Finite Group Databasebeta

← C2×#13081286 #15633368

Subgroups — C2×#13081286 #15633368

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623253C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081286C2116yesmaximal, direct product factor
4C2×#10622701C211yesmaximal, characteristic, complemented
5C2×#10622373C212yesmaximal, complemented
6C2×#10622483C212yesmaximal, complemented
7C2×#10622461C211yesmaximal, characteristic, complemented
8C2×#10622375C212yesmaximal, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622465C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66997—22no—
17C2×#66993C2212yes—
18C22×#4324C2211yescharacteristic
19C2×#66983—21no—
20C22×#4314C2212yes—
21#10623253—24no—
22#10623253C2218yescomplemented
23#10623084—24no—
24#10623084C2218yes—
25C2×#66946C2212yes—
26C2×#66941—21no—
27C2×#66941C2212yes—
28C2×#66940—21no—
29C2×#66940C2212yes—
30C2×#66937—22no—
31C2×#66927C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#476C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66885C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622701C2218yescomplemented
43C4×#4324C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622483C22116yescomplemented
50#10622465C22116yescomplemented
51#10622461C2218yescomplemented
52#10622443C2218yescomplemented
53#10622375C22116yescomplemented
54#10622373C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C2×#4339—28no—
61C2×#4339—48no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2312yes—
65C22×C4×D11—22no—
66C22×Dic22—22no—
67C22×Dic22D411yescharacteristic
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C4×D4×C11—22no—
73C4×D4×C11C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79#66997—216no—
80#66993—24no—
81#66993C2318yes—
82C2×#4324—24no—
83C2×#4324C2314yes—
84#66983—28no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4D412yes—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4314—28no—
98C2×#4314C2318yes—
99#66946—24no—
100#66946C2318yes—
101#66941—28no—
102#66941—24no—
103#66941C2318yes—
104#66940—28no—
105#66940—24no—
106#66940C2318yes—
107#66937—216no—
108#66927—22no—
109#66927C2314yes—
110C4×Dic22—22no—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#102C2318yes—
117#66896C2314yes—
118#66885C2318yes—
119Dic11⋊C8C2318yes—
120C8×Dic11C2318yes—
121#66874C2314yes—
122#66873C2318yes—
123#66873C2318yes—
124#66872C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3362—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—82no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11C2412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—44no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—28no—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—84no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D412yes—
149C22×Dic11C2×D412yes—
150#4339—432no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—44no—
157C2×D44—82no—
158C2×D44C2414yes—
159C2×C4×D11—28no—
160C2×C4×D11—48no—
161C2×Dic22—28no—
162C2×Dic22—21no—
163C2×Dic22—22no—
164C2×Dic22—84no—
165C2×Dic22SD1618yescomplemented
166C2×Dic22C2×D414yes—
167C2×Dic22#4114yescomplemented
168C2×Dic22C2412yes—
169C2×C8×C11—24no—
170C2×C8×C11C2414yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2412yes—
175C11×C4⋊C4C2414yes—
176C11×C22⋊C4—24no—
177C42×C11C2×D412yes—
178C42×C11C2412yes—
179#4324—28no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2×D414yes—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—24no—
187Dic11⋊C4C2×D418yes—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C4×Dic11C2×D414yes—
191C4×Dic11C2414yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C2412yes—
