Finite Group Databasebeta

← #14927231

Subgroups — #14927231

Order 2816.

2778 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C212yesmaximal, complemented
2#13076968C211yesmaximal, characteristic, complemented
3#13076961C211yesmaximal, characteristic, complemented
4#13076917C212yesmaximal, complemented
5#13074350C214yesmaximal, complemented
6#13074222C218yesmaximal, complemented
7#13073078C212yesmaximal, complemented
8#13073069C212yesmaximal, complemented
9#13072244C212yesmaximal, complemented
10#13072235C212yesmaximal, complemented
11#13071319C214yesmaximal, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C22×#4339C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×#67006C2214yes—
19#10623322—216no—
20C2×#66983C2212yes—
21C2×#66983C2212yes—
22C2×#66983C2214yes—
23C2×#66982C2214yes—
24C2×C4×C22⋊D11C2214yes—
25C2×C4×C22⋊D11C2214yes—
26C2×#66979C2212yes—
27C2×#66977C2212yes—
28C2×#66977C2212yes—
29C2×#66928C2212yescomplemented
30C2×#66927C2211yescharacteristic, complemented
31C2×#66922C2211yescharacteristic, complemented
32C4×C11×C22⋊C4C2214yes—
33C4×C11×C22⋊C4C2212yes—
34C4×C11×C22⋊C4C2212yes—
35C2×C11×#95C2212yes—
36#10622826C2218yes—
37#10622825C2214yes—
38#10622574C2218yes—
39#10622574C2218yes—
40#10622573C2218yes—
41#10622566C2218yes—
42#10622553C2218yescomplemented
43#10622552C2214yescomplemented
44#10622552C2212yescomplemented
45#10622552C2212yescomplemented
46#10622549C2212yescomplemented
47#10622548C2211yescharacteristic, complemented
48#10622548C2211yescharacteristic, complemented
49#10622542C2212yescomplemented
50#10622542C2212yescomplemented
51#10622541C2214yescomplemented
52#10622283C2218yescomplemented
53#10622281C2218yescomplemented
54#10622278C2218yescomplemented
55#10622266C2218yescomplemented
56C25×C11C2311yescharacteristic
57C23×C4×C11—42no—
58C23×C4×C11—42no—
59C23×C4×C11D418yescomplemented
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2312yes—
65C23×C4×C11C2312yes—
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C2×#4339—28no—
70C2×#4339—44no—
71C2×#4339—44no—
72C22×D44C2312yes—
73C22×D44C2314yes—
74C22×C4×D11C2314yes—
75C22×Dic22C2312yes—
76C2×C11×C22⋊C4—28no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C42×C11—42no—
80C2×C42×C11—42no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86#67006—216no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90#66983—28no—
91#66983—28no—
92#66983—216no—
93#66982—216no—
94C4×C22⋊D11—216no—
95C4×C22⋊D11—216no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101#66979—28no—
102C2×C4⋊Dic11C2314yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2314yes—
107#66977—28no—
108#66977—28no—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×C4×Dic11C2314yes—
112#66928—44no—
113#66927—42no—
114#66922—42no—
115C11×#95C2314yes—
116C11×#95C2314yes—
117C11⋊#95C2318yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120#35032—111nomaximal, Sylow
121C24×C11—24no—
122C24×C11—41no—
123C24×C11—41no—
124C24×C11—42no—
125C24×C11C2×D414yes—
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11C2414yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—416no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×D418yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D418yes—
147C22×C4×C11#4118yescomplemented
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—216no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—48no—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164#4339—432no—
165C2×D44—24no—
166C2×D44—28no—
167C2×D44—24no—
168C2×D44—24no—
169C2×D44—44no—
170C2×D44—44no—
171C2×C4×D11—28no—
172C2×C4×D11—44no—
173C2×C4×D11—44no—
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22—24no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—24no—
182C42×C11—42no—
183C42×C11—42no—
184C22⋊Dic11—28no—
185C22⋊Dic11—28no—
186C22⋊Dic11—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192C4⋊Dic11—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—28no—
