Finite Group Databasebeta

← C2×#13078972 #15623011

Subgroups — C2×#13078972 #15623011

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C2×#10623056C211yesmaximal, characteristic
3#13078972C2116yesmaximal, direct product factor
4C2×#10622326C212yesmaximal, complemented
5C2×#10622327C212yesmaximal, complemented
6C2×#10622310C212yesmaximal, complemented
7C2×#10622307C212yesmaximal, complemented
8C2×#10622746C211yesmaximal, characteristic, complemented
9C2×#10622744C211yesmaximal, characteristic, complemented
10C2×#10622726C211yesmaximal, characteristic, complemented
11C22×#66885C211yesmaximal, characteristic, complemented
12C2×C11×#405C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20#10623056—24no—
21#10623056C2218yes—
22#10623050—24no—
23#10623050C2218yescomplemented
24C2×#66948—21no—
25C2×#66948—21no—
26C2×#66943—21no—
27C2×#66941—21no—
28C2×#66935—22no—
29C2×#66931—22no—
30C2×#66928C2212yes—
31C2×#66927C2212yes—
32C2×#66923C2212yescomplemented
33C2×#66922C2212yescomplemented
34C11×#405C2218yescomplemented
35C2×C11×#97C2212yescomplemented
36C2×C4×C8×C11C2212yescomplemented
37#10622746C2218yescomplemented
38#10622744C2218yescomplemented
39#10622726C2218yescomplemented
40C2×#66885C2212yes—
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66885C2212yes—
44C2×#66885C2218yescomplemented
45C2×#66885C2211yescharacteristic, complemented
46C2×#66885C2211yescharacteristic, complemented
47C2×#66885C2212yescomplemented
48C2×#66880C2211yescharacteristic, complemented
49C2×#66880C2211yescharacteristic, complemented
50C2×#66880C2212yescomplemented
51#10622327C22116yescomplemented
52#10622326C22116yescomplemented
53#10622310C22116yescomplemented
54#10622307C22116yescomplemented
55C24×D11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C23×Dic11—21no—
59C2×#4339—22no—
60C2×#4339—24no—
61C2×#4339—24no—
62C2×#4339C2314yes—
63C22×D44—24no—
64C22×D44—24no—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44C2312yes—
70C22×D44C2311yescharacteristic
71C22×D44C2314yes—
72C22×C4×D11—21no—
73C22×Dic22—22no—
74C22×Dic22C2311yescharacteristic
75C2×C11×M16—24no—
76C2×C11×M16C2314yes—
77C22×C8×C11—24no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2312yes—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2314yes—
82C11×#117D414yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11C2312yes—
88C2×C22⋊Dic11—21no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91#66979—22no—
92#66979C2314yes—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—21no—
103#66948—28no—
104#66948—28no—
105#66943—28no—
106#66941—28no—
107#66935—216no—
108#66931—216no—
109#66928—24no—
110#66928C2318yes—
111#66927—24no—
112#66927C2318yes—
113#66923—24no—
114#66923C2318yescomplemented
115#66922—24no—
116#66922C2318yescomplemented
117C11×#97C2318yescomplemented
118C4×C8×C11C2318yescomplemented
119#66885C2318yes—
120#66885C2318yes—
121#66885C2318yes—
122#66885C2318yes—
123#66885C2314yescomplemented
124#66885C2314yescomplemented
125#66885C2318yescomplemented
126#66880C2314yescomplemented
127#66880C2314yescomplemented
128#66880C2318yescomplemented
129C2×#3136—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—82no—
136C23×D11—82no—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4114yes—
142C22×C4×C11#4114yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2412yes—
145C2×C22⋊D11—24no—
146C2×C22⋊D11—44no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—24no—
152C22×Dic11—82no—
153#4339—28no—
154#4339—28no—
155#4339—48no—
156C2×D44—21no—
157C2×D44—22no—
158C2×D44—24no—
159C2×D44—28no—
160C2×D44—28no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—28no—
164C2×D44—28no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—44no—
168C2×D44—48no—
169C2×D44—84no—
170C2×D44—84no—
171C2×D44C2414yes—
172C2×D44C2412yes—
173C2×C4×D11—24no—
174C2×C4×D11—44no—
175C2×Dic22—21no—
176C2×Dic22—28no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—84no—
180C2×Dic22C2412yes—
181C11×M16—28no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—28no—
185C2×C8×C11—24no—
186C2×C8×C11C2412yes—
187C2×C8×C11C2414yes—
188C2×C8×C11C2412yes—
189C11×C4⋊C4C2×D414yes—
190C11×C4⋊C4C2×D414yes—
191C11×C22⋊C4C2×D418yes—
192C42×C11C2×D414yes—
193C42×C11C2414yes—
194C22⋊Dic11—24no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197C4⋊Dic11—21no—
