Finite Group Databasebeta

← C11×#18366 #14595559

Subgroups — C11×#18366 #14595559

Order 2816.

1048 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3493C211yesmaximal, characteristic, complemented
2C11×#3217C212yesmaximal, complemented
3C11×#2619C211yesmaximal, characteristic, complemented
4C11×#1600C214yesmaximal, complemented
5C11×#1599C212yesmaximal, complemented
6C11×#1598C212yesmaximal, complemented
7C11×#1512C212yesmaximal, complemented
8C11×#1464C211yesmaximal, characteristic, complemented
9C11×#556—22no—
10C11×#555—22no—
11C11×#553—22no—
12C11×#552—22no—
13C11×#544C2211yescharacteristic
14C11×#538—21no—
15C11×#538C2212yes—
16C11×#537C2211yescharacteristic
17C2×C11×#127C2211yescharacteristic
18C11×#529—21no—
19C11×#529C2212yes—
20C11×#525—21no—
21C2×C11×#121—21no—
22C11×#520—21no—
23C2×C11×#117C2211yescharacteristic
24C11×#496—22no—
25C11×#490—22no—
26C11×#460—22no—
27C11×#459—22no—
28C11×#450C2214yes—
29C11×#447C2214yes—
30C11×#432C2212yes—
31C11×#394—21no—
32C11×#394C2212yes—
33C11×#392—21no—
34C11×#392C2212yes—
35C11×#390—21no—
36C11×#382C2211yescharacteristic
37C11×#328C2214yes—
38C11×#327C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C2×C11×#41—21no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11D411yescharacteristic
47C2×C11×SD16—24no—
48C2×C11×D8—24no—
49C11×C4⋊Q8—22no—
50C11×#127—22no—
51C11×#127—22no—
52C11×#126—22no—
53C11×#126—22no—
54C11×#126—22no—
55C11×#126—22no—
56C11×#125—21no—
57C11×#125—22no—
58C11×#125D412yescomplemented
59C11×#124—21no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124D412yescomplemented
63C11×#123—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8C2312yes—
71C11×#121—21no—
72C11×#121—21no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—21no—
77C11×#121—44no—
78C11×#121C2312yes—
79C11×#120—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11D412yescomplemented
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11D412yescomplemented
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—21no—
93C11×#117—22no—
94C11×#117—22no—
95C11×#117—22no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4C2311yescharacteristic
105C2×C42×C11D411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×C4⋊C8—22no—
108C11×#102—24no—
109C11×#102—24no—
110C11×C22⋊C8C2314yes—
111C11×#97—22no—
112C11×#95—21no—
113C11×#95C2312yes—
114#18366C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—22no—
116C24×C11C2×D411yescharacteristic
117C11×#41—42no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—42no—
134C2×D4×C11—82no—
135C2×D4×C11—82no—
136C2×D4×C11—82no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D412yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—41no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C11×SD16—84no—
154C11×D8—84no—
155C2×C8×C11—24no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—44no—
183C11×C22⋊C4—82no—
184C11×C22⋊C4—82no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—22no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192#3493C2×C1111yescharacteristic, complemented
193#3217C2×C1112yescomplemented
194#2619C2×C1111yescharacteristic, complemented
195#1600C2×C1114yescomplemented
196#1599C2×C1112yescomplemented
197#1598C2×C1112yescomplemented
198#1512C2×C1112yescomplemented
199#1464C2×C1111yescharacteristic, complemented
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C22×D411yescharacteristic
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—81no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—44no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—82no—
224D4×C11—82no—
225D4×C11—84no—
226D4×C11—82no—
227D4×C11—81no—
228D4×C11—82no—
229D4×C11—88no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—82no—
250C2×C4×C11—82no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12012yes—
254C2×C4×C11AGL(1,ℤ/8)12yes—
255C2×C4×C11C22×D412yes—
256C8×C11—44no—
257#556—22no—
258#555—22no—
259#553—22no—
260#552—22no—
261#544C22×C1111yescharacteristic
262#538—21no—
263#538C22×C1112yes—
264#537C22×C1111yescharacteristic
265C2×#127C22×C1111yescharacteristic
266#529—21no—
267#529C22×C1112yes—
268#525—21no—
269C2×#121—21no—
270#520—21no—
271C2×#117C22×C1111yescharacteristic
272#496—22no—
273#490—22no—
274#460—22no—
275#459—22no—
276#450C22×C1114yes—
277#447C22×C1114yes—
278#432C22×C1112yes—
279#394—21no—
280#394C22×C1112yes—
281#392—21no—
282#392C22×C1112yes—
283#390—21no—
284#382C22×C1111yescharacteristic
285#328C22×C1114yes—
286#327C22×C1114yes—
287#324C22×C1112yes—
288#323C22×C1112yes—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—42no—
