Finite Group Databasebeta

← C2×#13080920 #15630681

Subgroups — C2×#13080920 #15630681

Order 2816.

2374 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×#10623257C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic, complemented
3#13080920C2116yesmaximal, direct product factor
4C2×#10622422C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622425C212yesmaximal, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622424C212yesmaximal, complemented
9C2×C4×D88C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622416C212yesmaximal, complemented
12C2×C11×#487C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×#4343C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C2×#66999C2212yes—
19C22×#4325C2212yes—
20C22×D88C2211yescharacteristic
21C22×#4313C2212yes—
22#10623257—24no—
23#10623257—24no—
24#10623257C2218yescomplemented
25#10623257C2218yescomplemented
26C2×#66948—21no—
27C2×#66948C2212yes—
28C2×#66947—22no—
29C2×#66947—22no—
30C2×C4⋊C4×D11—21no—
31C2×C4⋊C4×D11C2212yes—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C11×#487C2218yescomplemented
36C2×C11×#103C2212yes—
37C2×C11×#103C2212yes—
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2211yescharacteristic
44#10622700C2218yescomplemented
45#10622696C2218yescomplemented
46C2×#66873C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622425C22116yescomplemented
50#10622424C22116yescomplemented
51#10622422C22116yescomplemented
52#10622416C22116yescomplemented
53C4×D88C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2312yes—
57C2×#4343—28no—
58C2×#4343—24no—
59C2×#4343—28no—
60C2×#4343—44no—
61C2×#4343—48no—
62C2×#4343C2318yes—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44D411yescharacteristic
66C22×D44C2311yescharacteristic
67C22×D44C2311yescharacteristic
68C22×C4×D11—22no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—22no—
72C22×C4×D11C2312yes—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8C2314yes—
78C11×C4⋊Q8C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2312yes—
83C2×C42×C11C2311yescharacteristic
84#66999—24no—
85#66999—28no—
86#66999C2318yes—
87C2×#4325—44no—
88C2×#4325C2318yes—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4D412yes—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C22×C11⋊C8C2312yes—
100C2×D88—24no—
101C2×D88C2314yes—
102C2×#4313—44no—
103C2×#4313C2318yes—
104#66948—28no—
105#66948—24no—
106#66948C2318yes—
107#66947—216no—
108#66947—216no—
109C4⋊C4×D11—24no—
110C4⋊C4×D11—28no—
111C4⋊C4×D11C2318yes—
112C4×D44—22no—
113C4×D44—22no—
114C4×D44D414yes—
115C4×D44C2314yes—
116C4×D44C2314yes—
117C4×D44C2314yes—
118C11×#103C2318yes—
119C11×#103C2318yes—
120C4×C8×C11C2314yes—
121#66899C2318yes—
122#66885C2314yes—
123#66885C2314yes—
124(C2×D11)⋊C8C2318yes—
125#66882C2314yes—
126#66873C2318yes—
127#66871C2318yes—
128C4⋊(C11⋊C8)C2314yes—
129C2×#3330—111nomaximal, Sylow
130C23×D11—21no—
131C23×D11—21no—
132C23×D11C2×D412yes—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11—44no—
138C2×Q8×C11C2414yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D412yes—
147#4343—216no—
148#4343—48no—
149#4343—416no—
150#4343—432no—
151C2×D44—28no—
152C2×D44—28no—
153C2×D44—24no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—48no—
160C2×D44—48no—
161C2×D44C2×D414yes—
162C2×D44#4114yescomplemented
163C2×D44C2412yes—
164C2×D44C2412yes—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C2×C4×D11C2×D414yes—
176C2×C4×D11C2414yes—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11C2412yes—
180C2×C8×C11C2412yes—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4C2414yes—
186C42×C11C2×D412yes—
187C42×C11C2412yes—
188#4325—48no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4C2×D418yes—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D414yes—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2412yes—
