Finite Group Databasebeta

← #14960506

Subgroups — #14960506

Order 2816.

4154 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
1C2×#10623336C211yesmaximal, characteristic, complemented
2#13076893C212yesmaximal, complemented
3#13074994C214yesmaximal, complemented
4#13074833C214yesmaximal, complemented
5#13074820C218yesmaximal, complemented
6#13074389C212yesmaximal, complemented
7#13072890C212yesmaximal, complemented
8#13071990C214yesmaximal, complemented
9#13071935C212yesmaximal, complemented
10#13071194C211yesmaximal, characteristic, complemented
11C22×C11×#120C211yesmaximal, characteristic, complemented
12C26×C11C2211yescharacteristic
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic, complemented
16C2×C11×#120—28no—
17C2×C11×#120C2214yes—
18C2×C11×#120C2214yes—
19C22×C11×C22⋊C4C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C2×#67006C2212yes—
22C2×#67006C2214yes—
23C2×#67006C2218yescomplemented
24C2×#67006C2212yescomplemented
25C22×C22⋊Dic11C2212yescomplemented
26#10623336—28no—
27C2×#66993C2212yescomplemented
28C2×#66992C2218yescomplemented
29C2×#66991C2214yescomplemented
30C2×#66989C2212yescomplemented
31C2×#66979C2211yescharacteristic, complemented
32#10622860C2212yes—
33#10622860C2214yes—
34#10622860C2218yescomplemented
35#10622836C2218yescomplemented
36#10622835C2218yescomplemented
37#10622833C2214yescomplemented
38#10622833C2218yescomplemented
39#10622833C2214yescomplemented
40#10622826C2214yescomplemented
41#10622824C2212yescomplemented
42#10622823C2214yescomplemented
43#10622573C2214yescomplemented
44#10622572C2218yescomplemented
45#10622569C2218yescomplemented
46#10622566C2214yescomplemented
47#10622565C2218yescomplemented
48#10622562C2214yescomplemented
49#10622560C2214yescomplemented
50#10622557C2218yescomplemented
51C25×C11—24no—
52C25×C11—48no—
53C25×C11—44no—
54C25×C11C2312yes—
55C25×C11C2314yes—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—28no—
59C22×D4×C11—44no—
60C22×D4×C11—48no—
61C22×D4×C11D418yescomplemented
62C22×D4×C11C2318yes—
63C22×D4×C11C2312yes—
64C22×D4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2312yes—
67C22×C22⋊D11C2312yes—
68C22×C22⋊D11C2314yes—
69C22×C22⋊D11C2318yes—
70C22×C22⋊D11C2314yescomplemented
71C23×Dic11C2314yescomplemented
72C2×#4339—24no—
73C2×#4339—44no—
74C22×D44C2311yescharacteristic, complemented
75C22×C4×D11C2312yescomplemented
76C22×Dic22C2311yescharacteristic, complemented
77C11×#120—216no—
78C11×#120—216no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84#67006—28no—
85#67006—28no—
86#67006—48no—
87#67006—416no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2312yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96C2×C22⋊Dic11C2314yescomplemented
97C2×C22⋊Dic11C2314yescomplemented
98#66993—28no—
99#66992—416no—
100#66991—216no—
101#66989—28no—
102C2×(C2×D11)⋊C4C2318yescomplemented
103#66979—24no—
104C2×C4⋊Dic11C2312yescomplemented
105C2×Dic11⋊C4C2318yescomplemented
106C2×C4×Dic11C2312yescomplemented
107C11⋊#95C2314yescomplemented
108C11⋊#95C2318yescomplemented
109C11⋊#95C2318yescomplemented
110C11⋊#95C2314yescomplemented
111#36702—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—28no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—28no—
117C24×C11—216no—
