Finite Group Databasebeta

← C2×#13083073 #15661545

Subgroups — C2×#13083073 #15661545

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#13083073C2132yesmaximal, direct product factor
2C2×#10623230C212yesmaximal, complemented
3C2×#10623231C211yesmaximal, characteristic, complemented
4C2×#10623221C214yesmaximal, complemented
5C2×#10623226C214yesmaximal, complemented
6C2×#10623225C214yesmaximal, complemented
7C2×#10623227C214yesmaximal, complemented
8C2×#10623223C214yesmaximal, complemented
9C2×#10623223C214yesmaximal, complemented
10C2×#10623222C212yesmaximal, complemented
11C2×D11×#125C211yesmaximal, characteristic, complemented
12C2×C11×#564C211yesmaximal, characteristic, complemented
13C11×#564C22116yescomplemented
14C2×C11×#125C2211yescharacteristic
15C2×C11×#125C2214yes—
16C2×C11×#125C2212yes—
17C2×C11×#125C2214yes—
18C2×C11×#125C2214yes—
19#10623231C22116yescomplemented
20#10623230C22132yescomplemented
21#10623227C22164yescomplemented
22#10623226C22164yescomplemented
23#10623225C22164yescomplemented
24#10623223C22164yescomplemented
25#10623223C22164yescomplemented
26#10623222C22132yescomplemented
27#10623221C22164yescomplemented
28D11×#125C22116yescomplemented
29C2×#66951C2214yes—
30C2×#66951C2214yes—
31C2×#66951C2214yes—
32C2×#66951C2214yes—
33C2×#66950C2214yes—
34C2×#66950C2214yes—
35C2×#66950C2212yes—
36C2×#66949C2214yes—
37C2×#66949C2214yes—
38C2×#66949C2214yes—
39C2×#66949C2214yes—
40C2×#66948C2212yes—
41C2×#66948C2214yes—
42C2×#66948C2214yes—
43C2×#66947C2214yes—
44C2×#66947C2214yes—
45C2×#66947C2214yes—
46C2×#66947C2214yes—
47C2×#66947C2214yes—
48C2×#66946C2214yes—
49C2×#66946C2212yes—
50C2×#66946C2214yes—
51C2×#66945C2214yes—
52C2×#66945C2214yes—
53C2×C4⋊C4×D11C2214yes—
54C2×C4⋊C4×D11C2212yes—
55C2×C4⋊C4×D11C2214yes—
56C2×#66943C2212yes—
57C2×#66943C2214yes—
58C2×#66942C2214yes—
59C2×#66942C2214yes—
60C2×#66941C2214yes—
61C2×#66940C2212yes—
62C2×#66929C2214yes—
63C2×#66928C2212yes—
64C2×C4×D44C2214yes—
65C2×C4×D44C2214yes—
66C2×C42×D11C2211yescharacteristic
67C2×#66923C2211yescharacteristic
68C2×C4×Dic22C2214yes—
69C22×D44C2314yes—
70C22×D44C2314yes—
71C22×D44C2312yes—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2312yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2314yes—
78C22×Dic22C2314yes—
79C22×Dic22C2312yes—
80C11×#125C2318yes—
81C11×#125C23132yes—
82C11×#125C23116yes—
83C11×#125C23132yes—
84C11×#125C23132yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C42×C11C2314yes—
95C2×C42×C11C2311yescharacteristic
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2311yescharacteristic
119#66951C23132yes—
120#66951C23132yes—
121#66951C23132yes—
122#66951C23132yes—
123#66950C23116yes—
124#66950C23132yes—
125#66950C23132yes—
126#66949C23132yes—
127#66949C23132yes—
128#66949C23132yes—
129#66949C23132yes—
130#66948C23116yes—
131#66948C23132yes—
132#66948C23132yes—
133#66947C23132yes—
134#66947C23132yes—
135#66947C23132yes—
