Finite Group Databasebeta

← #14684786

Subgroups — #14684786

Order 2816.

3274 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66990C211yesmaximal, characteristic
2C2×#10622568C212yesmaximal, complemented
3#13066864C214yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066857C211yesmaximal, characteristic, complemented
6#13066855C214yesmaximal, complemented
7C11×#1438C211yesmaximal, characteristic, complemented
8C25×D11C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11C2212yes—
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2212yescomplemented
13C22×C22⋊Dic11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yescomplemented
16C2×#66990—28no—
17C2×#66990C418yescomplemented
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2214yes—
21C2×C11×#95C2212yescomplemented
22C2×C11⋊#95C2214yescomplemented
23C2×C11⋊#95C2214yescomplemented
24C2×C11⋊#95C2212yescomplemented
25#10622568—28no—
26C25×C11C2311yescharacteristic
27C25×C11C2311yescharacteristic
28C24×D11—42no—
29C24×D11—42no—
30C24×D11—44no—
31C24×D11—44no—
32C24×D11C2×C414yes—
33C24×D11D418yes—
34C24×D11C2312yes—
35C22×D4×C11—24no—
36C22×D4×C11—42no—
37C22×D4×C11—42no—
38C22×D4×C11C2×C414yes—
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—24no—
42C22×C22⋊D11—24no—
43C22×C22⋊D11—44no—
44C22×C22⋊D11—44no—
45C22×C22⋊D11C2×C418yes—
46C23×Dic11C2314yes—
47C23×Dic11C2312yes—
48C2×C11×C22⋊C4—24no—
49C2×C11×C22⋊C4—44no—
50C2×C11×C22⋊C4—42no—
51C2×C11×C22⋊C4—44no—
52C2×C22⋊Dic11—24no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—44no—
55C2×C22⋊Dic11—42no—
56C2×C22⋊Dic11—44no—
57C2×C22⋊Dic11C2×C414yes—
58#66990—232no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—28no—
62C2×(C2×D11)⋊C4—28no—
63C2×(C2×D11)⋊C4—44no—
64C2×(C2×D11)⋊C4—44no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4—44no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C11×#95—42no—
69C11⋊#95—44no—
70C11⋊#95—44no—
71C11⋊#95—42no—
72#14657—111nomaximal, Sylow
73C24×C11—24no—
74C24×C11—24no—
75C24×C11—22no—
76C24×C11—22no—
77C24×C11—22no—
78C24×C11—24no—
79C24×C11—22no—
80C24×C11—24no—
81C24×C11—22no—
82C24×C11C22×C412yes—
83C24×C11C22×C412yes—
84C24×C11C2×D414yes—
85C24×C11C2411yescharacteristic
86C23×D11—24no—
87C23×D11—24no—
88C23×D11—24no—
89C23×D11—24no—
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—416no—
93C23×D11—44no—
94C23×D11—44no—
95C23×D11—416no—
96C23×D11—416no—
97C23×D11—48no—
98C23×D11—48no—
99C23×D11—48no—
100C23×D11—416no—
101C23×D11—416no—
102C23×D11—48no—
103C23×D11—48no—
104C23×D11—48no—
105C23×D11C22⋊C4116yescomplemented
106C23×D11C22×C414yes—
107C23×D11C2×D414yes—
108C23×D11C2×D414yes—
109C2×D4×C11—28no—
110C2×D4×C11—44no—
111C2×D4×C11—44no—
112C2×D4×C11—416no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11C22×C412yes—
124C2×C22⋊D11—216no—
125C2×C22⋊D11—416no—
126C2×C22⋊D11—48no—
127C2×C22⋊D11—416no—
128C2×C22⋊D11—48no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11C22×C414yes—
141C11×C22⋊C4—48no—
142C11×C22⋊C4—48no—
143C22⋊Dic11—28no—
144C22⋊Dic11—48no—
145C22⋊Dic11—48no—
146(C2×D11)⋊C4—216no—
147(C2×D11)⋊C4—416no—
148(C2×D11)⋊C4—416no—
149C22×#120—111no—
150C2×#379—112no—
151#1440—114no—
152#1440—112no—
153#1438—111no—
154#1438—114no—
155#1438D1111yescharacteristic, complemented
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—28no—
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—28no—
162C23×C11—28no—
163C23×C11—22no—
164C23×C11—28no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—44no—
175C23×C11—42no—
176C23×C11—44no—
