Finite Group Databasebeta

← C11×#18912 #14596105

Subgroups — C11×#18912 #14596105

Order 2816.

1218 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×#3497C211yesmaximal, characteristic, complemented
2C11×#3205C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic, complemented
4C2×C11×#460C211yesmaximal, characteristic, complemented
5C11×#1627C214yesmaximal, complemented
6C11×#1621C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C2×C11×2−1+4—21no—
11C22×C11×SD16—21no—
12C11×#550—21no—
13C11×#550C2212yescomplemented
14D4×Q8×C11—21no—
15D4×Q8×C11C2212yescomplemented
16C11×#548—22no—
17C11×#548—22no—
18C11×#537—22no—
19C11×#537—21no—
20C11×#532—22no—
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×#127C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#493—21no—
26C11×#493C2212yes—
27C11×#486—21no—
28C11×#486C2212yes—
29C11×#460—22no—
30C11×#460C2214yes—
31C11×#459—22no—
32C11×#459C2214yes—
33C11×#447—22no—
34C11×#447—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C11×2−1+4—44no—
44C11×2−1+4—44no—
45C2×C11×#41—24no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C2×C11×SD16—24no—
57C2×C11×SD16—44no—
58C2×C11×D8—24no—
59C2×C11×D8—24no—
60C22×C8×C11—21no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127—22no—
65C11×#127—21no—
66C11×#127—21no—
67C11×#127—21no—
68C11×#127D411yescharacteristic
69C11×#127C2312yes—
70C11×#127C2311yescharacteristic
71C11×#124—24no—
72C11×#124—21no—
73C11×#124—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×#121—24no—
79C11×#121—22no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—22no—
85C11×#121D412yes—
86C11×#121D412yes—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11D412yes—
90C4×Q8×C11C2312yes—
91C4×D4×C11—24no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11D412yes—
97C4×D4×C11C2312yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C11×#102—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2312yes—
113#18912C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—41no—
115C11×#41—416no—
116C11×#41—44no—
117C11×#41—48no—
118C11×#41—44no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—42no—
123C2×Q8×C11—24no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11—44no—
131C2×Q8×C11D814yescomplemented
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—82no—
150C2×D4×C11—82no—
151C2×D4×C11C2×D412yes—
152C2×D4×C11C2×D412yes—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C11×SD16—48no—
163C11×D8—84no—
164C11×D8—84no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—42no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C4⋊C4C2×D412yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190#3497C2×C1111yescharacteristic, complemented
191#3205C2×C1111yescharacteristic, complemented
192#3205C2×C1111yescharacteristic, complemented
193C2×#460C2×C1111yescharacteristic, complemented
194#1627C2×C1114yescomplemented
195#1621C2×C1114yescomplemented
196#1540C2×C1111yescharacteristic, complemented
197#1480C2×C1111yescharacteristic, complemented
198#1479C2×C1111yescharacteristic, complemented
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11#12011yescharacteristic
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11—48no—
209Q8×C11—41no—
210Q8×C11—41no—
211Q8×C11—42no—
212Q8×C11C2×D814yes—
213D4×C11—24no—
214D4×C11—42no—
215D4×C11—48no—
216D4×C11—44no—
217D4×C11—44no—
218D4×C11—44no—
219D4×C11—41no—
220D4×C11—42no—
221D4×C11—41no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—44no—
225D4×C11—42no—
226D4×C11—81no—
227D4×C11—82no—
228D4×C11—82no—
229D4×C11—84no—
230D4×C11—82no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—48no—
239C2×C4×C11—48no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—81no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11C2×D812yes—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C8×C11—42no—
253C8×C11—42no—
254C8×C11—42no—
255C2×2−1+4—21no—
256C22×SD16—21no—
257#550—21no—
258#550C22×C1112yescomplemented
259D4×Q8—21no—
260D4×Q8C22×C1112yescomplemented
261#548—22no—
262#548—22no—
263#537—22no—
264#537—21no—
265#532—22no—
266#532C22×C1111yescharacteristic
267#532C22×C1111yescharacteristic
268C2×#127C22×C1111yescharacteristic
269C2×C4×Q8C22×C1111yescharacteristic
270#493—21no—
271#493C22×C1112yes—
272#486—21no—
273#486C22×C1112yes—
274#460—22no—
275#460C22×C1114yes—
276#459—22no—
277#459C22×C1114yes—
278#447—22no—
279#447—22no—
280#431C22×C1111yescharacteristic
281#431C22×C1111yescharacteristic
282C2×C4⋊C8C22×C1111yescharacteristic
283C2×#102—21no—
284#332C22×C1112yescomplemented
285#331C22×C1112yescomplemented
286Q8⋊C8C22×C1114yescomplemented
287D4⋊C8C22×C1114yescomplemented
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—164no—
300C22×C11#44712yes—
301C22×C11C2×#12011yescharacteristic
302C4×C11—24no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#44712yes—
