Finite Group Databasebeta

← C2×#13069645 #14780657

Subgroups — C2×#13069645 #14780657

Order 2816.

2190 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic
3C22×#66869C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5C22×#66897C211yesmaximal, characteristic, complemented
6#13069645C218yesmaximal, direct product factor
7C2×#10622161C211yesmaximal, characteristic, complemented
8C22×C11×#124C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C2×C11×#124—24no—
13C2×C11×#124—22no—
14C2×C11×#124—24no—
15C2×C11×#124C2214yescomplemented
16C22×C11×C22⋊C4—22no—
17C22×C42×C11C2211yescharacteristic
18C2×#67006—22no—
19C22×#4326—21no—
20C2×#66995—24no—
21C2×#66995—22no—
22C2×#66995—24no—
23C2×#66995C2214yescomplemented
24C22×#4325—21no—
25#10623336—22no—
26#10623336—22no—
27#10623336—22no—
28#10623336C2214yes—
29C2×#66993—21no—
30C2×#66991—22no—
31C2×#66989—21no—
32C2×#66979C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35#10622838—22no—
36#10622838C2214yescomplemented
37C2×#66899—22no—
38C2×#66897—24no—
39C2×#66897C2214yescomplemented
40C2×#66869—24no—
41C2×#66869C2214yescomplemented
42#10622161C2214yescomplemented
43C25×C11D412yes—
44C22×Q8×C11—22no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—21no—
51C22×Q8×C11—22no—
52C22×Q8×C11D414yescomplemented
53C22×Q8×C11C2312yes—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11D412yes—
63C22×D4×C11C2312yes—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—24no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339D412yes—
76C2×#4339C2312yes—
77C22×D44D411yescharacteristic
78C22×C4×D11—21no—
79C22×Dic22D411yescharacteristic
80C11×#124—216no—
81C11×#124—28no—
82C11×#124—28no—
83C2×C11×C22⋊C4—216no—
84C2×C11×C22⋊C4—28no—
85C2×C42×C11—21no—
86C2×C42×C11—22no—
87C2×C42×C11D414yescomplemented
88C2×C42×C11C2312yes—
89#67006—28no—
90#67006—28no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—21no—
93C2×#4326—28no—
94C2×#4326—24no—
95#66995—216no—
96#66995—28no—
97#66995—28no—
98C2×#4325—28no—
99C2×#4325—24no—
100#66993—24no—
101#66993—24no—
102#66991—28no—
103#66991—28no—
104#66989—24no—
105#66989—24no—
106#66979—21no—
107#66979—21no—
108#66979D412yes—
109#66979C2312yes—
110C2×C4⋊Dic11D412yes—
111C2×C4×Dic11—21no—
112C2×#4318—21no—
113C2×#4318—22no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318D414yescomplemented
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66899—28no—
123#66897—28no—
124#66869—28no—
125C2×#2004—111nomaximal, Sylow
126C24×C11—22no—
127C24×C11—24no—
128C24×C11—22no—
129C24×C11—24no—
130C24×C11—48no—
131C24×C11C2×D411yescharacteristic
132C24×C11C2×D414yes—
133C23×D11—21no—
134C2×Q8×C11—24no—
135C2×Q8×C11—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C2×Q8×C11—24no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—41no—
145C2×Q8×C11—41no—
146C2×Q8×C11—42no—
147C2×Q8×C11—42no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11C2×D414yescomplemented
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—42no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—44no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—42no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D412yes—
186C22×C4×C11#4112yes—
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—216no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—88no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196#4339—24no—
