Finite Group Databasebeta

← C2×#13076647 #14959903

Subgroups — C2×#13076647 #14959903

Order 2816.

2998 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic
3#13076647C2116yesmaximal, direct product factor
4C2×#10622562C212yesmaximal, complemented
5C2×#10622274C211yesmaximal, characteristic, complemented
6C2×#10622596C211yesmaximal, characteristic, complemented
7C2×#10622574C212yesmaximal, complemented
8C2×#10622572C212yesmaximal, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622560C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66991—28no—
24C2×#66991C2218yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C2×#66949—28no—
34C2×#66949C2218yescomplemented
35C11×#394C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37#10622835C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622596C2218yescomplemented
43#10622574C22116yescomplemented
44#10622572C22116yescomplemented
45#10622562C22116yescomplemented
46#10622560C22116yescomplemented
47#10622277C2218yescomplemented
48#10622274C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—44no—
53C22×D4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11C2318yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—44no—
68C22×C4×D11D418yes—
69C22×C4×D11C2314yes—
70C22×Dic22—24no—
71C22×Dic22—44no—
72C22×Dic22C2314yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4—44no—
77C2×C11×C22⋊C4C2318yes—
78C2×C11×C22⋊C4C2318yes—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11—44no—
82C2×C22⋊Dic11C2318yes—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85#66991—232no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—44no—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2318yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2318yes—
102#66949—232no—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C2×#2816—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11C2414yes—
117C24×C11C2411yescharacteristic
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11C2×D414yes—
123C23×D11C2412yes—
124C2×D4×C11—28no—
125C2×D4×C11—48no—
126C2×D4×C11—416no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11C2×D414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—48no—
143C2×C22⋊D11—48no—
144C2×C22⋊D11—432no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C2×C4×D11—416no—
164C2×C4×D11—48no—
165C2×C4×D11C2×D4116yes—
166C2×Dic22—28no—
167C2×Dic22—48no—
168C2×Dic22—416no—
169C11×C4⋊C4—28no—
170C11×C22⋊C4—48no—
171C11×C22⋊C4—48no—
172C22⋊Dic11—216no—
173C22⋊Dic11—48no—
174C22⋊Dic11—48no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—28no—
179C4⋊Dic11—48no—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—48no—
183C22×C22⋊Q8—111no—
184C22×#121—111no—
185#2816—1116no—
186C2×#399—112no—
187C2×#398—111no—
188C2×#398—111no—
189C2×#394—111no—
190C2×#394—112no—
191C2×#394—112no—
192C2×#394D1111yescharacteristic, complemented
193C2×#393—112no—
194C2×#381—111no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—48no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11C22×D412yes—
210C23×C11H(5,𝔽2)14yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C112−1+414yes—
214C23×C11C2511yescharacteristic
215C22×D11—28no—
216C22×D11—28no—
217C22×D11—28no—
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11C22×D414yes—
225D4×C11—416no—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—48no—
239C2×C4×C11C22×D414yes—
240C22⋊D11—432no—
241C2×Dic11—28no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—48no—
257C2×Dic11—48no—
258C2×Dic11C22×D414yes—
259C4×D11—416no—
260Dic22—416no—
261C23×Q8—111no—
262C23×D4—112no—
263C23×D4C2×D1111yescharacteristic
264C24×C4—111no—
265C2×C22⋊Q8—118no—
266C2×C22⋊Q8—228no—
267C2×#121—118no—
268C2×#121—228no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C22⋊C4C2×D1112yes—
283#399—1116no—
284#398—118no—
285#398—118no—
286#394—118no—
287#394—1116no—
288#394—1116no—
289#394C2×D1118yescomplemented
290#393—1116no—
291#381—118no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—111no—
296C2×#95C2×D1111yescharacteristic
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—816no—
305C22×C11#53414yes—
306C22×C11#53514yes—
307C22×C11#53614yes—
308C22×C11#56218yes—
309C22×C11#56218yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C2×H(5,𝔽2)12yes—
312C22×C11C2×H(5,𝔽2)11yescharacteristic
313C22×C11C2×H(5,𝔽2)11yescharacteristic
314C22×C11C2×2−1+412yes—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—24no—
