Finite Group Databasebeta

← C2×#13069642 #14780654

Subgroups — C2×#13069642 #14780654

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
1C2×#10623361C211yesmaximal, characteristic
2C22×#67000C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5C22×#66887C211yesmaximal, characteristic, complemented
6#13069642C218yesmaximal, direct product factor
7C2×#10622193C211yesmaximal, characteristic, complemented
8C22×C11×#137C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C2×C11×#137—22no—
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137C2214yescomplemented
16C22×C11×Q16—21no—
17C22×C11×SD16—21no—
18C22×C11×M16C2211yescharacteristic
19#10623361—22no—
20#10623361—22no—
21#10623361—22no—
22#10623361C2214yes—
23C2×#67000—21no—
24C2×#67000—24no—
25C2×#67000—22no—
26C2×#67000—24no—
27C2×#67000C2214yescomplemented
28C2×#66993—21no—
29C2×#66990—22no—
30C2×#66983—22no—
31C22×(C2×D11)⋊C4—22no—
32C2×#66979C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66901—24no—
36C2×#66901C2214yescomplemented
37#10622838—22no—
38#10622838C2214yescomplemented
39C2×#66899—22no—
40C2×#66887—24no—
41C2×#66887C2214yescomplemented
42#10622193C2214yescomplemented
43C24×D11D412yes—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41D412yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11—22no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11—22no—
60C22×Q8×C11D411yescharacteristic
61C22×Q8×C11D414yescomplemented
62C22×Q8×C11C2312yes—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—24no—
69C23×Dic11—21no—
70C22×D44—22no—
71C22×D44—21no—
72C22×D44—21no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—21no—
76C22×D44—21no—
77C22×D44—22no—
78C22×D44D412yes—
79C22×D44C2312yes—
80C11×#137—216no—
81C11×#137—28no—
82C11×#137—28no—
83C2×C11×Q16—28no—
84C2×C11×Q16—24no—
85C2×C11×SD16—28no—
86C2×C11×SD16—24no—
87C2×C11×M16—22no—
88C2×C11×M16—21no—
89C2×C11×M16D414yescomplemented
90C2×C11×M16C2312yes—
91C22×C8×C11—21no—
92C2×C22⋊Dic11—21no—
93#67000—216no—
94#67000—24no—
95#67000—24no—
96#67000—28no—
97#67000—28no—
98#66993—24no—
99#66993—24no—
100#66990—28no—
101#66990—28no—
102#66983—28no—
103#66983—28no—
104C2×(C2×D11)⋊C4—216no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—28no—
107#66979—21no—
108#66979—21no—
109#66979D412yes—
110#66979C2312yes—
111C2×C4⋊Dic11D412yes—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11D414yescomplemented
116C2×C4×Dic11C2312yes—
117C2×#4318—21no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318C2312yes—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66899—28no—
124#66887—28no—
125C2×#2004—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—24no—
132C23×D11—48no—
133C23×D11C2×D414yes—
134C11×#41—24no—
135C11×#41—24no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—42no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—42no—
144C2×Q8×C11—24no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—24no—
148C2×Q8×C11—22no—
149C2×Q8×C11—24no—
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—22no—
155C2×Q8×C11—22no—
156C2×Q8×C11—22no—
157C2×Q8×C11—41no—
158C2×Q8×C11—41no—
159C2×Q8×C11—42no—
160C2×Q8×C11—42no—
161C2×Q8×C11—42no—
162C2×Q8×C11—42no—
163C2×Q8×C11—42no—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11C2×D414yescomplemented
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—21no—
