Finite Group Databasebeta

← C2×#13081656 #15634751

Subgroups — C2×#13081656 #15634751

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
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081656C2116yesmaximal, direct product factor
4C2×#10622789C212yesmaximal, complemented
5C2×#10622308C211yesmaximal, characteristic, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622432C212yesmaximal, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622399C212yesmaximal, complemented
10C2×#10622292C211yesmaximal, characteristic, complemented
11C2×#10622482C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000C2212yes—
18C22×#4325C2212yes—
19C2×#66993C2212yes—
20C22×#4323C2212yes—
21C2×#66983—21no—
22C22×D88C2212yes—
23C22×D88C2212yes—
24#10623116—24no—
25#10623116C2218yescomplemented
26#10623084—24no—
27#10623084C2218yescomplemented
28C2×#66947—22no—
29C2×#66946C2212yes—
30C2×#66946C2212yes—
31C2×#66937—22no—
32C2×#66928—21no—
33C2×#66927C2211yescharacteristic
34C2×#66927C2211yescharacteristic
35C2×C4×D44—21no—
36C2×C4×Dic22C2211yescharacteristic
37C4×C11×SD16C2218yescomplemented
38C2×C11×#106C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C4×C8×C11C2211yescharacteristic
42#10622789C22116yescomplemented
43C2×#66879C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622640C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622482C22116yescomplemented
51#10622432C22116yescomplemented
52#10622399C22116yescomplemented
53#10622308C2218yescomplemented
54#10622292C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
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×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×D44C2312yes—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×Dic22D411yescharacteristic
71C2×C11×SD16—24no—
72C2×C11×SD16C2314yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—22no—
76C4×Q8×C11C2314yes—
77C4×D4×C11—22no—
78C4×D4×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85#67000—24no—
86#67000C2318yes—
87C2×#4325—44no—
88C2×#4325C2318yes—
89#66993—24no—
90#66993C2318yes—
91C2×#4323—44no—
92C2×#4323C2318yes—
93#66983—28no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×C4⋊Dic11D411yescharacteristic
99C2×Dic11⋊C4D412yes—
100C2×C4×Dic11C2312yes—
101C22×C11⋊C8C2312yes—
102C2×D88—28no—
103C2×D88—44no—
104C2×D88C2318yes—
105C2×D88C2318yes—
106#66947—216no—
107#66946—24no—
108#66946—24no—
109#66946C2318yes—
110#66946C2318yes—
111#66937—216no—
112#66928—28no—
113#66927—22no—
114#66927—22no—
115#66927C2314yes—
116#66927C2314yes—
117C4×D44—28no—
118C4×Dic22D414yes—
119C4×Dic22C2314yes—
120C11×#106C2314yes—
121C11×#103C2314yes—
122C11×#102C2314yes—
123C4×C8×C11C2314yes—
124#66879C2318yes—
125Dic11⋊C8C2318yes—
126#66873C2318yes—
127#66873C2318yes—
128C4⋊(C11⋊C8)C2314yes—
129C2×#3399—111nomaximal, Sylow
130C24×C11—21no—
131C23×D11—22no—
132C23×D11—22no—
133C2×Q8×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11C2412yes—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11C2412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—84no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155#4339—432no—
156C2×D44—24no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—24no—
166C2×D44—44no—
167C2×D44—44no—
168C2×D44—82no—
169C2×D44—82no—
170C2×D44C2414yes—
171C2×D44C2414yes—
172C2×C4×D11—28no—
173C2×C4×D11—28no—
174C2×C4×D11—48no—
175C2×C4×D11—84no—
176C2×Dic22—24no—
177C2×Dic22C2×D414yes—
178C11×SD16—28no—
179C2×C8×C11—22no—
180C2×C8×C11#4114yescomplemented
181C2×C8×C11C2412yes—
182C2×C8×C11C2412yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4C2412yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189C42×C11—24no—
190C42×C11C2×D412yes—
191C42×C11C2412yes—
192#4325—48no—
193#4323—48no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11C2×D414yes—