177C23×C11—42no—
178C23×C11—44no—
179C23×C11—44no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C2×C22⋊C414yes—
184C23×C11C23×C411yescharacteristic
185C23×C11C22×D412yes—
186C23×C11H(5,𝔽2)12yes—
187C23×C11H(5,𝔽2)14yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C11H(5,𝔽2)14yes—
190C22×D11—28no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—28no—
194C22×D11—28no—
195C22×D11—28no—
196C22×D11—24no—
197C22×D11—28no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—28no—
201C22×D11—24no—
202C22×D11—416no—
203C22×D11—432no—
204C22×D11—432no—
205C22×D11—432no—
206C22×D11—464no—
207C22×D11—464no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11C2×C22⋊C418yes—
217D4×C11—416no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—44no—
229C22⋊D11—432no—
230C2×Dic11—24no—
231C2×Dic11—28no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—44no—
236C2×Dic11—44no—
237C2×Dic11—44no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C26—111no—
243C23×D4—112no—
244C23×D4C2×D1111yescharacteristic
245C2×#120—118no—
246C2×#120—228no—
247C22×C22⋊C4—111no—
248C22×C22⋊C4—112no—
249C22×C22⋊C4—112no—
250C22×C22⋊C4—114no—
251C22×C22⋊C4—114no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4C2×D1112yes—
254C22×C22⋊C4C2×D1112yescomplemented
255#379—228no—
256C2×#95—114no—
257C2×#95—114no—
258C2×#95—112no—
259C2×#95C2×D1112yescomplemented
260C22×C11—24no—
261C22×C11—28no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—48no—
265C22×C11—48no—
266C22×C11—42no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—84no—
271C22×C11—84no—
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11#51811yescharacteristic
274C22×C11#51811yescharacteristic
275C22×C11#51814yes—
276C22×C11#53412yes—
277C22×C11#53414yes—
278C22×C11#53414yes—
279C22×C11#53412yes—
280C22×C11#56012yes—
281C22×C11#56014yes—
282C22×C11#56014yes—
283C22×C11#56012yes—
284C22×C11H(3,𝔽4)12yes—
285C22×C11H(3,𝔽4)12yes—
286C2×D11—28no—
287C2×D11—28no—
288C2×D11—28no—
289C2×D11—464no—
290C2×D11—48no—
291C2×D11—48no—
292C2×D11—48no—
293C2×D11—48no—
294C2×D11—48no—
295C2×D11—48no—
296C4×C11—42no—
297C4×C11—84no—
298Dic11—44no—
299Dic11—84no—
300C25—112no—
301C25—114no—
302C25—118no—
303C25—444no—
304C25—442no—
305C25—442no—
306C25—444no—
307C25C22×D1111yescharacteristic
308C25C22×D1111yescharacteristic
309C22×D4—24no—
310C22×D4—42no—
311C22×D4—42no—
312C22×D4—118no—
313C22×D4—224no—
314C22×D4—224no—
315C22×D4—444no—
316C22×D4—444no—
317C22×D4C4×D1114yes—
318C23×C4—112no—
319C23×C4—114no—
320C23×C4C22×D1114yes—
321C23×C4C22×D1111yescharacteristic
322#120—2232no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—114no—
328C2×C22⋊C4—118no—
329C2×C22⋊C4—224no—
330C2×C22⋊C4—224no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—228no—
333C2×C22⋊C4—228no—
334C2×C22⋊C4—224no—
335C2×C22⋊C4—444no—
336C2×C22⋊C4—444no—
337C2×C22⋊C4—444no—
338C2×C22⋊C4—444no—
339C2×C22⋊C4—444no—
340C2×C22⋊C4—442no—
341C2×C22⋊C4—444no—
342#95—42no—
343#95—442no—
344#95—444no—
345#95—444no—
346C2×C11—44no—
347C2×C11—82no—
348C2×C11#230812yes—
349C2×C11#230811yescharacteristic
350C2×C11#237512yes—
351C2×C11#237512yes—
352C2×C11#281214yes—
353C2×C11#281214yes—
354D11—48no—
355C24—24no—
356C24—22no—
357C24—22no—
358C24—24no—
359C24—22no—
360C24—22no—
361C24—24no—
362C24—22no—
363C24—24no—
364C24—114no—
365C24—114no—
366C24—114no—
367C24—1116no—
368C24—224no—
369C24—224no—
370C24—224no—
371C24—224no—
372C24—224no—
373C24—224no—
374C24—444no—
375C24—444no—
376C24—4416no—
377C24—448no—
378C24—4416no—
379C24—4416no—
380C24—448no—
