Finite Group Databasebeta

← C2×#13080942 #15630705

Subgroups — C2×#13080942 #15630705

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×#10623257C211yesmaximal, characteristic, complemented
3#13080942C2116yesmaximal, direct product factor
4C2×#10622390C212yesmaximal, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622395C212yesmaximal, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622394C212yesmaximal, complemented
9C2×C4×#4314C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622384C212yesmaximal, complemented
12C2×C11×#486C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×#4341C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×#66999—21no—
18C2×#66993—21no—
19C2×#66992—22no—
20C2×#66991C2212yes—
21C2×D4×Dic11—21no—
22C22×#4323C2212yes—
23C22×#4314C2211yescharacteristic
24C22×#4313C2212yes—
25#10623257—24no—
26#10623257C2218yescomplemented
27#10623249—24no—
28#10623249C2218yescomplemented
29C2×#66948C2212yes—
30C2×#66947—22no—
31C2×C4⋊C4×D11C2212yes—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#486C2218yescomplemented
36C2×C11×#102C2212yes—
37C2×C11×#102C2212yes—
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66881C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622707C2218yescomplemented
45#10622685C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66872C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622395C22116yescomplemented
50#10622394C22116yescomplemented
51#10622390C22116yescomplemented
52#10622384C22116yescomplemented
53C4×#4314C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2312yes—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C23×Dic11—22no—
62C2×#4343—28no—
63C2×#4343—48no—
64C2×#4341—24no—
65C2×#4341—28no—
66C2×#4341—44no—
67C2×#4341C2318yes—
68C22×D44—22no—
69C22×D44D411yescharacteristic
70C22×D44C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—21no—
73C22×C4×D11C2312yes—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8C2314yes—
79C11×#127—22no—
80C11×#127C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—22no—
85#66999—28no—
86#66993—28no—
87#66992—216no—
88#66991—24no—
89#66991C2318yes—
90D4×Dic11—28no—
91C2×#4323—44no—
92C2×#4323C2318yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4D412yes—
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2312yes—
103C2×#4314—24no—
104C2×#4314C2314yes—
105C2×#4313—44no—
106C2×#4313C2318yes—
107#66948—24no—
108#66948C2318yes—
109#66947—216no—
110C4⋊C4×D11—24no—
111C4⋊C4×D11C2318yes—
112C4×D44—22no—
113C4×D44D414yes—
114C4×D44C2314yes—
115C4×D44C2314yes—
116C4×Dic22—22no—
117C4×Dic22C2314yes—
118C11×#102C2318yes—
119C11×#102C2318yes—
120C4×C8×C11C2314yes—
121#66896C2318yes—
122#66885C2314yes—
123(C2×D11)⋊C8C2318yes—
124#66881C2314yes—
125#66880C2314yes—
126#66874C2318yes—
127#66872C2318yes—
128C4⋊(C11⋊C8)C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11—22no—
131C23×D11—21no—
132C23×D11C2×D412yes—
133C2×Q8×C11—24no—
134C2×Q8×C11—44no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—44no—
141C2×D4×C11—82no—
142C2×D4×C11C2414yes—
143C22×C4×C11—22no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—84no—
151C22×Dic11—28no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—48no—
156C22×Dic11C2×D412yes—
157#4343—432no—
158#4341—216no—
159#4341—48no—
160#4341—416no—
161C2×D44—28no—
162C2×D44—24no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—48no—
167C2×D44C2×D414yes—
168C2×D44C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—24no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—48no—
174C2×C4×D11—44no—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2414yes—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22#4114yescomplemented
180C2×Dic22C2412yes—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11C2412yes—
184C2×C8×C11C2412yes—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4C2414yes—
188C42×C11C2×D412yes—
189C42×C11C2412yes—
190C22⋊Dic11—28no—
191#4323—48no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4C2×D418yes—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2×D414yes—
198C4⋊Dic11C2412yes—
199C4⋊Dic11C2412yes—
200Dic11⋊C4—28no—
201Dic11⋊C4—24no—
202C4×Dic11—24no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2414yes—
205#4314—28no—
206#4313—48no—
207C2×#550—111no—
208C2×#547—111no—
209#3332—1116no—
210C2×#486D1111yescharacteristic, complemented
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459—111no—
215C2×#449—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#417—112no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11C22×D414yes—
232Q8×C11—48no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—44no—
236D4×C11—48no—
237D4×C11—84no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—44no—
241C2×C4×C11AGL(1,ℤ/8)14yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4112yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—416no—
249C22⋊D11—88no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—416no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11C22×D414yes—
259D44—28no—
260D44—22no—
261D44—22no—
262D44—416no—
263D44—42no—
264C4×D11—28no—
265C4×D11—24no—
266C4×D11—24no—
267C4×D11—416no—
268C4×D11—48no—
269Dic22—24no—
270Dic22—22no—
271Dic22C2×#4114yescomplemented
272C8×C11—22no—
273C8×C11—22no—
274C11⋊C8—24no—
275C22×#41—112no—
276C22×#41—221no—
277C22×SD16—111no—
278C22×D8—112no—
279C22×M16—112no—
280#550—118no—
281#550—224no—
282#547—118no—
283#547—224no—
284C2×C4⋊Q8C2×D1111yescharacteristic
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—111no—
295C2×C4×D4—221no—
296C22×C4⋊C4—112no—
297#486C2×D1118yescomplemented
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459—118no—
302#449—1116no—
303C4×SD16—118no—
304#436—118no—
305C2×#106—111no—
306C2×#106—112no—
307C2×C4⋊C8—111no—
308#417—1116no—
309C2×#103—111no—
310C2×#103—112no—
