Finite Group Databasebeta

← C2×#13069785 #14781194

Subgroups — C2×#13069785 #14781194

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622618C211yesmaximal, characteristic
2C22×#66869C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13069785C218yesmaximal, direct product factor
5C2×#10622171C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#533C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C11×#533—22no—
11C11×#533—22no—
12C11×#533—22no—
13C11×#533C2214yescomplemented
14C2×C11×C4⋊Q8—21no—
15C2×C11×#125—21no—
16C2×C11×C22⋊Q8—22no—
17C2×C4×Q8×C11—22no—
18C2×C11×#117C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24#10622619—22no—
25#10622619C2214yes—
26#10622618—22no—
27#10622618C2214yes—
28C2×#66870—22no—
29C2×#66869—21no—
30C2×#66869—21no—
31C2×#66869—22no—
32C2×#66869—22no—
33C2×#66869C2214yes—
34#10622171C2214yescomplemented
35#10622169C2214yescomplemented
36#10622161C2214yescomplemented
37C22×Q8×C11—22no—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339—21no—
50C2×#4339—21no—
51C2×#4339Q812yescomplemented
52C2×#4339C2312yes—
53C22×D44Q811yescharacteristic, complemented
54C22×C4×D11—21no—
55C22×Dic22Q811yescharacteristic, complemented
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—24no—
58C11×#125—24no—
59C11×#125—24no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—28no—
62C4×Q8×C11—28no—
63C4×Q8×C11—28no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D412yes—
69C11×#117D412yes—
70C11×#117C2312yes—
71C11×#117C2312yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D412yes—
85C2×C42×C11D412yes—
86C2×C42×C11C2312yes—
87C2×C22⋊Dic11—21no—
88#66979—21no—
89#66979—21no—
90#66979—21no—
91#66979C2312yes—
92C2×C4⋊Dic11—21no—
93C2×C4×Dic11—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—21no—
101C2×#4318—21no—
102C2×#4318—21no—
103C2×#4318—21no—
104C2×#4318C2312yes—
105C2×#4318C2312yes—
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108#66870—28no—
109#66869—24no—
110#66869—24no—
111#66869—28no—
112C2×#2031—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—21no—
115C2×Q8×C11—28no—
116C2×Q8×C11—48no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—44no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q811yescharacteristic
130C22×C4×C11C2×Q811yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×C4×C11#4111yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—22no—
139C2×C22⋊D11—22no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C22×Dic11—21no—
145C22×Dic11—41no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—22no—
153#4339—22no—
154#4339—41no—
155#4339—41no—
156#4339—41no—
157#4339—41no—
158#4339—41no—
159#4339—41no—
160#4339—41no—
161#4339—41no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C2×Q812yescomplemented
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—41no—
171C2×C4×D11—41no—
172C2×C4×D11—41no—
173C2×C4×D11—41no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C2×Q812yescomplemented
180C11×C4⋊C4—216no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4C2×D414yes—
190C42×C11—22no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—22no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C42×C11C2×D414yes—
200C22⋊Dic11—22no—
201C22⋊Dic11—41no—
202C4⋊Dic11—22no—
203C4⋊Dic11—41no—
204C4×Dic11—22no—
205C4×Dic11—41no—
206#4318—22no—
207#4318—22no—
208#4318—22no—
209#4318—22no—
210#4318—41no—
211#4318—41no—
212#4318—41no—
213#4318—41no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—41no—
217C2×C11⋊C8—41no—
218C2×C11⋊C8—41no—
219C2×C11⋊C8—41no—
220C2×#533D1111yescharacteristic, complemented
221C2×#421—111no—
222C22×#104—111no—
223C2×#410—111no—
224#2031—118no—
225C2×#344—111no—
226C2×#339—111no—
227C2×H(3,ℤ/4)—111no—
228C23×C11—42no—
229C23×C11#12011yescharacteristic
230C23×C11#12011yescharacteristic
231C23×C11C22⋊Q811yescharacteristic
232C23×C11C22⋊Q811yescharacteristic
233C23×C11#12411yescharacteristic
234C23×C11#12411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—82no—
