Finite Group Databasebeta

← #14917365

Subgroups — #14917365

Order 2816.

2390 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×#10623066C211yesmaximal, characteristic
2#13071769C214yesmaximal, complemented
3#13071712C212yesmaximal, complemented
4#13071680C212yesmaximal, complemented
5#13071629C214yesmaximal, complemented
6#13071591C212yesmaximal, complemented
7#13071516C212yesmaximal, complemented
8#13071405C214yesmaximal, complemented
9#13071305C212yesmaximal, complemented
10#13071289C214yesmaximal, complemented
11#13071122C212yesmaximal, complemented
12#13071100C211yesmaximal, characteristic, complemented
13C11×#2314C211yesmaximal, characteristic, complemented
14C2×C11×#117C2211yescharacteristic
15C2×#66983C2212yes—
16C2×#66979C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18#10623066C4116yescomplemented
19C2×#66947C2214yes—
20C2×#66946C2212yes—
21C2×#66946C2212yes—
22C2×C4⋊C4×D11C2214yes—
23C2×#66937C2214yes—
24C2×(C22⋊D11)⋊C4C2214yes—
25C2×#66927C2211yescharacteristic
26C2×C4×D44C2214yes—
27C2×C4×D44C2212yes—
28C2×#66923C2211yescharacteristic
29C11×#388C2214yes—
30C11×#387C2214yes—
31C11×#384C2211yescharacteristic
32C11×#382C2211yescharacteristic
33C11×#380C2212yes—
34C4×C11×C4⋊C4C2212yes—
35#10622602C2214yes—
36#10622602C2214yes—
37#10622601C2212yes—
38#10622601C2212yes—
39#10622600C2214yes—
40#10622598C2212yes—
41#10622598C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622586C2212yes—
46#10622571C2214yes—
47#10622570C2214yes—
48#10622569C2214yes—
49#10622563C2212yes—
50#10622563C2212yes—
51#10622552C2214yes—
52C4×C4⋊Dic11C2212yes—
53C4×C4⋊Dic11C2212yes—
54#10622546C2214yes—
55C4×Dic11⋊C4C2214yes—
56#10622283C2214yes—
57#10622283C2214yes—
58#10622283C2214yes—
59#10622282C2214yes—
60#10622281C2214yes—
61#10622279C2214yes—
62#10622279C2214yes—
63#10622278C2214yes—
64#10622278C2214yes—
65#10622277C2214yes—
66#10622268C2214yes—
67#10622260C2214yes—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11C2314yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C22×D44C2312yes—
73C22×D44C2314yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C11×#117C2×C418yescomplemented
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2312yes—
84C2×C42×C11C2314yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11C2312yes—
88#66983C2×C4116yescomplemented
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97#66979—42no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11—42no—
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2312yes—
114#66947C2×C4132yescomplemented
115#66946—44no—
116#66946—44no—
117C4⋊C4×D11—48no—
118#66937C2×C4132yescomplemented
119(C22⋊D11)⋊C4—48no—
120#66927C2×C418yescomplemented
121C4×D44—48no—
122C4×D44C2×C4116yescomplemented
123#66923C2×C418yescomplemented
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2312yes—
135#34418—111nomaximal, Sylow
136C24×C11C2411yescharacteristic
137C23×D11C2414yes—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—44no—
148C2×C22⋊D11—44no—
149C2×C22⋊D11C22×C4116yes—
150C22×Dic11—24no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153C22×Dic11—42no—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2412yes—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—44no—
162C2×D44—44no—
163C2×D44C22×C418yes—
164C2×D44C22×C4116yes—
165C2×C4×D11—28no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11C22×C4116yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—44no—
177C11×C4⋊C4C22×C418yes—
178C11×C22⋊C4—44no—
179C11×C22⋊C4C22×C418yes—
180C42×C11—44no—
181C42×C11C22×C414yes—
182C42×C11C22×C414yes—
183C22⋊Dic11—42no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—44no—
186(C2×D11)⋊C4—44no—
187(C2×D11)⋊C4—44no—