136#66947C23132yes—
137#66947C23132yes—
138#66946C23132yes—
139#66946C23132yes—
140#66946C23116yes—
141#66945C23132yes—
142#66945C23132yes—
143C4⋊C4×D11C23132yes—
144C4⋊C4×D11C23116yes—
145C4⋊C4×D11C23132yes—
146#66943C23116yes—
147#66943C23132yes—
148#66942C23132yes—
149#66942C23132yes—
150#66941C23132yes—
151#66940C23116yes—
152#66929C23132yes—
153#66928C23116yes—
154C4×D44C23132yes—
155C4×D44C23132yes—
156C42×D11C2318yes—
157#66923C2318yes—
158C4×Dic22C23132yes—
159C2×#3553—111nomaximal, Sylow
160C23×D11C2414yes—
161C23×D11C2411yescharacteristic
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2414yes—
166C22×C4×C11C2414yes—
167C22×Dic11C2412yes—
168C22×Dic11C2411yescharacteristic
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C2×D44—216no—
172C2×D44—44no—
173C2×D44—48no—
174C2×D44C24116yes—
175C2×D44C24116yes—
176C2×D44C2418yes—
177C2×C4×D11—24no—
178C2×C4×D11—48no—
179C2×C4×D11—48no—
180C2×C4×D11—44no—
181C2×C4×D11—48no—
182C2×C4×D11—48no—
183C2×C4×D11C2414yes—
184C2×C4×D11C2418yes—
185C2×C4×D11C24116yes—
186C2×C4×D11C24116yes—
187C2×C4×D11C24116yes—
188C2×C4×D11C24116yes—
189C2×Dic22—48no—
190C2×Dic22—44no—
191C2×Dic22C24116yes—
192C2×Dic22C2418yes—
193C11×C4⋊C4C2418yes—
194C11×C4⋊C4C24116yes—
195C11×C4⋊C4C24116yes—
196C11×C4⋊C4C24116yes—
197C11×C4⋊C4C2418yes—
198C11×C4⋊C4C24116yes—
199C11×C4⋊C4C24116yes—
200C11×C4⋊C4C24116yes—
201C11×C4⋊C4C2418yes—
202C42×C11C24116yes—
203C42×C11C2414yes—
204(C2×D11)⋊C4C24116yes—
205(C2×D11)⋊C4C24116yes—
206(C2×D11)⋊C4C24116yes—
207(C2×D11)⋊C4C24116yes—
208(C2×D11)⋊C4C24116yes—
209(C2×D11)⋊C4C24116yes—
210(C2×D11)⋊C4C24116yes—
211(C2×D11)⋊C4C24116yes—
212(C2×D11)⋊C4C24116yes—
213C4⋊Dic11C24116yes—
214C4⋊Dic11C2418yes—
215C4⋊Dic11C24116yes—
216C4⋊Dic11C24116yes—
217Dic11⋊C4C24116yes—
218Dic11⋊C4C24116yes—
219Dic11⋊C4C24116yes—
220Dic11⋊C4C24116yes—
221Dic11⋊C4C24116yes—
222Dic11⋊C4C24116yes—
223C4×Dic11C24116yes—
224C4×Dic11C24116yes—
225C4×Dic11C2418yes—
226C4×Dic11C2414yes—
227#3553—1132no—
228C2×#564D1111yescharacteristic, complemented
229C2×#563—112no—
230C2×#562—111no—
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×C11C2511yescharacteristic
240C22×D11—24no—
241C22×D11—28no—
242C22×D11—28no—
243C22×D11—28no—
244C22×D112−1+414yes—
245C22×D11C2518yes—
246C22×D11C2512yes—
247C2×C4×C11—22no—
248C2×C4×C11—28no—
249C2×C4×C11—28no—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11C2518yes—
253C2×C4×C11C2514yes—
254C2×C4×C11C2512yes—
255C2×C4×C11C2518yes—
256C2×C4×C11C2518yes—
257C2×Dic11—22no—
258C2×Dic11—28no—
259C2×Dic11—28no—
260C2×Dic11—24no—
261C2×Dic11C2514yes—
262C2×Dic11C2512yes—
263C2×Dic11C2518yes—
264C2×Dic11C2518yes—
265D44—232no—
266D44—48no—
267D44—416no—
268C4×D11—28no—
269C4×D11—416no—
270C4×D11—416no—
271C4×D11—416no—
272C4×D11—416no—
273C4×D11—48no—
274Dic22—48no—
275Dic22—416no—
276#564C2×D11116yescomplemented
277#563—1132no—
278#562—1116no—
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—112no—
