Finite Group Databasebeta

← C2×#13081244 #15632525

Subgroups — C2×#13081244 #15632525

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10623110C211yesmaximal, characteristic, complemented
3#13081244C2116yesmaximal, direct product factor
4C2×#10622295C211yesmaximal, characteristic, complemented
5C2×#10622427C212yesmaximal, complemented
6C2×#10622387C212yesmaximal, complemented
7C2×#10622634C211yesmaximal, characteristic, complemented
8C2×#10622621C211yesmaximal, characteristic, complemented
9C2×#10622787C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622474C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×C11×SD16C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999C2212yes—
17C2×#66991C2212yes—
18C2×#66983—21no—
19C2×#66979—21no—
20C22×#4313C2212yes—
21#10623110—24no—
22#10623110C2218yescomplemented
23#10623094—24no—
24#10623094C2218yes—
25C2×#66949—22no—
26C2×#66945C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66938—22no—
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66923—21no—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C4×C11×SD16C2218yescomplemented
35C2×C11×#106C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41#10622787C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66882C2212yes—
45#10622634C2218yescomplemented
46#10622621C2218yescomplemented
47C2×#66872C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622474C22116yescomplemented
51#10622427C22116yescomplemented
52#10622387C22116yescomplemented
53#10622301C2218yescomplemented
54#10622295C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C22×D44D411yescharacteristic
60C22×C4×D11—22no—
61C22×C4×D11C2312yes—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C2×C11×SD16—24no—
65C2×C11×SD16C2314yes—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C4×D4×C11—22no—
71C4×D4×C11C2314yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79#66999—24no—
80#66999C2318yes—
81#66991—24no—
82#66991C2318yes—
83#66983—28no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4D412yes—
87#66979—28no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×C4×Dic11—22no—
96C22×C11⋊C8C2312yes—
97C2×#4313—28no—
98C2×#4313C2318yes—
99#66949—216no—
100#66945—24no—
101#66945C2318yes—
102C4⋊C4×D11—24no—
103C4⋊C4×D11C2318yes—
104#66938—216no—
105C4×D44—28no—
106C4×D44D414yes—
107C4×D44C2314yes—
108#66923—28no—
109#66922—22no—
110#66922—22no—
111#66922C2314yes—
112#66922C2314yes—
113C11×#106C2314yes—
114C11×#103C2314yes—
115C11×#102C2314yes—
116C4×C8×C11C2314yes—
117#66899C2318yes—
118#66896C2318yes—
119(C2×D11)⋊C8C2318yes—
120#66882C2318yes—
121#66882C2318yes—
122#66872C2318yes—
123#66871C2318yes—
124C4⋊(C11⋊C8)C2314yes—
125C2×#3357—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11C2×D412yes—
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—22no—
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
144C2×C22⋊D11—28no—
145C2×C22⋊D11—84no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11C2×D412yes—
149C2×D44—24no—
150C2×D44C2×D414yes—
151C2×C4×D11—28no—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—84no—
155C2×C4×D11C2×D414yes—
156C2×C4×D11C2414yes—
157C2×Dic22—24no—
158C2×Dic22—24no—
159C2×Dic22—82no—
160C2×Dic22—82no—
161C11×SD16—28no—
162C2×C8×C11—22no—
163C2×C8×C11#4114yes—
164C2×C8×C11C2412yes—
165C2×C8×C11C2412yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C2412yes—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—24no—
172C42×C11—24no—
173C42×C11C2×D412yes—
174C42×C11C2412yes—
