Finite Group Databasebeta

← C2×#13069832 #14781365

Subgroups — C2×#13069832 #14781365

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10622734C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic
4C22×#66888C211yesmaximal, characteristic, complemented
5C2×#10622542C211yesmaximal, characteristic, complemented
6#13069832C218yesmaximal, direct product factor
7C2×#10622161C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13#10623356—22no—
14#10623356—22no—
15#10623356—22no—
16#10623356C2214yes—
17C2×#66997—21no—
18C2×#66989—21no—
19C2×#66988—22no—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977—21no—
23C2×#66977—21no—
24C22×#4318C2211yescharacteristic
25C2×C11×#104—24no—
26C2×C11×#104C2214yes—
27#10622845—22no—
28#10622845C2214yes—
29C2×#66899—21no—
30C2×#66896—21no—
31C2×C11⋊#95—22no—
32C2×#66888—24no—
33C2×#66888C2214yescomplemented
34#10622734—22no—
35#10622734C2214yescomplemented
36C2×#66882—21no—
37C2×#66881—21no—
38#10622542—22no—
39#10622542C2214yescomplemented
40#10622161C2214yescomplemented
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D412yes—
48C2×C11×#41C2312yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11—21no—
56C23×Dic11D412yes—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22D412yes—
66C22×Dic22C2312yes—
67C2×C11×M16—21no—
68C2×C11×M16—22no—
69C2×C11×M16D414yes—
70C2×C11×M16C2312yes—
71C22×C8×C11—21no—
72C2×C42×C11—22no—
73C2×C42×C11—22no—
74C2×C42×C11—21no—
75C2×C42×C11C2312yes—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—21no—
79#66997—24no—
80#66997—24no—
81#66989—24no—
82#66989—24no—
83#66988—28no—
84#66988—28no—
85#66979—21no—
86#66979—21no—
87#66979D412yes—
88#66979C2312yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2312yes—
97#66977—24no—
98#66977—24no—
99#66977—24no—
100#66977—24no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C2×#4318—21no—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318C2312yes—
108C22×C11⋊C8—21no—
109C11×#104—28no—
110#66899—24no—
111#66896—24no—
112C11⋊#95—28no—
113#66888—28no—
114#66882—24no—
115#66881—24no—
116C2×#2038—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—42no—
126C11×#41—42no—
127C11×#41—42no—
128C11×#41—42no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D412yes—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—22no—
167C22×Dic11—44no—
168C22×Dic11—41no—
169C22×Dic11—41no—
170C22×Dic11C2×D414yes—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—24no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22—42no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C2×Dic22—42no—
188C2×Dic22—42no—
189C11×M16—24no—
190C11×M16—22no—
191C11×M16C2×D414yes—
192C2×C8×C11—24no—
193C2×C8×C11—22no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—42no—
197C22⋊Dic11—28no—
198C22⋊Dic11—28no—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—41no—
206C4⋊Dic11—41no—
207C4⋊Dic11C2×D412yes—
208C4⋊Dic11C2×D412yes—
209Dic11⋊C4—28no—
210Dic11⋊C4—28no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213#4318—22no—
214#4318—22no—
215#4318—42no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—42no—
218C2×#536—111no—
219C2×#428—111no—
220C22×#104D1111yescharacteristic
221C2×#417—111no—
222C22×#101—111no—
223C2×#391—111no—
224#2038—118no—
225C2×#339—111no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11#12011yescharacteristic
233C23×C11#12011yescharacteristic
234C23×C11#12112yes—
235C23×C11#12312yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—42no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—44no—
245D4×C11—42no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11—48no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—44no—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12112yes—
262C2×C4×C11#12312yes—
263C2×C4×C11#12312yes—
264C2×C4×C11#12312yes—
265C2×C4×C11#12412yes—
266C2×C4×C11#12412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—44no—
279C2×Dic11—44no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—44no—
283C2×Dic11—42no—
284C2×Dic11—82no—
285C2×Dic11—82no—
286Dic22—42no—
287Dic22—42no—
288Dic22—42no—
289Dic22—42no—
290Dic22—44no—
291Dic22—44no—
292C8×C11—24no—
293C11⋊C8—42no—
294C22×#41C2×D1111yescharacteristic
295C23×Q8—111no—
296C22×M16—111no—
297C22×M16C2×D1111yescharacteristic
298#536—114no—
299#536—222no—
300#536—222no—
301#536—222no—
302C2×C4⋊Q8—221no—
303C2×#124—221no—
304C2×#123—222no—
305C2×C22⋊Q8—221no—
306C2×C22⋊Q8—221no—
307C2×#117—111no—
308C22×C4⋊C4—111no—
309C22×C42C2×D1111yescharacteristic
310#428—114no—
311#428—222no—
312C2×#107—221no—
313C2×#106—221no—
314C2×#104—24no—
315C2×#104C2×D1114yes—
316#417—114no—
317#417—222no—
318C2×#103—221no—
319C2×#102—221no—
320C2×#101—114no—
321C2×#101—224no—
322#391—114no—
323#391—222no—
324C2×#95—222no—
325#339—114no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—84no—
336C22×C11#39412yes—
337C22×C11#39412yes—
338C22×C11#45412yes—
339C22×C11#45612yes—
340C22×C11C2×#12011yescharacteristic
341C22×C11C2×#12111yescharacteristic
342C22×C11C2×#12311yescharacteristic
343C4×C11—44no—
344C4×C11—42no—
345C4×C11#39412yes—
346C4×C11#39412yes—
347C4×C11C2×#12111yescharacteristic
