Finite Group Databasebeta

← C2×#13080944 #15630707

Subgroups — C2×#13080944 #15630707

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic, complemented
3#13080944C2116yesmaximal, direct product factor
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622348C212yesmaximal, complemented
6C2×#10622464C211yesmaximal, characteristic, complemented
7C2×#10622748C212yesmaximal, complemented
8C2×#10622456C211yesmaximal, characteristic, complemented
9C2×#10622347C212yesmaximal, complemented
10C2×C4×#4314C211yesmaximal, characteristic, complemented
11C2×#10622746C212yesmaximal, complemented
12C2×C11×#436C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C22×#4339C2212yes—
15C22×C11×M16C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993—21no—
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C22×C4⋊Dic11C2212yes—
21C22×D88C2212yes—
22C22×#4314C2211yescharacteristic
23#10623086—24no—
24#10623086C2218yescomplemented
25#10623084—24no—
26#10623084C2218yescomplemented
27C2×#66950—21no—
28C2×#66946—21no—
29C2×#66939—22no—
30C2×#66937—22no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#436C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C2×C4×C8×C11C2211yescharacteristic
39#10622748C22116yescomplemented
40#10622746C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66885C2211yescharacteristic
44C2×#66885C2212yes—
45C2×#66881C2212yes—
46C2×#66881C2211yescharacteristic
47C2×#66880C2212yes—
48C2×#66880C2211yescharacteristic
49#10622464C2218yescomplemented
50#10622456C2218yescomplemented
51#10622348C22116yescomplemented
52#10622347C22116yescomplemented
53#10622307C2218yescomplemented
54C4×#4314C2218yescomplemented
55C22×D4×C11D411yescharacteristic
56C23×C4×C11C2312yes—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C23×Dic11—22no—
61C2×#4341—28no—
62C2×#4341—48no—
63C2×#4339—24no—
64C2×#4339—28no—
65C2×#4339—44no—
66C2×#4339C2318yes—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2312yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—22no—
73C22×Dic22—21no—
74C22×Dic22C2311yescharacteristic
75C2×C11×M16—44no—
76C2×C11×M16C2318yes—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2312yes—
80C4×D4×C11D414yes—
81C4×D4×C11C2314yes—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D412yes—
84C2×C42×C11C2311yescharacteristic
85#66993—28no—
86#66983—24no—
87#66983—24no—
88#66983C2318yes—
89#66983C2318yes—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—24no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2318yes—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×D88—44no—
103C2×D88C2318yes—
104C2×#4314—24no—
105C2×#4314C2314yes—
106#66950—28no—
107#66946—28no—
108#66939—216no—
109#66937—216no—
110#66927—22no—
111#66927C2314yes—
112C4×D44—22no—
113C4×D44C2314yes—
114#66922—22no—
115#66922C2314yes—
116C4×Dic22—22no—
117C4×Dic22C2314yes—
118C11×C4⋊C8C2314yes—
119C11×C22⋊C8C2318yes—
120C4×C8×C11C2314yes—
121#66885C2318yes—
122#66885C2318yes—
123#66885C2314yes—
124#66885C2318yes—
125#66881C2318yes—
126#66881C2314yes—
127#66880C2318yes—
128#66880C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C23×D11—21no—
132C23×D11—22no—
133C2×D4×C11—24no—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2414yes—
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—28no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C2×C22⋊D11—48no—
148C2×C22⋊D11—84no—
149C22×Dic11—21no—
150C22×Dic11—28no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—48no—
155#4341—432no—
156#4339—216no—
157#4339—48no—
158#4339—416no—
159C2×D44—21no—
160C2×D44—22no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—22no—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—24no—
167C2×D44—44no—
168C2×D44—82no—
169C2×D44C2414yes—
170C2×D44C2412yes—
171C2×C4×D11—24no—
172C2×C4×D11—28no—
173C2×C4×D11—48no—
174C2×C4×D11—44no—
175C2×Dic22—21no—
176C2×Dic22—24no—
177C2×Dic22—22no—
178C2×Dic22—44no—
179C2×Dic22#4114yescomplemented
180C2×Dic22C2412yes—
181C11×M16—48no—
182C2×C8×C11—22no—
183C2×C8×C11—24no—
184C2×C8×C11—22no—
185C2×C8×C11C2414yes—
