Finite Group Databasebeta

← C2×#13069789 #14781198

Subgroups — C2×#13069789 #14781198

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×#10623001C211yesmaximal, characteristic, complemented
2C2×#10622752C211yesmaximal, characteristic
3C22×#66869C211yesmaximal, characteristic
4C2×#10622619C211yesmaximal, characteristic
5#13069789C218yesmaximal, direct product factor
6C2×#10622194C211yesmaximal, characteristic, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#339C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66977—22no—
16C22×#4318C2211yescharacteristic
17#10623001—22no—
18#10623001—22no—
19#10623001—22no—
20#10623001C2214yescomplemented
21C2×#66923—21no—
22C2×#66922—21no—
23C2×C4×Dic22—22no—
24#10622752—22no—
25#10622752C2214yes—
26C2×#66889—22no—
27#10622619—22no—
28#10622619C2214yes—
29C2×#66870—22no—
30C2×#66869—21no—
31C2×#66869—21no—
32C2×#66869—22no—
33C2×#66869C2214yes—
34C11×#339C2214yescomplemented
35#10622194C2214yescomplemented
36#10622169C2214yescomplemented
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—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×#117C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D412yes—
76C2×C42×C11C2312yes—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D412yes—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979—21no—
83#66979D412yes—
84#66979D412yes—
85#66979C2312yes—
86#66979C2312yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90#66977—28no—
91#66977—28no—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D412yes—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318C2312yes—
101C22×C11⋊C8—21no—
102#66923—24no—
103#66923—24no—
104#66922—24no—
105#66922—24no—
106C4×Dic22—28no—
107C4×Dic22—28no—
108#66889—28no—
109#66870—28no—
110#66869—24no—
111#66869—24no—
112C2×#2031—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—44no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×Q811yescharacteristic
127C22×C4×C11C2×Q811yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—41no—
153#4339—41no—
154#4339—41no—
155#4339—41no—
156#4339—41no—
157#4339—41no—
158#4339—41no—
159#4339—41no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C2×Q812yescomplemented
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—41no—
169C2×C4×D11—41no—
170C2×C4×D11—41no—
171C2×C4×D11—41no—
172C2×Dic22—28no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—48no—
179C2×Dic22C2×Q812yescomplemented
180C11×M16—22no—
181C11×M16—22no—
182C11×M16—41no—
183C11×M16—41no—
184C2×C8×C11—22no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—41no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—41no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—41no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11C2×D414yes—
203C4⋊Dic11—28no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208Dic11⋊C4—216no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11C2×D414yes—
213#4318—22no—
214#4318—22no—
215#4318—41no—
216#4318—41no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—41no—
219C2×C11⋊C8—41no—
220C2×#533—111no—
221C2×#421—111no—
222C22×#104—111no—
223C2×#410—111no—
224#2031—118no—
225C2×#344—111no—
226C2×#339D1111yescharacteristic, complemented
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—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—82no—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
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×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
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×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C22⋊D11—42no—
277C22⋊D11—42no—
278C22⋊D11—42no—
279C22⋊D11—42no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—42no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—42no—
295Dic22—22no—
296Dic22—22no—
297Dic22—416no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—42no—
301C11⋊C8—42no—
302C22×#41—111no—
303C22×M16—111no—
304C22×M16C2×D1111yescharacteristic
305#533—114no—
306#533—222no—
307#533—222no—
308#533—222no—
309C2×C4⋊Q8—221no—
310C2×#125—221no—
311C2×C22⋊Q8—222no—
312C2×C4×Q8—222no—
313C2×#117—111no—
314C2×#117—111no—
315C2×#117C2×D1111yescharacteristic
316C22×C42C2×D1111yescharacteristic
317#421—114no—
318#421—222no—
319C2×#104—114no—
320C2×#104—222no—
321C2×#104—221no—
322C2×#104—221no—
323C2×#104—222no—
324#410—114no—
325#410—222no—
326C2×#99—222no—
327#344—114no—
328#339C2×D1114yescomplemented
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—82no—
351C4×C11#39311yescharacteristic
352C4×C11#39311yescharacteristic
353C4×C11#39311yescharacteristic
354C4×C11#39311yescharacteristic
355C4×C11C2×C22⋊Q811yescharacteristic
356C4×C11C2×C22⋊Q811yescharacteristic
357C4×C11C2×#12411yescharacteristic
358C4×C11C2×#12411yescharacteristic
359Dic11—44no—
360Dic11—44no—
361Dic11—42no—
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—111no—
375C22×Q8—222no—
376C22×D4—111no—
377C22×D4—221no—
378C23×C4—21no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—112no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16—221no—
