Finite Group Databasebeta

← #14769182

Subgroups — #14769182

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623248C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic, complemented
3C2×D11×#102C212yesmaximal, complemented
4C4⋊C4×D44C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069041C212yesmaximal, complemented
7#13068930C212yesmaximal, complemented
8#13068617C211yesmaximal, characteristic, complemented
9#13068545C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#1982C211yesmaximal, characteristic, complemented
12C22×D4×D11—21no—
13C22×D4×D11C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×#66991—21no—
16C2×#66991C2212yes—
17C2×#66990—22no—
18C22×C8×D11C2212yescomplemented
19#10623248—24no—
20#10623248C418yescomplemented
21C2×C4⋊C4×D11C2212yescomplemented
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C11×#102C2212yescomplemented
27C2×C11×#102C2212yescomplemented
28C4×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#66896C2212yescomplemented
30C2×#66896C2212yescomplemented
31C2×#66885C2212yes—
32C2×(C2×D11)⋊C8C2212yescomplemented
33#10622600C2212yescomplemented
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36#10622548C2211yescharacteristic, complemented
37#10622541—21no—
38C2×C4×C11⋊C8C2211yescharacteristic, complemented
39#10622447—24no—
40D11×#102—28no—
41#10622281—22no—
42#10622189C2212yescomplemented
43#10622167C2211yescharacteristic, complemented
44#10622167C2211yescharacteristic, complemented
45C24×D11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C2×D4×D11—28no—
52C2×D4×D11—24no—
53C2×D4×D11—24no—
54C2×D4×D11—24no—
55C2×D4×D11—42no—
56C2×D4×D11—42no—
57C2×D4×D11—44no—
58C2×D4×D11—44no—
59C2×D4×D11C2×C418yescomplemented
60C22×D44D411yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—22no—
64C22×C4×D11C2312yes—
65C22×C8×C11C2312yes—
66C11×#127—22no—
67C11×#127C2×C414yescomplemented
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73#66991—24no—
74#66991—28no—
75#66991C2×C418yescomplemented
76#66990—216no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4D412yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—22no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C2×C8×D11—24no—
89C2×C8×D11—24no—
90C2×C8×D11—42no—
91C4⋊C4×D11—24no—
92C4⋊C4×D11—42no—
93C4×D44—22no—
94C4×D44—44no—
95C4×D44C2×C414yes—
96C4×D44C2×C414yescomplemented
97C4×D44D414yes—
98C11×C4⋊C8—22no—
99C11×#102—24no—
100C11×#102—42no—
101C11×#95—21no—
102#66896—24no—
103#66896—42no—
104C11⋊#95—22no—
105#66885—24no—
106(C2×D11)⋊C8—24no—
107#66873—22no—
108#66873D414yescomplemented
109C4×C11⋊C8—22no—
110D4×#102—111nomaximal, Sylow
111C24×C11—22no—
112C23×D11—21no—
113C23×D11—28no—
114C23×D11—44no—
115C23×D11—44no—
116C23×D11—44no—
117C23×D11—44no—
118C23×D11—82no—
119C23×D11—82no—
120C23×D11C2×D412yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—81no—
131C2×D4×C11—81no—
132C2×D4×C11C22×C414yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—28no—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—44no—
141C2×C22⋊D11—44no—
142C2×C22⋊D11—44no—
143C2×C22⋊D11—44no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11C2×D412yes—
147D4×D11—216no—
148D4×D11—48no—
149D4×D11—48no—
150D4×D11—48no—
151D4×D11—432no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22⋊C414yes—
156C2×D44D814yes—
157C2×D44SD1614yes—
158C2×D44C22×C412yes—
159C2×D44C2×D412yes—
160C2×D44#4112yes—
161C2×C4×D11—24no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—82no—
171C2×C4×D11C22×C414yes—
172C2×C4×D11C2×D414yes—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D412yescomplemented
180C42×C11—42no—
181C42×C11C22×C412yes—
182C42×C11C2×D412yes—
183C22⋊Dic11—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—44no—
186(C2×D11)⋊C4C22⋊C418yes—
187C4⋊Dic11—21no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11C22⋊C414yes—
193C4⋊Dic11C22×C412yes—
194Dic11⋊C4—44no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C2×D412yescomplemented
201C8×D11—48no—
202C2×D42—111no—
203C2×C8×D4—111no—
204C22×#102—112no—
205D4×C4⋊C4—111no—
206#1982D1111yescharacteristic, complemented
207#1957—111no—
208#1893—112no—
209#1874—112no—
210#1802—111no—
211#1786—112no—
212C4×#102—111no—
