Finite Group Databasebeta

← C2×#13069806 #14781238

Subgroups — C2×#13069806 #14781238

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic
2C22×#66881C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4C22×#66885C211yesmaximal, characteristic, complemented
5C2×#10622825C211yesmaximal, characteristic, complemented
6#13069806C218yesmaximal, direct product factor
7C2×#10622189C211yesmaximal, characteristic, complemented
8C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C23×C22⋊D11—21no—
11C23×D44C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C22⋊Dic11—21no—
15C2×#66983—22no—
16C2×#66983—24no—
17C2×#66983—24no—
18C2×#66983C2214yes—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×C11×C22⋊C8—24no—
24C2×C11×C22⋊C8C2214yescomplemented
25#10622825—22no—
26#10622825C2214yescomplemented
27C2×C11⋊#95—21no—
28C2×#66885—24no—
29C2×#66885—24no—
30C2×#66885C2214yescomplemented
31C2×#66885C2214yescomplemented
32C2×#66881—24no—
33C2×#66881C2214yescomplemented
34#10622189C2214yescomplemented
35C25×C11D411yescharacteristic
36C24×D11—21no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—28no—
48C22×C22⋊D11—24no—
49C22×C22⋊D11—44no—
50C22×C22⋊D11—44no—
51C23×Dic11—21no—
52C23×Dic11—21no—
53C23×Dic11—21no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—21no—
59C22×D44—22no—
60C22×D44D414yes—
61C22×D44C2312yes—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11D414yescomplemented
68C22×C8×C11C2312yes—
69C22×C8×C11C2312yes—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—44no—
72#66983—216no—
73#66983—28no—
74#66983—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—24no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D414yes—
86C2×C4⋊Dic11C2312yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C11×C22⋊C8—28no—
90C11⋊#95—24no—
91#66885—28no—
92#66885—28no—
93#66881—28no—
94C2×#2034—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11SD1614yes—
102C24×C11C2×D412yes—
103C24×C11C2×D411yescharacteristic
104C23×D11—24no—
105C23×D11—22no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11—42no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11—44no—
127C22×C4×C11—44no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—216no—
138C2×C22⋊D11—48no—
139C2×C22⋊D11—432no—
140C2×C22⋊D11—48no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C2×D44—24no—
154C2×D44—28no—
155C2×D44—28no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—42no—
162C2×D44—44no—
163C2×D44—42no—
164C2×D44—44no—
165C2×D44C2×D414yes—
166C2×C8×C11—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—44no—
173C2×C8×C11C2×D414yescomplemented
174C22⋊Dic11—48no—
175(C2×D11)⋊C4—216no—
176C4⋊Dic11—24no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184C4⋊Dic11C2×D414yes—
185C22×#121—111no—
186C22×#106—111no—
187C22×#102—111no—
188C22×#102—111no—
189C22×C22⋊C8D1111yescharacteristic, complemented
190C2×#380—111no—
191#2034—118no—
192C2×#340—111no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—28no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11#12012yes—
207C23×C11#12112yes—
208C23×C11#12312yes—
209C23×C11C2×SD1614yes—
210C23×C11C2×SD1612yes—
211C23×C11#13512yes—
212C23×C11AGL(1,ℤ/8)12yes—
213C23×C11AGL(1,ℤ/8)12yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—84no—
226C22×D11—84no—
227C22×D11—84no—
228C22×D11—84no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—48no—
238C2×C4×C11#12012yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12114yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12314yes—
243C2×C4×C11#12312yes—
244C2×C4×C11#12414yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—432no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—48no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—84no—
263C2×Dic11—84no—
264D44—24no—
265D44—24no—
266D44—42no—
267D44—42no—
268D44—48no—
269C8×C11—24no—
270C8×C11—42no—
271C23×D4—111no—
272C23×D4—221no—
273C24×C4C2×D1111yescharacteristic
274C23×C8C2×D1111yescharacteristic
275C23×C8C2×D1111yescharacteristic
276C2×#121—114no—
277C2×#121—224no—
278C2×#121—224no—
279C2×#121—222no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—111no—
283C22×C22⋊C4—221no—
284C22×C22⋊C4—221no—
285C2×#106—114no—
286C2×#106—224no—
287C2×#102—114no—
288C2×#102—114no—
289C2×#102—224no—
290C2×#102—224no—
291C2×C22⋊C8—24no—
292C2×C22⋊C8C2×D1114yescomplemented
293#380—114no—
294#380—222no—
295C2×#95—221no—
296#340—114no—
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—416no—
305C22×C11#39414yes—
306C22×C11#44914yes—
307C22×C11#45014yes—
308C22×C11#46514yes—
309C22×C11#46914yes—
310C22×C11#48114yes—
311C22×C11#48214yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11C2×#12111yescharacteristic
314C22×C11C2×#12311yescharacteristic
315C22×C11C22×SD1611yescharacteristic
316C22×C11C2×#13511yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C2×D11—82no—
326C2×D11—816no—
327C4×C11—42no—
328C4×C11#39414yes—
329C4×C11C2×#12111yescharacteristic
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×#12311yescharacteristic
332C4×C11C2×#12411yescharacteristic
333Dic11—44no—
334Dic11—82no—
335Dic11—82no—
