Finite Group Databasebeta

← C2×#13067669 #14729376

Subgroups — C2×#13067669 #14729376

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic, complemented
4#13067669C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#459C211yesmaximal, characteristic, complemented
9C22×D4×D11—21no—
10C23×D44—21no—
11C22×C11×D8—21no—
12C2×C11×#127C2211yescharacteristic, complemented
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323—21no—
15C22×#4323—22no—
16C2×#66983—21no—
17D4×D44—22no—
18D4×D44—22no—
19D4×D44—22no—
20D4×D44C2214yescomplemented
21C2×#66948—21no—
22C2×#66935—22no—
23C2×#66927C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C11×#459—22no—
26C11×#459C2214yescomplemented
27C2×C11×C4⋊C8C2211yescharacteristic, complemented
28C2×C11×#102—21no—
29C2×#66896—21no—
30#10622686—22no—
31#10622686C2214yescomplemented
32#10622685—22no—
33#10622685C2214yescomplemented
34C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
35C2×C4×C11⋊C8C2211yescharacteristic, complemented
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622123C2214yescomplemented
38#10622121C2214yescomplemented
39C24×D11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—21no—
45C22×C22⋊D11—22no—
46C2×D4×D11—24no—
47C2×D4×D11—24no—
48C2×D4×D11—44no—
49C2×D4×D11—44no—
50C22×D44—22no—
51C22×D44—24no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—24no—
55C22×D44—44no—
56C22×D44—44no—
57C22×D44D411yescharacteristic
58C22×D44D412yes—
59C22×C4×D11—21no—
60C2×C11×D8—24no—
61C2×C11×D8—44no—
62C22×C8×C11—21no—
63C11×#127—21no—
64C11×#127—21no—
65C11×#127—21no—
66C11×#127C2312yescomplemented
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11D412yes—
70C4×D4×C11C2312yes—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4323—24no—
75C2×#4323—28no—
76C2×#4323—48no—
77C2×#4323—44no—
78#66983—24no—
79#66983—24no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85#66948—24no—
86#66948—24no—
87#66935—28no—
88#66935—28no—
89#66927—21no—
90#66927—21no—
91#66927D412yes—
92#66927C2312yes—
93C4×D44—21no—
94C4×D44—21no—
95C4×D44D412yes—
96C4×D44C2312yes—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2312yescomplemented
99C11×#102—24no—
100#66896—24no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)C2312yescomplemented
103C4×C11⋊C8—21no—
104C4×C11⋊C8C2312yescomplemented
105C2×#1619—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—41no—
108C23×D11—21no—
109C23×D11—22no—
110C23×D11—28no—
111C23×D11—48no—
112C23×D11—48no—
113C23×D11—84no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11D814yescomplemented
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—28no—
138C2×C22⋊D11—48no—
139C22×Dic11—21no—
140D4×D11—48no—
141D4×D11—416no—
142D4×D11—48no—
143C2×D44—28no—
144C2×D44—21no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—44no—
152C2×D44—48no—
153C2×D44—48no—
154C2×D44—416no—
155C2×D44—48no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44D814yescomplemented
161C2×D44C2×D412yes—
162C2×D44C2×D414yes—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C11×D8—48no—
168C2×C8×C11—22no—
169C2×C8×C11—42no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2411yescharacteristic
178#4323—416no—
179#4323—48no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—22no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2×D412yes—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—42no—
189C2×D42—111no—
190C2×#493—111no—
191C2×#459—111no—
192C2×#459D1111yescharacteristic, complemented
193#1619—118no—
194C2×#331—111no—
195C2×D4⋊C8—111no—
196C2×D4⋊C8—111no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11#12011yescharacteristic
206C22×D11—22no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—416no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—416no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—88no—
