Finite Group Databasebeta

← C2×#13081662 #15634757

Subgroups — C2×#13081662 #15634757

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×#10623244C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic, complemented
3#13081662C2116yesmaximal, direct product factor
4C2×#10622767C212yesmaximal, complemented
5C2×#10622686C211yesmaximal, characteristic, complemented
6C2×#10622461C211yesmaximal, characteristic, complemented
7C2×#10622400C212yesmaximal, complemented
8C2×#10622763C212yesmaximal, complemented
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622398C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#459C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×D8C2212yes—
15C2×C11×#127C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2212yes—
18C2×#66989—21no—
19C2×#66989C2212yes—
20C2×#66988—22no—
21C2×D4×Dic11—21no—
22C2×D4×Dic11C2212yes—
23C22×#4324C2211yescharacteristic
24C22×#4323C2212yes—
25C22×#4323C2212yes—
26C2×#66983—21no—
27C22×#4314C2212yes—
28#10623244—24no—
29#10623244C2218yescomplemented
30#10623084—24no—
31#10623084C2218yescomplemented
32C2×#66946C2212yes—
33C2×#66937—22no—
34C2×#66927C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#459C2218yescomplemented
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×#66896C2211yescharacteristic
41#10622767C22116yescomplemented
42#10622763C22116yescomplemented
43C2×#66885C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622686C2218yescomplemented
47C4×#4324C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622461C2218yescomplemented
52#10622444C2218yescomplemented
53#10622400C22116yescomplemented
54#10622398C22116yescomplemented
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C23×Dic11—22no—
63C2×#4339—28no—
64C2×#4339—48no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44C2312yes—
68C22×C4×D11—22no—
69C22×Dic22D411yescharacteristic
70C22×Dic22C2311yescharacteristic
71C2×C11×D8—44no—
72C2×C11×D8C2318yes—
73C22×C8×C11C2312yes—
74C11×#127—22no—
75C11×#127C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84#66993—24no—
85#66993C2318yes—
86#66989—28no—
87#66989—24no—
88#66989C2318yes—
89#66988—216no—
90D4×Dic11—28no—
91D4×Dic11—24no—
92D4×Dic11C2318yes—
93C2×#4324—24no—
94C2×#4324C2314yes—
95C2×#4323—28no—
96C2×#4323—44no—
97C2×#4323C2318yes—
98C2×#4323C2318yes—
99#66983—28no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4D412yes—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2312yes—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×#4314—44no—
110C2×#4314C2318yes—
111#66946—24no—
112#66946C2318yes—
113#66937—216no—
114#66927—22no—
115#66927C2314yes—
116C4×Dic22—22no—
117C4×Dic22D414yes—
118C4×Dic22C2314yes—
119C4×Dic22C2314yes—
120C11×C4⋊C8C2314yes—
121C11×#102C2318yes—
122#66896C2314yes—
123#66885C2318yes—
124#66879C2318yes—
125Dic11⋊C8C2318yes—
126#66874C2314yes—
127#66872C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3399—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—21no—
132C23×D11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—44no—
142C2×D4×C11—82no—
143C2×D4×C11C2412yes—
144C2×D4×C11C2414yes—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—84no—
155C22×Dic11—28no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—84no—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161#4339—432no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—24no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—44no—
168C2×D44—82no—
169C2×D44C2414yes—
170C2×C4×D11—28no—
171C2×C4×D11—48no—
172C2×Dic22—24no—
173C2×Dic22—21no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22C2×D414yes—
177C2×Dic22C2412yes—
178C11×D8—48no—
179C2×C8×C11—24no—
180C2×C8×C11C2414yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2412yes—
183C11×C22⋊C4—24no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186C22⋊Dic11—28no—