292C22×C11—41no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—41no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C11#57511yescharacteristic
309C4×C11—22no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11—82no—
320C2×#41—21no—
321C22×D4—22no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4C23×C1112yes—
325C23×C4D4×C1111yescharacteristic
326C2×SD16—24no—
327C2×D8—24no—
328C4⋊Q8—22no—
329#127—22no—
330#127—22no—
331#126—22no—
332#126—22no—
333#126—22no—
334#126—22no—
335#125—21no—
336#125—22no—
337#125D4×C1112yescomplemented
338#124—21no—
339#124—22no—
340#124—22no—
341#124D4×C1112yescomplemented
342#123—22no—
343#123—22no—
344#123—22no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8C23×C1112yes—
350#121—21no—
351#121—21no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—21no—
356#121—44no—
357#121C23×C1112yes—
358#120—22no—
359C4×Q8—22no—
360C4×Q8—21no—
361C4×Q8D4×C1112yescomplemented
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—21no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4D4×C1112yescomplemented
369#117—22no—
370#117—22no—
371#117—21no—
372#117—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C1111yescharacteristic
378C2×C4⋊C4C23×C1111yescharacteristic
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4D4×C1111yescharacteristic
383C2×C22⋊C4C23×C1111yescharacteristic
384C2×C42D4×C1111yescharacteristic
385C2×C42C23×C1111yescharacteristic
386C4⋊C8—22no—
387#102—24no—
388#102—24no—
389C22⋊C8C23×C1114yes—
390#97—22no—
391#95—21no—
392#95C23×C1112yes—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—82no—
396C2×C11—81no—
397C2×C11—162no—
398C2×C11#300611yescharacteristic
399C2×C11#302111yescharacteristic
400C2×C11#302711yescharacteristic
401C24—22no—
402C24C2×D4×C1111yescharacteristic
403#41—42no—
404#41—42no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8C2×D4×C1112yes—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—24no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—42no—
420C2×D4—82no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C2×D4×C1112yes—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—41no—
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C24×C1111yescharacteristic
439SD16—84no—
440D8—84no—
441C2×C8—24no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4C2×D4×C1112yes—
456C4⋊C4C2×D4×C1112yes—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—44no—
469C22⋊C4—82no—
470C22⋊C4—82no—
471C42—22no—
472C42—22no—
473C42—21no—
474C42—21no—
475C42—22no—
476C42C2×D4×C1112yes—
477C42C2×D4×C1112yes—
478C11#1836611yescharacteristic, direct product factor, Sylow
479C23—21no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C22×D4×C1111yescharacteristic
493Q8—42no—
494Q8—42no—
495Q8—81no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—42no—
502D4—82no—
503D4—82no—
504D4—84no—
505D4—82no—
506D4—81no—
507D4—82no—
508D4—88no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C11×#12011yescharacteristic
531C2×C4C11×#12011yescharacteristic
532C2×C4C11×#12012yes—
533C2×C4C11×AGL(1,ℤ/8)12yes—
534C2×C4C22×D4×C1112yes—
535C8—44no—
536C22—21no—
537C22—21no—
538C22—42no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—41no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22C2×C11×#12011yescharacteristic
554C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
555C22C11×#57511yescharacteristic
556C4—22no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—22no—
561C4—42no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—82no—
567C2—21no—
568C2—21no—
569C2—81no—
570C2—82no—
571C2—162no—
572C2C11×#300611yescharacteristic
573C2C11×#302111yescharacteristic
574C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ 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×#3493C2semidirect
2. C11×#3217C2semidirect
3. C11×#2619C2semidirect
4. C11×#1600C2semidirect
5. C11×#1599C2semidirect
6. C11×#1598C2semidirect
7. C11×#1512C2semidirect
8. C11×#1464C2semidirect
58. C11×#125D4semidirect
62. C11×#124D4semidirect
82. C4×Q8×C11D4semidirect
89. C4×D4×C11D4semidirect
114. #18366C11direct (N × H)
192. #3493C2×C11semidirect
193. #3217C2×C11semidirect
194. #2619C2×C11semidirect
195. #1600C2×C11semidirect
196. #1599C2×C11semidirect
197. #1598C2×C11semidirect
198. #1512C2×C11semidirect
199. #1464C2×C11semidirect
337. #125D4×C11semidirect
341. #124D4×C11semidirect
361. C4×Q8D4×C11semidirect
368. C4×D4D4×C11semidirect
478. C11#18366direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#32172
C11×#26192
C11×#16002
C11×#15992
C11×#15982
C11×#15122
C11×#14642
#1836611