186C2×C8×C11C2412yes—
187C2×C8×C11C2412yes—
188C11×C4⋊C4C2×D414yes—
189C11×C22⋊C4C2×D418yes—
190C42×C11C2×D412yes—
191C42×C11C2412yes—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195C4⋊Dic11—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—28no—
200C4⋊Dic11C2414yes—
201C4⋊Dic11C2412yes—
202C4⋊Dic11C2412yes—
203Dic11⋊C4—24no—
204C4×Dic11—24no—
205D88—48no—
206#4314—28no—
207C2×#550—111no—
208C2×#547—111no—
209#3332—1116no—
210C2×#486—111no—
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459—111no—
215C2×#449—112no—
216C2×C4×SD16—111no—
217C2×#436D1111yescharacteristic, complemented
218C2×#417—112no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11C22×D414yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—44no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—42no—
232D4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—28no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11AGL(1,ℤ/8)14yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11C2511yescharacteristic
246C22⋊D11—416no—
247C22⋊D11—416no—
248C22⋊D11—88no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—416no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258D44—22no—
259D44—24no—
260D44—22no—
261D44—24no—
262D44—42no—
263D44—44no—
264D44—48no—
265D44—84no—
266C4×D11—416no—
267C4×D11—48no—
268Dic22—24no—
269Dic22—22no—
270Dic22—48no—
271Dic22C2×#4114yescomplemented
272C8×C11—22no—
273C8×C11—24no—
274C8×C11—22no—
275C22×#41—112no—
276C22×#41—221no—
277C22×SD16—111no—
278C22×D8—112no—
279C22×M16C2×D1112yes—
280#550—118no—
281#550—224no—
282#547—118no—
283#547—224no—
284C2×C4⋊Q8—111no—
285C2×#127—111no—
286C2×#127—221no—
287C2×#123—222no—
288C2×C22⋊Q8—221no—
289C2×#121—112no—
290C2×#121—112no—
291C2×#121—222no—
292C2×C4×Q8—111no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4—112no—
297#486—118no—
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459—118no—
302#449—1116no—
303C4×SD16—118no—
304#436C2×D1118yescomplemented
305C2×#106—112no—
306C2×#106—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308#417—1116no—
309C2×#103—112no—
310C2×#103—111no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×C22⋊C8C2×D1112yes—
316C2×C4×C8C2×D1111yescharacteristic
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—48no—
321C22×C11#54612yes—
322C22×C11C2×AGL(1,ℤ/8)12yes—
323C22×C11#57712yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—44no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—44no—
329C2×D11—42no—
330C2×D11—44no—
331C2×D11—88no—
332C2×D11—84no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11#54612yes—
336C4×C11C2×AGL(1,ℤ/8)14yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339Dic11—24no—
340Dic11—44no—
341Dic11—42no—
342Dic11—42no—
343C2×#41—118no—
344C2×#41—228no—
345C2×#41—228no—
346C2×#41—224no—
347C2×#41—444no—
348C2×#41—448no—
349C22×Q8—111no—
350C22×Q8—221no—
351C22×D4—111no—
352C22×D4—112no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4D4411yescharacteristic
359C23×C4—222no—
360C23×C4—221no—
361C23×C4—222no—
362C23×C4C22×D1112yes—
363C2×SD16—114no—
364C2×SD16—224no—
365C2×D8—118no—
366C2×D8—444no—
367C2×M16—44no—
368C2×M16C22×D1118yes—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1112yes—
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—114no—
375#127—228no—
376#127—222no—
377#123—2216no—
378C22⋊Q8—228no—
379#121—118no—
380#121—118no—
381#121—224no—
382#121—224no—
383#121—2216no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×D4—114no—
387C4×D4—228no—
388C4×D4—222no—
389C4×D4D4414yes—
390C4×D4C22×D1114yes—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—118no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4D4411yescharacteristic
400C2×C22⋊C4—221no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4D4412yes—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406#106—114no—
407#106—118no—
408C4⋊C8C22×D1114yes—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—114no—
414#102—118no—
415C22⋊C8C22×D1118yes—
416C4×C8C22×D1114yes—
417C2×C11—44no—
418C2×C11#333214yescomplemented
