescharacteristic, direct product factor, Sylow
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23C22×D4×C1111yescharacteristic
420Q8—28no—
421Q8—24no—
422Q8—24no—
423Q8—42no—
424Q8—42no—
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—48no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4C2×C11×C22⋊C414yes—
452C2×C4C2×C11×C22⋊C412yes—
453C2×C4C2×C11×C22⋊C414yes—
454C2×C4C2×C11×C22⋊C412yes—
455C2×C4C11×#13512yes—
456C2×C4C11×#13512yes—
457C2×C4C23×C4×C1111yescharacteristic
458C2×C4C22×D4×C1111yescharacteristic
459C2×C4C2×C11×#4111yescharacteristic
460C2×C4C2×C11×#4111yescharacteristic
461C2×C4C11×H(5,𝔽2)11yescharacteristic
462C2×C4C11×2−1+411yescharacteristic
463C8—22no—
464C8—41no—
465C8—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C22×C11×C22⋊C411yescharacteristic
474C22C11×#54811yescharacteristic
475C22C11×#55011yescharacteristic
476C22C2×C11×#13511yescharacteristic
477C22C2×C11×#13511yescharacteristic
478C22C11×#57711yescharacteristic
479C22C11×#57811yescharacteristic
480C4—24no—
481C4—24no—
482C4—22no—
483C4—42no—
484C4—42no—
485C4—44no—
486C4—81no—
487C4—82no—
488C4C11×#41614yes—
489C4C4×C11×#4111yescharacteristic
490C4C11×#52011yescharacteristic
491C4C11×#54811yescharacteristic
492C4C11×#55011yescharacteristic
493C2—82no—
494C2C11×#234111yescharacteristic
495C2C2×C11×#41611yescharacteristic
496C2C11×#289811yescharacteristic
497C2C11×#336011yescharacteristic
498C2C11×#336411yescharacteristic
499C2C11×#339311yescharacteristic
500C2C11×#339411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
LCSG ▷ C2×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
2. C2×C8×Q8×C11C2semidirect
3. C11×#2355C2semidirect
5. C11×#1981C2semidirect
7. C11×#1956C2semidirect
8. C11×#1805C2semidirect
10. C4×C11×#103C2semidirect
13. C11×#556C4semidirect
98. #22541C11direct (N × H)
163. C2×C8×Q8C2×C11semidirect
164. #2355C2×C11semidirect
166. #1981C2×C11semidirect
168. #1956C2×C11semidirect
169. #1805C2×C11semidirect
171. C4×#103C2×C11semidirect
228. #556C4×C11semidirect
411. C11#22541direct (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×Q8×C112
C11×#23552
C11×#19832
C11×#19812
C11×#19582
C11×#19562
C11×#18052
C11×#18022
C4×C11×#1032
C4×C11×#1022
#2254111