Finite Group Databasebeta

← #14764944

Subgroups — #14764944

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622834C211yesmaximal, characteristic
3#13069472C212yesmaximal, complemented
4#13069301C212yesmaximal, complemented
5#13069245C212yesmaximal, complemented
6#13068973C212yesmaximal, complemented
7#13068924C211yesmaximal, characteristic, complemented
8#13068811C211yesmaximal, characteristic, complemented
9#13068547C211yesmaximal, characteristic
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#450C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C22⋊Dic11—21no—
16C22×C22⋊Dic11—21no—
17C2×Q8×Dic11C2211yescharacteristic, complemented
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C11×#450C418yescomplemented
21C2×C11×#102C2212yes—
22C2×C11×C22⋊C8C2211yescharacteristic
23#10622843C2211yescharacteristic, complemented
24C2×#66899C2212yescomplemented
25#10622834—21no—
26#10622834—21no—
27#10622834C2212yes—
28#10622834C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66881C2212yescomplemented
34C2×C8×Dic11C2212yescomplemented
35#10622598C2211yescharacteristic, complemented
36#10622594—21no—
37C4⋊C4×Dic11—21no—
38C4⋊C4×Dic11C2211yescharacteristic, complemented
39#10622563—21no—
40C22⋊C4×Dic11—21no—
41#10622189C2212yescomplemented
42#10622188C2212yescomplemented
43#10622167C2212yescomplemented
44C25×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—42no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C23×Dic11D411yescharacteristic
55C23×Dic11D411yescharacteristic
56C2×C11×SD16—42no—
57C2×C11×SD16—42no—
58C2×C11×SD16C2×C418yescomplemented
59C22×C8×C11C2312yes—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8C2×C414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—44no—
71C2×C22⋊Dic11—44no—
72Q8×Dic11—42no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—42no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C11×#102C2×C418yescomplemented
89C11×C22⋊C8C2×C414yes—
90#66899—42no—
91#66896—42no—
92#66896—42no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C22⋊(C11⋊C8)—22no—
99#66881—42no—
100C8×Dic11—42no—
101#22043—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11—42no—
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—48no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—48no—
125C2×D4×C11C22×C414yes—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—41no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11SD1614yescomplemented
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C11×SD16—48no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11C22×C414yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C22⋊C4—24no—
158C22⋊Dic11—44no—
159C22⋊Dic11—44no—
160C22⋊Dic11—44no—
161C22⋊Dic11—44no—
162C22⋊Dic11—42no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—42no—
168C4⋊Dic11—42no—
169C4⋊Dic11—42no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C4×Dic11—41no—
173C4×Dic11—41no—
174C4×Dic11—42no—
175C4×Dic11—42no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×#450D1111yescharacteristic
180C4×C22⋊Q8—111no—
181C2×#390—111no—
182#1968—112no—
183#1934—112no—
184#1926—112no—
185#1880—112no—
186#1872—111no—
187#1853—111no—
188#1786—111no—
189C4×C22⋊C8—111no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—24no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—48no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11C4×D412yes—
209C23×C11C2×SD1612yes—
210C23×C11#13512yes—
211C23×C11C22×D411yescharacteristic
212Q8×C11—24no—
213Q8×C11—42no—
214D4×C11—24no—
215D4×C11—24no—
216D4×C11—48no—
217D4×C11—42no—
218D4×C11—42no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11C4×D412yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)12yes—
233C2×C4×C11H(5,𝔽2)12yes—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—44no—
244C2×Dic11—44no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—42no—
253C2×Dic11—41no—
254C2×Dic11—84no—
255C2×Dic11C2×SD1612yes—
256C2×Dic11C2×SD1612yes—
257C2×Dic11AGL(1,ℤ/8)12yes—
258C8×C11—24no—
259C11⋊C8—42no—
260C23×D4C2×D1111yescharacteristic
261C22×SD16C2×D1112yes—
262C2×C22⋊Q8C2×D1111yescharacteristic
263C2×C4×Q8—111no—
264C22×C4⋊C4—111no—
265C22×C22⋊C4—221no—
266C22×C22⋊C4—221no—
267C22×C42—111no—
268#450Dic1118yescomplemented
269C2×#106—112no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102C2×D1112yes—
274C2×C22⋊C8—111no—
275C2×C22⋊C8C2×D1111yescharacteristic
276C2×C4×C8—112no—
277#391—111no—
278#390—112no—
279#390—112no—
280#390—221no—
281#390—221no—
282#389—111no—
283#387—221no—
284#385—221no—
285#380—111no—
286C4×C4⋊C4—111no—
287C4×C4⋊C4—221no—
288C4×C22⋊C4—221no—
289#340—112no—
290#340—112no—
291#336—112no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—816no—
302C22×C11—82no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11C4×SD1614yes—
307C22×C11C2×C4×D411yescharacteristic
308C22×C11#53411yescharacteristic
309C22×C11#53511yescharacteristic
310C22×C11C22×SD1611yescharacteristic
311C22×C11C2×#13511yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C11#57511yescharacteristic
