Finite Group Databasebeta

← C11×#24329 #14601522

Subgroups — C11×#24329 #14601522

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C11C211yesmaximal, characteristic, complemented
2C2×C11×#476C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic
4C11×#2538C211yesmaximal, characteristic
5C11×#2058C212yesmaximal, complemented
6C11×#2023C212yesmaximal
7C11×#1990C211yesmaximal, characteristic, complemented
8C11×#1984C211yesmaximal, characteristic, complemented
9C11×#1880C212yesmaximal
10C11×#1865C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13Q82×C11—24no—
14Q82×C11—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8—22no—
17C2×C11×C4⋊Q8C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#476—24no—
26C4×C11×SD16—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2212yes—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C11×#396—22no—
36C11×#390C2212yes—
37C11×#389C2212yes—
38C11×#384C2211yescharacteristic
39C11×#380—21no—
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—
63C11×C22⋊Q8—44no—
64C4×Q8×C11—28no—
65C4×Q8×C11—24no—
66C4×Q8×C11—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11D414yes—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D412yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—22no—
90C2×C42×C11—21no—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C11×#106—22no—
94C11×#106—24no—
95C11×C4⋊C8—22no—
96C11×#103—22no—
97C11×#103—24no—
98C11×#102—22no—
99C11×#102—24no—
100C4×C8×C11—22no—
101C11×#95—22no—
102#24329C1111yesmaximal, characteristic, direct product factor, Sylow
103C24×C11—21no—
104C2×Q8×C11—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—81no—
112C2×Q8×C11—81no—
113C2×Q8×C11—82no—
114C2×Q8×C11—82no—
115C2×Q8×C11SD1614yescomplemented
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×Q812yes—
118C2×Q8×C11#4112yes—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11C2×Q812yes—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×SD16—28no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—21no—
147C2×C8×C11C2×Q812yes—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—44no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—44no—
167C11×C22⋊C4—82no—
168C42×C11—28no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C2×Q82C2×C1111yescharacteristic, complemented
175C2×#476C2×C1111yescharacteristic
176C2×C4×SD16C2×C1111yescharacteristic
177#2538C2×C1111yescharacteristic
178#2058C2×C1112yescomplemented
179#2023C2×C1112yes—
180#1990C2×C1111yescharacteristic, complemented
181#1984C2×C1111yescharacteristic, complemented
182#1880C2×C1112yes—
183#1865C2×C1112yescomplemented
184#1803C2×C1111yescharacteristic, complemented
185C23×C11—22no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C22×D411yescharacteristic
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—28no—
197Q8×C11—84no—
198Q8×C11—88no—
199Q8×C11C22⋊Q814yescomplemented
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—41no—
203D4×C11—41no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—84no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11C2×SD1614yes—
230C2×C4×C11C2×SD1612yes—
231C2×C4×C11#13712yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C8×C11—22no—
239C8×C11—41no—
240C8×C11—42no—
241C22×SD16C22×C1111yescharacteristic
242Q82—24no—
243Q82—24no—
244C2×C4⋊Q8—21no—
245C2×C4⋊Q8—22no—
246C2×C4⋊Q8C22×C1112yes—
247C2×C4⋊Q8C22×C1111yescharacteristic
248C2×C22⋊Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C22×C1112yes—
251C2×C4×Q8C22×C1111yescharacteristic
252C2×C4×Q8C22×C1111yescharacteristic
253C2×C4×D4C22×C1111yescharacteristic
254#476—24no—
255C4×SD16—24no—
256C2×#106C22×C1111yescharacteristic
257C2×#106C22×C1112yes—
258C2×C4⋊C8C22×C1111yescharacteristic
259C2×#103C22×C1112yes—
260C2×#103C22×C1111yescharacteristic
261C2×#102C22×C1112yes—
262C2×#102C22×C1111yescharacteristic
263C2×C4×C8C22×C1111yescharacteristic
264#396—22no—
265#390C22×C1112yes—
266#389C22×C1112yes—
267#384C22×C1111yescharacteristic
268#380—21no—
269#340C22×C1112yes—
270#340C22×C1112yes—
271#340C22×C1112yes—
272#336C22×C1112yes—
273#336C22×C1112yes—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11D4×Q811yescharacteristic
284C22×C11C22×SD1611yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C4×C11—24no—
289C4×C11—24no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—44no—
293C4×C11—42no—
294C4×C11—82no—
295C4×C11—81no—
296C4×C11#44814yes—
297C4×C11C2×C22⋊Q811yescharacteristic
298C4×C11#53611yescharacteristic
299C4×C11#54811yescharacteristic
