Finite Group Databasebeta

← C2×#13069802 #14781234

Subgroups — C2×#13069802 #14781234

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×#66872C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622825C211yesmaximal, characteristic, complemented
6#13069802C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×#121C211yesmaximal, characteristic
9C23×D4×C11—21no—
10C23×D4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C2×C11×#121—24no—
13C2×C11×#121—22no—
14C2×C11×#121—24no—
15C2×C11×#121C2214yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4—21no—
18C22×C22⋊Dic11—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66896—24no—
24C2×#66896—24no—
25C2×#66896C2214yescomplemented
26C2×#66896C2214yescomplemented
27#10622825—22no—
28#10622825C2214yescomplemented
29C2×C11⋊#95—21no—
30C2×C22⋊(C11⋊C8)—24no—
31C2×C22⋊(C11⋊C8)C2214yescomplemented
32C2×#66872—24no—
33C2×#66872C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11—21no—
36C25×C11D411yescharacteristic
37C22×D4×C11—28no—
38C22×D4×C11—24no—
39C22×D4×C11—22no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—44no—
46C22×D4×C11—44no—
47C22×D4×C11D414yes—
48C22×D4×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D412yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C23×Dic11—21no—
62C11×#121—216no—
63C11×#121—28no—
64C11×#121—28no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4D414yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—28no—
70C2×C11×C22⋊C4—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—44no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8D414yescomplemented
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2312yes—
89#66896—28no—
90#66896—28no—
91C11⋊#95—24no—
92C22⋊(C11⋊C8)—28no—
93#66872—28no—
94C2×#2034—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—24no—
102C24×C11—22no—
103C24×C11—42no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11SD1614yes—
110C24×C11C2×D412yes—
111C24×C11C2×D411yescharacteristic
112C2×D4×C11—216no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—48no—
122C2×D4×C11—432no—
123C2×D4×C11—48no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—44no—
128C2×D4×C11C2×D414yes—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D414yes—
169C11×C22⋊C4—216no—
170C22⋊Dic11—48no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11—42no—
177C2×C11⋊C8—28no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—44no—
184C2×C11⋊C8C2×D414yescomplemented
185C22×#121D1111yescharacteristic
186C22×#106—111no—
187C22×#102—111no—
188C22×#102—111no—
189C22×C22⋊C8—111no—
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—24no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—44no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—84no—
217C23×C11—84no—
218C23×C11—84no—
219C23×C11—84no—
220C23×C11#12012yes—
221C23×C11#12112yes—
222C23×C11#12312yes—
223C23×C11C2×SD1614yes—
224C23×C11C2×SD1612yes—
225C23×C11#13512yes—
226C23×C11AGL(1,ℤ/8)12yes—
227C23×C11AGL(1,ℤ/8)12yes—
228C23×C11C22×D411yescharacteristic
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—432no—
232D4×C11—42no—
233D4×C11—42no—
234D4×C11—48no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—48no—
248C2×C4×C11#12012yes—
249C2×C4×C11#12114yes—
250C2×C4×C11#12114yes—
251C2×C4×C11#12112yes—
252C2×C4×C11#12314yes—
253C2×C4×C11#12312yes—
254C2×C4×C11#12414yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—84no—
268C2×Dic11—84no—
269C11⋊C8—24no—
270C11⋊C8—42no—
271C23×D4—21no—
272C23×D4C2×D1111yescharacteristic
273C24×C4C2×D1111yescharacteristic
274C23×C8—111no—
275C23×C8—111no—
276C2×#121—24no—
277C2×#121—22no—
278C2×#121—24no—
279C2×#121C2×D1114yes—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C22⋊C4—21no—
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—114no—
292C2×C22⋊C8—224no—
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—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—816no—
313C22×C11#39414yes—
314C22×C11#44914yes—
315C22×C11#45014yes—
316C22×C11#46514yes—
317C22×C11#46914yes—
318C22×C11#48114yes—
319C22×C11#48214yes—
320C22×C11C2×#12011yescharacteristic
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12311yescharacteristic
323C22×C11C22×SD1611yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
327C4×C11—42no—
328C4×C11—44no—
329C4×C11#39414yes—
330C4×C11C2×#12111yescharacteristic
331C4×C11C2×#12111yescharacteristic
332C4×C11C2×#12311yescharacteristic
333C4×C11C2×#12411yescharacteristic
334Dic11—82no—