195C4⋊Dic11—44no—
196C4⋊Dic11—44no—
197Dic11⋊C4—28no—
198Dic11⋊C4—28no—
199C4×Dic11—28no—
200C2×#525—112no—
201#2857—111no—
202#2856—111no—
203#2850—112no—
204#2617—114no—
205#2602—118no—
206#2500—112no—
207#2499—112no—
208#2432—112no—
209#2431—112no—
210#2325—114no—
211C2×C4×C22⋊C4D1111yescharacteristic, complemented
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—22no—
215C23×C11—28no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11C22×D414yes—
225C23×C11C22×D412yes—
226C23×C11C2×#4114yes—
227C23×C11C2511yescharacteristic
228C22×D11—24no—
229C22×D11—28no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—28no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—216no—
242C2×C4×C11—28no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—48no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×C4×C11—48no—
250C2×C4×C11C22×D414yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2×#4114yes—
255C2×C4×C11H(5,𝔽2)12yes—
256C2×C4×C11H(5,𝔽2)12yes—
257C22⋊D11—416no—
258C22⋊D11—416no—
259C22⋊D11—416no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—28no—
267D44—48no—
268D44—88no—
269C4×D11—416no—
270Dic22—48no—
271C22×#41—112no—
272C24×C4C2×D1111yescharacteristic
273C2×C4⋊Q8—111no—
274C2×#127—111no—
275C2×#124—112no—
276#525—2216no—
277C2×#123—114no—
278C2×C22⋊Q8—112no—
279C2×C22⋊Q8—112no—
280C2×#121—114no—
281C2×#121—112no—
282C2×#121—112no—
283C2×#120—114no—
284C2×C4×D4—114no—
285C2×C4×D4—114no—
286C2×#117—112no—
287C22×C22⋊C4C2×D1112yes—
288C22×C42C2×D1111yescharacteristic
289C22×C42C2×D1111yescharacteristic
290#397—118no—
291#394—118no—
292#394—118no—
293#392—118no—
294#391—112no—
295#391—112no—
296#390—112no—
297#390—114no—
298#390—112no—
299#389—114no—
300#388—118no—
301#388—118no—
302#387—118no—
303#386—118no—
304#386—118no—
305#385—118no—
306#384—111no—
307#384—111no—
308#382—112no—
309#380—114no—
310C4×C22⋊C4C2×D1114yes—
311C4×C22⋊C4C2×D1112yes—
312C4×C22⋊C4C2×D1112yes—
313C2×#95C2×D1112yes—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—416no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11#53214yes—
325C22×C11C23×D411yescharacteristic
326C22×C11C22×#4112yes—
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11C2×H(5,𝔽2)11yescharacteristic
329C22×C11#58512yes—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—48no—
334C2×D11—48no—
335C4×C11—22no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—24no—
339C4×C11—44no—
340C4×C11#53414yes—
341Dic11—44no—
342Dic11—44no—
343Dic11—44no—
344C25C22×D1111yescharacteristic
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—112no—
349C22×D4—114no—
350C22×D4—114no—
351C22×D4—114no—
352C22×D4—112no—
353C22×D4—114no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—114no—
357C23×C4D4418yescomplemented
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1112yes—
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1112yes—
363C23×C4C22×D1112yes—
364C4⋊Q8—442no—
365#127—442no—
366#124—444no—
367#123—2216no—
368C22⋊Q8—228no—
369C22⋊Q8—228no—
370#121—228no—
371#121—228no—
372#121—2216no—
373#120—2216no—
374C4×D4—2216no—
375C4×D4—2216no—
376#117—228no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—114no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—118no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4C22×D1114yes—
394C2×C22⋊C4C22×D1114yes—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—114no—
398C2×C42C22×D1112yes—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1112yes—
402C2×C42C22×D1112yes—
403#95—118no—
404#95—118no—
405#95—118no—
406#95C22×D1114yes—
407#95C22×D1114yes—
408C2×C11—24no—
409C2×C11—44no—
410C2×C11C2×#53211yescharacteristic
411C2×C11C2×#53411yescharacteristic
412C2×C11#344911yescharacteristic
413C2×C11#350512yes—
414C2×C11#350612yes—
415D11—84no—
416C24—24no—
417C24—41no—
418C24—41no—
419C24—42no—
420C24—114no—
421C24C2×D4414yes—