199Dic11⋊C4—28no—
200Dic11⋊C4—28no—
201C2×C11⋊C8—24no—
202C2×C11⋊C8C2414yes—
203D88—28no—
204#4313—48no—
205C2×#547—111no—
206C2×#547—111no—
207#3330—1116no—
208C2×#487D1111yescharacteristic, complemented
209C2×#484—112no—
210C2×#474—111no—
211C2×#468—112no—
212C2×#461—111no—
213C2×#449—112no—
214C2×C4×D8—111no—
215C2×#436—111no—
216C2×#417—112no—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11C22×D414yes—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—44no—
233Q8×C11—48no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11AGL(1,ℤ/8)14yes—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11C2511yescharacteristic
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11C22×D414yes—
252D44—24no—
253D44—28no—
254D44—22no—
255D44—22no—
256D44—22no—
257D44—416no—
258D44—416no—
259D44—42no—
260D44C2×#4114yescomplemented
261C4×D11—28no—
262C4×D11—24no—
263C4×D11—24no—
264C4×D11—416no—
265C4×D11—416no—
266C4×D11—48no—
267C4×D11—48no—
268C8×C11—22no—
269C8×C11—22no—
270C11⋊C8—24no—
271C22×#41—112no—
272C22×#41—221no—
273C22×SD16—112no—
274C22×D8—111no—
275C22×M16—112no—
276#547—118no—
277#547—118no—
278#547—224no—
279#547—224no—
280C2×C4⋊Q8C2×D1111yescharacteristic
281C2×C4⋊Q8C2×D1111yescharacteristic
282C2×#123—222no—
283C2×#123—222no—
284C2×C22⋊Q8—112no—
285C2×C22⋊Q8—221no—
286C2×#121—112no—
287C2×#121—221no—
288C2×C4×D4—111no—
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C22×C4⋊C4—112no—
292C22×C4⋊C4—221no—
293#487C2×D1118yescomplemented
294#484—1116no—
295#474—118no—
296#468—1116no—
297#461—118no—
298#449—1116no—
299C4×D8—118no—
300#436—118no—
301C2×#107—111no—
302C2×#107—112no—
303C2×C4⋊C8—111no—
304#417—1116no—
305C2×#103—112no—
306C2×#103C2×D1112yes—
307C2×#103C2×D1112yes—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—112no—
311C2×C22⋊C8—112no—
312C2×C4×C8C2×D1111yescharacteristic
313C22×C11#54612yes—
314C22×C11C2×AGL(1,ℤ/8)12yes—
315C22×C11#57812yes—
316C22×C11C23×D411yescharacteristic
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—24no—
321C2×D11—48no—
322C2×D11—48no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—84no—
329C4×C11—22no—
330C4×C11—44no—
331C4×C11—44no—
332C4×C11#54612yes—
333C4×C11C2×AGL(1,ℤ/8)14yes—
334C4×C11C22×#4111yescharacteristic
335C4×C11C2×H(5,𝔽2)11yescharacteristic
336Dic11—24no—
337Dic11—42no—
338Dic11—42no—
339C2×#41—118no—
340C2×#41—224no—
341C2×#41—228no—
342C2×#41—228no—
343C2×#41—444no—
344C2×#41—448no—
345C22×Q8—21no—
346C22×Q8C22×D1112yes—
347C22×D4—111no—
348C22×D4—111no—
349C22×D4—111no—
350C22×D4—222no—
351C22×D4—222no—
352C23×C4—112no—
353C23×C4—222no—
354C23×C4—222no—
355C23×C4—221no—
356C23×C4—221no—
357C2×SD16—118no—
358C2×SD16—444no—
359C2×D8—114no—
360C2×D8—224no—
361C2×M16—118no—
362C2×M16—444no—
363C22×C8—112no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8C22×D1114yes—
369C4⋊Q8C22×D1114yes—
370#123—2216no—
371#123—2216no—
372C22⋊Q8—118no—
373C22⋊Q8—228no—
374C22⋊Q8—224no—
375#121—118no—
376#121—224no—
377#121—228no—
378C4×D4—114no—
379C4×D4—114no—
380C4×D4—114no—
381C4×D4—114no—
382C4×D4—222no—
383C4×D4—222no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4C22×D1112yes—
396C2×C22⋊C4—112no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42C22×D1111yescharacteristic
402#107—114no—
403#107—118no—
404C4⋊C8—114no—
405#103—118no—
406#103C22×D1118yes—
407#103C22×D1118yes—
408#102—114no—
409#102—114no—
410#102—118no—
411C22⋊C8—118no—
412C4×C8C22×D1114yes—
413C2×C11#333014yescomplemented
414C2×C11C2×#54611yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C11C2×#57811yescharacteristic
417D11—44no—
418D11—44no—
419D11—82no—
420C24—112no—
421C24—221no—
422C24—221no—
423#41—2216no—
