Finite Group Databasebeta

← C2×#13067171 #14721106

Subgroups — C2×#13067171 #14721106

Order 2816.

1498 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#10622277C211yesmaximal, characteristic, complemented
4#13067171C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622108C211yesmaximal, characteristic, complemented
7C2×#10622089C211yesmaximal, characteristic, complemented
8C2×C11×#328C211yesmaximal, characteristic, complemented
9C22×#4343C411yescharacteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×#66999C411yescharacteristic, complemented
13C2×#66983C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×C8×D11—21no—
16#10623158—22no—
17#10623158—22no—
18#10623158C414yescomplemented
19#10623158C2214yes—
20C2×#66948C411yescharacteristic, complemented
21C2×#66947—21no—
22C2×#66946—21no—
23C2×#66945C411yescharacteristic, complemented
24C2×#66935—21no—
25C2×(C22⋊D11)⋊C4—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95—21no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×(C2×D11)⋊C8—21no—
32D11×C22⋊C8—22no—
33D11×C22⋊C8C2214yescomplemented
34#10622277—22no—
35#10622277C2214yescomplemented
36C11×#328C2214yescomplemented
37#10622176C2214yescomplemented
38#10622108C2214yescomplemented
39#10622089C2214yescomplemented
40C24×D11D411yescharacteristic
41C22×Q8×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C2×#4343—22no—
48C2×#4343—44no—
49C2×#4343C2×C414yescomplemented
50C22×D44—21no—
51C22×D44—21no—
52C22×D44C2×C411yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11—44no—
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C412yes—
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D412yes—
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D412yes—
62C22×C4×D11C2312yes—
63C22×C8×C11—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8C2×C412yes—
67C11×C22⋊Q8C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4—21no—
71#66999—22no—
72#66999C2×C414yescomplemented
73#66983—21no—
74#66983—21no—
75#66983C2×C412yes—
76#66983C2312yes—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—44no—
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8—21no—
87C2×C8×D11—24no—
88C2×C8×D11—44no—
89#66948—22no—
90#66948C2×C414yescomplemented
91#66947—24no—
92#66947—24no—
93#66946—24no—
94#66946—24no—
95#66945—22no—
96#66945C2×C414yescomplemented
97#66935—24no—
98#66935—24no—
99(C22⋊D11)⋊C4—24no—
100(C22⋊D11)⋊C4—24no—
101C11×C22⋊C8—21no—
102C11×C22⋊C8C2312yes—
103C11×#95—21no—
104C11×#95C2312yes—
105C11⋊#95—21no—
106C11⋊#95—24no—
107C11⋊#95C2312yes—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)C2312yes—
110(C2×D11)⋊C8—24no—
111C2×#1516—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11—21no—
117C23×D11—42no—
118C23×D11C22⋊C411yescharacteristic
119C23×D11C22⋊C412yes—
120C23×D11C22⋊C411yescharacteristic
121C23×D11C2×D412yes—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11C22×C412yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—22no—
139C2×C22⋊D11—22no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22⋊C412yes—
151C22×Dic11C2×D412yes—
152#4343—48no—
153#4343—48no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—21no—
157C2×D44—42no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44C22×C412yes—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×C4×D11C22⋊C412yes—
172C2×C4×D11C22⋊C412yes—
173C2×C4×D11C22⋊C412yes—
174C2×C4×D11C22⋊C412yes—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C22×C412yes—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D412yes—
179C2×C8×C11—22no—
180C2×C8×C11—42no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—48no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—24no—
196C4×Dic11—24no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—42no—
199C8×D11—48no—
200C2×#525—111no—
201C22×C22⋊C8—111no—
202C2×#381—111no—
203#1516—118no—
204C2×#328—111no—
205C2×#328D1111yescharacteristic, complemented
206C2×#327—111no—
207C2×#327—111no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11#13512yes—
213C23×C11#13512yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11#9914yes—
234C22×D11C2×C22⋊C412yes—
235C22×D11C2×C22⋊C412yes—
236Q8×C11—42no—
237Q8×C11—42no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—84no—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C22⋊D11—42no—
257C22⋊D11—42no—
258C22⋊D11—44no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—84no—
269C2×Dic11C2×C22⋊C412yes—
270C2×Dic11C2×C22⋊C412yes—
271D44—42no—
272D44—42no—
273D44—48no—
274D44—48no—
275C4×D11—24no—
276C4×D11—24no—
277C4×D11—24no—
278C4×D11—24no—
279C4×D11—42no—
280C4×D11—42no—
281C4×D11—42no—
282C4×D11—42no—
283C4×D11—48no—
284C8×C11—42no—
285C11⋊C8—42no—
286C22×#41—111no—
287C24×C4—111no—
288C23×C8—221no—
289#525—114no—
290#525—114no—
291#525—222no—
292#525—222no—
293C2×#123—221no—
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×#121—111no—
297C2×#121—111no—
298C2×#120—221no—
299C2×C4×D4—221no—
300C2×C4×D4—221no—
301C2×#117—111no—
302C22×C22⋊C4—221no—
303C2×C22⋊C8—111no—
304C2×C22⋊C8—114no—
305C2×C22⋊C8—222no—
306C2×C22⋊C8—221no—
307C2×C22⋊C8C2×D1111yescharacteristic
308#381—114no—
309#381—222no—
310C2×#95—111no—
311C2×#95—221no—
312C2×#95C2×D1111yescharacteristic
313#328—114no—
314#328C2×D1114yescomplemented
315#327—114no—
316#327—114no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11C2×#9912yes—
324C22×C11#41612yes—
325C22×C11#41612yes—
326C22×C11#42112yes—
327C22×C11C22×C22⋊C411yescharacteristic