422C24C23×D1112yes—
423C24C23×D1111yescharacteristic
424#41—4432no—
425C2×Q8—224no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×D4—228no—
429C2×D4—228no—
430C2×D4—228no—
431C2×D4—2216no—
432C2×D4—224no—
433C2×D4—228no—
434C2×D4—224no—
435C2×D4—224no—
436C2×D4—444no—
437C2×D4—444no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—448no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—416no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—228no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4C2×D4418yes—
462C22×C4C2×D4414yes—
463C22×C4C2×D4414yes—
464C22×C4C2×D4418yes—
465C22×C4#433918yescomplemented
466C22×C4C23×D1114yes—
467C22×C4C23×D1112yes—
468C22×C4C23×D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1111yescharacteristic
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—228no—
475C4⋊C4—228no—
476C4⋊C4—228no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—228no—
482C22⋊C4—228no—
483C22⋊C4—228no—
484C22⋊C4—228no—
485C22⋊C4—228no—
486C22⋊C4—2216no—
487C22⋊C4—448no—
488C22⋊C4—448no—
489C42—24no—
490C42—22no—
491C42—22no—
492C42—42no—
493C42—42no—
494C42—228no—
495C11#3503211yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—22no—
499C23—28no—
500C23—24no—
501C23—22no—
502C23—22no—
503C23—24no—
504C23—44no—
505C23—44no—
506C23—48no—
507C23—48no—
508C23—224no—
509C23—228no—
510C23—224no—
511C23—224no—
512C23—228no—
513C23C22×D4414yes—
514C23C22×D4412yes—
515C23C2×#433914yes—
516C23C24×D1111yescharacteristic
517Q8—448no—
518D4—4416no—
519D4—4416no—
520D4—4416no—
521D4—448no—
522D4—888no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—216no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—48no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—228no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—228no—
547C2×C4—4416no—
548C2×C4C22×D4414yes—
549C2×C4C22×D4412yes—
550C2×C4C22×D4412yes—
551C2×C4C2×#433914yes—
552C2×C4C2×#433914yes—
553C2×C4#6703712yes—
554C2×C4#6703712yes—
555C22—22no—
556C22—24no—
557C22—22no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—416no—
563C22—44no—
564C22—44no—
565C22—444no—
566C22—444no—
567C22—448no—
568C22—444no—
569C22—448no—
570C22#1062300814yes—
571C22C23×D4411yescharacteristic
572C22C22×#433912yes—
573C22C2×#6703711yescharacteristic
574C22C2×#6703711yescharacteristic
575C22#1062345312yes—
576C4—24no—
577C4—22no—
578C4—24no—
579C4—24no—
580C4—44no—
581C4—444no—
582C4—444no—
583C4—444no—
584C4#1062302414yes—
585C2—24no—
586C2—44no—
587C2—884no—
588C2C2×#1062300811yescharacteristic
589C2C2×#1062302411yescharacteristic
590C2#1308194911yescharacteristic
591C2#1308245512yes—
592C2#1308246812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C4×C11×C22⋊C4C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#35032
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13076968C2semidirect
3. #13076961C2semidirect
4. #13076917C2semidirect
5. #13074350C2semidirect
6. #13074222C2semidirect
7. #13073078C2semidirect
8. #13073069C2semidirect
9. #13072244C2semidirect
10. #13072235C2semidirect
11. #13071319C2semidirect
12. C2×C4×C11×C22⋊C4C2semidirect
29. C2×#66928C22semidirect
30. C2×#66927C22semidirect
31. C2×#66922C22semidirect
42. #10622553C22semidirect
43. #10622552C22semidirect
44. #10622552C22semidirect
45. #10622552C22semidirect
46. #10622549C22semidirect
47. #10622548C22semidirect
48. #10622548C22semidirect
49. #10622542C22semidirect
50. #10622542C22semidirect
51. #10622541C22semidirect
52. #10622283C22semidirect
53. #10622281C22semidirect
54. #10622278C22semidirect
55. #10622266C22semidirect
59. C23×C4×C11D4semidirect
147. C22×C4×C11#41semidirect
211. C2×C4×C22⋊C4D11semidirect
357. C23×C4D44semidirect
465. C22×C4#4339semidirect
495. C11#35032semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130769682
#130769612
#130769172
#130743502
#130742222
#130730782
#130730692
#130722442
#130722352
#130713192
C2×C4×C11×C22⋊C42
#3503211