424#41—448no—
425#41—4416no—
426#41—4432no—
427C2×Q8—22no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—44no—
432C2×Q8C23×D1114yes—
433C2×D4—114no—
434C2×D4—114no—
435C2×D4—112no—
436C2×D4—112no—
437C2×D4—228no—
438C2×D4—228no—
439C2×D4—224no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—448no—
446C2×D4—448no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—112no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—228no—
453C22×C4—228no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—448no—
461C22×C4—448no—
462C22×C4—444no—
463C22×C4—444no—
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467SD16—448no—
468D8—228no—
469M16—448no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—114no—
473C2×C8—224no—
474C2×C8C23×D1112yes—
475C2×C8C23×D1112yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—114no—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—228no—
484C4⋊C4—228no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4C23×D1114yes—
488C22⋊C4—118no—
489C22⋊C4—228no—
490C22⋊C4—228no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C42D4×D1112yes—
494C42C23×D1112yes—
495C11C2×#333011yescharacteristic, complemented, Sylow
496C23—114no—
497C23—224no—
498C23—224no—
499C23—222no—
500C23—224no—
501C23—224no—
502C23—222no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23C2×D4×D1111yescharacteristic
509Q8—24no—
510Q8—24no—
511Q8—48no—
512Q8—44no—
513D4—114no—
514D4—228no—
515D4—222no—
516D4—222no—
517D4—222no—
518D4—224no—
519D4—4416no—
520D4—4416no—
521D4—442no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—114no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—228no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—4416no—
535C2×C4—4416no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—448no—
539C2×C4—448no—
540C2×C4#6696714yes—
541C2×C4C2×D4×D1112yes—
542C2×C4C2×D4×D1112yes—
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4#41×D1112yes—
545C2×C4#6704212yes—
546C2×C4C24×D1111yescharacteristic
547C8—22no—
548C8—22no—
549C8—224no—
550C22—224no—
551C22—224no—
552C22—224no—
553C22—224no—
554C22—448no—
555C22—448no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062320712yes—
563C22C2×#6696712yes—
564C22#1062329712yes—
565C22C22×D4×D1111yescharacteristic
566C4—22no—
567C4—44no—
568C4—44no—
569C4—224no—
570C4—442no—
571C4—442no—
572C4#1062320712yes—
573C4C2×#6696714yes—
574C4C2×#41×D1111yescharacteristic
575C4C2×#6704211yescharacteristic
576C2—444no—
577C2—444no—
578C2—882no—
579C2#1308092014yesdirect product factor
580C2C2×#1062320711yescharacteristic
581C2C22×#6696711yescharacteristic
582C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
hypercenterC2×#487D11
hypocenterC11C2×#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×#10623257C2semidirect
2. C2×#10623257C2semidirect
3. #13080920C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622425C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622424C2semidirect
9. C2×C4×D88C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622416C2semidirect
12. C2×C11×#487C2semidirect
24. #10623257C22semidirect
25. #10623257C22semidirect
35. C11×#487C22semidirect
44. #10622700C22semidirect
45. #10622696C22semidirect
49. #10622425C22semidirect
50. #10622424C22semidirect
51. #10622422C22semidirect
52. #10622416C22semidirect
53. C4×D88C22semidirect
54. #10622301C22semidirect
162. C2×D44#41semidirect
208. C2×#487D11semidirect
260. D44C2×#41semidirect
293. #487C2×D11semidirect
413. C2×C11#3330semidirect
495. C11C2×#3330semidirect
579. C2#13080920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232572
#130809202
C2×#106224222
C2×#106227002
C2×#106224252
C2×#106226962
C2×#106224242
C2×C4×D882
C2×#106223012
C2×#106224162
C2×C11×#4872
C2×#333011