Finite Group Databasebeta

← C2×#13079797 #15625853

Subgroups — C2×#13079797 #15625853

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic
3#13079797C2116yesmaximal, direct product factor
4C2×#10622296C212yesmaximal, complemented
5C2×#10622310C212yesmaximal, complemented
6C2×#10622336C212yesmaximal, complemented
7C2×#10622350C212yesmaximal
8C2×#10622463C211yesmaximal, characteristic, complemented
9C2×#10622464C211yesmaximal, characteristic, complemented
10C2×#10622455C211yesmaximal, characteristic, complemented
11C2×#10622459C211yesmaximal, characteristic, complemented
12C2×C11×#431C211yesmaximal, characteristic, complemented
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×#66982—21no—
16C2×C4×C22⋊D11—21no—
17C2×#66979C2212yes—
18C2×#66977—21no—
19C2×#66977—21no—
20C2×#66977C2211yescharacteristic
21#10623010—24no—
22#10623010C2218yes—
23C2×#66929—21no—
24C2×#66928C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66925—21no—
27#10623001—24no—
28#10623001C2218yescomplemented
29C2×#66923C2211yescharacteristic
30C2×#66923C2212yes—
31C2×#66922C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22—21no—
34C2×C4×Dic22—21no—
35C2×C4×Dic22C2211yescharacteristic
36C11×#431C2218yescomplemented
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2212yes—
40C2×C4×C8×C11C2212yes—
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×#66882C2212yes—
44C2×#66882C2212yes—
45C2×#66881C2212yes—
46C2×#66881C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49#10622464C2218yescomplemented
50#10622463C2218yescomplemented
51#10622459C2218yescomplemented
52#10622455C2218yescomplemented
53#10622350C22116yes—
54#10622336C22116yescomplemented
55#10622310C22116yescomplemented
56#10622296C22116yescomplemented
57C23×C4×C11D411yescharacteristic
58C23×C4×C11D411yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2312yes—
67C22×C8×C11C2312yes—
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D414yes—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2314yes—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—21no—
76#66983—22no—
77#66983C2314yes—
78#66982—28no—
79C4×C22⋊D11—28no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—24no—
85#66979C2318yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2312yes—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—28no—
93#66977—28no—
94#66977—22no—
95#66977C2314yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—21no—
104#66929—28no—
105#66928—22no—
106#66928C2314yes—
107C4×D44—22no—
108C4×D44C2314yes—
109#66925—28no—
110#66923—24no—
111#66923—22no—
112#66923C2318yes—
113#66923C2314yes—
114#66922—22no—
115#66922—22no—
116#66922C2314yes—
117#66922C2314yes—
118C4×Dic22—28no—
119C4×Dic22—28no—
120C4×Dic22—22no—
121C4×Dic22C2314yes—
122C11×C4⋊C8C2314yes—
123C11×C4⋊C8C2314yes—
124C11×C22⋊C8C2318yes—
125C4×C8×C11C2318yes—
126#66885C2318yes—
127#66885C2318yes—
128#66882C2318yes—
129#66882C2318yes—
130#66881C2318yes—
131#66881C2318yes—
132#66880C2318yes—
133#66880C2318yes—
134C2×#3233—111nomaximal, Sylow
135C24×C11C2×D411yescharacteristic
136C23×D11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2412yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—44no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C2×D44—21no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44C2412yes—
162C2×C4×D11—24no—
163C2×C4×D11—44no—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—44no—
170C2×Dic22—44no—
171C2×Dic22C2412yes—
172C2×C8×C11—24no—
173C2×C8×C11—24no—
174C2×C8×C11C2414yes—
175C2×C8×C11C2414yes—
176C42×C11C2×D414yes—
177C42×C11C2×D414yes—
178C42×C11C2×D412yes—
