Finite Group Databasebeta

← C2×#13082540 #15662272

Subgroups — C2×#13082540 #15662272

Order 2816.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082540C2132yesmaximal, direct product factor
2C2×#10623226C214yesmaximal, complemented
3C2×#10623045C218yesmaximal, complemented
4C2×#10623225C214yesmaximal, complemented
5C2×#10623228C212yesmaximal, complemented
6C2×#10623229C212yesmaximal, complemented
7C2×#10623041C212yesmaximal, complemented
8C2×#10623008C211yesmaximal, characteristic, complemented
9C2×#10623222C214yesmaximal, complemented
10C2×#10623035C212yesmaximal, complemented
11C2×C4×#4339C211yesmaximal, characteristic, complemented
12C22×C11×#125C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C22×#4339C2211yescharacteristic
15C2×C11×#125C2214yes—
16C2×C11×#125C2212yes—
17C2×C11×#125C2212yes—
18C2×C11×#125C22116yescomplemented
19C22×C11×C4⋊C4C2214yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C2×#66983C2214yes—
23C2×#66983C2218yes—
24C2×C4×C22⋊D11C2214yes—
25C2×C4×C22⋊D11C2218yes—
26C2×#66979C2211yescharacteristic
27#10623229C22132yescomplemented
28#10623228C22132yescomplemented
29#10623226C22164yescomplemented
30#10623225C22164yescomplemented
31#10623222C22164yescomplemented
32#10623045C221128yescomplemented
33C2×#66951C2218yes—
34C2×#66951C2218yes—
35#10623041C22132yescomplemented
36C2×#66950C2214yes—
37C2×#66950C2214yes—
38C2×#66948C2218yes—
39C2×#66948C2214yes—
40C2×#66948C2214yes—
41C2×#66947C2218yes—
42C2×#66947C2218yes—
43#10623035C22132yescomplemented
44C2×#66946C2218yes—
45C2×#66946C2214yes—
46C2×#66945C2218yes—
47C2×#66945C2214yes—
48C2×C4⋊C4×D11C2214yes—
49C2×#66943C2218yes—
50C2×#66940C2214yes—
51#10623008C22116yescomplemented
52C2×#66928C2212yes—
53C2×#66927C2211yescharacteristic
54C4×#4339C22116yescomplemented
55C2×C4×D44C2214yes—
56C2×C4×D44C2212yes—
57C2×#66925C2212yes—
58C2×C42×D11C2212yes—
59C2×#66922C2211yescharacteristic
60C2×C4×Dic22C2212yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2314yes—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2312yes—
65C22×C22⋊D11C2314yes—
66C2×#4339—216no—
67C2×#4339—28no—
68C2×#4339C2318yes—
69C2×#4339C23116yes—
70C22×D44C2311yescharacteristic
71C22×D44C2312yes—
72C22×D44C2314yes—
73C22×D44C2318yes—
74C22×C4×D11C2312yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2318yes—
78C22×Dic22C2311yescharacteristic
79C22×Dic22C2312yes—
80C11×#125C23116yes—
81C11×#125C23132yes—
82C11×#125C23116yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2318yes—
87C2×C11×C4⋊C4C23116yes—
88C2×C11×C4⋊C4C23132yes—
89C2×C42×C11C2312yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2318yes—
93C2×C22⋊Dic11C2312yes—
94#66983C23132yes—
95#66983C23164yes—
96C4×C22⋊D11C23132yes—
97C4×C22⋊D11C23164yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104#66979C2318yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2318yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2318yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2318yes—
113#66951C23164yes—
114#66951C23164yes—
115#66950C23132yes—
116#66950C23132yes—
117#66948C23132yes—
118#66948C23132yes—
119#66948C23164yes—