118C24×C11—28no—
119C24×C11—44no—
120C24×C11—44no—
121C24×C11—48no—
122C24×C11—44no—
123C24×C11—44no—
124C24×C11—44no—
125C24×C11—432no—
126C24×C11—416no—
127C24×C11—464no—
128C24×C11C2×D414yes—
129C24×C11C2×D414yes—
130C24×C11C2412yes—
131C24×C11C2412yes—
132C24×C11C2414yes—
133C24×C11C2411yescharacteristic
134C23×D11C2412yes—
135C2×D4×C11—216no—
136C2×D4×C11—216no—
137C2×D4×C11—416no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—48no—
143C2×D4×C11—432no—
144C2×D4×C11C2×D418yes—
145C2×D4×C11C2×D418yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—44no—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—48no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—48no—
162C22×Dic11—48no—
163C22×Dic11—44no—
164C22×Dic11C2418yes—
165C22×Dic11C2412yes—
166C22×Dic11C2414yes—
167#4339—416no—
168C2×D44—22no—
169C2×D44—42no—
170C2×C4×D11—24no—
171C2×C4×D11—44no—
172C2×Dic22—22no—
173C2×Dic22—42no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—28no—
177C22⋊Dic11—24no—
178C22⋊Dic11—28no—
179C22⋊Dic11—28no—
180C22⋊Dic11—216no—
181C22⋊Dic11—28no—
182C22⋊Dic11—44no—
183C22⋊Dic11—48no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—24no—
188Dic11⋊C4—48no—
189C4×Dic11—24no—
190C2×#535—111no—
191C22×#120D1111yescharacteristic, complemented
192#2846—112no—
193#2684—114no—
194#2669—114no—
195#2668—118no—
196#2622—112no—
197#2482—112no—
198#2410—114no—
199#2404—112no—
200#2308—111no—
201C23×C11—24no—
202C23×C11—216no—
203C23×C11—28no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—28no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—22no—
210C23×C11—28no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—28no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—432no—
218C23×C11—432no—
219C23×C11—416no—
220C23×C11—48no—
221C23×C11—416no—
222C23×C11—416no—
223C23×C11—432no—
224C23×C11—4128no—
225C23×C11—416no—
226C23×C11—48no—
227C23×C11—88no—
228C23×C11C22×D414yes—
229C23×C11C22×D414yes—
230C23×C11C22×D412yes—
231C23×C11H(5,𝔽2)18yes—
232C23×C11H(5,𝔽2)14yes—
233C23×C11C2511yescharacteristic
234C22×D11—22no—
235C22×D11—28no—
236C22×D11—24no—
237D4×C11—48no—
238D4×C11—48no—
239D4×C11—432no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—28no—
245C2×C4×C11—48no—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D412yes—
248C22⋊D11—48no—
249C22⋊D11—88no—
250C22⋊D11—88no—
251C22⋊D11—816no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—28no—
255C2×Dic11—28no—
256C2×Dic11—28no—
257C2×Dic11—28no—
258C2×Dic11—24no—
259C2×Dic11—88no—
260D44—44no—
261C4×D11—48no—
262Dic22—44no—
263C26C2×D1111yescharacteristic
264C22×#41—111no—
265C23×D4C2×D1112yes—
266C23×D4C2×D1111yescharacteristic
267#535—228no—
268C2×#127—112no—
269C2×#124—112no—
270C2×#121—114no—
271C2×#121—118no—
272C2×#120—28no—
273C2×#120—112no—
274C2×#120—112no—
275C2×#120—114no—
276C2×#120—118no—
277C2×#120C2×D1114yes—
278C2×#120C2×D1114yes—
279C2×#117—111no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1111yescharacteristic
282C22×C22⋊C4C2×D1112yes—
283#399—114no—
284#397—118no—
285#397—114no—
286#394—118no—
287#394—118no—
288#393—114no—
289#392—118no—
290#392—114no—
291#388—118no—
292#386—114no—
293#386—114no—
294#386—118no—
295#386—114no—
296#386—118no—
297#385—114no—
298#381—112no—
