Finite Group Databasebeta

← C2×#13069618 #14780562

Subgroups — C2×#13069618 #14780562

Order 2816.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4325C211yesmaximal, characteristic, complemented
2C22×#66999C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic
4C22×#66885C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
6#13069618C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44—21no—
11C23×D44C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66999—24no—
16C2×#66999—22no—
17C2×#66999—24no—
18C2×#66999C2214yescomplemented
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325—24no—
22C22×#4325C2214yescomplemented
23C22×(C2×D11)⋊C4—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4—21no—
27C23×C11⋊C8C2211yescharacteristic
28C2×#66948—24no—
29C2×#66948—22no—
30C2×#66948—24no—
31C2×#66948C2214yes—
32C2×C11×#103—24no—
33C2×C11×#103C2214yescomplemented
34C2×#66885—24no—
35C2×#66885C2214yescomplemented
36C2×(C2×D11)⋊C8—24no—
37C2×(C2×D11)⋊C8C2214yescomplemented
38#10622167C2214yescomplemented
39C24×D11—21no—
40C24×D11D411yescharacteristic
41C22×Q8×C11—22no—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11D414yescomplemented
48C22×Q8×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C23×Dic11D411yescharacteristic
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—28no—
59C22×D44—24no—
60C22×D44—21no—
61C22×D44—22no—
62C22×D44—44no—
63C22×D44—44no—
64C22×D44D414yes—
65C22×D44C2312yes—
66C22×C4×D11—22no—
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11D412yes—
73C22×C4×D11C2312yes—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11C2312yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D414yes—
81C2×C11×C4⋊C4C2312yes—
82#66999—216no—
83#66999—28no—
84#66999—28no—
85C2×#4325—232no—
86C2×#4325—28no—
87C2×#4325—28no—
88C2×#4325—28no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D414yescomplemented
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4—24no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8D414yescomplemented
102C22×C11⋊C8C2312yes—
103#66948—216no—
104#66948—28no—
105#66948—28no—
106C11×#103—28no—
107#66885—28no—
108(C2×D11)⋊C8—28no—
109C2×#2000—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—24no—
118C23×D11—22no—
119C23×D11—42no—
120C23×D11—42no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11—42no—
124C23×D11—42no—
125C23×D11SD1614yescomplemented
126C23×D11C2×D412yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—22no—
129C2×Q8×C11—28no—
130C2×Q8×C11—28no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—44no—
138C2×Q8×C11—44no—
139C2×Q8×C11C2×D414yescomplemented
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11C2×D412yes—
164C2×D44—216no—
165C2×D44—24no—
166C2×D44—28no—
167C2×D44—28no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—48no—
174C2×D44—432no—
175C2×D44—48no—
176C2×D44—42no—
177C2×D44—42no—
178C2×D44—44no—
179C2×D44—44no—
180C2×D44C2×D414yes—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11—44no—
194C2×C8×C11—22no—
195C2×C8×C11—22no—
196C2×C8×C11—22no—
197C2×C8×C11—44no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C2×D414yes—
201#4325—232no—
202(C2×D11)⋊C4—216no—
203(C2×D11)⋊C4—216no—
204C4⋊Dic11—24no—
205C4⋊Dic11—22no—
206C4⋊Dic11C2×D414yescomplemented
207Dic11⋊C4—216no—
208C2×C11⋊C8—28no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8C2×D414yescomplemented
212C23×SD16—111no—
213C22×C22⋊Q8—111no—
214C22×#121—111no—
215C22×#103D1111yescharacteristic, complemented
216C22×#102—111no—
217C22×C22⋊C8—111no—
218#2000—118no—
219C2×#340—111no—
220C23×C11#12012yes—
221C23×C11#12012yes—
222C23×C11#12112yes—
223C23×C11C2×SD1612yes—
224C23×C11#13512yes—
225C23×C11AGL(1,ℤ/8)12yes—
226C23×C11#13712yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—28no—
235C22×D11—28no—
236C22×D11—28no—
237C22×D11—24no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11—84no—
252C22×D11—84no—
253C22×D11—84no—
254C22×D11—84no—
255C22×D11C2×SD1614yescomplemented
256Q8×C11—24no—
257Q8×C11—24no—
258Q8×C11—42no—
259Q8×C11—42no—
260Q8×C11—48no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—48no—
268C2×C4×C11—48no—