120#66947C23164yes—
121#66947C23164yes—
122#66946C23132yes—
123#66946C23164yes—
124#66945C23132yes—
125#66945C23164yes—
126C4⋊C4×D11C23132yes—
127#66943C23164yes—
128#66940C23132yes—
129#66928C23116yes—
130#66927C2318yes—
131C4×D44C23116yes—
132C4×D44C23132yes—
133#66925C23116yes—
134C42×D11C23116yes—
135#66922C2318yes—
136C4×Dic22C23116yes—
137C2×#3512—111nomaximal, Sylow
138C24×C11C2411yescharacteristic
139C23×D11C2414yes—
140C23×D11C2412yes—
141C22×C4×C11—44no—
142C22×C4×C11—48no—
143C22×C4×C11#4118yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2418yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2418yes—
148C22×C4×C11C24116yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2414yes—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11C2418yes—
155C2×C22⋊D11C24116yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2414yes—
159#4339—232no—
160#4339—264no—
161C2×D44—28no—
162C2×D44—24no—
163C2×D44—416no—
164C2×D44—48no—
165C2×D44C2414yes—
166C2×D44C2418yes—
167C2×D44C24116yes—
168C2×D44C24132yes—
169C2×C4×D11—28no—
170C2×C4×D11—216no—
171C2×C4×D11—48no—
172C2×C4×D11—416no—
173C2×C4×D11C2418yes—
174C2×C4×D11C24116yes—
175C2×C4×D11C24116yes—
176C2×C4×D11C24132yes—
177C2×Dic22—28no—
178C2×Dic22—24no—
179C2×Dic22C2414yes—
180C2×Dic22C2418yes—
181C11×C4⋊C4C24116yes—
182C11×C4⋊C4C24132yes—
183C11×C4⋊C4C24116yes—
184C11×C4⋊C4C24132yes—
185C42×C11C2418yes—
186C42×C11C2414yes—
187C42×C11C2414yes—
188C22⋊Dic11C2418yes—
189(C2×D11)⋊C4C24116yes—
190(C2×D11)⋊C4C24116yes—
191(C2×D11)⋊C4C24116yes—
192(C2×D11)⋊C4C24132yes—
193(C2×D11)⋊C4C24132yes—
194(C2×D11)⋊C4C24132yes—
195C4⋊Dic11C2418yes—
196C4⋊Dic11C24116yes—
197C4⋊Dic11C24132yes—
198Dic11⋊C4C24116yes—
199Dic11⋊C4C24132yes—
200C4×Dic11C24116yes—
201C4×Dic11C2418yes—
202C4×Dic11C24132yes—
203#3512—1132no—
204C2×#553—114no—
205C2×#553—118no—
206C2×#552—114no—
207C2×#541—112no—
208C2×#540—112no—
209C2×#537—112no—
210C2×#532—111no—
211C2×#529—114no—
212C22×#125D1111yescharacteristic, complemented
213C2×#520—112no—
214C2×C4×#41—111no—
215C23×C11—24no—
216C23×C11C2×#4114yes—
217C23×C11C2512yes—
218C23×C11C2511yescharacteristic
219C22×D11—28no—
220C22×D11—24no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11C2518yes—
225C22×D11C2514yes—
226C2×C4×C11—24no—
227C2×C4×C11—216no—
228C2×C4×C11—24no—
229C2×C4×C11—48no—
230C2×C4×C11—416no—
231C2×C4×C11C2×#4114yes—
232C2×C4×C11C2×#4114yes—
233C2×C4×C11C2×#41116yes—
234C2×C4×C11C2514yes—
235C2×C4×C11C25116yes—
236C2×C4×C11C2514yes—
237C2×C4×C11C2512yes—
238C2×C4×C11C2512yes—
239C22⋊D11—216no—
240C22⋊D11—232no—
241C2×Dic11—28no—
242C2×Dic11—24no—
243C2×Dic11—28no—
244C2×Dic11C2518yes—
245C2×Dic11C2514yes—
246C2×Dic11C2518yes—
247D44—216no—
248D44—28no—
249D44—432no—
250D44—416no—
251C4×D11—216no—
252C4×D11—232no—
253C4×D11—416no—
254C4×D11—432no—
255Dic22—216no—
256Dic22—28no—
257C22×#41—111no—
258C22×#41—112no—
259#553—1164no—
260#553—11128no—
261#552—1164no—
262#541—1132no—
263#540—1132no—
264#537—1132no—
265#532—1116no—
266C2×C4⋊Q8—111no—
267C2×#127—111no—
268#529—1164no—
269C2×#126—118no—
270C2×#126—118no—
271C2×#125—118no—
272C2×#125C2×D1112yes—
