Finite Group Databasebeta

← C2×#13078593 #15621621

Subgroups — C2×#13078593 #15621621

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3#13078593C2116yesmaximal, direct product factor
4C2×#10622422C212yesmaximal, complemented
5C2×#10622428C212yesmaximal, complemented
6C2×#10622392C212yesmaximal, complemented
7C2×#10622387C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C22×#66871C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C2×#10622742C211yesmaximal, characteristic, complemented
12C2×C11×#417C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17#10623364—24no—
18#10623364C2218yes—
19C2×#66999C2212yes—
20C2×#66992—22no—
21C2×#66991C2212yes—
22C2×#66983—21no—
23C2×C4×C22⋊D11—22no—
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C2×#66977—21no—
27C23×C11⋊C8C2211yescharacteristic
28#10623035—24no—
29#10623035C2218yescomplemented
30C2×#66946—21no—
31C2×#66945C2212yes—
32C2×C4⋊C4×D11C2212yes—
33C2×#66940—21no—
34C11×#417C2218yescomplemented
35C2×C11×#103C2212yes—
36C2×C11×#102C2212yes—
37#10622846C2218yescomplemented
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622742C2218yescomplemented
43#10622734C2218yescomplemented
44C2×(C2×D11)⋊C8C2212yes—
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66882C2212yes—
47C2×#66881C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2218yescomplemented
51#10622428C22116yescomplemented
52#10622422C22116yescomplemented
53#10622392C22116yescomplemented
54#10622387C22116yescomplemented
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41C2314yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—22no—
66C22×C22⋊D11D412yes—
67C23×Dic11—21no—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339D414yes—
71C2×#4339C2314yes—
72C22×D44D411yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11C2312yes—
75C22×Dic22D411yescharacteristic
76C2×C11×M16—24no—
77C2×C11×M16C2314yes—
78C22×C8×C11C2312yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—22no—
85#66999—24no—
86#66999C2318yes—
87#66992—216no—
88#66991—24no—
89#66991C2318yes—
90#66983—28no—
91C4×C22⋊D11—216no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94#66979—22no—
95#66979C2314yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2312yes—
102#66977—28no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—22no—
107C22×C11⋊C8—24no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2314yes—
111#66946—28no—
112#66945—24no—
113#66945C2318yes—
114C4⋊C4×D11—24no—
115C4⋊C4×D11C2318yes—
116#66940—28no—
117C11×#103C2318yes—
118C11×#102C2318yes—
119#66899C2314yes—
120#66899C2314yes—
121#66896C2314yes—
122#66896C2314yes—
123(C2×D11)⋊C8C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66882C2318yes—
126#66881C2318yes—
127#66871C2318yes—
128#66871C2318yes—
129C2×#3098—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C23×D11C2×D412yes—
133C11×#41—28no—
134C11×#41—28no—
135C11×#41—48no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11C2412yes—
140C2×D4×C11—24no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—44no—
145C2×D4×C11C2412yes—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—44no—
151C22×C4×C11—82no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4114yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2412yes—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—84no—
161C2×C22⋊D11C2×D418yes—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—82no—
167C22×Dic11C2×D412yes—
168#4339—216no—
169#4339—28no—
170#4339—28no—
171C2×D44—24no—
172C2×D44C2×D414yes—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—84no—
177C2×C4×D11C2×D414yes—
178C2×C4×D11C2414yes—
179C2×Dic22—24no—
180C2×Dic22C2×D414yes—
181C11×M16—28no—
182C2×C8×C11—24no—
183C2×C8×C11C2414yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2414yes—
187C22⋊Dic11—28no—
188C22⋊Dic11—24no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—24no—
194C4⋊Dic11—22no—
195C4⋊Dic11C2414yes—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11—28no—
201C4×Dic11—24no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—28no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2412yes—
207C2×#537—111no—
208C2×#520—111no—
209#3098—1116no—
210C2×#484—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C22×#107—111no—
216C2×#417D1111yescharacteristic, complemented
217C2×#416—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11#12314yes—
226C23×C11C22×D412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11C22×D414yes—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—42no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—48no—
238D4×C11—42no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—84no—
245C2×C4×C11#12314yes—
246C2×C4×C11#12318yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4114yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4114yes—
253C2×C4×C11C2511yescharacteristic
254C22⋊D11—216no—
255C22⋊D11—88no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11—84no—
264C2×Dic11C22×D414yes—
265D44—28no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—88no—
270Dic22—28no—
271C8×C11—24no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C22×#41—111no—
275C22×#41C2×D1111yescharacteristic
276C22×M16C2×D1111yescharacteristic
277C23×C8—111no—
278#537—118no—
279#537—224no—
280C2×C22⋊Q8—112no—
281C2×C22⋊Q8—221no—
282C2×#121—112no—
283C2×#121—221no—
284C2×#121—222no—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—221no—
289C2×C4×D4—222no—
290C2×#117—111no—
291C2×#117—112no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4—112no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#485—1116no—
