Finite Group Databasebeta

← C2×#13074510 #14920489

Subgroups — C2×#13074510 #14920489

Order 2816.

3218 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13074510C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622561C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622835C212yesmaximal, complemented
9C2×#10622833C212yesmaximal, complemented
10C2×#10622559C212yesmaximal, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C24×Dic11C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×D4×Dic11—28no—
25C2×D4×Dic11C2218yescomplemented
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66932—28no—
34C2×#66932C2218yescomplemented
35C11×#392C2218yes—
36C2×C11×#95C2211yescharacteristic
37#10622835C2218yescomplemented
38#10622835C22116yescomplemented
39#10622833C22116yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622562C2218yescomplemented
45#10622561C22116yescomplemented
46#10622559C22116yescomplemented
47#10622272C2218yescomplemented
48#10622263C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C22×D4×C11—28no—
52C22×D4×C11—28no—
53C22×D4×C11—24no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11C2314yes—
57C22×D4×C11C2318yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—28no—
62C23×Dic11—44no—
63C23×Dic11—44no—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2318yes—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—44no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2318yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11—44no—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2314yes—
83C2×C22⋊Dic11C2318yes—
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87D4×Dic11—232no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2314yes—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4—44no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×C4×Dic11D418yescomplemented
101C2×C4×Dic11C2314yes—
102#66932—232no—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C2×#2636—111nomaximal, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11#4118yes—
121C24×C11C2412yes—
122C24×C11C2414yes—
123C24×C11C2411yescharacteristic
124C2×D4×C11—232no—
125C2×D4×C11—216no—
126C2×D4×C11—216no—
127C2×D4×C11—28no—
128C2×D4×C11—48no—
129C2×D4×C11—48no—
130C2×D4×C11—432no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×Dic11—216no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—48no—
157C22×Dic11—48no—
158C22×Dic11—432no—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2412yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—48no—
169C22⋊Dic11—28no—
170C22⋊Dic11—28no—
171C22⋊Dic11—216no—
172C22⋊Dic11—216no—
173C22⋊Dic11—48no—
174C22⋊Dic11—48no—
175C4⋊Dic11—28no—
176C4⋊Dic11—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179Dic11⋊C4—48no—
180Dic11⋊C4—48no—
181C4×Dic11C2×D4116yescomplemented
182C22×#126—111no—
183C22×C4×D4—111no—
184#2636—1116no—
185C2×#400—111no—
186C2×#399—111no—
187C2×#396—112no—
188C2×#394—112no—
189C2×#394—111no—
190C2×#392D1111yescharacteristic
191C2×#386—112no—
192C2×#385—112no—
193C2×#382—111no—
194C23×C11—216no—
195C23×C11—216no—
196C23×C11—216no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—48no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11C22×D412yes—
218C23×C11C2×#4118yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224D4×C11—232no—
225D4×C11—432no—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11—48no—
235C2×C4×C11C22×D414yes—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—432no—
253C2×Dic11—44no—
254C2×Dic11—48no—
255C2×Dic11—44no—
256C2×Dic11—48no—
257C2×Dic11C22×D414yes—
258C2×Dic11C22×D414yes—
259C23×D4C2×D1111yescharacteristic
260C23×D4C2×D1112yes—
261C24×C4—112no—
262C2×#126—118no—
263C2×#126—228no—
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—112no—
272C22×C22⋊C4—111no—
273C22×C22⋊C4—112no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4C2×D1112yes—
280C22×C42—111no—
281#400—118no—
282#399—118no—
283#396—1116no—
284#394—118no—
285#394—1116no—
286#392C2×D1118yes—
287#386—1116no—
288#385—1116no—
289#382—118no—
290C2×#95—111no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1111yescharacteristic
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—432no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—88no—
309C22×C11#52514yes—
310C22×C11#53514yes—
311C22×C11#53714yes—