273C2×#125C2×D1112yes—
274C2×#125C2×D1114yes—
275C2×#125C2×D11116yescomplemented
276C2×#124—112no—
277C2×#123—118no—
278C2×#123—118no—
279C2×C22⋊Q8—114no—
280C2×C22⋊Q8—114no—
281C2×#121—114no—
282C2×#121—118no—
283C2×#121—114no—
284C2×#121—114no—
285C2×#121—118no—
286#520—1132no—
287C4×#41—1116no—
288C2×C4×Q8—114no—
289C2×C4×Q8—112no—
290C2×C4×D4—114no—
291C2×C4×D4—118no—
292C2×C4×D4—114no—
293C2×C4×D4—118no—
294C2×C4×D4—112no—
295C2×C4×D4—114no—
296C2×#117—111no—
297C2×#117—114no—
298C2×#117—118no—
299C2×#117—112no—
300C22×C4⋊C4—114no—
301C22×C4⋊C4C2×D1112yes—
302C22×C4⋊C4C2×D1114yes—
303C22×C42—112no—
304C22×C42C2×D1111yescharacteristic
305C22×C11—24no—
306C22×C11—28no—
307C22×C11C22×#4114yes—
308C22×C11C22×#4112yes—
309C22×C11#58514yes—
310C22×C11C2611yescharacteristic
311C2×D11—28no—
312C2×D11—24no—
313C2×D11—28no—
314C2×D11—28no—
315C2×D11—28no—
316C2×D11—416no—
317C2×D11—48no—
318C4×C11—24no—
319C4×C11—216no—
320C4×C11—24no—
321C4×C11C22×#4114yes—
322C4×C11C22×#4114yes—
323Dic11—28no—
324Dic11—24no—
325Dic11—28no—
326C2×#41—118no—
327C2×#41—1116no—
328C2×#41—228no—
329C2×#41—2216no—
330C22×Q8—111no—
331C22×Q8—112no—
332C22×D4—112no—
333C22×D4—114no—
334C22×D4—111no—
335C22×D4—112no—
336C22×D4—118no—
337C22×D4—114no—
338C23×C4—114no—
339C23×C4—112no—
340C23×C4—118no—
341C23×C4—114no—
342C23×C4C22×D1114yes—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345C4⋊Q8—118no—
346#127—118no—
347#126—1164no—
348#126—1164no—
349#125—1164no—
350#125C22×D11116yes—
351#125C22×D11116yes—
352#125C22×D11132yes—
353#124—1116no—
354#123—1164no—
355#123—1164no—
356C22⋊Q8—1132no—
357C22⋊Q8—1132no—
358#121—1132no—
359#121—1164no—
360#121—1132no—
361#121—1132no—
362#121—1164no—
363C4×Q8—1132no—
364C4×Q8—1116no—
365C4×D4—1132no—
366C4×D4—1164no—
367C4×D4—1132no—
368C4×D4—1164no—
369C4×D4—1116no—
370C4×D4—1132no—
371#117—118no—
372#117—1132no—
373#117—1164no—
374#117—1116no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—1132no—
381C2×C4⋊C4C22×D1114yes—
382C2×C4⋊C4C22×D1118yes—
383C2×C4⋊C4C22×D1114yes—
384C2×C4⋊C4C22×D11116yes—
385C2×C4⋊C4C22×D1118yes—
386C2×C4⋊C4C22×D11132yes—
387C2×C22⋊C4—112no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—118no—
394C2×C42—112no—
395C2×C42—118no—
396C2×C42—114no—
397C2×C42—1116no—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1112yes—
400C2×C42C22×D1118yes—
401C2×C42C22×D1111yescharacteristic
402C2×C11—24no—
403C2×C11#351214yescomplemented
404C2×C11C23×#4111yescharacteristic
405C2×C11C2×#58512yes—
406D11—48no—
407D11—44no—
408C24—114no—
409C24—112no—
410C24C23×D1111yescharacteristic
411#41—2232no—
412#41—2264no—
413C2×Q8—114no—
414C2×Q8—118no—
415C2×Q8—224no—
416C2×Q8—228no—
417C2×D4—118no—
418C2×D4—1116no—
419C2×D4—114no—
420C2×D4—118no—
421C2×D4—1132no—
422C2×D4—1116no—
423C2×D4—228no—
424C2×D4—2216no—
425C2×D4—224no—
426C2×D4—228no—
427C2×D4—4416no—
428C2×D4—448no—
429C22×C4—44no—
430C22×C4—48no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—112no—
434C22×C4—118no—
435C22×C4—1116no—
436C22×C4—1116no—
437C22×C4—1132no—
438C22×C4—2216no—
439C22×C4—228no—
440C22×C4—448no—
441C22×C4—4416no—
