Finite Group Databasebeta

← C11×#18405 #14595598

Subgroups — C11×#18405 #14595598

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic, complemented
4C11×#2541C211yesmaximal, characteristic, complemented
5C11×#1600C218yesmaximal, complemented
6C11×#1503C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic, complemented
8C11×#1460C211yesmaximal, characteristic, complemented
9C11×#559—22no—
10C11×#556—21no—
11C11×#555—21no—
12C11×#553—22no—
13C11×#550—21no—
14C11×#547—21no—
15C11×#538C2214yes—
16C11×#535—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×#127—21no—
20C2×C11×#127C2211yescharacteristic
21C11×#525—22no—
22C2×C11×#121—22no—
23C11×#520—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#493—21no—
26C11×#492—21no—
27C11×#486—21no—
28C11×#486—21no—
29C11×#460—22no—
30C11×#459—22no—
31C11×#450C2214yes—
32C11×#447C2214yes—
33C11×#431C2211yescharacteristic
34C11×#431C2211yescharacteristic
35C11×#392C2214yes—
36C11×#390—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#328C2214yes—
39C11×#327C2214yes—
40C11×#323C2214yes—
41C2×C11×#41—22no—
42C2×C11×#41—21no—
43C22×D4×C11—24no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2312yes—
48C23×C4×C11D412yes—
49C2×C11×SD16—24no—
50C2×C11×D8—24no—
51C11×C4⋊Q8D411yescharacteristic, complemented
52C11×C4⋊Q8D411yescharacteristic, complemented
53C11×C4⋊Q8D411yescharacteristic, complemented
54C11×#127—22no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—44no—
60C11×#127D411yescharacteristic, complemented
61C11×#126—24no—
62C11×#125—21no—
63C11×#124—22no—
64C11×#124—24no—
65C11×#124—21no—
66C11×#123—24no—
67C11×#123—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8C2312yes—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—24no—
75C11×#121—21no—
76C11×#121—48no—
77C11×#121C2312yes—
78C11×#120—24no—
79C4×Q8×C11—22no—
80C4×Q8×C11—21no—
81C4×Q8×C11D412yescomplemented
82C4×D4×C11—22no—
83C4×D4×C11—24no—
84C4×D4×C11—24no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11D412yescomplemented
91C11×#117—22no—
92C11×#117—22no—
93C11×#117—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4C2312yes—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×#102—24no—
104C11×#102—24no—
105C11×C22⋊C8C2312yes—
106C11×C22⋊C8C2312yes—
107C4×C8×C11—21no—
108C4×C8×C11—21no—
109C11×#95C2312yes—
110#18405C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—22no—
112C24×C11C2×D412yes—
113C11×#41—42no—
114C11×#41—42no—
115C11×#41—84no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11C2×D412yes—
119C2×D4×C11—22no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—48no—
132C2×D4×C11—48no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—82no—
140C2×D4×C11—84no—
141C2×D4×C11C2×D412yes—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C11×SD16—84no—
153C11×D8—84no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C2×D412yes—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—48no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—42no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184#3506C2×C1111yescharacteristic, complemented
185#3208C2×C1111yescharacteristic, complemented
186#3205C2×C1111yescharacteristic, complemented
187#2541C2×C1111yescharacteristic, complemented
188#1600C2×C1118yescomplemented
189#1503C2×C1111yescharacteristic, complemented
190#1502C2×C1111yescharacteristic, complemented
191#1460C2×C1111yescharacteristic, complemented
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11C22×D411yescharacteristic
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—42no—
207D4×C11—42no—
208D4×C11—44no—
209D4×C11—44no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—82no—
217D4×C11—84no—
218D4×C11—84no—
219D4×C11—816no—
220D4×C11—82no—
221D4×C11—82no—
222D4×C11—82no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—82no—
236C2×C4×C11—84no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#13512yes—
242C2×C4×C11AGL(1,ℤ/8)12yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C8×C11—42no—
246C8×C11—42no—
247#559—22no—
248#556—21no—
249#555—21no—
250#553—22no—
251#550—21no—
252#547—21no—
253#538C22×C1114yes—
254#535—21no—
255#533C22×C1111yescharacteristic
256#532C22×C1111yescharacteristic
257C2×#127—21no—
258C2×#127C22×C1111yescharacteristic
259#525—22no—
260C2×#121—22no—
261#520—21no—
262C2×C4×D4C22×C1111yescharacteristic
263#493—21no—
264#492—21no—
265#486—21no—
266#486—21no—
267#460—22no—
268#459—22no—
269#450C22×C1114yes—
270#447C22×C1114yes—
271#431C22×C1111yescharacteristic
272#431C22×C1111yescharacteristic
273#392C22×C1114yes—
274#390—21no—
275C4×C4⋊C4C22×C1111yescharacteristic
276#328C22×C1114yes—
277#327C22×C1114yes—
278#323C22×C1114yes—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—82no—
