Finite Group Databasebeta

← C2×#13083071 #15661537

Subgroups — C2×#13083071 #15661537

Order 2816.

6566 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#13083071C2132yesmaximal, direct product factor
2C2×C11⋊#564C211yesmaximal, characteristic, complemented
3C2×#10623203C212yesmaximal, complemented
4C2×#10623167C214yesmaximal, complemented
5C2×#10623145C214yesmaximal, complemented
6C2×#10623181C214yesmaximal, complemented
7C2×#10623156C214yesmaximal, complemented
8C2×#10623133C214yesmaximal, complemented
9C2×#10623191C214yesmaximal, complemented
10C2×#10623211C212yesmaximal, complemented
11C2×D11×#125C211yesmaximal, characteristic, 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×#66991C2212yes—
23C2×#66991C2214yes—
24C2×#66988C2214yes—
25C2×#66988C2214yes—
26C2×#66988C2214yes—
27C2×D4×Dic11C2214yes—
28C2×D4×Dic11C2212yes—
29C2×C4×C22⋊D11C2214yes—
30C2×#66979C2214yes—
31C2×#66977C2214yes—
32C22×Dic11⋊C4C2214yes—
33D11×#125C22116yescomplemented
34C11⋊#564C22116yescomplemented
35#10623211C22132yescomplemented
36#10623203C22132yescomplemented
37#10623191C22164yescomplemented
38#10623181C22164yescomplemented
39#10623167C22164yescomplemented
40#10623156C22164yescomplemented
41#10623145C22164yescomplemented
42#10623133C22164yescomplemented
43C2×#66949C2214yes—
44C2×C4⋊C4×D11C2214yes—
45C2×C4⋊C4×D11C2212yes—
46C2×#66943C2212yes—
47C2×#66943C2214yes—
48C2×#66943C2214yes—
49C2×#66942C2214yes—
50C2×#66942C2214yes—
51C2×#66942C2214yes—
52C2×#66942C2214yes—
53C2×#66940C2214yes—
54C2×#66936C2214yes—
55C2×(C22⋊D11)⋊C4C2214yes—
56C2×(C22⋊D11)⋊C4C2214yes—
57C2×#66932C2214yes—
58C2×#66932C2214yes—
59C2×#66932C2214yes—
60C2×#66932C2214yes—
61C2×#66932C2214yes—
62C2×#66931C2214yes—
63C2×#66931C2214yes—
64C2×#66931C2214yes—
65C2×#66930C2214yes—
66C2×C42×D11C2211yescharacteristic
67C2×#66923C2211yescharacteristic
68C2×#66923C2212yes—
69C22×Q8×C11C2312yes—
70C22×D4×C11C2314yes—
71C22×D4×C11C2312yes—
72C23×C4×C11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11C2314yes—
75C23×Dic11C2314yes—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2312yes—
78C22×C4×D11C2314yes—
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#66991C23132yes—
101#66991C23116yes—
102#66988C23132yes—
103#66988C23132yes—
104#66988C23132yes—
105D4×Dic11C23116yes—
106D4×Dic11C23132yes—
107C4×C22⋊D11C23132yes—
108C2×(C2×D11)⋊C4C2314yes—
109#66979C23132yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2314yes—
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×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C23132yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133#66949C23132yes—
134C4⋊C4×D11C23132yes—
135C4⋊C4×D11C23116yes—
136#66943C23132yes—
137#66943C23132yes—
138#66943C23116yes—
139#66942C23132yes—
140#66942C23132yes—
141#66942C23132yes—
142#66942C23132yes—
143#66940C23132yes—
144#66936C23132yes—