179C42×C11C2×D412yes—
180C42×C11C2412yes—
181C42×C11C2412yes—
182C22⋊Dic11—28no—
183C22⋊Dic11—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2414yes—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204C4×Dic11—28no—
205C4×Dic11—24no—
206C2×#533—111no—
207C2×#529—111no—
208#3233—1116no—
209C2×#499—112no—
210C2×#488—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#477—111no—
214C2×#475—111no—
215C2×#476—111no—
216C2×#474—111no—
217C2×#431D1111yescharacteristic, complemented
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11C22×D412yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—28no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—44no—
236C2×C4×C11#13514yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C112−1+412yes—
244C2×C4×C112−1+412yes—
245C2×C4×C11C2511yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257D44—22no—
258D44—22no—
259D44—42no—
260C4×D11—48no—
261Dic22—22no—
262Dic22—22no—
263Dic22—48no—
264Dic22—42no—
265Dic22—48no—
266C8×C11—24no—
267C8×C11—24no—
268#533—118no—
269#533—224no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8—111no—
272#529—118no—
273#529—224no—
274C2×#126—221no—
275C2×#125—112no—
276C2×#125—111no—
277C2×#124—111no—
278C2×#123—221no—
279C2×C22⋊Q8—111no—
280C2×C22⋊Q8—221no—
281C2×C22⋊Q8—221no—
282C2×#121—111no—
283C2×C4×Q8—111no—
284C2×C4×Q8—221no—
285C2×C4×Q8—221no—
286C2×C4×D4—111no—
287C2×C4×D4—221no—
288C2×#117—112no—
289C2×#117—221no—
290C22×C42C2×D1111yescharacteristic
291#499—1116no—
292#488—1116no—
293#485—1116no—
294#482—1116no—
295#477—118no—
296#476—118no—
297#475—118no—
298#474—118no—
299#431C2×D1118yescomplemented
300C2×#107—112no—
301C2×#107—112no—
302C2×#106—112no—
303C2×#106—112no—
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×C4⋊C8C2×D1111yescharacteristic
306C2×#103—112no—
307C2×#103—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×C22⋊C8C2×D1112yes—
311C2×C4×C8C2×D1112yes—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—44no—
316C22×C11#53612yes—
317C22×C11C2×#13512yes—
318C22×C11#57512yes—
319C22×C11C23×D411yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—84no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11#53612yes—
329C4×C11C2×#13514yes—
330C4×C11C2×2−1+411yescharacteristic
331C4×C11C2×2−1+411yescharacteristic
332Dic11—42no—
333Dic11—44no—
334Dic11—42no—
335Dic11—44no—
336Dic11—42no—
337C22×Q8—111no—
338C22×Q8—221no—
339C22×Q8—221no—
340C22×D4—111no—
341C22×D4—221no—
342C23×C4—221no—
343C23×C4D4411yescharacteristic
344C23×C4D4411yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C22×C8C22×D1112yes—
347C22×C8C22×D1112yes—
348C4⋊Q8—114no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352#126—228no—
353#125—114no—
354#125—118no—
355#125—222no—
356#125—224no—
357#124—114no—
358#124—222no—
359#123—228no—
360C22⋊Q8—114no—
361C22⋊Q8—222no—
362C22⋊Q8—228no—
363C22⋊Q8—228no—
364#121—114no—
365#121—222no—
366C4×Q8—114no—
367C4×Q8—222no—
368C4×Q8—228no—
369C4×Q8—228no—
370C4×D4—114no—
371C4×D4—228no—
372C4×D4—222no—
373#117—118no—
374#117—224no—
375#117—228no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—222no—
395C2×C42—221no—
396C2×C42D4411yescharacteristic
397C2×C42D4411yescharacteristic
398C2×C42D4414yes—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1114yes—
402#107—118no—
403#107—118no—
404#106—118no—
405#106—118no—
406C4⋊C8C22×D1114yes—
407C4⋊C8C22×D1114yes—
408#103—118no—
409#103—118no—
410#102—118no—
411#102—118no—
412C22⋊C8C22×D1118yes—
413C4×C8C22×D1118yes—
414C2×C11—42no—
415C2×C11#323314yescomplemented
416C2×C11C2×#53611yescharacteristic
417C2×C11C22×#13511yescharacteristic
