Finite Group Databasebeta

← C2×#13081274 #15633355

Subgroups — C2×#13081274 #15633355

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×#10623074C211yesmaximal, characteristic, complemented
3#13081274C2116yesmaximal, direct product factor
4C2×#10622413C212yesmaximal, complemented
5C2×#10622307C211yesmaximal, characteristic, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622484C212yesmaximal, complemented
8C2×#10622778C212yesmaximal, complemented
9C2×#10622628C211yesmaximal, characteristic
10C2×C8×Dic22C211yesmaximal, characteristic, complemented
11C2×#10622369C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000C2212yes—
17C2×D4×Dic11C2212yes—
18C22×#4323C2212yes—
19C22×C4⋊Dic11—21no—
20C2×#66977—21no—
21#10623116—24no—
22#10623116C2218yescomplemented
23#10623074—24no—
24#10623074C2218yescomplemented
25C2×#66947—22no—
26C2×#66946C2212yes—
27C2×#66943C2212yes—
28C2×#66931—22no—
29C2×#66928—21no—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40#10622778C22116yescomplemented
41C2×#66885C2212yes—
42C2×#66885C2212yes—
43C2×Dic11⋊C8C2212yes—
44C2×C8×Dic11C2212yes—
45#10622634C2218yescomplemented
46#10622628C2218yes—
47C2×#66873C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622484C22116yescomplemented
51#10622413C22116yescomplemented
52#10622369C22116yescomplemented
53#10622307C2218yescomplemented
54C8×Dic22C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2312yes—
62C22×C4×D11—22no—
63C22×Dic22—21no—
64C22×Dic22D411yescharacteristic
65C2×C11×SD16—24no—
66C2×C11×SD16C2314yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80#67000—24no—
81#67000C2318yes—
82D4×Dic11—24no—
83D4×Dic11C2318yes—
84C2×#4323—28no—
85C2×#4323C2318yes—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—28no—
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2312yes—
94#66977—28no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4D412yes—
97C2×C4×Dic11C2312yes—
98C22×C11⋊C8C2312yes—
99#66947—216no—
100#66946—24no—
101#66946C2318yes—
102#66943—24no—
103#66943C2318yes—
104#66931—216no—
105#66928—28no—
106#66927—22no—
107#66927C2314yes—
108C4×D44—28no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22D414yes—
112C4×Dic22C2314yes—
113C11×#106C2314yes—
114C11×#103C2314yes—
115C11×#102C2314yes—
116C4×C8×C11C2314yes—
117#66899C2318yes—
118#66885C2318yes—
119#66885C2318yes—
120Dic11⋊C8C2318yes—
121C8×Dic11C2318yes—
122#66873C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3361—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C2412yes—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11#4114yes—
135C2×D4×C11C2412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—28no—
145C22×Dic11—22no—
146C22×Dic11—84no—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×D412yes—
149C2×D44—24no—
150C2×D44—22no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—44no—
155C2×D44—82no—
156C2×D44C2414yes—
157C2×C4×D11—28no—
158C2×C4×D11—84no—
159C2×Dic22—24no—
160C2×Dic22—24no—
161C2×Dic22—82no—
162C2×Dic22C2×D414yes—
163C11×SD16—28no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11C2412yes—
167C2×C8×C11C2412yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4C2412yes—
172C11×C4⋊C4C2412yes—
173C11×C22⋊C4—24no—
174C42×C11—24no—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177C22⋊Dic11—28no—
178#4323—216no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182C4⋊Dic11—28no—
183C4⋊Dic11—22no—
184C4⋊Dic11—24no—
185C4⋊Dic11C2×D414yes—
186C4⋊Dic11C2414yes—
187Dic11⋊C4—28no—
188Dic11⋊C4C2×D418yes—