195C2×C11⋊C8C2412yes—
196#4314—216no—
197C2×Q82—111no—
198C2×#550—111no—
199#3362—1116no—
200C2×#486—112no—
201C2×#486—111no—
202C2×#476—112no—
203C2×#476D1111yescharacteristic, complemented
204C2×#460—111no—
205C2×#460—112no—
206C2×C8×Q8—111no—
207C2×C4×SD16—112no—
208C2×C4×SD16—111no—
209C23×C11—22no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11—44no—
218Q8×C11—84no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11C2×SD1614yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C112−1+412yes—
234C2×C4×C11C2511yescharacteristic
235C22⋊D11—416no—
236C22⋊D11—88no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—42no—
242C2×Dic11C2×SD1618yes—
243C2×Dic11C22×D414yes—
244C2×Dic11C22×D414yes—
245D44—24no—
246D44—24no—
247D44—44no—
248D44—48no—
249D44—84no—
250C4×D11—416no—
251Dic22—24no—
252Dic22—22no—
253Dic22—88no—
254Dic22C2×SD16116yescomplemented
255Dic22C2×#4114yescomplemented
256C8×C11—24no—
257C11⋊C8—22no—
258C11⋊C8—22no—
259C22×#41—221no—
260C22×SD16—111no—
261C22×SD16—112no—
262Q82—118no—
263Q82—224no—
264#550—118no—
265#550—224no—
266C2×C4⋊Q8—112no—
267C2×C4⋊Q8—221no—
268C2×C4⋊Q8—222no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#127—112no—
271C2×#127—111no—
272C2×#121—222no—
273C2×#121—221no—
274C2×C4×Q8—111no—
275C2×C4×Q8—112no—
276C2×C4×Q8—111no—
277C2×C4×Q8—221no—
278C2×C4×D4—112no—
279C2×C4×D4C2×D1111yescharacteristic
280#486—118no—
281#486—1116no—
282#476—1116no—
283#476C2×D1118yescomplemented
284#460—118no—
285#460—1116no—
286C8×Q8—118no—
287C4×SD16—118no—
288C4×SD16—1116no—
289C2×#106—111no—
290C2×#106C2×D1112yes—
291C2×C4⋊C8—112no—
292C2×C4⋊C8C2×D1111yescharacteristic
293C2×#103—111no—
294C2×#102—111no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102C2×D1112yes—
299C2×C4×C8—112no—
300C2×C4×C8—111no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—84no—
305C22×C11#54812yes—
306C22×C11C22×SD1612yes—
307C22×C11#57612yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—44no—
310C2×D11—44no—
311C2×D11—44no—
312C2×D11—88no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—44no—
316C4×C11#54812yes—
317C4×C11C22×SD1614yes—
318C4×C11C22×#4111yescharacteristic
319C4×C11C2×2−1+411yescharacteristic
320Dic11—24no—
321Dic11—24no—
322Dic11—42no—
323Dic11C22×SD1618yes—
324C2×#41—228no—
325C2×#41—448no—
326C22×Q8—21no—
327C22×Q8—111no—
328C22×Q8—111no—
329C22×Q8—222no—
330C22×D4—112no—
331C22×D4—222no—
332C22×D4—222no—
333C22×D4—221no—
334C22×D4—221no—
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—222no—
338C2×SD16—114no—
339C2×SD16—118no—
340C2×SD16—228no—
341C2×SD16—224no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8C22×D1112yes—
345C4⋊Q8—22no—
346C4⋊Q8—118no—
347C4⋊Q8—224no—
348C4⋊Q8—228no—
349C4⋊Q8—2216no—
350C4⋊Q8C22×D1114yes—
351#127—118no—
352#127—114no—
353#127—224no—
354#127—222no—
355#121—2216no—
356#121—228no—
357C4×Q8—114no—
358C4×Q8—114no—
359C4×Q8—118no—
360C4×Q8—114no—
361C4×Q8—224no—
362C4×Q8—228no—
363C4×Q8—222no—
364C4×D4—22no—
365C4×D4—118no—
366C4×D4—224no—
367C4×D4C22×D1114yes—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1112yes—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—222no—
379C2×C42—112no—
380C2×C42—222no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#106—114no—
384#106C22×D1118yes—
385C4⋊C8—118no—
386C4⋊C8C22×D1114yes—
387#103—114no—
388#102—114no—
389#102—118no—
390#102—118no—
391#102—118no—
392#102C22×D1118yes—
393C4×C8—118no—
394C4×C8—114no—
395C2×C11—82no—
396C2×C11#336214yescomplemented
397C2×C11C2×#54811yescharacteristic
398C2×C11C23×SD1611yescharacteristic
399C2×C11C2×#57611yescharacteristic
400D11—84no—
401C24—21no—
402C24—222no—
403#41—4432no—
404C2×Q8—24no—
