Finite Group Databasebeta

← #14769385

Subgroups — #14769385

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×D4×D44C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622383C212yesmaximal, complemented
4#13071567C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069053C212yesmaximal, complemented
8#13068937C212yesmaximal, complemented
9#13068545C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#1802C211yesmaximal, characteristic, complemented
12C22×D4×D11C2212yes—
13C23×D44—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66983—21no—
16C22×#4313C2212yescomplemented
17D4×D44—24no—
18D4×D44C418yescomplemented
19C2×#66948C2212yes—
20C2×#66945C2212yescomplemented
21C2×#66935—22no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×#102C2212yes—
26C11×#384C2211yescharacteristic, complemented
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66885C2212yescomplemented
30C2×#66885C2212yescomplemented
31C2×(C2×D11)⋊C8C2212yescomplemented
32#10622603—22no—
33#10622601—21no—
34#10622600C2212yescomplemented
35C4⋊C4×Dic11—21no—
36C2×#66873C2212yescomplemented
37C2×#66873C2212yescomplemented
38C4×C4⋊Dic11C2211yescharacteristic, complemented
39C2×C4×C11⋊C8C2211yescharacteristic, complemented
40#10622451—24no—
41#10622383—28no—
42C11×#340C2212yescomplemented
43#10622167C2211yescharacteristic, complemented
44#10622167C2211yescharacteristic, complemented
45C24×D11—22no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C2×D4×D11—24no—
52C2×D4×D11—42no—
53C2×D4×D11—42no—
54C2×D4×D11C2×C418yes—
55C22×D44—22no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—28no—
59C22×D44—44no—
60C22×D44—44no—
61C22×D44D411yescharacteristic
62C22×D44C2312yes—
63C22×C4×D11C2312yes—
64C22×C8×C11C2312yes—
65C4×D4×C11—22no—
66C4×D4×C11C2×C414yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73#66983—28no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4D412yes—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4×Dic11—21no—
82C2×C4×Dic11—22no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C2×#4313—24no—
86C2×#4313—24no—
87C2×#4313—42no—
88#66948—24no—
89#66948C2×C418yes—
90#66945—24no—
91#66945—42no—
92#66935—216no—
93#66927—22no—
94#66927C2×C414yes—
95C4×D44C2×C414yes—
96C4×D44D414yes—
97C11×C4⋊C8—22no—
98C11×#102—24no—
99#66896—22no—
100#66896D414yescomplemented
101C11⋊#95—21no—
102C11⋊#95—22no—
103#66885—24no—
104#66885—42no—
105(C2×D11)⋊C8—24no—
106#66873—24no—
107#66873—42no—
108C4×C11⋊C8—22no—
109#22428—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11—22no—
112C23×D11—28no—
113C23×D11—44no—
114C23×D11—44no—
115C23×D11—44no—
116C23×D11—44no—
117C23×D11—82no—
118C23×D11—82no—
119C23×D11C2×D412yes—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11C22×C412yes—
124C2×D4×C11C2×D412yes—
125C2×D4×C11#4112yes—
126C22×C4×C11—21no—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—28no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—44no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D412yes—
140D4×D11—216no—
141D4×D11—48no—
142D4×D11—48no—
143D4×D11—48no—
144C2×D44—28no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—44no—
155C2×D44—44no—
156C2×D44—432no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—81no—
160C2×D44—81no—
161C2×D44C22⋊C414yes—
162C2×D44C22×C414yes—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11C22×C414yes—
168C2×C4×D11C2×D414yes—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—81no—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—24no—
179C42×C11C22×C412yes—
180C42×C11C2×D412yes—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—44no—
183(C2×D11)⋊C4—82no—
184(C2×D11)⋊C4C22⋊C418yes—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22⋊C414yes—
189C4⋊Dic11C2×D412yescomplemented
190C4×Dic11—44no—
191C4×Dic11—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C2×D412yescomplemented
198#4313—48no—
199C2×D42—111no—
200C2×#436—111no—
201C2×#418—112no—
202#2354—111no—
203#1982—111no—
204#1957—111no—
205#1895—112no—