198C4⋊Dic11—22no—
199C4⋊Dic11—28no—
200C4⋊Dic11—21no—
201C4⋊Dic11—24no—
202C4⋊Dic11C2412yes—
203C4⋊Dic11C2414yes—
204C4⋊Dic11C2412yes—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207C4×Dic11—24no—
208C2×#544—111no—
209C2×#535—111no—
210#3136—1116no—
211C2×#490—112no—
212C2×#489—112no—
213C2×#488—112no—
214C2×#486—112no—
215C2×#417—111no—
216C2×#418—111no—
217C2×#416—111no—
218C22×#102—111no—
219C2×#405D1111yescharacteristic, complemented
220C23×C11—22no—
221C23×C11—22no—
222C23×C11#12414yes—
223C23×C11C22×D412yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—42no—
228C22×D11—48no—
229C22×D11—44no—
230C22×D11—42no—
231C22×D11—44no—
232C22×D11—42no—
233C22×D11—44no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—816no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11#12414yes—
240C2×C4×C11#12418yes—
241C2×C4×C11C22×D414yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4112yes—
246C2×C4×C11C2×#4112yes—
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—48no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11—84no—
260D44—24no—
261D44—24no—
262D44—22no—
263D44—22no—
264D44—44no—
265D44—48no—
266D44—42no—
267D44—88no—
268D44—88no—
269C4×D11—48no—
270Dic22—22no—
271Dic22—22no—
272Dic22—42no—
273Dic22—88no—
274C8×C11—22no—
275C8×C11—22no—
276C8×C11—24no—
277C22×#41—111no—
278C23×D4—111no—
279C22×M16C2×D1111yescharacteristic
280C23×C8C2×D1111yescharacteristic
281#544—118no—
282#544—224no—
283#535—118no—
284#535—224no—
285C2×C4⋊Q8—112no—
286C2×C4⋊Q8—221no—
287C2×#127—112no—
288C2×#125—112no—
289C2×#125—221no—
290C2×#124—112no—
291C2×C22⋊Q8—222no—
292C2×#121—221no—
293C2×#121—221no—
294C2×#120—222no—
295C2×#117—111no—
296C2×#117C2×D1111yescharacteristic
297C22×C4⋊C4—111no—
298#490—1116no—
299#489—1116no—
300#488—1116no—
301#486—1116no—
302#418—118no—
303#417—118no—
304#416—118no—
305C2×#103—111no—
306C2×#103—112no—
307C2×#103—111no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—111no—
313C2×#102—112no—
314C2×#102—111no—
315C2×#102—118no—
316#405C2×D1118yescomplemented
317C2×#97C2×D1112yescomplemented
318C2×C4×C8C2×D1112yescomplemented
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11C2×#12414yes—
323C22×C11C2×#12412yes—
324C22×C11#57612yes—
325C22×C11#57712yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—44no—
328C2×D11—42no—
329C2×D11—44no—
330C2×D11—42no—
331C2×D11—44no—
332C2×D11—42no—
333C2×D11—816no—
334C2×D11—84no—
335C2×D11—88no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11C2×#12412yes—
339C4×C11C2×#12414yes—
340C4×C11C22×#4111yescharacteristic
341C4×C11C22×#4111yescharacteristic
342Dic11—42no—
343Dic11—42no—
344Dic11—44no—
345Dic11—42no—
346C25—221no—
347C2×#41—114no—
348C2×#41—222no—
349C2×#41—224no—
350C2×#41—224no—
351C22×Q8—111no—
352C22×Q8—222no—
353C22×D4—112no—
354C22×D4—111no—
355C22×D4—114no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4—222no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4—224no—
362C22×D4—224no—
363C23×C4—221no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—24no—
367C2×M16C22×D1114yes—
368C22×C8—24no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1114yes—
372C22×C8C22×D1112yes—
373C4⋊Q8—118no—
374C4⋊Q8—228no—
375C4⋊Q8—224no—
376#127—118no—
377#127—224no—
378#125—118no—
379#125—228no—
380#125—224no—
381#124—118no—
382#124—224no—
383C22⋊Q8—2216no—
384#121—228no—
385#121—228no—
386#120—2216no—
387#117—114no—
388#117—222no—
389#117D4414yes—
390#117C22×D1114yes—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4D4411yescharacteristic
401C2×C4⋊C4D4411yescharacteristic
402C2×C22⋊C4—221no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4D4412yes—
406C2×C42—221no—
407C2×C42C22×D1112yes—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—118no—
414#102—118no—
415#102—114no—
416#102—114no—
417#102—118no—
418#97C22×D1118yescomplemented
419C4×C8C22×D1118yescomplemented
420C2×C11—24no—
421C2×C11#313614yescomplemented
422C2×C11C22×#12411yescharacteristic
423C2×C11C2×#57611yescharacteristic
424C2×C11C2×#57711yescharacteristic
425D11—82no—
426D11—84no—
427C24—222no—
428C24—221no—
429C24—224no—
430C24—444no—
431C24—882no—
432C24—882no—
433C24C2×D4411yescharacteristic
434#41—228no—
435#41—228no—