299#379—112no—
300#379—114no—
301#379—118no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—28no—
307C22×C11—28no—
308C22×C11—28no—
309C22×C11—216no—
310C22×C11—432no—
311C22×C11—416no—
312C22×C11—464no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—48no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—88no—
321C22×C11#53414yes—
322C22×C11C23×D411yescharacteristic
323C22×C11C2×H(5,𝔽2)12yes—
324C22×C11C2×H(5,𝔽2)14yes—
325C2×D11—42no—
326C2×D11—44no—
327C2×D11—48no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—44no—
331Dic11—42no—
332Dic11—44no—
333Dic11—48no—
334C25—24no—
335C25—48no—
336C25—44no—
337C25C22×D1112yes—
338C25C22×D1114yes—
339C25C22×D1111yescharacteristic
340C25C22×D1111yescharacteristic
341C2×#41—224no—
342C2×#41—444no—
343C22×Q8—111no—
344C22×D4—28no—
345C22×D4—44no—
346C22×D4—48no—
347C22×D4—112no—
348C22×D4—114no—
349C22×D4—118no—
350C22×D4—114no—
351C22×D4—111no—
352C22×D4C22⋊D1118yescomplemented
353C22×D4C22×D1118yes—
354C22×D4C22×D1112yes—
355C22×D4C22×D1112yes—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1112yes—
360#127—228no—
361#124—228no—
362#121—2216no—
363#121—4416no—
364#120—216no—
365#120—216no—
366#120—228no—
367#120—228no—
368#120—448no—
369#120—4416no—
370#117—224no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—118no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—112no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1114yes—
388C2×C22⋊C4C22×D1114yes—
389C2×C42—112no—
390#95—114no—
391#95—114no—
392#95—118no—
393#95—118no—
394C2×C11—24no—
395C2×C11—44no—
396C2×C11—48no—
397C2×C11—44no—
398C2×C11C2×#53411yescharacteristic
399C2×C11#348412yes—
400C2×C11#353214yes—
401D11—82no—
402C24—28no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—216no—
407C24—28no—
408C24—28no—
409C24—44no—
410C24—44no—
411C24—48no—
412C24—44no—
413C24—44no—
414C24—44no—
415C24—432no—
416C24—416no—
417C24—464no—
418C24—112no—
419C24C2×C22⋊D1114yes—
420C24C2×C22⋊D1114yes—
421C24C23×D1114yes—
422C24C23×D1112yes—
423C24C23×D1112yes—
424C24C23×D1111yescharacteristic
425#41—4416no—
426C2×Q8—222no—
427C2×Q8—442no—
428C2×D4—216no—
429C2×D4—216no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—48no—
435C2×D4—416no—
436C2×D4—432no—
437C2×D4—228no—
438C2×D4—224no—
439C2×D4—2216no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—222no—
443C2×D4—442no—
444C2×D4—448no—
445C2×D4—448no—
446C2×D4—448no—
447C2×D4—448no—
448C2×D4C2×C22⋊D1118yes—
449C2×D4C2×C22⋊D1118yes—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—118no—
454C22×C4—112no—
455C22×C4—114no—
456C22×C4—224no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—448no—
460C22×C4C2×C22⋊D1114yes—
461C22×C4C23×D1114yes—
462C22×C4C23×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464C4⋊C4—224no—
465C4⋊C4—448no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—28no—
469C22⋊C4—228no—
470C22⋊C4—2216no—
471C22⋊C4—224no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C22⋊C4—448no—
475C22⋊C4—444no—
476C22⋊C4—448no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C42—224no—
480C11#3670211yescharacteristic, complemented, Sylow
481C23—24no—
482C23—216no—
483C23—28no—
484C23—22no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—22no—
