Finite Group Databasebeta

← C2×#13080568 #15630250

Subgroups — C2×#13080568 #15630250

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic, complemented
3#13080568C2116yesmaximal, direct product factor
4C2×#10622307C211yesmaximal, characteristic, complemented
5C2×#10622479C212yesmaximal, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622388C212yesmaximal, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622785C212yesmaximal, complemented
10C2×C8×D44C211yesmaximal, characteristic, complemented
11C2×#10622417C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2212yes—
18C22×#4323C2212yes—
19C2×#66983—21no—
20C2×#66979—21no—
21C22×C8×D11C2212yes—
22#10623108—24no—
23#10623108C2218yescomplemented
24#10623094—24no—
25#10623094C2218yescomplemented
26C2×#66948—22no—
27C2×#66948C2212yes—
28C2×#66945C2212yes—
29C2×#66938—22no—
30C2×#66927—21no—
31C2×#66927C2211yescharacteristic
32C2×C4×D44—21no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35C4×C11×SD16C2218yescomplemented
36C2×C11×#106C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C2×#66899C2212yes—
41#10622785C22116yescomplemented
42C2×#66885C2212yes—
43C2×#66885C2212yes—
44C2×(C2×D11)⋊C8C2212yes—
45#10622634C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622479C22116yescomplemented
51#10622417C22116yescomplemented
52#10622388C22116yescomplemented
53#10622307C2218yescomplemented
54C8×D44C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4343—24no—
60C2×#4343—28no—
61C2×#4343—44no—
62C2×#4343C2318yes—
63C22×D44—22no—
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44D411yescharacteristic
68C22×D44C2312yes—
69C22×C4×D11—22no—
70C22×C4×D11C2312yes—
71C22×Dic22—21no—
72C2×C11×SD16—24no—
73C2×C11×SD16C2314yes—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×Q8×C11—22no—
77C4×Q8×C11C2314yes—
78C4×D4×C11—22no—
79C4×D4×C11C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—22no—
87#66991—24no—
88#66991C2318yes—
89C2×#4323—44no—
90C2×#4323C2318yes—
91#66983—28no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4D412yes—
95#66979—28no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11C2312yes—
99C2×C4×Dic11—22no—
100C22×C11⋊C8C2312yes—
101C2×C8×D11—44no—
102C2×C8×D11C2318yes—
103#66948—24no—
104#66948—216no—
105#66948C2318yes—
106#66945—24no—
107#66945C2318yes—
108#66938—216no—
109#66927—28no—
110#66927—22no—
111#66927C2314yes—
112C4×D44—28no—
113C4×D44D414yes—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117C11×#106C2314yes—
118C11×#103C2314yes—
119C11×#102C2314yes—
120C4×C8×C11C2314yes—
121#66899C2318yes—
122#66885C2318yes—
123#66885C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66873C2318yes—
126#66871C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3305—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—22no—
131C23×D11C2×D412yes—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11#4114yes—
135C2×Q8×C11C2412yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—44no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—28no—
149C2×C22⋊D11—84no—
150C22×Dic11—22no—
151C22×Dic11C2×D412yes—
152#4343—216no—
153#4343—48no—
154#4343—416no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—22no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—48no—
164C2×D44—44no—
165C2×D44—82no—
166C2×D44—84no—
167C2×D44C2×D414yes—
168C2×D44C2414yes—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—48no—
173C2×C4×D11C2×D414yes—
174C2×C4×D11C2414yes—
175C2×Dic22—24no—
176C2×Dic22—82no—
177C11×SD16—28no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11C2412yes—
181C2×C8×C11C2412yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2412yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—24no—
188C42×C11—24no—
189C42×C11C2×D412yes—
190C42×C11C2412yes—
191C22⋊Dic11—28no—
192#4323—48no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4C2×D418yes—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11C2×D414yes—
