Finite Group Databasebeta

← #14753822

Subgroups — #14753822

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13068701C212yesmaximal, complemented
5#13068625C212yesmaximal, complemented
6#13068624C212yesmaximal, complemented
7#13068545C212yesmaximal
8#13068444C211yesmaximal, characteristic, complemented
9#13068442C211yesmaximal, characteristic, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C11×#1762C211yesmaximal, characteristic, complemented
12C22×D4×D11C2211yescharacteristic
13C23×C4×D11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11C2211yescharacteristic
16C2×C4×C22⋊D11—21no—
17C4×D4×D11—24no—
18C4×D4×D11C418yescomplemented
19C2×#66946C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C22⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#97C2211yescharacteristic, complemented
27C4×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×#66896C2212yes—
29C2×#66885C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×Dic11⋊C8C2212yescomplemented
32#10622600C2212yes—
33#10622590C2212yescomplemented
34C2×#66873C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic, complemented
37#10622545—21no—
38C2×#66867C2211yescharacteristic, complemented
39#10622318—24no—
40#10622277—21no—
41#10622264—21no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×C22⋊D11—21no—
50C23×Dic11—21no—
51C2×D4×D11—24no—
52C2×D4×D11—24no—
53C2×D4×D11—22no—
54C2×D4×D11C2×C414yes—
55C22×D44C2311yescharacteristic
56C22×C4×D11—21no—
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—28no—
60C22×C4×D11—48no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2312yes—
65C4×D4×C11—22no—
66C4×D4×C11C2×C414yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73D4×Dic11—22no—
74D4×Dic11C2×C414yes—
75C4×C22⋊D11—28no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87#66946—22no—
88#66946C2×C414yes—
89C4⋊C4×D11—22no—
90C4⋊C4×D11C2×C414yes—
91(C22⋊D11)⋊C4—28no—
92C22⋊C4×D11—28no—
93C4×D44—22no—
94C4×D44C2×C414yes—
95C42×D11C2×C414yes—
96C42×D11D414yes—
97C11×#102—24no—
98C11×#97—22no—
99C11×#95—21no—
100#66896—24no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105#66885—24no—
106(C2×D11)⋊C8—24no—
107Dic11⋊C8—24no—
108#66873—24no—
109#66867—22no—
110#20739—111nomaximal, Sylow
111C24×C11—21no—
112C23×D11—28no—
113C23×D11—21no—
114C23×D11—24no—
115C23×D11—42no—
116C23×D11—42no—
117C23×D11—44no—
118C23×D11C2×D411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11C22×C412yes—
122C2×D4×C11#4114yes—
123C22×C4×C11—21no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—28no—
131C2×C22⋊D11—24no—
132C22×Dic11—24no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—44no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139D4×D11—216no—
140D4×D11—28no—
141D4×D11—28no—
142C2×D44—21no—
143C2×D44—22no—
144C2×D44C22×C412yes—
145C2×D44#4114yes—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—44no—
155C2×C4×D11—432no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11C22⋊C414yes—
159C2×C4×D11C22⋊C414yes—
160C2×C4×D11C22×C412yes—
161C2×C4×D11C2×D412yes—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C22×C412yes—
169C11×C22⋊C4—24no—
170C42×C11—42no—
171C42×C11C22×C412yes—
172C42×C11C2×D412yes—
173C22⋊Dic11—24no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—44no—
177C4⋊Dic11—21no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11C22×C412yes—
181Dic11⋊C4—24no—
182C4×Dic11—42no—
183C4×Dic11C22⋊C414yes—
184C4×Dic11C22⋊C414yes—
185C4×Dic11C22×C412yes—
186C4×Dic11C2×D412yes—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C22×C4×D4—111no—
191C2×#432—111no—
192#2283—111no—
193#1823—112no—
194#1804—112no—
195#1804—112no—
196#1786—112no—
197#1762—111no—
198#1762—111no—
199#1762—111no—
200#1762D1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—42no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—216no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—416no—
214C22×D11—416no—
215C22×D11—48no—
216C22×D11—42no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—48no—
220C22×D11C2×C22⋊C412yes—
221C22×D11AGL(1,ℤ/8)14yes—
222D4×C11—22no—
223D4×C11—24no—
224D4×C11#11714yes—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—48no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4112yes—
239C2×C4×C11C2×#4112yes—
240C22⋊D11—216no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—48no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11C2×C22⋊C412yes—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254D44—22no—
255D44—24no—
256D44#11714yes—
257C4×D11—28no—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—24no—
261C4×D11—44no—
262C4×D11—48no—
263C4×D11—48no—
264C4×D11—48no—
265C8×C11—42no—
266C11⋊C8—42no—
267C23×D4—111no—
268C24×C4—221no—
269C2×C4×D4—111no—
270C2×C4×D4—118no—
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4—221no—
274C2×C4×D4—224no—
275C2×C4×D4—221no—
276C2×C4×D4C2×D1111yescharacteristic
277C22×C4⋊C4—111no—
278C22×C22⋊C4—221no—
279C22×C42—111no—
280#432—224no—
281C2×C4⋊C8—112no—
282C2×#102—112no—
283C2×#102—112no—
284C2×#102—112no—
285C2×#102C2×D1112yes—
286C2×C22⋊C8—112no—
287C2×#97—111no—
288C2×#97C2×D1111yescharacteristic, complemented
289#383—221no—
290#382—112no—
291#381—221no—
292#380—112no—
293C4×C4⋊C4—111no—
