Finite Group Databasebeta

← #14789907

Subgroups — #14789907

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C2×#10622376C212yesmaximal, complemented
3#121×Dic11C211yesmaximal, characteristic
4#13069953C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069570C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic
8#13068811C211yesmaximal, characteristic, complemented
9#13068804C211yesmaximal, characteristic, complemented
10#13068594C211yesmaximal, characteristic, complemented
11C11×#1874C211yesmaximal, characteristic
12C2×C11×#121C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×D4×Dic11—21no—
15C2×D4×Dic11C2211yescharacteristic
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66943—21no—
21C2×#66943—21no—
22C2×#66943—28no—
23C2×#66943C2212yes—
24C2×#66943C2212yes—
25C2×C11×#102C2212yes—
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622833—21no—
29C2×#66896C2212yes—
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66881C2212yes—
33C2×Dic11⋊C8C2212yes—
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66871C2212yes—
37#10622564—21no—
38C22⋊C4×Dic11—21no—
39#10622376—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11—21no—
51C23×Dic11D411yescharacteristic
52C23×Dic11D411yescharacteristic
53C22×C8×C11C2312yes—
54C11×#121—22no—
55C11×#121Q814yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—21no—
65D4×Dic11—24no—
66D4×Dic11—44no—
67C2×C4⋊Dic11—28no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66943—28no—
87#66943—28no—
88#66943—24no—
89#66943—24no—
90#66943—24no—
91#66943D418yescomplemented
92C11×#102—24no—
93C11×C22⋊C8—22no—
94#66896—24no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C22⋊(C11⋊C8)—22no—
99#66881—24no—
100Dic11⋊C8—24no—
101#66871—24no—
102#24305—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C2×D4×C11—24no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11C2×Q812yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—24no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C2×D414yes—
149C11×C4⋊C4C2×Q812yes—
150C11×C22⋊C4—24no—
151C22⋊Dic11—42no—
152C22⋊Dic11—42no—
153C22⋊Dic11—42no—
154C22⋊Dic11—42no—
155C4⋊Dic11—24no—
156C4⋊Dic11—28no—
157C4⋊Dic11—28no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—42no—
162C4⋊Dic11C2×D414yes—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—42no—
169C4×Dic11C2×D414yes—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C22×#125—111no—
174C2×#478—112no—
175C4×#121—111no—
176#2059—112no—
177#2025—112no—
178#1989—112no—
179#1874—111no—
180#1874D1111yescharacteristic
181#1853—111no—
182#1852—111no—
183#1797—111no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—22no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11C22⋊Q812yes—
196C23×C11#13512yes—
197C23×C11AGL(1,ℤ/8)12yes—
198C23×C11C22×D411yescharacteristic
199D4×C11—24no—
200D4×C11—48no—
201D4×C11—42no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—48no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C22⋊Q812yes—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C22×Q811yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C112−1+412yes—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—24no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—44no—
230C2×Dic11—44no—
231C2×Dic11—48no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—84no—
241C2×Dic11#12012yes—
242C2×Dic11#12012yes—
243C8×C11—42no—
244C11⋊C8—42no—
245C2×#125—112no—
246C2×#125—112no—
247C2×#125—221no—
248C2×#125—221no—
249C2×#125—228no—
250C2×#121C2×D1111yescharacteristic
251C2×C4×D4—111no—
252C2×C4×D4—221no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4—221no—
255C22×C4⋊C4—221no—
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C42—111no—
258#478—228no—
259C2×#107—112no—
260C2×#106—112no—
261C2×C4⋊C8—112no—
262C2×#102—112no—
263C2×#102C2×D1112yes—
264C2×C22⋊C8—111no—
265C2×C22⋊C8C2×D1111yescharacteristic
266#390—111no—
267#389—111no—
268#388—221no—
269#386—221no—
270#380—111no—
271C4×C4⋊C4—111no—
272C4×C22⋊C4—221no—
273#340—112no—
274#340—112no—
275#340—112no—
276#340C2×D1112yes—
277#336—112no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11#47814yescomplemented
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×C22⋊Q811yescharacteristic
