Finite Group Databasebeta

← C2×#13081250 #15633328

Subgroups — C2×#13081250 #15633328

Order 2816.

2402 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
1C2×#10623084C211yesmaximal, characteristic, complemented
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13081250C2116yesmaximal, direct product factor
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622373C212yesmaximal, complemented
6C2×#10622503C212yesmaximal, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622399C212yesmaximal, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622485C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C22×#4339—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999—21no—
18C2×#66993C2212yes—
19C22×#4323C2211yescharacteristic
20C2×#66983—21no—
21C22×D88C2212yes—
22#10623258—24no—
23#10623258C2218yescomplemented
24#10623084—24no—
25#10623084C2218yescomplemented
26C2×#66949—22no—
27C2×#66946C2212yes—
28C2×#66946C2212yes—
29C2×#66941C2212yes—
30C2×#66937—22no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#474C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66885C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622701C2218yescomplemented
43C4×#4323C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622503C22116yescomplemented
50#10622485C22116yescomplemented
51#10622456C2218yescomplemented
52#10622443C2218yescomplemented
53#10622399C22116yescomplemented
54#10622373C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×Q8×D11—28no—
61C2×Q8×D11—48no—
62C2×#4339—28no—
63C2×#4339—48no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44C2312yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×Dic22—22no—
72C22×Dic22D411yescharacteristic
73C22×C8×C11C2312yes—
74C11×C4⋊Q8—22no—
75C11×C4⋊Q8C2314yes—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83#66999—28no—
84#66993—24no—
85#66993C2318yes—
86C2×#4323—24no—
87C2×#4323C2314yes—
88#66983—28no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4D412yes—
96C2×C4×Dic11C2312yes—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×D88—28no—
100C2×D88C2318yes—
101#66949—216no—
102#66946—24no—
103#66946—24no—
104#66946C2318yes—
105#66946C2318yes—
106#66941—24no—
107#66941C2318yes—
108#66937—216no—
109#66927—22no—
110#66927C2314yes—
111C4×D44—22no—
112C4×D44C2314yes—
113C4×Dic22D414yes—
114C4×Dic22C2314yes—
115C11×#107C2318yes—
116C11×C4⋊C8C2314yes—
117C11×#102C2318yes—
118#66896C2314yes—
119#66885C2318yes—
120Dic11⋊C8C2318yes—
121C8×Dic11C2318yes—
122#66873C2314yes—
123#66873C2318yes—
124#66873C2318yes—
125#66871C2314yes—
126C4×C11⋊C8C2314yes—
127C2×#3358—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11—21no—
130C23×D11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—44no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11C2412yes—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—28no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C2×C22⋊D11—84no—
148C22×Dic11—21no—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D412yes—
151Q8×D11—432no—
152#4339—432no—
153C2×D44—21no—
154C2×D44—22no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—22no—
159C2×D44—24no—
160C2×D44—44no—
161C2×D44—82no—
162C2×D44#4114yescomplemented
163C2×D44C2414yes—
164C2×D44C2412yes—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11—24no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—44no—
171C2×Dic22—28no—
172C2×Dic22—48no—
173C2×Dic22D818yescomplemented
174C2×Dic22C2×D414yes—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4C2412yes—
181C11×C4⋊C4C2414yes—
182C11×C22⋊C4—24no—
183C42×C11C2×D412yes—
184C42×C11C2412yes—
185#4323—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×D414yes—
191C4⋊Dic11C2412yes—
192Dic11⋊C4—28no—
193Dic11⋊C4C2×D418yes—
194C4×Dic11C2×D414yes—
