Finite Group Databasebeta

← C11×#22273 #14599466

Subgroups — C11×#22273 #14599466

Order 2816.

906 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×#497C211yesmaximal, characteristic
2C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
3C4×C11×#124C211yesmaximal, characteristic
4C11×#1960C211yesmaximal, characteristic, complemented
5C11×#1959C211yesmaximal, characteristic
6C11×#1880C212yesmaximal
7C11×#1878C212yesmaximal, complemented
8C11×#1878C212yesmaximal, complemented
9C11×#1877C212yesmaximal
10C11×#1836C211yesmaximal, characteristic, complemented
11C11×#1745C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C11×#497C418yescomplemented
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C11×#391C2212yes—
27C11×#391C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#389—21no—
30C11×#389—21no—
31C11×#388—21no—
32C11×#388—21no—
33C11×#384C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4—21no—
36C4×C11×C4⋊C4—21no—
37C4×C11×C22⋊C4—21no—
38C4×C11×C22⋊C4—21no—
39C43×C11C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C2×C11×Q16—42no—
49C2×C11×Q16—42no—
50C2×C11×Q16C2×C418yescomplemented
51C2×C11×SD16—42no—
52C2×C11×SD16—42no—
53C2×C11×SD16C2×C418yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8C2×C414yescomplemented
58C11×#124—22no—
59C11×#124C2×C414yes—
60C4×Q8×C11—42no—
61C4×Q8×C11—42no—
62C4×Q8×C11—42no—
63C4×D4×C11—42no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C11×#103—42no—
88C11×#103—42no—
89C11×#103—42no—
90C11×#102—42no—
91C11×#97—22no—
92C11×#97C2×C414yescomplemented
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—22no—
98C11×#95—22no—
99#22273C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22×C412yes—
110C2×Q8×C11C22×C414yes—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C11×Q16—48no—
131C11×SD16—48no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C22×C414yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—42no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—44no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—42no—
151C11×C22⋊C4—42no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—41no—
158C42×C11—41no—
159C42×C11—44no—
160C42×C11—42no—
161C42×C11C22×C412yes—
162C42×C11#4112yes—
163C2×#497C2×C1111yescharacteristic
164C4×C4⋊Q8C2×C1111yescharacteristic, complemented
165C4×#124C2×C1111yescharacteristic
166#1960C2×C1111yescharacteristic, complemented
167#1959C2×C1111yescharacteristic
168#1880C2×C1112yes—
169#1878C2×C1112yescomplemented
170#1878C2×C1112yescomplemented
171#1877C2×C1112yes—
172#1836C2×C1111yescharacteristic, complemented
173#1745C2×C1111yescharacteristic, complemented
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—24no—
183Q8×C11—24no—
184Q8×C11—24no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—24no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—84no—
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11#13712yes—
223C2×C4×C11#13712yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)12yes—
227C2×C4×C11H(5,𝔽2)12yes—
228C8×C11—24no—
229C8×C11—42no—
230C22×Q16C22×C1112yes—
231C22×SD16C22×C1112yes—
232C2×C4⋊Q8C22×C1111yescharacteristic
233C2×#124C22×C1111yescharacteristic
234C2×C4×Q8C22×C1112yes—
235C2×C4×Q8C22×C1111yescharacteristic
236C2×C4×D4C22×C1111yescharacteristic
237#497C4×C1118yescomplemented
238C2×#103C22×C1112yes—
239C2×#103C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×#102C22×C1112yes—
242C2×#97C22×C1111yescharacteristic
243C2×#97C22×C1111yescharacteristic
244#391C22×C1112yes—
245#391C22×C1111yescharacteristic
246#390C22×C1111yescharacteristic
247#389—21no—
248#389—21no—
249#388—21no—
250#388—21no—
251#384C22×C1111yescharacteristic
252#382C22×C1111yescharacteristic
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C43C22×C1111yescharacteristic
258#340C22×C1112yes—
259#340C22×C1112yes—
260#336C22×C1112yes—
261#336C22×C1112yes—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C2×C4×D411yescharacteristic
270C22×C11#53511yescharacteristic
271C22×C11#53511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57511yescharacteristic
275C22×C11#57511yescharacteristic
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—82no—
287C4×C11#51812yes—
288C4×C11#54012yes—
