Finite Group Databasebeta

← C11×#61664 #14638857

Subgroups — C11×#61664 #14638857

Order 2816.

2136 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3549C211yesmaximal, characteristic, complemented
2C11×#3499C211yesmaximal, characteristic, complemented
3C11×#3329C214yesmaximal, complemented
4C11×#3303C214yesmaximal, complemented
5D4×C11×SD16C214yesmaximal, complemented
6C11×#3272C214yesmaximal, complemented
7C11×#3206C212yesmaximal, complemented
8C11×#3200C214yesmaximal, complemented
9C11×#3106C212yesmaximal, complemented
10C11×#3010C214yesmaximal, complemented
11C11×#2979C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yescomplemented
13C2×C11×AGL(1,ℤ/8)C2214yescomplemented
14C22×C11×SD16C2214yescomplemented
15C11×H(3,𝔽4)—22no—
16C11×#555—21no—
17C11×#555C2214yes—
18D4×Q8×C11C2214yescomplemented
19C11×#547—24no—
20C11×#547C2214yescomplemented
21D42×C11—21no—
22D42×C11C2214yes—
23C11×#536—22no—
24C11×#536C2212yescomplemented
25C11×#535—24no—
26C11×#535C2214yes—
27C11×#532—21no—
28C11×#532C2212yes—
29C11×#532C2211yescharacteristic
30C2×C11×C4⋊Q8—21no—
31C2×C11×C4⋊Q8C2211yescharacteristic, complemented
32C4×C11×#41C2211yescharacteristic, complemented
33C11×#492C2214yes—
34C11×#487C2214yescomplemented
35C11×#485C2218yescomplemented
36C11×#482C2214yescomplemented
37C11×#477C2212yescomplemented
38C11×#476C2212yescomplemented
39C11×#468C2218yescomplemented
40C11×#465C2218yescomplemented
41C11×#461C2214yescomplemented
42C11×#461C2214yescomplemented
43C11×#460C2212yes—
44C11×#459C2212yes—
45C11×#450C2218yescomplemented
46C11×#449C2214yescomplemented
47C11×#449C2218yescomplemented
48C11×#448C2218yescomplemented
49C11×#448C2218yescomplemented
50C4×C11×SD16C2214yescomplemented
51C4×C11×D8C2214yescomplemented
52C11×#436C2214yescomplemented
53C8×D4×C11C2214yescomplemented
54C11×#431C2212yescomplemented
55C11×#419C2214yescomplemented
56C11×#416C2214yescomplemented
57C11×#408C2214yescomplemented
58C11×2−1+4—44no—
59C11×2−1+4—44no—
60C2×C11×#41—22no—
61C2×C11×#41—24no—
62C2×C11×#41—22no—
63C2×C11×#41C2311yescharacteristic
64C2×C11×#41C2314yes—
65C2×C11×#41C2312yes—
66C22×Q8×C11—22no—
67C22×Q8×C11C2314yes—
68C22×Q8×C11C2312yes—
69C22×D4×C11—24no—
70C22×D4×C11C2314yes—
71C11×AGL(1,ℤ/8)—48no—
72C2×C11×SD16—48no—
73C2×C11×SD16C2314yes—
74C2×C11×SD16C2318yes—
75C2×C11×SD16C2318yes—
76C2×C11×D8C2314yes—
77C2×C11×M16C2314yes—
78C22×C8×C11C2314yes—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8—24no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8D411yescharacteristic
84C11×C4⋊Q8C2314yes—
85C11×C4⋊Q8C2312yes—
86C11×#127—24no—
87C11×#127D411yescharacteristic
88C11×#127C2312yes—
89C11×#124—24no—
90C11×#124—22no—
91C11×#124—28no—
92C11×#124—22no—
93C11×#124D412yes—
94C11×#123—24no—
95C11×#123—28no—
96C11×C22⋊Q8—28no—
97C11×C22⋊Q8C2318yes—
98C11×#121—24no—
99C11×#121—24no—
100C11×#121—22no—
101C11×#121—24no—
102C11×#121D414yes—
103C11×#121C2314yes—
104C11×#121C2318yes—
105C11×#120—24no—
106C11×#120—24no—
107C11×#120—28no—
108C4×Q8×C11C2312yes—
109C4×D4×C11—24no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11C2312yes—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yes—
115C11×#117—24no—
116C11×#117—21no—
117C11×#117C2311yescharacteristic
118C11×#117C2314yes—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—24no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C11×#107C2314yes—
124C11×#106C2314yes—
125C11×C4⋊C8C2312yes—
126C11×C4⋊C8C2312yes—
127C11×#103C2318yes—
128C11×#103C2314yes—
129C11×#103C2318yes—
130C11×#102C2314yes—
131C11×#102C2314yes—
132C11×#102C2314yes—
133C11×C22⋊C8C2314yes—
134C11×C22⋊C8C2318yes—
135C4×C8×C11C2314yes—