199C4⋊Dic11C2414yes—
200C4×Dic11—28no—
201C2×C11⋊C8—24no—
202C2×C11⋊C8C2414yes—
203C8×D11—48no—
204C2×#555—111no—
205C2×#550—111no—
206#3305—1116no—
207C2×#486—111no—
208C2×#482—112no—
209C2×#477—111no—
210C2×#466—112no—
211C2×#459—111no—
212C2×#449—112no—
213C2×C4×SD16D1111yescharacteristic, complemented
214C2×C8×D4—111no—
215C2×#416—112no—
216C23×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D411yescharacteristic
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11C22×D414yes—
229Q8×C11—24no—
230Q8×C11—22no—
231Q8×C11C2×#4114yes—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—42no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—48no—
243C2×C4×C11#13514yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—88no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—44no—
254C2×Dic11C22×D414yes—
255D44—28no—
256D44—24no—
257D44—24no—
258D44—416no—
259D44—44no—
260D44—48no—
261D44—84no—
262D44—88no—
263C4×D11—28no—
264C4×D11—24no—
265C4×D11—24no—
266C4×D11—416no—
267Dic22—84no—
268C8×C11—22no—
269C8×C11—22no—
270C11⋊C8—24no—
271C22×#41—112no—
272C22×SD16C2×D1111yescharacteristic
273C22×D8—112no—
274C23×C8—112no—
275#555—118no—
276#555—224no—
277#550—118no—
278#550—224no—
279C2×C4⋊Q8—111no—
280C2×#127—111no—
281C2×#127—221no—
282C2×#124—222no—
283C2×#121—112no—
284C2×#121—112no—
285C2×#121—222no—
286C2×#121—221no—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×D4—111no—
289C2×C4×D4—221no—
290C2×C4×D4C2×D1111yescharacteristic
291C2×#117—112no—
292C2×#117—221no—
293#486—118no—
294#482—1116no—
295#477—118no—
296#466—1116no—
297#459—118no—
298#449—1116no—
299C4×SD16C2×D1118yescomplemented
300C8×D4—118no—
301C2×#107—112no—
302C2×#106C2×D1111yescharacteristic
303C2×C4⋊C8—111no—
304#416—1116no—
305C2×#103—112no—
306C2×#103C2×D1111yescharacteristic
307C2×#102—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102C2×D1111yescharacteristic
311C2×C22⋊C8—112no—
312C2×C4×C8C2×D1111yescharacteristic
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—84no—
317C22×C11#54612yes—
318C22×C11C2×#13512yes—
319C22×C11#57612yes—
320C22×C11C23×D411yescharacteristic
321C2×D11—24no—
322C2×D11—24no—
323C2×D11—24no—
324C2×D11—48no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—88no—
329C4×C11—24no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11#54612yes—
334C4×C11C2×#13514yes—
335C4×C11C22×#4111yescharacteristic
336C4×C11C2×H(5,𝔽2)11yescharacteristic
337Dic11—24no—
338Dic11—44no—
339C2×#41—118no—
340C2×#41—224no—
341C2×#41—228no—
342C2×#41—444no—
343C22×Q8—221no—
344C22×Q8C22×D1111yescharacteristic
345C22×D4—111no—
346C22×D4—112no—
347C22×D4—222no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4C22×D1111yescharacteristic
353C23×C4—21no—
354C23×C4—112no—
355C23×C4—222no—
356C2×SD16—24no—
357C2×SD16C22×D1114yes—
358C2×D8—118no—
359C2×D8—444no—
360C22×C8—112no—
361C22×C8—118no—
362C22×C8—444no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C4⋊Q8—114no—
366C4⋊Q8—222no—
367#127—114no—
368#127—228no—
369#127—222no—
370#124—2216no—
371#121—118no—
372#121—118no—
373#121—2216no—
374#121—224no—
375#121—228no—
376#121—224no—
377C4×Q8—22no—
378C4×Q8C22×D1114yes—
379C4×D4—22no—
380C4×D4—114no—
381C4×D4—114no—
382C4×D4—228no—
383C4×D4C22×D1114yes—
384#117—118no—
385#117—224no—
386#117—228no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—112no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—222no—
398C2×C42—21no—
399C2×C42—222no—
400C2×C42C22×D1111yescharacteristic
401#107—118no—
402#106C22×D1114yes—
403C4⋊C8—114no—
404#103—118no—
405#103C22×D1114yes—
406#102—118no—
407#102—118no—
408#102—118no—
409#102C22×D1114yes—
410C22⋊C8—118no—
411C4×C8C22×D1114yes—
412C2×C11—82no—
413C2×C11#330514yescomplemented
414C2×C11C2×#54611yescharacteristic
415C2×C11C22×#13511yescharacteristic
