Finite Group Databasebeta

← C11×#18947 #14596140

Subgroups — C11×#18947 #14596140

Order 2816.

902 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×#3548C211yesmaximal, characteristic
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3235C211yesmaximal, characteristic, complemented
4C11×#3231C211yesmaximal, characteristic, complemented
5C11×#1654C212yesmaximal, complemented
6C11×#1647C212yesmaximal, complemented
7C11×#1635C212yesmaximal, complemented
8C11×#1635C212yesmaximal, complemented
9C11×#1552C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1480C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#554—21no—
14C11×#554—21no—
15C11×#550—21no—
16C11×#550—21no—
17C11×#547C2212yes—
18C11×#547C2212yes—
19C11×#540—22no—
20C11×#537—22no—
21C11×#537—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#501—21no—
27C11×#500C2211yescharacteristic
28C11×#498C2211yescharacteristic
29C11×#490—21no—
30C11×#487C2211yescharacteristic
31C11×#487C2211yescharacteristic
32C11×#485—22no—
33C11×#482—22no—
34C11×#479—22no—
35C11×#476C2212yes—
36C11×#476C2212yes—
37C11×#475—21no—
38C11×#474C2212yes—
39C11×#465—22no—
40C11×#461C2212yes—
41C11×#460—21no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×D4⋊C8C2212yes—
48C11×D4⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×SD16—22no—
56C22×C8×C11—21no—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×C4⋊Q8C2311yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127—22no—
64C11×#127D411yescharacteristic
65C11×#127D411yescharacteristic
66C11×#125—22no—
67C11×#125—21no—
68C11×#125D412yes—
69C11×#124—21no—
70C11×#124—21no—
71C11×#123—24no—
72C11×#123—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#121—24no—
84C11×#121—24no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121D412yes—
90C11×#121D412yes—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11C2312yes—
100C4×D4×C11C2312yes—
101C11×#117—21no—
102C11×#117D412yes—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#107—22no—
108C11×#106—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×#103—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#18947C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—81no—
128C11×#41—82no—
129C11×#41—81no—
130C11×#41—82no—
131C11×#41—84no—
132C11×#41—82no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×D412yes—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C11×SD16—82no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—81no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
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—22no—
187C11×C22⋊C4—41no—
188C42×C11—22no—
189C42×C11—41no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2411yescharacteristic
194#3548C2×C1111yescharacteristic
195#3246C2×C1111yescharacteristic, complemented
196#3235C2×C1111yescharacteristic, complemented
197#3231C2×C1111yescharacteristic, complemented
198#1654C2×C1112yescomplemented
199#1647C2×C1112yescomplemented
200#1635C2×C1112yescomplemented
201#1635C2×C1112yescomplemented
202#1552C2×C1111yescharacteristic, complemented
203#1496C2×C1111yescharacteristic, complemented
204#1480C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11#12011yescharacteristic
208Q8×C11—42no—
209Q8×C11—41no—
210Q8×C11—42no—
211Q8×C11—41no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—81no—
215Q8×C11—81no—
216D4×C11—22no—
217D4×C11—24no—
218D4×C11—22no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—81no—
222D4×C11—81no—
223D4×C11—82no—
224D4×C11—82no—
225D4×C11—84no—
226D4×C11—84no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—84no—
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#562—22no—
253#554—21no—
254#554—21no—
255#550—21no—
256#550—21no—
257#547C22×C1112yes—
258#547C22×C1112yes—
259#540—22no—
260#537—22no—
261#537—22no—
262#533C22×C1111yescharacteristic
263#533C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265#532C22×C1111yescharacteristic
266#501—21no—
267#500C22×C1111yescharacteristic
268#498C22×C1111yescharacteristic
269#490—21no—
270#487C22×C1111yescharacteristic
