Finite Group Databasebeta

← #14769202

Subgroups — #14769202

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic
3C2×D11×#103C212yesmaximal, complemented
4#13071516C211yesmaximal, characteristic
5#13069538C211yesmaximal, characteristic, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13069038C212yesmaximal, complemented
8#13068922C212yesmaximal, complemented
9#13068549C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×C8×D11C2212yes—
15Q8×D44—24no—
16Q8×D44C418yescomplemented
17C2×#66950—22no—
18C2×#66950C2212yes—
19C2×#66946—21no—
20C2×C4⋊C4×D11C2212yes—
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922—21no—
24C2×#66922C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33#10622602—22no—
34#10622600C2212yes—
35#10622586—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622447—24no—
41D11×#103—28no—
42C11×#340C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—42no—
50C2×Q8×D11—42no—
51C2×Q8×D11C2×C418yescomplemented
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11C2312yes—
56C22×Dic22—22no—
57C22×Dic22C2312yes—
58C22×C8×C11C2312yes—
59C4×Q8×C11—22no—
60C4×Q8×C11C2×C414yescomplemented
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4D412yes—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—42no—
84#66950—24no—
85#66950—216no—
86#66950C2×C418yescomplemented
87#66946—44no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—42no—
90C4×D44—28no—
91C4×D44C2×C414yes—
92C4×D44D414yes—
93#66922—22no—
94#66922—28no—
95#66922C2×C414yescomplemented
96C11×C4⋊C8—22no—
97C11×#103—24no—
98#66899—22no—
99#66899D414yescomplemented
100C11⋊#95—21no—
101C11⋊#95—22no—
102(C2×D11)⋊C8—24no—
103#66880—24no—
104#66880—42no—
105#66874—24no—
106#66874—42no—
107C4×C11⋊C8—22no—
108D4×#103—111nomaximal, Sylow
109C23×D11C2×D412yes—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11C2×D412yes—
126Q8×D11—216no—
127Q8×D11—48no—
128Q8×D11—48no—
129Q8×D11—48no—
130C2×D44C22⋊C414yes—
131C2×D44SD1614yes—
132C2×D44Q1614yes—
133C2×C4×D11—28no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—44no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11—82no—
143C2×C4×D11C22×C414yes—
144C2×C4×D11C2×D414yes—
145C2×Dic22—28no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—44no—
152C2×Dic22—44no—
153C2×Dic22C22×C414yes—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4C22×C412yes—
164C42×C11—24no—
165C42×C11C22×C412yes—
166C42×C11C2×D412yes—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4C22⋊C418yes—
170C4⋊Dic11—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C22⋊C414yes—
177C4⋊Dic11C2×D412yes—
178Dic11⋊C4—44no—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8C2×D412yes—
186C8×D11—48no—
187C2×D4×Q8—111no—
188C2×C8×D4—111no—
189C22×#103—112no—
190D4×C4⋊C4—111no—
191#1981—111no—
192#1956—111no—
193#1892—112no—
194#1872—112no—
195#1803D1111yescharacteristic, complemented
196#1787—112no—
197C4×#103—111no—
198C23×C11C22×D411yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11C2×C22⋊C414yes—
204C22×D11C2×SD1614yes—
205C22×D11C2×Q1614yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11C4×D414yescomplemented
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C2×SD1612yes—
224C2×C4×C11C2×Q1612yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11C2×C22⋊C414yes—
243D44#103116yescomplemented
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—416no—
249C4×D11—88no—
250Dic22—24no—
251Dic22—24no—
252Dic22—416no—
253Dic22—42no—
254Dic22—42no—
255C8×C11—42no—
256C11⋊C8—22no—
257C11⋊C8—41no—
258C23×Q8—112no—
259C23×C8—112no—
260D4×Q8—118no—
261D4×Q8—224no—
262C2×C4⋊Q8—111no—
263C2×C4⋊Q8—221no—
264C2×C22⋊Q8—112no—
265C2×C22⋊Q8—222no—
266C2×C4×Q8C2×D1111yescharacteristic
267C2×C4×D4—111no—
268C2×C4×D4—221no—
269C2×C4×D4—221no—
270C22×C4⋊C4—112no—
271C8×D4—224no—
272C2×C4⋊C8C2×D1111yescharacteristic
273C2×#103—111no—
274C2×#103—111no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103—112no—
279C2×#103—228no—
280C2×#103C2×D1112yes—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#389—221no—
284#385—222no—
285#384C2×D1111yescharacteristic
286#380—112no—
287C4×C4⋊C4—111no—
288#340—111no—
289#340—111no—
290#340C2×D1112yes—
291C22×C11C22×C22⋊C411yescharacteristic
292C22×C11D4211yescharacteristic
293C22×C11#54611yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C22×Q1611yescharacteristic
296C22×C11#57711yescharacteristic
297C22×C11#57811yescharacteristic
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—24no—
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11C2×#10318yescomplemented
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—82no—
309C4×C11C2×#10314yescomplemented
310C4×C11C2×C4×D411yescharacteristic
311C4×C11#51811yescharacteristic
312C4×C11D4211yescharacteristic
313C4×C11#54611yescharacteristic
314Dic11—24no—
315Dic11—44no—
