Finite Group Databasebeta

← C2×#13082760 #15660671

Subgroups — C2×#13082760 #15660671

Order 2816.

6554 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082760C2132yesmaximal, direct product factor
2C2×C11⋊#564C211yesmaximal, characteristic, complemented
3C2×#10623182C214yesmaximal, complemented
4C2×#10623177C214yesmaximal, complemented
5C2×#10623203C212yesmaximal, complemented
6C2×#10623152C214yesmaximal, complemented
7C2×#10623219C211yesmaximal, characteristic, complemented
8C2×#10623153C214yesmaximal, complemented
9C2×#10623131C214yesmaximal, complemented
10C2×#10623211C212yesmaximal, complemented
11C2×#10623180C214yesmaximal, complemented
12C2×C11×#562C211yesmaximal, characteristic, complemented
13C11×#562C22116yescomplemented
14C2×C11×#125C2211yescharacteristic
15C2×C11×#124C2212yes—
16C2×C11×#123C2214yes—
17C2×C11×C22⋊Q8C2214yes—
18C2×C11×#121C2214yes—
19C2×#66999C2212yes—
20C2×Q8×Dic11C2212yes—
21C2×#66997C2214yes—
22C2×#66992C2214yes—
23C2×#66991C2212yes—
24C2×#66989C2214yes—
25C2×#66988C2214yes—
26C2×#66988C2214yes—
27C2×D4×Dic11C2214yes—
28C2×D4×Dic11C2212yes—
29C2×#66982C2214yes—
30C2×#66977C2214yes—
31C2×#66977C2214yes—
32C22×C4×Dic11C2214yes—
33#10623219C22116yescomplemented
34C11⋊#564C22116yescomplemented
35#10623211C22132yescomplemented
36#10623203C22132yescomplemented
37#10623182C22164yescomplemented
38#10623180C22164yescomplemented
39#10623177C22164yescomplemented
40#10623153C22164yescomplemented
41#10623152C22164yescomplemented
42#10623131C22164yescomplemented
43C2×#66951C2214yes—
44C2×#66949C2214yes—
45C2×#66945C2212yes—
46C2×#66943C2214yes—
47C2×#66942C2214yes—
48C2×#66942C2214yes—
49C2×#66942C2214yes—
50C2×#66941C2214yes—
51C2×#66941C2212yes—
52C2×#66940C2214yes—
53C2×#66940C2214yes—
54C2×#66938C2214yes—
55C2×#66936C2214yes—
56C2×(C22⋊D11)⋊C4C2214yes—
57C2×#66932C2214yes—
58C2×#66932C2214yes—
59C2×#66932C2214yes—
60C2×#66932C2214yes—
61C2×#66931C2214yes—
62C2×#66931C2214yes—
63C2×#66931C2214yes—
64C2×#66930C2214yes—
65C2×#66930C2214yes—
66C2×C42×D11C2211yescharacteristic
67C2×#66923C2212yes—
68C2×#66923C2211yescharacteristic
69C22×Q8×C11C2312yes—
70C22×D4×C11C2312yes—
71C22×D4×C11C2314yes—
72C23×C4×C11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11C2314yes—
75C23×Dic11C2314yes—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2312yes—
78C22×Dic22C2314yes—
79C22×Dic22C2314yes—
80C11×#125C2318yes—
81C11×#124C23116yes—
82C11×#123C23132yes—
83C11×C22⋊Q8C23132yes—
84C11×#121C23132yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97#66999C23116yes—
98Q8×Dic11C23116yes—
99#66997C23132yes—
100#66992C23132yes—
101#66991C23116yes—
102#66989C23132yes—
103#66988C23132yes—
104#66988C23132yes—
105D4×Dic11C23132yes—
106D4×Dic11C23116yes—
107#66982C23132yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115#66977C23132yes—
116#66977C23132yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C23132yes—
133#66951C23132yes—
134#66949C23132yes—
135#66945C23116yes—
136#66943C23132yes—
137#66942C23132yes—
138#66942C23132yes—
139#66942C23132yes—
140#66941C23132yes—
141#66941C23116yes—