195C4×Dic11C2414yes—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200D88—216no—
201C2×#550—111no—
202C2×D4×Q8—111no—
203#3358—1116no—
204C2×#486—112no—
205C2×#486—111no—
206C2×#474—112no—
207C2×#474D1111yescharacteristic, complemented
208C2×#459—111no—
209C2×#459—112no—
210C2×C8×Q8—111no—
211C2×C4×D8—112no—
212C2×C4×D8—111no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—44no—
226Q8×C11—48no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11—48no—
236C2×C4×C11C2×D814yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C112−1+412yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—416no—
244C22⋊D11—88no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—42no—
248C2×Dic11C2×D818yes—
249C2×Dic11C22×D414yes—
250C2×Dic11C22×D414yes—
251D44—24no—
252D44—24no—
253D44—22no—
254D44—24no—
255D44—44no—
256D44—48no—
257D44—84no—
258D44C2×#4114yescomplemented
259C4×D11—48no—
260C4×D11—416no—
261C4×D11—416no—
262Dic22—416no—
263Dic22C2×D8116yescomplemented
264C8×C11—24no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×#41—221no—
268C23×Q8—221no—
269C22×D8—111no—
270C22×D8—112no—
271#550—118no—
272#550—224no—
273D4×Q8—118no—
274D4×Q8—224no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8C2×D1111yescharacteristic
277C2×#127—112no—
278C2×#127—111no—
279C2×C22⋊Q8—222no—
280C2×C22⋊Q8—221no—
281C2×#121—222no—
282C2×#121—221no—
283C2×C4×Q8—111no—
284C2×C4×D4—112no—
285C2×C4×D4—112no—
286C2×C4×D4—111no—
287C2×C4×D4C2×D1111yescharacteristic
288#486—118no—
289#486—1116no—
290#474—1116no—
291#474C2×D1118yescomplemented
292#459—118no—
293#459—1116no—
294C8×Q8—118no—
295C4×D8—118no—
296C4×D8—1116no—
297C2×#107—111no—
298C2×#107C2×D1112yes—
299C2×C4⋊C8—112no—
300C2×C4⋊C8C2×D1111yescharacteristic
301C2×#102—111no—
302C2×#102—112no—
303C2×#102—112no—
304C2×#102—112no—
305C2×#102—111no—
306C2×#102C2×D1112yes—
307C2×C4×C8—112no—
308C2×C4×C8—111no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—84no—
313C22×C11#54812yes—
314C22×C11C22×D812yes—
315C22×C11#57712yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—24no—
318C2×D11—48no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—88no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11#54812yes—
329C4×C11C22×D814yes—
330C4×C11C22×#4111yescharacteristic
331C4×C11C2×2−1+411yescharacteristic
332Dic11—24no—
333Dic11—42no—
334Dic11C22×D818yes—
335C2×#41—228no—
336C2×#41—448no—
337C22×Q8—21no—
338C22×Q8—111no—
339C22×Q8—222no—
340C22×Q8—228no—
341C22×Q8—448no—
342C22×D4—111no—
343C22×D4—112no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—221no—
347C22×D4—221no—
348C22×D4C22×D1111yescharacteristic
349C23×C4—21no—
350C23×C4—222no—
351C23×C4—222no—
352C23×C4—221no—
353C2×D8—114no—
354C2×D8—118no—
355C2×D8—228no—
356C2×D8—224no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8C22×D1112yes—
360C4⋊Q8—22no—
361C4⋊Q8—118no—
362C4⋊Q8—224no—
363C4⋊Q8C22×D1114yes—
364#127—118no—
365#127—114no—
366#127—224no—
367#127—222no—
368C22⋊Q8—2216no—
369C22⋊Q8—228no—
370#121—2216no—
371#121—228no—
372C4×Q8—114no—
373C4×Q8—114no—
374C4×D4—22no—
375C4×D4—118no—
376C4×D4—118no—
377C4×D4—114no—
378C4×D4—224no—
379C4×D4—224no—
380C4×D4—222no—
381C4×D4C22×D1114yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4—221no—
393C2×C42—112no—
394C2×C42C22×D1111yescharacteristic
395#107—114no—
396#107C22×D1118yes—
397C4⋊C8—118no—
398C4⋊C8C22×D1114yes—
399#102—114no—
400#102—118no—
401#102—114no—
402#102—118no—
403#102—118no—
404#102C22×D1118yes—
405C4×C8—118no—
406C4×C8—114no—
407C2×C11—82no—
408C2×C11#335814yescomplemented
409C2×C11C2×#54811yescharacteristic
410C2×C11C23×D811yescharacteristic
411C2×C11C2×#57711yescharacteristic
412D11—44no—
413D11—84no—
414C24—21no—
415C24—221no—
416C24—222no—
417#41—4432no—
418C2×Q8—24no—
419C2×Q8—44no—