136#61664C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11—24no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—28no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—44no—
144C11×#41—48no—
145C11×#41—416no—
146C11×#41—84no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—28no—
151C2×Q8×C11—44no—
152C2×Q8×C11—42no—
153C2×Q8×C11—42no—
154C2×Q8×C11—48no—
155C2×Q8×C11C2×D412yes—
156C2×Q8×C11C2414yes—
157C2×Q8×C11C2411yescharacteristic
158C2×D4×C11—21no—
159C2×D4×C11—24no—
160C2×D4×C11—28no—
161C2×D4×C11—24no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—24no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—88no—
168C2×D4×C11C2×D414yes—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D414yes—
171C2×D4×C11C2414yes—
172C2×D4×C11C2411yescharacteristic
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—24no—
176C22×C4×C11—22no—
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2414yes—
182C11×SD16—28no—
183C11×SD16—48no—
184C11×SD16—48no—
185C11×D8—28no—
186C11×M16—44no—
187C2×C8×C11—44no—
188C2×C8×C11C2414yes—
189C2×C8×C11C2414yes—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—28no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4C2×D414yes—
196C11×C4⋊C4C2412yes—
197C11×C4⋊C4C2414yes—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—28no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4C2×D418yes—
206C42×C11—21no—
207C42×C11—22no—
208C42×C11—24no—
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C42×C11C2412yes—
212#3549C2×C1111yescharacteristic, complemented
213#3499C2×C1111yescharacteristic, complemented
214#3329C2×C1114yescomplemented
215#3303C2×C1114yescomplemented
216D4×SD16C2×C1114yescomplemented
217#3272C2×C1114yescomplemented
218#3206C2×C1112yescomplemented
219#3200C2×C1114yescomplemented
220#3106C2×C1112yescomplemented
221#3010C2×C1114yescomplemented
222#2979C2×C1111yescharacteristic, complemented
223C23×C11—21no—
224C23×C11—24no—
225C23×C11—84no—
226C23×C11—88no—
227C23×C11C22×D414yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—42no—
233Q8×C11—48no—
234Q8×C11—44no—
235Q8×C11—82no—
236Q8×C11H(5,𝔽2)12yes—
237D4×C11—24no—
238D4×C11—28no—
239D4×C11—21no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—42no—
243D4×C11—44no—
244D4×C11—48no—
245D4×C11—44no—
246D4×C11—84no—
247D4×C11—82no—
248D4×C11—88no—
249D4×C11—84no—
250D4×C11H(5,𝔽2)12yes—
251C2×C4×C11—24no—
252C2×C4×C11—21no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—48no—
262C2×C4×C11—48no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C2511yescharacteristic
271C8×C11—24no—
272C8×C11—24no—
273C2×2−1+4C22×C1112yescomplemented
274C2×AGL(1,ℤ/8)C22×C1114yescomplemented
275C22×SD16C22×C1114yescomplemented
276H(3,𝔽4)—22no—
277#555—21no—
278#555C22×C1114yes—
279D4×Q8C22×C1114yescomplemented
280#547—24no—
281#547C22×C1114yescomplemented
282D42—21no—
283D42C22×C1114yes—
284#536—22no—
285#536C22×C1112yescomplemented
286#535—24no—
287#535C22×C1114yes—
288#532—21no—
289#532C22×C1112yes—
290#532C22×C1111yescharacteristic
291C2×C4⋊Q8—21no—
292C2×C4⋊Q8C22×C1111yescharacteristic, complemented
293C4×#41C22×C1111yescharacteristic, complemented
294#492C22×C1114yes—
295#487C22×C1114yescomplemented
296#485C22×C1118yescomplemented
297#482C22×C1114yescomplemented
298#477C22×C1112yescomplemented
299#476C22×C1112yescomplemented
300#468C22×C1118yescomplemented
301#465C22×C1118yescomplemented
302#461C22×C1114yescomplemented
303#461C22×C1114yescomplemented
304#460C22×C1112yes—
305#459C22×C1112yes—
306#450C22×C1118yescomplemented
307#449C22×C1114yescomplemented
308#449C22×C1118yescomplemented
309#448C22×C1118yescomplemented
310#448C22×C1118yescomplemented
311C4×SD16C22×C1114yescomplemented
312C4×D8C22×C1114yescomplemented