217C22×D11—832no—
218D4×C11—22no—
219D4×C11—24no—
220D4×C11—44no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—82no—
226D4×C11—82no—
227D4×C11—82no—
228D4×C11C2×D814yescomplemented
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11C2×D812yes—
239C2×C4×C11C2×D812yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—416no—
246C2×Dic11—22no—
247C2×Dic11—42no—
248D44—22no—
249D44—24no—
250D44—44no—
251D44—416no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—42no—
256D44—44no—
257D44—44no—
258D44—82no—
259D44C2×D814yescomplemented
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—44no—
263C8×C11—42no—
264C11⋊C8—24no—
265C11⋊C8—42no—
266C23×D4—221no—
267C23×D4—221no—
268C22×D8—21no—
269C22×D8—222no—
270C22×D8—221no—
271D42—114no—
272D42—222no—
273D42—222no—
274D42—222no—
275C2×#127—111no—
276C2×#127C2×D1111yescharacteristic, complemented
277C2×#121—221no—
278C2×#121—221no—
279C2×#120—222no—
280C2×C4×D4—111no—
281C2×C4×D4C2×D1111yescharacteristic
282#493—114no—
283#493—222no—
284#459—22no—
285#459—114no—
286#459—222no—
287#459C2×D1114yescomplemented
288C2×C4⋊C8—111no—
289C2×C4⋊C8C2×D1111yescharacteristic, complemented
290C2×#102—21no—
291C2×#102—221no—
292C2×C4×C8—111no—
293#331—114no—
294D4⋊C8—114no—
295D4⋊C8—114no—
296C22×C11—24no—
297C22×C11—48no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—82no—
303C22×C11—164no—
304C22×C11#44712yes—
305C22×C11#44712yes—
306C22×C11#45312yes—
307C22×C11C2×#12011yescharacteristic
308C2×D11—24no—
309C2×D11—48no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—832no—
316C2×D11—88no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11#44712yes—
321C4×C11#44712yes—
322C4×C11C22×D811yescharacteristic
323C4×C11C22×D811yescharacteristic
324C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
326Dic11—42no—
327C25—222no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—111no—
332C22×D4—112no—
333C22×D4—224no—
334C22×D4—222no—
335C22×D4—224no—
336C22×D4—224no—
337C22×D4—222no—
338C22×D4—224no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4—444no—
342C22×D4—444no—
343C22×D4—444no—
344C22×D4—444no—
345C22×D4C22⋊D1111yescharacteristic
346C23×C4—21no—
347C23×C4—221no—
348C2×D8—24no—
349C2×D8—44no—
350C2×D8—224no—
351C2×D8—228no—
352C2×D8—448no—
353C2×D8—444no—
354C22×C8—21no—
355C22×C8—221no—
356C22×C8—221no—
357#127—21no—
358#127—21no—
359#127—21no—
360#127—112no—
361#127—112no—
362#127—221no—
363#127—221no—
364#127C22×D1112yescomplemented
365#121—224no—
366#121—224no—
367#121—224no—
368#121—224no—
369#120—228no—
370#120—228no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—112no—
374C4×D4—112no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22⋊D1112yes—
378C4×D4C22×D1112yes—
379C2×C4⋊C4—111no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—221no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—112no—
387C4⋊C8—221no—
388C4⋊C8C22×D1112yescomplemented
389#102—24no—
390#102—224no—
391C4×C8—112no—
392C4×C8—221no—
393C2×C11—44no—
394C2×C11—162no—
395C2×C11#161914yescomplemented
396C2×C11C2×#44711yescharacteristic
397C2×C11C2×#44711yescharacteristic
398C2×C11C2×#45311yescharacteristic
399D11—44no—
400D11—84no—
401C24—21no—
402C24—41no—
403C24—228no—
404C24—221no—
405C24—222no—
406C24—448no—
407C24—448no—
408C24—884no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—114no—
423C2×D4—112no—
424C2×D4—114no—
425C2×D4—228no—
426C2×D4—228no—
427C2×D4—222no—
428C2×D4—221no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—444no—
435C2×D4—448no—
436C2×D4—4416no—
437C2×D4—448no—
438C2×D4—448no—
439C2×D4—448no—
440C2×D4—4416no—
441C2×D4—448no—
442C2×D4—448no—
443C2×D4—442no—