436#41—448no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—228no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—884no—
443C2×D4—114no—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—224no—
447C2×D4—222no—
448C2×D4—221no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—224no—
453C2×D4—228no—
454C2×D4—228no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—444no—
458C2×D4—444no—
459C2×D4—448no—
460C2×D4—884no—
461C2×D4—884no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—444no—
469C22×C4—882no—
470C22×C4C2×D4412yes—
471C22×C4C2×D4412yes—
472C22×C4C2×D4412yes—
473C22×C4C2×D4411yescharacteristic
474C22×C4#433914yes—
475C22×C4#433914yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—28no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—28no—
482C2×C8—24no—
483C2×C8C23×D1112yes—
484C2×C8C23×D1114yes—
485C2×C8C23×D1112yes—
486C4⋊C4—114no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C4⋊C4—228no—
496C4⋊C4C2×D4414yes—
497C4⋊C4C2×D4414yes—
498C22⋊C4—224no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4C2×D4418yes—
502C42—224no—
503C42C2×D4414yes—
504C42C23×D1114yes—
505C11C2×#313611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—224no—
509C23—222no—
510C23—442no—
511C23—448no—
512C23—444no—
513C23—442no—
514C23—444no—
515C23—442no—
516C23—444no—
517C23—884no—
518C23—884no—
519C23—8816no—
520C23#6692814yes—
521C23C22×D4412yes—
522C23C22×D4411yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—442no—
526Q8—888no—
527D4—224no—
528D4—224no—
529D4—222no—
530D4—222no—
531D4—448no—
532D4—448no—
533D4—444no—
534D4—442no—
535D4—888no—
536D4—888no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—444no—
546C2×C4—442no—
547C2×C4—448no—
548C2×C4—884no—
549C2×C4#6692814yes—
550C2×C4#6692818yes—
551C2×C4C22×D4414yes—
552C2×C4C22×D4414yes—
553C2×C4C22×D4412yes—
554C2×C4C22×D4411yescharacteristic
555C2×C4C2×#433912yes—
556C2×C4C2×#433912yes—
557C2×C4C2×#433914yes—
558C2×C4C2×#433914yes—
559C2×C4C24×D1111yescharacteristic
560C8—22no—
561C8—22no—
562C8—24no—
563C22—28no—
564C22—22no—
565C22—22no—
566C22—442no—
567C22—444no—
568C22—442no—
569C22—444no—
570C22—442no—
571C22—444no—
572C22—8816no—
573C22—888no—
574C22—884no—
575C22C2×#6692814yes—
576C22C2×#6692812yes—
577C22#1062328212yes—
578C22#1062328312yes—
579C22C23×D4411yescharacteristic
580C4—24no—
581C4—24no—
582C4—442no—
583C4—444no—
584C4—442no—
585C4—442no—
586C4C2×#6692814yes—
587C4C2×#6692812yes—
588C4C22×#433911yescharacteristic
589C4C22×#433911yescharacteristic
590C2—24no—
591C2—884no—
592C2—882no—
593C2#1307897214yesdirect product factor
594C2C22×#6692811yescharacteristic
595C2C2×#1062328311yescharacteristic
596C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC2×#10623056C2
hypercenterC2×#405D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13078972C2direct (N × H)
4. C2×#10622326C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622310C2semidirect
7. C2×#10622307C2semidirect
8. C2×#10622746C2semidirect
9. C2×#10622744C2semidirect
10. C2×#10622726C2semidirect
11. C22×#66885C2semidirect
12. C2×C11×#405C2semidirect
23. #10623050C22semidirect
32. C2×#66923C22semidirect
33. C2×#66922C22semidirect
34. C11×#405C22semidirect
35. C2×C11×#97C22semidirect
36. C2×C4×C8×C11C22semidirect
37. #10622746C22semidirect
38. #10622744C22semidirect
39. #10622726C22semidirect
44. C2×#66885C22semidirect
45. C2×#66885C22semidirect
46. C2×#66885C22semidirect
47. C2×#66885C22semidirect
48. C2×#66880C22semidirect
49. C2×#66880C22semidirect
50. C2×#66880C22semidirect
51. #10622327C22semidirect
52. #10622326C22semidirect
53. #10622310C22semidirect
54. #10622307C22semidirect
114. #66923C23semidirect
116. #66922C23semidirect
117. C11×#97C23semidirect
118. C4×C8×C11C23semidirect
123. #66885C23semidirect
124. #66885C23semidirect
125. #66885C23semidirect
126. #66880C23semidirect
127. #66880C23semidirect
128. #66880C23semidirect
219. C2×#405D11semidirect
316. #405C2×D11semidirect
317. C2×#97C2×D11semidirect
318. C2×C4×C8C2×D11semidirect
418. #97C22×D11semidirect
419. C4×C8C22×D11semidirect
421. C2×C11#3136semidirect
505. C11C2×#3136semidirect
593. C2#13078972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106230562
#130789722
C2×#106223262
C2×#106223272
C2×#106223102
C2×#106223072
C2×#106227462
C2×#106227442
C2×#106227262
C22×#668852
C2×C11×#4052
C2×#313611