Finite Group Databasebeta

← C2×#13081658 #15634753

Subgroups — C2×#13081658 #15634753

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2#13081658C2116yesmaximal, direct product factor
3C2×#10622687C212yesmaximal, complemented
4C2×#10622686C211yesmaximal, characteristic, complemented
5C2×#10622688C211yesmaximal, characteristic, complemented
6C2×#10622629C212yesmaximal, complemented
7C2×#10622628C211yesmaximal, characteristic, complemented
8C2×#10622685C212yesmaximal, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622627C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C11×#550—24no—
15C11×#550C2218yescomplemented
16C2×C11×#127C2212yes—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×#67000—21no—
24C22×#4324C2211yescharacteristic
25C22×#4324C2212yes—
26C22×#4323C2212yes—
27C22×#4323C2212yes—
28C22×#4323C2212yes—
29#10623116—24no—
30#10623116C2218yescomplemented
31C2×#66947—22no—
32C2×#66946—21no—
33C2×#66928C2212yes—
34C2×#66927C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×C4×Dic22C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2212yes—
39#10622688C2218yescomplemented
40#10622687C22116yescomplemented
41#10622686C2218yescomplemented
42#10622685C22116yescomplemented
43#10622637C2218yescomplemented
44C4×#4324C2218yescomplemented
45#10622629C22116yescomplemented
46#10622628C2218yescomplemented
47#10622627C22116yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66873C2212yes—
50C2×#66872C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—22no—
62C22×D4×C11C2312yes—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—22no—
65C23×C4×C11—21no—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44C2312yes—
69C22×C4×D11—22no—
70C22×Dic22C2311yescharacteristic
71C11×#127—22no—
72C11×#127—24no—
73C11×#127C2318yes—
74C11×#127C2314yes—
75C11×#121—28no—
76C11×#121—216no—
77C4×Q8×C11D414yes—
78C4×Q8×C11C2314yes—
79C4×D4×C11—22no—
80C4×D4×C11—24no—
81C4×D4×C11C2318yes—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2312yes—
90#67000—28no—
91C2×#4324—24no—
92C2×#4324—44no—
93C2×#4324C2314yes—
94C2×#4324C2318yes—
95C2×#4323—28no—
96C2×#4323—44no—
97C2×#4323—44no—
98C2×#4323C2318yes—
99C2×#4323C2318yes—
100C2×#4323C2318yes—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C22×C11⋊C8C2311yescharacteristic
110#66947—216no—
111#66946—28no—
112#66928—24no—
113#66928C2318yes—
114#66927—22no—
115#66927C2314yes—
116C4×D44—24no—
117C4×D44C2318yes—
118C4×Dic22—22no—
119C4×Dic22C2314yes—
120#66896C2318yes—
121#66896C2314yes—
122#66874C2314yes—
123#66873C2318yes—
124#66872C2314yes—
125C4⋊(C11⋊C8)C2314yes—
126C4⋊(C11⋊C8)C2318yes—
127#66867C2318yes—
128C4×C11⋊C8C2314yes—
129C2×#3399—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—21no—
132C23×D11—22no—
133C11×#41—432no—
134C2×Q8×C11—24no—
135C2×Q8×C11C2×D414yes—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—28no—
142C2×D4×C11—24no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—48no—
147C2×D4×C11—44no—
148C2×D4×C11—84no—
149C2×D4×C11—82no—
150C2×D4×C11C2414yes—
151C2×D4×C11C2412yes—
152C22×C4×C11—21no—
153C22×C4×C11—28no—
154C22×C4×C11—24no—
155C22×C4×C11—48no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×D44—22no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—44no—
170C2×D44—82no—
171C2×D44C2414yes—
172C2×C4×D11—28no—
173C2×C4×D11—84no—
174C2×Dic22—21no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22C2412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D414yes—
180C11×C4⋊C4C2×D418yes—
181C11×C4⋊C4C2412yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—28no—
184C42×C11C2×D412yes—
185C42×C11C2×D414yes—
186C42×C11C2412yes—
187C42×C11C2414yes—
188#4324—28no—
189#4324—48no—
190#4323—216no—
191#4323—48no—
192#4323—48no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—24no—
199C4×Dic11—24no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—24no—
202C2×C11⋊C8#4114yescomplemented
203C2×C11⋊C8C2412yes—
204C2×C11⋊C8C2414yes—
205C2×C11⋊C8C2412yes—
