Finite Group Databasebeta

← C2×#13069825 #14781357

Subgroups — C2×#13069825 #14781357

Order 2816.

1714 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C2×#10622734C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C22×#66887C211yesmaximal, characteristic, complemented
5C2×#10622552C211yesmaximal, characteristic, complemented
6#13069825C218yesmaximal, direct product factor
7C2×#10622161C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13#10623361—22no—
14#10623361—22no—
15#10623361—22no—
16#10623361C2214yes—
17C2×#67000—21no—
18C2×#66993—21no—
19C2×#66990—22no—
20C2×#66983—21no—
21C2×#66983—21no—
22C22×(C2×D11)⋊C4—22no—
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C2×C11×#104—24no—
27C2×C11×#104C2214yescomplemented
28#10622845—22no—
29#10622845C2214yescomplemented
30C2×#66899—21no—
31C2×#66896—21no—
32C2×#66887—24no—
33C2×#66887C2214yescomplemented
34#10622734—22no—
35#10622734C2214yescomplemented
36C2×#66882—21no—
37C2×#66881—21no—
38#10622552—22no—
39#10622552C2214yescomplemented
40#10622161C2214yescomplemented
41C24×D11D412yes—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D412yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C23×Dic11—21no—
59C22×D44—22no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44D412yes—
68C22×D44C2312yes—
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16D414yescomplemented
72C2×C11×M16C2312yes—
73C22×C8×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11C2312yes—
78C2×C22⋊Dic11—21no—
79#67000—24no—
80#67000—24no—
81#66993—24no—
82#66993—24no—
83#66990—28no—
84#66990—28no—
85#66983—24no—
86#66983—24no—
87#66983—24no—
88#66983—24no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—48no—
93#66979—21no—
94#66979—21no—
95#66979D412yes—
96#66979C2312yes—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11D411yescharacteristic
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11C2312yes—
105C2×C4×Dic11—21no—
106C2×#4318—21no—
107C2×#4318—22no—
108C2×#4318—22no—
109C2×#4318C2312yes—
110C22×C11⋊C8—21no—
111C11×#104—28no—
112#66899—24no—
113#66896—24no—
114#66887—28no—
115#66882—24no—
116#66881—24no—
117C2×#2037—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—44no—
125C23×D11—44no—
126C23×D11C2×D414yes—
127C11×#41—24no—
128C11×#41—24no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—42no—
136C11×#41—42no—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11C2×D412yes—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—84no—
171C2×C22⋊D11—84no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—44no—
176C22×Dic11—41no—
177C22×Dic11—41no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—24no—
181C2×D44—24no—
182C2×D44—22no—
183C2×D44—22no—
184C2×D44—22no—
185C2×D44—22no—
186C2×D44—22no—
187C2×D44—22no—
188C2×D44—42no—
189C2×D44—42no—
190C2×D44—42no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44—42no—
194C2×D44—42no—
195C2×D44—42no—
196C11×M16—24no—
197C11×M16—22no—
198C11×M16C2×D414yescomplemented
199C2×C8×C11—24no—
200C2×C8×C11—22no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—42no—
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—416no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213C4⋊Dic11—41no—
214C4⋊Dic11—41no—
215C4⋊Dic11C2×D412yes—
216C4⋊Dic11C2×D412yes—
217C4×Dic11—22no—
218C4×Dic11—22no—
219#4318—22no—
220#4318—22no—
221#4318—42no—
222C2×C11⋊C8—22no—
223C2×C11⋊C8—42no—
224C2×#535—111no—
225C2×#428—111no—
226C22×#104D1111yescharacteristic, complemented
227C2×#417—111no—
228C22×#100—111no—
229C2×#390—111no—
230#2037—118no—
231C2×#339—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11#12011yescharacteristic
239C23×C11#12011yescharacteristic
240C23×C11#12112yes—
241C23×C11#12312yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—416no—
249C22×D11—44no—
250C22×D11—44no—
251C22×D11—44no—
252C22×D11—44no—
253C22×D11—82no—
254C22×D11—82no—
255C22×D11—88no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—42no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—44no—