316Dic11—42no—
317Dic11—81no—
318C22×Q8—118no—
319C22×Q8—112no—
320C22×Q8—222no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×Q8—224no—
324C22×Q8—442no—
325C22×Q8—442no—
326C22×Q8C22×D1111yescharacteristic
327C22×D4—111no—
328C23×C4—112no—
329C23×C4—222no—
330C23×C4—222no—
331C22×C8—111no—
332C22×C8—111no—
333C22×C8—224no—
334C22×C8—224no—
335C22×C8—442no—
336C22×C8C22×D1112yes—
337C4⋊Q8—114no—
338C4⋊Q8—228no—
339C4⋊Q8—222no—
340C22⋊Q8—118no—
341C22⋊Q8—2216no—
342C22⋊Q8—224no—
343C4×Q8—22no—
344C4×Q8C4×D1114yescomplemented
345C4×D4—114no—
346C4×D4—114no—
347C4×D4—228no—
348C4×D4—444no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—442no—
361C2×C4⋊C4C22×D1112yes—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—112no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C42—21no—
367C2×C42—221no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—22no—
370#103—24no—
371#103—114no—
372#103—224no—
373#103—224no—
374#103—222no—
375#103—442no—
376#103—442no—
377C22⋊C8—224no—
378C4×C8—222no—
379#95—222no—
380#95—221no—
381C2×C11D4×C22⋊C411yescharacteristic
382C2×C11C22×#10311yescharacteristic
383C2×C11#289811yescharacteristic
384C2×C11D4×SD1611yescharacteristic
385C2×C11D4×Q1611yescharacteristic
386C2×C11#329811yescharacteristic
387C2×C11#329911yescharacteristic
388D11—28no—
389C24—112no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—114no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—2216no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—444no—
402C2×Q8—444no—
403C2×Q8—448no—
404C2×Q8—448no—
405C2×Q8—448no—
406C2×Q8C2×C4×D1112yes—
407C2×Q8D4×D1112yes—
408C2×Q8#434312yes—
409C2×D4—114no—
410C2×D4—114no—
411C2×D4—114no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—228no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4—444no—
429C22×C4—444no—
430C22×C4—882no—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—112no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—448no—
444C4⋊C4—24no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4—81no—
450C4⋊C4—114no—
451C4⋊C4—112no—
452C4⋊C4—228no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—444no—
459C4⋊C4C2×C4×D1112yes—
460C22⋊C4—118no—
461C22⋊C4—228no—
462C22⋊C4—444no—
463C42—24no—
464C42—442no—
465C42C2×C4×D1112yes—
466C42D4×D1112yes—
467C11D4×#10311yescharacteristic, complemented, Sylow
468C23—114no—
469C23—114no—
470C23—114no—
471C23—222no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23C2×D4×D1111yescharacteristic
476Q8—22no—
477Q8—22no—
478Q8—22no—
479Q8—224no—
480Q8—224no—
481Q8—4416no—
482Q8—442no—
483Q8—442no—
484Q8#6694614yescomplemented
485D4—1116no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—114no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—4416no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—888no—
515C2×C4C22⋊C4×D1112yes—
516C2×C4C22⋊C4×D1112yes—
517C2×C4SD16×D1112yes—
518C2×C4Q16×D1112yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×#434311yescharacteristic
523C2×C4#6704211yescharacteristic
524C2×C4#6704211yescharacteristic
525C8—42no—
526C8—222no—
527C8—441no—
528C22—118no—
529C22—224no—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—224no—
534C22—224no—
535C22C2×C22⋊C4×D1111yescharacteristic
536C22#1062314011yescharacteristic
537C22#1062316111yescharacteristic
538C22C2×SD16×D1111yescharacteristic
539C22C2×Q16×D1111yescharacteristic
540C22#1062330611yescharacteristic
541C22#1062331011yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—82no—
546C4—224no—
547C4—444no—
548C4—442no—
549C4—881no—
550C4D11×#10314yescomplemented
551C4C2×#6694611yescharacteristic
552C4#1062305211yescharacteristic
553C4#1062314011yescharacteristic
554C4#1062316111yescharacteristic
555C2—228no—
556C2#1307143611yescharacteristic
557C2C2×D11×#10311yescharacteristic
558C2#1307714711yescharacteristic
559C2#1308030711yescharacteristic
560C2#1308036311yescharacteristic
561C2#1308047811yescharacteristic
562C2#1308048911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11D4×#103
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. C2×D11×#103C2semidirect
5. #13069538C2semidirect
6. #13069417C2semidirect
7. #13069038C2semidirect
8. #13068922C2semidirect
9. #13068549C2semidirect
10. C4×#66899C2semidirect
11. C11×#1803C2semidirect
16. Q8×D44C4semidirect
51. C2×Q8×D11C2×C4semidirect
60. C4×Q8×C11C2×C4semidirect
86. #66950C2×C4semidirect
95. #66922C2×C4semidirect
99. #66899D4semidirect
195. #1803D11semidirect
209. Q8×C11C4×D4semidirect
243. D44#103semidirect
304. C2×D11C2×#103semidirect
309. C4×C11C2×#103semidirect
344. C4×Q8C4×D11semidirect
467. C11D4×#103semidirect
484. Q8#66946semidirect
550. C4D11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
C2×#106224472
C2×D11×#1032
#130715162
#130695382
#130694172
#130690382
#130689222
#130685492
C4×#668992
C11×#18032
D4×#10311