Finite Group Databasebeta

← C11×#18443 #14595636

Subgroups — C11×#18443 #14595636

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic
2C11×#3239C211yesmaximal, characteristic
3C11×#3230C211yesmaximal, characteristic, complemented
4C11×#2642C211yesmaximal, characteristic, complemented
5C11×#1617C214yesmaximal, complemented
6C11×#1615C214yesmaximal
7C11×#1506C211yesmaximal, characteristic, complemented
8C11×#1500C211yesmaximal, characteristic
9C11×#1470C211yesmaximal, characteristic, complemented
10C11×#564—21no—
11C11×#563—21no—
12C11×#557—21no—
13C11×#554—21no—
14C11×#552—21no—
15C11×#552—21no—
16C11×#552—22no—
17C11×#544—21no—
18C11×#544C2212yes—
19C11×#541—21no—
20C11×#541—22no—
21C11×#539C2212yes—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C2×C11×#125C2211yescharacteristic
26C11×#501—21no—
27C11×#500—21no—
28C11×#489—21no—
29C11×#487—21no—
30C11×#484C2214yes—
31C11×#484C2212yes—
32C11×#481C2212yes—
33C11×#477—22no—
34C11×#475—21no—
35C11×#474—21no—
36C11×#432C2211yescharacteristic
37C11×#431C2211yescharacteristic
38C11×#400—22no—
39C11×#400C2214yes—
40C11×#391—21no—
41C11×#391—21no—
42C11×#376C2211yescharacteristic
43C11×#328C2214yes—
44C11×#328C2212yes—
45C11×#327C2212yes—
46C11×#324C2214yes—
47C22×Q8×C11—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—21no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#125—22no—
65C11×#125—22no—
66C11×#125—21no—
67C11×#125—22no—
68C11×#125—22no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#125—21no—
74C11×#125—21no—
75C11×#125—21no—
76C11×#125D411yescharacteristic
77C11×#124D411yescharacteristic
78C11×#123—22no—
79C11×#123—21no—
80C11×#123—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8C2311yescharacteristic
89C11×C22⋊Q8C2312yes—
90C11×#121C2311yescharacteristic
91C4×Q8×C11—21no—
92C4×Q8×C11—22no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11D412yes—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C4×D4×C11D411yescharacteristic
100C11×#117—22no—
101C11×#117—21no—
102C11×#117—21no—
103C11×#117—22no—
104C11×#117—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D412yes—
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2312yes—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C11×#107—24no—
115C11×#107—22no—
116C11×#106—22no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×#103—22no—
120C11×#103—24no—
121C11×#102—22no—
122C11×C22⋊C8C2312yes—
123C11×C22⋊C8C2312yes—
124C11×#97—21no—
125C4×C8×C11—21no—
126C11×#95—21no—
127C11×#95—24no—
128C11×#95—24no—
129C11×#95C2312yes—
130#18443C1111yesmaximal, characteristic, direct product factor, Sylow
131C2×Q8×C11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11—44no—
134C2×Q8×C11—41no—
135C2×Q8×C11—41no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×D411yescharacteristic
138C2×D4×C11—21no—
139C2×D4×C11C2×D411yescharacteristic
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—21no—
197C42×C11—42no—
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202#3563C2×C1111yescharacteristic
203#3239C2×C1111yescharacteristic
204#3230C2×C1111yescharacteristic, complemented
205#2642C2×C1111yescharacteristic, complemented
206#1617C2×C1114yescomplemented
207#1615C2×C1114yes—
208#1506C2×C1111yescharacteristic, complemented
209#1500C2×C1111yescharacteristic
210#1470C2×C1111yescharacteristic, complemented
211C23×C11—21no—
212C23×C11C22×D411yescharacteristic
213Q8×C11—41no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—82no—
217Q8×C11—82no—
218Q8×C11—82no—
219D4×C11—41no—
220D4×C11—42no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—82no—
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C8×C11—42no—
247C8×C11—42no—
248#564—21no—
249#563—21no—
250#557—21no—
251#554—21no—
252#552—21no—
253#552—21no—
254#552—22no—
255#544—21no—
256#544C22×C1112yes—
257#541—21no—
258#541—22no—
259#539C22×C1112yes—
260#533C22×C1111yescharacteristic
261C2×C4⋊Q8C22×C1111yescharacteristic
262#529C22×C1111yescharacteristic
263C2×#125C22×C1111yescharacteristic
264#501—21no—
265#500—21no—
266#489—21no—
267#487—21no—
268#484C22×C1114yes—
269#484C22×C1112yes—
270#481C22×C1112yes—
271#477—22no—
272#475—21no—
273#474—21no—