170C2×D4×C11—22no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11C2×D412yes—
174C22×C4×C11—21no—
175C22×C4×C11—24no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—216no—
195C2×C22⋊D11—88no—
196C22×Dic11—24no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—44no—
200C2×D44—22no—
201C2×D44—22no—
202C2×D44—24no—
203C2×D44—24no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—42no—
211C2×D44—42no—
212C2×D44—42no—
213C2×D44—42no—
214C2×D44—42no—
215C2×D44—42no—
216C2×D44—42no—
217C2×D44—42no—
218C11×Q16—216no—
219C11×SD16—216no—
220C11×M16—24no—
221C11×M16—22no—
222C11×M16C2×D414yescomplemented
223C2×C8×C11—24no—
224C2×C8×C11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227(C2×D11)⋊C4—232no—
228(C2×D11)⋊C4—216no—
229C4⋊Dic11—22no—
230C4⋊Dic11C2×D414yes—
231C4×Dic11—24no—
232C4×Dic11—22no—
233C4×Dic11—22no—
234C4×Dic11—22no—
235C4×Dic11C2×D414yescomplemented
236#4318—22no—
237#4318—22no—
238#4318—42no—
239C2×C11⋊C8—22no—
240C2×C11⋊C8—42no—
241C22×#137D1111yescharacteristic, complemented
242C2×#535—111no—
243C22×#124—111no—
244C22×#104—111no—
245C2×#419—111no—
246C22×#100—111no—
247#2004—118no—
248C2×#339—111no—
249C23×C11—24no—
250C23×C11—22no—
251C23×C11—42no—
252C23×C11—44no—
253C23×C11#12011yescharacteristic
254C23×C11#12012yes—
255C23×C11#12011yescharacteristic
256C23×C11#12112yes—
257C23×C11C22×D411yescharacteristic
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—48no—
262C22×D11—416no—
263C22×D11—44no—
264C22×D11—44no—
265C22×D11—48no—
266C22×D11—84no—
267C22×D11—88no—
268Q8×C11—24no—
269Q8×C11—22no—
270Q8×C11—24no—
271Q8×C11—22no—
272Q8×C11—42no—
273Q8×C11—42no—
274Q8×C11—44no—
275Q8×C11—44no—
276Q8×C11—42no—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—42no—
280D4×C11—42no—
281D4×C11—44no—
282D4×C11—42no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—44no—
293C2×C4×C11#12011yescharacteristic
294C2×C4×C11#12012yes—
295C2×C4×C11#12011yescharacteristic
296C2×C4×C11#12012yes—
297C2×C4×C11#12012yes—
298C2×C4×C11#12112yes—
299C2×C4×C11#12112yes—
300C2×C4×C11#12112yes—
301C2×C4×C11#12112yes—
302C2×C4×C11#12112yes—
303C2×C4×C11#12712yes—
304C2×C4×C11#12712yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C22⋊D11—816no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—44no—
315C2×Dic11—48no—
316C2×Dic11—44no—
317D44—42no—
318D44—42no—
319D44—42no—
320D44—42no—
321D44—44no—
322D44—44no—
323C8×C11—24no—
324C11⋊C8—42no—
325C22×#41C2×D1111yescharacteristic
326C23×Q8C2×D1111yescharacteristic
327C23×D4—111no—
328C2×#137—22no—
329C2×#137—24no—
330C2×#137—24no—
331C2×#137C2×D1114yescomplemented
332C22×Q16—21no—
333C22×SD16—21no—
334C22×M16—111no—
335C22×M16C2×D1111yescharacteristic
336#535—114no—
337#535—222no—
338#535—222no—
339#535—222no—
340C2×#127—221no—
341C2×#124—114no—
342C2×#124—224no—
343C2×#124—222no—
344C2×#124—221no—
345C2×#124—224no—
346C2×#121—222no—
347C2×#120—222no—
348C2×#117—111no—
349C22×C22⋊C4—222no—
350C22×C42—111no—
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—42no—
364C22×C11—44no—
365C22×C11—84no—
366C22×C11#39212yes—
367C22×C11#39212yes—
368C22×C11#45514yes—
369C22×C11C2×#12011yescharacteristic
370C22×C11C2×#12011yescharacteristic
371C22×C11C2×#12111yescharacteristic
372C2×D11—48no—
373C2×D11—44no—
374C2×D11—48no—
375C2×D11—88no—
376C2×D11—88no—
377C2×D11—84no—
