Finite Group Databasebeta

← C2×#13080946 #15630709

Subgroups — C2×#13080946 #15630709

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623249C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080946C2116yesmaximal, direct product factor
4C2×#10622683C211yesmaximal, characteristic, complemented
5C2×#10622390C212yesmaximal, complemented
6C2×#10622464C211yesmaximal, characteristic, complemented
7C2×#10622772C212yesmaximal, complemented
8C2×#10622771C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622384C212yesmaximal, complemented
12C2×C11×#459C211yesmaximal, characteristic, complemented
13C22×#4341C2212yes—
14C22×#4339—21no—
15C22×C11×D8C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66993—21no—
19C2×#66992—22no—
20C2×#66991C2212yes—
21C2×#66991C2212yes—
22C2×D4×Dic11—21no—
23C22×#4324C2211yescharacteristic
24C2×#66977—21no—
25C22×#4313C2212yes—
26#10623249—24no—
27#10623249C2218yescomplemented
28#10623082—24no—
29#10623082C2218yescomplemented
30C2×C4⋊C4×D11C2212yes—
31C2×#66936—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#459C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2211yescharacteristic
40C2×#66896C2212yes—
41#10622772C22116yescomplemented
42#10622771C22116yescomplemented
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66881C2212yes—
45C2×#66880C2212yes—
46#10622683C2218yescomplemented
47C4×#4324C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622464C2218yescomplemented
52#10622451C2218yescomplemented
53#10622390C22116yescomplemented
54#10622384C22116yescomplemented
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C22×D4×C11C2312yes—
59C23×C4×C11—21no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11—22no—
62C22×C22⋊D11—22no—
63C23×Dic11—22no—
64C2×#4341—24no—
65C2×#4341—28no—
66C2×#4341—44no—
67C2×#4341C2318yes—
68C2×#4339—28no—
69C2×#4339—48no—
70C22×D44D411yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11C2312yes—
73C22×Dic22—21no—
74C22×Dic22C2311yescharacteristic
75C2×C11×D8—44no—
76C2×C11×D8C2318yes—
77C22×C8×C11C2312yes—
78C11×#127—22no—
79C11×#127C2314yes—
80C4×D4×C11—22no—
81C4×D4×C11C2314yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87#66993—28no—
88#66992—216no—
89#66991—24no—
90#66991—24no—
91#66991C2318yes—
92#66991C2318yes—
93D4×Dic11—28no—
94C2×#4324—24no—
95C2×#4324C2314yes—
96C2×(C2×D11)⋊C4D412yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2312yes—
101#66977—28no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4313—44no—
108C2×#4313C2318yes—
109C4⋊C4×D11—24no—
110C4⋊C4×D11C2318yes—
111#66936—216no—
112C4×D44D414yes—
113C4×D44C2314yes—
114#66922—22no—
115#66922C2314yes—
116C4×Dic22—22no—
117C4×Dic22C2314yes—
118C11×C4⋊C8C2314yes—
119C11×#102C2318yes—
120#66896C2318yes—
121#66896C2314yes—
122#66896C2318yes—
123(C2×D11)⋊C8C2318yes—
124#66881C2318yes—
125#66880C2318yes—
126#66874C2314yes—
127#66872C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11—22no—
132C23×D11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—44no—
142C2×D4×C11—82no—
143C2×D4×C11C2414yes—
144C2×D4×C11C2412yes—
145C22×C4×C11—21no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—84no—
157C22×Dic11—28no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—48no—
162C22×Dic11C2×D412yes—
163#4341—216no—
164#4341—48no—
165#4341—416no—
166#4339—432no—
167C2×D44—24no—
168C2×D44C2×D414yes—
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—21no—
176C2×Dic22—24no—
177C2×Dic22—22no—
178C2×Dic22—44no—
179C2×Dic22#4114yescomplemented
180C2×Dic22C2412yes—
181C11×D8—48no—
182C2×C8×C11—24no—
183C2×C8×C11C2414yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2412yes—
186C11×C22⋊C4—24no—
187C42×C11C2×D412yes—
188C42×C11C2412yes—
189C22⋊Dic11—28no—
190C22⋊Dic11—28no—
191#4324—28no—
192(C2×D11)⋊C4C2×D418yes—
193C4⋊Dic11—21no—
194C4⋊Dic11—22no—
195C4⋊Dic11—24no—
196C4⋊Dic11C2×D414yes—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2414yes—
