Finite Group Databasebeta

← C2×#13082241 #15660876

Subgroups — C2×#13082241 #15660876

Order 2816.

8418 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082241C2132yesmaximal, direct product factor
2C2×#10623253C211yesmaximal, characteristic, complemented
3C2×#10623063C214yesmaximal, complemented
4C2×#10623201C214yesmaximal, complemented
5C2×#10623084C212yesmaximal, complemented
6C2×#10623130C214yesmaximal, complemented
7C2×#10623256C211yesmaximal, characteristic, complemented
8C2×#10623199C214yesmaximal, complemented
9C2×#10623127C214yesmaximal, complemented
10C2×#10623053C214yesmaximal, complemented
11C2×C4×#4341C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×#4341C2212yes—
15C22×#4341C2214yes—
16C22×#4339C2214yes—
17C11×#555C22116yescomplemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#124C2214yes—
20C2×C11×#121C2214yes—
21C2×C4×D4×C11C2212yes—
22C2×C11×#117C2214yes—
23C2×#67000C2212yes—
24C2×#66997C2214yes—
25C2×#66993C2214yes—
26C2×#66993C2214yes—
27C2×#66992C2218yes—
28C2×D4×Dic11C2212yes—
29C2×#66983C2214yes—
30C2×C4×C22⋊D11C2214yes—
31C22×C4×Dic11C2214yes—
32#10623256C22116yescomplemented
33#10623253C22116yescomplemented
34#10623201C22164yescomplemented
35#10623199C22164yescomplemented
36#10623130C22164yescomplemented
37#10623127C22164yescomplemented
38#10623084C22132yescomplemented
39C4×#4341C22132yescomplemented
40#10623063C22164yescomplemented
41#10623053C22164yescomplemented
42C2×#66948C2214yes—
43C2×#66946C2214yes—
44C2×#66946C2214yes—
45C2×#66945C2212yes—
46C2×#66941C2214yes—
47C2×#66940C2214yes—
48C2×#66940C2212yes—
49C2×#66938C2218yes—
50C2×#66937C2218yes—
51C2×#66937C2218yes—
52C2×(C22⋊D11)⋊C4C2218yes—
53C2×(C22⋊D11)⋊C4C2218yes—
54C2×(C22⋊D11)⋊C4C2214yes—
55C2×#66930C2214yes—
56C2×#66928C2214yes—
57C2×#66927C2211yescharacteristic
58C2×#66925C2218yes—
59C2×C42×D11C2214yes—
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2212yes—
62C22×Q8×C11C2312yes—
63C22×D4×C11C2312yes—
64C22×D4×C11C2314yes—
65C23×C4×C11C2314yes—
66C22×C22⋊D11C2318yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2318yes—
69C23×Dic11C2314yes—
70C23×Dic11C2314yes—
71C2×#4343—48no—
72C2×#4343C23116yes—
73C2×#4341—216no—
74C2×#4341—416no—
75C2×#4341C23116yes—
76C2×#4341C23132yes—
77C2×#4339—232no—
78C2×#4339C23132yes—
79C22×D44C2314yes—
80C22×D44C2312yes—
81C22×D44C2314yes—
82C22×C4×D11C2318yes—
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2314yes—
85C22×C4×D11C2312yes—
86C22×Dic22C2314yes—
87C22×Dic22C2312yes—
88C11×C4⋊Q8C2318yes—
89C11×#124C23132yes—
90C11×#121C23132yes—
91C4×D4×C11C23116yes—
92C11×#117C23132yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2314yes—
99C2×C22⋊Dic11C2314yes—
100#67000C23116yes—
101#66997C23132yes—
102#66993C23132yes—
103#66993C23132yes—
104#66992C23164yes—
105D4×Dic11C23116yes—
106#66983C23132yes—
107C4×C22⋊D11C23132yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2318yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C23132yes—
122#66948C23132yes—
123#66946C23132yes—
124#66946C23132yes—
125#66945C23116yes—
126#66941C23132yes—
127#66940C23132yes—
128#66940C23116yes—
129#66938C23164yes—
130#66937C23164yes—
131#66937C23164yes—
132(C22⋊D11)⋊C4C23164yes—
133(C22⋊D11)⋊C4C23164yes—
