Finite Group Databasebeta

← C2×#13069815 #14781232

Subgroups — C2×#13069815 #14781232

Order 2816.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C22×#66872C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C8C211yesmaximal, characteristic
6C2×#10622600C211yesmaximal, characteristic
7#13069815C218yesmaximal, direct product factor
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×#66950—22no—
20C2×#66950—24no—
21C2×#66950—24no—
22C2×#66950C2214yes—
23C2×C11⋊#95—21no—
24C2×(C2×D11)⋊C8—24no—
25C2×(C2×D11)⋊C8C2214yes—
26C2×#66880—24no—
27C2×#66880C2214yescomplemented
28#10622600—22no—
29#10622600C2214yes—
30C2×#66874—24no—
31C2×#66874C2214yescomplemented
32C2×#66872—24no—
33C2×#66872C2214yescomplemented
34C11×#340C2214yescomplemented
35C24×D11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11D411yescharacteristic
42C22×C4×D11—22no—
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11—22no—
48C22×C4×D11D412yes—
49C22×C4×D11C2312yes—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—21no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D414yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—44no—
74C2×C4⋊Dic11—28no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8D414yes—
83C22×C11⋊C8C2312yes—
84#66950—216no—
85#66950—28no—
86#66950—28no—
87C11⋊#95—24no—
88(C2×D11)⋊C8—28no—
89#66880—28no—
90#66874—28no—
91#66872—28no—
92C2×#2035—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11SD1614yes—
101C23×D11C2×D412yes—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—24no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11C2×D412yes—
130C2×C4×D11—24no—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11—44no—
143C2×Dic22—24no—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—42no—
152C2×Dic22—44no—
153C2×Dic22—42no—
154C2×Dic22—44no—
155C2×Dic22C2×D414yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—44no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×D414yes—
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4—48no—
168C4⋊Dic11—216no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—42no—
172C2×C11⋊C8—28no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C2×D414yes—
176C22×C22⋊Q8—111no—
177C22×#106—111no—
178C22×#103—111no—
179C22×#103—111no—
180C22×C22⋊C8—111no—
181C2×#380—111no—
182#2035—118no—
183C2×#340D1111yescharacteristic, complemented
184C23×C11#12012yes—
185C23×C11#12112yes—
186C23×C11#12312yes—
187C23×C11C2×SD1612yes—
188C23×C11#13512yes—
189C23×C11#13712yes—
190C23×C11#13712yes—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11C2×SD1614yes—
206C2×C4×C11—24no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12114yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12114yes—
218C2×C4×C11#12314yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12414yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—48no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—84no—
239C4×D11—42no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—42no—
243C4×D11—48no—
244Dic22—24no—
245Dic22—24no—
246Dic22—42no—
247Dic22—42no—
248Dic22—48no—
249C8×C11—42no—
250C11⋊C8—24no—
251C23×Q8—111no—
252C24×C4—111no—
253C23×C8—111no—
254C23×C8C2×D1111yescharacteristic
255C2×C22⋊Q8—114no—
256C2×C22⋊Q8—222no—
257C2×C22⋊Q8—224no—
258C2×C22⋊Q8—224no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—221no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C4⋊C4C2×D1111yescharacteristic
263C22×C22⋊C4—221no—
264C22×C22⋊C4—221no—
265C2×#106—114no—
266C2×#106—224no—
267C2×#103—114no—
268C2×#103—114no—
269C2×#103—224no—
270C2×#103—224no—
271C2×C22⋊C8—114no—
272C2×C22⋊C8—224no—
273#380—114no—
274#380—222no—
275C2×#95—221no—
276#340C2×D1114yescomplemented
277C22×C11#39414yes—
278C22×C11#44814yes—
279C22×C11#45214yes—
280C22×C11#46514yes—
281C22×C11#47014yes—
282C22×C11#48314yes—
283C22×C11#48514yes—
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11C2×#12311yescharacteristic
287C22×C11C22×SD1611yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C2×D11—24no—
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—416no—
299C4×C11—44no—
300C4×C11—82no—
301C4×C11#39414yes—
302C4×C11C2×#12111yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12411yescharacteristic
306Dic11—44no—
307Dic11—42no—
308Dic11—82no—
309C25—111no—
310C22×Q8—114no—
311C22×Q8—112no—
312C22×Q8—222no—
313C22×Q8—221no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×Q8—222no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—111no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4—221no—