442C22×C4#434318yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1118yes—
445C22×C4C23×D1112yes—
446C22×C4C23×D1118yes—
447C22×C4C23×D11116yes—
448C22×C4C23×D1114yes—
449C22×C4C23×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C4⋊C4—118no—
452C4⋊C4—1132no—
453C4⋊C4—1116no—
454C4⋊C4—1132no—
455C4⋊C4—1116no—
456C4⋊C4C23×D11116yes—
457C4⋊C4C23×D11132yes—
458C4⋊C4C23×D11116yes—
459C4⋊C4C23×D11132yes—
460C22⋊C4—118no—
461C22⋊C4—1116no—
462C22⋊C4—1116no—
463C22⋊C4—1132no—
464C22⋊C4—1132no—
465C22⋊C4—1116no—
466C22⋊C4—1132no—
467C42—118no—
468C42—1116no—
469C42—1132no—
470C42C23×D1114yes—
471C42C23×D1114yes—
472C42C23×D1118yes—
473C11C2×#351211yescharacteristic, complemented, Sylow
474C23—24no—
475C23—118no—
476C23—114no—
477C23—228no—
478C23—224no—
479C23—228no—
480C23—228no—
481C23—228no—
482C23C2×#434314yes—
483C23C24×D1112yes—
484C23C24×D1111yescharacteristic
485Q8—228no—
486Q8—2216no—
487D4—2216no—
488D4—2232no—
489D4—228no—
490D4—2216no—
491D4—4432no—
492D4—4416no—
493C2×C4—24no—
494C2×C4—216no—
495C2×C4—24no—
496C2×C4—48no—
497C2×C4—416no—
498C2×C4—118no—
499C2×C4—114no—
500C2×C4—118no—
501C2×C4—228no—
502C2×C4—224no—
503C2×C4—228no—
504C2×C4—2232no—
505C2×C4—2216no—
506C2×C4—4416no—
507C2×C4—4432no—
508C2×C4C2×#434314yes—
509C2×C4C2×#434314yes—
510C2×C4C2×#4343116yes—
511C2×C4C24×D1114yes—
512C2×C4C24×D11116yes—
513C2×C4C24×D1114yes—
514C2×C4C24×D1112yes—
515C2×C4C24×D1112yes—
516C22—24no—
517C22—28no—
518C22—228no—
519C22—224no—
520C22—228no—
521C22—228no—
522C22—228no—
523C22—4416no—
524C22—448no—
525C22C22×#434314yes—
526C22C22×#434312yes—
527C22#1062345314yes—
528C22C25×D1111yescharacteristic
529C4—24no—
530C4—216no—
531C4—24no—
532C4—224no—
533C4—228no—
534C4—228no—
535C4C22×#434314yes—
536C4C22×#434314yes—
537C2—24no—
538C2—448no—
539C2—444no—
540C2#1308254014yesdirect product factor
541C2C23×#434311yescharacteristic
542C2C2×#1062345312yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#125C2
socleC23×C11C25
hypercenterC22×#125D11
hypocenterC11C2×#3512
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #13082540C2direct (N × H)
2. C2×#10623226C2semidirect
3. C2×#10623045C2semidirect
4. C2×#10623225C2semidirect
5. C2×#10623228C2semidirect
6. C2×#10623229C2semidirect
7. C2×#10623041C2semidirect
8. C2×#10623008C2semidirect
9. C2×#10623222C2semidirect
10. C2×#10623035C2semidirect
11. C2×C4×#4339C2semidirect
12. C22×C11×#125C2semidirect
18. C2×C11×#125C22semidirect
27. #10623229C22semidirect
28. #10623228C22semidirect
29. #10623226C22semidirect
30. #10623225C22semidirect
31. #10623222C22semidirect
32. #10623045C22semidirect
35. #10623041C22semidirect
43. #10623035C22semidirect
51. #10623008C22semidirect
54. C4×#4339C22semidirect
212. C22×#125D11semidirect
275. C2×#125C2×D11semidirect
403. C2×C11#3512semidirect
473. C11C2×#3512semidirect
540. C2#13082540direct (N × H)

Maximal subgroups

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

subgroupindex
#130825402
C2×#106232262
C2×#106230452
C2×#106232252
C2×#106232282
C2×#106232292
C2×#106230412
C2×#106230082
C2×#106232222
C2×#106230352
C2×C4×#43392
C22×C11×#1252
C2×#351211