310C4×C11C22×D811yescharacteristic
311C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C11#57712yes—
3132−1+4—44no—
3142−1+4—44no—
315C2×#41—24no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—21no—
319C2×#41—21no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8D4×C1111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C2×SD16—24no—
327C2×SD16—44no—
328C2×D8—24no—
329C2×D8—24no—
330C22×C8—21no—
331C4⋊Q8—22no—
332C4⋊Q8D4×C1111yescharacteristic
333C4⋊Q8C23×C1111yescharacteristic
334#127—22no—
335#127—21no—
336#127—21no—
337#127—21no—
338#127D4×C1111yescharacteristic
339#127C23×C1112yes—
340#127C23×C1111yescharacteristic
341#124—24no—
342#124—21no—
343#124—21no—
344C22⋊Q8—22no—
345C22⋊Q8—24no—
346C22⋊Q8—22no—
347C22⋊Q8—24no—
348#121—24no—
349#121—22no—
350#121—24no—
351#121—24no—
352#121—21no—
353#121—21no—
354#121—22no—
355#121D4×C1112yes—
356#121D4×C1112yes—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8D4×C1112yes—
360C4×Q8C23×C1112yes—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4D4×C1112yes—
367C4×D4C23×C1112yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C1111yescharacteristic
370C2×C42—21no—
371C2×C42C23×C1111yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8C23×C1112yes—
375C4⋊C8C23×C1112yes—
376#102—24no—
377#102—24no—
378#102—24no—
379C22⋊C8—21no—
380C22⋊C8—21no—
381C4×C8—21no—
382C4×C8C23×C1112yes—
383C2×C11—22no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11—162no—
387C2×C11C2×#44711yescharacteristic
388C2×C11#301011yescharacteristic
389C2×C11#302111yescharacteristic
390C24—41no—
391#41—416no—
392#41—44no—
393#41—48no—
394#41—44no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—21no—
404C2×Q8—44no—
405C2×Q8—48no—
406C2×Q8—44no—
407C2×Q8C11×D814yescomplemented
408C2×Q8C2×D4×C1112yes—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—24no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—82no—
426C2×D4—82no—
427C2×D4C2×D4×C1112yes—
428C2×D4C2×D4×C1112yes—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438SD16—48no—
439D8—84no—
440D8—84no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—42no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4C2×D4×C1112yes—
452C4⋊C4C2×D4×C1112yes—
453C4⋊C4C2×D4×C1112yes—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C42—22no—
461C42—22no—
462C42C2×D4×C1111yescharacteristic
463C42C2×D4×C1111yescharacteristic
464C42C2×D4×C1111yescharacteristic
465C42C24×C1111yescharacteristic
466C11#1891211yescharacteristic, direct product factor, Sylow
467C23—22no—
468C23—22no—
469C23—42no—
470C23—82no—
471C23—82no—
472C23—82no—
473C23C11×#12011yescharacteristic
474Q8—22no—
475Q8—24no—
476Q8—48no—
477Q8—41no—
478Q8—41no—
479Q8—42no—
480Q8C2×C11×D814yes—
481D4—24no—
482D4—42no—
483D4—48no—
484D4—44no—
485D4—44no—
486D4—44no—
487D4—41no—
488D4—42no—
489D4—41no—
490D4—42no—
491D4—42no—
492D4—44no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497D4—84no—
498D4—82no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—81no—
512C2×C4C11×#12011yescharacteristic
513C2×C4C11×#12011yescharacteristic
514C2×C4C11×#12011yescharacteristic
515C2×C4C2×C11×D812yes—
516C2×C4C11×AGL(1,ℤ/8)12yes—
517C2×C4C22×D4×C1111yescharacteristic
518C2×C4C22×D4×C1111yescharacteristic
519C2×C4C22×D4×C1111yescharacteristic
520C8—42no—
521C8—42no—
522C8—42no—
523C22—21no—
524C22—21no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—164no—
535C22C11×#44712yes—
536C22C2×C11×#12011yescharacteristic
537C4—24no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4C11×#44712yes—
545C4C22×C11×D811yescharacteristic
546C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
547C4C11×#57712yes—
548C2—22no—
549C2—82no—
550C2—82no—
551C2—162no—
552C2C2×C11×#44711yescharacteristic
553C2C11×#301011yescharacteristic
554C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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
1. C11×#3497C2semidirect
2. C11×#3205C2semidirect
3. C11×#3205C2semidirect
4. C2×C11×#460C2semidirect
5. C11×#1627C2semidirect
6. C11×#1621C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1479C2semidirect
13. C11×#550C22semidirect
15. D4×Q8×C11C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
113. #18912C11direct (N × H)
131. C2×Q8×C11D8semidirect
190. #3497C2×C11semidirect
191. #3205C2×C11semidirect
192. #3205C2×C11semidirect
193. C2×#460C2×C11semidirect
194. #1627C2×C11semidirect
195. #1621C2×C11semidirect
196. #1540C2×C11semidirect
197. #1480C2×C11semidirect
198. #1479C2×C11semidirect
258. #550C22×C11semidirect
260. D4×Q8C22×C11semidirect
284. #332C22×C11semidirect
285. #331C22×C11semidirect
286. Q8⋊C8C22×C11semidirect
287. D4⋊C8C22×C11semidirect
407. C2×Q8C11×D8semidirect
466. C11#18912direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#32052
C2×C11×#4602
C11×#16272
C11×#16212
C11×#15402
C11×#14802
C11×#14792
#1891211