197#4339—24no—
198#4339—22no—
199#4339—22no—
200#4339—22no—
201#4339—22no—
202#4339—42no—
203#4339—42no—
204#4339—42no—
205#4339—42no—
206C2×D44—21no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44C2×D412yes—
210C2×C4×D11—22no—
211C2×C4×D11—22no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×Dic22—22no—
215C2×Dic22—21no—
216C2×Dic22—22no—
217C2×Dic22C2×D412yes—
218C11×C22⋊C4—232no—
219C42×C11—24no—
220C42×C11—22no—
221C42×C11C2×D414yescomplemented
222C22⋊Dic11—216no—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225#4326—216no—
226#4325—216no—
227C4⋊Dic11—22no—
228C4⋊Dic11C2×D414yes—
229C4×Dic11—22no—
230C4×Dic11—22no—
231#4318—24no—
232#4318—22no—
233#4318—22no—
234#4318—22no—
235#4318—42no—
236#4318C2×D414yescomplemented
237C2×C11⋊C8—24no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—22no—
240C2×C11⋊C8—42no—
241C22×#137—111no—
242C2×#535—111no—
243C22×#124D1111yescharacteristic, complemented
244C22×#104—111no—
245C2×#419—111no—
246C22×#100—111no—
247#2004—118no—
248C2×#339—111no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—48no—
254C23×C11—416no—
255C23×C11—44no—
256C23×C11—44no—
257C23×C11—48no—
258C23×C11—84no—
259C23×C11—88no—
260C23×C11#12011yescharacteristic
261C23×C11#12011yescharacteristic
262C23×C11#12012yes—
263C23×C11#12112yes—
264C23×C11C22×D411yescharacteristic
265C22×D11—22no—
266C22×D11—42no—
267C22×D11—44no—
268Q8×C11—24no—
269Q8×C11—24no—
270Q8×C11—42no—
271Q8×C11—42no—
272Q8×C11—44no—
273Q8×C11—44no—
274D4×C11—42no—
275D4×C11—42no—
276D4×C11—42no—
277D4×C11—42no—
278D4×C11—44no—
279D4×C11—44no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—44no—
283C2×C4×C11—48no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—44no—
287C2×C4×C11—44no—
288C2×C4×C11#12012yes—
289C2×C4×C11#12012yes—
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12012yes—
293C2×C4×C11#12112yes—
294C2×C4×C11#12112yes—
295C2×C4×C11#12112yes—
296C2×C4×C11#12112yes—
297C2×C4×C11#12112yes—
298C2×C4×C11#12712yes—
299C2×C4×C11#12712yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C22⋊D11—42no—
307C22⋊D11—42no—
308C22⋊D11—44no—
309C22⋊D11—816no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—42no—
313C2×Dic11—44no—
314D44—22no—
315D44—22no—
316D44—42no—
317C4×D11—42no—
318C4×D11—42no—
319C4×D11—44no—
320Dic22—22no—
321Dic22—22no—
322Dic22—42no—
323C11⋊C8—24no—
324C11⋊C8—42no—
325C22×#41—111no—
326C23×Q8C2×D1111yescharacteristic
327C23×D4C2×D1111yescharacteristic
328C2×#137—114no—
329C2×#137—224no—
330C2×#137—222no—
331C2×#137—224no—
332C22×Q16—221no—
333C22×SD16—221no—
334C22×M16—111no—
335C22×M16—111no—
336#535—114no—
337#535—222no—
338#535—222no—
339#535—222no—
340C2×#127—221no—
341C2×#124—24no—
342C2×#124—22no—
343C2×#124—24no—
344C2×#124—221no—
345C2×#124C2×D1114yescomplemented
346C2×#121—222no—
347C2×#120—222no—
348C2×#117—111no—
349C22×C22⋊C4—22no—
350C22×C42C2×D1111yescharacteristic
351C2×#104—114no—
352C2×#104—224no—
353#419—114no—
354#419—222no—
355C2×#103—222no—
356C2×#100—114no—
357C2×#100—224no—
358#339—114no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—24no—
362C22×C11—24no—
363C22×C11—48no—
364C22×C11—44no—
365C22×C11—48no—
366C22×C11—84no—
367C22×C11—88no—
368C22×C11—88no—
369C22×C11#39212yes—
370C22×C11#39212yes—
371C22×C11#45514yes—
372C22×C11C2×#12011yescharacteristic
373C22×C11C2×#12011yescharacteristic