324C23×C4—222no—
325C23×C4—222no—
326C23×C4—222no—
327C23×C4—222no—
328C23×C4—222no—
329C23×C4—222no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—114no—
336C22×C8—112no—
337C22×C8—222no—
338C22×C8—222no—
339C22×C8C22×D1112yes—
340C22⋊Q8—228no—
341C22⋊Q8—2216no—
342C22⋊Q8—228no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4D4414yes—
355C2×C4⋊C4C22×D1112yes—
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—228no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—444no—
361#106—228no—
362#103—228no—
363#103—228no—
364C22⋊C8—228no—
365#95—224no—
366C2×C11#203518yescomplemented
367C2×C11C2×#39411yescharacteristic
368C2×C11C2×#44811yescharacteristic
369C2×C11C2×#45211yescharacteristic
370C2×C11C2×#46511yescharacteristic
371C2×C11C2×#47011yescharacteristic
372C2×C11C2×#48311yescharacteristic
373C2×C11C2×#48511yescharacteristic
374D11—44no—
375C24—114no—
376C24—112no—
377C24—222no—
378C24—222no—
379C24—222no—
380C24—222no—
381C24—222no—
382C24—222no—
383C24D4×D1111yescharacteristic
384C2×Q8—114no—
385C2×Q8—224no—
386C2×Q8—222no—
387C2×Q8—228no—
388C2×Q8—228no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—444no—
394C2×Q8—442no—
395C2×Q8—442no—
396C2×Q8—444no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—112no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4—444no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4C2×D4412yes—
431C22×C4#433912yes—
432C22×C4#433912yes—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1112yes—
435C22×C4D4×D1112yes—
436C22×C4#434312yes—
437C22×C4C23×D1111yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—44no—
442C2×C8—114no—
443C2×C8—228no—
444C2×C8—222no—
445C2×C8—222no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—2216no—
452C4⋊C4—222no—
453C4⋊C4—222no—
454C4⋊C4—442no—
455C4⋊C4C2×D4414yes—
456C22⋊C4—2216no—
457C22⋊C4—448no—
458C11C2×#203511yescharacteristic, complemented, Sylow
459C23—114no—
460C23—228no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—228no—
468C23—228no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23—444no—
473C23#6693512yes—
474C23#6693712yes—
475C23#6694712yes—
476C23#6696512yes—
477C23SD16×D1112yes—
478C23#6696812yes—
479C23#6697112yes—
480C23C2×D4×D1111yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485Q8—448no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—444no—
501C2×C4—448no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—448no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—884no—
511C2×C4#6692814yes—
512C2×C4#6693512yes—
513C2×C4#6693714yes—
514C2×C4#6693712yes—
515C2×C4#6694714yes—
516C2×C4#6694712yes—
517C2×C4#6694814yes—
518C2×C4C22×D4411yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434311yescharacteristic
524C8—42no—
525C8—224no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—4416no—
534C22#1062228514yes—
535C22#1062239114yes—
536C22#1062239614yes—
537C22#1062241914yes—
538C22#1062242914yes—
539C22#1062247514yes—
540C22#1062250114yes—
541C22C2×#6693511yescharacteristic
542C22C2×#6693711yescharacteristic
543C22C2×#6694711yescharacteristic
544C22C2×#6696511yescharacteristic
545C22C2×SD16×D1111yescharacteristic
546C22C2×#6696811yescharacteristic
547C22C2×#6697111yescharacteristic
548C4—44no—
549C4—82no—
550C4—442no—
551C4—444no—
552C4—882no—
553C4#1062228514yes—
554C4C2×#6692811yescharacteristic
555C4C2×#6693711yescharacteristic
556C4C2×#6694711yescharacteristic
557C4C2×#6694811yescharacteristic
558C2—444no—
559C2#1306981518yesdirect product factor
560C2C2×#1062228511yescharacteristic
561C2C2×#1062241911yescharacteristic
562C2C2×#1062239611yescharacteristic
563C2C2×#1062239111yescharacteristic
564C2C2×#1062242911yescharacteristic
565C2C2×#1062247511yescharacteristic
566C2C2×#1062250111yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC24×D11D4
hypercenterC2×#340D11
hypocenterC11C2×#2035
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#66872C2semidirect
3. C22×#66880C2semidirect
4. C22×#66874C2semidirect
7. #13069815C2direct (N × H)
8. C2×C11×#340C2semidirect
27. C2×#66880C22semidirect
31. C2×#66874C22semidirect
33. C2×#66872C22semidirect
34. C11×#340C22semidirect
183. C2×#340D11semidirect
276. #340C2×D11semidirect
366. C2×C11#2035semidirect
458. C11C2×#2035semidirect
559. C2#13069815direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#668722
C22×#668802
C22×#668742
C22×(C2×D11)⋊C82
C2×#106226002
#130698152
C2×C11×#3402
C2×#203511