206#1875—112no—
207#1802D1111yescharacteristic, complemented
208#1786—112no—
209C4×#102—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—416no—
226C22×D11—416no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—88no—
234C22×D11—88no—
235C22×D11—88no—
236C22×D11—88no—
237C22×D11—88no—
238C22×D11C2×C22⋊C414yes—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11C4×D414yes—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—48no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11AGL(1,ℤ/8)12yes—
255C2×C4×C11AGL(1,ℤ/8)12yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C22⋊D11—416no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11C2×C22⋊C414yes—
272D44—24no—
273D44—24no—
274D44—28no—
275D44—416no—
276D44—42no—
277D44—42no—
278D44—48no—
279D44—84no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—24no—
284C8×C11—42no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C23×D4—112no—
288C23×D4—221no—
289C22×M16—112no—
290D42—118no—
291D42—224no—
292C2×#127—111no—
293C2×#121—112no—
294C2×#121—221no—
295C2×#120—222no—
296C2×C4×D4—111no—
297C2×C4×D4C2×D1111yescharacteristic
298C2×#117—112no—
299#436—224no—
300C2×C4⋊C8C2×D1111yescharacteristic, complemented
301#418—228no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—112no—
305C2×#102—112no—
306C2×#102—112no—
307C2×#102—112no—
308C2×#102C2×D1112yes—
309C2×C22⋊C8—112no—
310C2×C4×C8—111no—
311#390—221no—
312#388—222no—
313#384C2×D1111yescharacteristic, complemented
314#380—112no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—221no—
317#340—111no—
318#340—111no—
319#340C2×D1112yescomplemented
320C22×C11—24no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11C22×C22⋊C411yescharacteristic
328C22×C11D4211yescharacteristic
329C22×C11#54611yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C11#57611yescharacteristic
333C22×C11#57711yescharacteristic
334C2×D11—24no—
335C2×D11—24no—
336C2×D11—24no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—832no—
345C2×D11—82no—
346C2×D11—82no—
347C2×D11—82no—
348C2×D11—82no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—82no—
352C4×C11#41814yescomplemented
353C4×C11C2×C4×D411yescharacteristic
354C4×C11#51811yescharacteristic
355C4×C11D4211yescharacteristic
356C4×C11#54611yescharacteristic
357Dic11—24no—
358Dic11—42no—
359Dic11—81no—
360C25—222no—
361C22×D4—118no—
362C22×D4—111no—
363C22×D4—112no—
364C22×D4—228no—
365C22×D4—222no—
366C22×D4—224no—
367C22×D4—222no—
368C22×D4—224no—
369C22×D4—224no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—444no—
373C22×D4—444no—
374C22×D4—442no—
375C22×D4—442no—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4—112no—
379C2×M16—224no—
380C2×M16—224no—
381C2×M16—442no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1112yes—
385#127—114no—
386#127—222no—
387#121—118no—
388#121—224no—
389#121—228no—
390#120—2216no—
391C4×D4—22no—
392C4×D4—114no—
393C4×D4—114no—
394C4×D4C4×D1114yes—
395#117—224no—
396#117—442no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—112no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C42—222no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412C4⋊C8—22no—
413#102—24no—
414#102—114no—
415#102—224no—
416#102—224no—
417#102—222no—
418#102—442no—
419#102—442no—
420C22⋊C8—224no—
421C4×C8—222no—
422#95—222no—
423#95—221no—
424C2×C11—44no—
425C2×C11D4×C22⋊C411yescharacteristic
426C2×C11C2×#41811yescharacteristic
427C2×C11#289711yescharacteristic
428C2×C11#327211yescharacteristic
429C2×C11#327411yescharacteristic
430C2×C11#332411yescharacteristic
431C2×C11#332511yescharacteristic
432D11—44no—
433D11—84no—
434C24—21no—
435C24—112no—
436C24—228no—
437C24—222no—
438C24—444no—
439C24—444no—
440C24—444no—
441C24—444no—
442C24—882no—
443C24—882no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—114no—
448C2×D4—114no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—2216no—
452C2×D4—224no—
453C2×D4—224no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C2×D4—4432no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4—448no—