199Dic11⋊C4C2×D418yes—
200C4×Dic11C2×D414yes—
201C4×Dic11C2414yes—
202C2×C11⋊C8—24no—
203C2×C11⋊C8C2414yes—
204D88—216no—
205D88—48no—
206C2×#559—111no—
207C2×#550—111no—
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×SD16D1111yescharacteristic, complemented
218C23×C11—22no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—42no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—42no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—48no—
245C2×C4×C11AGL(1,ℤ/8)14yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C11C2511yescharacteristic
252C22⋊D11—416no—
253C22⋊D11—88no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11C22×D414yes—
257C2×Dic11C22×D414yes—
258D44—24no—
259D44—24no—
260D44—24no—
261D44—24no—
262D44—44no—
263D44—44no—
264D44—48no—
265D44—48no—
266D44—84no—
267D44—84no—
268C4×D11—416no—
269C4×D11—88no—
270Dic22—28no—
271C8×C11—22no—
272C8×C11C2×#4114yescomplemented
273C11⋊C8—24no—
274C22×#41—221no—
275C22×SD16—112no—
276C22×SD16C2×D1111yescharacteristic
277C22×D8—112no—
278C22×D8—112no—
279C22×D8—112no—
280#559—118no—
281#559—224no—
282#550—118no—
283#550—224no—
284C2×#127—112no—
285C2×#127—111no—
286C2×#127—111no—
287C2×#124—112no—
288C2×#124—221no—
289C2×#123—222no—
290C2×#121—222no—
291C2×#121—221no—
292C2×C4×Q8—111no—
293C2×C4×Q8C2×D1111yescharacteristic
294C2×C4×D4—112no—
295C2×C4×D4—112no—
296C2×C4×D4—221no—
297C2×C4×D4C2×D1111yescharacteristic
298#496—1116no—
299#493—118no—
300#463—1116no—
301#460—118no—
302#459—118no—
303#459—1116no—
304#446—118no—
305#442—1116no—
306C4×SD16C2×D1118yescomplemented
307C2×#106C2×D1111yescharacteristic
308C2×C4⋊C8—112no—
309C2×C4⋊C8—111no—
310C2×#103C2×D1111yescharacteristic
311C2×#102—112no—
312C2×#102—112no—
313C2×#102C2×D1111yescharacteristic
314C2×#97—112no—
315C2×C4×C8C2×D1111yescharacteristic
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—84no—
320C22×C11#55012yes—
321C22×C11C2×AGL(1,ℤ/8)12yes—
322C22×C11#57612yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—88no—
331C2×D11—88no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11#55012yes—
337C4×C11C2×AGL(1,ℤ/8)14yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C2×H(5,𝔽2)11yescharacteristic
340Dic11—24no—
341Dic11—24no—
342C2×#41—228no—
343C2×#41—448no—
344C22×Q8—111no—
345C22×Q8C22×D1111yescharacteristic
346C22×D4—112no—
347C22×D4—112no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4—221no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—222no—
357C23×C4—222no—
358C2×SD16—24no—
359C2×SD16—118no—
360C2×SD16—444no—
361C2×SD16C22×D1114yes—
362C2×D8—118no—
363C2×D8—118no—
364C2×D8—118no—
365C2×D8—228no—
366C2×D8—444no—
367C2×D8—444no—
368C22×C8—112no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371#127—118no—
372#127—114no—
373#127—114no—
374#127—224no—
375#127—222no—
376#127—222no—
377#124—118no—
378#124—228no—
379#124—224no—
380#123—2216no—
381#121—2216no—
382#121—228no—
383C4×Q8—22no—
384C4×Q8—114no—
385C4×Q8—114no—
386C4×Q8C22×D1114yes—
387C4×D4—22no—
388C4×D4—118no—
389C4×D4—118no—
390C4×D4—228no—
391C4×D4—224no—
392C4×D4—224no—
393C4×D4C22×D1114yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—112no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C42—21no—
405C2×C42—112no—
406C2×C42C22×D1111yescharacteristic
407#106C22×D1114yes—
408C4⋊C8—118no—
409C4⋊C8—114no—
410#103C22×D1114yes—
411#102—118no—
412#102—118no—
413#102C22×D1114yes—
414#97—118no—
415C4×C8C22×D1114yes—
416C2×C11—82no—
417C2×C11#339914yescomplemented
418C2×C11C2×#55011yescharacteristic
419C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
420C2×C11C2×#57611yescharacteristic
421D11—84no—
422D11—84no—
423C24—21no—
424C24—222no—
425C24—222no—
426#41—4432no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—114no—