335Dic11—82no—
336C25—21no—
337C25C22⋊D1111yescharacteristic
338C22×D4—28no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—44no—
347C22×D4—44no—
348C22×D4C22⋊D1114yes—
349C22×D4C22×D1112yes—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4C22⋊D1112yes—
360C23×C4C22⋊D1111yescharacteristic
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C22×C8—114no—
364C22×C8—112no—
365C22×C8—112no—
366C22×C8—222no—
367C22×C8—222no—
368C22×C8—222no—
369C22×C8—222no—
370C22×C8—222no—
371#121—216no—
372#121—28no—
373#121—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22⋊D1114yes—
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—444no—
390#106—228no—
391#102—228no—
392#102—228no—
393C22⋊C8—228no—
394#95—224no—
395C2×C11—44no—
396C2×C11—84no—
397C2×C11#203418yescomplemented
398C2×C11C2×#39411yescharacteristic
399C2×C11C2×#45011yescharacteristic
400C2×C11C2×#44911yescharacteristic
401C2×C11C2×#46511yescharacteristic
402C2×C11C2×#46911yescharacteristic
403C2×C11C2×#48211yescharacteristic
404C2×C11C2×#48111yescharacteristic
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24#432414yes—
420C24C2×C22⋊D1112yes—
421C24C2×C22⋊D1111yescharacteristic
422C2×D4—216no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—48no—
432C2×D4—432no—
433C2×D4—48no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4C2×C22⋊D1114yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4D4×D1112yes—
468C22×C4#434112yes—
469C22×C4#434112yes—
470C22×C4#434112yes—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—114no—
477C2×C8—228no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—444no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4C2×C22⋊D1114yes—
493C22⋊C4—216no—
494C22⋊C4—448no—
495C11C2×#203411yescharacteristic, complemented, Sylow
496C23—22no—
497C23—22no—
498C23—22no—
499C23—28no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—28no—
504C23—28no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—48no—
515C23—48no—
516C23—42no—
517C23—42no—
518C23—48no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23#6698512yes—
524C23C2×#432414yes—
525C23C2×#432412yes—
526C23#6698812yes—
527C23#6699212yes—
528C23#6700212yes—
529C23#6700312yes—
530C23#6700612yes—
531C23C22×C22⋊D1111yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
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#6698814yes—
560C2×C4#6698812yes—
561C2×C4#6698914yes—
562C2×C4#6699114yes—
563C2×C4#6699214yes—
564C2×C4#6699212yes—
565C2×C4#6700612yes—
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C2×#434111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C8—224no—
573C8—442no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—416no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—816no—
589C22—82no—
590C22#1062264714yes—
591C22#1062264814yes—
592C22#1062265214yes—
593C22#1062265414yes—
594C22#1062283114yes—
595C22#1062283514yes—
596C22#1062285114yes—
597C22C2×#6698511yescharacteristic
598C22C22×#432411yescharacteristic
599C22C2×#6698811yescharacteristic
600C22C2×#6699211yescharacteristic
601C22C2×#6700211yescharacteristic
602C22C2×#6700311yescharacteristic
603C22C2×#6700611yescharacteristic
604C4—44no—
605C4—42no—
606C4—882no—
607C4—882no—
608C4#1062283514yes—
609C4C2×#6698811yescharacteristic
610C4C2×#6698911yescharacteristic
611C4C2×#6699111yescharacteristic
612C4C2×#6699211yescharacteristic
613C2—44no—
614C2—84no—
615C2#1306980218yesdirect product factor
616C2C2×#1062283511yescharacteristic
617C2C2×#1062283111yescharacteristic
618C2C2×#1062285111yescharacteristic
619C2C2×#1062265411yescharacteristic
620C2C2×#1062265211yescharacteristic
621C2C2×#1062264811yescharacteristic
622C2C2×#1062264711yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C2×D4
hypercenterC22×#121D11
hypocenterC11C2×#2034
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66872C2semidirect
2. C22×#66896C2semidirect
3. C22×#66896C2semidirect
4. C22×C22⋊(C11⋊C8)C2semidirect
5. C2×#10622825C2semidirect
6. #13069802C2direct (N × H)
7. C2×#10622167C2semidirect
25. C2×#66896C22semidirect
26. C2×#66896C22semidirect
28. #10622825C22semidirect
31. C2×C22⋊(C11⋊C8)C22semidirect
33. C2×#66872C22semidirect
34. #10622167C22semidirect
86. C22×C11⋊C8D4semidirect
184. C2×C11⋊C8C2×D4semidirect
397. C2×C11#2034semidirect
495. C11C2×#2034semidirect
615. C2#13069802direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668722
C22×#668962
C22×C22⋊(C11⋊C8)2
C2×#106228252
#130698022
C2×#106221672
C22×C11×#1212
C2×#203411