Finite Group Databasebeta

← C2×#13069787 #14781196

Subgroups — C2×#13069787 #14781196

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10622618C211yesmaximal, characteristic
3C22×#66889C211yesmaximal, characteristic
4C2×#10622619C211yesmaximal, characteristic
5#13069787C218yesmaximal, direct product factor
6C2×#10622197C211yesmaximal, characteristic, complemented
7C2×#10622170C211yesmaximal, characteristic, complemented
8C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623048—22no—
17#10623048—22no—
18#10623048—22no—
19#10623048C2214yescomplemented
20C2×#66943—21no—
21C2×#66941—21no—
22C2×#66931—22no—
23C2×C4×Dic22—22no—
24C2×#66889—21no—
25C2×#66889—21no—
26C2×#66889—22no—
27C2×#66889C2214yes—
28#10622619—22no—
29#10622619C2214yes—
30#10622618—22no—
31#10622618C2214yes—
32C2×#66870—22no—
33C2×#66869—22no—
34C11×H(3,ℤ/4)C2214yescomplemented
35#10622197C2214yescomplemented
36#10622170C2214yescomplemented
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—21no—
39C23×Dic11—21no—
40C2×#4339—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×#4339Q812yescomplemented
51C2×#4339C2312yes—
52C22×D44Q811yescharacteristic, complemented
53C22×C4×D11—21no—
54C22×Dic22—22no—
55C22×Dic22Q811yescharacteristic, complemented
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16C2312yes—
62C22×C8×C11—21no—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D412yes—
69C11×#117C2312yes—
70C11×#117C2312yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11D412yes—
77C2×C22⋊Dic11D412yes—
78#66979—21no—
79#66979—21no—
80#66979D412yes—
81#66979C2312yes—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D412yes—
93C2×C4×Dic11C2312yes—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318C2312yes—
100C22×C11⋊C8—21no—
101#66943—24no—
102#66943—24no—
103#66941—24no—
104#66941—24no—
105#66931—28no—
106#66931—28no—
107C4×Dic22—28no—
108C4×Dic22—28no—
109#66889—24no—
110#66889—24no—
111#66870—28no—
112#66869—28no—
113C2×#2031—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×Q811yescharacteristic
124C22×C4×C11C2×Q811yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—22no—
133C2×C22⋊D11—22no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—44no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—22no—
153#4339—41no—
154#4339—41no—
155#4339—41no—
156#4339—41no—
157#4339—41no—
158#4339—41no—
159#4339—41no—
160#4339—41no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C2×Q812yescomplemented
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—41no—
170C2×C4×D11—41no—
171C2×C4×D11—41no—
172C2×C4×D11—41no—
173C2×Dic22—28no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—48no—
180C2×Dic22C2×Q812yescomplemented
181C11×M16—22no—
182C11×M16—22no—
183C11×M16—41no—
184C11×M16—41no—
185C2×C8×C11—22no—
186C2×C8×C11—41no—
187C2×C8×C11—41no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—41no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—41no—
196C42×C11—22no—
197C42×C11—22no—
198C42×C11—41no—
199C42×C11C2×D414yes—
200C22⋊Dic11—22no—
201C22⋊Dic11C2×D414yes—
202C4⋊Dic11—28no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11C2×D412yes—
214C4×Dic11C2×D412yes—
215#4318—22no—
216#4318—22no—
217#4318—41no—
218#4318—41no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—41no—
221C2×C11⋊C8—41no—
222C2×#533—111no—
223C2×#421—111no—
224C22×#104—111no—
225C2×#410—111no—
226#2031—118no—
227C2×#344—111no—
228C2×#339—111no—
229C2×H(3,ℤ/4)D1111yescharacteristic, complemented
230C23×C11—42no—
231C23×C11#12011yescharacteristic
232C23×C11#12011yescharacteristic
233C23×C11C22⋊Q811yescharacteristic
234C23×C11C22⋊Q811yescharacteristic
235C23×C11#12411yescharacteristic
236C23×C11#12411yescharacteristic