134(C22⋊D11)⋊C4C23132yes—
135#66930C23132yes—
136#66928C23132yes—
137#66927C2318yes—
138#66925C23164yes—
139C42×D11C2318yes—
140C42×D11C23132yes—
141C4×Dic22C23116yes—
142C2×#3483—111nomaximal, Sylow
143C24×C11C2414yes—
144C23×D11C2414yes—
145C23×D11C2411yescharacteristic
146C2×Q8×C11—44no—
147C2×Q8×C11C2418yes—
148C2×D4×C11—28no—
149C2×D4×C11—48no—
150C2×D4×C11C2418yes—
151C2×D4×C11C24116yes—
152C22×C4×C11—216no—
153C22×C4×C11C2414yes—
154C22×C4×C11C24116yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C2×C22⋊D11—232no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—416no—
161C2×C22⋊D11C24132yes—
162C2×C22⋊D11C24116yes—
163C2×C22⋊D11C24132yes—
164C22×Dic11—216no—
165C22×Dic11—216no—
166C22×Dic11C24116yes—
167C22×Dic11C24116yes—
168C22×Dic11C2412yes—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2411yescharacteristic
172#4343—432no—
173#4341—264no—
174#4341—464no—
175#4339—2128no—
176C2×D44—216no—
177C2×D44—48no—
178C2×D44—44no—
179C2×D44C24116yes—
180C2×D44C2418yes—
181C2×D44C24116yes—
182C2×C4×D11—232no—
183C2×C4×D11—216no—
184C2×C4×D11—24no—
185C2×C4×D11—28no—
186C2×C4×D11C24132yes—
187C2×C4×D11C2414yes—
188C2×C4×D11C24116yes—
189C2×C4×D11C2418yes—
190C2×Dic22—48no—
191C2×Dic22#41116yescomplemented
192C2×Dic22C24116yes—
193C2×Dic22C2418yes—
194C11×C4⋊C4C24116yes—
195C11×C4⋊C4C2418yes—
196C11×C22⋊C4C24116yes—
197C11×C22⋊C4C24132yes—
198C42×C11C2414yes—
199C42×C11C24116yes—
200C22⋊Dic11C24116yes—
201(C2×D11)⋊C4C24132yes—
202(C2×D11)⋊C4C24132yes—
203(C2×D11)⋊C4C24116yes—
204C4⋊Dic11C2418yes—
205Dic11⋊C4C24116yes—
206Dic11⋊C4C24116yes—
207Dic11⋊C4C24132yes—
208C4×Dic11C24116yes—
209C4×Dic11C24116yes—
210C4×Dic11C2414yes—
211C4×Dic11C24116yes—
212C4×Dic11C2418yes—
213C4×Dic11C24116yes—
214#3483—1132no—
215C2×Q82—111no—
216C2×#555—114no—
217C2×#555—114no—
218C2×#555D1111yescharacteristic, complemented
219C2×#550—114no—
220C2×#550—112no—
221C2×#532—111no—
222C2×#532—114no—
223C2×#532—114no—
224C2×C4×#41—112no—
225C2×C4×#41—114no—
226C23×C11—28no—
227C23×C11—28no—
228C23×C11—28no—
229C23×C11C2518yes—
230C23×C11C2511yescharacteristic
231C22×D11—216no—
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—28no—
235C22×D11C2518yes—
236C22×D11C2512yes—
237Q8×C11—48no—
238D4×C11—216no—
239D4×C11—416no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—232no—
244C2×C4×C11C2×#4118yes—
245C2×C4×C11C2518yes—
246C2×C4×C11C2512yes—
247C2×C4×C11C2518yes—
248C2×C4×C11C2514yes—
249C22⋊D11—264no—
250C22⋊D11—232no—
251C22⋊D11—432no—
252C2×Dic11—24no—
253C2×Dic11—28no—
254C2×Dic11—232no—
255C2×Dic11—232no—
256C2×Dic11C2×#41116yes—
257C2×Dic11H(5,𝔽2)14yes—
258C2×Dic11C2514yes—
259C2×Dic11C2518yes—
260C2×Dic11C2518yes—
261C2×Dic11C2512yes—
262D44—232no—
263D44—416no—
264D44—48no—
265C4×D11—216no—
266C4×D11—264no—
267C4×D11—232no—
268C4×D11—28no—
269Dic22—416no—
270Dic22C2×#41132yescomplemented
271C22×#41—112no—
272C22×#41—112no—
273C22×#41—114no—
274C22×#41—114no—
275Q82—1116no—
276#555—1164no—
277#555—1164no—
278#555C2×D11116yescomplemented
279#550—1164no—
280#550—1132no—
281#532—1116no—
282#532—1164no—
283#532—1164no—
284C2×C4⋊Q8—114no—
285C2×C4⋊Q8—114no—
286C2×C4⋊Q8C2×D1111yescharacteristic
287C2×#127—114no—
288C2×#127—114no—