199Dic11⋊C4—28no—
200Dic11⋊C4—24no—
201C4×Dic11—24no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2412yes—
206#4313—48no—
207C2×#550—111no—
208C2×#547—111no—
209#3332—1116no—
210C2×#486—111no—
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459D1111yescharacteristic, complemented
215C2×#449—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#417—112no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—44no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—42no—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11C22×D414yes—
232D4×C11—22no—
233D4×C11—24no—
234D4×C11—22no—
235D4×C11—24no—
236D4×C11—44no—
237D4×C11—42no—
238D4×C11—48no—
239D4×C11—84no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—48no—
244C2×C4×C11AGL(1,ℤ/8)14yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×C4×C11C2511yescharacteristic
251C22⋊D11—416no—
252C22⋊D11—416no—
253C22⋊D11—88no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—416no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11C22×D414yes—
263D44—28no—
264C4×D11—28no—
265C4×D11—24no—
266C4×D11—24no—
267C4×D11—416no—
268Dic22—24no—
269Dic22—22no—
270Dic22—48no—
271Dic22C2×#4114yescomplemented
272C8×C11—24no—
273C11⋊C8—22no—
274C11⋊C8—22no—
275C22×#41—112no—
276C22×#41—221no—
277C22×SD16—111no—
278C22×D8C2×D1112yes—
279C22×M16—112no—
280#550—118no—
281#550—224no—
282#547—118no—
283#547—224no—
284C2×C4⋊Q8—111no—
285C2×#127—221no—
286C2×#127C2×D1111yescharacteristic
287C2×#123—222no—
288C2×C22⋊Q8—221no—
289C2×#121—112no—
290C2×#121—112no—
291C2×#121—222no—
292C2×C4×Q8—111no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4—112no—
297#486—118no—
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459C2×D1118yescomplemented
302#449—1116no—
303C4×SD16—118no—
304#436—118no—
305C2×#106—112no—
306C2×#106—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308#417—1116no—
309C2×#103—112no—
310C2×#103—111no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—111no—
314C2×#102C2×D1112yes—
315C2×C22⋊C8—112no—
316C2×C4×C8—111no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—42no—
323C22×C11—88no—
324C22×C11—84no—
325C22×C11#54612yes—
326C22×C11C2×AGL(1,ℤ/8)12yes—
327C22×C11#57712yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—48no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11#54612yes—
336C4×C11C2×AGL(1,ℤ/8)14yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339Dic11—24no—
340Dic11—24no—
341Dic11—44no—
342Dic11—42no—
343C2×#41—118no—
344C2×#41—228no—
345C2×#41—224no—
346C2×#41—228no—
347C2×#41—448no—
348C2×#41—444no—
349C22×Q8—111no—
350C22×Q8—221no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—111no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4C22×D1111yescharacteristic
358C22×D4C22×D1112yes—
359C23×C4—21no—
360C23×C4—112no—
361C23×C4—222no—
362C23×C4—222no—
363C2×SD16—114no—
364C2×SD16—224no—
365C2×D8—44no—
366C2×D8C22×D1118yes—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8C22×D1112yes—
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—22no—
375#127—228no—
376#127C22×D1114yes—
377#123—2216no—
378C22⋊Q8—228no—
379#121—118no—
380#121—118no—
381#121—2216no—
382#121—224no—
383#121—224no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×D4—22no—
387C4×D4—114no—
388C4×D4—114no—
389C4×D4—228no—
390C4×D4C22×D1114yes—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—118no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—112no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406#106—118no—
407#106—114no—
408C4⋊C8C22×D1114yes—
409#103—118no—
410#103—114no—
411#102—118no—
412#102—114no—
413#102—118no—
414#102C22×D1118yes—
415C22⋊C8—118no—
416C4×C8—114no—
417C2×C11—82no—
418C2×C11—84no—
419C2×C11#333214yescomplemented
420C2×C11C2×#54611yescharacteristic
421C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C11C2×#57711yescharacteristic
