Finite Group Databasebeta

← C11×#18941 #14596134

Subgroups — C11×#18941 #14596134

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic
2C11×#3249C211yesmaximal, characteristic, complemented
3C11×#3235C211yesmaximal, characteristic, complemented
4C11×#3210C211yesmaximal, characteristic, complemented
5C11×#1644C212yesmaximal, complemented
6C11×#1641C212yesmaximal, complemented
7C11×#1632C212yesmaximal, complemented
8C11×#1631C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1480C211yesmaximal, 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×#490—21no—
30C11×#487C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#482—22no—
33C11×#477—21no—
34C11×#477C2212yes—
35C11×#476C2212yes—
36C11×#474C2212yes—
37C11×#467—22no—
38C11×#464—22no—
39C11×#462—21no—
40C11×#462C2212yes—
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×Q16—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×#107—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#18941C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—81no—
128C11×#41—81no—
129C11×#41—82no—
130C11×#41—82no—
131C11×#41—82no—
132C11×#41—84no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C2×D412yes—
138C2×Q8×C11C2×D412yes—
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×Q16—82no—
157C11×Q16—82no—
158C11×SD16—82no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—81no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4C2×D412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—41no—
190C42×C11—22no—
191C42×C11—41no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2411yescharacteristic
196#3548C2×C1111yescharacteristic
197#3249C2×C1111yescharacteristic, complemented
198#3235C2×C1111yescharacteristic, complemented
199#3210C2×C1111yescharacteristic, complemented
200#1644C2×C1112yescomplemented
201#1641C2×C1112yescomplemented
202#1632C2×C1112yescomplemented
203#1631C2×C1112yescomplemented
204#1551C2×C1111yescharacteristic, complemented
205#1497C2×C1111yescharacteristic, complemented
206#1480C2×C1111yescharacteristic, complemented
207C23×C11—22no—
208C23×C11—22no—
209C23×C11#12011yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—81no—
218D4×C11—24no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—81no—
225D4×C11—82no—
226D4×C11—82no—
227D4×C11—84no—
228D4×C11—84no—
229C2×C4×C11—21no—
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—44no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—84no—
243C2×C4×C11—84no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C8×C11—41no—
251C8×C11—41no—
252C8×C11—42no—
253C8×C11—42no—
254#562—22no—
255#554—21no—
256#554C22×C1112yes—
257#550—21no—
258#550C22×C1112yes—
259#547—21no—
260#547—21no—
261#540—22no—
262#537—22no—
263#537—22no—
264#533C22×C1111yescharacteristic
265#533C22×C1111yescharacteristic
266#532C22×C1111yescharacteristic
267#532C22×C1111yescharacteristic
268#501—21no—
269#494C22×C1111yescharacteristic
270#492C22×C1111yescharacteristic
271#490—21no—
272#487C22×C1111yescharacteristic
273#486C22×C1111yescharacteristic
274#482—22no—
275#477—21no—
276#477C22×C1112yes—
277#476C22×C1112yes—
278#474C22×C1112yes—
279#467—22no—
280#464—22no—
281#462—21no—
282#462C22×C1112yes—
283#452—22no—
284#432C22×C1111yescharacteristic
285#431C22×C1111yescharacteristic
286C2×C4⋊C8C22×C1111yescharacteristic
287#333C22×C1112yes—
288#331C22×C1112yes—
289Q8⋊C8C22×C1112yes—
290Q8⋊C8C22×C1112yes—
291D4⋊C8C22×C1112yes—
292D4⋊C8C22×C1112yes—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11C2×#12011yescharacteristic
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—81no—
312C4×C11—81no—
313C4×C11#57611yescharacteristic
314C4×C11#57711yescharacteristic
315C4×C11#57812yes—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—21no—
319C2×#41D4×C1112yes—
320C2×Q16—22no—
321C2×Q16—22no—
322C2×SD16—22no—
323C22×C8—21no—