378C4×C11—42no—
379C4×C11—44no—
380C4×C11#39212yes—
381C4×C11#39212yes—
382C4×C11C2×#12011yescharacteristic
383C4×C11C2×#12111yescharacteristic
384C4×C11C2×#12111yescharacteristic
385C4×C11C2×#12711yescharacteristic
386Dic11—44no—
387Dic11—44no—
388C25—112no—
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—22no—
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41C22⋊D1112yes—
396C2×#41C22×D1112yes—
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×Q8C22⋊D1111yescharacteristic
406C22×Q8C22⋊D1114yescomplemented
407C22×Q8C22×D1112yes—
408C22×D4—21no—
409C22×D4—112no—
410C22×D4—112no—
411C22×D4—224no—
412C22×D4—221no—
413C22×D4—222no—
414C22×D4—221no—
415C22×D4—222no—
416C22×D4—222no—
417C22×D4—221no—
418C22×D4—221no—
419C22×D4—222no—
420C22×D4C22⋊D1111yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—221no—
424C23×C4C22×D1111yescharacteristic
425#137—216no—
426#137—28no—
427#137—28no—
428C2×Q16—28no—
429C2×Q16—24no—
430C2×SD16—28no—
431C2×SD16—24no—
432C2×M16—22no—
433C2×M16—21no—
434C2×M16—112no—
435C2×M16—221no—
436C2×M16—222no—
437C2×M16—222no—
438C2×M16C22⋊D1114yescomplemented
439C2×M16C22×D1112yes—
440C22×C8—21no—
441C22×C8—221no—
442#127—224no—
443#127—224no—
444#124—228no—
445#124—2216no—
446#124—224no—
447#124—224no—
448#124—228no—
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—228no—
459C2×C22⋊C4—2216no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—221no—
462C2×C42—114no—
463C2×C42—112no—
464C2×C42—221no—
465C2×C42—221no—
466C2×C42—222no—
467#104—228no—
468#103—228no—
469#100—228no—
470C2×C11—21no—
471C2×C11—21no—
472C2×C11—22no—
473C2×C11—82no—
474C2×C11#200414yescomplemented
475C2×C11C2×#39211yescharacteristic
476C2×C11C2×#45512yes—
477D11—84no—
478C24—21no—
479C24—114no—
480C24—224no—
481C24—222no—
482C24—222no—
483C24—224no—
484C24—448no—
485C24D4×D1111yescharacteristic
486#41—24no—
487#41—24no—
488#41—22no—
489#41—22no—
490#41—22no—
491#41—22no—
492#41—42no—
493#41—42no—
494#41—42no—
495#41—42no—
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8—22no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—22no—
502C2×Q8—24no—
503C2×Q8—22no—
504C2×Q8—24no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—41no—
510C2×Q8—41no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C2×C22⋊D1112yes—
517C2×Q8C2×C22⋊D1114yescomplemented
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—2216no—
526C2×D4—222no—
527C2×D4—224no—
528C2×D4—222no—
529C2×D4—224no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—442no—
537C2×D4—442no—
538C2×D4—442no—
539C2×D4—442no—
540C2×D4—442no—
541C2×D4—442no—
542C2×D4—442no—
543C2×D4—442no—
544C2×D4—888no—
545C2×D4C2×C22⋊D1112yes—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—224no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—444no—
560C22×C4D4×D1111yescharacteristic
561C22×C4D4×D1112yes—
562C22×C4D4×D1111yescharacteristic
563C22×C4D4×D1111yescharacteristic
564C22×C4#434112yes—
565C22×C4C2×C22⋊D1112yes—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1112yes—
569C22×C4C23×D1111yescharacteristic
570Q16—216no—
571SD16—216no—
572M16—24no—
573M16—22no—
574M16—222no—
575M16—222no—
576M16—442no—
577M16C2×C22⋊D1114yescomplemented
578C2×C8—24no—
579C2×C8—22no—
580C2×C8—222no—
581C2×C8—442no—
582C4⋊C4—114no—
583C4⋊C4—222no—
584C22⋊C4—2232no—
585C22⋊C4—2216no—
