Finite Group Databasebeta

← C2×#13081275 #15633356

Subgroups — C2×#13081275 #15633356

Order 2816.

1970 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10623261C211yesmaximal, characteristic, complemented
3#13081275C2116yesmaximal, direct product factor
4C2×#10622413C212yesmaximal, complemented
5C2×#10622701C211yesmaximal, characteristic, complemented
6C2×#10622504C212yesmaximal, complemented
7C2×#10622432C212yesmaximal, complemented
8C2×#10622456C211yesmaximal, characteristic
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4325C211yesmaximal, characteristic, complemented
11C2×#10622485C212yesmaximal, complemented
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2212yes—
16C2×#66999—22no—
17C22×#4325C2211yescharacteristic
18C22×D88C2212yes—
19#10623261—24no—
20#10623261C2218yescomplemented
21#10623116—24no—
22#10623116C2218yescomplemented
23C2×#66950—21no—
24C2×#66947—22no—
25C2×#66946C2212yes—
26C2×#66946C2212yes—
27C2×C4⋊C4×D11—21no—
28C2×#66943C2212yes—
29C2×#66928—21no—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#477C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66885C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622701C2218yescomplemented
43C4×#4325C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2211yescharacteristic
46C2×#66873C2212yes—
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622504C22116yescomplemented
50#10622485C22116yescomplemented
51#10622456C2218yes—
52#10622443C2218yescomplemented
53#10622432C22116yescomplemented
54#10622413C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2312yes—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×Dic22D411yescharacteristic
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#67000—24no—
77#67000C2318yes—
78#66999—216no—
79C2×#4325—24no—
80C2×#4325C2314yes—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4D412yes—
91C2×C4×Dic11C2312yes—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×D88—28no—
95C2×D88C2318yes—
96#66950—28no—
97#66947—216no—
98#66946—24no—
99#66946—24no—
100#66946C2318yes—
101#66946C2318yes—
102C4⋊C4×D11—28no—
103#66943—24no—
104#66943C2318yes—
105#66928—28no—
106#66927—22no—
107#66927C2314yes—
108C4×D44—22no—
109C4×D44—28no—
110C4×D44C2314yes—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C11×#107C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#103C2318yes—
116#66899C2314yes—
117#66885C2318yes—
118Dic11⋊C8C2318yes—
119C8×Dic11C2318yes—
120#66873C2314yes—
121#66873C2318yes—
122#66873C2318yes—
123#66872C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3361—111nomaximal, Sylow
126C23×D11—21no—
127C23×D11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—82no—
133C2×Q8×C11C2412yes—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D412yes—
143C2×D44—21no—
144C2×D44—24no—
145C2×D44—22no—
146C2×D44—24no—
147C2×D44—24no—
148C2×D44—22no—
149C2×D44—24no—
150C2×D44—44no—
151C2×D44—82no—
152C2×D44#4114yes—
153C2×D44C2414yes—
154C2×D44C2412yes—
155C2×C4×D11—28no—
156C2×C4×D11—28no—
157C2×C4×D11—24no—
158C2×C4×D11—44no—
159C2×C4×D11—84no—
160C2×C4×D11—84no—
161C2×Dic22—24no—
162C2×Dic22C2×D414yes—
163C2×C8×C11—24no—
164C2×C8×C11C2414yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C2412yes—
170C11×C4⋊C4C2414yes—
171C42×C11—24no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174#4325—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—24no—
180C4⋊Dic11—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11C2×D414yes—