142#66940C23132yes—
143#66940C23132yes—
144#66938C23132yes—
145#66936C23132yes—
146(C22⋊D11)⋊C4C23132yes—
147#66932C23132yes—
148#66932C23132yes—
149#66932C23132yes—
150#66932C23132yes—
151#66931C23132yes—
152#66931C23132yes—
153#66931C23132yes—
154#66930C23132yes—
155#66930C23132yes—
156C42×D11C2318yes—
157#66923C2318yes—
158#66923C23116yes—
159C2×#3531—111nomaximal, Sylow
160C24×C11C2414yes—
161C23×D11C2411yescharacteristic
162C2×Q8×C11—44no—
163C2×Q8×C11C2418yes—
164C2×D4×C11—48no—
165C2×D4×C11—44no—
166C2×D4×C11C2418yes—
167C2×D4×C11C24116yes—
168C22×C4×C11—48no—
169C22×C4×C11C2414yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2412yes—
173C22×C4×C11C24116yes—
174C2×C22⋊D11—48no—
175C2×C22⋊D11C24116yes—
176C22×Dic11—216no—
177C22×Dic11—48no—
178C22×Dic11C24116yes—
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2414yes—
182C22×Dic11C2412yes—
183C22×Dic11C24116yes—
184C22×Dic11C2411yescharacteristic
185C2×C4×D11—24no—
186C2×C4×D11—44no—
187C2×C4×D11C2414yes—
188C2×C4×D11C2418yes—
189C2×Dic22—48no—
190C2×Dic22—48no—
191C2×Dic22C24116yes—
192C2×Dic22C24116yes—
193C11×C4⋊C4C24116yes—
194C11×C4⋊C4C24116yes—
195C11×C4⋊C4C2418yes—
196C11×C22⋊C4C24116yes—
197C11×C22⋊C4C24116yes—
198C11×C22⋊C4C24116yes—
199C42×C11C2414yes—
200C22⋊Dic11C24116yes—
201C22⋊Dic11C24116yes—
202C22⋊Dic11C24116yes—
203C22⋊Dic11C24116yes—
204C22⋊Dic11C24116yes—
205(C2×D11)⋊C4C24116yes—
206(C2×D11)⋊C4C24116yes—
207C4⋊Dic11C2418yes—
208C4⋊Dic11C2418yes—
209C4⋊Dic11C2418yes—
210C4⋊Dic11C24116yes—
211C4⋊Dic11C24116yes—
212Dic11⋊C4C24116yes—
213Dic11⋊C4C24116yes—
214Dic11⋊C4C24116yes—
215Dic11⋊C4C24116yes—
216Dic11⋊C4C24116yes—
217Dic11⋊C4C24116yes—
218Dic11⋊C4C24116yes—
219Dic11⋊C4C24116yes—
220Dic11⋊C4C24116yes—
221C4×Dic11C2418yes—
222C4×Dic11C2414yes—
223C4×Dic11C24116yes—
224C4×Dic11C24116yes—
225C4×Dic11C24116yes—
226C4×Dic11C24116yes—
227#3531—1132no—
228C2×#564—111no—
229C2×#563—112no—
230C2×#563—114no—
231C2×#563—114no—
232C2×#562—114no—
233C2×#562D1111yescharacteristic, complemented
234C2×#533—111no—
235C2×#533—114no—
236C2×#529—112no—
237C2×#529—114no—
238C2×#529—114no—
239C23×C11—28no—
240C23×C11—28no—
241C23×C11—28no—
242C23×C11C2518yes—
243C23×C11C2511yescharacteristic
244C22×D11—22no—
245C22×D11—24no—
246C22×D11C2512yes—
247Q8×C11—48no—
248D4×C11—416no—
249D4×C11—48no—
250C2×C4×C11—22no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11—24no—
254C2×C4×C11—416no—
255C2×C4×C11C2518yes—
256C2×C4×C11C2518yes—
257C2×C4×C11C2512yes—
258C2×C4×C11C2514yes—
259C22⋊D11—416no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—232no—
265C2×Dic11—416no—
266C2×Dic112−1+414yes—
267C2×Dic11C2518yes—
268C2×Dic11C2518yes—
269C2×Dic11C2518yes—
270C2×Dic11C2514yes—
271C2×Dic11C2512yes—
272C4×D11—28no—
273C4×D11—48no—
274Dic22—416no—
275Dic22—416no—
276#564—1116no—
277#563—1132no—
278#563—1164no—
279#563—1164no—
280#562—1164no—
281#562C2×D11116yescomplemented
282#533—1116no—
283#533—1164no—
284C2×C4⋊Q8—114no—
285C2×C4⋊Q8—114no—
286C2×C4⋊Q8—112no—
287#529—1132no—
288#529—1164no—
289#529—1164no—
290C2×#126—114no—
291C2×#126—114no—