187C22⋊Dic11—28no—
188C22⋊Dic11—28no—
189#4324—28no—
190#4323—216no—
191#4323—48no—
192(C2×D11)⋊C4—28no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D414yes—
195C4⋊Dic11C2412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4C2×D418yes—
198C4×Dic11—24no—
199C4×Dic11C2×D414yes—
200C4×Dic11C2414yes—
201C2×C11⋊C8—22no—
202C2×C11⋊C8#4114yescomplemented
203C2×C11⋊C8C2412yes—
204C2×C11⋊C8C2412yes—
205#4314—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×#459D1111yescharacteristic, complemented
215C2×#446—111no—
216C2×#442—112no—
217C2×C4×SD16—111no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—44no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—42no—
226C23×C11C22×D411yescharacteristic
227C22×D11—24no—
228C22×D11—44no—
229C22×D11—44no—
230C22×D11—44no—
231D4×C11—24no—
232D4×C11—22no—
233D4×C11—24no—
234D4×C11—22no—
235D4×C11—44no—
236D4×C11—42no—
237D4×C11—48no—
238D4×C11—84no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—48no—
243C2×C4×C11AGL(1,ℤ/8)14yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—416no—
251C22⋊D11—88no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—88no—
259C2×Dic11C22×D414yes—
260C2×Dic11C22×D414yes—
261D44—24no—
262D44—24no—
263D44—44no—
264D44—48no—
265D44—84no—
266C4×D11—416no—
267Dic22—28no—
268Dic22—22no—
269Dic22—22no—
270Dic22—42no—
271C8×C11—24no—
272C11⋊C8—22no—
273C11⋊C8C2×#4114yescomplemented
274C22×#41—221no—
275C22×SD16—111no—
276C22×SD16—112no—
277C22×D8—112no—
278C22×D8—112no—
279C22×D8C2×D1112yes—
280#559—118no—
281#559—224no—
282#550—118no—
283#550—224no—
284C2×#127—112no—
285C2×#127—111no—
286C2×#127C2×D1111yescharacteristic
287C2×#124—112no—
288C2×#124—221no—
289C2×#123—222no—
290C2×#121—222no—
291C2×#121—221no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
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—1116no—
303#459C2×D1118yescomplemented
304#446—118no—
305#442—1116no—
306C4×SD16—118no—
307C2×#106—111no—
308C2×C4⋊C8—112no—
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—112no—
313C2×#102C2×D1112yes—
314C2×#97—112no—
315C2×C4×C8—111no—
316C22×C11—44no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—84no—
323C22×C11—88no—
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—22no—
333C4×C11—42no—
334C4×C11#55012yes—
335C4×C11C2×AGL(1,ℤ/8)14yes—
336C4×C11C22×#4111yescharacteristic
337C4×C11C2×H(5,𝔽2)11yescharacteristic
338Dic11—24no—
339Dic11—24no—
340Dic11—42no—
341Dic11—42no—
342C2×#41—228no—
343C2×#41—448no—
344C22×Q8—111no—
345C22×Q8—111no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—112no—
349C22×D4—222no—
350C22×D4—222no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4C22×D1112yes—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—222no—
357C23×C4—222no—
358C2×SD16—114no—
359C2×SD16—118no—
360C2×SD16—224no—
361C2×SD16—444no—
362C2×D8—44no—
363C2×D8—118no—
364C2×D8—118no—
365C2×D8—228no—
366C2×D8—444no—
367C2×D8C22×D1118yes—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8C22×D1112yes—
371#127—22no—
372#127—118no—
373#127—114no—
374#127—224no—
375#127—222no—
376#127C22×D1114yes—
377#124—118no—
378#124—224no—
379#124—228no—
380#123—2216no—
381#121—2216no—
382#121—228no—
383C4×Q8—114no—
384C4×Q8—114no—
385C4×Q8—114no—
386C4×Q8—222no—
387C4×D4—22no—
388C4×D4—118no—
389C4×D4—118no—
390C4×D4—224no—
391C4×D4—224no—
392C4×D4—228no—
393C4×D4C22×D1114yes—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
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—112no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#106—114no—
408C4⋊C8—118no—
409C4⋊C8C22×D1114yes—
410#103—114no—
411#102—114no—
412#102—118no—
413#102C22×D1118yes—
414#97—118no—
415C4×C8—114no—
416C2×C11—82no—
417C2×C11—84no—
418C2×C11#339914yescomplemented
419C2×C11C2×#55011yescharacteristic