311C2×#102—112no—
312C2×#102—111no—
313C2×#102C2×D1112yes—
314C2×#102C2×D1112yes—
315C2×C22⋊C8—112no—
316C2×C4×C8C2×D1111yescharacteristic
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—88no—
321C22×C11#54612yes—
322C22×C11C2×AGL(1,ℤ/8)12yes—
323C22×C11#57712yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—24no—
326C2×D11—24no—
327C2×D11—24no—
328C2×D11—48no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—84no—
333C4×C11—22no—
334C4×C11—44no—
335C4×C11#54612yes—
336C4×C11C2×AGL(1,ℤ/8)14yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339Dic11—24no—
340Dic11—24no—
341Dic11—42no—
342Dic11—42no—
343C2×#41—118no—
344C2×#41—224no—
345C2×#41—228no—
346C2×#41—228no—
347C2×#41—444no—
348C2×#41—448no—
349C22×Q8—21no—
350C22×Q8—111no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—111no—
354C22×D4—111no—
355C22×D4—222no—
356C22×D4—222no—
357C22×D4—222no—
358C22×D4C22×D1112yes—
359C23×C4—112no—
360C23×C4—222no—
361C23×C4—222no—
362C23×C4—221no—
363C2×SD16—114no—
364C2×SD16—224no—
365C2×D8—118no—
366C2×D8—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—112no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—22no—
373C4⋊Q8C22×D1114yes—
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—114no—
387C4×D4—114no—
388C4×D4—114no—
389C4×D4—228no—
390C4×D4—222no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—118no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1112yes—
400C2×C22⋊C4—112no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—221no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406#106—114no—
407#106—118no—
408C4⋊C8—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—114no—
413#102C22×D1118yes—
414#102C22×D1118yes—
415C22⋊C8—118no—
416C4×C8C22×D1114yes—
417C2×C11—84no—
418C2×C11#333214yescomplemented
419C2×C11C2×#54611yescharacteristic
420C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
421C2×C11C2×#57711yescharacteristic
422D11—44no—
423D11—82no—
424C24—22no—
425C24—112no—
426C24—221no—
427#41—2216no—
428#41—448no—
429#41—4416no—
430#41—4432no—
431C2×Q8—24no—
432C2×Q8—44no—
433C2×Q8—114no—
434C2×Q8—112no—
435C2×Q8—221no—
436C2×Q8—222no—
437C2×D4—24no—
438C2×D4—22no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—44no—
443C2×D4—82no—
444C2×D4—114no—
445C2×D4—112no—
446C2×D4—228no—
447C2×D4—228no—
448C2×D4—228no—
449C2×D4—224no—
450C2×D4—221no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—884no—
456C2×D4C23×D1114yes—
457C22×C4—22no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—228no—
462C22×C4—228no—
463C22×C4—221no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—224no—
469C22×C4—448no—
470C22×C4—448no—
471C22×C4—444no—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476D8—448no—
477M16—448no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—114no—
481C2×C8—224no—
482C2×C8C23×D1112yes—
483C2×C8C23×D1112yes—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—114no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—228no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—224no—
493C4⋊C4C23×D1114yes—
494C22⋊C4—118no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42—224no—
499C42D4×D1112yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—114no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—222no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23C2×D4×D1111yescharacteristic
515Q8—48no—
516Q8—114no—
517Q8—222no—
518Q8—224no—
519D4—24no—
520D4—24no—
521D4—48no—
522D4—44no—
523D4—84no—
524D4—228no—
525D4—222no—
526D4—222no—
527D4—4416no—
528D4—4416no—
529D4—442no—
530D4—888no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—114no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—228no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—4416no—
544C2×C4—4416no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—448no—
548C2×C4#6696414yes—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1112yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4#41×D1112yes—
553C2×C4#6704212yes—
554C2×C4C24×D1111yescharacteristic
555C8—22no—
556C8—22no—
557C8—224no—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—88no—
562C22—224no—
563C22—224no—
564C22—224no—
565C22—448no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—884no—
570C22#1062320712yes—
571C22C2×#6696412yes—
572C22#1062329312yes—
573C22C22×D4×D1111yescharacteristic
574C4—22no—
575C4—44no—
576C4—224no—
577C4—224no—
578C4—442no—
579C4—442no—
580C4#1062320712yes—
581C4C2×#6696414yes—
582C4C2×#41×D1111yescharacteristic
583C4C2×#6704211yescharacteristic
584C2—84no—
585C2—444no—
586C2—882no—
587C2#1308094214yesdirect product factor
588C2C2×#1062320711yescharacteristic
589C2C22×#6696411yescharacteristic
590C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
hypercenterC2×#486D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#10623249C2semidirect
2. C2×#10623257C2semidirect
3. #13080942C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622395C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622394C2semidirect
9. C2×C4×#4314C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622384C2semidirect
12. C2×C11×#486C2semidirect
26. #10623257C22semidirect
28. #10623249C22semidirect
35. C11×#486C22semidirect
44. #10622707C22semidirect
45. #10622685C22semidirect
49. #10622395C22semidirect
50. #10622394C22semidirect
51. #10622390C22semidirect
52. #10622384C22semidirect
53. C4×#4314C22semidirect
54. #10622301C22semidirect
179. C2×Dic22#41semidirect
210. C2×#486D11semidirect
271. Dic22C2×#41semidirect
297. #486C2×D11semidirect
418. C2×C11#3332semidirect
501. C11C2×#3332semidirect
587. C2#13080942direct (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×#106232572
#130809422
C2×#106223902
C2×#106227072
C2×#106223952
C2×#106226852
C2×#106223942
C2×C4×#43142
C2×#106223012
C2×#106223842
C2×C11×#4862
C2×#333211