240Q8×C11—416no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12411yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×Q811yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C22⋊D11—42no—
280C22⋊D11—42no—
281C22⋊D11—42no—
282C22⋊D11—42no—
283C2×Dic11—22no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—42no—
287C2×Dic11—82no—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—42no—
295C4×D11—42no—
296Dic22—22no—
297Dic22—22no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—42no—
301C11⋊C8—42no—
302C22×#41—111no—
303C22×M16—111no—
304C22×M16—111no—
305#533—22no—
306#533—22no—
307#533—22no—
308#533C2×D1114yescomplemented
309C2×C4⋊Q8—21no—
310C2×#125—21no—
311C2×C22⋊Q8—22no—
312C2×C4×Q8—22no—
313C2×#117—111no—
314C2×#117C2×D1111yescharacteristic
315C2×#117C2×D1111yescharacteristic
316C22×C42C2×D1111yescharacteristic
317#421—114no—
318#421—222no—
319C2×#104—114no—
320C2×#104—221no—
321C2×#104—221no—
322C2×#104—222no—
323C2×#104—222no—
324#410—114no—
325#410—222no—
326C2×#99—222no—
327#344—114no—
328#339—114no—
329H(3,ℤ/4)—114no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11#39311yescharacteristic
338C22×C11#39311yescharacteristic
339C22×C11#39311yescharacteristic
340C22×C11#39311yescharacteristic
341C22×C11C2×#12011yescharacteristic
342C22×C11C2×C22⋊Q811yescharacteristic
343C22×C11C2×#12411yescharacteristic
344C2×D11—42no—
345C2×D11—82no—
346C2×D11—82no—
347C2×D11—82no—
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11#39311yescharacteristic
353C4×C11#39311yescharacteristic
354C4×C11#39311yescharacteristic
355C4×C11#39311yescharacteristic
356C4×C11C2×C22⋊Q811yescharacteristic
357C4×C11C2×C22⋊Q811yescharacteristic
358C4×C11C2×#12411yescharacteristic
359C4×C11C2×#12411yescharacteristic
360Dic11—42no—
361Dic11—82no—
362C2×#41—112no—
363C2×#41—112no—
364C2×#41—221no—
365C2×#41—221no—
366C2×#41—221no—
367C2×#41—221no—
368C2×#41—221no—
369C2×#41—221no—
370C2×#41—221no—
371C2×#41—221no—
372C2×#41—221no—
373C2×#41—221no—
374C22×Q8—22no—
375C22×Q8—111no—
376C22×D4—111no—
377C22×D4—221no—
378C23×C4—21no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—112no—
382C2×M16—112no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—221no—
392C2×M16—221no—
393C22×C8—221no—
394C22×C8—221no—
395C4⋊Q8—24no—
396C4⋊Q8—24no—
397#125—24no—
398#125—24no—
399C22⋊Q8—28no—
400C22⋊Q8—28no—
401C4×Q8—28no—
402C4×Q8—28no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—21no—
407#117—112no—
408#117—221no—
409#117—221no—
410#117—221no—
411#117C22⋊D1112yes—
412#117C22⋊D1112yes—
413#117C22×D1112yes—
414#117C22×D1112yes—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—221no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4C22⋊D1112yes—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—221no—
428C2×C42C22⋊D1112yes—
429C2×C42C22⋊D1111yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1112yes—
432C2×C42C22×D1112yes—
433#104—224no—
434#104—224no—
435#104—228no—
436#99—228no—
437C2×C11—21no—
438C2×C11—21no—
439C2×C11—21no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11#203112yescomplemented
444C2×C11C2×#39311yescharacteristic
445D11—82no—
446C24—221no—
447C24C2×C22⋊D1111yescharacteristic
448#41—222no—
449#41—222no—
450#41—222no—
451#41—222no—
452#41—222no—
453#41—222no—
454#41—222no—
455#41—222no—
456#41—441no—
457#41—441no—
458#41—441no—
459#41—441no—
460#41—441no—
461#41—441no—
462#41—441no—
463#41—441no—
464C2×Q8—28no—
465C2×Q8—48no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×D4—112no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—441no—
481C2×D4—441no—
482C2×D4—441no—
483C2×D4—441no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—44no—
491C22×C4—221no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—441no—
495C22×C4—441no—
496C22×C4—441no—
497C22×C4—441no—
498C22×C4—441no—
499C22×C4Q8×D1111yescharacteristic
500C22×C4Q8×D1111yescharacteristic
501C22×C4#434311yescharacteristic
502C22×C4#434311yescharacteristic
503C22×C4#434311yescharacteristic
504C22×C4#434311yescharacteristic