431C2×Q8—224no—
432C2×Q8C23×D1112yes—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—114no—
437C2×D4—114no—
438C2×D4—228no—
439C2×D4—228no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—224no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—224no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—448no—
451C2×D4—444no—
452C2×D4—444no—
453C2×D4—882no—
454C2×D4—882no—
455C2×D4—884no—
456C2×D4C23×D1112yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—44no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—228no—
465C22×C4—228no—
466C22×C4—448no—
467C22×C4—884no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—28no—
472SD16—448no—
473D8—2216no—
474D8—448no—
475D8—448no—
476C2×C8—22no—
477C2×C8—114no—
478C2×C8—224no—
479C2×C8#433914yescomplemented
480C2×C8C23×D1112yes—
481C2×C8C23×D1112yes—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—114no—
486C4⋊C4—118no—
487C4⋊C4C23×D1112yes—
488C4⋊C4C23×D1112yes—
489C22⋊C4—24no—
490C22⋊C4—228no—
491C22⋊C4—228no—
492C22⋊C4—228no—
493C22⋊C4—228no—
494C42—24no—
495C42—114no—
496C42—114no—
497C42D4×D1112yes—
498C42C23×D1112yes—
499C11C2×#339911yescharacteristic, complemented, Sylow
500C23—22no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—224no—
505C23—224no—
506C23—444no—
507C23—444no—
508C23—444no—
509C23—444no—
510C23—444no—
511C23—444no—
512C23C2×D4×D1111yescharacteristic
513Q8—22no—
514Q8—22no—
515Q8—42no—
516Q8—228no—
517D4—22no—
518D4—22no—
519D4—42no—
520D4—224no—
521D4—224no—
522D4—224no—
523D4—224no—
524D4—4416no—
525D4—448no—
526D4—448no—
527D4—444no—
528D4—444no—
529D4—884no—
530D4—884no—
531D4—888no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—48no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—4416no—
545C2×C4—888no—
546C2×C4#6696714yes—
547C2×C4C2×#433912yes—
548C2×C4C2×D4×D1112yes—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#6704212yes—
552C2×C4C24×D1111yescharacteristic
553C8—22no—
554C8—224no—
555C8C2×#433914yescomplemented
556C22—42no—
557C22—42no—
558C22—42no—
559C22—84no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22—444no—
566C22—888no—
567C22—888no—
568C22#1062308412yes—
569C22C2×#6696712yes—
570C22#1062330012yes—
571C22C22×D4×D1111yescharacteristic
572C4—22no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—224no—
577C4—224no—
578C4#1062308412yes—
579C4C2×#6696714yes—
580C4C22×#433911yescharacteristic
581C4C2×#6704211yescharacteristic
582C2—82no—
583C2—884no—
584C2—884no—
585C2#1308165614yesdirect product factor
586C2C2×#1062308411yescharacteristic
587C2C22×#6696711yescharacteristic
588C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3399
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623084C2semidirect
3. #13081656C2direct (N × H)
4. C2×#10622789C2semidirect
5. C2×#10622308C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622432C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622292C2semidirect
11. C2×#10622482C2semidirect
12. C2×C4×C11×SD16C2semidirect
25. #10623116C22semidirect
27. #10623084C22semidirect
37. C4×C11×SD16C22semidirect
42. #10622789C22semidirect
45. #10622640C22semidirect
46. #10622628C22semidirect
50. #10622482C22semidirect
51. #10622432C22semidirect
52. #10622399C22semidirect
53. #10622308C22semidirect
54. #10622292C22semidirect
180. C2×C8×C11#41semidirect
217. C2×C4×SD16D11semidirect
272. C8×C11C2×#41semidirect
306. C4×SD16C2×D11semidirect
417. C2×C11#3399semidirect
479. C2×C8#4339semidirect
499. C11C2×#3399semidirect
555. C8C2×#4339semidirect
585. C2#13081656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106230842
#130816562
C2×#106227892
C2×#106223082
C2×#106226402
C2×#106224322
C2×#106226282
C2×#106223992
C2×#106222922
C2×#106224822
C2×C4×C11×SD162
C2×#339911