Finite Group Databasebeta

← C11×#18952 #14596145

Subgroups — C11×#18952 #14596145

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3228C211yesmaximal, characteristic, complemented
4C11×#3214C211yesmaximal, characteristic
5C11×#1651C212yesmaximal, complemented
6C11×#1650C212yesmaximal, complemented
7C11×#1628C212yesmaximal, complemented
8C11×#1627C212yesmaximal, complemented
9C11×#1552C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1480C211yesmaximal, characteristic, complemented
12C11×#563—22no—
13C11×#559—21no—
14Q82×C11—21no—
15C11×#556—21no—
16C11×#556C2212yes—
17D4×Q8×C11—21no—
18D4×Q8×C11C2212yes—
19C11×#542—22no—
20C11×#542—22no—
21C11×#536—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#500C2211yescharacteristic
27C11×#498C2211yescharacteristic
28C11×#496—21no—
29C11×#489—21no—
30C11×#486C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#482—22no—
33C11×#478—22no—
34C11×#476—21no—
35C11×#475C2212yes—
36C11×#465—22no—
37C11×#461—21no—
38C11×#461C2212yes—
39C11×#460C2212yes—
40C11×#459C2212yes—
41C11×#449—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C22×Q8×C11—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C2×C11×D8—22no—
57C22×C8×C11—21no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×#127D411yescharacteristic
68C11×#127C2311yescharacteristic
69C11×#126—24no—
70C11×#126—24no—
71C11×#125—21no—
72C11×#125D412yes—
73C11×#124—24no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#124—21no—
77C11×#124—21no—
78C11×#123—24no—
79C11×#123—24no—
80C11×C22⋊Q8—24no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—24no—
87C11×C22⋊Q8D412yes—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121D412yes—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2312yes—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11C2312yes—
104C11×#117—21no—
105C11×#117—22no—
106C11×#117D412yes—
107C2×C42×C11C2311yescharacteristic
108C11×#107—22no—
109C11×#106—22no—
110C11×#106—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18952C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—81no—
128C11×#41—81no—
129C11×#41—82no—
130C2×Q8×C11—24no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—82no—
137C2×Q8×C11—82no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—41no—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C11×SD16—82no—
154C11×SD16—82no—
155C11×D8—82no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—81no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C42×C11—24no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2411yescharacteristic
195#3550C2×C1111yescharacteristic, complemented
196#3246C2×C1111yescharacteristic, complemented
197#3228C2×C1111yescharacteristic, complemented
198#3214C2×C1111yescharacteristic
199#1651C2×C1112yescomplemented
200#1650C2×C1112yescomplemented
201#1628C2×C1112yescomplemented
202#1627C2×C1112yescomplemented
203#1552C2×C1111yescharacteristic, complemented
204#1497C2×C1111yescharacteristic, complemented
205#1480C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—41no—
208C23×C11#12011yescharacteristic
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—42no—
212Q8×C11—41no—
213Q8×C11—42no—
214Q8×C11—41no—
215Q8×C11—42no—
216Q8×C11—81no—
217Q8×C11—84no—
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—41no—
225D4×C11—81no—
226D4×C11—82no—
227D4×C11—82no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—82no—
241C2×C4×C11—84no—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C8×C11—41no—
249C8×C11—41no—
250C8×C11—42no—
251C8×C11—42no—
252#563—22no—
253#559—21no—
254Q82—21no—
255#556—21no—
256#556C22×C1112yes—
257D4×Q8—21no—
258D4×Q8C22×C1112yes—
259#542—22no—
260#542—22no—
261#536—22no—
262#533C22×C1111yescharacteristic
263#533C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265#532C22×C1111yescharacteristic
266#500C22×C1111yescharacteristic
267#498C22×C1111yescharacteristic
268#496—21no—
269#489—21no—
270#486C22×C1111yescharacteristic
271#486C22×C1111yescharacteristic
272#482—22no—
273#478—22no—
274#476—21no—
275#475C22×C1112yes—
276#465—22no—
277#461—21no—
278#461C22×C1112yes—
279#460C22×C1112yes—
280#459C22×C1112yes—
281#449—22no—
282#432C22×C1111yescharacteristic
283#431C22×C1111yescharacteristic
284C2×C4⋊C8C22×C1111yescharacteristic
285#332C22×C1112yes—