175C22⋊Dic11—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4C2×D418yes—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11C2×D414yes—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2414yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188C4×Dic11—28no—
189C2×C11⋊C8—24no—
190C2×C11⋊C8C2414yes—
191#4313—216no—
192C2×#555—111no—
193C2×#554—111no—
194#3357—1116no—
195C2×#500—111no—
196C2×#485—112no—
197C2×#480—112no—
198C2×#477—111no—
199C2×#476—111no—
200C2×#468—112no—
201C2×C4×SD16D1111yescharacteristic, complemented
202C2×#436—111no—
203C2×#428—112no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11C22×D414yes—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—48no—
227C2×C4×C11#13714yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C112−1+412yes—
233C2×C4×C11C2511yescharacteristic
234C22⋊D11—88no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11C22×D414yes—
241D44—28no—
242C4×D11—28no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—88no—
246Dic22—84no—
247Dic22—84no—
248C8×C11—22no—
249C8×C11C2×#4114yes—
250C11⋊C8—24no—
251C22×SD16C2×D1111yescharacteristic
252C22×M16—112no—
253#555—118no—
254#555—224no—
255#554—118no—
256#554—224no—
257C2×C4⋊Q8—111no—
258C2×C4⋊Q8—111no—
259C2×#125—221no—
260C2×#124—222no—
261C2×C22⋊Q8—112no—
262C2×C22⋊Q8—222no—
263C2×#121—112no—
264C2×#121—221no—
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×D4—111no—
267C2×C4×D4—221no—
268C2×C4×D4C2×D1111yescharacteristic
269C2×#117—112no—
270C2×#117—221no—
271C22×C4⋊C4—112no—
272#500—118no—
273#485—1116no—
274#480—1116no—
275#477—118no—
276#476—118no—
277#468—1116no—
278C4×SD16C2×D1118yescomplemented
279#436—118no—
280#428—1116no—
281C2×#107—112no—
282C2×#107—112no—
283C2×#107—112no—
284C2×#106—112no—
285C2×#106C2×D1111yescharacteristic
286C2×C4⋊C8—111no—
287C2×#103—112no—
288C2×#103C2×D1111yescharacteristic
289C2×#102—112no—
290C2×#102C2×D1111yescharacteristic
291C2×C22⋊C8—112no—
292C2×C4×C8C2×D1111yescharacteristic
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—84no—
297C22×C11#54712yes—
298C22×C11C2×#13712yes—
299C22×C11#57612yes—
300C22×C11C23×D411yescharacteristic
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—48no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#54712yes—
310C4×C11C2×#13714yes—
311C4×C11C22×#4111yescharacteristic
312C4×C11C2×2−1+411yescharacteristic
313Dic11—24no—
314Dic11—44no—
315Dic11—44no—
316C22×Q8—221no—
317C22×Q8—221no—
318C22×Q8C22×D1111yescharacteristic
319C22×D4—111no—
320C22×D4—222no—
321C22×D4C22×D1111yescharacteristic
322C23×C4—21no—
323C23×C4—112no—
324C23×C4—222no—
325C2×SD16—24no—
326C2×SD16C22×D1114yes—
327C2×M16—118no—
328C2×M16—228no—
329C22×C8—112no—
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332C4⋊Q8—114no—
333C4⋊Q8—114no—
334C4⋊Q8—222no—
335C4⋊Q8—222no—
336#125—228no—
337#124—2216no—
338C22⋊Q8—118no—
339C22⋊Q8—2216no—
340C22⋊Q8—224no—
341#121—118no—
342#121—228no—
343#121—224no—
344C4×Q8—22no—
345C4×Q8C22×D1114yes—
346C4×D4—22no—
347C4×D4—114no—
348C4×D4—114no—
349C4×D4—228no—
350C4×D4C22×D1114yes—
351#117—118no—
352#117—224no—
353#117—228no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—112no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C42—21no—
372C2×C42—222no—
373C2×C42C22×D1111yescharacteristic
374#107—118no—
375#107—118no—
376#107—118no—
377#106—118no—
378#106C22×D1114yes—
379C4⋊C8—114no—
380#103—118no—
381#103C22×D1114yes—
382#102—118no—
383#102C22×D1114yes—
384C22⋊C8—118no—
385C4×C8C22×D1114yes—
386C2×C11—82no—
