Finite Group Databasebeta

← C11×#18937 #14596130

Subgroups — C11×#18937 #14596130

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3237C211yesmaximal, characteristic, complemented
4C11×#3210C211yesmaximal, characteristic, complemented
5C11×#1643C212yesmaximal, complemented
6C11×#1642C212yesmaximal, complemented
7C11×#1632C212yesmaximal, complemented
8C11×#1631C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic, complemented
10C11×#1496C211yesmaximal, characteristic, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#554—21no—
14C11×#554C2212yes—
15C11×#550—21no—
16C11×#550C2212yes—
17C11×#547—21no—
18C11×#547—21no—
19C11×#540—22no—
20C11×#537—22no—
21C11×#537—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#501—21no—
27C11×#494C2211yescharacteristic
28C11×#492C2211yescharacteristic
29C11×#491—21no—
30C11×#487C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#485—22no—
33C11×#477C2212yes—
34C11×#476C2212yes—
35C11×#475—21no—
36C11×#475C2212yes—
37C11×#465—22no—
38C11×#464—22no—
39C11×#461C2212yes—
40C11×#460—21no—
41C11×#452—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#333C2212yes—
46C11×#331C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—21no—
54C2×C11×#41D412yes—
55C2×C11×Q16—22no—
56C2×C11×SD16—22no—
57C2×C11×SD16—22no—
58C22×C8×C11—21no—
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127—22no—
66C11×#127D411yescharacteristic
67C11×#127C2311yescharacteristic
68C11×#125—22no—
69C11×#125—21no—
70C11×#125—21no—
71C11×#124—21no—
72C11×#124D412yes—
73C11×#123—24no—
74C11×#123—24no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8D412yes—
83C11×#121—24no—
84C11×#121—24no—
85C11×#121—22no—
86C11×#121—24no—
87C11×#121—24no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—22no—
92C11×#121D412yes—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2312yes—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11C2312yes—
103C11×#117—21no—
104C11×#117—21no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
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×#103—22no—
118C11×#103—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#18937C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C11×#41—82no—
129C11×#41—84no—
130C11×#41—84no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C11×Q16—82no—
155C11×SD16—82no—
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—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
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#3237C2×C1111yescharacteristic, complemented
197#3210C2×C1111yescharacteristic, complemented
198#1643C2×C1112yescomplemented
199#1642C2×C1112yescomplemented
200#1632C2×C1112yescomplemented
201#1631C2×C1112yescomplemented
202#1551C2×C1111yescharacteristic, complemented
203#1496C2×C1111yescharacteristic, complemented
204#1481C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11#12011yescharacteristic
208Q8×C11—24no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—81no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—41no—
220D4×C11—42no—
221D4×C11—41no—
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—44no—
236C2×C4×C11—44no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—84no—
240C2×C4×C11—84no—
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C8×C11—41no—
248C8×C11—41no—
249C8×C11—42no—
250C8×C11—42no—
251#562—22no—
252#554—21no—
253#554C22×C1112yes—
254#550—21no—
255#550C22×C1112yes—
256#547—21no—
257#547—21no—
258#540—22no—
259#537—22no—
260#537—22no—
261#533C22×C1111yescharacteristic
262#533C22×C1111yescharacteristic
263#532C22×C1111yescharacteristic
264#532C22×C1111yescharacteristic
265#501—21no—
266#494C22×C1111yescharacteristic
267#492C22×C1111yescharacteristic
268#491—21no—
269#487C22×C1111yescharacteristic
270#486C22×C1111yescharacteristic
271#485—22no—
272#477C22×C1112yes—
273#476C22×C1112yes—
274#475—21no—
275#475C22×C1112yes—
276#465—22no—
277#464—22no—
278#461C22×C1112yes—
279#460—21no—
280#452—22no—
281#432C22×C1111yescharacteristic
282#431C22×C1111yescharacteristic
283C2×C4⋊C8C22×C1111yescharacteristic
284#333C22×C1112yes—
285#331C22×C1112yes—
286Q8⋊C8C22×C1112yes—
287Q8⋊C8C22×C1112yes—
288D4⋊C8C22×C1112yes—