324C4⋊Q8D4×C1111yescharacteristic
325C4⋊Q8D4×C1111yescharacteristic
326C4⋊Q8D4×C1111yescharacteristic
327C4⋊Q8C23×C1111yescharacteristic
328C4⋊Q8C23×C1111yescharacteristic
329C4⋊Q8C23×C1111yescharacteristic
330#127—22no—
331#127D4×C1111yescharacteristic
332#127C23×C1111yescharacteristic
333#125—22no—
334#125—21no—
335#125—21no—
336#124—21no—
337#124D4×C1112yes—
338#123—24no—
339#123—24no—
340C22⋊Q8—22no—
341C22⋊Q8—24no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8D4×C1112yes—
348#121—24no—
349#121—24no—
350#121—22no—
351#121—24no—
352#121—24no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—22no—
357#121D4×C1112yes—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C23×C1112yes—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4C23×C1112yes—
368#117—21no—
369#117—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C42C23×C1111yescharacteristic
373#107—22no—
374#107—22no—
375#106—22no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8C23×C1112yes—
379C4⋊C8C23×C1112yes—
380#103—22no—
381#103—22no—
382#103—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388#97—21no—
389C4×C8C23×C1111yescharacteristic
390C4×C8C23×C1111yescharacteristic
391C2×C11—41no—
392C2×C11—82no—
393C2×C11—82no—
394C2×C11#301111yescharacteristic
395C2×C11#301211yescharacteristic
396C2×C11#301911yescharacteristic
397#41—81no—
398#41—81no—
399#41—82no—
400#41—82no—
401#41—82no—
402#41—84no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8C2×D4×C1112yes—
408C2×Q8C2×D4×C1112yes—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×D4×C1112yes—
418C2×D4C2×D4×C1112yes—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426Q16—82no—
427Q16—82no—
428SD16—82no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—81no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4C2×D4×C1112yes—
451C4⋊C4C2×D4×C1112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—41no—
460C42—22no—
461C42—41no—
462C42C2×D4×C1111yescharacteristic
463C42C2×D4×C1111yescharacteristic
464C42C2×D4×C1111yescharacteristic
465C42C24×C1111yescharacteristic
466C11#1894111yescharacteristic, direct product factor, Sylow
467C23—22no—
468C23—22no—
469C23C11×#12011yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475Q8—41no—
476Q8—41no—
477Q8—81no—
478D4—24no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—42no—
484D4—81no—
485D4—82no—
486D4—82no—
487D4—84no—
488D4—84no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4C11×#12011yescharacteristic
505C2×C4C11×#12011yescharacteristic
506C2×C4C11×#12011yescharacteristic
507C2×C4C22×D4×C1111yescharacteristic
508C2×C4C22×D4×C1111yescharacteristic
509C2×C4C22×D4×C1111yescharacteristic
510C8—41no—
511C8—41no—
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22C2×C11×#12011yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—81no—
533C4—81no—
534C4C11×#57611yescharacteristic
535C4C11×#57711yescharacteristic
536C4C11×#57812yes—
537C2—41no—
538C2—82no—
539C2—82no—
540C2C11×#301111yescharacteristic
541C2C11×#301211yescharacteristic
542C2C11×#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×#3249C2semidirect
3. C11×#3235C2semidirect
4. C11×#3210C2semidirect
5. C11×#1644C2semidirect
6. C11×#1641C2semidirect
7. C11×#1632C2semidirect
8. C11×#1631C2semidirect
9. C11×#1551C2semidirect
10. C11×#1497C2semidirect
11. C11×#1480C2semidirect
126. #18941C11direct (N × H)
197. #3249C2×C11semidirect
198. #3235C2×C11semidirect
199. #3210C2×C11semidirect
200. #1644C2×C11semidirect
201. #1641C2×C11semidirect
202. #1632C2×C11semidirect
203. #1631C2×C11semidirect
204. #1551C2×C11semidirect
205. #1497C2×C11semidirect
206. #1480C2×C11semidirect
466. C11#18941direct (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×#32492
C11×#32352
C11×#32102
C11×#16442
C11×#16412
C11×#16322
C11×#16312
C11×#15512
C11×#14972
C11×#14802
#1894111