Finite Group Databasebeta

← C2×#13081285 #15633367

Subgroups — C2×#13081285 #15633367

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×Q8×Dic22C211yesmaximal, characteristic, complemented
2C2×#10623084C211yesmaximal, characteristic
3#13081285C2116yesmaximal, direct product factor
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622373C212yesmaximal, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622483C212yesmaximal, complemented
8C2×#10622640C211yesmaximal, characteristic, complemented
9C2×#10622776C212yesmaximal, complemented
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622401C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×Q8×Dic11C2212yes—
18C22×#4325C2212yes—
19C2×#66993C2212yes—
20C2×#66983—21no—
21Q8×Dic22—24no—
22Q8×Dic22C2218yescomplemented
23#10623084—24no—
24#10623084C2218yes—
25C2×#66946C2212yes—
26C2×#66941—22no—
27C2×#66941C2212yes—
28C2×#66937—22no—
29C2×#66927C2211yescharacteristic
30C2×#66922—21no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40#10622776C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622640C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622483C22116yescomplemented
51#10622401C22116yescomplemented
52#10622373C22116yescomplemented
53#10622307C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
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—21no—
67C22×Dic22—22no—
68C22×Dic22D411yescharacteristic
69C2×C11×SD16—24no—
70C2×C11×SD16C2314yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×D4×C11—22no—
76C4×D4×C11C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83Q8×Dic11—24no—
84Q8×Dic11C2318yes—
85C2×#4325—28no—
86C2×#4325C2318yes—
87#66993—24no—
88#66993C2318yes—
89#66983—28no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2312yes—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4D412yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2312yes—
99C22×C11⋊C8C2312yes—
100#66946—24no—
101#66946C2318yes—
102#66941—216no—
103#66941—24no—
104#66941C2318yes—
105#66937—216no—
106#66927—22no—
107#66927C2314yes—
108#66922—22no—
109#66922—28no—
110#66922C2314yes—
111C4×Dic22—28no—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2314yes—
115C11×#103C2314yes—
116C11×#102C2314yes—
117C4×C8×C11C2314yes—
118#66896C2318yes—
119#66885C2318yes—
120#66885C2318yes—
121Dic11⋊C8C2318yes—
122C8×Dic11C2318yes—
123#66873C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3362—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11#4114yescomplemented
132C2×Q8×C11C2412yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—48no—
148C2×C22⋊D11—84no—
149C22×Dic11—22no—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152#4339—432no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44—82no—
160C2×D44C2414yes—
161C2×C4×D11—28no—
162C2×C4×D11—48no—
163C2×Dic22—28no—
164C2×Dic22—24no—
165C2×Dic22—82no—
166C2×Dic22—84no—
167C2×Dic22SD1618yescomplemented
168C2×Dic22C2×D414yes—
169C11×SD16—28no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2412yes—
173C2×C8×C11C2412yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2412yes—
178C11×C4⋊C4C2412yes—
179C11×C22⋊C4—24no—
180C42×C11—24no—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183#4325—216no—
184(C2×D11)⋊C4—28no—
185C4⋊Dic11—28no—
186C4⋊Dic11—24no—
187C4⋊Dic11—22no—
188C4⋊Dic11C2×D414yes—
189C4⋊Dic11C2414yes—
190Dic11⋊C4—28no—
191Dic11⋊C4C2×D418yes—
192C4×Dic11—28no—
193C4×Dic11C2×D414yes—
194C4×Dic11C2414yes—
195C2×C11⋊C8—24no—
196C2×C11⋊C8C2414yes—
197C2×Q82—111no—
198C2×#550—111no—
199#3362—1116no—
200C2×#486—112no—
201C2×#486—111no—
202C2×#476—112no—
203C2×#476—111no—
204C2×#460—112no—
205C2×#460—111no—
206C2×C8×Q8—111no—
207C2×C4×SD16—112no—
208C2×C4×SD16D1111yescharacteristic, complemented
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—24no—
219Q8×C11—22no—
220Q8×C11C2×#4114yescomplemented
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—42no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11C2×SD1614yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C112−1+412yes—
238C2×C4×C11C2511yescharacteristic
239C22⋊D11—416no—
240C22⋊D11—88no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—44no—
244C2×Dic11C2×SD1618yes—
245C2×Dic11C22×D414yes—
246C2×Dic11C22×D414yes—
247D44—24no—
248D44—24no—
249D44—44no—
250D44—48no—
251D44—84no—
252C4×D11—416no—
253Dic22—88no—
254Dic22—84no—
255Dic22C2×SD16116yescomplemented
256C8×C11—22no—
257C8×C11—22no—
258C11⋊C8—24no—
259C22×#41—221no—
260C22×SD16—112no—
261C22×SD16C2×D1111yescharacteristic
262Q82—118no—
263Q82—224no—
264#550—118no—
265#550—224no—
266C2×C4⋊Q8—112no—
267C2×C4⋊Q8—111no—
268C2×C4⋊Q8—221no—
269C2×C4⋊Q8—222no—
270C2×#127—112no—
271C2×#127—111no—
272C2×#121—222no—
273C2×#121—221no—
274C2×C4×Q8—111no—
275C2×C4×Q8—112no—
276C2×C4×Q8—221no—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—112no—
279C2×C4×D4C2×D1111yescharacteristic
280#486—1116no—
281#486—118no—
282#476—118no—
283#476—1116no—
284#460—1116no—
285#460—118no—
286C8×Q8—118no—
287C4×SD16—1116no—
