Finite Group Databasebeta

← C2×#13081632 #15634725

Subgroups — C2×#13081632 #15634725

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2#13081632C2116yesmaximal, direct product factor
3C2×#10622687C212yesmaximal, complemented
4C2×#10622689C211yesmaximal, characteristic, complemented
5C2×#10622688C212yesmaximal, complemented
6C2×#10622629C212yesmaximal, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622685C211yesmaximal, characteristic, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622631C212yesmaximal, complemented
11C2×C4×#4323C211yesmaximal, characteristic, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C11×#550—24no—
15C11×#550C2218yescomplemented
16C2×C11×#127C2212yes—
17C2×C11×#127C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C2×#66999—21no—
24C22×#4324C2212yes—
25C22×#4324C2212yes—
26C22×#4324C2212yes—
27C22×#4323C2211yescharacteristic
28C22×#4323C2212yes—
29#10623115—24no—
30#10623115C2218yescomplemented
31C2×#66951—22no—
32C2×#66945—21no—
33C2×#66928C2212yes—
34C2×C4×D44C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39#10622689C2218yescomplemented
40#10622688C22116yescomplemented
41#10622687C22116yescomplemented
42#10622685C2218yescomplemented
43#10622637C2218yescomplemented
44#10622632C2218yescomplemented
45#10622631C22116yescomplemented
46#10622629C22116yescomplemented
47C4×#4323C2218yescomplemented
48C2×#66874C2212yes—
49C2×#66873C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2312yes—
64C23×C4×C11—22no—
65C23×C4×C11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22C2312yes—
69C11×#127—24no—
70C11×#127—22no—
71C11×#127C2314yes—
72C11×#127C2318yes—
73C11×#121—28no—
74C11×#121—216no—
75C4×Q8×C11D414yes—
76C4×Q8×C11C2314yes—
77C4×D4×C11—24no—
78C4×D4×C11—22no—
79C4×D4×C11C2314yes—
80C4×D4×C11C2318yes—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88#66999—28no—
89C2×#4324—28no—
90C2×#4324—44no—
91C2×#4324—44no—
92C2×#4324C2318yes—
93C2×#4324C2318yes—
94C2×#4324C2318yes—
95C2×#4323—24no—
96C2×#4323—44no—
97C2×#4323C2314yes—
98C2×#4323C2318yes—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—22no—
106C2×C4×Dic11—22no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2312yes—
109C22×C11⋊C8C2311yescharacteristic
110#66951—216no—
111#66945—28no—
112#66928—24no—
113#66928C2318yes—
114C4×D44—22no—
115C4×D44C2314yes—
116#66922—22no—
117#66922C2314yes—
118C4×Dic22—24no—
119C4×Dic22C2318yes—
120#66896C2314yes—
121#66896C2318yes—
122#66874C2318yes—
123#66873C2314yes—
124#66871C2314yes—
125C4⋊(C11⋊C8)C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127#66867C2318yes—
128C4×C11⋊C8C2314yes—
129C2×#3397—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11—22no—
132C23×D11—21no—
133C11×#41—432no—
134C2×Q8×C11—24no—
135C2×Q8×C11C2×D414yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—48no—
147C2×D4×C11—44no—
148C2×D4×C11—84no—
149C2×D4×C11—82no—
150C2×D4×C11C2412yes—
151C2×D4×C11C2414yes—
152C22×C4×C11—21no—
153C22×C4×C11—28no—
154C22×C4×C11—24no—
155C22×C4×C11—48no—
156C22×C4×C11—44no—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—22no—
164C2×D44—21no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44C2412yes—
168C2×C4×D11—24no—
169C2×C4×D11—44no—
170C2×Dic22—22no—
171C2×Dic22—24no—
172C2×Dic22—24no—
173C2×Dic22C2414yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D414yes—
176C11×C4⋊C4C2×D418yes—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—24no—
180C42×C11C2×D414yes—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183C42×C11C2414yes—
184#4324—216no—
185#4324—48no—
186#4324—48no—
187#4323—28no—
188#4323—48no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11C2412yes—
196Dic11⋊C4—28no—
197C4×Dic11—28no—
198C2×C11⋊C8—24no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8#4114yescomplemented
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×C11⋊C8C2412yes—