296C2×#125—114no—
297C2×#125—111no—
298C2×#125C2×D1111yescharacteristic
299C2×#125C2×D1112yes—
300C2×#125C2×D1114yes—
301C2×#125C2×D1114yes—
302C2×#125C2×D1114yes—
303C2×#124—112no—
304C2×#123—114no—
305C2×#123—114no—
306C2×#123—114no—
307C2×#123—114no—
308C2×#123—114no—
309C2×C22⋊Q8—114no—
310C2×C22⋊Q8—114no—
311C2×C22⋊Q8—114no—
312C2×C22⋊Q8—114no—
313C2×C22⋊Q8—112no—
314C2×C22⋊Q8—114no—
315C2×C22⋊Q8—114no—
316C2×#121—112no—
317C2×#121—114no—
318C2×#121—114no—
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—112no—
329C22×C4⋊C4—114no—
330C22×C4⋊C4—114no—
331C22×C42—111no—
332C22×C11C2×2−1+412yes—
333C22×C11#58514yes—
334C22×C11C2611yescharacteristic
335C2×D11—24no—
336C2×D11—28no—
337C2×D11—28no—
338C2×D11—28no—
339C2×D11—28no—
340C2×D11—416no—
341C2×D11C2×2−1+414yes—
342C4×C11—22no—
343C4×C11—28no—
344C4×C11—28no—
345C4×C11—24no—
346C4×C11—28no—
347Dic11—22no—
348Dic11—28no—
349Dic11—28no—
350Dic11—24no—
351C22×Q8—114no—
352C22×Q8—112no—
353C22×D4—114no—
354C22×D4—114no—
355C22×D4—112no—
356C23×C4—111no—
357C23×C4—114no—
358C23×C4—112no—
359C23×C4—114no—
360C23×C4—114no—
361C23×C4—114no—
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—118no—
373#125C22×D1118yes—
374#125C22×D11116yes—
375#125C22×D11132yes—
376#125C22×D11132yes—
377#125C22×D11132yes—
378#124—1116no—
379#123—1132no—
380#123—1132no—
381#123—1132no—
382#123—1132no—
383#123—1132no—
384C22⋊Q8—1116no—
385C22⋊Q8—1132no—
386C22⋊Q8—1132no—
387C22⋊Q8—1132no—
388C22⋊Q8—1132no—
389C22⋊Q8—1132no—
390C22⋊Q8—1132no—
391#121—1116no—
392#121—1132no—
393#121—1132no—
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—112no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—1116no—
414C2×C4⋊C4—1132no—
415C2×C4⋊C4—1132no—
416C2×C4⋊C4C22×D1114yes—
417C2×C4⋊C4C22×D1114yes—
418C2×C4⋊C4C22×D1112yes—
419C2×C4⋊C4C22×D1114yes—
420C2×C4⋊C4C22×D1114yes—
421C2×C4⋊C4C22×D1112yes—
422C2×C4⋊C4C22×D1114yes—
423C2×C4⋊C4C22×D1114yes—
424C2×C4⋊C4C22×D1112yes—
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⋊C4—114no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C42—111no—
435C2×C42—114no—
436C2×C42—114no—
437C2×C42—112no—
438C2×C42—118no—
439C2×C42C22×D1114yes—
440C2×C42C22×D1111yescharacteristic
441C2×C11#355314yescomplemented
442C2×C11C22×2−1+411yescharacteristic
443C2×C11C2×#58512yes—
444D11—24no—
445D11—48no—
446C24—111no—
447C24—114no—
448C2×Q8—1116no—
449C2×Q8—118no—
450C2×Q8—448no—
451C2×Q8—444no—
452C2×D4—1116no—
453C2×D4—1116no—
454C2×D4—118no—
455C2×D4—2216no—
456C2×D4—448no—
457C2×D4—444no—
458C22×C4—112no—
459C22×C4—111no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—118no—
464C22×C4—1116no—
465C22×C4—1116no—
466C22×C4—1116no—
467C22×C4—1116no—
468C22×C4—224no—
469C22×C4—448no—
470C22×C4—448no—
471C22×C4—448no—
472C22×C4—448no—
473C22×C4—444no—
474C22×C4C23×D1114yes—
475C22×C4C23×D1111yescharacteristic
476C22×C4C23×D1112yes—
477C22×C4C23×D1114yes—