206C2×#559—111no—
207C2×#550D1111yescharacteristic, complemented
208#3399—1116no—
209C2×#496—112no—
210C2×#493—111no—
211C2×#460—111no—
212C2×#463—112no—
213C2×#459—112no—
214C2×#459—111no—
215C2×#446—111no—
216C2×#442—112no—
217C2×C4×SD16—111no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—44no—
221C23×C11—42no—
222C23×C11—44no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—44no—
226C23×C11C22×D411yescharacteristic
227C22×D11—24no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231Q8×C11—28no—
232D4×C11—24no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—24no—
236D4×C11—416no—
237D4×C11—44no—
238D4×C11—42no—
239D4×C11—48no—
240D4×C11—88no—
241D4×C11—84no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—416no—
247C2×C4×C11—42no—
248C2×C4×C11—48no—
249C2×C4×C11AGL(1,ℤ/8)14yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D414yes—
252C2×C4×C11C22×D414yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4112yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C11C2511yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262D44—24no—
263D44—24no—
264D44—44no—
265D44—48no—
266D44—84no—
267C4×D11—88no—
268Dic22—22no—
269Dic22—22no—
270Dic22—42no—
271C11⋊C8—22no—
272C11⋊C8—24no—
273C11⋊C8C2×#4114yescomplemented
274C22×#41—21no—
275C22×SD16—111no—
276C22×SD16—112no—
277C22×D8—112no—
278C22×D8—112no—
279C22×D8—112no—
280#559—118no—
281#559—224no—
282#550—24no—
283#550C2×D1118yescomplemented
284C2×#127—111no—
285C2×#127C2×D1111yescharacteristic
286C2×#127C2×D1112yes—
287C2×#124—112no—
288C2×#124—221no—
289C2×#123—222no—
290C2×#121—21no—
291C2×#121—22no—
292C2×C4×Q8—111no—
293C2×C4×Q8C2×D1111yescharacteristic
294C2×C4×D4—112no—
295C2×C4×D4—221no—
296C2×C4×D4C2×D1111yescharacteristic
297C2×C4×D4C2×D1112yes—
298#496—1116no—
299#493—118no—
300#463—1116no—
301#460—118no—
302#459—1116no—
303#459—118no—
304#446—118no—
305#442—1116no—
306C4×SD16—118no—
307C2×#106—111no—
308C2×C4⋊C8—112no—
309C2×C4⋊C8—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#97—112no—
315C2×C4×C8—111no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—44no—
322C22×C11—88no—
323C22×C11—84no—
324C22×C11#55012yes—
325C22×C11C2×AGL(1,ℤ/8)12yes—
326C22×C11#57612yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—88no—
332C4×C11—24no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11#55012yes—
337C4×C11C2×AGL(1,ℤ/8)14yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C2×H(5,𝔽2)11yescharacteristic
340Dic11—42no—
341Dic11—42no—
342C2×#41—28no—
343C2×#41—48no—
344C22×Q8—111no—
345C22×Q8C22⋊D1111yescharacteristic
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—112no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4C22×D1112yes—
354C22×D4C22×D1111yescharacteristic
355C23×C4—22no—
356C23×C4—21no—
357C23×C4—222no—
358C2×SD16—114no—
359C2×SD16—118no—
360C2×SD16—224no—
361C2×SD16—444no—
362C2×D8—118no—
363C2×D8—118no—
364C2×D8—118no—
365C2×D8—228no—
366C2×D8—444no—
367C2×D8—444no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—112no—
371#127—24no—
372#127—22no—
373#127—114no—
374#127—222no—
375#127C22×D1118yes—
376#127C22×D1114yes—
377#124—118no—
378#124—228no—
379#124—224no—
380#123—2216no—
381#121—28no—
382#121—216no—
383C4×Q8—114no—
384C4×Q8—222no—
385C4×Q8C22⋊D1114yes—
386C4×Q8C22×D1114yes—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—118no—
390C4×D4—228no—
391C4×D4—224no—
392C4×D4C22×D1114yes—
393C4×D4C22×D1118yes—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22⋊D1111yescharacteristic
397C2×C4⋊C4C22⋊D1112yes—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—22no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C42—221no—
405C2×C42C22×D1112yes—
406C2×C42C22×D1111yescharacteristic
407#106—114no—
408C4⋊C8—114no—
409C4⋊C8—118no—
410#103—114no—
411#102—114no—
412#102—118no—
413#102—118no—
414#97—118no—
415C4×C8—114no—
416C2×C11—84no—
417C2×C11—82no—
418C2×C11#339914yescomplemented
419C2×C11C2×#55011yescharacteristic