271#487C22×C1111yescharacteristic
272#485—22no—
273#482—22no—
274#479—22no—
275#476C22×C1112yes—
276#476C22×C1112yes—
277#475—21no—
278#474C22×C1112yes—
279#465—22no—
280#461C22×C1112yes—
281#460—21no—
282#432C22×C1111yescharacteristic
283#431C22×C1111yescharacteristic
284C2×C4⋊C8C22×C1111yescharacteristic
285#332C22×C1112yes—
286#332C22×C1112yes—
287D4⋊C8C22×C1112yes—
288D4⋊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—42no—
298C22×C11—42no—
299C22×C11—42no—
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—81no—
310C4×C11—81no—
311C4×C11#57611yescharacteristic
312C4×C11#57712yes—
313C4×C11#57711yescharacteristic
314C2×#41—22no—
315C2×#41—22no—
316C2×#41—21no—
317C2×#41—21no—
318C2×SD16—22no—
319C22×C8—21no—
320C4⋊Q8D4×C1111yescharacteristic
321C4⋊Q8D4×C1111yescharacteristic
322C4⋊Q8C23×C1111yescharacteristic
323C4⋊Q8C23×C1111yescharacteristic
324C4⋊Q8C23×C1111yescharacteristic
325C4⋊Q8C23×C1111yescharacteristic
326#127—22no—
327#127D4×C1111yescharacteristic
328#127D4×C1111yescharacteristic
329#125—22no—
330#125—21no—
331#125D4×C1112yes—
332#124—21no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344#121—24no—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—22no—
349#121—22no—
350#121—21no—
351#121—21no—
352#121D4×C1112yes—
353#121D4×C1112yes—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4C23×C1112yes—
363C4×D4C23×C1112yes—
364#117—21no—
365#117D4×C1112yes—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C42C23×C1111yescharacteristic
369#107—22no—
370#107—22no—
371#106—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#103—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—82no—
392C2×C11#300911yescharacteristic
393C2×C11#301211yescharacteristic
394C2×C11#302011yescharacteristic
395#41—81no—
396#41—82no—
397#41—81no—
398#41—82no—
399#41—84no—
400#41—82no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4C2×D4×C1112yes—
416C2×D4C2×D4×C1112yes—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424SD16—82no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—81no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4C2×D4×C1112yes—
445C4⋊C4C2×D4×C1112yes—
446C4⋊C4C2×D4×C1112yes—
447C4⋊C4C2×D4×C1112yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—41no—
456C42—22no—
457C42—41no—
458C42C2×D4×C1111yescharacteristic
459C42C2×D4×C1111yescharacteristic
460C42C2×D4×C1111yescharacteristic
461C42C24×C1111yescharacteristic
462C11#1894711yescharacteristic, direct product factor, Sylow
463C23—22no—
464C23—22no—
465C23C11×#12011yescharacteristic
466Q8—42no—
467Q8—41no—
468Q8—42no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—81no—
473Q8—81no—
474D4—22no—
475D4—24no—
476D4—22no—
477D4—42no—
478D4—42no—
479D4—81no—
480D4—81no—
481D4—82no—
482D4—82no—
483D4—84no—
484D4—84no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—84no—
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—42no—
517C22—42no—
518C22—42no—
519C22C2×C11×#12011yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C4C11×#57611yescharacteristic
531C4C11×#57712yes—
532C4C11×#57711yescharacteristic
533C2—41no—
534C2—82no—
535C2—82no—
536C2C11×#300911yescharacteristic
537C2C11×#301211yescharacteristic
538C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3548C2
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
2. C11×#3246C2semidirect
3. C11×#3235C2semidirect
4. C11×#3231C2semidirect
5. C11×#1654C2semidirect
6. C11×#1647C2semidirect
7. C11×#1635C2semidirect
8. C11×#1635C2semidirect
9. C11×#1552C2semidirect
10. C11×#1496C2semidirect
11. C11×#1480C2semidirect
126. #18947C11direct (N × H)
195. #3246C2×C11semidirect
196. #3235C2×C11semidirect
197. #3231C2×C11semidirect
198. #1654C2×C11semidirect
199. #1647C2×C11semidirect
200. #1635C2×C11semidirect
201. #1635C2×C11semidirect
202. #1552C2×C11semidirect
203. #1496C2×C11semidirect
204. #1480C2×C11semidirect
462. C11#18947direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#32462
C11×#32352
C11×#32312
C11×#16542
C11×#16472
C11×#16352
C11×#15522
C11×#14962
C11×#14802
#1894711