348C4×C11C2×#12111yescharacteristic
349C4×C11C2×#12311yescharacteristic
350C4×C11C2×#12411yescharacteristic
351Dic11—44no—
352Dic11—42no—
353Dic11—42no—
354Dic11—82no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41D4412yes—
362C2×#41C22×D1112yes—
363C22×Q8—112no—
364C22×Q8—112no—
365C22×Q8—221no—
366C22×Q8—221no—
367C22×Q8—222no—
368C22×Q8—221no—
369C22×Q8—221no—
370C22×Q8—222no—
371C22×Q8—222no—
372C22×Q8—222no—
373C22×Q8D4411yescharacteristic
374C22×D4—21no—
375C22×D4D4411yescharacteristic
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—112no—
379C23×C4—221no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—21no—
382C2×M16—22no—
383C2×M16—112no—
384C2×M16—221no—
385C2×M16—222no—
386C2×M16—222no—
387C2×M16C22⋊D1114yes—
388C2×M16C22×D1112yes—
389C22×C8—21no—
390C22×C8—221no—
391C4⋊Q8—224no—
392C4⋊Q8—224no—
393#124—224no—
394#124—224no—
395#123—228no—
396#123—228no—
397C22⋊Q8—224no—
398C22⋊Q8—224no—
399C22⋊Q8—224no—
400C22⋊Q8—224no—
401#117—112no—
402#117—112no—
403#117—221no—
404#117—221no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—221no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—21no—
421C2×C42—221no—
422C2×C42C22×D1112yes—
423#107—224no—
424#106—224no—
425#104—28no—
426#103—224no—
427#102—224no—
428#101—228no—
429#95—228no—
430C2×C11—21no—
431C2×C11—21no—
432C2×C11—22no—
433C2×C11—82no—
434C2×C11#203814yescomplemented
435C2×C11C2×#39411yescharacteristic
436C2×C11C2×#45411yescharacteristic
437C2×C11C2×#45611yescharacteristic
438C24—21no—
439C24D4×D1111yescharacteristic
440#41—24no—
441#41—24no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—42no—
447#41—42no—
448#41—42no—
449#41—42no—
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—224no—
456C2×Q8—224no—
457C2×Q8—222no—
458C2×Q8—222no—
459C2×Q8—222no—
460C2×Q8—222no—
461C2×Q8—222no—
462C2×Q8—222no—
463C2×Q8—442no—
464C2×Q8—442no—
465C2×Q8—442no—
466C2×Q8—442no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×Q8—442no—
470C2×Q8—442no—
471C2×Q8C2×D4412yes—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4C2×D4412yes—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—114no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—444no—
498C22×C4—441no—
499C22×C4—441no—
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4#433912yes—
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4#434112yes—
507C22×C4#434112yes—
508C22×C4C2×C22⋊D1112yes—
509C22×C4C23×D1111yescharacteristic
510M16—24no—
511M16—22no—
512M16—222no—
513M16—222no—
514M16—442no—
515M16C2×C22⋊D1114yes—
516C2×C8—24no—
517C2×C8—22no—
518C2×C8—222no—
519C2×C8—442no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—228no—
523C4⋊C4—228no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—441no—
529C4⋊C4—441no—
530C22⋊C4—228no—
531C22⋊C4—228no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C42—22no—
535C42—22no—
536C42—42no—
537C42—222no—
538C42—222no—
539C11C2×#203811yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#6693511yescharacteristic
547C23#6693511yescharacteristic
548C23#6693612yes—
549C23#6699112yes—
550C23C2×D4×D1111yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—442no—
555Q8—442no—
556Q8—442no—
557Q8—442no—
558Q8—444no—
559Q8—444no—
560D4—22no—
561D4—22no—
562D4—42no—
563D4—42no—
564D4—44no—
565D4—42no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—48no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—444no—
585C2×C4—442no—
586C2×C4—882no—
587C2×C4—882no—
588C2×C4#6693511yescharacteristic
589C2×C4#6693511yescharacteristic
590C2×C4#6693612yes—
591C2×C4#6693812yes—
592C2×C4#6693812yes—
593C2×C4#6693912yes—
594C2×C4#6693912yes—
595C2×C4#6698312yes—
596C2×C4#6698312yes—
597C2×C4#6699112yes—
598C2×C4#6699212yes—
599C2×C4#6699212yes—
600C2×C4C22×D4411yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—24no—
607C8—442no—
608C22—24no—
609C22—24no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1062243912yes—
619C22#1062244012yes—
620C22#1062257412yes—
621C22#1062257412yes—
622C22C2×#6693511yescharacteristic
623C22C2×#6693611yescharacteristic
624C22C2×#6699111yescharacteristic
625C4—44no—
626C4—42no—
627C4—442no—
628C4—442no—
629C4—444no—
630C4—882no—
631C4#1062257412yes—
632C4#1062257412yes—
633C4C2×#6693811yescharacteristic
634C4C2×#6693911yescharacteristic
635C4C2×#6698311yescharacteristic
636C4C2×#6699211yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—82no—
641C2#1306983214yesdirect product factor
642C2C2×#1062257411yescharacteristic
643C2C2×#1062244011yescharacteristic
644C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC22×C11×#41C22
hypercenterC22×#104D11
hypocenterC11C2×#2038
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
4. C22×#66888C2semidirect
5. C2×#10622542C2semidirect
6. #13069832C2direct (N × H)
7. C2×#10622161C2semidirect
33. C2×#66888C22semidirect
35. #10622734C22semidirect
39. #10622542C22semidirect
40. #10622161C22semidirect
434. C2×C11#2038semidirect
539. C11C2×#2038semidirect
641. C2#13069832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106227342
C2×#106228452
C22×#668882
C2×#106225422
#130698322
C2×#106221612
C22×C11×#1042
C2×#203811