289C22×C11—84no—
290C22×C11—84no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—44no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11#44912yes—
306C4×C11#44912yes—
307C4×C11#45312yes—
308C2×#41—22no—
309C2×#41—21no—
310C22×D4—24no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4D4×C1111yescharacteristic
314C22×D4C23×C1112yes—
315C23×C4D4×C1112yes—
316C2×SD16—24no—
317C2×D8—24no—
318C4⋊Q8D4×C1111yescharacteristic, complemented
319C4⋊Q8D4×C1111yescharacteristic, complemented
320C4⋊Q8D4×C1111yescharacteristic, complemented
321#127—22no—
322#127—21no—
323#127—21no—
324#127—21no—
325#127—21no—
326#127—44no—
327#127D4×C1111yescharacteristic, complemented
328#126—24no—
329#125—21no—
330#124—22no—
331#124—24no—
332#124—21no—
333#123—24no—
334#123—24no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8C23×C1112yes—
338#121—22no—
339#121—22no—
340#121—22no—
341#121—24no—
342#121—21no—
343#121—48no—
344#121C23×C1112yes—
345#120—24no—
346C4×Q8—22no—
347C4×Q8—21no—
348C4×Q8D4×C1112yescomplemented
349C4×D4—22no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4D4×C1112yescomplemented
358#117—22no—
359#117—22no—
360#117—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C1111yescharacteristic
364C2×C22⋊C4—24no—
365C2×C22⋊C4C23×C1112yes—
366C2×C42—21no—
367C2×C42C23×C1111yescharacteristic
368C4⋊C8—21no—
369C4⋊C8—21no—
370#102—24no—
371#102—24no—
372C22⋊C8C23×C1112yes—
373C22⋊C8C23×C1112yes—
374C4×C8—21no—
375C4×C8—21no—
376#95C23×C1112yes—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—82no—
380C2×C11—82no—
381C2×C11—162no—
382C2×C11C2×#44911yescharacteristic
383C2×C11C2×#45311yescharacteristic
384C2×C11#302711yescharacteristic
385C24—22no—
386C24C2×D4×C1112yes—
387#41—42no—
388#41—42no—
389#41—84no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8C2×D4×C1112yes—
393C2×D4—22no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—44no—
405C2×D4—48no—
406C2×D4—48no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—82no—
414C2×D4—84no—
415C2×D4C2×D4×C1112yes—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—44no—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C24×C1111yescharacteristic
426SD16—84no—
427D8—84no—
428C2×C8—22no—
429C2×C8—22no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4C2×D4×C1112yes—
441C4⋊C4C2×D4×C1112yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—48no—
451C42—24no—
452C42—22no—
453C42—42no—
454C42C2×D4×C1111yescharacteristic
455C42C2×D4×C1111yescharacteristic
456C42C2×D4×C1111yescharacteristic
457C42C2×D4×C1111yescharacteristic
458C11#1840511yescharacteristic, direct product factor, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—42no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×D4×C1111yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474D4—42no—
475D4—44no—
476D4—44no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—82no—
484D4—84no—
485D4—84no—
486D4—816no—
487D4—82no—
488D4—82no—
489D4—82no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—82no—
503C2×C4—84no—
504C2×C4C11×#12011yescharacteristic
505C2×C4C11×#12011yescharacteristic
506C2×C4C11×#12011yescharacteristic
507C2×C4C11×#12011yescharacteristic
508C2×C4C11×#13512yes—
509C2×C4C11×AGL(1,ℤ/8)12yes—
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C22×D4×C1111yescharacteristic
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—44no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22C2×C11×#12011yescharacteristic
530C22C2×C11×#13511yescharacteristic
531C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4C11×#44912yes—
541C4C11×#44912yes—
542C4C11×#45312yes—
543C2—21no—
544C2—21no—
545C2—82no—
546C2—82no—
547C2—162no—
548C2C2×C11×#44911yescharacteristic
549C2C2×C11×#45311yescharacteristic
550C2C11×#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×#3506C2semidirect
2. C11×#3208C2semidirect
3. C11×#3205C2semidirect
4. C11×#2541C2semidirect
5. C11×#1600C2semidirect
6. C11×#1503C2semidirect
7. C11×#1502C2semidirect
8. C11×#1460C2semidirect
51. C11×C4⋊Q8D4semidirect
52. C11×C4⋊Q8D4semidirect
53. C11×C4⋊Q8D4semidirect
60. C11×#127D4semidirect
81. C4×Q8×C11D4semidirect
90. C4×D4×C11D4semidirect
110. #18405C11direct (N × H)
184. #3506C2×C11semidirect
185. #3208C2×C11semidirect
186. #3205C2×C11semidirect
187. #2541C2×C11semidirect
188. #1600C2×C11semidirect
189. #1503C2×C11semidirect
190. #1502C2×C11semidirect
191. #1460C2×C11semidirect
318. C4⋊Q8D4×C11semidirect
319. C4⋊Q8D4×C11semidirect
320. C4⋊Q8D4×C11semidirect
327. #127D4×C11semidirect
348. C4×Q8D4×C11semidirect
357. C4×D4D4×C11semidirect
458. C11#18405direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#32082
C11×#32052
C11×#25412
C11×#16002
C11×#15032
C11×#15022
C11×#14602
#1840511