213C23×C11—24no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—416no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—416no—
234C22×D11—88no—
235C22×D11—88no—
236C22×D11—88no—
237C22×D11—88no—
238C22×D11—88no—
239C22×D11C2×C22⋊C414yes—
240C22×D11C2×D814yes—
241C22×D11C2×SD1614yes—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—48no—
247D4×C11—84no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×D812yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C22⋊D11—416no—
267C22⋊D11—416no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11C2×C22⋊C414yes—
277D44—22no—
278D44—22no—
279D44—22no—
280D44#102116yescomplemented
281D44C4×D414yescomplemented
282C4×D11—24no—
283C4×D11—24no—
284C4×D11—24no—
285C4×D11—24no—
286C4×D11—48no—
287C4×D11—88no—
288C8×C11—42no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291C23×D4—112no—
292C23×D4—221no—
293C23×C8—112no—
294D42—118no—
295D42—224no—
296C2×#127C2×D1111yescharacteristic
297C2×#121—112no—
298C2×#121—221no—
299C2×#120—222no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C22×C4⋊C4—112no—
304C8×D4—224no—
305C2×C4⋊C8C2×D1111yescharacteristic, complemented
306C2×#102—111no—
307C2×#102—112no—
308C2×#102—112no—
309C2×#102—111no—
310C2×#102—112no—
311C2×#102—228no—
312C2×#102C2×D1112yescomplemented
313C2×#102C2×D1112yescomplemented
314C2×C22⋊C8—112no—
315C2×C4×C8—111no—
316#389—221no—
317#385—222no—
318#384—111no—
319#380—112no—
320C4×C4⋊C4C2×D1111yescharacteristic, complemented
321#340—112no—
322#340—111no—
323#340—111no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11D4211yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11C22×D811yescharacteristic
335C22×C11C22×SD1611yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57711yescharacteristic
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—832no—
352C2×D11C2×#10218yescomplemented
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11C2×#10214yescomplemented
357C4×C11C2×C4×D411yescharacteristic
358C4×C11#51811yescharacteristic
359C4×C11D4211yescharacteristic
360C4×C11#54611yescharacteristic
361Dic11—24no—
362Dic11—42no—
363Dic11—82no—
364C25—222no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—118no—
368C22×D4—111no—
369C22×D4—111no—
370C22×D4—224no—
371C22×D4—222no—
372C22×D4—224no—
373C22×D4—224no—
374C22×D4—228no—
375C22×D4—222no—
376C22×D4—442no—
377C22×D4—442no—
378C22×D4—444no—
379C22×D4—444no—
380C22×D4C22×D1112yes—
381C23×C4—112no—
382C23×C4—222no—
383C23×C4—221no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—224no—
387C22×C8—224no—
388C22×C8—442no—
389C22×C8C22×D1112yes—
390#127—22no—
391#127C4×D1114yescomplemented
392#121—118no—
393#121—228no—
394#121—224no—
395#120—2216no—
396C4×D4—114no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—222no—
400C4×D4—444no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—112no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C42—21no—
416C2×C42C22×D1111yescharacteristic
417C4⋊C8—22no—
418#102—24no—
419#102—42no—
420#102—114no—
421#102—222no—
422#102—224no—
423#102—224no—
424#102—442no—
425C22⋊C8—224no—
426C4×C8—222no—
427#95—21no—
428#95—222no—
429C2×C11—84no—
430C2×C11D4×C22⋊C411yescharacteristic
431C2×C11C22×#10211yescharacteristic
432C2×C11#289711yescharacteristic
433C2×C11D4×D811yescharacteristic
434C2×C11D4×SD1611yescharacteristic
435C2×C11#329411yescharacteristic
436C2×C11#329511yescharacteristic
437D11—28no—
438D11—44no—
439C24—22no—
440C24—112no—
441C24—228no—
442C24—221no—
443C24—444no—
444C24—444no—
445C24—444no—
446C24—444no—
447C24—882no—
448C24—882no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—81no—
459C2×D4—81no—
460C2×D4—114no—
461C2×D4—114no—
462C2×D4—114no—
463C2×D4—112no—
464C2×D4—112no—
465C2×D4—112no—
466C2×D4—228no—
467C2×D4—2216no—
468C2×D4—228no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—448no—
473C2×D4—448no—
474C2×D4—448no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—4432no—
478C2×D4—444no—
479C2×D4—444no—
480C2×D4C2×C4×D1114yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—114no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—444no—