269C2×C4×C11#12014yes—
270C2×C4×C11#12012yes—
271C2×C4×C11#12012yes—
272C2×C4×C11#12114yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12114yes—
275C2×C4×C11#12714yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—44no—
289C2×Dic11—48no—
290D44—24no—
291D44—24no—
292D44—432no—
293D44—42no—
294D44—42no—
295D44—48no—
296C4×D11—42no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—42no—
300C4×D11—48no—
301C8×C11—42no—
302C11⋊C8—24no—
303C23×Q8C2×D1111yescharacteristic
304C23×D4—111no—
305C23×D4—221no—
306C24×C4—111no—
307C22×SD16—114no—
308C22×SD16—224no—
309C22×SD16—224no—
310C22×SD16—224no—
311C23×C8—111no—
312C23×C8C2×D1111yescharacteristic
313C2×C22⋊Q8—114no—
314C2×C22⋊Q8—224no—
315C2×C22⋊Q8—222no—
316C2×C22⋊Q8—224no—
317C2×#121—114no—
318C2×#121—222no—
319C2×#121—224no—
320C2×#121—224no—
321C22×C4⋊C4—111no—
322C22×C4⋊C4—221no—
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C22⋊C4—221no—
325C22×C22⋊C4—221no—
326C2×#103—24no—
327C2×#103C2×D1114yescomplemented
328C2×#102—114no—
329C2×#102—224no—
330C2×C22⋊C8—114no—
331C2×C22⋊C8—224no—
332#340—114no—
333C22×C11#39214yes—
334C22×C11#44814yes—
335C22×C11#44914yes—
336C22×C11#45014yes—
337C22×C11#45214yes—
338C22×C11#46514yes—
339C22×C11#46814yes—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×#12011yescharacteristic
342C22×C11C2×#12111yescharacteristic
343C22×C11C22×SD1611yescharacteristic
344C22×C11C2×#13511yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—416no—
354C2×D11—42no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—82no—
359C2×D11—82no—
360C2×D11—816no—
361C2×D11—82no—
362C2×D11—82no—
363C4×C11—44no—
364C4×C11—44no—
365C4×C11#39214yes—
366C4×C11C2×#12011yescharacteristic
367C4×C11C2×#12111yescharacteristic
368C4×C11C2×#12111yescharacteristic
369C4×C11C2×#12711yescharacteristic
370Dic11—42no—
371Dic11—44no—
372C25—111no—
373C25—221no—
374C22×Q8—22no—
375C22×Q8—21no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8D4414yescomplemented
381C22×Q8C22×D1112yes—
382C22×D4—114no—
383C22×D4—112no—
384C22×D4—224no—
385C22×D4—228no—
386C22×D4—222no—
387C22×D4—222no—
388C22×D4—222no—
389C22×D4—222no—
390C22×D4—221no—
391C22×D4—222no—
392C22×D4—444no—
393C22×D4—444no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—111no—
397C23×C4—112no—
398C23×C4—112no—
399C23×C4—221no—
400C23×C4—222no—
401C23×C4—222no—
402C23×C4—222no—
403C23×C4—222no—
404C23×C4—222no—
405C23×C4—222no—
406C23×C4C22×D1111yescharacteristic
407C2×SD16—228no—
408C2×SD16—228no—
409C2×SD16—2232no—
410C2×SD16—228no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—114no—
415C22×C8—112no—
416C22×C8—222no—
417C22×C8—222no—
418C22×C8C22×D1112yes—
419C22⋊Q8—228no—
420C22⋊Q8—2216no—
421C22⋊Q8—228no—
422#121—228no—
423#121—2216no—
424#121—228no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4—228no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22⋊D1114yes—
434C2×C4⋊C4C22×D1112yes—
435C2×C22⋊C4—224no—
436C2×C22⋊C4—224no—
437C2×C22⋊C4—228no—
438C2×C22⋊C4—228no—
439#103—28no—
440#102—228no—
441C22⋊C8—228no—
442C2×C11#200018yescomplemented
443C2×C11C2×#39211yescharacteristic
444C2×C11C2×#45011yescharacteristic
445C2×C11C2×#44811yescharacteristic
446C2×C11C2×#44911yescharacteristic
447C2×C11C2×#45211yescharacteristic
448C2×C11C2×#46511yescharacteristic
449C2×C11C2×#46811yescharacteristic
450D11—44no—
451D11—84no—
452C24—114no—
453C24—112no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24—224no—
461C24—222no—
462C24—442no—
463C24—442no—
464C24—442no—
465C24—442no—
466C24—442no—
467C24—442no—
468C24D4×D1111yescharacteristic
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—42no—
478C2×Q8—44no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8C2×D4414yescomplemented
482C2×D4—114no—
483C2×D4—2216no—
484C2×D4—228no—
485C2×D4—228no—
486C2×D4—224no—
487C2×D4—222no—
488C2×D4—222no—
489C2×D4—222no—
490C2×D4—222no—
491C2×D4—222no—
492C2×D4—448no—
493C2×D4—448no—
494C2×D4—4432no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—444no—
498C2×D4—444no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—112no—
508C22×C4—224no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—444no—