294C22×C11#53611yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11#57511yescharacteristic
298C22×C11#57511yescharacteristic
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—44no—
302C4×C11#54812yes—
303C4×C11D4×Q812yes—
304Dic11—22no—
305Dic11—22no—
306Dic11—41no—
307Dic11—44no—
308Dic11—41no—
309Dic11—81no—
310Dic11—81no—
311C22×D4—21no—
312C22×D4C22×D1111yescharacteristic
313C23×C4—21no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—221no—
317C23×C4—221no—
318C23×C4C22×D1111yescharacteristic
319C22×C8—112no—
320C22×C8C22×D1112yes—
321#125—118no—
322#125—224no—
323#125—224no—
324#125—228no—
325#125—228no—
326#125—224no—
327#121—22no—
328#121Dic2214yes—
329C4×D4—224no—
330C4×D4—444no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—112no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—228no—
342C2×C4⋊C4—228no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C4⋊C4C22×D1112yes—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—224no—
357C2×C42—221no—
358#107—224no—
359#106—224no—
360C4⋊C8—224no—
361#102—24no—
362#102—224no—
363C22⋊C8—22no—
364C22⋊C8—222no—
365#95—221no—
366#95—221no—
367#95—221no—
368C2×C11—24no—
369C2×C11—82no—
370C2×C11#240911yescharacteristic
371C2×C11#300211yescharacteristic
372C2×C11#300611yescharacteristic
373C2×C11C2×#47811yescharacteristic
374C2×C11#308011yescharacteristic
375C2×C11#323211yescharacteristic
376C2×C11#323411yescharacteristic
377C24—21no—
378C24D4×D1111yescharacteristic
379C2×D4—24no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4C2×Dic2212yes—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—224no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—442no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—442no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4C2×Dic2212yes—
413C22×C4D4×D1111yescharacteristic
414C22×C4#434112yes—
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—114no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—224no—
430C4⋊C4—228no—
431C4⋊C4—222no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—442no—
435C4⋊C4C2×Dic2212yes—
436C4⋊C4D4×D1114yes—
437C22⋊C4—24no—
438C22⋊C4—442no—
439C22⋊C4—442no—
440C22⋊C4—442no—
441C22⋊C4—442no—
442C42—114no—
443C42—222no—
444C42—222no—
445C42—222no—
446C42—442no—
447C11#2430511yescharacteristic, complemented, Sylow
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23#6693112yes—
460C23#6696412yes—
461C23#6696912yes—
462C23C2×D4×D1111yescharacteristic
463D4—24no—
464D4—48no—
465D4—42no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—48no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—224no—
490C2×C4—444no—
491C2×C4—444no—
492C2×C4—448no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—884no—
502C2×C4#6693112yes—
503C2×C4C22×Dic2211yescharacteristic
504C2×C4C2×D4×D1112yes—
505C2×C4C2×#434111yescharacteristic
506C2×C4#6704312yes—
507C8—42no—
508C8—442no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22#1062237614yescomplemented
523C22C2×#6693111yescharacteristic
524C22D11×#12011yescharacteristic
525C22#1062317911yescharacteristic
526C22C2×#6696411yescharacteristic
527C22C2×#6696911yescharacteristic
528C22#1062330411yescharacteristic
529C22#1062330811yescharacteristic
530C4—22no—
531C4—44no—
532C4—42no—
533C4—222no—
534C4—222no—
535C4—441no—
536C4—444no—
537C4—441no—
538C4—881no—
539C4—881no—
540C4D4×Dic2212yes—
541C4#1062312912yes—
542C2—24no—
543C2—82no—
544C2#1307197811yescharacteristic
545C2#1307783311yescharacteristic
546C2#1307786311yescharacteristic
547C2C2×#1062237611yescharacteristic
548C2#1307843611yescharacteristic
549C2#1307978311yescharacteristic
550C2#1307980311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1874D11
hypocenterC11#24305
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
2. C2×#10622376C2semidirect
4. #13069953C2semidirect
5. #13069760C2semidirect
6. #13069570C2semidirect
8. #13068811C2semidirect
9. #13068804C2semidirect
10. #13068594C2semidirect
91. #66943D4semidirect
291. C22×C11#478semidirect
447. C11#24305semidirect
522. C22#10622376semidirect

Maximal subgroups

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

subgroupindex
C22×#669432
C2×#106223762
#121×Dic112
#130699532
#130697602
#130695702
#130689342
#130688112
#130688042
#130685942
C11×#18742
#2430511