189C4×Dic11C2×D414yes—
190C4×Dic11C2414yes—
191C2×C11⋊C8—24no—
192C2×C11⋊C8C2414yes—
193C2×#559—111no—
194C2×#554—111no—
195#3361—1116no—
196C2×#488—112no—
197C2×#486—111no—
198C2×#477—111no—
199C2×#478—112no—
200C2×#463—112no—
201C2×#459—111no—
202C2×C8×Q8—111no—
203C2×C4×SD16D1111yescharacteristic, complemented
204C2×C4×D8—112no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11C22×D411yescharacteristic
210C22×D11—24no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—42no—
217D4×C11—24no—
218D4×C11—22no—
219D4×C11C2×#4114yes—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—48no—
228C2×C4×C11#13514yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C112−1+412yes—
234C2×C4×C11C2511yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—44no—
239C2×Dic11—88no—
240C2×Dic11C22×D414yes—
241C2×Dic11C22×D414yes—
242D44—24no—
243D44—24no—
244D44—44no—
245D44—48no—
246D44—84no—
247C4×D11—88no—
248Dic22—28no—
249Dic22—84no—
250C8×C11—22no—
251C8×C11—22no—
252C11⋊C8—24no—
253C22×SD16C2×D1111yescharacteristic
254C22×D8—112no—
255#559—118no—
256#559—224no—
257#554—118no—
258#554—224no—
259C2×C4⋊Q8—111no—
260C2×#127—111no—
261C2×#125—112no—
262C2×#124—112no—
263C2×#124—221no—
264C2×#123—222no—
265C2×C22⋊Q8—222no—
266C2×C22⋊Q8—221no—
267C2×C4×Q8—111no—
268C2×C4×Q8C2×D1111yescharacteristic
269C2×C4×D4—112no—
270C2×C4×D4—112no—
271C2×C4×D4—221no—
272C2×C4×D4C2×D1111yescharacteristic
273C22×C4⋊C4—221no—
274#488—1116no—
275#486—118no—
276#478—1116no—
277#477—118no—
278#463—1116no—
279#459—118no—
280C8×Q8—118no—
281C4×SD16C2×D1118yescomplemented
282C4×D8—1116no—
283C2×#107—112no—
284C2×#106C2×D1111yescharacteristic
285C2×C4⋊C8—112no—
286C2×C4⋊C8—111no—
287C2×#103—112no—
288C2×#103C2×D1111yescharacteristic
289C2×#102—112no—
290C2×#102—112no—
291C2×#102—112no—
292C2×#102C2×D1111yescharacteristic
293C2×C4×C8—112no—
294C2×C4×C8C2×D1111yescharacteristic
295C22×C11—24no—
296C22×C11—48no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11#54812yes—
300C22×C11C2×#13512yes—
301C22×C11#57612yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—44no—
306C2×D11—88no—
307C4×C11—22no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11#54812yes—
312C4×C11C2×#13514yes—
313C4×C11C22×#4111yescharacteristic
314C4×C11C2×2−1+411yescharacteristic
315Dic11—24no—
316Dic11—24no—
317Dic11—44no—
318C22×Q8—111no—
319C22×Q8—221no—
320C22×Q8C22×D1111yescharacteristic
321C22×D4—112no—
322C22×D4—221no—
323C22×D4—221no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—222no—
327C23×C4—222no—
328C2×SD16—24no—
329C2×SD16C22×D1114yes—
330C2×D8—118no—
331C2×D8—228no—
332C22×C8—112no—
333C22×C8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335C4⋊Q8—114no—
336C4⋊Q8—222no—
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—2216no—
346C22⋊Q8—228no—
347C4×Q8—22no—
348C4×Q8—114no—
349C4×Q8—114no—
350C4×Q8C22×D1114yes—
351C4×D4—22no—
352C4×D4—118no—
353C4×D4—118no—
354C4×D4—228no—
355C4×D4—224no—
356C4×D4—224no—
357C4×D4C22×D1114yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C42—21no—
374C2×C42—112no—
375C2×C42C22×D1111yescharacteristic
376#107—118no—
377#106C22×D1114yes—
378C4⋊C8—118no—
379C4⋊C8—114no—
380#103—118no—
381#103C22×D1114yes—
382#102—118no—
383#102—118no—
384#102—118no—
385#102C22×D1114yes—
386C4×C8—118no—
387C4×C8C22×D1114yes—
388C2×C11—44no—
389C2×C11#336114yescomplemented
390C2×C11C2×#54811yescharacteristic
391C2×C11C22×#13511yescharacteristic
392C2×C11C2×#57611yescharacteristic
393D11—84no—
394C24—21no—
