Finite Group Databasebeta

← C2×#13069622 #14780566

Subgroups — C2×#13069622 #14780566

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×#4314C211yesmaximal, characteristic, complemented
2C22×#66950C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5C22×#66873C211yesmaximal, characteristic, complemented
6C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
7#13069622C218yesmaximal, direct product factor
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D44—21no—
10C23×D44C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4—21no—
17C22×(C2×D11)⋊C4—21no—
18C22×C4⋊Dic11—21no—
19C23×C11⋊C8C2211yescharacteristic
20C22×#4314—24no—
21C22×#4314—24no—
22C22×#4314—24no—
23C22×#4314C2214yescomplemented
24C2×#66950—22no—
25C2×#66950—24no—
26C2×#66950—24no—
27C2×#66950C2214yescomplemented
28C2×#66948—24no—
29C2×#66948—22no—
30C2×#66948—24no—
31C2×#66948C2214yes—
32C2×(C2×D11)⋊C8—24no—
33C2×(C2×D11)⋊C8C2214yescomplemented
34C2×#66874—24no—
35C2×#66874C2214yescomplemented
36C2×#66873—24no—
37C2×#66873C2214yescomplemented
38C11×#340C2214yescomplemented
39C24×D11—21no—
40C24×D11D411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C23×Dic11D411yescharacteristic
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—28no—
51C22×D44—24no—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—44no—
55C22×D44—44no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11D412yes—
65C22×C4×D11C2312yes—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—22no—
71C22×Dic22—21no—
72C22×Dic22D414yescomplemented
73C22×Dic22C2312yes—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11D414yescomplemented
77C22×C8×C11C2312yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4D414yes—
83C2×C11×C4⋊C4D414yescomplemented
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11—24no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8—22no—
95C22×C11⋊C8C2312yes—
96C2×#4314—232no—
97C2×#4314—28no—
98C2×#4314—28no—
99C2×#4314—28no—
100#66950—216no—
101#66950—28no—
102#66950—28no—
103#66948—216no—
104#66948—28no—
105#66948—28no—
106(C2×D11)⋊C8—28no—
107#66874—28no—
108#66873—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—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11C2×D412yes—
151C2×D44—216no—
152C2×D44—24no—
153C2×D44—28no—
154C2×D44—28no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—48no—
161C2×D44—432no—
162C2×D44—48no—
163C2×D44—42no—
164C2×D44—44no—
165C2×D44—42no—
166C2×D44—44no—
167C2×D44C2×D414yes—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—24no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11—44no—
181C2×Dic22—28no—
182C2×Dic22—24no—
183C2×Dic22—28no—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—22no—
189C2×Dic22—42no—
190C2×Dic22—44no—
191C2×Dic22—42no—
192C2×Dic22—44no—
193C2×Dic22C2×D414yescomplemented
194C2×C8×C11—28no—
195C2×C8×C11—22no—
196C2×C8×C11—22no—
197C2×C8×C11C2×D414yescomplemented
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4C2×D414yes—
203C11×C4⋊C4C2×D414yescomplemented
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—216no—
206C4⋊Dic11—216no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—44no—
211#4314—232no—
212C23×SD16—111no—
213C22×C22⋊Q8—111no—
214C22×#121—111no—
215C22×#103—111no—
216C22×#102—111no—
217C22×C22⋊C8—111no—
218#2000—118no—
219C2×#340D1111yescharacteristic, complemented
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
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—48no—
263C2×C4×C11—48no—
264C2×C4×C11#12014yes—
265C2×C4×C11#12012yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#12114yes—
268C2×C4×C11#12114yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12714yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—48no—
284C2×Dic11—44no—
285D44—24no—
286D44—24no—
287D44—432no—
288D44—42no—
289D44—42no—
290D44—48no—
291C4×D11—42no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—42no—
295C4×D11—48no—
296Dic22—24no—
297Dic22—24no—
298Dic22—42no—
299Dic22—42no—
300Dic22—48no—
301C8×C11—24no—
302C11⋊C8—42no—
303C23×Q8—111no—
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—222no—
315C2×C22⋊Q8—224no—
316C2×C22⋊Q8—224no—
317C2×#121—114no—
318C2×#121—222no—
319C2×#121—224no—
320C2×#121—224no—
321C22×C4⋊C4—221no—
322C22×C4⋊C4C2×D1111yescharacteristic
323C22×C4⋊C4C2×D1111yescharacteristic
324C22×C22⋊C4—221no—
325C22×C22⋊C4—221no—
326C2×#103—114no—
327C2×#103—224no—
328C2×#102—114no—
329C2×#102—224no—
330C2×C22⋊C8—114no—
331C2×C22⋊C8—224no—
332#340C2×D1114yescomplemented
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—44no—
371Dic11—42no—
372C25—111no—
373C25—221no—
374C22×Q8—114no—
375C22×Q8—112no—
376C22×Q8—222no—
377C22×Q8—221no—
378C22×Q8—222no—
379C22×Q8—222no—
380C22×Q8—222no—