387C2×C11#335714yescomplemented
388C2×C11C2×#54711yescharacteristic
389C2×C11C22×#13711yescharacteristic
390C2×C11C2×#57611yescharacteristic
391D11—44no—
392C24—21no—
393C24—112no—
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—882no—
400C2×Q8—882no—
401C2×Q8C23×D1112yes—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—114no—
406C2×D4—228no—
407C2×D4—224no—
408C2×D4—884no—
409C2×D4C23×D1112yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—44no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—228no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—884no—
424C22×C4D4×D1111yescharacteristic
425C22×C4D4×D1111yescharacteristic
426C22×C4C23×D1111yescharacteristic
427SD16—28no—
428M16—2216no—
429C2×C8—22no—
430C2×C8—114no—
431C2×C8—224no—
432C2×C8#433914yes—
433C2×C8C23×D1112yes—
434C2×C8C23×D1112yes—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—114no—
439C4⋊C4—114no—
440C4⋊C4—114no—
441C4⋊C4—228no—
442C4⋊C4—228no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—224no—
446C4⋊C4—224no—
447C4⋊C4C23×D1112yes—
448C4⋊C4C23×D1112yes—
449C22⋊C4—24no—
450C22⋊C4—118no—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—228no—
454C42—24no—
455C42—228no—
456C42D4×D1112yes—
457C42C23×D1112yes—
458C11C2×#335711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—114no—
464C23—224no—
465C23—224no—
466C23—224no—
467C23C2×D4×D1111yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—884no—
472Q8—884no—
473D4—22no—
474D4—22no—
475D4—42no—
476D4—228no—
477D4—888no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—48no—
486C2×C4—114no—
487C2×C4—224no—
488C2×C4—228no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—444no—
494C2×C4—444no—
495C2×C4—888no—
496C2×C4#6696814yes—
497C2×C4C2×#433912yes—
498C2×C4C2×D4×D1112yes—
499C2×C4C2×D4×D1112yes—
500C2×C4C2×D4×D1111yescharacteristic
501C2×C4#6704312yes—
502C2×C4C24×D1111yescharacteristic
503C8—22no—
504C8—224no—
505C8C2×#433914yes—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—84no—
510C22—224no—
511C22—224no—
512C22—224no—
513C22—448no—
514C22#1062308212yes—
515C22C2×#6696812yes—
516C22#1062330012yes—
517C22C22×D4×D1111yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—224no—
523C4—444no—
524C4—444no—
525C4#1062308212yes—
526C4C2×#6696814yes—
527C4C22×#433911yescharacteristic
528C4C2×#6704311yescharacteristic
529C2—82no—
530C2—444no—
531C2#1308124414yesdirect product factor
532C2C2×#1062308211yescharacteristic
533C2C22×#6696811yescharacteristic
534C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3357
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
2. C2×#10623110C2semidirect
3. #13081244C2direct (N × H)
4. C2×#10622295C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622387C2semidirect
7. C2×#10622634C2semidirect
8. C2×#10622621C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622474C2semidirect
12. C2×C4×C11×SD16C2semidirect
22. #10623110C22semidirect
34. C4×C11×SD16C22semidirect
41. #10622787C22semidirect
45. #10622634C22semidirect
46. #10622621C22semidirect
50. #10622474C22semidirect
51. #10622427C22semidirect
52. #10622387C22semidirect
53. #10622301C22semidirect
54. #10622295C22semidirect
201. C2×C4×SD16D11semidirect
278. C4×SD16C2×D11semidirect
387. C2×C11#3357semidirect
458. C11C2×#3357semidirect
531. C2#13081244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106231102
#130812442
C2×#106222952
C2×#106224272
C2×#106223872
C2×#106226342
C2×#106226212
C2×#106227872
C2×#106223012
C2×#106224742
C2×C4×C11×SD162
C2×#335711