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—82no—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11C22⋊Q811yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11#12411yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12411yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C22⋊D11—42no—
275C22⋊D11—42no—
276C22⋊D11—42no—
277C22⋊D11—42no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—42no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—41no—
292D44—41no—
293C4×D11—42no—
294C4×D11—42no—
295C4×D11—42no—
296C4×D11—42no—
297Dic22—22no—
298Dic22—22no—
299Dic22—416no—
300Dic22—41no—
301Dic22—41no—
302C8×C11—42no—
303C11⋊C8—42no—
304C22×#41—111no—
305C22×M16—111no—
306C22×M16C2×D1111yescharacteristic
307#533—114no—
308#533—222no—
309#533—222no—
310#533—222no—
311C2×C4⋊Q8—221no—
312C2×#125—221no—
313C2×C22⋊Q8—222no—
314C2×C4×Q8—222no—
315C2×#117—111no—
316C2×#117C2×D1111yescharacteristic
317C2×#117C2×D1111yescharacteristic
318C22×C42—111no—
319#421—114no—
320#421—222no—
321C2×#104—114no—
322C2×#104—221no—
323C2×#104—221no—
324C2×#104—222no—
325C2×#104—222no—
326#410—114no—
327#410—222no—
328C2×#99—222no—
329#344—114no—
330#339—114no—
331H(3,ℤ/4)C2×D1114yescomplemented
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11#39311yescharacteristic
340C22×C11#39311yescharacteristic
341C22×C11#39311yescharacteristic
342C22×C11#39311yescharacteristic
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×C22⋊Q811yescharacteristic
345C22×C11C2×#12411yescharacteristic
346C2×D11—42no—
347C2×D11—82no—
348C2×D11—82no—
349C2×D11—82no—
350C4×C11—44no—
351C4×C11—82no—
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—24no—
361Dic11—44no—
362Dic11—42no—
363Dic11—42no—
364C2×#41—112no—
365C2×#41—112no—
366C2×#41—221no—
367C2×#41—221no—
368C2×#41—221no—
369C2×#41—221no—
370C2×#41—221no—
371C2×#41—221no—
372C2×#41—221no—
373C2×#41—221no—
374C2×#41—221no—
375C2×#41—221no—
376C22×Q8—111no—
377C22×Q8—222no—
378C22×D4—111no—
379C22×D4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—112no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—221no—
392C2×M16—221no—
393C2×M16—221no—
394C2×M16C22×D1112yes—
395C22×C8—21no—
396C22×C8—221no—
397C4⋊Q8—224no—
398C4⋊Q8—224no—
399#125—224no—
400#125—224no—
401C22⋊Q8—228no—
402C22⋊Q8—228no—
403C4×Q8—228no—
404C4×Q8—228no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—112no—
411#117—112no—
412#117—221no—
413#117—221no—
414#117D4412yes—
415#117C22×D1112yes—
416#117C22×D1112yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—112no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42D4412yes—
436#104—224no—
437#104—224no—
438#104—228no—
439#99—228no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11#203112yescomplemented
447C2×C11C2×#39311yescharacteristic
448D11—82no—
449C24—221no—
450C24D4×D1111yescharacteristic
451#41—222no—
452#41—222no—
453#41—222no—
454#41—222no—
455#41—222no—
456#41—222no—
457#41—222no—
458#41—222no—
459#41—441no—
460#41—441no—
461#41—441no—
462#41—441no—
463#41—441no—
464#41—441no—
465#41—441no—
466#41—441no—
467C2×Q8—112no—
468C2×Q8—228no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—448no—
475C2×D4—112no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—441no—
484C2×D4—441no—
485C2×D4—441no—
486C2×D4—441no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—444no—
498C22×C4—441no—
499C22×C4—441no—
500C22×C4—441no—
501C22×C4—441no—
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4#433911yescharacteristic
505C22×C4#433911yescharacteristic
506C22×C4#433911yescharacteristic
507C22×C4#433911yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4#434111yescharacteristic
512C22×C4#434111yescharacteristic
513C22×C4Q8×D1111yescharacteristic
514C22×C4Q8×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516M16—22no—
517M16—22no—
518M16—41no—
519M16—41no—
520M16—222no—
521M16—222no—
