Finite Group Databasebeta

← C2×#13081635 #15634728

Subgroups — C2×#13081635 #15634728

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081635C2116yesmaximal, direct product factor
4C2×#10622789C212yesmaximal, complemented
5C2×#10622698C211yesmaximal, characteristic, complemented
6C2×#10622776C212yesmaximal, complemented
7C2×#10622432C212yesmaximal, complemented
8C2×#10622456C211yesmaximal, characteristic, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000C2212yes—
18C2×Q8×Dic11C2212yes—
19C22×#4325C2212yes—
20C22×#4325C2212yes—
21C2×#66993C2212yes—
22C22×#4323C2211yescharacteristic
23C2×#66983—21no—
24C22×D88C2212yes—
25#10623263—24no—
26#10623263C2218yescomplemented
27#10623084—24no—
28#10623084C2218yescomplemented
29C2×#66951—22no—
30C2×#66950—21no—
31C2×#66946C2212yes—
32C2×#66945—21no—
33C2×#66937—22no—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#461C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66896C2211yescharacteristic
41#10622789C22116yescomplemented
42#10622776C22116yescomplemented
43C2×#66885C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622698C2218yescomplemented
47C4×#4323C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622456C2218yescomplemented
52#10622444C2218yescomplemented
53#10622432C22116yescomplemented
54#10622430C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—22no—
68C22×Dic22D411yescharacteristic
69C2×C11×SD16—44no—
70C2×C11×SD16C2318yes—
71C22×C8×C11C2312yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81#67000—24no—
82#67000C2318yes—
83Q8×Dic11—24no—
84Q8×Dic11C2318yes—
85C2×#4325—28no—
86C2×#4325—44no—
87C2×#4325C2318yes—
88C2×#4325C2318yes—
89#66993—24no—
90#66993C2318yes—
91C2×#4323—24no—
92C2×#4323C2314yes—
93#66983—28no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11D411yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4D412yes—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2312yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×D88—44no—
107C2×D88C2318yes—
108#66951—216no—
109#66950—28no—
110#66946—24no—
111#66946C2318yes—
112#66945—28no—
113#66937—216no—
114#66927—22no—
115#66927C2314yes—
116C4×D44—22no—
117C4×D44C2314yes—
118C4×Dic22D414yes—
119C4×Dic22C2314yes—
120C11×C4⋊C8C2314yes—
121C11×#103C2318yes—
122#66896C2314yes—
123#66885C2318yes—
124#66879C2318yes—
125Dic11⋊C8C2318yes—
126#66873C2314yes—
127#66871C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3397—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—21no—
132C23×D11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11C2414yes—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11C2412yes—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—84no—
152C22×Dic11—21no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155#4339—432no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44—24no—
159C2×D44—24no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—44no—
165C2×D44—82no—
166C2×D44C2412yes—
167C2×D44C2414yes—
168C2×C4×D11—28no—
169C2×C4×D11—24no—
170C2×C4×D11—48no—
171C2×C4×D11—44no—
172C2×Dic22—24no—
173C2×Dic22C2×D414yes—
174C11×SD16—48no—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4C2412yes—
181C11×C22⋊C4—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184#4325—216no—
185#4325—48no—
186#4323—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—24no—
191C4⋊Dic11—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2×D414yes—
194C4⋊Dic11C2412yes—
195Dic11⋊C4C2×D418yes—
196C4×Dic11—28no—
197C4×Dic11C2×D414yes—
198C4×Dic11C2414yes—
199C2×C11⋊C8—22no—
200C2×C11⋊C8#4114yescomplemented
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2412yes—
203D88—48no—
204C2×#556—111no—
205C2×#550—111no—
206#3397—1116no—
207C2×#496—112no—
