Finite Group Databasebeta

← C11×#18382 #14595575

Subgroups — C11×#18382 #14595575

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3187C212yesmaximal, complemented
3C11×#2543C211yesmaximal, characteristic
4C11×#1611C212yesmaximal, complemented
5C11×#1608C212yesmaximal, complemented
6C11×#1599C212yesmaximal, complemented
7C11×#1596C212yesmaximal, complemented
8C2×C11×#328C212yesmaximal, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C11×#554—24no—
11C11×#554—22no—
12D4×Q8×C11—22no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C11×#518—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#483C2214yes—
24C11×#481—22no—
25C11×#465—24no—
26C11×#450C2214yes—
27C11×#448—22no—
28C2×C11×C22⋊C8C2212yes—
29C11×#398C2211yescharacteristic
30C11×#397C2211yescharacteristic
31C11×#394C2211yescharacteristic
32C11×#392C2211yescharacteristic
33C11×#388—21no—
34C11×#386—21no—
35C11×#386—21no—
36C2×C11×#95C2211yescharacteristic
37C11×#328C2214yes—
38C11×#328C2214yes—
39C11×#324C2212yes—
40C11×#323C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yescomplemented
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C2×C11×SD16—24no—
51C22×C8×C11—22no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—24no—
55C11×#125—22no—
56C11×#125—24no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8D414yescomplemented
68C11×C22⋊Q8C2314yes—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—44no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D412yescomplemented
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4C2311yescharacteristic
95C2×C42×C11D411yescharacteristic
96C11×#106—24no—
97C11×#103—24no—
98C11×#102—24no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8C2314yes—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95C2311yescharacteristic
105C11×#95C2311yescharacteristic
106#18382C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11—21no—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—82no—
114C2×Q8×C11—82no—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—81no—
125C2×D4×C11—81no—
126C2×D4×C11SD1614yescomplemented
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C11×SD16—84no—
149C2×C8×C11—24no—
150C2×C8×C11—82no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4C2×D414yes—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—81no—
175C42×C11—24no—
176C42×C11—21no—
177C42×C11—21no—
178#3501C2×C1111yescharacteristic, complemented
179#3187C2×C1112yescomplemented
180#2543C2×C1111yescharacteristic
181#1611C2×C1112yescomplemented
182#1608C2×C1112yescomplemented
183#1599C2×C1112yescomplemented
184#1596C2×C1112yescomplemented
185C2×#328C2×C1112yescomplemented
186#1459C2×C1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11#12012yes—
201C23×C11C2×SD1612yes—
202C23×C11C2×SD1612yes—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205Q8×C11—44no—
206Q8×C11—44no—
207Q8×C11—82no—
208Q8×C11—82no—
209D4×C11—28no—
210D4×C11—44no—
211D4×C11—84no—
212D4×C11—84no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—21no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—81no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11—82no—
239C2×C4×C11—82no—
240C2×C4×C11—84no—
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11C2×SD1612yes—
244C2×C4×C11C22×D412yes—
245C8×C11—44no—
246#554—24no—
247#554—22no—
248D4×Q8—22no—
249#544C22×C1112yes—
250#543—21no—
251#543C22×C1112yes—
252#533—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8C22×C1112yes—
255C2×#121—21no—
256C2×#121C22×C1111yescharacteristic
257#518—21no—
258C2×C4×D4C22×C1111yescharacteristic
259#483C22×C1114yes—
260#481—22no—
261#465—24no—
262#450C22×C1114yes—
263#448—22no—
264C2×C22⋊C8C22×C1112yes—
265#398C22×C1111yescharacteristic
266#397C22×C1111yescharacteristic
267#394C22×C1111yescharacteristic
268#392C22×C1111yescharacteristic
269#388—21no—
270#386—21no—
271#386—21no—
272C2×#95C22×C1111yescharacteristic
273#328C22×C1114yes—
274#328C22×C1114yes—
275#324C22×C1112yes—
276#323C22×C1112yes—
277C22×C11—21no—
278C22×C11—22no—
279C22×C11—21no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11#44814yes—
296C22×C11C2×#12011yescharacteristic
297C22×C11C22×SD1611yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C4×C11—22no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—22no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11—44no—