292C2×#126—114no—
293C2×#126—114no—
294C2×#126—114no—
295C2×#125—114no—
296C2×#125—114no—
297C2×#125—114no—
298C2×#125—114no—
299C2×#125—112no—
300C2×#125—111no—
301C2×#125C2×D1111yescharacteristic
302C2×#124—114no—
303C2×#124—114no—
304C2×#124C2×D1112yes—
305C2×#123—114no—
306C2×#123—114no—
307C2×#123—114no—
308C2×#123—114no—
309C2×#123C2×D1114yes—
310C2×C22⋊Q8—112no—
311C2×C22⋊Q8—114no—
312C2×C22⋊Q8—114no—
313C2×C22⋊Q8—114no—
314C2×C22⋊Q8—114no—
315C2×C22⋊Q8—114no—
316C2×C22⋊Q8—114no—
317C2×C22⋊Q8C2×D1114yes—
318C2×#121—112no—
319C2×#121—114no—
320C2×#121C2×D1114yes—
321C2×C4×Q8—112no—
322C2×C4×Q8—114no—
323C2×C4×Q8—114no—
324C2×C4×D4—112no—
325C2×C4×D4—114no—
326C2×C4×D4—114no—
327C2×#117—112no—
328C2×#117—114no—
329C2×#117—114no—
330C22×C42—114no—
331C22×C42—111no—
332C22×C11—28no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—416no—
336C22×C11C2×2−1+412yes—
337C22×C11#58514yes—
338C22×C11C2611yescharacteristic
339C2×D11—22no—
340C2×D11—24no—
341C2×D11—44no—
342C4×C11—22no—
343C4×C11—28no—
344C4×C11—28no—
345C4×C11—24no—
346Dic11—28no—
347Dic11—24no—
348Dic11—28no—
349Dic11—28no—
350Dic11C2×2−1+414yes—
351C22×Q8—114no—
352C22×Q8—114no—
353C22×Q8C22×D1112yes—
354C22×D4—114no—
355C22×D4C22×D1112yes—
356C22×D4C22×D1114yes—
357C23×C4—114no—
358C23×C4—114no—
359C23×C4—111no—
360C23×C4—112no—
361C23×C4C22×D1114yes—
362C4⋊Q8—1132no—
363C4⋊Q8—1132no—
364C4⋊Q8—1116no—
365#126—1132no—
366#126—1132no—
367#126—1132no—
368#126—1132no—
369#126—1132no—
370#125—1132no—
371#125—1132no—
372#125—1132no—
373#125—1132no—
374#125—1116no—
375#125—118no—
376#125C22×D1118yes—
377#124—1132no—
378#124—1132no—
379#124C22×D11116yes—
380#123—1132no—
381#123—1132no—
382#123—1132no—
383#123—1132no—
384#123C22×D11132yes—
385C22⋊Q8—1116no—
386C22⋊Q8—1132no—
387C22⋊Q8—1132no—
388C22⋊Q8—1132no—
389C22⋊Q8—1132no—
390C22⋊Q8—1132no—
391C22⋊Q8—1132no—
392C22⋊Q8C22×D11132yes—
393#121—1116no—
394#121—1132no—
395#121C22×D11132yes—
396C4×Q8—1116no—
397C4×Q8—1132no—
398C4×Q8—1132no—
399C4×D4—1116no—
400C4×D4—1132no—
401C4×D4—1132no—
402#117—1116no—
403#117—1132no—
404#117—1132no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4C22×D1112yes—
420C2×C4⋊C4C22×D1114yes—
421C2×C4⋊C4C22×D1114yes—
422C2×C22⋊C4—114no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4C22×D1114yes—
430C2×C22⋊C4C22×D1114yes—
431C2×C22⋊C4C22×D1114yes—
432C2×C42—114no—
433C2×C42—112no—
434C2×C42—114no—
435C2×C42—114no—
436C2×C42—114no—
437C2×C42—111no—
438C2×C42—1132no—
439C2×C42—118no—
440C2×C42C22×D1111yescharacteristic
441C2×C11—48no—
442C2×C11#353114yescomplemented
443C2×C11C22×2−1+411yescharacteristic
444C2×C11C2×#58512yes—
445D11—42no—
446C24—111no—
447C24C23×D1114yes—
448C2×Q8—44no—
449C2×Q8—1116no—
450C2×Q8—1116no—
451C2×Q8—448no—
452C2×Q8—448no—
453C2×Q8C23×D1118yes—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—1116no—
457C2×D4—448no—
458C2×D4C23×D1118yes—
459C2×D4C23×D11116yes—
460C22×C4—48no—
461C22×C4—111no—
462C22×C4—1116no—
463C22×C4—114no—
464C22×C4—112no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—1116no—
468C22×C4—114no—
469C22×C4—118no—