204C2×#556—111no—
205C2×#550D1111yescharacteristic, complemented
206#3397—1116no—
207C2×#496—112no—
208C2×#492—111no—
209C2×#460—112no—
210C2×#463—112no—
211C2×#461—111no—
212C2×#459—111no—
213C2×#446—111no—
214C2×#440—112no—
215C2×C4×D8—111no—
216C23×C11—22no—
217C23×C11—24no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229Q8×C11—28no—
230D4×C11—22no—
231D4×C11—24no—
232D4×C11—24no—
233D4×C11—22no—
234D4×C11—416no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—48no—
238D4×C11—88no—
239D4×C11—84no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—416no—
245C2×C4×C11—42no—
246C2×C4×C11—48no—
247C2×C4×C11AGL(1,ℤ/8)14yes—
248C2×C4×C11C22×D414yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D412yes—
253C2×C4×C11C2×#4112yes—
254C2×C4×C11H(5,𝔽2)12yes—
255C2×C4×C11C2511yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260D44—22no—
261D44—22no—
262D44—42no—
263C4×D11—48no—
264Dic22—24no—
265Dic22—24no—
266Dic22—44no—
267C11⋊C8—24no—
268C11⋊C8—22no—
269C11⋊C8C2×#4114yescomplemented
270C22×#41—21no—
271C22×SD16—112no—
272C22×SD16—112no—
273C22×SD16—112no—
274C22×D8—111no—
275C22×D8—112no—
276#556—118no—
277#556—224no—
278#550—24no—
279#550C2×D1118yescomplemented
280C2×C4⋊Q8—111no—
281C2×#127C2×D1111yescharacteristic
282C2×#127C2×D1112yes—
283C2×#126—222no—
284C2×#124—112no—
285C2×C22⋊Q8—221no—
286C2×#121—21no—
287C2×#121—22no—
288C2×C4×Q8—112no—
289C2×C4×Q8C2×D1111yescharacteristic
290C2×C4×D4—111no—
291C2×C4×D4C2×D1111yescharacteristic
292C2×C4×D4C2×D1112yes—
293C2×#117—221no—
294#496—1116no—
295#492—118no—
296#463—1116no—
297#461—118no—
298#460—1116no—
299#459—118no—
300#446—118no—
301#440—1116no—
302C4×D8—118no—
303C2×#107—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—112no—
306C2×#103—112no—
307C2×#102—111no—
308C2×#102—112no—
309C2×#102—111no—
310C2×#97—112no—
311C2×C4×C8—111no—
312C22×C11—42no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—84no—
319C22×C11—88no—
320C22×C11#55012yes—
321C22×C11C2×AGL(1,ℤ/8)12yes—
322C22×C11#57712yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—84no—
328C4×C11—24no—
329C4×C11—24no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11#55012yes—
333C4×C11C2×AGL(1,ℤ/8)14yes—
334C4×C11C22×#4111yescharacteristic
335C4×C11C2×H(5,𝔽2)11yescharacteristic
336Dic11—44no—
337Dic11—42no—
338C2×#41—28no—
339C2×#41—48no—
340C22×Q8—112no—
341C22×Q8C22⋊D1111yescharacteristic
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—111no—
347C22×D4C22×D1111yescharacteristic
348C22×D4C22×D1112yes—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—221no—
352C2×SD16—118no—
353C2×SD16—118no—
354C2×SD16—118no—
355C2×SD16—228no—
356C2×SD16—444no—
357C2×SD16—444no—
358C2×D8—114no—
359C2×D8—118no—
360C2×D8—224no—
361C2×D8—444no—
362C22×C8—111no—
363C22×C8—112no—
364C22×C8—111no—
365C4⋊Q8—114no—
366C4⋊Q8—222no—
367#127—22no—
368#127—24no—
369#127C22×D1114yes—
370#127C22×D1118yes—
371#126—2216no—
372#124—118no—
373#124—224no—
374C22⋊Q8—228no—
375#121—28no—
376#121—216no—
377C4×Q8—118no—
378C4×Q8—224no—
379C4×Q8C22⋊D1114yes—
380C4×Q8C22×D1114yes—
381C4×D4—22no—
382C4×D4—24no—
383C4×D4—114no—
384C4×D4—222no—
385C4×D4C22×D1114yes—
386C4×D4C22×D1118yes—
387#117—228no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4C22⋊D1111yescharacteristic
393C2×C4⋊C4C22⋊D1112yes—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—222no—
400C2×C42—222no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1112yes—
403#107—114no—
404C4⋊C8—114no—
405C4⋊C8—118no—
406#103—118no—
407#102—114no—
408#102—118no—
409#102—114no—
410#97—118no—
411C4×C8—114no—
412C2×C11—82no—
413C2×C11—84no—
414C2×C11#339714yescomplemented
415C2×C11C2×#55011yescharacteristic
416C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
417C2×C11C2×#57711yescharacteristic
418D11—82no—
419C24—22no—
420C24—21no—
421C24—221no—