306C4×C11—41no—
307C4×C11—44no—
308C4×C11—81no—
309C4×C11—81no—
310C22×Q8—21no—
311C22×Q8D4×C1112yescomplemented
312C22×D4—21no—
313C22×D4—21no—
314C22×D4D4×C1111yescharacteristic
315C22×D4C23×C1111yescharacteristic
316C23×C4—21no—
317C23×C4D4×C1111yescharacteristic
318C23×C4C23×C1111yescharacteristic
319C2×SD16—24no—
320C22×C8—22no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—24no—
324#125—22no—
325#125—24no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8D4×C1114yescomplemented
337C22⋊Q8C23×C1114yes—
338#121—22no—
339#121—22no—
340#121—44no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—22no—
346C4×D4—22no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C1112yescomplemented
353C2×C4⋊C4C23×C1111yescharacteristic
354C2×C4⋊C4C23×C1111yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4D4×C1111yescharacteristic
363C2×C22⋊C4C23×C1111yescharacteristic
364C2×C42D4×C1111yescharacteristic
365#106—24no—
366#103—24no—
367#102—24no—
368C22⋊C8—22no—
369C22⋊C8C23×C1114yes—
370#95—21no—
371#95—21no—
372#95—21no—
373#95C23×C1111yescharacteristic
374#95C23×C1111yescharacteristic
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—24no—
378C2×C11—42no—
379C2×C11—161no—
380C2×C11C2×#44811yescharacteristic
381C2×C11#301811yescharacteristic
382C2×C11#302611yescharacteristic
383C24—21no—
384C24C2×D4×C1111yescharacteristic
385C24C2×D4×C1111yescharacteristic
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—82no—
390C2×Q8—82no—
391C2×Q8C2×D4×C1114yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—81no—
401C2×D4—81no—
402C2×D4C11×SD1614yescomplemented
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—81no—
415C22×C4—81no—
416C22×C4—81no—
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1112yes—
423C22×C4C24×C1111yescharacteristic
424SD16—84no—
425C2×C8—24no—
426C2×C8—82no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—24no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C4⋊C4C2×D4×C1114yes—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—42no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—42no—
450C22⋊C4—81no—
451C42—24no—
452C42—21no—
453C42—21no—
454C11#1838211yescharacteristic, direct product factor, Sylow
455C23—21no—
456C23—21no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23C11×#12012yes—
469C23C2×C11×SD1612yes—
470C23C2×C11×SD1612yes—
471C23C11×#13712yes—
472C23C22×D4×C1111yescharacteristic
473Q8—44no—
474Q8—44no—
475Q8—82no—
476Q8—82no—
477D4—28no—
478D4—44no—
479D4—84no—
480D4—84no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—21no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—84no—
509C2×C4C11×#12011yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C2×C11×SD1612yes—
512C2×C4C22×D4×C1112yes—
513C8—44no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—22no—
518C22—22no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22C11×#44814yes—
533C22C2×C11×#12011yescharacteristic
534C22C22×C11×SD1611yescharacteristic
535C22C2×C11×#13711yescharacteristic
536C4—22no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—41no—
542C4—44no—
543C4—41no—
544C4—44no—
545C4—81no—
546C4—81no—
547C2—21no—
548C2—21no—
549C2—24no—
550C2—42no—
551C2—161no—
552C2C2×C11×#44811yescharacteristic
553C2C11×#301811yescharacteristic
554C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2543C2
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
1. C11×#3501C2semidirect
2. C11×#3187C2semidirect
4. C11×#1611C2semidirect
5. C11×#1608C2semidirect
6. C11×#1599C2semidirect
7. C11×#1596C2semidirect
8. C2×C11×#328C2semidirect
9. C11×#1459C2semidirect
42. C22×Q8×C11D4semidirect
67. C11×C22⋊Q8D4semidirect
83. C2×C11×C4⋊C4D4semidirect
106. #18382C11direct (N × H)
126. C2×D4×C11SD16semidirect
178. #3501C2×C11semidirect
179. #3187C2×C11semidirect
181. #1611C2×C11semidirect
182. #1608C2×C11semidirect
183. #1599C2×C11semidirect
184. #1596C2×C11semidirect
185. C2×#328C2×C11semidirect
186. #1459C2×C11semidirect
311. C22×Q8D4×C11semidirect
336. C22⋊Q8D4×C11semidirect
352. C2×C4⋊C4D4×C11semidirect
402. C2×D4C11×SD16semidirect
454. C11#18382direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#31872
C11×#25432
C11×#16112
C11×#16082
C11×#15992
C11×#15962
C2×C11×#3282
C11×#14592
#1838211