Finite Group Databasebeta

← #14769388

Subgroups — #14769388

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622828C212yesmaximal, complemented
3#13071565C211yesmaximal, characteristic, complemented
4#13069544C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069055C212yesmaximal, complemented
7#13068939C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068547C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×D42×C11C211yesmaximal, characteristic
12C23×D4×C11—21no—
13C23×D4×C11C2212yes—
14D42×C11—24no—
15D42×C11C418yescomplemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C11×#120—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66979C2212yescomplemented
23C22×#4318C2212yescomplemented
24#10622834—21no—
25#10622828—28no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2211yescharacteristic
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31C2×#66896C2212yescomplemented
32C2×#66896C2212yescomplemented
33#10622825C2212yescomplemented
34C2×C22⋊(C11⋊C8)C2212yescomplemented
35#10622625—24no—
36C4⋊C4×Dic11—21no—
37#10622564—22no—
38#10622548C2211yescharacteristic, complemented
39C4×C4⋊Dic11C2211yescharacteristic, complemented
40C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
41C2×C4×C11⋊C8C2211yescharacteristic, complemented
42#10622167C2212yescomplemented
43#10622167C2211yescharacteristic, complemented
44#10622167C2211yescharacteristic, complemented
45C25×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11—24no—
48C22×D4×C11—22no—
49C22×D4×C11—28no—
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—24no—
53C22×D4×C11—21no—
54C22×D4×C11—42no—
55C22×D4×C11—42no—
56C22×D4×C11—44no—
57C22×D4×C11—44no—
58C22×D4×C11C2×C418yes—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2312yes—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C11×#127—22no—
65C11×#127C2×C414yes—
66C11×#121—24no—
67C11×#121—28no—
68C11×#121C2×C418yes—
69C11×#120—216no—
70C4×D4×C11—22no—
71C4×D4×C11C2×C414yes—
72C4×D4×C11C2×C414yes—
73C4×D4×C11D414yes—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82#66979—24no—
83#66979—42no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—22no—
91C2×#4318—24no—
92C2×#4318—24no—
93C2×#4318—42no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2311yescharacteristic
97#66896—24no—
98#66896—22no—
99#66896—24no—
100#66896—24no—
101#66896—42no—
102#66896—42no—
103#66896D414yescomplemented
104C11⋊#95—21no—
105C11⋊#95—22no—
106C22⋊(C11⋊C8)—24no—
107C4⋊(C11⋊C8)—22no—
108C4×C11⋊C8—22no—
109#22428—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—28no—
113C24×C11—44no—
114C24×C11—44no—
115C24×C11—44no—
116C24×C11—44no—
117C24×C11—82no—
118C24×C11—82no—
119C24×C11C2×D412yes—
120C2×D4×C11—216no—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—432no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—81no—
146C2×D4×C11—81no—
147C2×D4×C11C22⋊C414yes—
148C2×D4×C11C22×C414yes—
149C2×D4×C11C22×C412yes—
150C2×D4×C11C2×D412yes—
151C2×D4×C11#4112yes—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—24no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22⋊C414yes—
171C11×C4⋊C4C22×C412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4C22⋊C418yes—
175C42×C11C22×C412yes—
176C42×C11C2×D412yes—
177C22⋊Dic11—44no—
178C22⋊Dic11—82no—
179C4⋊Dic11—22no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—22no—
184C4⋊Dic11—42no—
185C4⋊Dic11—81no—
186C4⋊Dic11C2×D412yescomplemented
187C4×Dic11—44no—
188C4×Dic11—42no—
189#4318—48no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2×D412yescomplemented
199C2×D42D1111yescharacteristic
200C2×#436—111no—
201C2×#418—112no—
202#2354—111no—
203#1982—111no—
204#1957—111no—
205#1895—112no—
206#1875—112no—
207#1802—111no—
208#1786—112no—
209C4×#102—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—416no—