420C2×Q8—118no—
421C2×Q8—114no—
422C2×Q8—228no—
423C2×Q8—448no—
424C2×Q8—4432no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—114no—
429C2×D4—112no—
430C2×D4—114no—
431C2×D4—228no—
432C2×D4—228no—
433C2×D4—221no—
434C2×D4—222no—
435C2×D4—224no—
436C2×D4—224no—
437C2×D4—222no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—448no—
441C2×D4—444no—
442C2×D4—882no—
443C2×D4—884no—
444C2×D4C23×D1112yes—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—44no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—228no—
452C22×C4—228no—
453C22×C4—221no—
454C22×C4—224no—
455C22×C4—448no—
456C22×C4—448no—
457C22×C4—444no—
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4C23×D1111yescharacteristic
461D8—2216no—
462D8—228no—
463C2×C8—24no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8C23×D1114yes—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—118no—
473C4⋊C4—114no—
474C4⋊C4—112no—
475C4⋊C4—228no—
476C4⋊C4—221no—
477C4⋊C4C23×D1114yes—
478C4⋊C4C23×D1112yes—
479C22⋊C4—24no—
480C22⋊C4—228no—
481C22⋊C4—228no—
482C22⋊C4—224no—
483C42—114no—
484C42—114no—
485C42D4×D1112yes—
486C42C23×D1112yes—
487C11C2×#335811yescharacteristic, complemented, Sylow
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—224no—
493C23—222no—
494C23—224no—
495C23—442no—
496C23—442no—
497C23—444no—
498C23—444no—
499C23—444no—
500C23C2×D4×D1111yescharacteristic
501Q8—48no—
502Q8—1116no—
503Q8—4416no—
504D4—22no—
505D4—22no—
506D4—42no—
507D4—114no—
508D4—224no—
509D4—222no—
510D4—224no—
511D4—224no—
512D4—4416no—
513D4—448no—
514D4—444no—
515D4—884no—
516D4—888no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—118no—
524C2×C4—114no—
525C2×C4—114no—
526C2×C4—224no—
527C2×C4—222no—
528C2×C4—4416no—
529C2×C4—4416no—
530C2×C4—442no—
531C2×C4—448no—
532C2×C4D8×D1114yes—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×D4×D1112yes—
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#6704012yes—
537C2×C4#41×D1112yes—
538C2×C4C24×D1111yescharacteristic
539C8—24no—
540C8—222no—
541C8—222no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—84no—
546C22—224no—
547C22—448no—
548C22—442no—
549C22—442no—
550C22—444no—
551C22—444no—
552C22—444no—
553C22—888no—
554C22#1062316412yes—
555C22C2×D8×D1112yes—
556C22#1062330912yes—
557C22C22×D4×D1111yescharacteristic
558C4—22no—
559C4—42no—
560C4—44no—
561C4—118no—
562C4—224no—
563C4—442no—
564C4#1062316412yes—
565C4C2×D8×D1114yes—
566C4C2×#6704011yescharacteristic
567C4C2×#41×D1111yescharacteristic
568C2—82no—
569C2—444no—
570C2—884no—
571C2#1308125014yesdirect product factor
572C2C2×#1062316411yescharacteristic
573C2C22×D8×D1111yescharacteristic
574C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11C2×#3358
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. C2×#10623258C2semidirect
3. #13081250C2direct (N × H)
4. C2×#10622701C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622399C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622485C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#474C2semidirect
23. #10623258C22semidirect
25. #10623084C22semidirect
34. C11×#474C22semidirect
42. #10622701C22semidirect
43. C4×#4323C22semidirect
49. #10622503C22semidirect
50. #10622485C22semidirect
51. #10622456C22semidirect
52. #10622443C22semidirect
53. #10622399C22semidirect
54. #10622373C22semidirect
162. C2×D44#41semidirect
173. C2×Dic22D8semidirect
207. C2×#474D11semidirect
258. D44C2×#41semidirect
263. Dic22C2×D8semidirect
291. #474C2×D11semidirect
408. C2×C11#3358semidirect
487. C11C2×#3358semidirect
571. C2#13081250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106232582
#130812502
C2×#106227012
C2×#106223732
C2×#106225032
C2×#106224562
C2×#106223992
C2×#106224432
C2×#106224852
C2×C4×#43232
C2×C11×#4742
C2×#335811