296#484—1116no—
297#482—1116no—
298#480—1116no—
299#428—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#107—112no—
303C2×#107—118no—
304C2×#106—112no—
305#417C2×D1118yescomplemented
306#416—118no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103C2×D1112yes—
310C2×#102—111no—
311C2×#102—111no—
312C2×#102C2×D1112yes—
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—84no—
323C22×C11C2×#12314yes—
324C22×C11C2×#12312yes—
325C22×C11#57612yes—
326C22×C11#57812yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—48no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11C2×#12314yes—
335C4×C11C2×#12312yes—
336C4×C11C22×#4111yescharacteristic
337C4×C11C22×#4111yescharacteristic
338Dic11—24no—
339Dic11—42no—
340Dic11—44no—
341Dic11—42no—
342C2×#41—22no—
343C2×#41—24no—
344C2×#41—24no—
345C2×#41—114no—
346C2×#41—114no—
347C2×#41—224no—
348C2×#41—224no—
349C2×#41C22×D1114yes—
350C22×Q8—111no—
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4—112no—
354C22×D4—111no—
355C22×D4—222no—
356C22×D4C22×D1111yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—112no—
360C23×C4—222no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—24no—
364C2×M16C22×D1114yes—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—114no—
368C22×C8—224no—
369C22×C8C22×D1112yes—
370C22⋊Q8—118no—
371C22⋊Q8—228no—
372C22⋊Q8—224no—
373#121—118no—
374#121—228no—
375#121—224no—
376#121—2216no—
377C4×Q8—228no—
378C4×D4—228no—
379C4×D4—2216no—
380#117—114no—
381#117—118no—
382#117—224no—
383#117—222no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4C22×D1112yes—
397C2×C4⋊C4C22×D1114yes—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—221no—
402C2×C42—222no—
403C2×C42—221no—
404#107—118no—
405#107—118no—
406#107—118no—
407#106—118no—
408#103—114no—
409#103—114no—
410#103C22×D1118yes—
411#102—114no—
412#102—114no—
413#102C22×D1118yes—
414C22⋊C8—118no—
415C22⋊C8—118no—
416C2×C11—24no—
417C2×C11—82no—
418C2×C11#309814yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#57611yescharacteristic
421C2×C11C2×#57811yescharacteristic
422D11—44no—
423C24—21no—
424C24—112no—
425C24D4×D1111yescharacteristic
426#41—28no—
427#41—28no—
428#41—48no—
429#41—2216no—
430#41—228no—
431#41—228no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—114no—
436C2×Q8—224no—
437C2×Q8C23×D1112yes—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—44no—
443C2×D4—118no—
444C2×D4—114no—
445C2×D4—228no—
446C2×D4—228no—
447C2×D4—224no—
448C2×D4—884no—
449C2×D4C23×D1112yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—44no—
455C22×C4—82no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—884no—
467C22×C4—882no—
468C22×C4#433914yes—
469C22×C4D4×D1112yes—
470C22×C4D4×D1111yescharacteristic
471C22×C4#434114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—28no—
475C2×C8—24no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—228no—
481C2×C8C23×D1114yes—
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—114no—
487C4⋊C4—228no—
488C4⋊C4—228no—
489C4⋊C4—221no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4—221no—
493C4⋊C4C23×D1114yes—
494C22⋊C4—228no—
495C22⋊C4—228no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42—228no—
499C42—224no—
500C11C2×#309811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—22no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—114no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23#6693614yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—42no—
517Q8—228no—
518D4—22no—
519D4—22no—
520D4—48no—
521D4—42no—
522D4—2216no—
523D4—228no—
524D4—888no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—48no—
530C2×C4—84no—
531C2×C4—114no—
532C2×C4—224no—
533C2×C4—228no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4—442no—
542C2×C4—888no—
543C2×C4—884no—
544C2×C4#6693614yes—
545C2×C4#6693618yes—
546C2×C4C2×#433912yes—
547C2×C4C2×#433914yes—
548C2×C4C2×D4×D1112yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×#434112yes—
551C2×C4C2×#434114yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—222no—
555C8—222no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—84no—
563C22—224no—
564C22—224no—
565C22—224no—
566C22—448no—
567C22C2×#6693614yes—
568C22C2×#6693612yes—
569C22#1062330512yes—
570C22#1062331012yes—
571C22C22×D4×D1111yescharacteristic
572C4—44no—
573C4—42no—
574C4—224no—
575C4—442no—
576C4—444no—
577C4—442no—
578C4C2×#6693614yes—
579C4C2×#6693612yes—
580C4C22×#433911yescharacteristic
581C4C22×#434111yescharacteristic
582C2—24no—
583C2—82no—
584C2—444no—
585C2#1307859314yesdirect product factor
586C2C22×#6693611yescharacteristic
587C2C2×#1062330511yescharacteristic
588C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#417D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. #13078593C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622734C2semidirect
9. C22×#66871C2semidirect
10. C2×#10622846C2semidirect
11. C2×#10622742C2semidirect
12. C2×C11×#417C2semidirect
29. #10623035C22semidirect
34. C11×#417C22semidirect
37. #10622846C22semidirect
42. #10622742C22semidirect
43. #10622734C22semidirect
50. C2×#66871C22semidirect
51. #10622428C22semidirect
52. #10622422C22semidirect
53. #10622392C22semidirect
54. #10622387C22semidirect
216. C2×#417D11semidirect
305. #417C2×D11semidirect
418. C2×C11#3098semidirect
500. C11C2×#3098semidirect
585. C2#13078593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106230352
#130785932
C2×#106224222
C2×#106224282
C2×#106223922
C2×#106223872
C2×#106227342
C22×#668712
C2×#106228462
C2×#106227422
C2×C11×#4172
C2×#309811