Finite Group Databasebeta

← C11×#18381 #14595574

Subgroups — C11×#18381 #14595574

Order 2816.

1266 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3187C212yesmaximal, complemented
3C11×#2564C211yesmaximal, characteristic, complemented
4C11×#1616C212yesmaximal, complemented
5C11×#1613C212yesmaximal, complemented
6C11×#1604C212yesmaximal, complemented
7C11×#1601C212yesmaximal, complemented
8C2×C11×#327C212yesmaximal, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537C2212yes—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic, complemented
19C2×C11×#121—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C11×#483—22no—
23C11×#481C2214yescomplemented
24C11×#465—24no—
25C11×#450—22no—
26C11×#448C2214yescomplemented
27C2×C11×C22⋊C8C2212yescomplemented
28C11×#400C2211yescharacteristic, complemented
29C11×#399C2211yescharacteristic, complemented
30C11×#395C2211yescharacteristic, complemented
31C11×#393C2211yescharacteristic, complemented
32C11×#387—21no—
33C11×#386—21no—
34C11×#385—21no—
35C11×#380—21no—
36C2×C11×#95C2211yescharacteristic, complemented
37C11×#327C2214yescomplemented
38C11×#327C2214yescomplemented
39C11×#324C2212yescomplemented
40C11×#323C2212yescomplemented
41C11×H(5,𝔽2)—44no—
42C11×H(5,𝔽2)—44no—
43C2×C11×#41—24no—
44C2×C11×#41—22no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—24no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11D412yes—
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C2×C11×SD16—24no—
56C22×C8×C11—22no—
57C11×C4⋊Q8—21no—
58C11×#127—21no—
59C11×#124—22no—
60C11×#123—24no—
61C11×#123—24no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121D414yes—
73C11×#121C2314yes—
74C11×#120—24no—
75C11×#120—24no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4C2311yescharacteristic
94C2×C42×C11D411yescharacteristic
95C11×#106—24no—
96C11×#103—24no—
97C11×#102—24no—
98C11×C22⋊C8—22no—
99C11×C22⋊C8C2314yes—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95C2311yescharacteristic
106C11×#95C2311yescharacteristic
107#18381C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C11×#41—44no—
113C11×#41—416no—
114C11×#41—44no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—81no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—22no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—416no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—44no—
131C2×D4×C11—44no—
132C2×D4×C11—82no—
133C2×D4×C11—82no—
134C2×D4×C11SD1614yescomplemented
135C2×D4×C11C2×D414yes—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C11×SD16—84no—
158C2×C8×C11—24no—
159C2×C8×C11—82no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4C2×D414yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181#3496C2×C1111yescharacteristic
182#3187C2×C1112yescomplemented
183#2564C2×C1111yescharacteristic, complemented
184#1616C2×C1112yescomplemented
185#1613C2×C1112yescomplemented
186#1604C2×C1112yescomplemented
187#1601C2×C1112yescomplemented
188C2×#327C2×C1112yescomplemented
189#1459C2×C1111yescharacteristic, complemented
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—24no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—82no—
200C23×C11—82no—
201C23×C11—82no—
202C23×C11—82no—
203C23×C11#12012yes—
204C23×C11C2×SD1612yes—
205C23×C11C2×SD1612yes—
206C23×C11AGL(1,ℤ/8)12yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—44no—
209Q8×C11—44no—
210D4×C11—28no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—44no—
214D4×C11—48no—
215D4×C11—44no—
216D4×C11—44no—
217D4×C11—48no—
218D4×C11—82no—
219D4×C11—82no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11—84no—
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11C2×SD1612yes—
252C2×C4×C11C22×D412yes—
253C8×C11—44no—
254C2×H(5,𝔽2)—21no—
255#547—22no—
256#546—24no—
257D42—22no—
258#537C22×C1112yes—
259#534—21no—
260#534C22×C1112yes—
261#532—21no—
262C2×C22⋊Q8C22×C1111yescharacteristic, complemented
263C2×#121—21no—
264C2×#121C22×C1112yes—
265C2×C4×D4C22×C1111yescharacteristic
266#483—22no—
267#481C22×C1114yescomplemented
268#465—24no—
269#450—22no—
270#448C22×C1114yescomplemented
271C2×C22⋊C8C22×C1112yescomplemented
272#400C22×C1111yescharacteristic, complemented
273#399C22×C1111yescharacteristic, complemented
274#395C22×C1111yescharacteristic, complemented
275#393C22×C1111yescharacteristic, complemented
276#387—21no—
277#386—21no—
278#385—21no—
279#380—21no—
280C2×#95C22×C1111yescharacteristic, complemented
281#327C22×C1114yescomplemented
282#327C22×C1114yescomplemented
283#324C22×C1112yescomplemented
284#323C22×C1112yescomplemented
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—21no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—81no—
299C22×C11—164no—
300C22×C11—164no—
301C22×C11#45014yes—
302C22×C11C2×#12011yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11—22no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11—81no—
316H(5,𝔽2)—44no—
317H(5,𝔽2)—44no—
318C2×#41—24no—