420C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C11C2×#57611yescharacteristic
422D11—84no—
423C24—21no—
424C24—22no—
425C24—222no—
426#41—4432no—
427C2×Q8—114no—
428C2×Q8—112no—
429C2×Q8—224no—
430C2×Q8—221no—
431C2×Q8—222no—
432C2×Q8—222no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—44no—
442C2×D4—82no—
443C2×D4—114no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—222no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4—444no—
453C2×D4—882no—
454C2×D4—884no—
455C2×D4C23×D1112yes—
456C2×D4C23×D1114yes—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—44no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—228no—
463C22×C4—228no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—448no—
467C22×C4—884no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—228no—
472SD16—448no—
473D8—48no—
474D8—2216no—
475D8—448no—
476C2×C8—24no—
477C2×C8—114no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—222no—
481C2×C8C23×D1114yes—
482C4⋊C4—21no—
483C4⋊C4—114no—
484C4⋊C4—118no—
485C4⋊C4—112no—
486C4⋊C4—221no—
487C4⋊C4—224no—
488C4⋊C4C23×D1112yes—
489C22⋊C4—24no—
490C22⋊C4—228no—
491C22⋊C4—228no—
492C22⋊C4—228no—
493C22⋊C4—228no—
494C42—114no—
495C42—114no—
496C42—224no—
497C42D4×D1112yes—
498C42C23×D1112yes—
499C11C2×#339911yescharacteristic, complemented, Sylow
500C23—22no—
501C23—24no—
502C23—42no—
503C23—44no—
504C23—44no—
505C23—42no—
506C23—42no—
507C23—44no—
508C23—224no—
509C23—444no—
510C23—444no—
511C23—444no—
512C23C2×D4×D1111yescharacteristic
513Q8—228no—
514Q8—222no—
515Q8—222no—
516Q8—442no—
517D4—22no—
518D4—24no—
519D4—24no—
520D4—22no—
521D4—48no—
522D4—42no—
523D4—44no—
524D4—84no—
525D4—224no—
526D4—224no—
527D4—4416no—
528D4—448no—
529D4—444no—
530D4—884no—
531D4—888no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—48no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—4416no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—888no—
546C2×C4#6696414yes—
547C2×C4C2×D4×D1112yes—
548C2×C4C2×D4×D1112yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4#6703712yes—
551C2×C4#41×D1112yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—114no—
555C8—222no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—84no—
563C22—88no—
564C22—444no—
565C22—444no—
566C22—444no—
567C22—888no—
568C22#1062313012yes—
569C22C2×#6696412yes—
570C22#1062330512yes—
571C22C22×D4×D1111yescharacteristic
572C4—22no—
573C4—42no—
574C4—224no—
575C4—224no—
576C4—442no—
577C4—442no—
578C4#1062313012yes—
579C4C2×#6696414yes—
580C4C2×#6703711yescharacteristic
581C4C2×#41×D1111yescharacteristic
582C2—82no—
583C2—84no—
584C2—884no—
585C2#1308166214yesdirect product factor
586C2C2×#1062313011yescharacteristic
587C2C22×#6696411yescharacteristic
588C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3399
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. C2×#10623084C2semidirect
3. #13081662C2direct (N × H)
4. C2×#10622767C2semidirect
5. C2×#10622686C2semidirect
6. C2×#10622461C2semidirect
7. C2×#10622400C2semidirect
8. C2×#10622763C2semidirect
9. C2×#10622444C2semidirect
10. C2×#10622398C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#459C2semidirect
29. #10623244C22semidirect
31. #10623084C22semidirect
37. C11×#459C22semidirect
41. #10622767C22semidirect
42. #10622763C22semidirect
46. #10622686C22semidirect
47. C4×#4324C22semidirect
51. #10622461C22semidirect
52. #10622444C22semidirect
53. #10622400C22semidirect
54. #10622398C22semidirect
202. C2×C11⋊C8#41semidirect
214. C2×#459D11semidirect
273. C11⋊C8C2×#41semidirect
303. #459C2×D11semidirect
418. C2×C11#3399semidirect
499. C11C2×#3399semidirect
585. C2#13081662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232442
C2×#106230842
#130816622
C2×#106227672
C2×#106226862
C2×#106224612
C2×#106224002
C2×#106227632
C2×#106224442
C2×#106223982
C2×C4×#43242
C2×C11×#4592
C2×#339911