374C22×C11C2×#12111yescharacteristic
375C2×D11—42no—
376C2×D11—44no—
377C2×D11—84no—
378C4×C11—44no—
379C4×C11—44no—
380C4×C11#39212yes—
381C4×C11#39212yes—
382C4×C11C2×#12011yescharacteristic
383C4×C11C2×#12111yescharacteristic
384C4×C11C2×#12111yescharacteristic
385C4×C11C2×#12711yescharacteristic
386Dic11—42no—
387Dic11—44no—
388C25C22⋊D1112yes—
389C2×#41—112no—
390C2×#41—112no—
391C2×#41—221no—
392C2×#41—221no—
393C2×#41—222no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—222no—
397C22×Q8—22no—
398C22×Q8—21no—
399C22×Q8—21no—
400C22×Q8—21no—
401C22×Q8—22no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—22no—
405C22×Q8—111no—
406C22×Q8C22⋊D1114yescomplemented
407C22×Q8C22×D1112yes—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—22no—
416C22×D4—111no—
417C22×D4—221no—
418C22×D4—224no—
419C22×D4C22⋊D1112yes—
420C22×D4C22×D1112yes—
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—221no—
424C23×C4C22×D1111yescharacteristic
425#137—228no—
426#137—2216no—
427#137—228no—
428C2×Q16—224no—
429C2×Q16—228no—
430C2×SD16—224no—
431C2×SD16—228no—
432C2×M16—114no—
433C2×M16—112no—
434C2×M16—112no—
435C2×M16—221no—
436C2×M16—222no—
437C2×M16—221no—
438C2×M16—222no—
439C2×M16—222no—
440C22×C8—221no—
441C22×C8—221no—
442#127—224no—
443#127—224no—
444#124—216no—
445#124—28no—
446#124—28no—
447#124—224no—
448#124—224no—
449#121—228no—
450#121—228no—
451#120—228no—
452#120—228no—
453#117—112no—
454#117—112no—
455#117—221no—
456#117—221no—
457C2×C4⋊C4—112no—
458C2×C22⋊C4—216no—
459C2×C22⋊C4—28no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—221no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—221no—
465C2×C42C22⋊D1114yescomplemented
466C2×C42C22×D1112yes—
467#104—228no—
468#103—228no—
469#100—228no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—22no—
473C2×C11—84no—
474C2×C11#200414yescomplemented
475C2×C11C2×#39211yescharacteristic
476C2×C11C2×#45512yes—
477D11—82no—
478C24—22no—
479C24—24no—
480C24—22no—
481C24—24no—
482C24—48no—
483C24—221no—
484C24C2×C22⋊D1111yescharacteristic
485C24C2×C22⋊D1114yes—
486#41—224no—
487#41—224no—
488#41—222no—
489#41—222no—
490#41—222no—
491#41—222no—
492#41—442no—
493#41—442no—
494#41—442no—
495#41—442no—
496C2×Q8—24no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—112no—
514C2×Q8—221no—
515C2×Q8—222no—
516C2×Q8—222no—
517C2×Q8C2×C22⋊D1114yescomplemented
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—112no—
537C2×D4—222no—
538C2×D4—222no—
539C2×D4—2216no—
540C2×D4—222no—
541C2×D4—221no—
542C2×D4—222no—
543C2×D4—442no—
544C2×D4—442no—
545C2×D4—888no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—44no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—222no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—442no—
559C22×C4—442no—
560C22×C4D4×D1111yescharacteristic
561C22×C4D4×D1111yescharacteristic
562C22×C4D4×D1112yes—
563C22×C4D4×D1111yescharacteristic
564C22×C4D4×D1111yescharacteristic
565C22×C4#434112yes—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1112yes—
568C22×C4C2×C22⋊D1112yes—
569C22×C4C23×D1111yescharacteristic
570Q16—2216no—
571SD16—2216no—
572M16—114no—
573M16—224no—
574M16—222no—
575M16—222no—
576M16—222no—
577M16—442no—
578C2×C8—224no—
579C2×C8—222no—
580C2×C8—222no—
581C2×C8—442no—
582C4⋊C4—114no—
583C4⋊C4—222no—
584C22⋊C4—232no—
585C22⋊C4—2216no—
586C22⋊C4—222no—
