Finite Group Databasebeta

← C11×#18214 #14595407

Subgroups — C11×#18214 #14595407

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic, complemented
2C11×#3101C211yesmaximal, characteristic, complemented
3C11×#3100C211yesmaximal, characteristic
4C11×#2536C211yesmaximal, characteristic, complemented
5C11×#1609C214yesmaximal, complemented
6C11×#1597C214yesmaximal, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#1517C211yesmaximal, characteristic, complemented
9C11×#1461C211yesmaximal, characteristic, complemented
10C11×#559—21no—
11C11×#557—21no—
12C11×#556—21no—
13C11×#556—22no—
14C11×#554—21no—
15C11×#552—22no—
16C11×#539C2214yes—
17C11×#536—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C2×C11×C22⋊Q8—21no—
22C11×#520—21no—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C11×#483C2212yes—
26C11×#480C2212yes—
27C11×#476—21no—
28C11×#474—21no—
29C11×#461—21no—
30C11×#459—21no—
31C11×#450C2212yes—
32C11×#447C2212yes—
33C4×C11×SD16—22no—
34C4×C11×D8—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C11×#398C2212yes—
38C11×#394C2212yes—
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C11×#380—21no—
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#324C2214yes—
45C2×C11×#41—21no—
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C2×C11×SD16—22no—
50C2×C11×D8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8D411yescharacteristic
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#126—24no—
58C11×#125—22no—
59C11×#125—24no—
60C11×#125—21no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#124—21no—
64C11×#123—24no—
65C11×#123—24no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—44no—
71C11×C22⋊Q8C2312yes—
72C11×#121—21no—
73C11×#121C2312yes—
74C4×Q8×C11—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11D412yes—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
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×C11D412yes—
91C11×#117—22no—
92C11×#117—24no—
93C11×#117—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C42×C11D412yes—
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#106—22no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×C22⋊C8C2312yes—
114C11×C22⋊C8C2312yes—
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117C11×#95—22no—
118C11×#95—21no—
119C11×#95C2312yes—
120#18214C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C11×#41—42no—
123C11×#41—42no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D412yes—
131C2×D4×C11—22no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×SD16—44no—
152C11×D8—44no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—24no—
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—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—44no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4—44no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—24no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192#3507C2×C1111yescharacteristic, complemented
193#3101C2×C1111yescharacteristic, complemented
194#3100C2×C1111yescharacteristic
195#2536C2×C1111yescharacteristic, complemented
196#1609C2×C1114yescomplemented
197#1597C2×C1114yescomplemented
198#1518C2×C1111yescharacteristic, complemented
199#1517C2×C1111yescharacteristic, complemented
200#1461C2×C1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—42no—
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—84no—
242C2×C4×C11—82no—
243C2×C4×C11—82no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#13512yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C8×C11—42no—
253C8×C11—42no—
254#559—21no—
255#557—21no—
256#556—21no—
257#556—22no—
258#554—21no—
259#552—22no—
260#539C22×C1114yes—
261#536—21no—
262#533C22×C1111yescharacteristic
263#532C22×C1111yescharacteristic
264#529—22no—
265C2×C22⋊Q8—21no—
266#520—21no—
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269#483C22×C1112yes—
270#480C22×C1112yes—
271#476—21no—
272#474—21no—
273#461—21no—
274#459—21no—
275#450C22×C1112yes—
276#447C22×C1112yes—
277C4×SD16—22no—
278C4×D8—22no—
279#431C22×C1111yescharacteristic
280#431C22×C1111yescharacteristic
281#398C22×C1112yes—
282#394C22×C1112yes—
283#388—22no—
284#382C22×C1111yescharacteristic
285#380—21no—
286#328C22×C1114yes—
287#327C22×C1114yes—
