Finite Group Databasebeta

← C11×#24341 #14601534

Subgroups — C11×#24341 #14601534

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C11C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2580C211yesmaximal, characteristic
5C11×#2057C212yesmaximal, complemented
6C11×#2023C212yesmaximal
7C11×#1993C211yesmaximal, characteristic, complemented
8C11×#1985C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1863C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13Q82×C11—24no—
14Q82×C11—24no—
15C2×C11×C4⋊Q8—22no—
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#474—24no—
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2211yescharacteristic
31C2×C11×#102C2212yes—
32C2×C11×#102C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#399—21no—
35C11×#393—21no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#385—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—22no—
46C22×Q8×C11—21no—
47C22×Q8×C11D411yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16Q814yescomplemented
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C4⋊Q8—216no—
58C11×C4⋊Q8—28no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yes—
63C4×Q8×C11—28no—
64C4×Q8×C11—24no—
65C4×Q8×C11—24no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yes—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D412yes—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C42×C11—22no—
87C2×C42×C11—21no—
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C11×#107—22no—
91C11×#107—24no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#102—22no—
96C11×#102—24no—
97C11×#97—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—22no—
101#24341C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C2×Q8×C11—28no—
104C2×Q8×C11—22no—
105C2×Q8×C11—24no—
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—82no—
111C2×Q8×C11—82no—
112C2×Q8×C11—82no—
113C2×Q8×C11C2×D412yes—
114C2×Q8×C11C2×Q812yes—
115C2×Q8×C11#4112yes—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×Q812yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—42no—
128C22×C4×C11—82no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2411yescharacteristic
134C11×SD16—28no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11C2×Q812yes—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—82no—
157C11×C4⋊C4C2×D414yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—82no—
162C42×C11—28no—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11C2×D412yes—
167C42×C11C2×D412yes—
168C2×Q82C2×C1111yescharacteristic, complemented
169C2×#474C2×C1111yescharacteristic
170C2×#440C2×C1111yescharacteristic
171#2580C2×C1111yescharacteristic
172#2057C2×C1112yescomplemented
173#2023C2×C1112yes—
174#1993C2×C1111yescharacteristic, complemented
175#1985C2×C1111yescharacteristic, complemented
176#1880C2×C1112yes—
177#1863C2×C1112yescomplemented
178#1805C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C22×D411yescharacteristic
185Q8×C11—28no—
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—84no—
190Q8×C11—88no—
191Q8×C11C22⋊Q814yes—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—41no—
195D4×C11—41no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—84no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12012yes—
219C2×C4×C11#13714yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×Q811yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C8×C11—22no—
227C8×C11—41no—
228C8×C11—42no—
229C22×SD16C22×C1111yescharacteristic
230Q82—24no—
231Q82—24no—
232C2×C4⋊Q8—22no—
233C2×C4⋊Q8—21no—
234C2×C4⋊Q8C22×C1112yes—
235C2×C4⋊Q8C22×C1111yescharacteristic
236C2×C4×Q8—21no—
237C2×C4×Q8C22×C1112yes—
238C2×C4×Q8C22×C1111yescharacteristic
239C2×C4×Q8C22×C1111yescharacteristic
240C2×C4×D4C22×C1111yescharacteristic
241#474—24no—
242#440—24no—
243C2×#107C22×C1111yescharacteristic
244C2×#107C22×C1112yes—
245C2×C4⋊C8C22×C1111yescharacteristic
246C2×#103C22×C1112yes—
247C2×#103C22×C1111yescharacteristic
248C2×#102C22×C1112yes—
249C2×#102C22×C1111yescharacteristic
250C2×#97C22×C1111yescharacteristic
251#399—21no—
252#393—21no—
253#390C22×C1112yes—
254#389C22×C1112yes—
255#385—22no—
256#382C22×C1111yescharacteristic
257#340C22×C1112yes—
258#340C22×C1112yes—
259#340C22×C1112yes—
260#336C22×C1112yes—
261#336C22×C1112yes—
262C22×C11—44no—
263C22×C11—42no—
264C22×C11—82no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11C2×#12011yescharacteristic
268C22×C11#54811yescharacteristic