405C2×Q8—82no—
406C2×Q8—118no—
407C2×Q8—114no—
408C2×Q8—114no—
409C2×Q8—112no—
410C2×Q8—228no—
411C2×Q8—221no—
412C2×Q8—222no—
413C2×Q8—884no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—114no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—222no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—448no—
426C2×D4—444no—
427C2×D4—882no—
428C2×D4—884no—
429C2×D4C23×D1112yes—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—44no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—228no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—448no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—2216no—
444SD16—228no—
445C2×C8—24no—
446C2×C8—112no—
447C2×C8—112no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8C23×D1114yes—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—118no—
455C4⋊C4—114no—
456C4⋊C4—112no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—221no—
460C4⋊C4—224no—
461C4⋊C4C23×D1114yes—
462C4⋊C4C23×D1112yes—
463C22⋊C4—24no—
464C22⋊C4—228no—
465C42—114no—
466C42—114no—
467C42—228no—
468C42—224no—
469C42D4×D1112yes—
470C42C23×D1112yes—
471C11C2×#336211yescharacteristic, complemented, Sylow
472C23—22no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—224no—
477C23—444no—
478C23—444no—
479C23—444no—
480C23C2×D4×D1111yescharacteristic
481Q8—84no—
482Q8—1116no—
483Q8—114no—
484Q8—224no—
485Q8—222no—
486Q8—888no—
487D4—22no—
488D4—22no—
489D4—42no—
490D4—224no—
491D4—224no—
492D4—4416no—
493D4—448no—
494D4—444no—
495D4—884no—
496D4—888no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—48no—
503C2×C4—118no—
504C2×C4—114no—
505C2×C4—114no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—4416no—
511C2×C4—442no—
512C2×C4SD16×D1114yes—
513C2×C4C2×D4×D1112yes—
514C2×C4C2×D4×D1112yes—
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4#6704012yes—
517C2×C4#41×D1112yes—
518C2×C4C24×D1111yescharacteristic
519C8—24no—
520C8—222no—
521C8—222no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—84no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—888no—
530C22#1062316412yes—
531C22C2×SD16×D1112yes—
532C22#1062330512yes—
533C22C22×D4×D1111yescharacteristic
534C4—22no—
535C4—42no—
536C4—44no—
537C4—118no—
538C4—224no—
539C4—224no—
540C4—442no—
541C4#1062316412yes—
542C4C2×SD16×D1114yes—
543C4C2×#6704011yescharacteristic
544C4C2×#41×D1111yescharacteristic
545C2—82no—
546C2—884no—
547C2#1308128614yesdirect product factor
548C2C2×#1062316411yescharacteristic
549C2C22×SD16×D1111yescharacteristic
550C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×#476D11
hypocenterC11C2×#3362
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623253C2semidirect
3. #13081286C2direct (N × H)
4. C2×#10622701C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622483C2semidirect
7. C2×#10622461C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622465C2semidirect
11. C2×C4×#4324C2semidirect
12. C2×C11×#476C2semidirect
22. #10623253C22semidirect
34. C11×#476C22semidirect
42. #10622701C22semidirect
43. C4×#4324C22semidirect
49. #10622483C22semidirect
50. #10622465C22semidirect
51. #10622461C22semidirect
52. #10622443C22semidirect
53. #10622375C22semidirect
54. #10622373C22semidirect
165. C2×Dic22SD16semidirect
167. C2×Dic22#41semidirect
203. C2×#476D11semidirect
254. Dic22C2×SD16semidirect
255. Dic22C2×#41semidirect
283. #476C2×D11semidirect
396. C2×C11#3362semidirect
471. C11C2×#3362semidirect
547. C2#13081286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232532
C2×#106230842
#130812862
C2×#106227012
C2×#106223732
C2×#106224832
C2×#106224612
C2×#106223752
C2×#106224432
C2×#106224652
C2×C4×#43242
C2×C11×#4762
C2×#336211