420C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C11C2×#57611yescharacteristic
422D11—84no—
423C24—22no—
424C24—21no—
425C24—222no—
426#41—432no—
427C2×Q8—24no—
428C2×Q8—112no—
429C2×Q8—221no—
430C2×Q8—222no—
431C2×Q8—222no—
432C2×Q8C2×C22⋊D1114yes—
433C2×D4—24no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—28no—
442C2×D4—24no—
443C2×D4—48no—
444C2×D4—44no—
445C2×D4—84no—
446C2×D4—82no—
447C2×D4—114no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—222no—
452C2×D4—224no—
453C2×D4—444no—
454C2×D4—882no—
455C2×D4C23×D1114yes—
456C2×D4C23×D1112yes—
457C22×C4—21no—
458C22×C4—28no—
459C22×C4—24no—
460C22×C4—48no—
461C22×C4—44no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—228no—
465C22×C4—884no—
466C22×C4C2×C22⋊D1112yes—
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1112yes—
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—228no—
472SD16—448no—
473D8—2216no—
474D8—448no—
475D8—448no—
476C2×C8—114no—
477C2×C8—112no—
478C2×C8—112no—
479C2×C8—114no—
480C2×C8—222no—
481C2×C8—224no—
482C4⋊C4—21no—
483C4⋊C4—112no—
484C4⋊C4—221no—
485C4⋊C4—224no—
486C4⋊C4C2×C22⋊D1114yes—
487C4⋊C4C2×C22⋊D1118yes—
488C4⋊C4C23×D1112yes—
489C22⋊C4—28no—
490C22⋊C4—24no—
491C22⋊C4—228no—
492C22⋊C4—228no—
493C22⋊C4—228no—
494C42—224no—
495C42C2×C22⋊D1114yes—
496C42C2×C22⋊D1112yes—
497C42C23×D1112yes—
498C42C23×D1114yes—
499C11C2×#339911yescharacteristic, complemented, Sylow
500C23—24no—
501C23—22no—
502C23—44no—
503C23—42no—
504C23—44no—
505C23—42no—
506C23—42no—
507C23—44no—
508C23—224no—
509C23—444no—
510C23—444no—
511C23—444no—
512C23C22×C22⋊D1111yescharacteristic
513Q8—28no—
514Q8—222no—
515Q8—222no—
516Q8—442no—
517D4—24no—
518D4—22no—
519D4—22no—
520D4—24no—
521D4—416no—
522D4—48no—
523D4—44no—
524D4—42no—
525D4—88no—
526D4—84no—
527D4—224no—
528D4—224no—
529D4—448no—
530D4—444no—
531D4—884no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—416no—
537C2×C4—42no—
538C2×C4—48no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—888no—
544C2×C4#6698514yes—
545C2×C4#41×D1112yes—
546C2×C4#6704212yes—
547C2×C4C22×C22⋊D1114yes—
548C2×C4C22×C22⋊D1112yes—
549C2×C4C22×C22⋊D1114yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C24×D1111yescharacteristic
553C8—114no—
554C8—222no—
555C8—224no—
556C22—44no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—44no—
561C22—42no—
562C22—88no—
563C22—84no—
564C22—444no—
565C22—444no—
566C22—444no—
567C22—888no—
568C22C2×#6698512yes—
569C22#1062336512yes—
570C22#1062336612yes—
571C22C23×C22⋊D1111yescharacteristic
572C4—24no—
573C4—24no—
574C4—22no—
575C4—42no—
576C4—442no—
577C4—442no—
578C4C2×#6698514yes—
579C4#1062336512yes—
580C4C2×#41×D1111yescharacteristic
581C4C2×#6704211yescharacteristic
582C2—84no—
583C2—82no—
584C2—884no—
585C2#1308165814yesdirect product factor
586C2C2×#1062336511yescharacteristic
587C2C22×#6698511yescharacteristic
588C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3399
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. #13081658C2direct (N × H)
3. C2×#10622687C2semidirect
4. C2×#10622686C2semidirect
5. C2×#10622688C2semidirect
6. C2×#10622629C2semidirect
7. C2×#10622628C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622627C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#550C2semidirect
15. C11×#550C22semidirect
30. #10623116C22semidirect
39. #10622688C22semidirect
40. #10622687C22semidirect
41. #10622686C22semidirect
42. #10622685C22semidirect
43. #10622637C22semidirect
44. C4×#4324C22semidirect
45. #10622629C22semidirect
46. #10622628C22semidirect
47. #10622627C22semidirect
202. C2×C11⋊C8#41semidirect
207. C2×#550D11semidirect
273. C11⋊C8C2×#41semidirect
283. #550C2×D11semidirect
418. C2×C11#3399semidirect
499. C11C2×#3399semidirect
585. C2#13081658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
#130816582
C2×#106226872
C2×#106226862
C2×#106226882
C2×#106226292
C2×#106226282
C2×#106226852
C2×#106226372
C2×#106226272
C2×C4×#43242
C2×C11×#5502
C2×#339911