465C2×D4—448no—
466C2×D4—448no—
467C2×D4—444no—
468C2×D4—444no—
469C2×D4—442no—
470C2×D4—442no—
471C2×D4—881no—
472C2×D4—881no—
473C2×D4C2×C4×D1112yes—
474C2×D4D4×D1112yes—
475C2×D4#434312yes—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—112no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493M16—448no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—112no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—114no—
509C4⋊C4—112no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4C2×C4×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—118no—
516C22⋊C4—228no—
517C22⋊C4—444no—
518C22⋊C4—882no—
519C42—444no—
520C42—442no—
521C42C2×C4×D1112yes—
522C42D4×D1112yes—
523C11#2242811yescharacteristic, complemented, Sylow
524C23—22no—
525C23—22no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—114no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—222no—
538C23—224no—
539C23—4416no—
540C23—4416no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—888no—
548C23—888no—
549C23—888no—
550C23—888no—
551C23—888no—
552C23C2×D4×D1111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—224no—
557D4—224no—
558D4—228no—
559D4—4416no—
560D4—4416no—
561D4—442no—
562D4—448no—
563D4—442no—
564D4—884no—
565D4#6694614yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—48no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—114no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4C22⋊C4×D1112yes—
589C2×C4C22⋊C4×D1112yes—
590C2×C4#6696412yes—
591C2×C4#6696712yes—
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4C2×D4×D1111yescharacteristic
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704211yescharacteristic
597C2×C4#6704211yescharacteristic
598C8—42no—
599C8—222no—
600C8—441no—
601C22—24no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—224no—
609C22—224no—
610C22—224no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—8832no—
619C22—882no—
620C22—882no—
621C22—882no—
622C22—882no—
623C22C2×C22⋊C4×D1111yescharacteristic
624C22#1062314011yescharacteristic
625C22#1062316111yescharacteristic
626C22C2×#6696411yescharacteristic
627C22C2×#6696711yescharacteristic
628C22#1062330511yescharacteristic
629C22#1062330911yescharacteristic
630C4—22no—
631C4—42no—
632C4—82no—
633C4—224no—
634C4—442no—
635C4—881no—
636C4#1062238314yescomplemented
637C4C2×#6694611yescharacteristic
638C4#1062305211yescharacteristic
639C4#1062314011yescharacteristic
640C4#1062316111yescharacteristic
641C2—44no—
642C2—444no—
643C2—884no—
644C2#1307143611yescharacteristic
645C2C2×#1062238311yescharacteristic
646C2#1307714011yescharacteristic
647C2#1308021911yescharacteristic
648C2#1308023911yescharacteristic
649C2#1308084411yescharacteristic
650C2#1308085511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#22428
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622383C2semidirect
4. #13071567C2semidirect
5. #13069542C2semidirect
6. #13069421C2semidirect
7. #13069053C2semidirect
8. #13068937C2semidirect
9. #13068545C2semidirect
10. C4×#66896C2semidirect
11. C11×#1802C2semidirect
16. C22×#4313C22semidirect
18. D4×D44C4semidirect
20. C2×#66945C22semidirect
24. C2×C11×C4⋊C8C22semidirect
26. C11×#384C22semidirect
29. C2×#66885C22semidirect
30. C2×#66885C22semidirect
31. C2×(C2×D11)⋊C8C22semidirect
34. #10622600C22semidirect
36. C2×#66873C22semidirect
37. C2×#66873C22semidirect
38. C4×C4⋊Dic11C22semidirect
39. C2×C4×C11⋊C8C22semidirect
42. C11×#340C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
100. #66896D4semidirect
189. C4⋊Dic11C2×D4semidirect
197. C2×C11⋊C8C2×D4semidirect
207. #1802D11semidirect
300. C2×C4⋊C8C2×D11semidirect
313. #384C2×D11semidirect
319. #340C2×D11semidirect
352. C4×C11#418semidirect
523. C11#22428semidirect
636. C4#10622383semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D442
C2×#106224512
C2×#106223832
#130715672
#130695422
#130694212
#130690532
#130689372
#130685452
C4×#668962
C11×#18022
#2242811