269C22×C11D4×Q811yescharacteristic
270C22×C11C2×#13712yes—
271C22×C11#57612yes—
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—42no—
277C4×C11—44no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11—81no—
281C4×C11C2×C22⋊Q811yescharacteristic
282C4×C11#53611yescharacteristic
283C4×C11#54811yescharacteristic
284C4×C11D4×Q811yescharacteristic
285C22×Q8—22no—
286C22×Q8—21no—
287C22×Q8D4×C1111yescharacteristic
288C22×Q8C23×C1111yescharacteristic
289C22×D4C23×C1111yescharacteristic
290C23×C4—21no—
291C2×SD16—22no—
292C2×SD16—22no—
293C2×SD16Q8×C1114yescomplemented
294C22×C8C23×C1111yescharacteristic
295C22×C8C23×C1112yes—
296C22×C8C23×C1111yescharacteristic
297C4⋊Q8—216no—
298C4⋊Q8—28no—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301C4⋊Q8—22no—
302C4⋊Q8D4×C1114yes—
303C4×Q8—28no—
304C4×Q8—24no—
305C4×Q8—24no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8D4×C1114yes—
310C4×D4—22no—
311C4×D4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4D4×C1112yes—
318C2×C4⋊C4D4×C1111yescharacteristic
319C2×C4⋊C4C23×C1111yescharacteristic
320C2×C4⋊C4C23×C1112yes—
321C2×C4⋊C4C23×C1112yes—
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C42—22no—
327C2×C42—21no—
328C2×C42C23×C1112yes—
329C2×C42C23×C1111yescharacteristic
330#107—22no—
331#107—24no—
332C4⋊C8—22no—
333#103—22no—
334#103—24no—
335#102—22no—
336#102—24no—
337#97—22no—
338#95—21no—
339#95—21no—
340#95—22no—
341C2×C11—82no—
342C2×C11#240911yescharacteristic
343C2×C11#300411yescharacteristic
344C2×C11#300811yescharacteristic
345C2×C11#337512yes—
346C2×C11#338512yes—
347C24—21no—
348C2×Q8—28no—
349C2×Q8—22no—
350C2×Q8—24no—
351C2×Q8—24no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—82no—
356C2×Q8—82no—
357C2×Q8—82no—
358C2×Q8C2×D4×C1112yes—
359C2×Q8C2×Q8×C1112yes—
360C2×Q8C11×#4112yes—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C2×Q8×C1112yes—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—42no—
373C22×C4—82no—
374C22×C4C2×D4×C1112yes—
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377C22×C4C2×D4×C1112yes—
378C22×C4C24×C1111yescharacteristic
379SD16—28no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—22no—
388C2×C8C2×Q8×C1112yes—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—82no—
402C4⋊C4C2×D4×C1114yes—
403C4⋊C4C2×D4×C1112yes—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—82no—
407C42—28no—
408C42—24no—
409C42—22no—
410C42—22no—
411C42C2×D4×C1112yes—
412C42C2×D4×C1112yes—
413C11#2434111yescharacteristic, direct product factor, Sylow
414C23—22no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—42no—
419C23C22×D4×C1111yescharacteristic
420Q8—28no—
421Q8—22no—
422Q8—22no—
423Q8—22no—
424Q8—84no—
425Q8—88no—
426Q8C11×C22⋊Q814yes—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—84no—
452C2×C4C11×#12012yes—
453C2×C4C11×#12012yes—
454C2×C4C11×#13714yes—
455C2×C4C22×D4×C1111yescharacteristic
456C2×C4C22×D4×C1111yescharacteristic
457C2×C4C22×Q8×C1111yescharacteristic
458C2×C4C2×C11×#4111yescharacteristic
459C2×C4C11×2−1+411yescharacteristic
460C2×C4C11×2−1+411yescharacteristic
461C8—22no—
462C8—41no—
463C8—42no—
464C22—42no—
465C22—44no—
466C22—81no—
467C22—81no—
468C22—82no—
469C22C2×C11×#12011yescharacteristic
470C22C11×#54811yescharacteristic
471C22D4×Q8×C1111yescharacteristic
472C22C2×C11×#13712yes—
473C22C11×#57612yes—
474C4—24no—
475C4—22no—
476C4—24no—
477C4—22no—
478C4—42no—
479C4—44no—
480C4—42no—
481C4—81no—
482C4—82no—
483C4C2×C11×C22⋊Q811yescharacteristic
484C4C11×#53611yescharacteristic
485C4C11×#54811yescharacteristic
486C4D4×Q8×C1111yescharacteristic
487C2—82no—
488C2C11×#240911yescharacteristic
489C2C11×#300411yescharacteristic
490C2C11×#300811yescharacteristic
491C2C11×#337512yes—
492C2C11×#338512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
1. C2×Q82×C11C2semidirect
5. C11×#2057C2semidirect
7. C11×#1993C2semidirect
8. C11×#1985C2semidirect
10. C11×#1863C2semidirect
11. C11×#1805C2semidirect
53. C2×C11×SD16Q8semidirect
101. #24341C11direct (N × H)
168. C2×Q82C2×C11semidirect
172. #2057C2×C11semidirect
174. #1993C2×C11semidirect
175. #1985C2×C11semidirect
177. #1863C2×C11semidirect
178. #1805C2×C11semidirect
293. C2×SD16Q8×C11semidirect
413. C11#24341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q82×C112
C2×C11×#4742
C2×C11×#4402
C11×#25802
C11×#20572
C11×#20232
C11×#19932
C11×#19852
C11×#18802
C11×#18632
C11×#18052
#2434111