418C2×C11C2×#57511yescharacteristic
419D11—82no—
420C24—221no—
421C24C2×D4411yescharacteristic
422C2×Q8—112no—
423C2×Q8—221no—
424C2×Q8—224no—
425C2×Q8—224no—
426C2×Q8—222no—
427C2×Q8—222no—
428C2×Q8—444no—
429C2×Q8—444no—
430C2×D4—112no—
431C2×D4—224no—
432C2×D4—221no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—444no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—444no—
447C22×C4C2×D4414yes—
448C22×C4C2×D4412yes—
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4414yes—
454C22×C4C2×D4411yescharacteristic
455C22×C4C23×D1112yes—
456C22×C4C23×D1111yescharacteristic
457C2×C8—24no—
458C2×C8—24no—
459C2×C8C23×D1114yes—
460C2×C8C23×D1114yes—
461C4⋊C4—114no—
462C4⋊C4—114no—
463C4⋊C4—112no—
464C4⋊C4—112no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—224no—
470C4⋊C4—224no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—228no—
474C4⋊C4—228no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C22⋊C4—228no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—228no—
484C42—224no—
485C42C2×D4414yes—
486C42C2×D4412yes—
487C42C2×D4414yes—
488C42C2×D4412yes—
489C42C23×D1112yes—
490C42C23×D1112yes—
491C11C2×#323311yescharacteristic, complemented, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—222no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23C22×D4412yes—
500C23C22×D4411yescharacteristic
501Q8—222no—
502Q8—222no—
503Q8—448no—
504Q8—448no—
505Q8—442no—
506D4—222no—
507D4—222no—
508D4—448no—
509D4—442no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—28no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—44no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—442no—
525C2×C4—444no—
526C2×C4—442no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—448no—
530C2×C4#6695714yes—
531C2×C4C22×D4412yes—
532C2×C4C22×D4412yes—
533C2×C4C22×D4412yes—
534C2×C4C22×D4412yes—
535C2×C4C22×D4412yes—
536C2×C4C22×D4411yescharacteristic
537C2×C4#6704312yes—
538C2×C4#6704312yes—
539C2×C4C24×D1111yescharacteristic
540C8—24no—
541C8—24no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—44no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—884no—
550C22#1062305712yes—
551C22C2×#6695712yes—
552C22#1062327912yes—
553C22C23×D4411yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—22no—
558C4—442no—
559C4—442no—
560C4—444no—
561C4—442no—
562C4—444no—
563C4#1062305712yes—
564C4C2×#6695714yes—
565C4C2×#6704311yescharacteristic
566C4C2×#6704311yescharacteristic
567C2—42no—
568C2—882no—
569C2#1307979714yesdirect product factor
570C2C2×#1062305711yescharacteristic
571C2C22×#6695711yescharacteristic
572C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#431C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#431D11
hypocenterC11C2×#3233
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
3. #13079797C2direct (N × H)
4. C2×#10622296C2semidirect
5. C2×#10622310C2semidirect
6. C2×#10622336C2semidirect
8. C2×#10622463C2semidirect
9. C2×#10622464C2semidirect
10. C2×#10622455C2semidirect
11. C2×#10622459C2semidirect
12. C2×C11×#431C2semidirect
28. #10623001C22semidirect
36. C11×#431C22semidirect
49. #10622464C22semidirect
50. #10622463C22semidirect
51. #10622459C22semidirect
52. #10622455C22semidirect
54. #10622336C22semidirect
55. #10622310C22semidirect
56. #10622296C22semidirect
217. C2×#431D11semidirect
299. #431C2×D11semidirect
415. C2×C11#3233semidirect
491. C11C2×#3233semidirect
569. C2#13079797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106230102
#130797972
C2×#106222962
C2×#106223102
C2×#106223362
C2×#106223502
C2×#106224632
C2×#106224642
C2×#106224552
C2×#106224592
C2×C11×#4312
C2×#323311