288#324C22×C1114yes—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×#13511yescharacteristic
303C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11—81no—
315C4×C11#44912yes—
316C4×C11#44912yes—
317C2×#41—21no—
318C22×Q8D4×C1111yescharacteristic
319C22×D4C23×C1111yescharacteristic
320C23×C4—21no—
321C2×SD16—22no—
322C2×D8—22no—
323C4⋊Q8—22no—
324C4⋊Q8D4×C1111yescharacteristic
325C4⋊Q8D4×C1111yescharacteristic
326C4⋊Q8D4×C1111yescharacteristic
327#127D4×C1111yescharacteristic
328#126—24no—
329#126—24no—
330#125—22no—
331#125—24no—
332#125—21no—
333#124—22no—
334#124—22no—
335#124—21no—
336#123—24no—
337#123—24no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—24no—
341C22⋊Q8—21no—
342C22⋊Q8—44no—
343C22⋊Q8C23×C1112yes—
344#121—21no—
345#121C23×C1112yes—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8D4×C1112yes—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—24no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4D4×C1112yes—
363#117—22no—
364#117—24no—
365#117—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4D4×C1111yescharacteristic
370C2×C4⋊C4C23×C1111yescharacteristic
371C2×C4⋊C4C23×C1112yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C42D4×C1112yes—
376C2×C42C23×C1111yescharacteristic
377#107—22no—
378#106—22no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381#103—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385C22⋊C8C23×C1112yes—
386C22⋊C8C23×C1112yes—
387C4×C8—21no—
388C4×C8—21no—
389#95—22no—
390#95—21no—
391#95C23×C1112yes—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—82no—
395C2×C11—82no—
396C2×C11C2×#44911yescharacteristic
397C2×C11#302011yescharacteristic
398C2×C11#302511yescharacteristic
399C24—21no—
400#41—42no—
401#41—42no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8C2×D4×C1112yes—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—42no—
415C2×D4C2×D4×C1112yes—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4C2×D4×C1112yes—
425C22×C4C2×D4×C1112yes—
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C24×C1111yescharacteristic
429SD16—44no—
430D8—44no—
431C2×C8—22no—
432C2×C8—22no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—44no—
449C4⋊C4—42no—
450C4⋊C4C2×D4×C1112yes—
451C4⋊C4C2×D4×C1112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C42—24no—
463C42—22no—
464C42—22no—
465C42—22no—
466C42C2×D4×C1111yescharacteristic
467C42C2×D4×C1111yescharacteristic
468C42C2×D4×C1111yescharacteristic
469C42C2×D4×C1111yescharacteristic
470C11#1821411yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23C22×D4×C1111yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485D4—22no—
486D4—22no—
487D4—42no—
488D4—42no—
489D4—41no—
490D4—41no—
491D4—42no—
492D4—42no—
493D4—42no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—84no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4C11×#12011yescharacteristic
515C2×C4C11×#12011yescharacteristic
516C2×C4C11×#12011yescharacteristic
517C2×C4C11×#12011yescharacteristic
518C2×C4C11×#13512yes—
519C2×C4C11×AGL(1,ℤ/8)12yes—
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C22×D4×C1111yescharacteristic
522C8—42no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22C2×C11×#12011yescharacteristic
537C22C2×C11×#13511yescharacteristic
538C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—82no—
549C4—81no—
550C4C11×#44912yes—
551C4C11×#44912yes—
552C2—21no—
553C2—21no—
554C2—82no—
555C2—82no—
556C2C2×C11×#44911yescharacteristic
557C2C11×#302011yescharacteristic
558C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3100C2
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×#3507C2semidirect
2. C11×#3101C2semidirect
4. C11×#2536C2semidirect
5. C11×#1609C2semidirect
6. C11×#1597C2semidirect
7. C11×#1518C2semidirect
8. C11×#1517C2semidirect
9. C11×#1461C2semidirect
120. #18214C11direct (N × H)
192. #3507C2×C11semidirect
193. #3101C2×C11semidirect
195. #2536C2×C11semidirect
196. #1609C2×C11semidirect
197. #1597C2×C11semidirect
198. #1518C2×C11semidirect
199. #1517C2×C11semidirect
200. #1461C2×C11semidirect
470. C11#18214direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#31012
C11×#31002
C11×#25362
C11×#16092
C11×#15972
C11×#15182
C11×#15172
C11×#14612
#1821411