264D4×C11—42no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—42no—
268C2×C4×C11—48no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—44no—
274C2×C4×C11#12011yescharacteristic
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11#12112yes—
279C2×C4×C11#12112yes—
280C2×C4×C11#12112yes—
281C2×C4×C11#12312yes—
282C2×C4×C11#12312yes—
283C2×C4×C11#12312yes—
284C2×C4×C11#12412yes—
285C2×C4×C11#12412yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C22⋊D11—88no—
293C22⋊D11—88no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—44no—
299C2×Dic11—42no—
300C2×Dic11—82no—
301C2×Dic11—82no—
302D44—42no—
303D44—42no—
304D44—42no—
305D44—42no—
306D44—44no—
307D44—44no—
308C8×C11—24no—
309C11⋊C8—42no—
310C22×#41C2×D1111yescharacteristic
311C23×D4—111no—
312C22×M16—111no—
313C22×M16C2×D1111yescharacteristic
314#535—114no—
315#535—222no—
316#535—222no—
317#535—222no—
318C2×#127—221no—
319C2×#124—221no—
320C2×#121—221no—
321C2×#121—221no—
322C2×#120—222no—
323C2×#117—111no—
324C22×C4⋊C4—111no—
325C22×C22⋊C4—222no—
326C22×C42C2×D1111yescharacteristic
327#428—114no—
328#428—222no—
329C2×#107—221no—
330C2×#106—221no—
331C2×#104—24no—
332C2×#104C2×D1114yescomplemented
333#417—114no—
334#417—222no—
335C2×#103—221no—
336C2×#102—221no—
337C2×#100—114no—
338C2×#100—224no—
339#390—114no—
340#390—222no—
341#339—114no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—24no—
347C22×C11—24no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—84no—
352C22×C11#39412yes—
353C22×C11#39412yes—
354C22×C11#45312yes—
355C22×C11#45512yes—
356C22×C11C2×#12011yescharacteristic
357C22×C11C2×#12111yescharacteristic
358C22×C11C2×#12311yescharacteristic
359C2×D11—48no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—88no—
364C2×D11—88no—
365C2×D11—84no—
366C4×C11—44no—
367C4×C11—42no—
368C4×C11#39412yes—
369C4×C11#39412yes—
370C4×C11C2×#12111yescharacteristic
371C4×C11C2×#12111yescharacteristic
372C4×C11C2×#12311yescharacteristic
373C4×C11C2×#12411yescharacteristic
374Dic11—42no—
375Dic11—42no—
376Dic11—82no—
377C25—112no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41D4412yes—
385C2×#41C22×D1112yes—
386C22×Q8D4411yescharacteristic
387C22×D4—21no—
388C22×D4—112no—
389C22×D4—112no—
390C22×D4—222no—
391C22×D4—222no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4—222no—
395C22×D4—221no—
396C22×D4—221no—
397C22×D4—222no—
398C22×D4—222no—
399C22×D4—222no—
400C22×D4D4411yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4—221no—
404C23×C4C22×D1111yescharacteristic
405C2×M16—21no—
406C2×M16—22no—
407C2×M16—112no—
408C2×M16—221no—
409C2×M16—222no—
410C2×M16—222no—
411C2×M16C22⋊D1114yescomplemented
412C2×M16C22×D1112yes—
413C22×C8—21no—
414C22×C8—221no—
415#127—224no—
416#127—224no—
417#124—224no—
418#124—224no—
419#121—224no—
420#121—224no—
421#121—224no—
422#121—224no—
423#120—228no—
424#120—228no—
425#117—112no—
426#117—112no—
427#117—221no—
428#117—221no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—228no—
441C2×C22⋊C4—448no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—21no—
445C2×C42—221no—
446C2×C42C22×D1112yes—
447#107—224no—
448#106—224no—
449#104—28no—
450#103—224no—
451#102—224no—
452#100—228no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—22no—
456C2×C11—82no—
457C2×C11#203714yescomplemented
458C2×C11C2×#39411yescharacteristic
459C2×C11C2×#45311yescharacteristic
460C2×C11C2×#45511yescharacteristic
461D11—84no—
462C24—21no—
463C24—114no—
464C24—222no—
465C24—224no—
466C24—222no—
467C24—224no—
468C24—444no—
469C24—444no—
470C24D4×D1111yescharacteristic
471#41—24no—
472#41—24no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—22no—
477#41—42no—
478#41—42no—
479#41—42no—
480#41—42no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8C2×D4412yes—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—228no—
493C2×D4—228no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4—224no—
497C2×D4—224no—
498C2×D4—222no—
499C2×D4—222no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—442no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4—442no—
