Finite Group Databasebeta

← C2×#13080566 #15630248

Subgroups — C2×#13080566 #15630248

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
2#13080566C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622648C212yesmaximal, complemented
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622651C212yesmaximal, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622851C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
11C2×#10622846C212yesmaximal, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C11×#550—24no—
15C11×#550C2218yescomplemented
16C2×C11×#127—21no—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—22no—
19C2×C11×#121C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66991—21no—
25C22×#4323C2212yes—
26C2×#66983C2212yes—
27C2×#66979C2212yes—
28C23×C11⋊C8C2212yes—
29#10623094—24no—
30#10623094C2218yescomplemented
31C2×#66945—21no—
32C2×#66938—22no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35#10622851C22116yescomplemented
36#10622846C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622685C2218yescomplemented
44#10622683C2218yescomplemented
45#10622651C22116yescomplemented
46#10622648C22116yescomplemented
47C4×#4325C2218yescomplemented
48#10622634C2218yescomplemented
49D4×C11⋊C8C2218yescomplemented
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—24no—
56C2×C11×#41—28no—
57C2×C11×#41—44no—
58C2×C11×#41C2318yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2312yes—
66C23×C4×C11—22no—
67C23×C4×C11C2312yes—
68C22×C22⋊D11—22no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22—21no—
72C11×#127—28no—
73C11×#127—22no—
74C11×#127C2314yes—
75C11×#121—24no—
76C11×#121—216no—
77C11×#121C2318yes—
78C4×Q8×C11—22no—
79C4×Q8×C11C2314yes—
80C4×D4×C11—28no—
81C4×D4×C11D414yes—
82C4×D4×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—22no—
91C2×#4325—24no—
92C2×#4325C2314yes—
93#66991—28no—
94C2×#4323—44no—
95C2×#4323C2318yes—
96#66983—24no—
97#66983C2318yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—22no—
100#66979—24no—
101#66979C2318yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—22no—
106C22×C11⋊C8—44no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110C22×C11⋊C8C2318yes—
111#66945—28no—
112#66938—216no—
113C4×D44—22no—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117#66899C2314yes—
118#66899C2318yes—
119#66896C2318yes—
120#66896C2318yes—
121#66896C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66873C2314yes—
124#66872C2314yes—
125#66871C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3305—111nomaximal, Sylow
129C24×C11—22no—
130C24×C11C2×D412yes—
131C23×D11—21no—
132C11×#41—216no—
133C11×#41—48no—
134C11×#41—416no—
135C2×Q8×C11—21no—
136C2×Q8×C11—22no—
137C2×Q8×C11#4114yes—
138C2×Q8×C11C2412yes—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—22no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—48no—
148C2×D4×C11—44no—
149C2×D4×C11—82no—
150C2×D4×C11—84no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2414yes—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—28no—
158C22×C4×C11—48no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2414yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—28no—
166C2×C22⋊D11—84no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C2×D44—21no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44C2412yes—
173C2×C4×D11—24no—
174C2×C4×D11—44no—
175C2×Dic22—24no—
176C2×Dic22—82no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D414yes—
180C11×C4⋊C4C2412yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4C2×D418yes—
183C42×C11—24no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186C22⋊Dic11—28no—
187#4325—28no—
188#4323—48no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—28no—