145(C22⋊D11)⋊C4C23132yes—
146(C22⋊D11)⋊C4C23132yes—
147#66932C23132yes—
148#66932C23132yes—
149#66932C23132yes—
150#66932C23132yes—
151#66932C23132yes—
152#66931C23132yes—
153#66931C23132yes—
154#66931C23132yes—
155#66930C23132yes—
156C42×D11C2318yes—
157#66923C2318yes—
158#66923C23116yes—
159C2×#3553—111nomaximal, Sylow
160C24×C11C2414yes—
161C23×D11C2411yescharacteristic
162C2×Q8×C11—44no—
163C2×Q8×C11C2418yes—
164C2×D4×C11—48no—
165C2×D4×C11—44no—
166C2×D4×C11C24116yes—
167C2×D4×C11C2418yes—
168C22×C4×C11—48no—
169C22×C4×C11C2414yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2412yes—
172C22×C4×C11C2414yes—
173C22×C4×C11C24116yes—
174C2×C22⋊D11—216no—
175C2×C22⋊D11C24116yes—
176C22×Dic11—48no—
177C22×Dic11—48no—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2414yes—
182C22×Dic11C2414yes—
183C22×Dic11C24116yes—
184C22×Dic11C24116yes—
185C2×C4×D11—24no—
186C2×C4×D11—48no—
187C2×C4×D11—44no—
188C2×C4×D11C2414yes—
189C2×C4×D11C2418yes—
190C2×C4×D11C24116yes—
191C2×Dic22—48no—
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—
206C4⋊Dic11C2418yes—
207C4⋊Dic11C2418yes—
208C4⋊Dic11C2418yes—
209C4⋊Dic11C24116yes—
210C4⋊Dic11C24116yes—
211C4⋊Dic11C24116yes—
212Dic11⋊C4C24116yes—
213Dic11⋊C4C24116yes—
214Dic11⋊C4C24116yes—
215Dic11⋊C4C24116yes—
216Dic11⋊C4C24116yes—
217Dic11⋊C4C24116yes—
218Dic11⋊C4C24116yes—
219Dic11⋊C4C24116yes—
220Dic11⋊C4C24116yes—
221Dic11⋊C4C24116yes—
222C4×Dic11C2414yes—
223C4×Dic11C2418yes—
224C4×Dic11C24116yes—
225C4×Dic11C24116yes—
226C4×Dic11C24116yes—
227#3553—1132no—
228C2×#564—111no—
229C2×#563—112no—
230C2×#562D1111yescharacteristic, complemented
231C2×#554—114no—
232C2×#553—114no—
233C2×#552—114no—
234C2×#541—114no—
235C2×#539—114no—
236C2×#539—114no—
237C2×#529—112no—
238C22×#125—111no—
239C23×C11—28no—
240C23×C11—28no—
241C23×C11—28no—
242C23×C11C2518yes—
243C23×C11C2511yescharacteristic
244C22×D11—24no—
245C22×D112−1+414yes—
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×C11C2512yes—
257C2×C4×C11C2514yes—
258C2×C4×C11C2518yes—
259C22⋊D11—232no—
260C2×Dic11—22no—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—416no—
266C2×Dic11—416no—
267C2×Dic11C2514yes—
268C2×Dic11C2518yes—
269C2×Dic11C2512yes—
270C2×Dic11C2518yes—
271C2×Dic11C2518yes—
272C4×D11—28no—
273C4×D11—416no—
274C4×D11—48no—
275Dic22—416no—
276#564—1116no—
277#563—1132no—
278#562C2×D11116yescomplemented
279#554—1164no—
280#553—1164no—
281#552—1164no—
282#541—1164no—
283#539—1164no—
284#539—1164no—
285C2×C4⋊Q8—114no—
286#529—1132no—
287C2×#126—114no—
288C2×#126—114no—
289C2×#126—114no—
290C2×#126—114no—
291C2×#126—114no—
292C2×#125—1116no—
293C2×#125—114no—
294C2×#125—114no—
295C2×#125—114no—
296C2×#125—114no—
297C2×#125—112no—
298C2×#125—114no—
299C2×#125—114no—
300C2×#125—111no—
301C2×#125—112no—
302C2×#125C2×D1111yescharacteristic
303C2×#124C2×D1112yes—