221C23×C11—416no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—88no—
233C23×C11—88no—
234C23×C11—88no—
235C23×C11—88no—
236C23×C11—88no—
237C23×C11C2×C22⋊C414yes—
238C23×C11C22×D411yescharacteristic
239D4×C11—24no—
240D4×C11—22no—
241D4×C11—24no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—28no—
245D4×C11—416no—
246D4×C11—416no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—48no—
250D4×C11—84no—
251D4×C11C4×D414yes—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—48no—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C414yes—
266C2×C4×C11C2×C22⋊C412yes—
267C2×C4×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11AGL(1,ℤ/8)12yes—
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—42no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C11⋊C8—22no—
285C11⋊C8—42no—
286C11⋊C8—41no—
287C23×D4—21no—
288C23×D4C2×D1112yes—
289C22×M16—112no—
290D42—24no—
291D42Dic1118yescomplemented
292C2×#127C2×D1111yescharacteristic
293C2×#121—21no—
294C2×#121C2×D1112yes—
295C2×#120—22no—
296C2×C4×D4C2×D1111yescharacteristic
297C2×C4×D4C2×D1111yescharacteristic
298C2×#117—112no—
299#436—224no—
300C2×C4⋊C8—111no—
301#418—228no—
302C2×#102—111no—
303C2×#102—112no—
304C2×#102—112no—
305C2×#102—112no—
306C2×#102—111no—
307C2×#102—112no—
308C2×#102—112no—
309C2×C22⋊C8—112no—
310C2×C4×C8—111no—
311#390—221no—
312#388—222no—
313#384—111no—
314#380—112no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—221no—
317#340—112no—
318#340—111no—
319#340—111no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—832no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11C22×C22⋊C411yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11#54611yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C4×C11—24no—
350C4×C11—22no—
351C4×C11—42no—
352C4×C11#41814yescomplemented
353C4×C11C2×C4×D411yescharacteristic
354C4×C11#51811yescharacteristic
355C4×C11D4211yescharacteristic
356C4×C11#54611yescharacteristic
357Dic11—42no—
358Dic11—82no—
359Dic11—81no—
360C25—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—28no—
365C22×D4—22no—
366C22×D4—21no—
367C22×D4—24no—
368C22×D4—21no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—44no—
372C22×D4—44no—
373C22×D4C2×Dic1118yes—
374C22×D4C22⋊D1111yescharacteristic
375C22×D4C22×D1112yes—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4C22×D1112yes—
379C2×M16—224no—
380C2×M16—224no—
381C2×M16—442no—
382C22×C8—111no—
383C22×C8—112no—
384C22×C8—111no—
385#127—22no—
386#127C2×Dic1114yes—
387#121—24no—
388#121—28no—
389#121C2×Dic1118yes—
390#120—216no—
391C4×D4—22no—
392C4×D4C2×Dic1114yes—
393C4×D4C2×Dic1114yes—
394C4×D4C22⋊D1114yes—
395#117—224no—
396#117—442no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4C22⋊D1112yes—
409C2×C42—222no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412C4⋊C8—222no—
413#102—114no—
414#102—224no—
415#102—224no—
416#102—224no—
417#102—222no—
418#102—442no—
419#102—442no—
420C22⋊C8—224no—
421C4×C8—222no—
422#95—221no—
423#95—222no—
424C2×C11—44no—
425C2×C11—44no—
426C2×C11—84no—
427C2×C11D4×C22⋊C411yescharacteristic
428C2×C11C2×#41811yescharacteristic
429C2×C11#289711yescharacteristic
430C2×C11#327211yescharacteristic
431C2×C11#327411yescharacteristic
432C2×C11#332411yescharacteristic
433C2×C11#332511yescharacteristic
434C24—21no—
435C24—22no—
436C24—28no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—82no—
442C24—82no—
443C24C2×C22⋊D1112yes—
444C2×D4—216no—
445C2×D4—28no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—28no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—432no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4C22⋊Dic1114yes—
472C2×D4D4×D1112yes—
473C2×D4#434112yes—
474C2×D4C22×Dic1114yes—