188(C2×D11)⋊C4—44no—
189(C2×D11)⋊C4—44no—
190(C2×D11)⋊C4C22×C4116yes—
191(C2×D11)⋊C4C22×C4116yes—
192C4⋊Dic11—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—41no—
197C4⋊Dic11—41no—
198C4⋊Dic11C22×C418yes—
199Dic11⋊C4—28no—
200Dic11⋊C4—44no—
201Dic11⋊C4C22×C4116yes—
202C4×Dic11—24no—
203C4×Dic11—24no—
204C4×Dic11—44no—
205C4×Dic11—42no—
206C4×Dic11—44no—
207C2×#540—111no—
208#2377—114no—
209#2370—112no—
210#2366—112no—
211#2361—114no—
212#2357—112no—
213D4×C4⋊C4—112no—
214#2335—114no—
215#2324—112no—
216#2322—114no—
217#2314D1111yescharacteristic, complemented
218C4×#121—112no—
219#2296—111no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11C23×C412yes—
225C23×C11C2511yescharacteristic
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11C23×C418yes—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—28no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11C23×C414yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C414yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C112−1+412yes—
252C22⋊D11—416no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—44no—
267C2×Dic11—44no—
268C2×Dic11C23×C418yes—
269C2×Dic11H(5,𝔽2)14yes—
270D44—216no—
271D44—416no—
272C4×D11—416no—
273C4×D11—88no—
274C4×D11—88no—
275#540—1116no—
276C2×#127—111no—
277C2×#125—111no—
278C2×#123—114no—
279C2×#121—112no—
280C2×#121—114no—
281C2×C4×D4—112no—
282C2×C4×D4—112no—
283C2×C4×D4—114no—
284C2×C4×D4—112no—
285C2×C4×D4—114no—
286C2×#117—111no—
287C2×#117C2×D1111yescharacteristic
288C22×C4⋊C4—114no—
289C22×C42—111no—
290#390—112no—
291#390—112no—
292#390—114no—
293#390—114no—
294#389—112no—
295#389—112no—
296#389—112no—
297#389—112no—
298#389—114no—
299#388—114no—
300#388—114no—
301#388—114no—
302#388—114no—
303#388C2×D1114yes—
304#387—114no—
305#387—114no—
306#387C2×D1114yes—
307#386—114no—
308#386—114no—
309#386—114no—
310#386—114no—
311#385—114no—
312#385—114no—
313#385—112no—
314#385—112no—
315#385—114no—
316#384C2×D1111yescharacteristic
317#382C2×D1111yescharacteristic
318#381—114no—
319#380—114no—
320#380C2×D1112yes—
321C4×C4⋊C4—112no—
322C4×C4⋊C4—112no—
323C4×C4⋊C4—114no—
324C4×C4⋊C4—112no—
325C4×C4⋊C4—112no—
326C4×C4⋊C4C2×D1112yes—
327C4×C22⋊C4—114no—
328C4×C22⋊C4—114no—
329C22×C11—22no—
330C22×C11—24no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11C24×C411yescharacteristic
335C22×C11C2×H(5,𝔽2)11yescharacteristic
336C22×C11C2×H(5,𝔽2)12yes—
337C22×C11C2×2−1+411yescharacteristic
338C22×C11#58512yes—
339C2×D11—28no—
340C2×D11—28no—
341C2×D11—28no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C4×C11—22no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—44no—
350C4×C11—44no—
351C4×C11#52014yes—
352Dic11—28no—
353Dic11—24no—
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357C22×D4—114no—
358C22×D4—112no—
359C22×D4—114no—
360C23×C4—114no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—114no—
364C23×C4—114no—
365C23×C4C22×D1111yescharacteristic
366#127—118no—
367#125—118no—
368#123—1132no—
369#121—1116no—
370#121—1132no—
371C4×D4—1116no—
372C4×D4—448no—
373C4×D4—444no—
374C4×D4—444no—
375C4×D4—448no—
376#117—442no—
377#117C4×D1118yescomplemented
378C2×C4⋊C4—112no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—448no—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C4⋊C4C22×D1114yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—112no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4C22×D1114yes—
403C2×C22⋊C4C22×D1112yes—
404C2×C42—112no—
405C2×C42—112no—
406C2×C42—114no—
407C2×C42—112no—
408C2×C42—114no—
409C2×C42—442no—
410C2×C42C22×D1114yes—
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#95—112no—
414#95—114no—
415#95—112no—
416#95—114no—