304C2×#123—114no—
305C2×#123—114no—
306C2×#123—114no—
307C2×#123—114no—
308C2×#123C2×D1114yes—
309C2×C22⋊Q8—112no—
310C2×C22⋊Q8—114no—
311C2×C22⋊Q8—114no—
312C2×C22⋊Q8—114no—
313C2×C22⋊Q8—114no—
314C2×C22⋊Q8—114no—
315C2×C22⋊Q8C2×D1114yes—
316C2×#121—112no—
317C2×#121—114no—
318C2×#121C2×D1114yes—
319C2×C4×Q8—112no—
320C2×C4×Q8—114no—
321C2×C4×D4—112no—
322C2×C4×D4—114no—
323C2×C4×D4—114no—
324C2×C4×D4—114no—
325C2×C4×D4—114no—
326C2×#117—114no—
327C2×#117—114no—
328C22×C4⋊C4—114no—
329C22×C4⋊C4—112no—
330C22×C4⋊C4—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—24no—
340C2×D11—28no—
341C2×D11C2×2−1+414yes—
342C4×C11—22no—
343C4×C11—28no—
344C4×C11—28no—
345C4×C11—24no—
346Dic11—22no—
347Dic11—28no—
348Dic11—28no—
349Dic11—28no—
350Dic11—24no—
351C22×Q8—114no—
352C22×Q8C22×D1112yes—
353C22×D4—114no—
354C22×D4C22×D1114yes—
355C22×D4C22×D1112yes—
356C23×C4—114no—
357C23×C4—114no—
358C23×C4—111no—
359C23×C4—114no—
360C23×C4—112no—
361C23×C4C22×D1114yes—
362C4⋊Q8—1132no—
363#126—1132no—
364#126—1132no—
365#126—1132no—
366#126—1132no—
367#126—1132no—
368#125—1132no—
369#125—1116no—
370#125—1132no—
371#125—1132no—
372#125—1132no—
373#125—1132no—
374#125—1132no—
375#125—118no—
376#125—1116no—
377#125C22×D1118yes—
378#124C22×D11116yes—
379#123—1132no—
380#123—1132no—
381#123—1132no—
382#123—1132no—
383#123C22×D11132yes—
384C22⋊Q8—1116no—
385C22⋊Q8—1132no—
386C22⋊Q8—1132no—
387C22⋊Q8—1132no—
388C22⋊Q8—1132no—
389C22⋊Q8—1132no—
390C22⋊Q8C22×D11132yes—
391#121—1116no—
392#121—1132no—
393#121C22×D11132yes—
394C4×Q8—1116no—
395C4×Q8—1132no—
396C4×D4—1116no—
397C4×D4—1132no—
398C4×D4—1132no—
399C4×D4—1132no—
400C4×D4—1132no—
401#117—1132no—
402#117—1132no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
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—1132no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—1116no—
421C2×C4⋊C4—1132no—
422C2×C4⋊C4C22×D1114yes—
423C2×C4⋊C4C22×D1112yes—
424C2×C4⋊C4C22×D1114yes—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4C22×D1114yes—
432C2×C22⋊C4C22×D1114yes—
433C2×C22⋊C4C22×D1114yes—
434C2×C42—111no—
435C2×C42—114no—
436C2×C42—114no—
437C2×C42—114no—
438C2×C42—112no—
439C2×C42—118no—
440C2×C42C22×D1111yescharacteristic
441C2×C11—48no—
442C2×C11#355314yescomplemented
443C2×C11C22×2−1+411yescharacteristic
444C2×C11C2×#58512yes—
445D11—24no—
446C24—111no—
447C24C23×D1114yes—
448C2×Q8—44no—
449C2×Q8—1116no—
450C2×Q8—448no—
451C2×Q8C23×D1118yes—
452C2×D4—48no—
453C2×D4—44no—
454C2×D4—1116no—
455C2×D4—2216no—
456C2×D4C23×D11116yes—
457C2×D4C23×D1118yes—
458C22×C4—48no—
459C22×C4—112no—
460C22×C4—114no—
461C22×C4—111no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—1116no—
465C22×C4—1116no—
466C22×C4—114no—
467C22×C4—118no—
468C22×C4—1116no—
469C22×C4—224no—
470C22×C4—448no—
471C22×C4—444no—
472C22×C4—448no—
473C22×C4—448no—
474C22×C4C23×D1114yes—