586C22⋊C4—222no—
587C22⋊C4—222no—
588C42—114no—
589C42—224no—
590C42—222no—
591C42—222no—
592C42—222no—
593C11C2×#200411yescharacteristic, complemented, Sylow
594C23—24no—
595C23—22no—
596C23—44no—
597C23—42no—
598C23—224no—
599C23—224no—
600C23—224no—
601C23—448no—
602C23—4416no—
603C23—448no—
604C23—444no—
605C23—444no—
606C23—884no—
607C23—888no—
608C23#6699011yescharacteristic
609C23#6699012yes—
610C23#6699011yescharacteristic
611C23#6699112yes—
612C23C2×D4×D1111yescharacteristic
613Q8—24no—
614Q8—22no—
615Q8—24no—
616Q8—22no—
617Q8—42no—
618Q8—42no—
619Q8—44no—
620Q8—44no—
621Q8—42no—
622D4—22no—
623D4—22no—
624D4—42no—
625D4—42no—
626D4—44no—
627D4—42no—
628D4—442no—
629D4—442no—
630D4—442no—
631D4—444no—
632D4—444no—
633D4—442no—
634D4—8816no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—44no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—448no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4#6699011yescharacteristic
651C2×C4#6699012yes—
652C2×C4#6699011yescharacteristic
653C2×C4#6699112yes—
654C2×C4#6699212yes—
655C2×C4#6699212yes—
656C2×C4#6699212yes—
657C2×C4#6699212yes—
658C2×C4#6699312yes—
659C2×C4#6699312yes—
660C2×C4#6700612yes—
661C2×C4#6700612yes—
662C2×C4C2×D4×D1111yescharacteristic
663C2×C4C2×D4×D1111yescharacteristic
664C2×C4C2×#434111yescharacteristic
665C2×C4C22×C22⋊D1111yescharacteristic
666C2×C4C22×C22⋊D1111yescharacteristic
667C2×C4C22×C22⋊D1111yescharacteristic
668C8—24no—
669C8—442no—
670C22—24no—
671C22—24no—
672C22—22no—
673C22—22no—
674C22—44no—
675C22—42no—
676C22—84no—
677C22—448no—
678C22—448no—
679C22—444no—
680C22—884no—
681C22—888no—
682C22—888no—
683C22#1062281514yes—
684C22#1062283612yes—
685C22#1062283612yes—
686C22C2×#6699011yescharacteristic
687C22C2×#6699011yescharacteristic
688C22C2×#6699111yescharacteristic
689C4—42no—
690C4—44no—
691C4—444no—
692C4—444no—
693C4#1062283612yes—
694C4#1062283612yes—
695C4C2×#6699211yescharacteristic
696C4C2×#6699211yescharacteristic
697C4C2×#6699311yescharacteristic
698C4C2×#6700611yescharacteristic
699C2—21no—
700C2—21no—
701C2—22no—
702C2—82no—
703C2—884no—
704C2#1306964214yesdirect product factor
705C2C2×#1062283611yescharacteristic
706C2C2×#1062281512yes—
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11#120
prime radicalC2×#10623361C2
hypercenterC22×#137D11
hypocenterC11C2×#2004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#67000C2semidirect
3. C22×#66901C2semidirect
4. C2×#10622838C2semidirect
5. C22×#66887C2semidirect
6. #13069642C2direct (N × H)
7. C2×#10622193C2semidirect
8. C22×C11×#137C2semidirect
15. C2×C11×#137C22semidirect
27. C2×#67000C22semidirect
36. C2×#66901C22semidirect
38. #10622838C22semidirect
41. C2×#66887C22semidirect
42. #10622193C22semidirect
61. C22×Q8×C11D4semidirect
89. C2×C11×M16D4semidirect
115. C2×C4×Dic11D4semidirect
165. C2×Q8×C11C2×D4semidirect
222. C11×M16C2×D4semidirect
235. C4×Dic11C2×D4semidirect
241. C22×#137D11semidirect
331. C2×#137C2×D11semidirect
406. C22×Q8C22⋊D11semidirect
438. C2×M16C22⋊D11semidirect
474. C2×C11#2004semidirect
517. C2×Q8C2×C22⋊D11semidirect
577. M16C2×C22⋊D11semidirect
593. C11C2×#2004semidirect
704. C2#13069642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233612
C22×#670002
C22×#669012
C2×#106228382
C22×#668872
#130696422
C2×#106221932
C22×C11×#1372
C2×#200411