510C2×D4—442no—
511C2×D4—442no—
512C2×D4—884no—
513C2×D4—884no—
514C2×D4C2×D4412yes—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—444no—
528C22×C4—441no—
529C22×C4—441no—
530C22×C4C2×D4411yescharacteristic
531C22×C4C2×D4411yescharacteristic
532C22×C4#433912yes—
533C22×C4D4×D1111yescharacteristic
534C22×C4D4×D1111yescharacteristic
535C22×C4D4×D1111yescharacteristic
536C22×C4#434112yes—
537C22×C4#434112yes—
538C22×C4C2×C22⋊D1112yes—
539C22×C4C23×D1111yescharacteristic
540M16—24no—
541M16—22no—
542M16—222no—
543M16—222no—
544M16—442no—
545M16C2×C22⋊D1114yescomplemented
546C2×C8—24no—
547C2×C8—22no—
548C2×C8—222no—
549C2×C8—442no—
550C4⋊C4—112no—
551C4⋊C4—112no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—222no—
555C4⋊C4—222no—
556C4⋊C4—441no—
557C4⋊C4—441no—
558C22⋊C4—228no—
559C22⋊C4—228no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C22⋊C4—4416no—
563C42—22no—
564C42—22no—
565C42—42no—
566C42—222no—
567C42—222no—
568C11C2×#203711yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—224no—
576C23—224no—
577C23—224no—
578C23—444no—
579C23—444no—
580C23—4416no—
581C23—444no—
582C23—444no—
583C23—444no—
584C23—444no—
585C23—882no—
586C23—882no—
587C23—888no—
588C23#6693511yescharacteristic
589C23#6693511yescharacteristic
590C23#6693612yes—
591C23#6699112yes—
592C23C2×D4×D1111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—42no—
596D4—22no—
597D4—22no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—42no—
602D4—442no—
603D4—442no—
604D4—442no—
605D4—442no—
606D4—444no—
607D4—444no—
608D4—888no—
609D4—888no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—48no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—444no—
624C2×C4—442no—
625C2×C4—882no—
626C2×C4—882no—
627C2×C4#6693511yescharacteristic
628C2×C4#6693511yescharacteristic
629C2×C4#6693612yes—
630C2×C4#6693812yes—
631C2×C4#6693812yes—
632C2×C4#6693912yes—
633C2×C4#6693912yes—
634C2×C4#6698312yes—
635C2×C4#6698312yes—
636C2×C4#6699112yes—
637C2×C4#6699212yes—
638C2×C4#6699212yes—
639C2×C4C22×D4411yescharacteristic
640C2×C4C2×#433911yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4C2×#434111yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C8—24no—
646C8—442no—
647C22—24no—
648C22—24no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—84no—
657C22—448no—
658C22—444no—
659C22—444no—
660C22—444no—
661C22—884no—
662C22—888no—
663C22—888no—
664C22#1062243512yes—
665C22#1062243812yes—
666C22#1062257412yes—
667C22#1062257412yes—
668C22C2×#6693511yescharacteristic
669C22C2×#6693611yescharacteristic
670C22C2×#6699111yescharacteristic
671C4—44no—
672C4—42no—
673C4—442no—
674C4—442no—
675C4—882no—
676C4#1062257412yes—
677C4#1062257412yes—
678C4C2×#6693811yescharacteristic
679C4C2×#6693911yescharacteristic
680C4C2×#6698311yescharacteristic
681C4C2×#6699211yescharacteristic
682C2—21no—
683C2—21no—
684C2—22no—
685C2—82no—
686C2—884no—
687C2#1306982514yesdirect product factor
688C2C2×#1062257411yescharacteristic
689C2C2×#1062243511yescharacteristic
690C2C2×#1062243811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC2×#10623361C2
hypercenterC22×#104D11
hypocenterC11C2×#2037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#10622734C2semidirect
3. C2×#10622845C2semidirect
4. C22×#66887C2semidirect
5. C2×#10622552C2semidirect
6. #13069825C2direct (N × H)
7. C2×#10622161C2semidirect
8. C22×C11×#104C2semidirect
27. C2×C11×#104C22semidirect
29. #10622845C22semidirect
33. C2×#66887C22semidirect
35. #10622734C22semidirect
39. #10622552C22semidirect
40. #10622161C22semidirect
71. C2×C11×M16D4semidirect
198. C11×M16C2×D4semidirect
226. C22×#104D11semidirect
332. C2×#104C2×D11semidirect
411. C2×M16C22⋊D11semidirect
457. C2×C11#2037semidirect
545. M16C2×C22⋊D11semidirect
568. C11C2×#2037semidirect
687. C2#13069825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106227342
C2×#106228452
C22×#668872
C2×#106225522
#130698252
C2×#106221612
C22×C11×#1042
C2×#203711