494C22×C4—444no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—882no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—112no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—448no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—114no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—444no—
520C4⋊C4—442no—
521C4⋊C4—881no—
522C4⋊C4D4×D1112yescomplemented
523C22⋊C4—118no—
524C22⋊C4—228no—
525C22⋊C4—224no—
526C22⋊C4—444no—
527C42—42no—
528C42C2×C4×D1112yes—
529C42D4×D1112yes—
530C11D4×#10211yescharacteristic, complemented, Sylow
531C23—24no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—114no—
539C23—114no—
540C23—114no—
541C23—222no—
542C23—222no—
543C23—222no—
544C23—222no—
545C23—222no—
546C23—222no—
547C23—222no—
548C23—4416no—
549C23—4416no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—888no—
555C23—888no—
556C23—888no—
557C23—888no—
558C23—888no—
559C23C2×D4×D1111yescharacteristic
560D4—24no—
561D4—24no—
562D4—42no—
563D4—48no—
564D4—42no—
565D4—84no—
566D4—114no—
567D4—1116no—
568D4—222no—
569D4—222no—
570D4—222no—
571D4—4416no—
572D4—4416no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—114no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—448no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—888no—
596C2×C4C22⋊C4×D1112yes—
597C2×C4C22⋊C4×D1112yes—
598C2×C4D8×D1112yes—
599C2×C4SD16×D1112yes—
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4#6703711yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704211yescharacteristic
606C8—42no—
607C8—222no—
608C8—441no—
609C22—44no—
610C22—44no—
611C22—44no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—118no—
617C22—224no—
618C22—224no—
619C22—224no—
620C22—224no—
621C22—224no—
622C22—224no—
623C22—224no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—8832no—
631C22C2×C22⋊C4×D1111yescharacteristic
632C22#1062314011yescharacteristic
633C22#1062314311yescharacteristic
634C22C2×D8×D1111yescharacteristic
635C22C2×SD16×D1111yescharacteristic
636C22#1062330511yescharacteristic
637C22#1062330611yescharacteristic
638C4—22no—
639C4—42no—
640C4—81no—
641C4—224no—
642C4—442no—
643C4—882no—
644C4D11×#10214yescomplemented
645C4C4×D4×D1111yescharacteristic
646C4#1062307611yescharacteristic
647C4#1062320711yescharacteristic
648C4#1062324811yescharacteristic
649C2—84no—
650C2—228no—
651C2—444no—
652C2#1307143711yescharacteristic
653C2C2×D11×#10211yescharacteristic
654C2#1307714111yescharacteristic
655C2#1308028811yescharacteristic
656C2#1308030711yescharacteristic
657C2#1308043211yescharacteristic
658C2#1308044311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1982C2
socleC23×C11C22×D4
prime radicalC2×#10623248C2
cosocleC22×C4×C11C24
hypercenter#1982D11
hypocenterC11D4×#102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#10622447C2semidirect
3. C2×D11×#102C2semidirect
4. C4⋊C4×D44C2semidirect
5. #13069423C2semidirect
6. #13069041C2semidirect
7. #13068930C2semidirect
8. #13068617C2semidirect
9. #13068545C2semidirect
10. C4×#66873C2semidirect
11. C11×#1982C2semidirect
18. C22×C8×D11C22semidirect
20. #10623248C4semidirect
21. C2×C4⋊C4×D11C22semidirect
25. C2×C11×C4⋊C8C22semidirect
26. C2×C11×#102C22semidirect
27. C2×C11×#102C22semidirect
28. C4×C11×C4⋊C4C22semidirect
29. C2×#66896C22semidirect
30. C2×#66896C22semidirect
32. C2×(C2×D11)⋊C8C22semidirect
33. #10622600C22semidirect
36. #10622548C22semidirect
38. C2×C4×C11⋊C8C22semidirect
42. #10622189C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
59. C2×D4×D11C2×C4semidirect
67. C11×#127C2×C4semidirect
75. #66991C2×C4semidirect
96. C4×D44C2×C4semidirect
108. #66873D4semidirect
179. C11×C4⋊C4C2×D4semidirect
200. C2×C11⋊C8C2×D4semidirect
206. #1982D11semidirect
280. D44#102semidirect
281. D44C4×D4semidirect
305. C2×C4⋊C8C2×D11semidirect
312. C2×#102C2×D11semidirect
313. C2×#102C2×D11semidirect
320. C4×C4⋊C4C2×D11semidirect
352. C2×D11C2×#102semidirect
356. C4×C11C2×#102semidirect
391. #127C4×D11semidirect
522. C4⋊C4D4×D11semidirect
530. C11D4×#102semidirect
644. C4D11×#102semidirect

Maximal subgroups

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

subgroupindex
C2×#106232482
C2×#106224472
C2×D11×#1022
C4⋊C4×D442
#130694232
#130690412
#130689302
#130686172
#130685452
C4×#668732
C11×#19822
D4×#10211