525C22×C4—444no—
526C22×C4—444no—
527C22×C4—444no—
528C22×C4C2×D4412yes—
529C22×C4#433912yes—
530C22×C4D4×D1111yescharacteristic
531C22×C4D4×D1112yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1112yes—
534C22×C4C2×C22⋊D1112yes—
535C22×C4C23×D1111yescharacteristic
536SD16—2232no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—44no—
541C2×C8—114no—
542C2×C8—228no—
543C2×C8—222no—
544C2×C8—222no—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—114no—
548C4⋊C4—2216no—
549C4⋊C4—224no—
550C4⋊C4—222no—
551C4⋊C4C2×C22⋊D1114yes—
552C22⋊C4—2216no—
553C22⋊C4—2216no—
554C11C2×#200011yescharacteristic, complemented, Sylow
555C23—114no—
556C23—222no—
557C23—222no—
558C23—222no—
559C23—228no—
560C23—222no—
561C23—222no—
562C23—222no—
563C23—228no—
564C23—228no—
565C23—224no—
566C23—444no—
567C23—444no—
568C23—444no—
569C23—444no—
570C23—442no—
571C23—442no—
572C23—442no—
573C23—442no—
574C23—448no—
575C23—442no—
576C23—442no—
577C23—448no—
578C23—448no—
579C23—884no—
580C23—884no—
581C23—884no—
582C23—884no—
583C23#6693512yes—
584C23#6693712yes—
585C23SD16×D1112yes—
586C23#6696712yes—
587C23#6697112yes—
588C23#6697212yes—
589C23#6699012yes—
590C23C2×D4×D1111yescharacteristic
591Q8—24no—
592Q8—24no—
593Q8—42no—
594Q8—42no—
595Q8—48no—
596D4—224no—
597D4—224no—
598D4—4432no—
599D4—442no—
600D4—442no—
601D4—448no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—48no—
608C2×C4—42no—
609C2×C4—48no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—444no—
617C2×C4—448no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—448no—
623C2×C4#6693514yes—
624C2×C4#6693512yes—
625C2×C4#6693714yes—
626C2×C4#6693712yes—
627C2×C4#6698314yes—
628C2×C4#6699012yes—
629C2×C4#6699314yes—
630C2×C4C22×D4411yescharacteristic
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C22×C22⋊D1111yescharacteristic
636C8—42no—
637C8—224no—
638C22—224no—
639C22—224no—
640C22—224no—
641C22—4416no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—442no—
646C22—444no—
647C22—444no—
648C22—444no—
649C22—882no—
650C22—8816no—
651C22—882no—
652C22—882no—
653C22—882no—
654C22#1062241914yes—
655C22#1062242014yes—
656C22#1062242414yes—
657C22#1062242514yes—
658C22#1062257314yes—
659C22#1062278214yes—
660C22#1062280014yes—
661C22C2×#6693511yescharacteristic
662C22C2×#6693711yescharacteristic
663C22C2×SD16×D1111yescharacteristic
664C22C2×#6696711yescharacteristic
665C22C2×#6697111yescharacteristic
666C22C2×#6697211yescharacteristic
667C22C2×#6699011yescharacteristic
668C4—44no—
669C4—44no—
670C4—444no—
671C4—442no—
672C4#1062257314yes—
673C4C2×#6693511yescharacteristic
674C4C2×#6693711yescharacteristic
675C4C2×#6698311yescharacteristic
676C4C2×#6699311yescharacteristic
677C2—444no—
678C2—884no—
679C2#1306961818yesdirect product factor
680C2C2×#1062257311yescharacteristic
681C2C2×#1062278211yescharacteristic
682C2C2×#1062241911yescharacteristic
683C2C2×#1062242411yescharacteristic
684C2C2×#1062280011yescharacteristic
685C2C2×#1062242011yescharacteristic
686C2C2×#1062242511yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC22×#66948C2
hypercenterC22×#103D11
hypocenterC11C2×#2000
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#4325C2semidirect
2. C22×#66999C2semidirect
4. C22×#66885C2semidirect
5. C22×(C2×D11)⋊C8C2semidirect
6. #13069618C2direct (N × H)
7. C2×#10622167C2semidirect
8. C22×C11×#103C2semidirect
18. C2×#66999C22semidirect
22. C22×#4325C22semidirect
33. C2×C11×#103C22semidirect
35. C2×#66885C22semidirect
37. C2×(C2×D11)⋊C8C22semidirect
38. #10622167C22semidirect
47. C22×Q8×C11D4semidirect
95. C2×C4⋊Dic11D4semidirect
101. C22×C11⋊C8D4semidirect
125. C23×D11SD16semidirect
139. C2×Q8×C11C2×D4semidirect
206. C4⋊Dic11C2×D4semidirect
211. C2×C11⋊C8C2×D4semidirect
215. C22×#103D11semidirect
255. C22×D11C2×SD16semidirect
327. C2×#103C2×D11semidirect
380. C22×Q8D44semidirect
442. C2×C11#2000semidirect
481. C2×Q8C2×D44semidirect
554. C11C2×#2000semidirect
679. C2#13069618direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43252
C22×#669992
C22×#669482
C22×#668852
C22×(C2×D11)⋊C82
#130696182
C2×#106221672
C22×C11×#1032
C2×#200011