191C4⋊Dic11—22no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2412yes—
196C4×Dic11—28no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—48no—
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2412yes—
203C2×C11⋊C8C2414yes—
204C2×#555—111no—
205C2×#550D1111yescharacteristic, complemented
206#3305—1116no—
207C2×#486—111no—
208C2×#482—112no—
209C2×#477—111no—
210C2×#466—112no—
211C2×#459—111no—
212C2×#449—112no—
213C2×C4×SD16—111no—
214C2×C8×D4—111no—
215C2×#416—112no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11C22×D414yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229Q8×C11—24no—
230Q8×C11—22no—
231Q8×C11C2×#4114yes—
232D4×C11—28no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—416no—
236D4×C11—44no—
237D4×C11—48no—
238D4×C11—84no—
239D4×C11—88no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—416no—
249C2×C4×C11—42no—
250C2×C4×C11#13514yes—
251C2×C4×C11C22×D414yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4112yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—88no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—44no—
263D44—22no—
264D44—22no—
265D44—42no—
266C4×D11—48no—
267Dic22—84no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—24no—
271C22×#41C2×D1112yes—
272C22×SD16—111no—
273C22×D8—112no—
274C23×C8—112no—
275#555—118no—
276#555—224no—
277#550—24no—
278#550C2×D1118yescomplemented
279C2×C4⋊Q8—111no—
280C2×#127—21no—
281C2×#127C2×D1111yescharacteristic
282C2×#124—222no—
283C2×#121—22no—
284C2×#121—112no—
285C2×#121—221no—
286C2×#121C2×D1112yes—
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×D4—21no—
289C2×C4×D4—111no—
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×SD16—118no—
300C8×D4—118no—
301C2×#107—112no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304#416—1116no—
305C2×#103—112no—
306C2×#103—111no—
307C2×#102—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—111no—
311C2×C22⋊C8—112no—
312C2×C4×C8—111no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—48no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—88no—
321C22×C11#54612yes—
322C22×C11C2×#13512yes—
323C22×C11#57612yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—84no—
329C4×C11—24no—
330C4×C11—24no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11#54612yes—
334C4×C11C2×#13514yes—
335C4×C11C22×#4111yescharacteristic
336C4×C11C2×H(5,𝔽2)11yescharacteristic
337Dic11—42no—
338Dic11—44no—
339C2×#41—24no—
340C2×#41—28no—
341C2×#41—44no—
342C2×#41C22×D1118yes—
343C22×Q8—221no—
344C22×Q8C22×D1111yescharacteristic
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—111no—
350C22×D4—222no—
351C22×D4C22⋊D1111yescharacteristic
352C22×D4C22×D1112yes—
353C23×C4—22no—
354C23×C4—221no—
355C23×C4C22×D1112yes—
356C2×SD16—114no—
357C2×SD16—224no—
358C2×D8—118no—
359C2×D8—444no—
360C22×C8—111no—
361C22×C8—112no—
362C22×C8—111no—
363C22×C8—118no—
364C22×C8—444no—
365C4⋊Q8—114no—
366C4⋊Q8—222no—
367#127—28no—
368#127—22no—
369#127C22×D1114yes—
370#124—2216no—
371#121—24no—
372#121—216no—
373#121—118no—
374#121—228no—
375#121—224no—
376#121C22×D1118yes—
377C4×Q8—22no—
378C4×Q8C22×D1114yes—
379C4×D4—28no—
380C4×D4—114no—
381C4×D4—222no—
382C4×D4C22⋊D1114yes—
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—22no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4C22⋊D1112yes—
398C2×C42—21no—
399C2×C42—222no—
400C2×C42C22×D1111yescharacteristic
401#107—118no—
402#106—114no—
403C4⋊C8—114no—
404#103—114no—
405#103—118no—
406#102—118no—
407#102—118no—
408#102—118no—
409#102—114no—
410C22⋊C8—118no—
411C4×C8—114no—
412C2×C11—44no—
413C2×C11—84no—
414C2×C11#330514yescomplemented
415C2×C11C2×#54611yescharacteristic
416C2×C11C22×#13511yescharacteristic
417C2×C11C2×#57611yescharacteristic
418D11—82no—
419C24—22no—