319C2×#41—22no—
320C22×Q8C23×C1111yescharacteristic
321C22×D4—24no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—21no—
325C22×D4D4×C1111yescharacteristic
326C22×D4D4×C1112yes—
327C23×C4—21no—
328C23×C4D4×C1111yescharacteristic
329C23×C4C23×C1111yescharacteristic
330C2×SD16—24no—
331C22×C8—22no—
332C4⋊Q8—21no—
333#127—21no—
334#124—22no—
335#123—24no—
336#123—24no—
337C22⋊Q8—24no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340#121—22no—
341#121—22no—
342#121—24no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121D4×C1114yes—
348#121C23×C1114yes—
349#120—24no—
350#120—24no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4D4×C1112yes—
360C2×C4⋊C4C23×C1111yescharacteristic
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4D4×C1111yescharacteristic
368C2×C22⋊C4C23×C1111yescharacteristic
369C2×C42D4×C1111yescharacteristic
370#106—24no—
371#103—24no—
372#102—24no—
373C22⋊C8—22no—
374C22⋊C8C23×C1114yes—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95C23×C1111yescharacteristic
381#95C23×C1111yescharacteristic
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—24no—
385C2×C11—42no—
386C2×C11—84no—
387C2×C11C2×#45011yescharacteristic
388C2×C11#301811yescharacteristic
389C2×C11#302611yescharacteristic
390C24—22no—
391C24—22no—
392C24C2×D4×C1111yescharacteristic
393C24C2×D4×C1111yescharacteristic
394#41—44no—
395#41—416no—
396#41—44no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—81no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—416no—
410C2×D4—44no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—82no—
415C2×D4—82no—
416C2×D4C11×SD1614yescomplemented
417C2×D4C2×D4×C1114yes—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1112yes—
437C22×C4C2×D4×C1112yes—
438C22×C4C24×C1111yescharacteristic
439SD16—84no—
440C2×C8—24no—
441C2×C8—82no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—81no—
451C4⋊C4C2×D4×C1114yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C22⋊C4—81no—
461C42—21no—
462C42—21no—
463C11#1838111yescharacteristic, direct product factor, Sylow
464C23—21no—
465C23—21no—
466C23—24no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—44no—
472C23—44no—
473C23—82no—
474C23—82no—
475C23—82no—
476C23—82no—
477C23C11×#12012yes—
478C23C2×C11×SD1612yes—
479C23C2×C11×SD1612yes—
480C23C11×AGL(1,ℤ/8)12yes—
481C23C22×D4×C1111yescharacteristic
482Q8—44no—
483Q8—44no—
484D4—28no—
485D4—44no—
486D4—44no—
487D4—44no—
488D4—48no—
489D4—44no—
490D4—44no—
491D4—48no—
492D4—82no—
493D4—82no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—48no—
506C2×C4—41no—
507C2×C4—44no—
508C2×C4—41no—
509C2×C4—44no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—81no—
522C2×C4—84no—
523C2×C4C11×#12011yescharacteristic
524C2×C4C11×#12011yescharacteristic
525C2×C4C2×C11×SD1612yes—
526C2×C4C22×D4×C1112yes—
527C8—44no—
528C22—21no—
529C22—22no—
530C22—21no—
531C22—22no—
532C22—22no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—41no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—81no—
542C22—164no—
543C22—164no—
544C22C11×#45014yes—
545C22C2×C11×#12011yescharacteristic
546C22C22×C11×SD1611yescharacteristic
547C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
548C4—22no—
549C4—22no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—44no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C2—21no—
560C2—21no—
561C2—24no—
562C2—42no—
563C2—84no—
564C2C2×C11×#45011yescharacteristic
565C2C11×#301811yescharacteristic
566C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3187C2semidirect
3. C11×#2564C2semidirect
4. C11×#1616C2semidirect
5. C11×#1613C2semidirect
6. C11×#1604C2semidirect
7. C11×#1601C2semidirect
8. C2×C11×#327C2semidirect
9. C11×#1459C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
23. C11×#481C22semidirect
26. C11×#448C22semidirect
27. C2×C11×C22⋊C8C22semidirect
28. C11×#400C22semidirect
29. C11×#399C22semidirect
30. C11×#395C22semidirect
31. C11×#393C22semidirect
36. C2×C11×#95C22semidirect
37. C11×#327C22semidirect
38. C11×#327C22semidirect
39. C11×#324C22semidirect
40. C11×#323C22semidirect
107. #18381C11direct (N × H)
134. C2×D4×C11SD16semidirect
182. #3187C2×C11semidirect
183. #2564C2×C11semidirect
184. #1616C2×C11semidirect
185. #1613C2×C11semidirect
186. #1604C2×C11semidirect
187. #1601C2×C11semidirect
188. C2×#327C2×C11semidirect
189. #1459C2×C11semidirect
262. C2×C22⋊Q8C22×C11semidirect
267. #481C22×C11semidirect
270. #448C22×C11semidirect
271. C2×C22⋊C8C22×C11semidirect
272. #400C22×C11semidirect
273. #399C22×C11semidirect
274. #395C22×C11semidirect
275. #393C22×C11semidirect
280. C2×#95C22×C11semidirect
281. #327C22×C11semidirect
282. #327C22×C11semidirect
283. #324C22×C11semidirect
284. #323C22×C11semidirect
416. C2×D4C11×SD16semidirect
463. C11#18381direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#31872
C11×#25642
C11×#16162
C11×#16132
C11×#16042
C11×#16012
C2×C11×#3272
C11×#14592
#1838111