395C24—222no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—114no—
400C2×Q8—224no—
401C2×Q8—224no—
402C2×Q8—882no—
403C2×Q8C23×D1112yes—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—114no—
407C2×D4—224no—
408C2×D4—224no—
409C2×D4—222no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4—444no—
413C2×D4—882no—
414C2×D4#433914yes—
415C2×D4C23×D1112yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—44no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—228no—
424C22×C4—228no—
425C22×C4—222no—
426C22×C4—884no—
427C22×C4—884no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431SD16—28no—
432D8—2216no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—114no—
436C2×C8—224no—
437C2×C8C23×D1112yes—
438C2×C8C23×D1112yes—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—114no—
443C4⋊C4—118no—
444C4⋊C4—114no—
445C4⋊C4—228no—
446C4⋊C4—228no—
447C4⋊C4—222no—
448C4⋊C4—224no—
449C4⋊C4C23×D1112yes—
450C4⋊C4C23×D1112yes—
451C22⋊C4—24no—
452C22⋊C4—228no—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—228no—
456C42—24no—
457C42—114no—
458C42—114no—
459C42D4×D1112yes—
460C42C23×D1112yes—
461C11C2×#336111yescharacteristic, complemented, Sylow
462C23—24no—
463C23—22no—
464C23—42no—
465C23—42no—
466C23—224no—
467C23—444no—
468C23—444no—
469C23—444no—
470C23C2×D4×D1111yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—42no—
474Q8—228no—
475Q8—884no—
476D4—24no—
477D4—22no—
478D4—224no—
479D4—224no—
480D4—448no—
481D4—444no—
482D4—884no—
483D4C2×#433914yes—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—48no—
492C2×C4—114no—
493C2×C4—114no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—444no—
498C2×C4—888no—
499C2×C4—888no—
500C2×C4#6696914yes—
501C2×C4C2×#433912yes—
502C2×C4C2×D4×D1112yes—
503C2×C4C2×D4×D1112yes—
504C2×C4C2×D4×D1111yescharacteristic
505C2×C4#6704312yes—
506C2×C4C24×D1111yescharacteristic
507C8—22no—
508C8—22no—
509C8—224no—
510C22—24no—
511C22—48no—
512C22—42no—
513C22—42no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—888no—
518C22#1062308312yes—
519C22C2×#6696912yes—
520C22#1062330012yes—
521C22C22×D4×D1111yescharacteristic
522C4—22no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—224no—
527C4—224no—
528C4—444no—
529C4#1062308312yes—
530C4C2×#6696914yes—
531C4C22×#433911yescharacteristic
532C4C2×#6704311yescharacteristic
533C2—44no—
534C2—884no—
535C2#1308127414yesdirect product factor
536C2C2×#1062308311yescharacteristic
537C2C22×#6696911yescharacteristic
538C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3361
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×#10623116C2semidirect
2. C2×#10623074C2semidirect
3. #13081274C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622307C2semidirect
6. C2×#10622634C2semidirect
7. C2×#10622484C2semidirect
8. C2×#10622778C2semidirect
10. C2×C8×Dic22C2semidirect
11. C2×#10622369C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. #10623116C22semidirect
24. #10623074C22semidirect
34. C4×C11×SD16C22semidirect
40. #10622778C22semidirect
45. #10622634C22semidirect
50. #10622484C22semidirect
51. #10622413C22semidirect
52. #10622369C22semidirect
53. #10622307C22semidirect
54. C8×Dic22C22semidirect
203. C2×C4×SD16D11semidirect
281. C4×SD16C2×D11semidirect
389. C2×C11#3361semidirect
461. C11C2×#3361semidirect
535. C2#13081274direct (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×#106230742
#130812742
C2×#106224132
C2×#106223072
C2×#106226342
C2×#106224842
C2×#106227782
C2×#106226282
C2×C8×Dic222
C2×#106223692
C2×C4×C11×SD162
C2×#336111