274#432C22×C1111yescharacteristic
275#431C22×C1111yescharacteristic
276#400—22no—
277#400C22×C1114yes—
278#391—21no—
279#391—21no—
280#376C22×C1111yescharacteristic
281#328C22×C1114yes—
282#328C22×C1112yes—
283#327C22×C1112yes—
284#324C22×C1114yes—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11C2×#12011yescharacteristic
291C22×C11#57812yes—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—41no—
304C4×C11—82no—
305C4×C11—82no—
306C4×C11#45412yes—
307C22×Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C1111yescharacteristic
316C4⋊Q8D4×C1111yescharacteristic
317#126—22no—
318#126—22no—
319#126—22no—
320#126—22no—
321#126—21no—
322#125—22no—
323#125—22no—
324#125—22no—
325#125—22no—
326#125—21no—
327#125—22no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—21no—
332#125—21no—
333#125—21no—
334#125—21no—
335#125—21no—
336#125D4×C1111yescharacteristic
337#124D4×C1111yescharacteristic
338#123—22no—
339#123—21no—
340#123—22no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—21no—
347C22⋊Q8—22no—
348C22⋊Q8C23×C1111yescharacteristic
349C22⋊Q8C23×C1112yes—
350#121C23×C1111yescharacteristic
351C4×Q8—21no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8D4×C1111yescharacteristic
356C4×Q8D4×C1112yes—
357C4×D4—21no—
358C4×D4—22no—
359C4×D4D4×C1111yescharacteristic
360#117—22no—
361#117—21no—
362#117—21no—
363#117—22no—
364#117—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C1111yescharacteristic
368C2×C4⋊C4D4×C1112yes—
369C2×C4⋊C4D4×C1111yescharacteristic
370C2×C4⋊C4C23×C1112yes—
371C2×C4⋊C4C23×C1112yes—
372C2×C42—21no—
373C2×C42C23×C1111yescharacteristic
374#107—22no—
375#107—24no—
376#106—22no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379#103—22no—
380#103—24no—
381#102—22no—
382C22⋊C8C23×C1112yes—
383C22⋊C8C23×C1112yes—
384#97—21no—
385C4×C8—21no—
386#95—21no—
387#95—24no—
388#95—24no—
389#95C23×C1112yes—
390C2×C11—22no—
391C2×C11—81no—
392C2×C11#301111yescharacteristic
393C2×C11C2×#45411yescharacteristic
394C2×C11#302811yescharacteristic
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—44no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8C2×D4×C1112yes—
401C2×Q8C2×D4×C1111yescharacteristic
402C2×D4—21no—
403C2×D4C2×D4×C1111yescharacteristic
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4C2×D4×C1112yes—
409C22×C4C2×D4×C1111yescharacteristic
410C22×C4C2×D4×C1111yescharacteristic
411C22×C4C2×D4×C1112yes—
412C22×C4C24×C1111yescharacteristic
413C2×C8—22no—
414C2×C8—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4C2×D4×C1111yescharacteristic
445C4⋊C4C2×D4×C1111yescharacteristic
446C4⋊C4C2×D4×C1112yes—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—42no—
462C42C2×D4×C1111yescharacteristic
463C42C2×D4×C1111yescharacteristic
464C42C2×D4×C1111yescharacteristic
465C42C2×D4×C1111yescharacteristic
466C11#1844311yescharacteristic, direct product factor, Sylow
467C23—21no—
468C23C22×D4×C1111yescharacteristic
469Q8—41no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473Q8—82no—
474Q8—82no—
475D4—41no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4C11×#12011yescharacteristic
497C2×C4C11×#12011yescharacteristic
498C2×C4C11×#12011yescharacteristic
499C2×C4C11×#12011yescharacteristic
500C2×C4C22×D4×C1111yescharacteristic
501C2×C4C22×D4×C1111yescharacteristic
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×C11×#12011yescharacteristic
510C22C11×#57812yes—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4—82no—
525C4C11×#45412yes—
526C2—22no—
527C2—81no—
528C2C11×#301111yescharacteristic
529C2C2×C11×#45411yescharacteristic
530C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#121C23
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
3. C11×#3230C2semidirect
4. C11×#2642C2semidirect
5. C11×#1617C2semidirect
7. C11×#1506C2semidirect
9. C11×#1470C2semidirect
130. #18443C11direct (N × H)
204. #3230C2×C11semidirect
205. #2642C2×C11semidirect
206. #1617C2×C11semidirect
208. #1506C2×C11semidirect
210. #1470C2×C11semidirect
466. C11#18443direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#32392
C11×#32302
C11×#26422
C11×#16172
C11×#16152
C11×#15062
C11×#15002
C11×#14702
#1844311