286#332C22×C1112yes—
287Q8⋊C8C22×C1112yes—
288Q8⋊C8C22×C1112yes—
289D4⋊C8C22×C1112yes—
290D4⋊C8C22×C1112yes—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11C2×#12011yescharacteristic
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—81no—
311C4×C11#57611yescharacteristic
312C4×C11#57712yes—
313C4×C11#57711yescharacteristic
314C2×#41—21no—
315C2×#41—21no—
316C22×Q8—22no—
317C2×SD16—22no—
318C2×SD16—22no—
319C2×D8—22no—
320C22×C8—21no—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8D4×C1111yescharacteristic
325C4⋊Q8D4×C1111yescharacteristic
326C4⋊Q8D4×C1111yescharacteristic
327C4⋊Q8C23×C1111yescharacteristic
328C4⋊Q8C23×C1111yescharacteristic
329C4⋊Q8C23×C1111yescharacteristic
330#127D4×C1111yescharacteristic
331#127C23×C1111yescharacteristic
332#126—24no—
333#126—24no—
334#125—21no—
335#125D4×C1112yes—
336#124—24no—
337#124—22no—
338#124—22no—
339#124—21no—
340#124—21no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8—24no—
350C22⋊Q8D4×C1112yes—
351#121—21no—
352#121—21no—
353#121—21no—
354#121D4×C1112yes—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8C23×C1112yes—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C23×C1112yes—
367#117—21no—
368#117—22no—
369#117D4×C1112yes—
370C2×C42C23×C1111yescharacteristic
371#107—22no—
372#106—22no—
373#106—22no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8C23×C1112yes—
377C4⋊C8C23×C1112yes—
378#103—22no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386#97—21no—
387C4×C8C23×C1111yescharacteristic
388C4×C8C23×C1111yescharacteristic
389C2×C11—41no—
390C2×C11—82no—
391C2×C11—161no—
392C2×C11#301011yescharacteristic
393C2×C11#301211yescharacteristic
394C2×C11#302011yescharacteristic
395#41—81no—
396#41—81no—
397#41—82no—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—82no—
405C2×Q8—82no—
406C2×Q8C2×D4×C1112yes—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—41no—
414C2×D4C2×D4×C1112yes—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—41no—
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421SD16—82no—
422SD16—82no—
423D8—82no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—81no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4C2×D4×C1112yes—
444C4⋊C4C2×D4×C1112yes—
445C4⋊C4C2×D4×C1112yes—
446C4⋊C4C2×D4×C1112yes—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C42—24no—
457C42—22no—
458C42—22no—
459C42C2×D4×C1111yescharacteristic
460C42C2×D4×C1111yescharacteristic
461C42C2×D4×C1111yescharacteristic
462C42C24×C1111yescharacteristic
463C11#1895211yescharacteristic, direct product factor, Sylow
464C23—22no—
465C23—41no—
466C23C11×#12011yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—42no—
470Q8—41no—
471Q8—42no—
472Q8—41no—
473Q8—42no—
474Q8—81no—
475Q8—84no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—42no—
480D4—41no—
481D4—42no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—84no—
500C2×C4C11×#12011yescharacteristic
501C2×C4C11×#12011yescharacteristic
502C2×C4C11×#12011yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C22×D4×C1111yescharacteristic
506C8—41no—
507C8—41no—
508C8—42no—
509C8—42no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C2×C11×#12011yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—81no—
530C4C11×#57611yescharacteristic
531C4C11×#57712yes—
532C4C11×#57711yescharacteristic
533C2—41no—
534C2—82no—
535C2—161no—
536C2C11×#301011yescharacteristic
537C2C11×#301211yescharacteristic
538C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3214C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3550C2semidirect
2. C11×#3246C2semidirect
3. C11×#3228C2semidirect
5. C11×#1651C2semidirect
6. C11×#1650C2semidirect
7. C11×#1628C2semidirect
8. C11×#1627C2semidirect
9. C11×#1552C2semidirect
10. C11×#1497C2semidirect
11. C11×#1480C2semidirect
126. #18952C11direct (N × H)
195. #3550C2×C11semidirect
196. #3246C2×C11semidirect
197. #3228C2×C11semidirect
199. #1651C2×C11semidirect
200. #1650C2×C11semidirect
201. #1628C2×C11semidirect
202. #1627C2×C11semidirect
203. #1552C2×C11semidirect
204. #1497C2×C11semidirect
205. #1480C2×C11semidirect
463. C11#18952direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32462
C11×#32282
C11×#32142
C11×#16512
C11×#16502
C11×#16282
C11×#16272
C11×#15522
C11×#14972
C11×#14802
#1895211