313#436C22×C1114yescomplemented
314C8×D4C22×C1114yescomplemented
315#431C22×C1112yescomplemented
316#419C22×C1114yescomplemented
317#416C22×C1114yescomplemented
318#408C22×C1114yescomplemented
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—22no—
323C22×C11—28no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—168no—
329C22×C11C23×D411yescharacteristic
330C4×C11—21no—
331C4×C11—22no—
332C4×C11—24no—
333C4×C11—22no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11—44no—
337C4×C11#57714yes—
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339C4×C11C2×H(5,𝔽2)11yescharacteristic
3402−1+4—44no—
3412−1+4—44no—
342C2×#41—22no—
343C2×#41—24no—
344C2×#41—22no—
345C2×#41C23×C1111yescharacteristic
346C2×#41C23×C1114yes—
347C2×#41C23×C1112yes—
348C22×Q8—22no—
349C22×Q8C23×C1114yes—
350C22×Q8C23×C1112yes—
351C22×D4—24no—
352C22×D4C23×C1114yes—
353AGL(1,ℤ/8)—48no—
354C2×SD16—48no—
355C2×SD16C23×C1114yes—
356C2×SD16C23×C1118yes—
357C2×SD16C23×C1118yes—
358C2×D8C23×C1114yes—
359C2×M16C23×C1114yes—
360C22×C8C23×C1114yes—
361C4⋊Q8—22no—
362C4⋊Q8—24no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8D4×C1111yescharacteristic
366C4⋊Q8C23×C1114yes—
367C4⋊Q8C23×C1112yes—
368#127—24no—
369#127D4×C1111yescharacteristic
370#127C23×C1112yes—
371#124—24no—
372#124—22no—
373#124—28no—
374#124—22no—
375#124D4×C1112yes—
376#123—24no—
377#123—28no—
378C22⋊Q8—28no—
379C22⋊Q8C23×C1118yes—
380#121—24no—
381#121—24no—
382#121—22no—
383#121—24no—
384#121D4×C1114yes—
385#121C23×C1114yes—
386#121C23×C1118yes—
387#120—24no—
388#120—24no—
389#120—28no—
390C4×Q8C23×C1112yes—
391C4×D4—24no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4C23×C1112yes—
395C4×D4C23×C1114yes—
396C4×D4C23×C1114yes—
397#117—24no—
398#117—21no—
399#117C23×C1111yescharacteristic
400#117C23×C1114yes—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C42—21no—
404C2×C42C23×C1111yescharacteristic
405#107C23×C1114yes—
406#106C23×C1114yes—
407C4⋊C8C23×C1112yes—
408C4⋊C8C23×C1112yes—
409#103C23×C1118yes—
410#103C23×C1114yes—
411#103C23×C1118yes—
412#102C23×C1114yes—
413#102C23×C1114yes—
414#102C23×C1114yes—
415C22⋊C8C23×C1114yes—
416C22⋊C8C23×C1118yes—
417C4×C8C23×C1114yes—
418C2×C11—41no—
419C2×C11—44no—
420C2×C11—42no—
421C2×C11—84no—
422C2×C11#348411yescharacteristic
423C2×C11C2×#57712yes—
424C24—24no—
425#41—22no—
426#41—22no—
427#41—28no—
428#41—42no—
429#41—42no—
430#41—44no—
431#41—48no—
432#41—416no—
433#41—84no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—28no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—48no—
442C2×Q8C2×D4×C1112yes—
443C2×Q8C24×C1114yes—
444C2×Q8C24×C1111yescharacteristic
445C2×D4—21no—
446C2×D4—24no—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—24no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—88no—
455C2×D4C2×D4×C1114yes—
456C2×D4C2×D4×C1112yes—
457C2×D4C2×D4×C1114yes—
458C2×D4C24×C1114yes—
459C2×D4C24×C1111yescharacteristic
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4C2×D4×C1112yes—
467C22×C4C24×C1111yescharacteristic
468C22×C4C24×C1114yes—
469SD16—28no—
470SD16—48no—
471SD16—48no—
472D8—28no—
473M16—44no—
474C2×C8—44no—
475C2×C8C24×C1114yes—
476C2×C8C24×C1114yes—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4C2×D4×C1114yes—
483C4⋊C4C24×C1112yes—
484C4⋊C4C24×C1114yes—
485C22⋊C4—21no—
486C22⋊C4—24no—
487C22⋊C4—28no—
488C22⋊C4—22no—
489C22⋊C4—28no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4C2×D4×C1118yes—
493C42—21no—
494C42—22no—
495C42—24no—
496C42C2×D4×C1111yescharacteristic
497C42C2×D4×C1111yescharacteristic
498C42C24×C1112yes—
499C11#6166411yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—24no—
502C23—84no—
503C23—88no—