318C2×D11—416no—
319C2×D11—44no—
320C2×D11—44no—
321C4×C11—24no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—44no—
325Dic11—24no—
326Dic11—42no—
327Dic11—42no—
328Dic11—44no—
329Dic11—44no—
330C25—111no—
331C25C22×D1112yes—
332C22×Q8—114no—
333C22×Q8—224no—
334C22×Q8—444no—
335C22×D4—24no—
336C22×D4—44no—
337C22×D4—118no—
338C22×D4—228no—
339C22×D4—444no—
340C22×D4—444no—
341C22×D4C22×D1114yes—
342C23×C4—111no—
343C23×C4—118no—
344C23×C4—114no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—444no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354C22⋊Q8—2232no—
355#121—2232no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—224no—
365C2×C4⋊C4—444no—
366C2×C4⋊C4—444no—
367C2×C4⋊C4C22×D1114yes—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4—444no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4C22×D1118yes—
383C2×C22⋊C4C22×D1118yes—
384#95—118no—
385#95—114no—
386#95—118no—
387#95—118no—
388#95C22×D1114yes—
389C2×C11—84no—
390C2×C11#281618yescomplemented
391C2×C11C2×#53411yescharacteristic
392C2×C11C2×#53511yescharacteristic
393C2×C11C2×#53611yescharacteristic
394C2×C11C2×#56212yes—
395C2×C11C2×#56212yes—
396D11—44no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—114no—
405C24—112no—
406C24—224no—
407C24—222no—
408C24—222no—
409C24—224no—
410C24C23×D1114yes—
411C24C23×D1111yescharacteristic
412C2×Q8—228no—
413C2×Q8—448no—
414C2×Q8—4416no—
415C2×D4—28no—
416C2×D4—48no—
417C2×D4—416no—
418C2×D4—2216no—
419C2×D4—448no—
420C2×D4—448no—
421C2×D4—4432no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—114no—
432C22×C4—112no—
433C22×C4—1116no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—4416no—
451C22×C4—448no—
452C22×C4D4×D1114yes—
453C22×C4C23×D1114yes—
454C22×C4C23×D1112yes—
455C22×C4C23×D1112yes—
456C22×C4C23×D1112yes—
457C4⋊C4—28no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—448no—
462C4⋊C4—448no—
463C22⋊C4—48no—
464C22⋊C4—48no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—2216no—
468C22⋊C4—448no—
469C22⋊C4—448no—
470C22⋊C4—448no—
471C11C2×#281611yescharacteristic, complemented, Sylow
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—114no—
487C23—228no—
488C23—228no—
489C23—224no—
490C23—222no—
491C23—222no—
492C23—224no—
493C23—228no—
494C23—448no—
495C23—448no—
496C23C2×D4×D1112yes—
497C23#6703714yes—
498C23#6703712yes—
499C23#6704212yes—
500C23#6704314yes—
501C23C24×D1111yescharacteristic
502Q8—4416no—
503D4—416no—
504D4—4432no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—114no—
519C2×C4—228no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—4416no—
533C2×C4—444no—
534C2×C4—448no—
535C2×C4—444no—
536C2×C4—448no—
537C2×C4C2×D4×D1114yes—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—816no—
546C22—224no—
547C22—224no—
548C22—224no—
549C22—444no—
550C22—444no—
551C22—4416no—
552C22#1062312014yes—
553C22#1062313814yes—
554C22#1062315218yes—
555C22#1062319818yes—
556C22#1062320614yes—
557C22C22×D4×D1111yescharacteristic
558C22C2×#6703712yes—
559C22C2×#6703711yescharacteristic
560C22C2×#6704211yescharacteristic
561C22C2×#6704312yes—
562C4—24no—
563C4—42no—
564C4—42no—
565C4—44no—
566C4—224no—
567C4—442no—
568C4—444no—
569C4—442no—
570C4—444no—
571C2—84no—
572C2—444no—
573C2#1307664718yesdirect product factor
574C2C2×#1062312011yescharacteristic
575C2C2×#1062313811yescharacteristic
576C2C2×#1062320611yescharacteristic
577C2C2×#1062315212yes—
578C2C2×#1062319812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#394D11
hypocenterC11C2×#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13076647C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622274C2semidirect
6. C2×#10622596C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622560C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#394C2semidirect
34. C2×#66949C22semidirect
35. C11×#394C22semidirect
37. #10622835C22semidirect
42. #10622596C22semidirect
43. #10622574C22semidirect
44. #10622572C22semidirect
45. #10622562C22semidirect
46. #10622560C22semidirect
47. #10622277C22semidirect
48. #10622274C22semidirect
192. C2×#394D11semidirect
289. #394C2×D11semidirect
390. C2×C11#2816semidirect
471. C11C2×#2816semidirect
573. C2#13076647direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669912
#130766472
C2×#106225622
C2×#106222742
C2×#106225962
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106225602
C2×#106222772
C2×C11×#3942
C2×#281611