300C4×C11D4×Q811yescharacteristic
301C22×Q8—22no—
302C22×Q8—21no—
303C22×Q8D4×C1111yescharacteristic
304C22×Q8C23×C1111yescharacteristic
305C22×D4C23×C1111yescharacteristic
306C23×C4—21no—
307C2×SD16—22no—
308C2×SD16—22no—
309C2×SD16Q8×C1114yescomplemented
310C22×C8C23×C1111yescharacteristic
311C22×C8C23×C1112yes—
312C22×C8C23×C1111yescharacteristic
313C4⋊Q8—216no—
314C4⋊Q8—28no—
315C4⋊Q8—24no—
316C4⋊Q8—24no—
317C4⋊Q8—22no—
318C4⋊Q8D4×C1114yes—
319C22⋊Q8—44no—
320C4×Q8—28no—
321C4×Q8—24no—
322C4×Q8—24no—
323C4×Q8—22no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8D4×C1114yes—
327C4×D4—22no—
328C4×D4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4D4×C1111yescharacteristic
337C2×C4⋊C4D4×C1112yes—
338C2×C4⋊C4C23×C1111yescharacteristic
339C2×C4⋊C4C23×C1112yes—
340C2×C4⋊C4C23×C1112yes—
341C2×C4⋊C4C23×C1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C42—22no—
346C2×C42—21no—
347C2×C42C23×C1112yes—
348C2×C42C23×C1111yescharacteristic
349#106—22no—
350#106—24no—
351C4⋊C8—22no—
352#103—22no—
353#103—24no—
354#102—22no—
355#102—24no—
356C4×C8—22no—
357#95—22no—
358C2×C11—82no—
359C2×C11#240911yescharacteristic
360C2×C11C2×#44811yescharacteristic
361C2×C11#301211yescharacteristic
362C2×C11#336211yescharacteristic
363C2×C11#336911yescharacteristic
364C2×C11Q8×SD1611yescharacteristic
365C2×C11#338511yescharacteristic
366C24—21no—
367C2×Q8—28no—
368C2×Q8—22no—
369C2×Q8—24no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—81no—
375C2×Q8—81no—
376C2×Q8—82no—
377C2×Q8—82no—
378C2×Q8C11×SD1614yescomplemented
379C2×Q8C2×D4×C1112yes—
380C2×Q8C2×Q8×C1112yes—
381C2×Q8C11×#4112yes—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4C2×Q8×C1112yes—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1112yes—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C24×C1111yescharacteristic
401SD16—28no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8C2×Q8×C1112yes—
411C4⋊C4—28no—
412C4⋊C4—28no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—44no—
425C4⋊C4—81no—
426C4⋊C4C2×D4×C1114yes—
427C4⋊C4C2×D4×C1112yes—
428C22⋊C4—42no—
429C22⋊C4—44no—
430C22⋊C4—82no—
431C42—28no—
432C42—24no—
433C42—22no—
434C42—22no—
435C42C2×D4×C1112yes—
436C42C2×D4×C1112yes—
437C11#2432911yescharacteristic, direct product factor, Sylow
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23C22×D4×C1111yescharacteristic
446Q8—22no—
447Q8—22no—
448Q8—22no—
449Q8—28no—
450Q8—84no—
451Q8—88no—
452Q8C11×C22⋊Q814yescomplemented
453D4—22no—
454D4—22no—
455D4—41no—
456D4—41no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—84no—
480C2×C4C11×#12012yes—
481C2×C4C11×#12012yes—
482C2×C4C2×C11×SD1614yes—
483C2×C4C2×C11×SD1612yes—
484C2×C4C11×#13712yes—
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C2×C4C22×Q8×C1111yescharacteristic
488C2×C4C2×C11×#4111yescharacteristic
489C2×C4C11×2−1+411yescharacteristic
490C2×C4C11×2−1+411yescharacteristic
491C8—22no—
492C8—41no—
493C8—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22C2×C11×#12011yescharacteristic
502C22C11×#54811yescharacteristic
503C22D4×Q8×C1111yescharacteristic
504C22C22×C11×SD1611yescharacteristic
505C22C2×C11×#13711yescharacteristic
506C22C11×#57611yescharacteristic
507C22C11×#57711yescharacteristic
508C4—24no—
509C4—24no—
510C4—22no—
511C4—42no—
512C4—44no—
513C4—42no—
514C4—81no—
515C4—82no—
516C4C11×#44814yes—
517C4C2×C11×C22⋊Q811yescharacteristic
518C4C11×#53611yescharacteristic
519C4C11×#54811yescharacteristic
520C4D4×Q8×C1111yescharacteristic
521C2—82no—
522C2C11×#240911yescharacteristic
523C2C2×C11×#44811yescharacteristic
524C2C11×#301211yescharacteristic
525C2C11×#336211yescharacteristic
526C2C11×#336911yescharacteristic
527C2Q8×C11×SD1611yescharacteristic
528C2C11×#338511yescharacteristic
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×#2058C2semidirect
7. C11×#1990C2semidirect
8. C11×#1984C2semidirect
10. C11×#1865C2semidirect
11. C11×#1803C2semidirect
53. C2×C11×SD16Q8semidirect
102. #24329C11direct (N × H)
115. C2×Q8×C11SD16semidirect
174. C2×Q82C2×C11semidirect
178. #2058C2×C11semidirect
180. #1990C2×C11semidirect
181. #1984C2×C11semidirect
183. #1865C2×C11semidirect
184. #1803C2×C11semidirect
199. Q8×C11C22⋊Q8semidirect
309. C2×SD16Q8×C11semidirect
378. C2×Q8C11×SD16semidirect
437. C11#24329direct (N × H)
452. Q8C11×C22⋊Q8semidirect

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×#4762
C2×C4×C11×SD162
C11×#25382
C11×#20582
C11×#20232
C11×#19902
C11×#19842
C11×#18802
C11×#18652
C11×#18032
#2432911