489C23—28no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—28no—
495C23—48no—
496C23—48no—
497C23—432no—
498C23—432no—
499C23—416no—
500C23—48no—
501C23—416no—
502C23—416no—
503C23—432no—
504C23—4128no—
505C23—416no—
506C23—48no—
507C23—88no—
508C23—228no—
509C23—224no—
510C23—222no—
511C23#6703718yes—
512C23#6703714yes—
513C23C22×C22⋊D1114yes—
514C23C22×C22⋊D1114yes—
515C23C22×C22⋊D1112yes—
516C23C24×D1111yescharacteristic
517Q8—444no—
518D4—48no—
519D4—48no—
520D4—432no—
521D4—444no—
522D4—448no—
523D4—888no—
524D4—888no—
525D4—8816no—
526C2×C4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—48no—
532C2×C4—228no—
533C2×C4—228no—
534C2×C4—228no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—448no—
540C2×C4—888no—
541C2×C4C22×C22⋊D1112yes—
542C2×C4C22×C22⋊D1112yes—
543C22—24no—
544C22—28no—
545C22—24no—
546C22—24no—
547C22—28no—
548C22—28no—
549C22—28no—
550C22—216no—
551C22—432no—
552C22—416no—
553C22—464no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22—44no—
558C22—48no—
559C22—44no—
560C22—44no—
561C22—88no—
562C22—442no—
563C22—444no—
564C22—448no—
565C22#1062333514yes—
566C22C2×#6703712yes—
567C22C2×#6703714yes—
568C22C23×C22⋊D1111yescharacteristic
569C4—22no—
570C4—22no—
571C4—44no—
572C4—442no—
573C4—444no—
574C4—448no—
575C2—24no—
576C2—44no—
577C2—48no—
578C2—44no—
579C2—882no—
580C2C2×#1062333511yescharacteristic
581C2#1308225112yes—
582C2#1308277114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#120C2
hypercenterC22×#120D11
hypocenterC11#36702
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623336C2semidirect
2. #13076893C2semidirect
3. #13074994C2semidirect
4. #13074833C2semidirect
5. #13074820C2semidirect
6. #13074389C2semidirect
7. #13072890C2semidirect
8. #13071990C2semidirect
9. #13071935C2semidirect
10. #13071194C2semidirect
11. C22×C11×#120C2semidirect
15. C22×#4339C22semidirect
23. C2×#67006C22semidirect
24. C2×#67006C22semidirect
25. C22×C22⋊Dic11C22semidirect
27. C2×#66993C22semidirect
28. C2×#66992C22semidirect
29. C2×#66991C22semidirect
30. C2×#66989C22semidirect
31. C2×#66979C22semidirect
34. #10622860C22semidirect
35. #10622836C22semidirect
36. #10622835C22semidirect
37. #10622833C22semidirect
38. #10622833C22semidirect
39. #10622833C22semidirect
40. #10622826C22semidirect
41. #10622824C22semidirect
42. #10622823C22semidirect
43. #10622573C22semidirect
44. #10622572C22semidirect
45. #10622569C22semidirect
46. #10622566C22semidirect
47. #10622565C22semidirect
48. #10622562C22semidirect
49. #10622560C22semidirect
50. #10622557C22semidirect
61. C22×D4×C11D4semidirect
70. C22×C22⋊D11C23semidirect
71. C23×Dic11C23semidirect
74. C22×D44C23semidirect
75. C22×C4×D11C23semidirect
76. C22×Dic22C23semidirect
96. C2×C22⋊Dic11C23semidirect
97. C2×C22⋊Dic11C23semidirect
102. C2×(C2×D11)⋊C4C23semidirect
104. C2×C4⋊Dic11C23semidirect
105. C2×Dic11⋊C4C23semidirect
106. C2×C4×Dic11C23semidirect
107. C11⋊#95C23semidirect
108. C11⋊#95C23semidirect
109. C11⋊#95C23semidirect
110. C11⋊#95C23semidirect
191. C22×#120D11semidirect
352. C22×D4C22⋊D11semidirect
480. C11#36702semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
#130768932
#130749942
#130748332
#130748202
#130743892
#130728902
#130719902
#130719352
#130711942
C22×C11×#1202
#3670211