478C22×C4C23×D1114yes—
479C4⋊C4—1116no—
480C4⋊C4—1116no—
481C4⋊C4—1116no—
482C4⋊C4—118no—
483C4⋊C4—1116no—
484C4⋊C4—1116no—
485C4⋊C4—1116no—
486C4⋊C4—1116no—
487C4⋊C4—1116no—
488C4⋊C4—1116no—
489C4⋊C4C23×D11116yes—
490C4⋊C4C23×D11116yes—
491C4⋊C4C23×D1118yes—
492C4⋊C4C23×D11116yes—
493C4⋊C4C23×D11116yes—
494C4⋊C4C23×D1118yes—
495C4⋊C4C23×D11116yes—
496C4⋊C4C23×D11116yes—
497C4⋊C4C23×D1118yes—
498C22⋊C4—1116no—
499C22⋊C4—1116no—
500C22⋊C4—1116no—
501C22⋊C4—1116no—
502C22⋊C4—1116no—
503C22⋊C4—1116no—
504C22⋊C4—1116no—
505C22⋊C4—1116no—
506C22⋊C4—1116no—
507C42—114no—
508C42—118no—
509C42—1116no—
510C42—1116no—
511C42C23×D1114yes—
512C42C23×D11116yes—
513C11C2×#355311yescharacteristic, complemented, Sylow
514C23—114no—
515C23—112no—
516C23—118no—
517C23—224no—
518C23—228no—
519C23—228no—
520C23—228no—
521C23C24×D1111yescharacteristic
522Q8—4416no—
523Q8—448no—
524D4—2232no—
525D4—4416no—
526D4—448no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—24no—
532C2×C4—114no—
533C2×C4—112no—
534C2×C4—118no—
535C2×C4—118no—
536C2×C4—228no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—228no—
540C2×C4—228no—
541C2×C4—4416no—
542C2×C4—4416no—
543C2×C4—4416no—
544C2×C4—4416no—
545C2×C4—448no—
546C2×C4C24×D1118yes—
547C2×C4C24×D1112yes—
548C2×C4C24×D1114yes—
549C2×C4C24×D1118yes—
550C2×C4C24×D1118yes—
551C22—114no—
552C22—224no—
553C22—228no—
554C22—228no—
555C22—228no—
556C22—228no—
557C22—4416no—
558C22D11×2−1+412yes—
559C22#1062345714yes—
560C22C25×D1111yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—28no—
565C4—24no—
566C4—222no—
567C4—224no—
568C4—228no—
569C4—228no—
570C2—224no—
571C2—448no—
572C2#1308307314yesdirect product factor
573C2C2×D11×2−1+411yescharacteristic
574C2C2×#1062345712yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#564C2
socleC23×C11C25
hypercenterC2×#564D11
hypocenterC11C2×#3553
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
1. #13083073C2direct (N × H)
2. C2×#10623230C2semidirect
3. C2×#10623231C2semidirect
4. C2×#10623221C2semidirect
5. C2×#10623226C2semidirect
6. C2×#10623225C2semidirect
7. C2×#10623227C2semidirect
8. C2×#10623223C2semidirect
9. C2×#10623223C2semidirect
10. C2×#10623222C2semidirect
11. C2×D11×#125C2semidirect
12. C2×C11×#564C2semidirect
13. C11×#564C22semidirect
19. #10623231C22semidirect
20. #10623230C22semidirect
21. #10623227C22semidirect
22. #10623226C22semidirect
23. #10623225C22semidirect
24. #10623223C22semidirect
25. #10623223C22semidirect
26. #10623222C22semidirect
27. #10623221C22semidirect
28. D11×#125C22semidirect
228. C2×#564D11semidirect
276. #564C2×D11semidirect
441. C2×C11#3553semidirect
513. C11C2×#3553semidirect
572. C2#13083073direct (N × H)

Maximal subgroups

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

subgroupindex
#130830732
C2×#106232302
C2×#106232312
C2×#106232212
C2×#106232262
C2×#106232252
C2×#106232272
C2×#106232232
C2×#106232222
C2×D11×#1252
C2×C11×#5642
C2×#355311