505C22×C4#434311yescharacteristic
506C22×C4#434311yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—222no—
514M16—222no—
515M16—222no—
516M16—222no—
517M16—441no—
518M16—441no—
519M16—441no—
520M16—441no—
521C2×C8—222no—
522C2×C8—222no—
523C2×C8—441no—
524C2×C8—441no—
525C2×C8—441no—
526C2×C8—441no—
527C4⋊C4—216no—
528C4⋊C4—28no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—222no—
534C4⋊C4—441no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—222no—
539C22⋊C4—441no—
540C22⋊C4C2×C22⋊D1114yes—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—222no—
549C42—441no—
550C42C2×C22⋊D1112yes—
551C42C2×C22⋊D1112yes—
552C42C2×C22⋊D1114yes—
553C11C2×#203111yescharacteristic, complemented, Sylow
554C23—42no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—882no—
559C23#6699911yescharacteristic
560C23#6699911yescharacteristic
561C23#6700011yescharacteristic
562C23#6700011yescharacteristic
563C23#6700611yescharacteristic
564C23#6700611yescharacteristic
565C23C22×C22⋊D1111yescharacteristic
566Q8—416no—
567Q8—222no—
568Q8—222no—
569Q8—441no—
570Q8—441no—
571D4—222no—
572D4—222no—
573D4—442no—
574D4—442no—
575D4—442no—
576D4—442no—
577D4—441no—
578D4—441no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—222no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—882no—
598C2×C4#6699911yescharacteristic
599C2×C4#6699911yescharacteristic
600C2×C4#6699911yescharacteristic
601C2×C4#6699911yescharacteristic
602C2×C4#6699911yescharacteristic
603C2×C4#6699911yescharacteristic
604C2×C4#6699911yescharacteristic
605C2×C4#6699911yescharacteristic
606C2×C4#6699911yescharacteristic
607C2×C4#6699911yescharacteristic
608C2×C4#6700011yescharacteristic
609C2×C4#6700011yescharacteristic
610C2×C4#6700011yescharacteristic
611C2×C4#6700011yescharacteristic
612C2×C4#6700011yescharacteristic
613C2×C4#6700011yescharacteristic
614C2×C4#6700011yescharacteristic
615C2×C4#6700011yescharacteristic
616C2×C4#6700011yescharacteristic
617C2×C4#6700011yescharacteristic
618C2×C4#6700611yescharacteristic
619C2×C4#6700611yescharacteristic
620C2×C4C2×Q8×D1111yescharacteristic
621C2×C4C2×#434311yescharacteristic
622C2×C4C2×#434311yescharacteristic
623C2×C4C2×#434311yescharacteristic
624C2×C4C22×C22⋊D1111yescharacteristic
625C2×C4C22×C22⋊D1111yescharacteristic
626C8—442no—
627C8—442no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—442no—
636C22—882no—
637C22—882no—
638C22—882no—
639C22#1062284411yescharacteristic
640C22#1062284411yescharacteristic
641C22#1062284411yescharacteristic
642C22#1062284411yescharacteristic
643C22C2×#6699911yescharacteristic
644C22C2×#6700011yescharacteristic
645C22C2×#6700611yescharacteristic
646C4—24no—
647C4—42no—
648C4—44no—
649C4—44no—
650C4—442no—
651C4—882no—
652C4#1062284411yescharacteristic
653C4#1062284411yescharacteristic
654C4#1062284411yescharacteristic
655C4#1062284411yescharacteristic
656C4C2×#6699911yescharacteristic
657C4C2×#6699911yescharacteristic
658C4C2×#6700011yescharacteristic
659C4C2×#6700011yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—882no—
667C2#1306978512yesdirect product factor
668C2C2×#1062284411yescharacteristic
subgroupG/H
centerC2×C4#67000
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC22×C11#393
prime radicalC22×#4339C22
hypercenterC2×#533D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
4. #13069785C2direct (N × H)
5. C2×#10622171C2semidirect
6. C2×#10622161C2semidirect
7. C2×#10622169C2semidirect
8. C2×C11×#533C2semidirect
13. C11×#533C22semidirect
34. #10622171C22semidirect
35. #10622169C22semidirect
36. #10622161C22semidirect
51. C2×#4339Q8semidirect
53. C22×D44Q8semidirect
55. C22×Dic22Q8semidirect
167. C2×D44C2×Q8semidirect
179. C2×Dic22C2×Q8semidirect
220. C2×#533D11semidirect
308. #533C2×D11semidirect
443. C2×C11#2031semidirect
553. C11C2×#2031semidirect
667. C2#13069785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226182
C22×#668692
C2×#106226192
#130697852
C2×#106221712
C2×#106221612
C2×#106221692
C2×C11×#5332
C2×#203111