288C4×SD16C2×D1118yescomplemented
289C2×#106—112no—
290C2×#106C2×D1111yescharacteristic
291C2×C4⋊C8—112no—
292C2×C4⋊C8—111no—
293C2×#103C2×D1111yescharacteristic
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102C2×D1111yescharacteristic
299C2×C4×C8—112no—
300C2×C4×C8C2×D1111yescharacteristic
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—24no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11#54812yes—
318C4×C11C22×SD1614yes—
319C4×C11C22×#4111yescharacteristic
320C4×C11C2×2−1+411yescharacteristic
321Dic11—24no—
322Dic11—44no—
323Dic11C22×SD1618yes—
324C2×#41—228no—
325C2×#41—448no—
326C22×Q8—111no—
327C22×Q8—222no—
328C22×Q8—221no—
329C22×Q8C22×D1111yescharacteristic
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—24no—
339C2×SD16—118no—
340C2×SD16—228no—
341C2×SD16C22×D1114yes—
342C22×C8—112no—
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4⋊Q8—118no—
346C4⋊Q8—114no—
347C4⋊Q8—228no—
348C4⋊Q8—224no—
349C4⋊Q8—2216no—
350C4⋊Q8—222no—
351#127—118no—
352#127—114no—
353#127—224no—
354#127—222no—
355#121—2216no—
356#121—228no—
357C4×Q8—22no—
358C4×Q8—114no—
359C4×Q8—114no—
360C4×Q8—118no—
361C4×Q8—228no—
362C4×Q8—224no—
363C4×Q8C22×D1114yes—
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—112no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—222no—
379C2×C42—21no—
380C2×C42—112no—
381C2×C42—222no—
382C2×C42C22×D1111yescharacteristic
383#106—118no—
384#106C22×D1114yes—
385C4⋊C8—118no—
386C4⋊C8—114no—
387#103C22×D1114yes—
388#102—118no—
389#102—118no—
390#102—118no—
391#102—118no—
392#102C22×D1114yes—
393C4×C8—118no—
394C4×C8C22×D1114yes—
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—21no—
405C2×Q8—22no—
406C2×Q8—118no—
407C2×Q8—114no—
408C2×Q8—228no—
409C2×Q8—224no—
410C2×Q8—882no—
411C2×Q8—884no—
412C2×Q8#433914yescomplemented
413C2×Q8C23×D1112yes—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—114no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—222no—
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—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—44no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—228no—
438C22×C4—222no—
439C22×C4—448no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—28no—
444SD16—2216no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—114no—
448C2×C8—224no—
449C2×C8C23×D1112yes—
450C2×C8C23×D1112yes—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—118no—
455C4⋊C4—114no—
456C4⋊C4—114no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—222no—
460C4⋊C4—224no—
461C4⋊C4C23×D1112yes—
462C4⋊C4C23×D1112yes—
463C22⋊C4—24no—
464C22⋊C4—228no—
465C42—24no—
466C42—114no—
467C42—114no—
468C42—228no—
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—24no—
482Q8—22no—
483Q8—1116no—
484Q8—884no—
485Q8—888no—
486Q8C2×#433914yescomplemented
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—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—48no—
505C2×C4—118no—
506C2×C4—114no—
507C2×C4—114no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—4416no—
511C2×C4—444no—
512C2×C4SD16×D1114yes—
513C2×C4C2×#433912yes—
514C2×C4C2×D4×D1112yes—
515C2×C4C2×D4×D1112yes—
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4#6704312yes—
518C2×C4C24×D1111yescharacteristic
519C8—22no—
520C8—22no—
521C8—224no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—84no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—888no—
530C22#1062308312yes—
531C22C2×SD16×D1112yes—
532C22#1062330012yes—
533C22C22×D4×D1111yescharacteristic
534C4—24no—
535C4—22no—
536C4—42no—
537C4—42no—
538C4—118no—
539C4—224no—
540C4—444no—
541C4#1062308312yes—
542C4C2×SD16×D1114yes—
543C4C22×#433911yescharacteristic
544C4C2×#6704311yescharacteristic
545C2—82no—
546C2—884no—
547C2#1308128514yesdirect product factor
548C2C2×#1062308311yescharacteristic
549C2C22×SD16×D1111yescharacteristic
550C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3362
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic22C2semidirect
3. #13081285C2direct (N × H)
4. C2×#10622307C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622483C2semidirect
8. C2×#10622640C2semidirect
9. C2×#10622776C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622401C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. Q8×Dic22C22semidirect
34. C4×C11×SD16C22semidirect
40. #10622776C22semidirect
45. #10622640C22semidirect
46. #10622621C22semidirect
50. #10622483C22semidirect
51. #10622401C22semidirect
52. #10622373C22semidirect
53. #10622307C22semidirect
54. C8×Dic22C22semidirect
131. C2×Q8×C11#41semidirect
167. C2×Dic22SD16semidirect
208. C2×C4×SD16D11semidirect
220. Q8×C11C2×#41semidirect
255. Dic22C2×SD16semidirect
288. C4×SD16C2×D11semidirect
396. C2×C11#3362semidirect
412. C2×Q8#4339semidirect
471. C11C2×#3362semidirect
486. Q8C2×#4339semidirect
547. C2#13081285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106230842
#130812852
C2×#106223072
C2×#106223732
C2×#106226212
C2×#106224832
C2×#106226402
C2×#106227762
C2×C8×Dic222
C2×#106224012
C2×C4×C11×SD162
C2×#336211