417#95—112no—
418#95—114no—
419#95—114no—
420#95—112no—
421#95C22×D1114yes—
422#95C22×D1114yes—
423#95C22×D1114yes—
424C2×C11—42no—
425C2×C11C2×#52011yescharacteristic
426C2×C11C4×H(5,𝔽2)12yes—
427C2×C11#353711yescharacteristic
428C2×C11#353911yescharacteristic
429C2×C11#355412yes—
430D11—48no—
431C24—114no—
432C24C23×D1111yescharacteristic
433C2×D4—1116no—
434C2×D4—118no—
435C2×D4—1116no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—444no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—444no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—114no—
445C22×C4—112no—
446C22×C4—1116no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—228no—
451C22×C4—224no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4—444no—
455C22×C4—444no—
456C22×C4—444no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—442no—
462C22×C4C2×C4×D1114yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—44no—
472C4⋊C4—118no—
473C4⋊C4—1116no—
474C4⋊C4—224no—
475C4⋊C4—228no—
476C4⋊C4—224no—
477C4⋊C4—444no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C4⋊C4C2×C4×D1118yes—
483C22⋊C4—44no—
484C22⋊C4—1116no—
485C22⋊C4—1116no—
486C22⋊C4—228no—
487C22⋊C4—444no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C22⋊C4—442no—
493C22⋊C4C2×C4×D1118yes—
494C42—44no—
495C42—224no—
496C42—224no—
497C42—442no—
498C42—444no—
499C42—444no—
500C42C2×C4×D1114yes—
501C42C2×C4×D1114yes—
502C11#3441811yescharacteristic, complemented, Sylow
503C23—21no—
504C23—21no—
505C23—22no—
506C23—22no—
507C23—118no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23C22×C4×D1112yes—
515C23C24×D1111yescharacteristic
516D4—2216no—
517D4—4416no—
518D4—4416no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—28no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—118no—
533C2×C4—114no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—4416no—
548C2×C4—444no—
549C2×C4—444no—
550C2×C4—888no—
551C2×C4—888no—
552C2×C4C22×C4×D1114yes—
553C2×C4C22×C4×D1114yes—
554C2×C4C22×C4×D1112yes—
555C2×C4C22×C4×D1112yes—
556C2×C4#6704212yes—
557C2×C4#6704312yes—
558C22—22no—
559C22—24no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—228no—
564C22—228no—
565C22—228no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22C23×C4×D1111yescharacteristic
571C22C2×#6704211yescharacteristic
572C22C2×#6704311yescharacteristic
573C22D11×H(5,𝔽2)12yes—
574C22#1062345712yes—
575C4—22no—
576C4—24no—
577C4—24no—
578C4—44no—
579C4—44no—
580C4—228no—
581C4—224no—
582C4—442no—
583C4—442no—
584C4—442no—
585C4#1062305414yes—
586C2—42no—
587C2—448no—
588C2C2×#1062305411yescharacteristic
589C2#1308182212yes—
590C2#1308285411yescharacteristic
591C2#1308287811yescharacteristic
592C2#1308308512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2314C2
socle, cosocleC23×C11C25
prime radicalC2×#10623066C2
hypercenter#2314D11
hypocenterC11#34418
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13071769C2semidirect
3. #13071712C2semidirect
4. #13071680C2semidirect
5. #13071629C2semidirect
6. #13071591C2semidirect
7. #13071516C2semidirect
8. #13071405C2semidirect
9. #13071305C2semidirect
10. #13071289C2semidirect
11. #13071122C2semidirect
12. #13071100C2semidirect
13. C11×#2314C2semidirect
18. #10623066C4semidirect
77. C11×#117C2×C4semidirect
88. #66983C2×C4semidirect
114. #66947C2×C4semidirect
118. #66937C2×C4semidirect
120. #66927C2×C4semidirect
122. C4×D44C2×C4semidirect
123. #66923C2×C4semidirect
217. #2314D11semidirect
377. #117C4×D11semidirect
502. C11#34418semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
#130717692
#130717122
#130716802
#130716292
#130715912
#130715162
#130714052
#130713052
#130712892
#130711222
#130711002
C11×#23142
#3441811