381C24—448no—
382C24—448no—
383C24—4416no—
384C24—4416no—
385C24—448no—
386C24—448no—
387C24C2×C4×D1112yes—
388C24C2×C4×D1112yes—
389C24D4×D1114yes—
390C24C23×D1111yescharacteristic
391C2×D4—28no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—416no—
395C2×D4—2216no—
396C2×D4—4416no—
397C2×D4—448no—
398C2×D4—4416no—
399C2×D4—448no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—114no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4C2×C4×D1112yes—
423C22⋊C4—48no—
424C22⋊C4—48no—
425C22⋊C4—2216no—
426C22⋊C4—228no—
427C22⋊C4—4416no—
428C22⋊C4—4416no—
429C22⋊C4—448no—
430C22⋊C4—448no—
431C11#1465711yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—28no—
435C23—24no—
436C23—28no—
437C23—28no—
438C23—24no—
439C23—22no—
440C23—22no—
441C23—22no—
442C23—28no—
443C23—42no—
444C23—42no—
445C23—44no—
446C23—44no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—44no—
451C23—42no—
452C23—42no—
453C23—44no—
454C23—44no—
455C23—44no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—118no—
460C23—224no—
461C23—224no—
462C23—228no—
463C23—228no—
464C23—228no—
465C23—224no—
466C23—224no—
467C23—228no—
468C23—228no—
469C23—228no—
470C23—224no—
471C23—224no—
472C23—4432no—
473C23—4416no—
474C23—4464no—
475C23—4464no—
476C23—4432no—
477C23—4432no—
478C23—444no—
479C23—444no—
480C23—444no—
481C23—444no—
482C23—444no—
483C23—444no—
484C23—444no—
485C23—444no—
486C23C22⋊C4×D1114yes—
487C23C22×C4×D1111yescharacteristic
488C23C2×D4×D1112yes—
489C23#6703712yes—
490C23#6703714yes—
491C23#6703712yes—
492C23#6704214yes—
493D4—416no—
494D4—4432no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—224no—
507C2×C4—228no—
508C2×C4—442no—
509C2×C4—444no—
510C2×C4—442no—
511C2×C4—444no—
512C2×C4—444no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—444no—
516C2×C4—444no—
517C2×C4—444no—
518C22—28no—
519C22—24no—
520C22—48no—
521C22—48no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—42no—
526C22—44no—
527C22—44no—
528C22—84no—
529C22—84no—
530C22—228no—
531C22—228no—
532C22—228no—
533C22—4464no—
534C22—448no—
535C22—448no—
536C22—448no—
537C22—448no—
538C22—448no—
539C22—448no—
540C22C2×C22⋊C4×D1111yescharacteristic
541C22#1062301711yescharacteristic
542C22#1062301711yescharacteristic
543C22#1062307614yes—
544C22#1062312012yes—
545C22#1062312014yes—
546C22#1062312512yes—
547C22#1062313614yes—
548C22#1062315114yes—
549C22#1062315114yes—
550C22#1062318412yes—
551C22#1062319712yes—
552C22#1062321412yes—
553C22#1062325112yes—
554C4—42no—
555C4—84no—
556C4—444no—
557C4—884no—
558C2—44no—
559C2—82no—
560C2—448no—
561C2#1307119012yes—
562C2#1307119211yescharacteristic
563C2#1307175312yes—
564C2#1307175412yes—
565C2#1307661014yes—
566C2#1307661214yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66990C2
hypercenter#1438D11
hypocenterC11#14657
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622568C2semidirect
3. #13066864C2semidirect
4. #13066863C2semidirect
5. #13066857C2semidirect
6. #13066855C2semidirect
7. C11×#1438C2semidirect
12. C22×C11×C22⋊C4C22semidirect
15. C22×C22⋊Dic11C22semidirect
17. C2×#66990C4semidirect
21. C2×C11×#95C22semidirect
22. C2×C11⋊#95C22semidirect
23. C2×C11⋊#95C22semidirect
24. C2×C11⋊#95C22semidirect
105. C23×D11C22⋊C4semidirect
155. #1438D11semidirect
254. C22×C22⋊C4C2×D11semidirect
259. C2×#95C2×D11semidirect
431. C11#14657semidirect

Maximal subgroups

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

subgroupindex
C22×#669902
C2×#106225682
#130668642
#130668632
#130668572
#130668552
C11×#14382
#1465711