294C4×C4⋊C4C2×D1111yescharacteristic, complemented
295C4×C22⋊C4—221no—
296#376—221no—
297#340—112no—
298#340—112no—
299#340—112no—
300#340C2×D1112yescomplemented
301C22×C11—24no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11C22×C22⋊C411yescharacteristic
307C22×C11#52512yes—
308C22×C11C2×AGL(1,ℤ/8)12yes—
309C22×C11#57511yescharacteristic
310C22×C11#57511yescharacteristic
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—24no—
316C2×D11—432no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11#41814yes—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11—82no—
326C4×C11C2×#11711yescharacteristic
327C4×C11C2×#11711yescharacteristic
328C4×C11#52512yes—
329Dic11—22no—
330Dic11—22no—
331Dic11—22no—
332Dic11—42no—
333Dic11—82no—
334C25—221no—
335C22×D4—114no—
336C22×D4—111no—
337C22×D4—222no—
338C22×D4—221no—
339C22×D4—224no—
340C22×D4—224no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C23×C4—228no—
348C23×C4—221no—
349C23×C4—221no—
350C23×C4—221no—
351C23×C4—448no—
352C22×C8—112no—
353C22×C8C22×D1112yes—
354C4×D4—22no—
355C4×D4—114no—
356C4×D4—114no—
357C4×D4—114no—
358C4×D4—228no—
359C4×D4—222no—
360C4×D4—228no—
361C4×D4—222no—
362C4×D4—222no—
363C4×D4C4×D1114yes—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C22×D1112yes—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—222no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—224no—
386#102—24no—
387#102—224no—
388#102—224no—
389#102—224no—
390C22⋊C8—224no—
391#97—22no—
392#97—222no—
393#95—21no—
394#95—222no—
395#95—222no—
396#95—222no—
397#95—221no—
398C2×C11—44no—
399C2×C11#228011yescharacteristic
400C2×C11C2×#41811yescharacteristic
401C2×C11#289611yescharacteristic
402C2×C11#311412yes—
403C2×C11#311412yes—
404D11—24no—
405D11—44no—
406C24—21no—
407C24—111no—
408C24—224no—
409C24—228no—
410C24—221no—
411C24—444no—
412C24—442no—
413C24—442no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—112no—
417C2×D4—114no—
418C2×D4—224no—
419C2×D4—228no—
420C2×D4—2216no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—222no—
424C2×D4—221no—
425C2×D4C2×C4×D1112yes—
426C2×D4#433914yes—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—44no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—114no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—444no—
450C22×C4—4432no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—221no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4C2×C4×D1112yes—
472C22⋊C4—24no—
473C22⋊C4—224no—
474C22⋊C4—224no—
475C22⋊C4—224no—
476C22⋊C4—444no—
477C42—42no—
478C42—114no—
479C42—114no—
480C42—112no—
481C42—112no—
482C42—442no—
483C42C2×C4×D1112yes—
484C42D4×D1112yes—
485C11#2073911yescharacteristic, complemented, Sylow
486C23—22no—
487C23—24no—
488C23—42no—
489C23—41no—
490C23—41no—
491C23—112no—
492C23—114no—
493C23—2216no—
494C23—221no—
495C23—221no—
496C23—222no—
497C23—222no—
498C23—224no—
499C23—448no—
500C23—448no—
501C23—4416no—
502C23—4416no—
503C23—442no—
504C23—441no—
505C23—441no—
506C23C2×D4×D1111yescharacteristic
507D4—22no—
508D4—24no—
509D4—114no—
510D4—2216no—
511D4—222no—
512D4—224no—
513D4#6692514yes—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—228no—
527C2×C4—222no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—444no—
536C2×C4—448no—
537C2×C4—448no—
538C2×C4—448no—
539C2×C4—448no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4C22⋊C4×D1112yes—
545C2×C4C22⋊C4×D1112yes—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C2×#433912yes—
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4#41×D1112yes—
550C8—42no—
551C8—442no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—44no—
556C22—44no—
557C22—114no—
558C22—222no—
559C22—222no—
560C22—224no—
561C22—224no—
562C22—224no—
563C22—4432no—
564C22—442no—
565C22—442no—
566C22—444no—
567C22—444no—
568C22C2×C22⋊C4×D1111yescharacteristic
569C22#1062307812yes—
570C22D11×AGL(1,ℤ/8)12yes—
571C22#1062330411yescharacteristic
572C22#1062330811yescharacteristic
573C4—22no—
574C4—22no—
575C4—42no—
576C4—82no—
577C4—222no—
578C4—222no—
579C4—222no—
580C4—442no—
581C4—882no—
582C4C2×#6692511yescharacteristic
583C4D11×#11711yescharacteristic
584C4#1062307812yes—
585C2—44no—
586C2—224no—
587C2—444no—
588C2#1307099711yescharacteristic
589C2D11×#41811yescharacteristic
590C2#1307713211yescharacteristic
591C2#1307875212yes—
592C2#1307875812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#20739
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#10622318C2semidirect
3. #13071012C2semidirect
4. #13068701C2semidirect
5. #13068625C2semidirect
6. #13068624C2semidirect
8. #13068444C2semidirect
9. #13068442C2semidirect
10. #13068441C2semidirect
11. C11×#1762C2semidirect
18. C4×D4×D11C4semidirect
26. C2×C11×#97C22semidirect
27. C4×C11×C4⋊C4C22semidirect
31. C2×Dic11⋊C8C22semidirect
33. #10622590C22semidirect
36. C4×C4⋊Dic11C22semidirect
38. C2×#66867C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
200. #1762D11semidirect
288. C2×#97C2×D11semidirect
294. C4×C4⋊C4C2×D11semidirect
300. #340C2×D11semidirect
485. C11#20739semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C2×#106223182
#130710122
#130687012
#130686252
#130686242
#130685452
#130684442
#130684422
#130684412
C11×#17622
#2073911