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11#51812yes—
318C4×C11#53812yes—
319Dic11—22no—
320Dic11—22no—
321Dic11—22no—
322Dic11—41no—
323Dic11—81no—
324Dic11—82no—
325Dic11—81no—
326C25—21no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4C2×Dic1114yes—
333C22×D4C22×D1112yes—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—221no—
337C23×C4C22×D1111yescharacteristic
338C2×SD16—42no—
339C2×SD16—42no—
340C2×SD16C2×Dic1118yescomplemented
341C22×C8—112no—
342C22×C8C22×D1112yes—
343C22⋊Q8—22no—
344C22⋊Q8C2×Dic1114yes—
345C4×Q8—442no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—442no—
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—444no—
362C2×C22⋊C4—444no—
363C2×C42—111no—
364C2×C42—111no—
365C2×C42—111no—
366C2×C42—111no—
367C2×C42—221no—
368C2×C42—221no—
369C2×C42—442no—
370#106—442no—
371#103—442no—
372#102—442no—
373#102—442no—
374#102C2×Dic1118yescomplemented
375C22⋊C8—222no—
376C22⋊C8C2×Dic1114yes—
377C4×C8—442no—
378#95—221no—
379#95—221no—
380#95—221no—
381#95—221no—
382#95—221no—
383C2×C11—24no—
384C2×C11—84no—
385C2×C11#232111yescharacteristic
386C2×C11C2×C4×SD1611yescharacteristic
387C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
388C2×C11#318711yescharacteristic
389C2×C11#318811yescharacteristic
390C2×C11#320811yescharacteristic
391C2×C11#321111yescharacteristic
392C24—24no—
393C24—22no—
394C24—42no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—42no—
400C24D4×D1111yescharacteristic
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8C22×Dic1112yes—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—48no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—48no—
415C2×D4C22×Dic1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—114no—
424C22×C4—111no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—441no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4D4×D1111yescharacteristic
437C22×C4#434112yes—
438C22×C4C22×Dic1112yes—
439C22×C4C23×D1111yescharacteristic
440SD16—48no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8—222no—
446C2×C8C22×Dic1114yes—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4—442no—
454C4⋊C4—442no—
455C4⋊C4—442no—
456C4⋊C4C22×Dic1112yes—
457C22⋊C4—24no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—444no—
461C22⋊C4—444no—
462C22⋊C4—442no—
463C42—222no—
464C42—222no—
465C42—441no—
466C42—441no—
467C42—442no—
468C42—442no—
469C11#2204311yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—24no—
475C23—48no—
476C23—48no—
477C23—48no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23—84no—
488C23SD16×D1112yes—
489C23#6696912yes—
490C23D4×Dic1112yes—
491C23C2×D4×D1111yescharacteristic
492Q8—24no—
493Q8—42no—
494D4—24no—
495D4—24no—
496D4—48no—
497D4—42no—
498D4—42no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—112no—
510C2×C4—112no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—444no—
522C2×C4—444no—
523C2×C4—442no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—442no—
531C2×C4—441no—
532C2×C4—884no—
533C2×C4D4×Dic1112yes—
534C2×C4C2×#434111yescharacteristic
535C2×C4#6703712yes—
536C2×C4#6703712yes—
537C2×C4C23×Dic1111yescharacteristic
538C8—24no—
539C8—442no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—816no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22SD16×Dic1114yes—
555C22#1062312011yescharacteristic
556C22#1062312311yescharacteristic
557C22C2×SD16×D1111yescharacteristic
558C22C2×#6696911yescharacteristic
559C22D11×AGL(1,ℤ/8)11yescharacteristic
560C22#1062330411yescharacteristic
561C22C2×D4×Dic1111yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—222no—
566C4—222no—
567C4—222no—
568C4—441no—
569C4—882no—
570C4—881no—
571C4—881no—
572C4#1062312412yes—
573C4#1062332912yes—
574C2—24no—
575C2—84no—
576C2#1307127711yescharacteristic
577C2C2×SD16×Dic1111yescharacteristic
578C2AGL(1,ℤ/8)×Dic1111yescharacteristic
579C2#1307937011yescharacteristic
580C2#1307938411yescharacteristic
581C2#1307955511yescharacteristic
582C2#1307958411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#450D11
hypocenterC11#22043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×Dic11C2semidirect
3. #13069472C2semidirect
4. #13069301C2semidirect
5. #13069245C2semidirect
6. #13068973C2semidirect
7. #13068924C2semidirect
8. #13068811C2semidirect
10. C22⋊C8×Dic11C2semidirect
17. C2×Q8×Dic11C22semidirect
20. C11×#450C4semidirect
23. #10622843C22semidirect
24. C2×#66899C22semidirect
33. C2×#66881C22semidirect
34. C2×C8×Dic11C22semidirect
35. #10622598C22semidirect
38. C4⋊C4×Dic11C22semidirect
41. #10622189C22semidirect
42. #10622188C22semidirect
43. #10622167C22semidirect
58. C2×C11×SD16C2×C4semidirect
88. C11×#102C2×C4semidirect
145. C22×Dic11SD16semidirect
268. #450Dic11semidirect
340. C2×SD16C2×Dic11semidirect
374. #102C2×Dic11semidirect
469. C11#22043semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic112
C2×#106228342
#130694722
#130693012
#130692452
#130689732
#130689242
#130688112
#130685472
C22⋊C8×Dic112
C2×C11×#4502
#2204311