522M16—441no—
523M16—441no—
524C2×C8—22no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—222no—
528C2×C8—441no—
529C2×C8—441no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—228no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—41no—
543C22⋊C4—114no—
544C22⋊C4—222no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—112no—
549C42—112no—
550C42—222no—
551C42—221no—
552C42—221no—
553C42—222no—
554C42—222no—
555C42—222no—
556C42C2×D4414yes—
557C11C2×#203111yescharacteristic, complemented, Sylow
558C23—42no—
559C23—222no—
560C23—441no—
561C23—441no—
562C23—882no—
563C23#6693511yescharacteristic
564C23#6693511yescharacteristic
565C23#6693811yescharacteristic
566C23#6693811yescharacteristic
567C23#6694911yescharacteristic
568C23#6694911yescharacteristic
569C23C2×D4×D1111yescharacteristic
570Q8—222no—
571Q8—222no—
572Q8—4416no—
573Q8—441no—
574Q8—441no—
575D4—222no—
576D4—222no—
577D4—442no—
578D4—442no—
579D4—442no—
580D4—442no—
581D4—441no—
582D4—441no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—444no—
593C2×C4—444no—
594C2×C4—442no—
595C2×C4—444no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4#6692811yescharacteristic
603C2×C4#6692811yescharacteristic
604C2×C4#6692811yescharacteristic
605C2×C4#6692811yescharacteristic
606C2×C4#6693511yescharacteristic
607C2×C4#6693511yescharacteristic
608C2×C4#6693811yescharacteristic
609C2×C4#6693811yescharacteristic
610C2×C4#6693811yescharacteristic
611C2×C4#6693811yescharacteristic
612C2×C4#6693811yescharacteristic
613C2×C4#6693811yescharacteristic
614C2×C4#6694911yescharacteristic
615C2×C4#6694911yescharacteristic
616C2×C4#6694911yescharacteristic
617C2×C4#6694911yescharacteristic
618C2×C4#6694911yescharacteristic
619C2×C4#6694911yescharacteristic
620C2×C4#6695011yescharacteristic
621C2×C4#6695011yescharacteristic
622C2×C4#6695011yescharacteristic
623C2×C4#6695011yescharacteristic
624C2×C4C22×D4411yescharacteristic
625C2×C4C2×#433911yescharacteristic
626C2×C4C2×#433911yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4C2×Q8×D1111yescharacteristic
630C8—42no—
631C8—442no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—442no—
640C22—882no—
641C22—882no—
642C22—882no—
643C22#1062228611yescharacteristic
644C22#1062228611yescharacteristic
645C22#1062228611yescharacteristic
646C22#1062228611yescharacteristic
647C22C2×#6693511yescharacteristic
648C22C2×#6693811yescharacteristic
649C22C2×#6694911yescharacteristic
650C4—44no—
651C4—82no—
652C4—224no—
653C4—442no—
654C4—444no—
655C4—442no—
656C4#1062228611yescharacteristic
657C4#1062228611yescharacteristic
658C4#1062228611yescharacteristic
659C4#1062228611yescharacteristic
660C4C2×#6692811yescharacteristic
661C4C2×#6693811yescharacteristic
662C4C2×#6694911yescharacteristic
663C4C2×#6695011yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—882no—
671C2#1306978712yesdirect product factor
672C2C2×#1062228611yescharacteristic
subgroupG/H
centerC2×C4#66928
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×H(3,ℤ/4)C2
socleC22×C11#393
prime radicalC22×#4339C22
hypercenterC2×H(3,ℤ/4)D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
5. #13069787C2direct (N × H)
6. C2×#10622197C2semidirect
7. C2×#10622170C2semidirect
8. C2×C11×H(3,ℤ/4)C2semidirect
19. #10623048C22semidirect
34. C11×H(3,ℤ/4)C22semidirect
35. #10622197C22semidirect
36. #10622170C22semidirect
50. C2×#4339Q8semidirect
52. C22×D44Q8semidirect
55. C22×Dic22Q8semidirect
166. C2×D44C2×Q8semidirect
180. C2×Dic22C2×Q8semidirect
229. C2×H(3,ℤ/4)D11semidirect
331. H(3,ℤ/4)C2×D11semidirect
446. C2×C11#2031semidirect
557. C11C2×#2031semidirect
671. C2#13069787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106226182
C22×#668892
C2×#106226192
#130697872
C2×#106221972
C2×#106221702
C2×C11×H(3,ℤ/4)2
C2×#203111