208C2×#492—111no—
209C2×#460—112no—
210C2×#463—112no—
211C2×#461D1111yescharacteristic, complemented
212C2×#459—111no—
213C2×#446—111no—
214C2×#440—112no—
215C2×C4×D8—111no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—42no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—42no—
227C22×D11—44no—
228C22×D11—42no—
229Q8×C11—24no—
230Q8×C11—24no—
231Q8×C11—44no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—42no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—48no—
241C2×C4×C11AGL(1,ℤ/8)14yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—416no—
249C22⋊D11—88no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—42no—
254C2×Dic11C22×D414yes—
255C2×Dic11C22×D414yes—
256D44—22no—
257D44—24no—
258D44—22no—
259D44—24no—
260D44—42no—
261D44—44no—
262D44—48no—
263D44—84no—
264C4×D11—416no—
265C4×D11—48no—
266Dic22—28no—
267C8×C11—24no—
268C11⋊C8—22no—
269C11⋊C8C2×#4114yescomplemented
270C22×#41—221no—
271C22×SD16—112no—
272C22×SD16—112no—
273C22×SD16C2×D1112yes—
274C22×D8—111no—
275C22×D8—112no—
276#556—118no—
277#556—224no—
278#550—118no—
279#550—224no—
280C2×C4⋊Q8C2×D1111yescharacteristic
281C2×#127—112no—
282C2×#127—111no—
283C2×#126—222no—
284C2×#124—112no—
285C2×C22⋊Q8—221no—
286C2×#121—222no—
287C2×#121—221no—
288C2×C4×Q8—111no—
289C2×C4×Q8—112no—
290C2×C4×D4—112no—
291C2×C4×D4—111no—
292C2×C4×D4C2×D1111yescharacteristic
293C2×#117—221no—
294#496—1116no—
295#492—118no—
296#463—1116no—
297#461C2×D1118yescomplemented
298#460—1116no—
299#459—118no—
300#446—118no—
301#440—1116no—
302C4×D8—118no—
303C2×#107—111no—
304C2×C4⋊C8—112no—
305C2×C4⋊C8C2×D1111yescharacteristic
306C2×#103C2×D1112yes—
307C2×#102—111no—
308C2×#102—112no—
309C2×#102—111no—
310C2×#97—112no—
311C2×C4×C8—111no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—84no—
316C22×C11#55012yes—
317C22×C11C2×AGL(1,ℤ/8)12yes—
318C22×C11#57712yes—
319C22×C11C23×D411yescharacteristic
320C2×D11—42no—
321C2×D11—44no—
322C2×D11—42no—
323C2×D11—44no—
324C2×D11—42no—
325C2×D11—44no—
326C2×D11—88no—
327C2×D11—84no—
328C4×C11—22no—
329C4×C11—44no—
330C4×C11—42no—
331C4×C11#55012yes—
332C4×C11C2×AGL(1,ℤ/8)14yes—
333C4×C11C22×#4111yescharacteristic
334C4×C11C2×H(5,𝔽2)11yescharacteristic
335Dic11—24no—
336Dic11—24no—
337Dic11—42no—
338C2×#41—228no—
339C2×#41—448no—
340C22×Q8—111no—
341C22×Q8C22×D1112yes—
342C22×D4—111no—
343C22×D4—112no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—221no—
347C22×D4—221no—
348C22×D4C22×D1111yescharacteristic
349C23×C4—21no—
350C23×C4—222no—
351C23×C4—221no—
352C2×SD16—44no—
353C2×SD16—118no—
354C2×SD16—118no—
355C2×SD16—228no—
356C2×SD16—444no—
357C2×SD16C22×D1118yes—
358C2×D8—114no—
359C2×D8—118no—
360C2×D8—224no—
361C2×D8—444no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8C22×D1112yes—
365C4⋊Q8—22no—
366C4⋊Q8C22×D1114yes—
367#127—118no—
368#127—114no—
369#127—224no—
370#127—222no—
371#126—2216no—
372#124—118no—
373#124—224no—
374C22⋊Q8—228no—
375#121—2216no—
376#121—228no—
377C4×Q8—114no—
378C4×Q8—114no—
379C4×Q8—118no—
380C4×Q8—224no—
381C4×D4—22no—
382C4×D4—118no—
383C4×D4—114no—
384C4×D4—224no—
385C4×D4—222no—
386C4×D4C22×D1114yes—
387#117—228no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C42—112no—
401C2×C42—222no—
402C2×C42C22×D1111yescharacteristic
403#107—114no—
404C4⋊C8—118no—
405C4⋊C8C22×D1114yes—
406#103C22×D1118yes—
407#102—114no—
408#102—118no—
409#102—114no—
410#97—118no—
411C4×C8—114no—
412C2×C11—82no—
413C2×C11#339714yescomplemented
414C2×C11C2×#55011yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C11C2×#57711yescharacteristic
417D11—82no—
418D11—84no—
419C24—21no—
420C24—221no—
421C24—222no—
422#41—4432no—
423C2×Q8—22no—
424C2×Q8—24no—
425C2×Q8—24no—
426C2×Q8—114no—