422#41—432no—
423C2×Q8—24no—
424C2×Q8—114no—
425C2×Q8—222no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×Q8C2×C22⋊D1114yes—
429C2×D4—22no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—28no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—24no—
439C2×D4—48no—
440C2×D4—44no—
441C2×D4—84no—
442C2×D4—82no—
443C2×D4—112no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—221no—
447C2×D4C23×D1112yes—
448C2×D4C23×D1114yes—
449C22×C4—21no—
450C22×C4—28no—
451C22×C4—24no—
452C22×C4—48no—
453C22×C4—44no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—444no—
458C22×C4C2×C22⋊D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1112yes—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—2216no—
464SD16—448no—
465SD16—448no—
466D8—228no—
467D8—448no—
468C2×C8—114no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—114no—
472C2×C8—224no—
473C2×C8—222no—
474C4⋊C4—21no—
475C4⋊C4—112no—
476C4⋊C4—221no—
477C4⋊C4—224no—
478C4⋊C4—228no—
479C4⋊C4—224no—
480C4⋊C4C2×C22⋊D1114yes—
481C4⋊C4C2×C22⋊D1118yes—
482C4⋊C4C23×D1112yes—
483C22⋊C4—28no—
484C22⋊C4—24no—
485C22⋊C4—228no—
486C22⋊C4—224no—
487C22⋊C4—228no—
488C42—228no—
489C42C2×C22⋊D1112yes—
490C42C2×C22⋊D1114yes—
491C42C23×D1112yes—
492C42C23×D1114yes—
493C11C2×#339711yescharacteristic, complemented, Sylow
494C23—24no—
495C23—22no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—44no—
500C23—44no—
501C23—42no—
502C23—222no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23C22×C22⋊D1111yescharacteristic
507Q8—28no—
508Q8—224no—
509Q8—224no—
510Q8—444no—
511D4—22no—
512D4—24no—
513D4—24no—
514D4—22no—
515D4—416no—
516D4—48no—
517D4—42no—
518D4—44no—
519D4—88no—
520D4—84no—
521D4—222no—
522D4—222no—
523D4—442no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—416no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—442no—
534C2×C4—444no—
535C2×C4—448no—
536C2×C4#6698514yes—
537C2×C4#41×D1112yes—
538C2×C4#6704212yes—
539C2×C4C22×C22⋊D1114yes—
540C2×C4C22×C22⋊D1112yes—
541C2×C4C22×C22⋊D1114yes—
542C2×C4C22×C22⋊D1112yes—
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C24×D1111yescharacteristic
545C8—114no—
546C8—224no—
547C8—222no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—44no—
552C22—44no—
553C22—42no—
554C22—88no—
555C22—84no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—884no—
560C22C2×#6698512yes—
561C22#1062336512yes—
562C22#1062336712yes—
563C22C23×C22⋊D1111yescharacteristic
564C4—24no—
565C4—24no—
566C4—22no—
567C4—42no—
568C4—442no—
569C4—444no—
570C4C2×#6698514yes—
571C4#1062336512yes—
572C4C2×#41×D1111yescharacteristic
573C4C2×#6704211yescharacteristic
574C2—84no—
575C2—82no—
576C2—882no—
577C2#1308163214yesdirect product factor
578C2C2×#1062336511yescharacteristic
579C2C22×#6698511yescharacteristic
580C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. #13081632C2direct (N × H)
3. C2×#10622687C2semidirect
4. C2×#10622689C2semidirect
5. C2×#10622688C2semidirect
6. C2×#10622629C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622685C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622631C2semidirect
11. C2×C4×#4323C2semidirect
12. C2×C11×#550C2semidirect
15. C11×#550C22semidirect
30. #10623115C22semidirect
39. #10622689C22semidirect
40. #10622688C22semidirect
41. #10622687C22semidirect
42. #10622685C22semidirect
43. #10622637C22semidirect
44. #10622632C22semidirect
45. #10622631C22semidirect
46. #10622629C22semidirect
47. C4×#4323C22semidirect
200. C2×C11⋊C8#41semidirect
205. C2×#550D11semidirect
269. C11⋊C8C2×#41semidirect
279. #550C2×D11semidirect
414. C2×C11#3397semidirect
493. C11C2×#3397semidirect
577. C2#13081632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130816322
C2×#106226872
C2×#106226892
C2×#106226882
C2×#106226292
C2×#106226322
C2×#106226852
C2×#106226372
C2×#106226312
C2×C4×#43232
C2×C11×#5502
C2×#339711