423D11—44no—
424C24—21no—
425C24—22no—
426C24—112no—
427#41—2216no—
428#41—4432no—
429#41—448no—
430#41—4416no—
431C2×Q8—114no—
432C2×Q8—112no—
433C2×Q8—221no—
434C2×Q8—224no—
435C2×Q8—222no—
436C2×Q8—444no—
437C2×D4—21no—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—44no—
446C2×D4—82no—
447C2×D4—114no—
448C2×D4—228no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—224no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—884no—
455C2×D4C23×D1114yes—
456C2×D4C23×D1112yes—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—44no—
460C22×C4—112no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—228no—
464C22×C4—228no—
465C22×C4—221no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—221no—
469C22×C4—222no—
470C22×C4—448no—
471C22×C4—448no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476D8—48no—
477M16—448no—
478C2×C8—24no—
479C2×C8—112no—
480C2×C8—112no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8C23×D1114yes—
484C4⋊C4—21no—
485C4⋊C4—114no—
486C4⋊C4—114no—
487C4⋊C4—112no—
488C4⋊C4—228no—
489C4⋊C4—222no—
490C4⋊C4—221no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4C23×D1112yes—
494C22⋊C4—24no—
495C22⋊C4—118no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—224no—
499C42D4×D1112yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—22no—
503C23—24no—
504C23—42no—
505C23—44no—
506C23—44no—
507C23—42no—
508C23—44no—
509C23—42no—
510C23—114no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23C2×D4×D1111yescharacteristic
515Q8—114no—
516Q8—224no—
517Q8—222no—
518Q8—448no—
519D4—22no—
520D4—24no—
521D4—22no—
522D4—24no—
523D4—48no—
524D4—42no—
525D4—44no—
526D4—84no—
527D4—228no—
528D4—4416no—
529D4—4416no—
530D4—888no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—42no—
534C2×C4—48no—
535C2×C4—114no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—228no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—4416no—
545C2×C4—4416no—
546C2×C4—444no—
547C2×C4—442no—
548C2×C4#6696414yes—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1112yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4#6703712yes—
553C2×C4#41×D1112yes—
554C2×C4C24×D1111yescharacteristic
555C8—24no—
556C8—222no—
557C8—222no—
558C22—42no—
559C22—44no—
560C22—44no—
561C22—42no—
562C22—44no—
563C22—42no—
564C22—84no—
565C22—88no—
566C22—224no—
567C22—224no—
568C22—224no—
569C22—448no—
570C22#1062314312yes—
571C22C2×#6696412yes—
572C22#1062330612yes—
573C22C22×D4×D1111yescharacteristic
574C4—22no—
575C4—42no—
576C4—224no—
577C4—224no—
578C4—444no—
579C4—442no—
580C4#1062314312yes—
581C4C2×#6696414yes—
582C4C2×#6703711yescharacteristic
583C4C2×#41×D1111yescharacteristic
584C2—82no—
585C2—84no—
586C2—444no—
587C2#1308094614yesdirect product factor
588C2C2×#1062314311yescharacteristic
589C2C22×#6696411yescharacteristic
590C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623249C2semidirect
2. C2×#10623082C2semidirect
3. #13080946C2direct (N × H)
4. C2×#10622683C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622464C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622771C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622384C2semidirect
12. C2×C11×#459C2semidirect
27. #10623249C22semidirect
29. #10623082C22semidirect
35. C11×#459C22semidirect
41. #10622772C22semidirect
42. #10622771C22semidirect
46. #10622683C22semidirect
47. C4×#4324C22semidirect
51. #10622464C22semidirect
52. #10622451C22semidirect
53. #10622390C22semidirect
54. #10622384C22semidirect
179. C2×Dic22#41semidirect
214. C2×#459D11semidirect
271. Dic22C2×#41semidirect
301. #459C2×D11semidirect
419. C2×C11#3332semidirect
501. C11C2×#3332semidirect
587. C2#13080946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232492
C2×#106230822
#130809462
C2×#106226832
C2×#106223902
C2×#106224642
C2×#106227722
C2×#106227712
C2×C4×#43242
C2×#106224512
C2×#106223842
C2×C11×#4592
C2×#333211