183C4⋊Dic11C2412yes—
184Dic11⋊C4—28no—
185Dic11⋊C4C2×D418yes—
186C4×Dic11C2×D414yes—
187C4×Dic11C2414yes—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2412yes—
192D88—216no—
193C2×#559—111no—
194C2×#554—111no—
195#3361—1116no—
196C2×#488—112no—
197C2×#486—111no—
198C2×#477D1111yescharacteristic, complemented
199C2×#478—112no—
200C2×#463—112no—
201C2×#459—111no—
202C2×C8×Q8—111no—
203C2×C4×SD16—111no—
204C2×C4×D8—112no—
205C23×C11C22×D411yescharacteristic
206C22×D11—24no—
207C22×D11—22no—
208C22×D11—24no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—42no—
217Q8×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11#13514yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C112−1+412yes—
231C2×C4×C11C2511yescharacteristic
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11C22×D414yes—
237C2×Dic11C22×D414yes—
238D44—24no—
239D44—24no—
240D44—22no—
241D44—24no—
242D44—44no—
243D44—48no—
244D44—84no—
245D44C2×#4114yes—
246C4×D11—48no—
247C4×D11—88no—
248C4×D11—88no—
249Dic22—28no—
250C8×C11—24no—
251C11⋊C8—22no—
252C11⋊C8—22no—
253C22×SD16—111no—
254C22×D8—112no—
255#559—118no—
256#559—224no—
257#554—118no—
258#554—224no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#127—111no—
261C2×#125—112no—
262C2×#124—112no—
263C2×#124—221no—
264C2×#123—222no—
265C2×C22⋊Q8—221no—
266C2×C22⋊Q8—222no—
267C2×C4×Q8—111no—
268C2×C4×Q8C2×D1111yescharacteristic
269C2×C4×D4—112no—
270C2×C4×D4—112no—
271C2×C4×D4—111no—
272C2×C4×D4—221no—
273C22×C4⋊C4—221no—
274#488—1116no—
275#486—118no—
276#478—1116no—
277#477C2×D1118yescomplemented
278#463—1116no—
279#459—118no—
280C8×Q8—118no—
281C4×SD16—118no—
282C4×D8—1116no—
283C2×#107C2×D1112yes—
284C2×#106—111no—
285C2×C4⋊C8—112no—
286C2×C4⋊C8C2×D1111yescharacteristic
287C2×#103—111no—
288C2×#103C2×D1112yes—
289C2×#102—112no—
290C2×#102—112no—
291C2×#102—112no—
292C2×#102—111no—
293C2×C4×C8—112no—
294C2×C4×C8—111no—
295C22×C11#54812yes—
296C22×C11C2×#13512yes—
297C22×C11#57612yes—
298C22×C11C23×D411yescharacteristic
299C2×D11—24no—
300C2×D11—48no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—44no—
306C2×D11—88no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11—42no—
311C4×C11#54812yes—
312C4×C11C2×#13514yes—
313C4×C11C22×#4111yescharacteristic
314C4×C11C2×2−1+411yescharacteristic
315Dic11—24no—
316Dic11—24no—
317Dic11—42no—
318C22×Q8—21no—
319C22×Q8—111no—
320C22×Q8C22×D1111yescharacteristic
321C22×D4—111no—
322C22×D4—112no—
323C22×D4—221no—
324C22×D4—221no—
325C23×C4—222no—
326C23×C4—222no—
327C23×C4—221no—
328C2×SD16—114no—
329C2×SD16—224no—
330C2×D8—118no—
331C2×D8—228no—
332C22×C8—111no—
333C22×C8—111no—
334C22×C8C22×D1112yes—
335C4⋊Q8—22no—
336C4⋊Q8C22×D1114yes—
337#127—114no—
338#127—222no—
339#125—118no—
340#125—224no—
341#124—118no—
342#124—228no—
343#124—224no—
344#123—2216no—
345C22⋊Q8—228no—
346C22⋊Q8—2216no—
347C4×Q8—22no—
348C4×Q8—114no—
349C4×Q8—114no—
350C4×Q8C22×D1114yes—
351C4×D4—118no—
352C4×D4—118no—
353C4×D4—114no—
354C4×D4—228no—
355C4×D4—224no—
356C4×D4—224no—
357C4×D4—222no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—221no—
373C2×C42—21no—
374C2×C42—112no—
375C2×C42C22×D1111yescharacteristic
376#107C22×D1118yes—
377#106—114no—
378C4⋊C8—118no—
379C4⋊C8C22×D1114yes—
380#103—114no—
381#103C22×D1118yes—
382#102—118no—
383#102—114no—
384#102—118no—
385#102—118no—
386C4×C8—118no—
387C4×C8—114no—
388C2×C11#336114yescomplemented
389C2×C11C2×#54811yescharacteristic
390C2×C11C22×#13511yescharacteristic