420C24—221no—
421C24C2×C22⋊D1112yes—
422#41—216no—
423#41—48no—
424#41—416no—
425C2×Q8—22no—
426C2×Q8—21no—
427C2×Q8—224no—
428C2×Q8—882no—
429C2×Q8#434114yes—
430C2×Q8C23×D1112yes—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—82no—
442C2×D4—84no—
443C2×D4—112no—
444C2×D4—228no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—884no—
449C2×D4C2×C22⋊D1114yes—
450C2×D4C23×D1114yes—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—28no—
456C22×C4—48no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—444no—
461C22×C4C2×C22⋊D1114yes—
462C22×C4C2×C22⋊D1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C23×D1114yes—
466C22×C4C23×D1111yescharacteristic
467SD16—228no—
468D8—448no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—114no—
472C2×C8—222no—
473C2×C8—222no—
474C2×C8—224no—
475C2×C8—448no—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—112no—
479C4⋊C4—114no—
480C4⋊C4—221no—
481C4⋊C4—222no—
482C4⋊C4—224no—
483C4⋊C4C2×C22⋊D1114yes—
484C4⋊C4C23×D1112yes—
485C22⋊C4—28no—
486C22⋊C4—228no—
487C22⋊C4—228no—
488C22⋊C4—224no—
489C22⋊C4C2×C22⋊D1118yes—
490C42—24no—
491C42—228no—
492C42C2×C22⋊D1112yes—
493C42C23×D1112yes—
494C11C2×#330511yescharacteristic, complemented, Sylow
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—44no—
500C23—44no—
501C23—44no—
502C23—222no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23C22×C22⋊D1114yes—
507C23C22×C22⋊D1111yescharacteristic
508Q8—24no—
509Q8—22no—
510Q8—884no—
511Q8C2×#434114yes—
512D4—28no—
513D4—24no—
514D4—24no—
515D4—416no—
516D4—44no—
517D4—48no—
518D4—84no—
519D4—88no—
520D4—222no—
521D4—222no—
522D4—442no—
523D4—888no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—28no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—416no—
533C2×C4—42no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—442no—
537C2×C4—444no—
538C2×C4—448no—
539C2×C4#6700314yes—
540C2×C4C2×#434112yes—
541C2×C4#6703712yes—
542C2×C4C22×C22⋊D1114yes—
543C2×C4C22×C22⋊D1112yes—
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1112yes—
546C2×C4C24×D1111yescharacteristic
547C8—222no—
548C8—222no—
549C8—224no—
550C22—24no—
551C22—24no—
552C22—24no—
553C22—48no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22—88no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062333712yes—
563C22C2×#6700312yes—
564C22#1062336612yes—
565C22C23×C22⋊D1111yescharacteristic
566C4—24no—
567C4—24no—
568C4—22no—
569C4—42no—
570C4—442no—
571C4—444no—
572C4#1062333712yes—
573C4C2×#6700314yes—
574C4C22×#434111yescharacteristic
575C4C2×#6703711yescharacteristic
576C2—44no—
577C2—84no—
578C2—882no—
579C2#1308056614yesdirect product factor
580C2C2×#1062333711yescharacteristic
581C2C22×#6700311yescharacteristic
582C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3305
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. #13080566C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622651C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622851C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×D4×C11⋊C8C2semidirect
11. C2×#10622846C2semidirect
12. C2×C11×#550C2semidirect
15. C11×#550C22semidirect
30. #10623094C22semidirect
35. #10622851C22semidirect
36. #10622846C22semidirect
43. #10622685C22semidirect
44. #10622683C22semidirect
45. #10622651C22semidirect
46. #10622648C22semidirect
47. C4×#4325C22semidirect
48. #10622634C22semidirect
49. D4×C11⋊C8C22semidirect
205. C2×#550D11semidirect
278. #550C2×D11semidirect
414. C2×C11#3305semidirect
494. C11C2×#3305semidirect
579. C2#13080566direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
#130805662
C2×#106226832
C2×#106226482
C2×#106226342
C2×#106226512
C2×#106226852
C2×#106228512
C2×C4×#43252
C2×D4×C11⋊C82
C2×#106228462
C2×C11×#5502
C2×#330511