504C23C22×D4×C1114yes—
505C23C22×D4×C1111yescharacteristic
506Q8—21no—
507Q8—24no—
508Q8—24no—
509Q8—42no—
510Q8—48no—
511Q8—44no—
512Q8—82no—
513Q8C11×H(5,𝔽2)12yes—
514D4—24no—
515D4—28no—
516D4—21no—
517D4—24no—
518D4—24no—
519D4—42no—
520D4—44no—
521D4—48no—
522D4—44no—
523D4—84no—
524D4—82no—
525D4—88no—
526D4—84no—
527D4C11×H(5,𝔽2)12yes—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—48no—
539C2×C4—48no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—48no—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1114yes—
545C2×C4C22×D4×C1112yes—
546C2×C4C22×D4×C1112yes—
547C2×C4C25×C1111yescharacteristic
548C8—24no—
549C8—24no—
550C22—21no—
551C22—22no—
552C22—24no—
553C22—22no—
554C22—28no—
555C22—42no—
556C22—44no—
557C22—44no—
558C22—44no—
559C22—168no—
560C22C23×D4×C1111yescharacteristic
561C4—21no—
562C4—22no—
563C4—24no—
564C4—22no—
565C4—44no—
566C4—44no—
567C4—42no—
568C4C11×#57714yes—
569C4C2×C11×H(5,𝔽2)11yescharacteristic
570C4C2×C11×H(5,𝔽2)11yescharacteristic
571C2—44no—
572C2—41no—
573C2—42no—
574C2—84no—
575C2C11×#348411yescharacteristic
576C2C2×C11×#57712yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#532 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3549C2semidirect
2. C11×#3499C2semidirect
3. C11×#3329C2semidirect
4. C11×#3303C2semidirect
5. D4×C11×SD16C2semidirect
6. C11×#3272C2semidirect
7. C11×#3206C2semidirect
8. C11×#3200C2semidirect
9. C11×#3106C2semidirect
10. C11×#3010C2semidirect
11. C11×#2979C2semidirect
12. C2×C11×2−1+4C22semidirect
13. C2×C11×AGL(1,ℤ/8)C22semidirect
14. C22×C11×SD16C22semidirect
18. D4×Q8×C11C22semidirect
20. C11×#547C22semidirect
24. C11×#536C22semidirect
31. C2×C11×C4⋊Q8C22semidirect
32. C4×C11×#41C22semidirect
34. C11×#487C22semidirect
35. C11×#485C22semidirect
36. C11×#482C22semidirect
37. C11×#477C22semidirect
38. C11×#476C22semidirect
39. C11×#468C22semidirect
40. C11×#465C22semidirect
41. C11×#461C22semidirect
42. C11×#461C22semidirect
45. C11×#450C22semidirect
46. C11×#449C22semidirect
47. C11×#449C22semidirect
48. C11×#448C22semidirect
49. C11×#448C22semidirect
50. C4×C11×SD16C22semidirect
51. C4×C11×D8C22semidirect
52. C11×#436C22semidirect
53. C8×D4×C11C22semidirect
54. C11×#431C22semidirect
55. C11×#419C22semidirect
56. C11×#416C22semidirect
57. C11×#408C22semidirect
136. #61664C11direct (N × H)
212. #3549C2×C11semidirect
213. #3499C2×C11semidirect
214. #3329C2×C11semidirect
215. #3303C2×C11semidirect
216. D4×SD16C2×C11semidirect
217. #3272C2×C11semidirect
218. #3206C2×C11semidirect
219. #3200C2×C11semidirect
220. #3106C2×C11semidirect
221. #3010C2×C11semidirect
222. #2979C2×C11semidirect
273. C2×2−1+4C22×C11semidirect
274. C2×AGL(1,ℤ/8)C22×C11semidirect
275. C22×SD16C22×C11semidirect
279. D4×Q8C22×C11semidirect
281. #547C22×C11semidirect
285. #536C22×C11semidirect
292. C2×C4⋊Q8C22×C11semidirect
293. C4×#41C22×C11semidirect
295. #487C22×C11semidirect
296. #485C22×C11semidirect
297. #482C22×C11semidirect
298. #477C22×C11semidirect
299. #476C22×C11semidirect
300. #468C22×C11semidirect
301. #465C22×C11semidirect
302. #461C22×C11semidirect
303. #461C22×C11semidirect
306. #450C22×C11semidirect
307. #449C22×C11semidirect
308. #449C22×C11semidirect
309. #448C22×C11semidirect
310. #448C22×C11semidirect
311. C4×SD16C22×C11semidirect
312. C4×D8C22×C11semidirect
313. #436C22×C11semidirect
314. C8×D4C22×C11semidirect
315. #431C22×C11semidirect
316. #419C22×C11semidirect
317. #416C22×C11semidirect
318. #408C22×C11semidirect
499. C11#61664direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35492
C11×#34992
C11×#33292
C11×#33032
D4×C11×SD162
C11×#32722
C11×#32062
C11×#32002
C11×#31062
C11×#30102
C11×#29792
#6166411