336C25—221no—
337C25D4411yescharacteristic
338C22×D4—114no—
339C22×D4—112no—
340C22×D4—228no—
341C22×D4—224no—
342C22×D4—221no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4—222no—
348C22×D4—444no—
349C22×D4—444no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4D4412yes—
360C23×C4D4411yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8C22⋊D1114yescomplemented
369C22×C8C22×D1112yes—
370C22×C8C22×D1112yes—
371#121—228no—
372#121—228no—
373#121—2216no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C22⋊C4—228no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—444no—
390#106—228no—
391#102—228no—
392#102—228no—
393C22⋊C8—28no—
394#95—224no—
395C2×C11—44no—
396C2×C11#203418yescomplemented
397C2×C11C2×#39411yescharacteristic
398C2×C11C2×#45011yescharacteristic
399C2×C11C2×#44911yescharacteristic
400C2×C11C2×#46511yescharacteristic
401C2×C11C2×#46911yescharacteristic
402C2×C11C2×#48211yescharacteristic
403C2×C11C2×#48111yescharacteristic
404D11—84no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—224no—
412C24—222no—
413C24—442no—
414C24—442no—
415C24—442no—
416C24—442no—
417C24—442no—
418C24—442no—
419C24#431414yes—
420C24C2×D4412yes—
421C24C2×D4411yescharacteristic
422C2×D4—114no—
423C2×D4—2216no—
424C2×D4—224no—
425C2×D4—228no—
426C2×D4—228no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—448no—
433C2×D4—4432no—
434C2×D4—448no—
435C2×D4—444no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—444no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—224no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4C2×D4412yes—
468C22×C4C2×D4411yescharacteristic
469C22×C4#433912yes—
470C22×C4D4×D1112yes—
471C22×C4D4×D1112yes—
472C22×C4#434112yes—
473C22×C4#434112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—28no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—44no—
483C2×C8C2×C22⋊D1114yescomplemented
484C4⋊C4—114no—
485C4⋊C4—224no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C22⋊C4—2216no—
494C22⋊C4—448no—
495C11C2×#203411yescharacteristic, complemented, Sylow
496C23—28no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—28no—
504C23—28no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—224no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—448no—
517C23—448no—
518C23—448no—
519C23—884no—
520C23—884no—
521C23—884no—
522C23—884no—
523C23#6693512yes—
524C23#6693912yes—
525C23C2×#431414yes—
526C23C2×#431412yes—
527C23#6695712yes—
528C23#6696112yes—
529C23#6696112yes—
530C23#6698312yes—
531C23C22×D4411yescharacteristic
532D4—224no—
533D4—224no—
534D4—4432no—
535D4—442no—
536D4—442no—
537D4—448no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—48no—
547C2×C4—224no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—448no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—884no—
558C2×C4—884no—
559C2×C4#6693512yes—
560C2×C4#6693614yes—
561C2×C4#6693814yes—
562C2×C4#6693912yes—
563C2×C4#6698312yes—
564C2×C4#6699114yes—
565C2×C4#6699214yes—
566C2×C4C2×#433911yescharacteristic
567C2×C4C2×D4×D1111yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C8—24no—
573C8—42no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—416no—
582C22—444no—
583C22—444no—
584C22—444no—
585C22—882no—
586C22—882no—
587C22—882no—
588C22—8816no—
589C22—882no—
590C22#1062234414yes—
591C22#1062234714yes—
592C22#1062234814yes—
593C22#1062235014yes—
594C22#1062257414yes—
595C22#1062272714yes—
596C22#1062274814yes—
597C22C2×#6693511yescharacteristic
598C22C2×#6693911yescharacteristic
599C22C22×#431411yescharacteristic
600C22C2×#6695711yescharacteristic
601C22C2×#6696111yescharacteristic
602C22C2×#6696111yescharacteristic
603C22C2×#6698311yescharacteristic
604C4—42no—
605C4—444no—
606C4—882no—
607C4—882no—
608C4#1062257414yes—
609C4C2×#6693611yescharacteristic
610C4C2×#6693811yescharacteristic
611C4C2×#6699111yescharacteristic
612C4C2×#6699211yescharacteristic
613C2—44no—
614C2—884no—
615C2#1306980618yesdirect product factor
616C2C2×#1062257411yescharacteristic
617C2C2×#1062234411yescharacteristic
618C2C2×#1062234711yescharacteristic
619C2C2×#1062272711yescharacteristic
620C2C2×#1062274811yescharacteristic
621C2C2×#1062235011yescharacteristic
622C2C2×#1062234811yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC22×#66983C2
hypercenterC22×C22⋊C8D11
hypocenterC11C2×#2034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66881C2semidirect
3. C22×#66885C2semidirect
4. C22×#66885C2semidirect
5. C2×#10622825C2semidirect
6. #13069806C2direct (N × H)
7. C2×#10622189C2semidirect
8. C22×C11×C22⋊C8C2semidirect
24. C2×C11×C22⋊C8C22semidirect
26. #10622825C22semidirect
30. C2×#66885C22semidirect
31. C2×#66885C22semidirect
33. C2×#66881C22semidirect
34. #10622189C22semidirect
67. C22×C8×C11D4semidirect
173. C2×C8×C11C2×D4semidirect
189. C22×C22⋊C8D11semidirect
292. C2×C22⋊C8C2×D11semidirect
368. C22×C8C22⋊D11semidirect
396. C2×C11#2034semidirect
483. C2×C8C2×C22⋊D11semidirect
495. C11C2×#2034semidirect
615. C2#13069806direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#668812
C22×#668852
C2×#106228252
#130698062
C2×#106221892
C22×C11×C22⋊C82
C2×#203411