289C22×Q8C23×C1111yescharacteristic
290C22×Q8C23×C1112yes—
291C22×D4C23×C1111yescharacteristic
292C23×C4—21no—
293C2×Q16—42no—
294C2×Q16—42no—
295C2×Q16C2×C4×C1118yescomplemented
296C2×SD16—42no—
297C2×SD16—42no—
298C2×SD16C2×C4×C1118yes—
299C22×C8C23×C1112yes—
300C22×C8C23×C1112yes—
301C4⋊Q8—22no—
302C4⋊Q8C2×C4×C1114yescomplemented
303#124—22no—
304#124C2×C4×C1114yes—
305C4×Q8—42no—
306C4×Q8—42no—
307C4×Q8—42no—
308C4×D4—42no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C23×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1112yes—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C42—21no—
324C2×C42—22no—
325C2×C42D4×C1111yescharacteristic
326C2×C42D4×C1111yescharacteristic
327C2×C42D4×C1111yescharacteristic
328C2×C42D4×C1111yescharacteristic
329C2×C42C23×C1111yescharacteristic
330C2×C42C23×C1111yescharacteristic
331C2×C42C23×C1111yescharacteristic
332#103—42no—
333#103—42no—
334#103—42no—
335#102—42no—
336#97—22no—
337#97C2×C4×C1114yescomplemented
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—22no—
343#95—22no—
344C2×C11—82no—
345C2×C11#232811yescharacteristic
346C2×C11C4×#13711yescharacteristic
347C2×C11C4×#13711yescharacteristic
348C2×C11#321511yescharacteristic
349C2×C11#321611yescharacteristic
350C2×C11#321811yescharacteristic
351C2×C11#321911yescharacteristic
352C24—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8C22×C4×C1112yes—
362C2×Q8C22×C4×C1114yes—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4C22×C4×C1112yes—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1111yescharacteristic
378C22×C4C2×D4×C1111yescharacteristic
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C24×C1111yescharacteristic
382Q16—48no—
383SD16—48no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8C22×C4×C1114yes—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—42no—
397C4⋊C4—44no—
398C4⋊C4—42no—
399C4⋊C4—42no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—42no—
403C22⋊C4—42no—
404C22⋊C4—42no—
405C42—22no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—41no—
410C42—41no—
411C42—44no—
412C42—42no—
413C42C22×C4×C1112yes—
414C42C11×#4112yes—
415C11#2227311yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C22×D4×C1111yescharacteristic
424Q8—24no—
425Q8—24no—
426Q8—24no—
427Q8—42no—
428Q8—42no—
429Q8—42no—
430D4—24no—
431D4—42no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—84no—
462C2×C4C4×D4×C1112yes—
463C2×C4C4×D4×C1112yes—
464C2×C4C11×#13712yes—
465C2×C4C11×#13712yes—
466C2×C4C23×C4×C1111yescharacteristic
467C2×C4C2×C11×#4111yescharacteristic
468C2×C4C11×H(5,𝔽2)12yes—
469C2×C4C11×H(5,𝔽2)12yes—
470C8—24no—
471C8—42no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C2×C4×D4×C1111yescharacteristic
480C22C11×#53511yescharacteristic
481C22C11×#53511yescharacteristic
482C22C2×C11×#13711yescharacteristic
483C22C2×C11×#13711yescharacteristic
484C22C11×#57511yescharacteristic
485C22C11×#57511yescharacteristic
486C4—22no—
487C4—22no—
488C4—22no—
489C4—22no—
490C4—41no—
491C4—41no—
492C4—42no—
493C4—44no—
494C4—81no—
495C4—81no—
496C4—82no—
497C4C11×#51812yes—
498C4C11×#54012yes—
499C2—82no—
500C2C11×#232811yescharacteristic
501C2C4×C11×#13711yescharacteristic
502C2C4×C11×#13711yescharacteristic
503C2C11×#321511yescharacteristic
504C2C11×#321611yescharacteristic
505C2C11×#321811yescharacteristic
506C2C11×#321911yescharacteristic
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 ◁ C43×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×C4⋊Q8C2semidirect
4. C11×#1960C2semidirect
7. C11×#1878C2semidirect
8. C11×#1878C2semidirect
10. C11×#1836C2semidirect
11. C11×#1745C2semidirect
19. C11×#497C4semidirect
50. C2×C11×Q16C2×C4semidirect
57. C11×C4⋊Q8C2×C4semidirect
92. C11×#97C2×C4semidirect
99. #22273C11direct (N × H)
164. C4×C4⋊Q8C2×C11semidirect
166. #1960C2×C11semidirect
169. #1878C2×C11semidirect
170. #1878C2×C11semidirect
172. #1836C2×C11semidirect
173. #1745C2×C11semidirect
237. #497C4×C11semidirect
295. C2×Q16C2×C4×C11semidirect
302. C4⋊Q8C2×C4×C11semidirect
337. #97C2×C4×C11semidirect
415. C11#22273direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4972
C4×C11×C4⋊Q82
C4×C11×#1242
C11×#19602
C11×#19592
C11×#18802
C11×#18782
C11×#18772
C11×#18362
C11×#17452
#2227311