470C22×C4—224no—
471C22×C4—2216no—
472C22×C4—444no—
473C22×C4—448no—
474C22×C4C23×D1114yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1111yescharacteristic
477C22×C4C23×D1112yes—
478C22×C4C23×D11116yes—
479C4⋊C4—1116no—
480C4⋊C4—1116no—
481C4⋊C4—118no—
482C4⋊C4—1116no—
483C4⋊C4—1116no—
484C4⋊C4—1116no—
485C4⋊C4—1116no—
486C4⋊C4—118no—
487C4⋊C4—1116no—
488C4⋊C4—118no—
489C4⋊C4—1116no—
490C4⋊C4—1116no—
491C4⋊C4—1116no—
492C4⋊C4—1116no—
493C4⋊C4C23×D1118yes—
494C4⋊C4C23×D11116yes—
495C4⋊C4C23×D11116yes—
496C22⋊C4—1116no—
497C22⋊C4—1116no—
498C22⋊C4—1116no—
499C22⋊C4—1116no—
500C22⋊C4—1116no—
501C22⋊C4—1116no—
502C22⋊C4—1116no—
503C22⋊C4C23×D11116yes—
504C22⋊C4C23×D11116yes—
505C22⋊C4C23×D11116yes—
506C42—1116no—
507C42—118no—
508C42—1116no—
509C42—1116no—
510C42—1116no—
511C42—114no—
512C42C23×D1114yes—
513C11C2×#353111yescharacteristic, complemented, Sylow
514C23—28no—
515C23—28no—
516C23—28no—
517C23—112no—
518C23—224no—
519C23—222no—
520C23C24×D1118yes—
521C23C24×D1111yescharacteristic
522Q8—48no—
523Q8—4416no—
524Q8—4416no—
525D4—416no—
526D4—48no—
527D4—4416no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—416no—
533C2×C4—114no—
534C2×C4—112no—
535C2×C4—118no—
536C2×C4—114no—
537C2×C4—118no—
538C2×C4—118no—
539C2×C4—228no—
540C2×C4—2232no—
541C2×C4—228no—
542C2×C4—224no—
543C2×C4—228no—
544C2×C4—228no—
545C2×C4—448no—
546C2×C4—4416no—
547C2×C4C24×D1118yes—
548C2×C4C24×D1118yes—
549C2×C4C24×D1112yes—
550C2×C4C24×D1114yes—
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—222no—
556C22—224no—
557C22—444no—
558C22#1062345514yes—
559C22D11×2−1+412yes—
560C22C25×D1111yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—24no—
565C4—114no—
566C4—228no—
567C4—228no—
568C4—224no—
569C4—228no—
570C2—48no—
571C2—442no—
572C2#1308276014yesdirect product factor
573C2C2×D11×2−1+411yescharacteristic
574C2C2×#1062345512yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#562C2
socleC23×C11C25
hypercenterC2×#562D11
hypocenterC11C2×#3531
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13082760C2direct (N × H)
2. C2×C11⋊#564C2semidirect
3. C2×#10623182C2semidirect
4. C2×#10623177C2semidirect
5. C2×#10623203C2semidirect
6. C2×#10623152C2semidirect
7. C2×#10623219C2semidirect
8. C2×#10623153C2semidirect
9. C2×#10623131C2semidirect
10. C2×#10623211C2semidirect
11. C2×#10623180C2semidirect
12. C2×C11×#562C2semidirect
13. C11×#562C22semidirect
33. #10623219C22semidirect
34. C11⋊#564C22semidirect
35. #10623211C22semidirect
36. #10623203C22semidirect
37. #10623182C22semidirect
38. #10623180C22semidirect
39. #10623177C22semidirect
40. #10623153C22semidirect
41. #10623152C22semidirect
42. #10623131C22semidirect
233. C2×#562D11semidirect
281. #562C2×D11semidirect
442. C2×C11#3531semidirect
513. C11C2×#3531semidirect
572. C2#13082760direct (N × H)

Maximal subgroups

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

subgroupindex
#130827602
C2×C11⋊#5642
C2×#106231822
C2×#106231772
C2×#106232032
C2×#106231522
C2×#106232192
C2×#106231532
C2×#106231312
C2×#106232112
C2×#106231802
C2×C11×#5622
C2×#353111