289D4⋊C8C22×C1112yes—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11C2×#12011yescharacteristic
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#57712yes—
311C4×C11#57711yescharacteristic
312C4×C11#57811yescharacteristic
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41D4×C1112yes—
317C2×Q16—22no—
318C2×SD16—22no—
319C2×SD16—22no—
320C22×C8—21no—
321C4⋊Q8D4×C1111yescharacteristic
322C4⋊Q8D4×C1111yescharacteristic
323C4⋊Q8D4×C1111yescharacteristic
324C4⋊Q8C23×C1111yescharacteristic
325C4⋊Q8C23×C1111yescharacteristic
326C4⋊Q8C23×C1111yescharacteristic
327#127—22no—
328#127D4×C1111yescharacteristic
329#127C23×C1111yescharacteristic
330#125—22no—
331#125—21no—
332#125—21no—
333#124—21no—
334#124D4×C1112yes—
335#123—24no—
336#123—24no—
337C22⋊Q8—22no—
338C22⋊Q8—24no—
339C22⋊Q8—22no—
340C22⋊Q8—24no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8D4×C1112yes—
345#121—24no—
346#121—24no—
347#121—22no—
348#121—24no—
349#121—24no—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—22no—
354#121D4×C1112yes—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8C23×C1112yes—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4C23×C1112yes—
365#117—21no—
366#117—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C42C23×C1111yescharacteristic
370#107—22no—
371#106—22no—
372#106—22no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8C23×C1112yes—
376C4⋊C8C23×C1112yes—
377#103—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#102—22no—
382#102—22no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385#97—21no—
386C4×C8C23×C1111yescharacteristic
387C4×C8C23×C1111yescharacteristic
388C2×C11—41no—
389C2×C11—82no—
390C2×C11—82no—
391C2×C11#300911yescharacteristic
392C2×C11#301311yescharacteristic
393C2×C11#301911yescharacteristic
394#41—82no—
395#41—82no—
396#41—84no—
397#41—84no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8C2×D4×C1112yes—
403C2×Q8C2×D4×C1112yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C2×D4×C1112yes—
413C2×D4C2×D4×C1112yes—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421Q16—82no—
422SD16—82no—
423SD16—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—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4C2×D4×C1112yes—
446C4⋊C4C2×D4×C1112yes—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—41no—
455C42—22no—
456C42—41no—
457C42C2×D4×C1111yescharacteristic
458C42C2×D4×C1111yescharacteristic
459C42C2×D4×C1111yescharacteristic
460C42C24×C1111yescharacteristic
461C11#1893711yescharacteristic, direct product factor, Sylow
462C23—22no—
463C23—22no—
464C23C11×#12011yescharacteristic
465Q8—24no—
466Q8—42no—
467Q8—42no—
468Q8—42no—
469Q8—41no—
470Q8—41no—
471Q8—81no—
472D4—22no—
473D4—22no—
474D4—42no—
475D4—42no—
476D4—41no—
477D4—42no—
478D4—41no—
479D4—81no—
480D4—82no—
481D4—82no—
482D4—84no—
483D4—84no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—84no—
497C2×C4—84no—
498C2×C4C11×#12011yescharacteristic
499C2×C4C11×#12011yescharacteristic
500C2×C4C11×#12011yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C2×C4C22×D4×C1111yescharacteristic
503C2×C4C22×D4×C1111yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22C2×C11×#12011yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—81no—
527C4—81no—
528C4C11×#57712yes—
529C4C11×#57711yescharacteristic
530C4C11×#57811yescharacteristic
531C2—41no—
532C2—82no—
533C2—82no—
534C2C11×#300911yescharacteristic
535C2C11×#301311yescharacteristic
536C2C11×#301911yescharacteristic
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×#3237C2semidirect
4. C11×#3210C2semidirect
5. C11×#1643C2semidirect
6. C11×#1642C2semidirect
7. C11×#1632C2semidirect
8. C11×#1631C2semidirect
9. C11×#1551C2semidirect
10. C11×#1496C2semidirect
11. C11×#1481C2semidirect
126. #18937C11direct (N × H)
195. #3246C2×C11semidirect
196. #3237C2×C11semidirect
197. #3210C2×C11semidirect
198. #1643C2×C11semidirect
199. #1642C2×C11semidirect
200. #1632C2×C11semidirect
201. #1631C2×C11semidirect
202. #1551C2×C11semidirect
203. #1496C2×C11semidirect
204. #1481C2×C11semidirect
461. C11#18937direct (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×#32372
C11×#32102
C11×#16432
C11×#16422
C11×#16322
C11×#16312
C11×#15512
C11×#14962
C11×#14812
#1893711