328C22×C11C2×#13511yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—28no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—48no—
339C2×D11—44no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—84no—
344C2×D11C2×#9914yes—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—82no—
352Dic11—22no—
353Dic11—22no—
354Dic11—42no—
355Dic11—82no—
356C25—111no—
357C2×#41—114no—
358C2×#41—222no—
359C2×#41—444no—
360C22×Q8C4×D1111yescharacteristic
361C22×D4—111no—
362C22×D4—221no—
363C22×D4—221no—
364C22×D4—221no—
365C23×C4—21no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—111no—
372C23×C4—112no—
373C23×C4—112no—
374C23×C4—112no—
375C23×C4—221no—
376C23×C4—221no—
377C23×C4—444no—
378C23×C4C22×D1111yescharacteristic
379C22×C8—21no—
380C22×C8—224no—
381C22×C8—221no—
382C22×C8—444no—
383#123—224no—
384#123—224no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—114no—
388C22⋊Q8—222no—
389C22⋊Q8C4×D1112yes—
390C22⋊Q8C22×D1112yes—
391#121—112no—
392#121—112no—
393#121—114no—
394#121—222no—
395#121—221no—
396#121—221no—
397#120—224no—
398#120—224no—
399C4×D4—224no—
400C4×D4—224no—
401C4×D4—224no—
402C4×D4—224no—
403#117—114no—
404#117—222no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C4×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—444no—
416C2×C42—221no—
417C22⋊C8—21no—
418C22⋊C8—112no—
419C22⋊C8—224no—
420C22⋊C8—221no—
421C22⋊C8C22×D1112yes—
422#95—21no—
423#95—112no—
424#95—224no—
425#95—221no—
426#95C22×D1112yes—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—22no—
430C2×C11#151614yescomplemented
431C2×C11C22×#9911yescharacteristic
432C2×C11C2×#41611yescharacteristic
433C2×C11C2×#42111yescharacteristic
434D11—24no—
435D11—42no—
436D11—82no—
437C24—111no—
438C24—111no—
439C24—112no—
440C24—112no—
441C24—224no—
442C24—222no—
443C24—222no—
444C24—221no—
445C24—442no—
446C24D4×D1111yescharacteristic
447#41—448no—
448#41—448no—
449C2×Q8—21no—
450C2×Q8—42no—
451C2×Q8C2×C4×D1112yes—
452C2×D4—112no—
453C2×D4—224no—
454C2×D4—224no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—221no—
458C2×D4—442no—
459C2×D4—444no—
460C2×D4—444no—
461C2×D4—442no—
462C2×D4—442no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—444no—
490C22×C4—444no—
491C22×C4—444no—
492C22×C4—444no—
493C22×C4—444no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×C4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C2×C8—22no—
505C2×C8—42no—
506C2×C8—222no—
507C2×C8—448no—
508C2×C8—442no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—112no—
513C4⋊C4—224no—
514C4⋊C4—221no—
515C4⋊C4C2×C4×D1112yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—448no—
524C42—224no—
525C11C2×#151611yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—112no—
529C23—114no—
530C23—112no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—224no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—442no—
543C23—442no—
544C23—448no—
545C23—448no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23C22⋊C4×D1111yescharacteristic
550C23C22⋊C4×D1111yescharacteristic
551C23#6696912yes—
552C23#6697212yes—
553C23C2×D4×D1111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—442no—
557D4—442no—
558D4—448no—
559D4—448no—
560D4—442no—
561D4—442no—
562D4—444no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—84no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—448no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—884no—
598C2×C4C22⋊C4×D1111yescharacteristic
599C2×C4C22⋊C4×D1111yescharacteristic
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C8—42no—
603C8—442no—
604C22—21no—
605C22—21no—
606C22—24no—
607C22—24no—
608C22—21no—
609C22—21no—
610C22—114no—
611C22—222no—
612C22—228no—
613C22—222no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—444no—
618C22—444no—
619C22—448no—
620C22—444no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—884no—
625C22D11×#9912yes—
626C22#1062241712yes—
627C22#1062241712yes—
628C22#1062243412yes—
629C22C2×C22⋊C4×D1111yescharacteristic
630C22C2×#6696911yescharacteristic
631C22C2×#6697211yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—82no—
639C4—222no—
640C4—222no—
641C4—442no—
642C4—882no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—224no—
647C2—442no—
648C2—882no—
649C2#1306717114yesdirect product factor
650C2C2×D11×#9911yescharacteristic
651C2C2×#1062241711yescharacteristic
652C2C2×#1062243411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623158C2
cosocleC22×C4×C11C24
hypercenterC2×#328D11
hypocenterC11C2×#1516
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊C8C2semidirect
3. C2×#10622277C2semidirect
4. #13067171C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622108C2semidirect
7. C2×#10622089C2semidirect
8. C2×C11×#328C2semidirect
9. C22×#4343C4semidirect
12. C2×#66999C4semidirect
18. #10623158C4semidirect
20. C2×#66948C4semidirect
23. C2×#66945C4semidirect
33. D11×C22⋊C8C22semidirect
35. #10622277C22semidirect
36. C11×#328C22semidirect
37. #10622176C22semidirect
38. #10622108C22semidirect
39. #10622089C22semidirect
49. C2×#4343C2×C4semidirect
72. #66999C2×C4semidirect
90. #66948C2×C4semidirect
96. #66945C2×C4semidirect
205. C2×#328D11semidirect
314. #328C2×D11semidirect
430. C2×C11#1516semidirect
525. C11C2×#1516semidirect
649. C2#13067171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×C22⋊C82
C2×#106222772
#130671712
C2×#106221762
C2×#106221082
C2×#106220892
C2×C11×#3282
C2×#151611