427C2×Q8—224no—
428C2×Q8C23×D1114yes—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—112no—
433C2×D4—114no—
434C2×D4—228no—
435C2×D4—228no—
436C2×D4—221no—
437C2×D4—222no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—222no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—224no—
444C2×D4—448no—
445C2×D4—444no—
446C2×D4—882no—
447C2×D4—884no—
448C2×D4C23×D1112yes—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—228no—
456C22×C4—221no—
457C22×C4—224no—
458C22×C4—448no—
459C22×C4—444no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—48no—
464SD16—2216no—
465SD16—448no—
466D8—228no—
467D8—448no—
468C2×C8—24no—
469C2×C8—114no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—222no—
473C2×C8C23×D1114yes—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—114no—
478C4⋊C4—118no—
479C4⋊C4—112no—
480C4⋊C4—228no—
481C4⋊C4—221no—
482C4⋊C4C23×D1112yes—
483C22⋊C4—24no—
484C22⋊C4—228no—
485C22⋊C4—228no—
486C22⋊C4—228no—
487C22⋊C4—224no—
488C42—114no—
489C42—114no—
490C42—228no—
491C42D4×D1112yes—
492C42C23×D1112yes—
493C11C2×#339711yescharacteristic, complemented, Sylow
494C23—22no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—222no—
499C23—224no—
500C23—444no—
501C23—442no—
502C23—444no—
503C23—442no—
504C23—442no—
505C23—444no—
506C23C2×D4×D1111yescharacteristic
507Q8—24no—
508Q8—24no—
509Q8—44no—
510Q8—228no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—222no—
515D4—224no—
516D4—222no—
517D4—224no—
518D4—4416no—
519D4—448no—
520D4—442no—
521D4—444no—
522D4—884no—
523D4—888no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—48no—
530C2×C4—114no—
531C2×C4—114no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—4416no—
536C2×C4—442no—
537C2×C4—448no—
538C2×C4#6696714yes—
539C2×C4C2×D4×D1112yes—
540C2×C4C2×D4×D1112yes—
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4#6703712yes—
543C2×C4#41×D1112yes—
544C2×C4C24×D1111yescharacteristic
545C8—24no—
546C8—114no—
547C8—222no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—84no—
552C22—444no—
553C22—442no—
554C22—442no—
555C22—444no—
556C22—444no—
557C22—442no—
558C22—888no—
559C22—884no—
560C22#1062313012yes—
561C22C2×#6696712yes—
562C22#1062330912yes—
563C22C22×D4×D1111yescharacteristic
564C4—22no—
565C4—42no—
566C4—44no—
567C4—224no—
568C4—224no—
569C4—442no—
570C4#1062313012yes—
571C4C2×#6696714yes—
572C4C2×#6703711yescharacteristic
573C4C2×#41×D1111yescharacteristic
574C2—82no—
575C2—884no—
576C2—882no—
577C2#1308163514yesdirect product factor
578C2C2×#1062313011yescharacteristic
579C2C22×#6696711yescharacteristic
580C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
hypercenterC2×#461D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
2. C2×#10623084C2semidirect
3. #13081635C2direct (N × H)
4. C2×#10622789C2semidirect
5. C2×#10622698C2semidirect
6. C2×#10622776C2semidirect
7. C2×#10622432C2semidirect
8. C2×#10622456C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622430C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#461C2semidirect
26. #10623263C22semidirect
28. #10623084C22semidirect
37. C11×#461C22semidirect
41. #10622789C22semidirect
42. #10622776C22semidirect
46. #10622698C22semidirect
47. C4×#4323C22semidirect
51. #10622456C22semidirect
52. #10622444C22semidirect
53. #10622432C22semidirect
54. #10622430C22semidirect
200. C2×C11⋊C8#41semidirect
211. C2×#461D11semidirect
269. C11⋊C8C2×#41semidirect
297. #461C2×D11semidirect
413. C2×C11#3397semidirect
493. C11C2×#3397semidirect
577. C2#13081635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106230842
#130816352
C2×#106227892
C2×#106226982
C2×#106227762
C2×#106224322
C2×#106224562
C2×#106224442
C2×#106224302
C2×C4×#43232
C2×C11×#4612
C2×#339711