587C22⋊C4—222no—
588C42—24no—
589C42—22no—
590C42—222no—
591C42—222no—
592C42C2×C22⋊D1114yescomplemented
593C11C2×#200411yescharacteristic, complemented, Sylow
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—48no—
599C23—416no—
600C23—44no—
601C23—44no—
602C23—48no—
603C23—84no—
604C23—88no—
605C23—222no—
606C23—442no—
607C23—444no—
608C23#6699011yescharacteristic
609C23#6699011yescharacteristic
610C23#6699212yes—
611C23#6700612yes—
612C23C22×C22⋊D1111yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—42no—
616Q8—42no—
617Q8—44no—
618Q8—44no—
619Q8—222no—
620Q8—222no—
621Q8—442no—
622D4—42no—
623D4—42no—
624D4—42no—
625D4—42no—
626D4—44no—
627D4—44no—
628D4—222no—
629D4—222no—
630D4—442no—
631D4—444no—
632D4—442no—
633D4—442no—
634D4—8816no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—48no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—224no—
644C2×C4—222no—
645C2×C4—442no—
646C2×C4—444no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—444no—
650C2×C4#6699012yes—
651C2×C4#6699012yes—
652C2×C4#6699011yescharacteristic
653C2×C4#6699011yescharacteristic
654C2×C4#6699112yes—
655C2×C4#6699112yes—
656C2×C4#6699212yes—
657C2×C4#6699212yes—
658C2×C4#6699212yes—
659C2×C4#6699312yes—
660C2×C4#6699312yes—
661C2×C4#6700612yes—
662C2×C4C2×D4×D1111yescharacteristic
663C2×C4C2×D4×D1111yescharacteristic
664C2×C4C2×D4×D1111yescharacteristic
665C2×C4C2×#434111yescharacteristic
666C2×C4C22×C22⋊D1111yescharacteristic
667C2×C4C22×C22⋊D1111yescharacteristic
668C8—224no—
669C8—442no—
670C22—24no—
671C22—24no—
672C22—22no—
673C22—22no—
674C22—48no—
675C22—48no—
676C22—44no—
677C22—84no—
678C22—88no—
679C22—88no—
680C22—444no—
681C22—442no—
682C22—884no—
683C22#1062267414yes—
684C22#1062283612yes—
685C22#1062283612yes—
686C22C2×#6699011yescharacteristic
687C22C2×#6699211yescharacteristic
688C22C2×#6700611yescharacteristic
689C4—44no—
690C4—44no—
691C4—444no—
692C4—442no—
693C4#1062283612yes—
694C4#1062283612yes—
695C4C2×#6699011yescharacteristic
696C4C2×#6699111yescharacteristic
697C4C2×#6699211yescharacteristic
698C4C2×#6699311yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—84no—
703C2—882no—
704C2#1306964514yesdirect product factor
705C2C2×#1062283611yescharacteristic
706C2C2×#1062267412yes—
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#124C2
socleC23×C11#120
prime radicalC2×#10623336C2
hypercenterC22×#124D11
hypocenterC11C2×#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C22×#66869C2semidirect
4. C2×#10622838C2semidirect
5. C22×#66897C2semidirect
6. #13069645C2direct (N × H)
7. C2×#10622161C2semidirect
8. C22×C11×#124C2semidirect
15. C2×C11×#124C22semidirect
23. C2×#66995C22semidirect
36. #10622838C22semidirect
39. C2×#66897C22semidirect
41. C2×#66869C22semidirect
42. #10622161C22semidirect
52. C22×Q8×C11D4semidirect
87. C2×C42×C11D4semidirect
117. C2×#4318D4semidirect
151. C2×Q8×C11C2×D4semidirect
221. C42×C11C2×D4semidirect
236. #4318C2×D4semidirect
243. C22×#124D11semidirect
345. C2×#124C2×D11semidirect
406. C22×Q8C22⋊D11semidirect
465. C2×C42C22⋊D11semidirect
474. C2×C11#2004semidirect
517. C2×Q8C2×C22⋊D11semidirect
592. C42C2×C22⋊D11semidirect
593. C11C2×#2004semidirect
704. C2#13069645direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233362
C22×#668692
C2×#106228382
C22×#668972
#130696452
C2×#106221612
C22×C11×#1242
C2×#200411