419C2×C11C2×#54611yescharacteristic
420C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C11C2×#57711yescharacteristic
422D11—84no—
423D11—82no—
424C24—221no—
425C24—222no—
426C24C2×D4412yes—
427#41—2216no—
428#41—448no—
429#41—4416no—
430#41—4432no—
431C2×Q8—114no—
432C2×Q8—112no—
433C2×Q8—221no—
434C2×Q8—224no—
435C2×Q8—222no—
436C2×Q8—444no—
437C2×D4—24no—
438C2×D4—114no—
439C2×D4—112no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—228no—
443C2×D4—221no—
444C2×D4—224no—
445C2×D4—222no—
446C2×D4—224no—
447C2×D4—222no—
448C2×D4—224no—
449C2×D4—222no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—444no—
454C2×D4—882no—
455C2×D4—884no—
456C2×D4C2×D4414yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—221no—
460C22×C4—228no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—228no—
466C22×C4—448no—
467C22×C4—448no—
468C22×C4—444no—
469C22×C4C2×D4414yes—
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4412yes—
472C22×C4C2×D4411yescharacteristic
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476D8—448no—
477M16—48no—
478C2×C8—22no—
479C2×C8—24no—
480C2×C8—22no—
481C2×C8C23×D1112yes—
482C2×C8C23×D1112yes—
483C2×C8C23×D1114yes—
484C4⋊C4—112no—
485C4⋊C4—114no—
486C4⋊C4—112no—
487C4⋊C4—221no—
488C4⋊C4—222no—
489C4⋊C4—228no—
490C4⋊C4—221no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4C2×D4414yes—
494C22⋊C4—224no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4C2×D4418yes—
498C42—224no—
499C42C2×D4412yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—222no—
506C23—224no—
507C23—442no—
508C23—444no—
509C23—444no—
510C23—442no—
511C23—444no—
512C23—442no—
513C23C22×D4414yes—
514C23C22×D4411yescharacteristic
515Q8—114no—
516Q8—224no—
517Q8—222no—
518Q8—448no—
519D4—28no—
520D4—222no—
521D4—224no—
522D4—222no—
523D4—224no—
524D4—4416no—
525D4—4416no—
526D4—448no—
527D4—444no—
528D4—442no—
529D4—884no—
530D4—888no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—4416no—
542C2×C4—4416no—
543C2×C4—442no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4—448no—
547C2×C4#6696114yes—
548C2×C4C22×D4412yes—
549C2×C4C22×D4414yes—
550C2×C4C22×D4412yes—
551C2×C4C22×D4411yescharacteristic
552C2×C4#6703712yes—
553C2×C4#41×D1112yes—
554C2×C4C24×D1111yescharacteristic
555C8—22no—
556C8—24no—
557C8—22no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—48no—
562C22—444no—
563C22—442no—
564C22—442no—
565C22—444no—
566C22—444no—
567C22—442no—
568C22—884no—
569C22—888no—
570C22#1062308512yes—
571C22C2×#6696112yes—
572C22#1062328212yes—
573C22C23×D4411yescharacteristic
574C4—24no—
575C4—22no—
576C4—224no—
577C4—442no—
578C4—444no—
579C4—442no—
580C4#1062308512yes—
581C4C2×#6696114yes—
582C4C2×#6703711yescharacteristic
583C4C2×#41×D1111yescharacteristic
584C2—44no—
585C2—884no—
586C2—882no—
587C2#1308094414yesdirect product factor
588C2C2×#1062308511yescharacteristic
589C2C22×#6696111yescharacteristic
590C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
hypercenterC2×#436D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. C2×#10623086C2semidirect
3. #13080944C2direct (N × H)
4. C2×#10622307C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622464C2semidirect
7. C2×#10622748C2semidirect
8. C2×#10622456C2semidirect
9. C2×#10622347C2semidirect
10. C2×C4×#4314C2semidirect
11. C2×#10622746C2semidirect
12. C2×C11×#436C2semidirect
24. #10623086C22semidirect
26. #10623084C22semidirect
35. C11×#436C22semidirect
39. #10622748C22semidirect
40. #10622746C22semidirect
49. #10622464C22semidirect
50. #10622456C22semidirect
51. #10622348C22semidirect
52. #10622347C22semidirect
53. #10622307C22semidirect
54. C4×#4314C22semidirect
179. C2×Dic22#41semidirect
217. C2×#436D11semidirect
271. Dic22C2×#41semidirect
304. #436C2×D11semidirect
418. C2×C11#3332semidirect
501. C11C2×#3332semidirect
587. C2#13080944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106230862
#130809442
C2×#106223072
C2×#106223482
C2×#106224642
C2×#106227482
C2×#106224562
C2×#106223472
C2×C4×#43142
C2×#106227462
C2×C11×#4362
C2×#333211