475C22×C4C23×D1111yescharacteristic
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D11116yes—
479C4⋊C4—1116no—
480C4⋊C4—1116no—
481C4⋊C4—1116no—
482C4⋊C4—1116no—
483C4⋊C4—118no—
484C4⋊C4—1116no—
485C4⋊C4—1116no—
486C4⋊C4—1116no—
487C4⋊C4—1116no—
488C4⋊C4—1116no—
489C4⋊C4—118no—
490C4⋊C4—1116no—
491C4⋊C4—1116no—
492C4⋊C4—1116no—
493C4⋊C4—118no—
494C4⋊C4—1116no—
495C4⋊C4C23×D11116yes—
496C4⋊C4C23×D1118yes—
497C4⋊C4C23×D11116yes—
498C22⋊C4—1116no—
499C22⋊C4—1116no—
500C22⋊C4—1116no—
501C22⋊C4—1116no—
502C22⋊C4—1116no—
503C22⋊C4—1116no—
504C22⋊C4C23×D11116yes—
505C22⋊C4C23×D11116yes—
506C22⋊C4C23×D11116yes—
507C42—114no—
508C42—118no—
509C42—1116no—
510C42—1116no—
511C42—1116no—
512C42C23×D1114yes—
513C11C2×#355311yescharacteristic, complemented, Sylow
514C23—28no—
515C23—28no—
516C23—28no—
517C23—114no—
518C23—112no—
519C23—224no—
520C23C24×D1118yes—
521C23C24×D1111yescharacteristic
522Q8—48no—
523Q8—4416no—
524D4—416no—
525D4—48no—
526D4—2232no—
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—416no—
532C2×C4—114no—
533C2×C4—118no—
534C2×C4—112no—
535C2×C4—118no—
536C2×C4—118no—
537C2×C4—228no—
538C2×C4—224no—
539C2×C4—228no—
540C2×C4—228no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—4416no—
544C2×C4—448no—
545C2×C4—4416no—
546C2×C4—4416no—
547C2×C4C24×D1118yes—
548C2×C4C24×D1112yes—
549C2×C4C24×D1114yes—
550C2×C4C24×D1118yes—
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—114no—
556C22—224no—
557C22—228no—
558C22#1062345514yes—
559C22D11×2−1+412yes—
560C22C25×D1111yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—24no—
565C4—222no—
566C4—228no—
567C4—224no—
568C4—228no—
569C4—228no—
570C2—48no—
571C2—224no—
572C2#1308307114yesdirect 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×#3553
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13083071C2direct (N × H)
2. C2×C11⋊#564C2semidirect
3. C2×#10623203C2semidirect
4. C2×#10623167C2semidirect
5. C2×#10623145C2semidirect
6. C2×#10623181C2semidirect
7. C2×#10623156C2semidirect
8. C2×#10623133C2semidirect
9. C2×#10623191C2semidirect
10. C2×#10623211C2semidirect
11. C2×D11×#125C2semidirect
12. C2×C11×#562C2semidirect
13. C11×#562C22semidirect
33. D11×#125C22semidirect
34. C11⋊#564C22semidirect
35. #10623211C22semidirect
36. #10623203C22semidirect
37. #10623191C22semidirect
38. #10623181C22semidirect
39. #10623167C22semidirect
40. #10623156C22semidirect
41. #10623145C22semidirect
42. #10623133C22semidirect
230. C2×#562D11semidirect
278. #562C2×D11semidirect
442. C2×C11#3553semidirect
513. C11C2×#3553semidirect
572. C2#13083071direct (N × H)

Maximal subgroups

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

subgroupindex
#130830712
C2×C11⋊#5642
C2×#106232032
C2×#106231672
C2×#106231452
C2×#106231812
C2×#106231562
C2×#106231332
C2×#106231912
C2×#106232112
C2×D11×#1252
C2×C11×#5622
C2×#355311