312C22×C11#53818yes—
313C22×C11#53918yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11C2×H(5,𝔽2)11yescharacteristic
318C22×C11C2×2−1+411yescharacteristic
319C4×C11—24no—
320C4×C11—42no—
321C4×C11—44no—
322Dic11—24no—
323Dic11—24no—
324Dic11—42no—
325Dic11—44no—
326Dic11—42no—
327Dic11—44no—
328C25C22×D1111yescharacteristic
329C25C22×D1112yes—
330C22×D4—28no—
331C22×D4—28no—
332C22×D4—24no—
333C22×D4—44no—
334C22×D4—44no—
335C22×D4C22×D1114yes—
336C22×D4C22×D1118yes—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—118no—
344C23×C4—228no—
345C23×C4—444no—
346C23×C4—444no—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350#126—2232no—
351C4×D4—2232no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—444no—
363C2×C4⋊C4—444no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4—444no—
378C2×C22⋊C4C22×D1114yes—
379C2×C22⋊C4C22×D1118yes—
380C2×C42—118no—
381C2×C42—114no—
382#95—118no—
383#95—114no—
384#95—118no—
385#95—118no—
386#95C22×D1114yes—
387C2×C11—48no—
388C2×C11—82no—
389C2×C11#263618yescomplemented
390C2×C11C2×#52511yescharacteristic
391C2×C11C2×#53511yescharacteristic
392C2×C11C2×#53711yescharacteristic
393C2×C11C2×#53812yes—
394C2×C11C2×#53912yes—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24#434118yes—
407C24C23×D1112yes—
408C24C23×D1114yes—
409C24C23×D1111yescharacteristic
410C2×D4—232no—
411C2×D4—216no—
412C2×D4—216no—
413C2×D4—28no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—432no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—114no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—114no—
431C22×C4—2216no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—222no—
446C22×C4—448no—
447C22×C4—448no—
448C22×C4—4432no—
449C22×C4D4×D1114yes—
450C22×C4C23×D1114yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—448no—
458C4⋊C4—448no—
459C22⋊C4—28no—
460C22⋊C4—48no—
461C22⋊C4—2216no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C22⋊C4—2216no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C42—1116no—
468C11C2×#263611yescharacteristic, complemented, Sylow
469C23—216no—
470C23—216no—
471C23—216no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—48no—
484C23—48no—
485C23—48no—
486C23—48no—
487C23—44no—
488C23—44no—
489C23—48no—
490C23—48no—
491C23—44no—
492C23C2×D4×D1112yes—
493C23C2×#434118yes—
494C23C2×#434114yes—
495C23#6703714yes—
496C23#6703712yes—
497C23#6704312yes—
498C23C24×D1111yescharacteristic
499D4—232no—
500D4—432no—
501C2×C4—28no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—44no—
509C2×C4—48no—
510C2×C4—114no—
511C2×C4—114no—
512C2×C4—228no—
513C2×C4—228no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—4432no—
529C2×C4—448no—
530C2×C4—444no—
531C2×C4—448no—
532C2×C4—444no—
533C2×C4C2×D4×D1114yes—
534C22—28no—
535C22—28no—
536C22—28no—
537C22—44no—
538C22—432no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—44no—
545C22—44no—
546C22—42no—
547C22—88no—
548C22#1062311714yes—
549C22#1062312418yes—
550C22#1062313318yes—
551C22#1062313914yes—
552C22#1062324614yes—
553C22C22×D4×D1111yescharacteristic
554C22C22×#434112yes—
555C22C2×#6703712yes—
556C22C2×#6703711yescharacteristic
557C22C2×#6704311yescharacteristic
558C4—24no—
559C4—42no—
560C4—44no—
561C4—224no—
562C4—224no—
563C4—444no—
564C4—442no—
565C4—444no—
566C4—442no—
567C2—48no—
568C2—82no—
569C2#1307451018yesdirect product factor
570C2C2×#1062311711yescharacteristic
571C2C2×#1062324611yescharacteristic
572C2C2×#1062313911yescharacteristic
573C2C2×#1062312412yes—
574C2C2×#1062313312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2636
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13074510C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622559C2semidirect
11. C2×#10622263C2semidirect
25. C2×D4×Dic11C22semidirect
34. C2×#66932C22semidirect
37. #10622835C22semidirect
38. #10622835C22semidirect
39. #10622833C22semidirect
44. #10622562C22semidirect
45. #10622561C22semidirect
46. #10622559C22semidirect
47. #10622272C22semidirect
48. #10622263C22semidirect
100. C2×C4×Dic11D4semidirect
181. C4×Dic11C2×D4semidirect
389. C2×C11#2636semidirect
468. C11C2×#2636semidirect
569. C2#13074510direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×D4×Dic112
#130745102
C2×#106222722
C2×#106225622
C2×#106225612
C2×#106228352
C2×#106228332
C2×#106225592
C2×#106222632
C2×C11×#3922
C2×#263611