391C2×C11C2×#57611yescharacteristic
392D11—44no—
393D11—84no—
394C24—221no—
395C24—222no—
396C2×Q8—21no—
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—82no—
401C2×Q8—114no—
402C2×Q8—224no—
403C2×Q8C23×D1112yes—
404C2×D4—114no—
405C2×D4—112no—
406C2×D4—114no—
407C2×D4—221no—
408C2×D4—224no—
409C2×D4—222no—
410C2×D4—224no—
411C2×D4—222no—
412C2×D4—224no—
413C2×D4—224no—
414C2×D4—444no—
415C2×D4—882no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—228no—
422C22×C4—228no—
423C22×C4—221no—
424C22×C4—224no—
425C22×C4—444no—
426C22×C4—884no—
427C22×C4—884no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—228no—
432D8—2216no—
433C2×C8—24no—
434C2×C8—112no—
435C2×C8—112no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8C23×D1114yes—
439C4⋊C4—24no—
440C4⋊C4—24no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—114no—
444C4⋊C4—118no—
445C4⋊C4—112no—
446C4⋊C4—228no—
447C4⋊C4—228no—
448C4⋊C4—221no—
449C4⋊C4C23×D1114yes—
450C4⋊C4C23×D1112yes—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—224no—
456C42—24no—
457C42—114no—
458C42—114no—
459C42D4×D1112yes—
460C42C23×D1112yes—
461C11C2×#336111yescharacteristic, complemented, Sylow
462C23—224no—
463C23—222no—
464C23—224no—
465C23—442no—
466C23—442no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23C2×D4×D1111yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—42no—
474Q8—84no—
475Q8—228no—
476D4—114no—
477D4—224no—
478D4—222no—
479D4—224no—
480D4—224no—
481D4—448no—
482D4—444no—
483D4—884no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—114no—
492C2×C4—114no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—442no—
497C2×C4—448no—
498C2×C4—888no—
499C2×C4—888no—
500C2×C4#6697214yes—
501C2×C4C2×D4×D1112yes—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1111yescharacteristic
504C2×C4#6704012yes—
505C2×C4#41×D1112yes—
506C2×C4C24×D1111yescharacteristic
507C8—24no—
508C8—222no—
509C8—222no—
510C22—224no—
511C22—448no—
512C22—442no—
513C22—442no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—888no—
518C22#1062316412yes—
519C22C2×#6697212yes—
520C22#1062330512yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—44no—
526C4—224no—
527C4—224no—
528C4—442no—
529C4#1062316412yes—
530C4C2×#6697214yes—
531C4C2×#6704011yescharacteristic
532C4C2×#41×D1111yescharacteristic
533C2—444no—
534C2—884no—
535C2#1308127514yesdirect product factor
536C2C2×#1062316411yescharacteristic
537C2C22×#6697211yescharacteristic
538C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenterC2×#477D11
hypocenterC11C2×#3361
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623261C2semidirect
3. #13081275C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622701C2semidirect
6. C2×#10622504C2semidirect
7. C2×#10622432C2semidirect
9. C2×#10622443C2semidirect
10. C2×C4×#4325C2semidirect
11. C2×#10622485C2semidirect
12. C2×C11×#477C2semidirect
20. #10623261C22semidirect
22. #10623116C22semidirect
34. C11×#477C22semidirect
42. #10622701C22semidirect
43. C4×#4325C22semidirect
49. #10622504C22semidirect
50. #10622485C22semidirect
52. #10622443C22semidirect
53. #10622432C22semidirect
54. #10622413C22semidirect
198. C2×#477D11semidirect
277. #477C2×D11semidirect
388. C2×C11#3361semidirect
461. C11C2×#3361semidirect
535. C2#13081275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106232612
#130812752
C2×#106224132
C2×#106227012
C2×#106225042
C2×#106224322
C2×#106224562
C2×#106224432
C2×C4×#43252
C2×#106224852
C2×C11×#4772
C2×#336111