444C2×D4—442no—
445C2×D4—442no—
446C2×D4—442no—
447C2×D4#432314yescomplemented
448C2×D4C2×C22⋊D1112yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462D8—48no—
463D8—4416no—
464D8—448no—
465C2×C8—22no—
466C2×C8—42no—
467C2×C8—224no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—442no—
471C4⋊C4—21no—
472C4⋊C4—112no—
473C4⋊C4—221no—
474C4⋊C4C2×C22⋊D1112yes—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—228no—
478C22⋊C4—222no—
479C22⋊C4—222no—
480C42D4×D1111yescharacteristic
481C42D4×D1111yescharacteristic
482C42C2×C22⋊D1111yescharacteristic
483C42C23×D1111yescharacteristic
484C11C2×#161911yescharacteristic, complemented, Sylow
485C23—22no—
486C23—24no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—224no—
494C23—222no—
495C23—224no—
496C23—4416no—
497C23—4416no—
498C23—442no—
499C23—442no—
500C23—444no—
501C23—444no—
502C23—444no—
503C23—888no—
504C23—8832no—
505C23#6699011yescharacteristic
506D4—22no—
507D4—24no—
508D4—44no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—82no—
514D4—82no—
515D4—82no—
516D4—114no—
517D4—224no—
518D4—222no—
519D4—444no—
520D4—4416no—
521D4—4416no—
522D4—444no—
523D4—442no—
524D4—442no—
525D4—442no—
526D4—442no—
527D4—444no—
528D4—882no—
529D4C2×#432314yescomplemented
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—222no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4D8×D1112yes—
542C2×C4#6696412yes—
543C2×C4C2×#432312yes—
544C2×C4#6699011yescharacteristic
545C2×C4#6699011yescharacteristic
546C2×C4#6699011yescharacteristic
547C2×C4#6700212yes—
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C22×C22⋊D1111yescharacteristic
551C8—42no—
552C8—224no—
553C8—442no—
554C22—24no—
555C22—42no—
556C22—48no—
557C22—42no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—164no—
562C22—224no—
563C22—442no—
564C22—448no—
565C22—442no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—8832no—
570C22—888no—
571C22#1062264912yes—
572C22#1062276912yes—
573C22#1062281112yes—
574C22C2×#6699011yescharacteristic
575C4—21no—
576C4—21no—
577C4—42no—
578C4—442no—
579C4#1062264912yes—
580C4#1062276912yes—
581C4C2×D8×D1111yescharacteristic
582C4C2×#6696411yescharacteristic
583C4C22×#432311yescharacteristic
584C4C2×#6700211yescharacteristic
585C2—44no—
586C2—162no—
587C2—444no—
588C2—884no—
589C2#1306766914yesdirect product factor
590C2C2×#1062276911yescharacteristic
591C2C2×#1062264911yescharacteristic
592C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#459C2
socleC23×C11#120
hypercenterC2×#459D11
hypocenterC11C2×#1619
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×D4×D44C2semidirect
2. C2×#10622686C2semidirect
3. C2×#10622685C2semidirect
4. #13067669C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#459C2semidirect
12. C2×C11×#127C22semidirect
20. D4×D44C22semidirect
26. C11×#459C22semidirect
27. C2×C11×C4⋊C8C22semidirect
31. #10622686C22semidirect
33. #10622685C22semidirect
34. C2×C4⋊(C11⋊C8)C22semidirect
35. C2×C4×C11⋊C8C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622121C22semidirect
66. C11×#127C23semidirect
98. C11×C4⋊C8C23semidirect
102. C4⋊(C11⋊C8)C23semidirect
104. C4×C11⋊C8C23semidirect
127. C2×D4×C11D8semidirect
160. C2×D44D8semidirect
192. C2×#459D11semidirect
228. D4×C11C2×D8semidirect
259. D44C2×D8semidirect
276. C2×#127C2×D11semidirect
287. #459C2×D11semidirect
289. C2×C4⋊C8C2×D11semidirect
364. #127C22×D11semidirect
388. C4⋊C8C22×D11semidirect
395. C2×C11#1619semidirect
447. C2×D4#4323semidirect
484. C11C2×#1619semidirect
529. D4C2×#4323semidirect
589. C2#13067669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106226862
C2×#106226852
#130676692
C2×#106221232
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4592
C2×#161911