381C22×Q8—222no—
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—112no—
414C22×C8—222no—
415C22×C8—222no—
416C22×C8—222no—
417C22×C8D4414yescomplemented
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—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4—228no—
431C2×C4⋊C4D4414yes—
432C2×C4⋊C4D4414yescomplemented
433C2×C4⋊C4C22×D1112yes—
434C2×C4⋊C4C22×D1112yes—
435C2×C22⋊C4—224no—
436C2×C22⋊C4—224no—
437C2×C22⋊C4—228no—
438C2×C22⋊C4—228no—
439#103—228no—
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—114no—
470C2×Q8—224no—
471C2×Q8—222no—
472C2×Q8—228no—
473C2×Q8—228no—
474C2×Q8—222no—
475C2×Q8—222no—
476C2×Q8—222no—
477C2×Q8—222no—
478C2×Q8—444no—
479C2×Q8—442no—
480C2×Q8—442no—
481C2×Q8—444no—
482C2×D4—114no—
483C2×D4—2216no—
484C2×D4—228no—
485C2×D4—224no—
486C2×D4—228no—
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—444no—
496C2×D4—442no—
497C2×D4—444no—
498C2×D4—442no—
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—222no—
509C22×C4—224no—
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×C4C2×D4412yes—
530C22×C4C2×D4412yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4D4×D1112yes—
533C22×C4D4×D1112yes—
534C22×C4#434312yes—
535C22×C4C23×D1111yescharacteristic
536SD16—2232no—
537C2×C8—28no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—222no—
541C2×C8—222no—
542C2×C8—222no—
543C2×C8—444no—
544C2×C8C2×D4414yescomplemented
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—2216no—
550C4⋊C4C2×D4414yes—
551C4⋊C4C2×D4414yescomplemented
552C22⋊C4—2216no—
553C22⋊C4—2216no—
554C11C2×#200011yescharacteristic, complemented, Sylow
555C23—114no—
556C23—228no—
557C23—222no—
558C23—222no—
559C23—222no—
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—442no—
575C23—442no—
576C23—448no—
577C23—448no—
578C23—448no—
579C23—884no—
580C23—884no—
581C23—884no—
582C23—884no—
583C23#6693512yes—
584C23#6693512yes—
585C23#6694812yes—
586C23#6696412yes—
587C23SD16×D1112yes—
588C23#6696912yes—
589C23#6697112yes—
590C23C2×D4×D1111yescharacteristic
591Q8—224no—
592Q8—224no—
593Q8—442no—
594Q8—442no—
595Q8—448no—
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—42no—
608C2×C4—48no—
609C2×C4—48no—
610C2×C4—222no—
611C2×C4—224no—
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#6692714yes—
624C2×C4#6693514yes—
625C2×C4#6693512yes—
626C2×C4#6693512yes—
627C2×C4#6694814yes—
628C2×C4#6694814yes—
629C2×C4#6694812yes—
630C2×C4C22×D4411yescharacteristic
631C2×C4C22×D4411yescharacteristic
632C2×C4C22×D4411yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C2×#434311yescharacteristic
636C8—24no—
637C8—442no—
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#1062228414yes—
655C22#1062238914yes—
656C22#1062239414yes—
657C22#1062241914yes—
658C22#1062242314yes—
659C22#1062247714yes—
660C22#1062249914yes—
661C22C2×#6693511yescharacteristic
662C22C2×#6693511yescharacteristic
663C22C2×#6694811yescharacteristic
664C22C2×#6696411yescharacteristic
665C22C2×SD16×D1111yescharacteristic
666C22C2×#6696911yescharacteristic
667C22C2×#6697111yescharacteristic
668C4—44no—
669C4—44no—
670C4—442no—
671C4—444no—
672C4#1062228414yes—
673C4C2×#6692711yescharacteristic
674C4C2×#6693511yescharacteristic
675C4C2×#6694811yescharacteristic
676C4C2×#6694811yescharacteristic
677C2—444no—
678C2—884no—
679C2#1306962218yesdirect product factor
680C2C2×#1062228411yescharacteristic
681C2C2×#1062238911yescharacteristic
682C2C2×#1062241911yescharacteristic
683C2C2×#1062239411yescharacteristic
684C2C2×#1062242311yescharacteristic
685C2C2×#1062247711yescharacteristic
686C2C2×#1062249911yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC22×#66948C2
hypercenterC2×#340D11
hypocenterC11C2×#2000
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C23×#4314C2semidirect
2. C22×#66950C2semidirect
4. C22×#66874C2semidirect
5. C22×#66873C2semidirect
6. C22×(C2×D11)⋊C8C2semidirect
7. #13069622C2direct (N × H)
8. C2×C11×#340C2semidirect
23. C22×#4314C22semidirect
27. C2×#66950C22semidirect
33. C2×(C2×D11)⋊C8C22semidirect
35. C2×#66874C22semidirect
37. C2×#66873C22semidirect
38. C11×#340C22semidirect
72. C22×Dic22D4semidirect
76. C22×C8×C11D4semidirect
83. C2×C11×C4⋊C4D4semidirect
125. C23×D11SD16semidirect
193. C2×Dic22C2×D4semidirect
197. C2×C8×C11C2×D4semidirect
203. C11×C4⋊C4C2×D4semidirect
219. C2×#340D11semidirect
255. C22×D11C2×SD16semidirect
332. #340C2×D11semidirect
417. C22×C8D44semidirect
432. C2×C4⋊C4D44semidirect
442. C2×C11#2000semidirect
544. C2×C8C2×D44semidirect
551. C4⋊C4C2×D44semidirect
554. C11C2×#2000semidirect
679. C2#13069622direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43142
C22×#669502
C22×#669482
C22×#668742
C22×#668732
C22×(C2×D11)⋊C82
#130696222
C2×C11×#3402
C2×#200011