416C2×C11C2×#57611yescharacteristic
417D11—44no—
418D11—84no—
419C24—21no—
420C24—112no—
421C24—222no—
422#41—2216no—
423#41—448no—
424#41—4416no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—224no—
428C2×Q8—882no—
429C2×Q8#433914yes—
430C2×Q8C23×D1112yes—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—114no—
435C2×D4—114no—
436C2×D4—228no—
437C2×D4—228no—
438C2×D4—228no—
439C2×D4—224no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—222no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—448no—
446C2×D4—444no—
447C2×D4—882no—
448C2×D4—884no—
449C2×D4—884no—
450C2×D4C23×D1112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—44no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—448no—
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467SD16—28no—
468D8—448no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—114no—
472C2×C8—224no—
473C2×C8—448no—
474C2×C8C23×D1112yes—
475C2×C8C23×D1112yes—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—114no—
480C4⋊C4—114no—
481C4⋊C4—222no—
482C4⋊C4—224no—
483C4⋊C4C23×D1112yes—
484C4⋊C4C23×D1112yes—
485C22⋊C4—24no—
486C22⋊C4—118no—
487C22⋊C4—228no—
488C22⋊C4—228no—
489C22⋊C4—228no—
490C42—24no—
491C42—228no—
492C42D4×D1112yes—
493C42C23×D1112yes—
494C11C2×#330511yescharacteristic, complemented, Sylow
495C23—22no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—114no—
500C23—224no—
501C23—224no—
502C23—224no—
503C23—224no—
504C23—444no—
505C23—444no—
506C23—444no—
507C23C2×D4×D1111yescharacteristic
508Q8—24no—
509Q8—22no—
510Q8—884no—
511Q8C2×#433914yes—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—228no—
516D4—224no—
517D4—224no—
518D4—4416no—
519D4—448no—
520D4—444no—
521D4—884no—
522D4—888no—
523D4—888no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—114no—
533C2×C4—224no—
534C2×C4—228no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—4416no—
539C2×C4—444no—
540C2×C4#6696914yes—
541C2×C4C2×#433912yes—
542C2×C4C2×D4×D1112yes—
543C2×C4C2×D4×D1112yes—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#6704212yes—
546C2×C4C24×D1111yescharacteristic
547C8—22no—
548C8—22no—
549C8—224no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—84no—
554C22—224no—
555C22—224no—
556C22—224no—
557C22—448no—
558C22—444no—
559C22—444no—
560C22—444no—
561C22—888no—
562C22#1062308112yes—
563C22C2×#6696912yes—
564C22#1062330012yes—
565C22C22×D4×D1111yescharacteristic
566C4—24no—
567C4—22no—
568C4—42no—
569C4—42no—
570C4—224no—
571C4—444no—
572C4#1062308112yes—
573C4C2×#6696914yes—
574C4C22×#433911yescharacteristic
575C4C2×#6704211yescharacteristic
576C2—82no—
577C2—444no—
578C2—884no—
579C2#1308056814yesdirect product factor
580C2C2×#1062308111yescharacteristic
581C2C22×#6696911yescharacteristic
582C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3305
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×#10623094C2semidirect
2. C2×#10623108C2semidirect
3. #13080568C2direct (N × H)
4. C2×#10622307C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622634C2semidirect
7. C2×#10622388C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622785C2semidirect
10. C2×C8×D44C2semidirect
11. C2×#10622417C2semidirect
12. C2×C4×C11×SD16C2semidirect
23. #10623108C22semidirect
25. #10623094C22semidirect
35. C4×C11×SD16C22semidirect
41. #10622785C22semidirect
45. #10622634C22semidirect
46. #10622628C22semidirect
50. #10622479C22semidirect
51. #10622417C22semidirect
52. #10622388C22semidirect
53. #10622307C22semidirect
54. C8×D44C22semidirect
213. C2×C4×SD16D11semidirect
299. C4×SD16C2×D11semidirect
413. C2×C11#3305semidirect
494. C11C2×#3305semidirect
579. C2#13080568direct (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×#106231082
#130805682
C2×#106223072
C2×#106224792
C2×#106226342
C2×#106223882
C2×#106226282
C2×#106227852
C2×C8×D442
C2×#106224172
C2×C4×C11×SD162
C2×#330511