392C2×M16C22×D1112yes—
393C22×C8—21no—
394C22×C8—221no—
395C4⋊Q8—224no—
396C4⋊Q8—224no—
397#125—224no—
398#125—224no—
399C22⋊Q8—228no—
400C22⋊Q8—228no—
401C4×Q8—228no—
402C4×Q8—228no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—112no—
407#117—112no—
408#117—112no—
409#117—112no—
410#117—221no—
411#117—221no—
412#117—221no—
413#117—221no—
414#117C22×D1112yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—224no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—112no—
428C2×C42—221no—
429C2×C42D4411yescharacteristic
430C2×C42D4411yescharacteristic
431C2×C42D4412yes—
432C2×C42C22×D1112yes—
433#104—228no—
434#104—224no—
435#104—224no—
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—
447C24D4×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—112no—
465C2×Q8—228no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—448no—
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—44no—
489C22×C4—41no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—441no—
496C22×C4—441no—
497C22×C4—441no—
498C22×C4—441no—
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4#433911yescharacteristic
502C22×C4#433911yescharacteristic
503C22×C4#433911yescharacteristic
504C22×C4#433911yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4#434111yescharacteristic
509C22×C4#434111yescharacteristic
510C22×C4Q8×D1111yescharacteristic
511C22×C4Q8×D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—22no—
514M16—22no—
515M16—41no—
516M16—41no—
517M16—222no—
518M16—222no—
519M16—441no—
520M16—441no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—222no—
525C2×C8—441no—
526C2×C8—441no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—2216no—
530C4⋊C4—228no—
531C4⋊C4—222no—
532C4⋊C4—222no—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C22⋊C4—22no—
536C22⋊C4—41no—
537C22⋊C4—114no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—22no—
545C42—22no—
546C42—41no—
547C42—114no—
548C42—222no—
549C42—222no—
550C42—222no—
551C42C2×D4412yes—
552C42C2×D4412yes—
553C11C2×#203111yescharacteristic, complemented, Sylow
554C23—42no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—882no—
559C23#6693511yescharacteristic
560C23#6693511yescharacteristic
561C23#6693811yescharacteristic
562C23#6693811yescharacteristic
563C23#6694911yescharacteristic
564C23#6694911yescharacteristic
565C23C2×D4×D1111yescharacteristic
566Q8—222no—
567Q8—222no—
568Q8—4416no—
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—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—444no—
591C2×C4—444no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4#6692811yescharacteristic
599C2×C4#6692811yescharacteristic
600C2×C4#6692811yescharacteristic
601C2×C4#6692811yescharacteristic
602C2×C4#6693511yescharacteristic
603C2×C4#6693511yescharacteristic
604C2×C4#6693811yescharacteristic
605C2×C4#6693811yescharacteristic
606C2×C4#6693811yescharacteristic
607C2×C4#6693811yescharacteristic
608C2×C4#6693811yescharacteristic
609C2×C4#6693811yescharacteristic
610C2×C4#6694911yescharacteristic
611C2×C4#6694911yescharacteristic
612C2×C4#6694911yescharacteristic
613C2×C4#6694911yescharacteristic
614C2×C4#6694911yescharacteristic
615C2×C4#6694911yescharacteristic
616C2×C4#6695011yescharacteristic
617C2×C4#6695011yescharacteristic
618C2×C4#6695011yescharacteristic
619C2×C4#6695011yescharacteristic
620C2×C4C22×D4411yescharacteristic
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C2×Q8×D1111yescharacteristic
626C8—42no—
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#1062228611yescharacteristic
640C22#1062228611yescharacteristic
641C22#1062228611yescharacteristic
642C22#1062228611yescharacteristic
643C22C2×#6693511yescharacteristic
644C22C2×#6693811yescharacteristic
645C22C2×#6694911yescharacteristic
646C4—24no—
647C4—42no—
648C4—82no—
649C4—444no—
650C4—444no—
651C4—442no—
652C4#1062228611yescharacteristic
653C4#1062228611yescharacteristic
654C4#1062228611yescharacteristic
655C4#1062228611yescharacteristic
656C4C2×#6692811yescharacteristic
657C4C2×#6693811yescharacteristic
658C4C2×#6694911yescharacteristic
659C4C2×#6695011yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—882no—
667C2#1306978912yesdirect product factor
668C2C2×#1062228611yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC22×C11#393
prime radicalC22×#4339C22
hypercenterC2×#339D11
hypocenterC11C2×#2031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
5. #13069789C2direct (N × H)
6. C2×#10622194C2semidirect
7. C2×#10622169C2semidirect
8. C2×C11×#339C2semidirect
20. #10623001C22semidirect
34. C11×#339C22semidirect
35. #10622194C22semidirect
36. #10622169C22semidirect
50. C2×#4339Q8semidirect
52. C22×D44Q8semidirect
55. C22×Dic22Q8semidirect
165. C2×D44C2×Q8semidirect
179. C2×Dic22C2×Q8semidirect
226. C2×#339D11semidirect
328. #339C2×D11semidirect
443. C2×C11#2031semidirect
553. C11C2×#2031semidirect
667. C2#13069789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106227522
C22×#668692
C2×#106226192
#130697892
C2×#106221942
C2×#106221692
C2×C11×#3392
C2×#203111