289C2×#127—111no—
290C2×#124—112no—
291C2×#124—118no—
292C2×#124—114no—
293C2×#124C2×D1114yes—
294C2×#121—118no—
295C2×#121—114no—
296C2×#121—114no—
297C2×#121—118no—
298C2×#121—118no—
299C2×#121C2×D1114yes—
300C4×#41—1132no—
301C4×#41—1164no—
302C2×C4×Q8—112no—
303C2×C4×Q8—114no—
304C2×C4×Q8—112no—
305C2×C4×D4—112no—
306C2×C4×D4—114no—
307C2×C4×D4—114no—
308C2×C4×D4—114no—
309C2×C4×D4—114no—
310C2×C4×D4—118no—
311C2×C4×D4—118no—
312C2×C4×D4C2×D1112yes—
313C2×#117—112no—
314C2×#117—114no—
315C2×#117—118no—
316C2×#117C2×D1114yes—
317C22×C42—114no—
318C22×C42—111no—
319C22×C42—114no—
320C22×C11—28no—
321C22×C11—28no—
322C22×C11—28no—
323C22×C11—416no—
324C22×C11C22×#4114yes—
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2611yescharacteristic
327C2×D11—216no—
328C2×D11—24no—
329C2×D11—22no—
330C2×D11—28no—
331C2×D11—416no—
332C2×D11—44no—
333C4×C11—28no—
334C4×C11—28no—
335C4×C11—22no—
336C4×C11C22×#4118yes—
337Dic11—24no—
338Dic11—28no—
339Dic11C22×#41116yes—
340Dic11C2×H(5,𝔽2)14yes—
341C2×#41—1116no—
342C2×#41—1116no—
343C2×#41—1132no—
344C2×#41—1132no—
345C2×#41—2232no—
346C2×#41—2216no—
347C2×#41—4416no—
348C2×#41—448no—
349C22×Q8—112no—
350C22×Q8—114no—
351C22×Q8C22×D1112yes—
352C22×D4—114no—
353C22×D4—118no—
354C22×D4—118no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—112no—
358C22×D4C22×D1112yes—
359C22×D4C22×D1114yes—
360C23×C4—114no—
361C23×C4—114no—
362C23×C4—118no—
363C23×C4—112no—
364C23×C4—114no—
365C23×C4—111no—
366C23×C4C22×D1114yes—
367C4⋊Q8—1132no—
368C4⋊Q8—1132no—
369C4⋊Q8C22×D1118yes—
370#127—1132no—
371#127—1132no—
372#127—118no—
373#124—1116no—
374#124—1164no—
375#124—1132no—
376#124C22×D11132yes—
377#121—1164no—
378#121—1132no—
379#121—1132no—
380#121—1164no—
381#121—1164no—
382#121C22×D11132yes—
383C4×Q8—1116no—
384C4×Q8—1132no—
385C4×Q8—1116no—
386C4×D4—1116no—
387C4×D4—1132no—
388C4×D4—1132no—
389C4×D4—1132no—
390C4×D4—1132no—
391C4×D4—1164no—
392C4×D4—1164no—
393C4×D4C22×D11116yes—
394#117—1116no—
395#117—1132no—
396#117—1164no—
397#117C22×D11132yes—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—118no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1114yes—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—118no—
408C2×C22⋊C4C22×D1114yes—
409C2×C22⋊C4C22×D1118yes—
410C2×C42—111no—
411C2×C42—114no—
412C2×C42—114no—
413C2×C42—112no—
414C2×C42—114no—
415C2×C42—114no—
416C2×C42—1132no—
417C2×C42—118no—
418C2×C42—1132no—
419C2×C42C22×D1114yes—
420C2×C42C22×D1111yescharacteristic
421C2×C11—48no—
422C2×C11#348314yescomplemented
423C2×C11C23×#4112yes—
424C2×C11C22×H(5,𝔽2)11yescharacteristic
425D11—48no—
426D11—42no—
427C24—111no—
428C24—114no—
429C24C23×D1114yes—
430#41—22128no—
431#41—2264no—
432#41—4464no—
433#41—4432no—
434C2×Q8—44no—
435C2×Q8—1116no—
436C2×Q8—118no—
437C2×Q8—1116no—
438C2×Q8—448no—
439C2×Q8C23×D1118yes—
440C2×D4—28no—
441C2×D4—48no—
442C2×D4—1116no—
443C2×D4—1132no—
444C2×D4—1132no—
445C2×D4—1116no—
446C2×D4—1116no—
447C2×D4—118no—
448C2×D4—2232no—
449C2×D4—2216no—
450C2×D4—2216no—
451C2×D4—448no—
452C2×D4—444no—
453C2×D4—4416no—
454C2×D4C23×D1118yes—
455C2×D4C23×D11116yes—
456C22×C4—216no—
457C22×C4—111no—
458C22×C4—114no—
459C22×C4—1116no—
460C22×C4—1116no—