475C2×D4C22×Dic1112yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4C22×Dic1114yes—
488C22×C4C2×C22⋊D1112yes—
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1114yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493M16—448no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—222no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—222no—
501C2×C8—221no—
502C2×C8—222no—
503C4⋊C4—21no—
504C4⋊C4—112no—
505C4⋊C4—221no—
506C4⋊C4—222no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—222no—
510C4⋊C4—442no—
511C4⋊C4—881no—
512C4⋊C4C22⋊Dic1114yes—
513C4⋊C4C22×Dic1112yes—
514C22⋊C4—24no—
515C22⋊C4—28no—
516C22⋊C4—444no—
517C22⋊C4—882no—
518C22⋊C4C22⋊Dic1118yes—
519C42—444no—
520C42—442no—
521C42C22×Dic1112yes—
522C42C2×C22⋊D1112yes—
523C11#2242811yescharacteristic, complemented, Sylow
524C23—22no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—24no—
534C23—416no—
535C23—416no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—88no—
547C23—88no—
548C23—88no—
549C23—88no—
550C23—88no—
551C23C2×C22⋊Dic1114yes—
552C23C22×C22⋊D1111yescharacteristic
553D4—24no—
554D4—22no—
555D4—24no—
556D4—22no—
557D4—22no—
558D4—28no—
559D4—416no—
560D4—416no—
561D4—42no—
562D4—42no—
563D4—48no—
564D4—84no—
565D4D4×Dic1114yes—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—48no—
578C2×C4—222no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—442no—
587C2×C4#6698512yes—
588C2×C4#6698512yes—
589C2×C4C2×C22⋊Dic1112yes—
590C2×C4C2×C22⋊Dic1114yes—
591C2×C4C2×C22⋊Dic1112yes—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4C2×#434111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4C23×Dic1111yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—222no—
599C8—442no—
600C8—441no—
601C22—24no—
602C22—24no—
603C22—24no—
604C22—24no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—832no—
619C22—82no—
620C22—82no—
621C22—82no—
622C22—82no—
623C22C2×#6698511yescharacteristic
624C22C2×#6698511yescharacteristic
625C22D4×C22⋊D1111yescharacteristic
626C22#1062333711yescharacteristic
627C22#1062336611yescharacteristic
628C22#1062336711yescharacteristic
629C22C22×C22⋊Dic1111yescharacteristic
630C4—24no—
631C4—22no—
632C4—42no—
633C4—442no—
634C4—881no—
635C4—882no—
636C4#1062282814yescomplemented
637C4C2×D4×Dic1111yescharacteristic
638C4#1062332911yescharacteristic
639C4D4×C22⋊D1111yescharacteristic
640C4#1062333711yescharacteristic
641C2—44no—
642C2—44no—
643C2—84no—
644C2D4×C22⋊Dic1111yescharacteristic
645C2C2×#1062282811yescharacteristic
646C2#1307714211yescharacteristic
647C2#1308021211yescharacteristic
648C2#1308023211yescharacteristic
649C2#1308084711yescharacteristic
650C2#1308085811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×D42D11
hypocenterC11#22428
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622828C2semidirect
3. #13071565C2semidirect
4. #13069544C2semidirect
5. #13069423C2semidirect
6. #13069055C2semidirect
7. #13068939C2semidirect
8. #13068616C2semidirect
9. #13068547C2semidirect
10. C4×#66896C2semidirect
15. D42×C11C4semidirect
22. C2×#66979C22semidirect
23. C22×#4318C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
31. C2×#66896C22semidirect
32. C2×#66896C22semidirect
33. #10622825C22semidirect
34. C2×C22⋊(C11⋊C8)C22semidirect
38. #10622548C22semidirect
39. C4×C4⋊Dic11C22semidirect
40. C2×C4⋊(C11⋊C8)C22semidirect
41. C2×C4×C11⋊C8C22semidirect
42. #10622167C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
103. #66896D4semidirect
186. C4⋊Dic11C2×D4semidirect
198. C2×C11⋊C8C2×D4semidirect
291. D42Dic11semidirect
352. C4×C11#418semidirect
523. C11#22428semidirect
636. C4#10622828semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228282
#130715652
#130695442
#130694232
#130690552
#130689392
#130686162
#130685472
C4×#668962
C2×D42×C112
#2242811