461C22×C4—112no—
462C22×C4—114no—
463C22×C4—1132no—
464C22×C4—118no—
465C22×C4—1116no—
466C22×C4—114no—
467C22×C4—2232no—
468C22×C4—2216no—
469C22×C4—224no—
470C22×C4—2216no—
471C22×C4—2216no—
472C22×C4—228no—
473C22×C4C23×D11116yes—
474C22×C4C23×D1114yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1111yescharacteristic
477C22×C4C23×D1112yes—
478C4⋊C4—1116no—
479C4⋊C4—1132no—
480C4⋊C4—1116no—
481C4⋊C4—118no—
482C4⋊C4C23×D1118yes—
483C4⋊C4C23×D11116yes—
484C22⋊C4—1116no—
485C22⋊C4—1132no—
486C22⋊C4—1116no—
487C22⋊C4—1132no—
488C22⋊C4C23×D11116yes—
489C22⋊C4C23×D11132yes—
490C42—1116no—
491C42—118no—
492C42—114no—
493C42—1116no—
494C42—1116no—
495C42—1116no—
496C42C23×D11116yes—
497C42C23×D1114yes—
498C11C2×#348311yescharacteristic, complemented, Sylow
499C23—28no—
500C23—28no—
501C23—28no—
502C23—112no—
503C23—118no—
504C23—2216no—
505C23—224no—
506C23—222no—
507C23—228no—
508C23C24×D1118yes—
509C23C24×D1111yescharacteristic
510Q8—48no—
511Q8—1132no—
512Q8—4416no—
513D4—216no—
514D4—416no—
515D4—2264no—
516D4—2232no—
517D4—2232no—
518D4—4416no—
519D4—448no—
520D4—4432no—
521C2×C4—28no—
522C2×C4—28no—
523C2×C4—22no—
524C2×C4—232no—
525C2×C4—1116no—
526C2×C4—114no—
527C2×C4—112no—
528C2×C4—118no—
529C2×C4—114no—
530C2×C4—118no—
531C2×C4—2264no—
532C2×C4—2232no—
533C2×C4—228no—
534C2×C4—2232no—
535C2×C4—2232no—
536C2×C4—224no—
537C2×C4—228no—
538C2×C4—2216no—
539C2×C4#41×D1118yes—
540C2×C4C24×D1118yes—
541C2×C4C24×D1118yes—
542C2×C4C24×D1112yes—
543C2×C4C24×D1114yes—
544C22—28no—
545C22—28no—
546C22—28no—
547C22—416no—
548C22—2216no—
549C22—224no—
550C22—222no—
551C22—228no—
552C22—4416no—
553C22—444no—
554C22C2×#41×D1114yes—
555C22D11×H(5,𝔽2)12yes—
556C22C25×D1111yescharacteristic
557C4—28no—
558C4—28no—
559C4—22no—
560C4—1116no—
561C4—114no—
562C4—224no—
563C4—228no—
564C4C2×#41×D1118yes—
565C2—48no—
566C2—448no—
567C2—442no—
568C2#1308224114yesdirect product factor
569C2C22×#41×D1112yes—
570C2C2×D11×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#555C2
socleC23×C11C25
hypercenterC2×#555D11
hypocenterC11C2×#3483
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13082241C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623063C2semidirect
4. C2×#10623201C2semidirect
5. C2×#10623084C2semidirect
6. C2×#10623130C2semidirect
7. C2×#10623256C2semidirect
8. C2×#10623199C2semidirect
9. C2×#10623127C2semidirect
10. C2×#10623053C2semidirect
11. C2×C4×#4341C2semidirect
12. C2×C11×#555C2semidirect
17. C11×#555C22semidirect
32. #10623256C22semidirect
33. #10623253C22semidirect
34. #10623201C22semidirect
35. #10623199C22semidirect
36. #10623130C22semidirect
37. #10623127C22semidirect
38. #10623084C22semidirect
39. C4×#4341C22semidirect
40. #10623063C22semidirect
41. #10623053C22semidirect
191. C2×Dic22#41semidirect
218. C2×#555D11semidirect
270. Dic22C2×#41semidirect
278. #555C2×D11semidirect
422. C2×C11#3483semidirect
498. C11C2×#3483semidirect
568. C2#13082241direct (N × H)

Maximal subgroups

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

subgroupindex
#130822412
C2×#106232532
C2×#106230632
C2×#106232012
C2×#106230842
C2×#106231302
C2×#106232562
C2×#106231992
C2×#106231272
C2×#106230532
C2×C4×#43412
C2×C11×#5552
C2×#348311