Finite Group Databasebeta

← #14920937

Subgroups — #14920937

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074646C214yesmaximal, complemented
2#13074601C214yesmaximal, complemented
3#13074591C211yesmaximal, characteristic, complemented
4#13074577C212yesmaximal, complemented
5#13074447C211yesmaximal, characteristic, complemented
6#13074408C212yesmaximal, complemented
7#13074367C211yesmaximal, characteristic
8#13071872C214yesmaximal, complemented
9#13071859C214yesmaximal, complemented
10#127×Dic11C211yesmaximal, characteristic, complemented
11#125×Dic11C211yesmaximal, characteristic, complemented
12#13071132C212yesmaximal, complemented
13#13071078C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic, complemented
15C11×#2641C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×#66991C2212yes—
19C2×D4×Dic11C2212yes—
20C2×D4×Dic11C2214yes—
21C2×(C22⋊D11)⋊C4C2214yes—
22C2×#66930C2214yes—
23C2×#66925C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C11×#394C2214yes—
27C11×#394C2214yes—
28C11×#390C2212yes—
29C11×#390C2212yes—
30C11×#376C2211yescharacteristic
31#10622836C2214yes—
32#10622835C2214yes—
33#10622834C2212yes—
34#10622834C2214yes—
35#10622834C2212yes—
36#10622607C2214yes—
37#10622600C2212yes—
38#10622598C2212yes—
39#10622597C2214yes—
40#10622594C2214yes—
41C4⋊C4×Dic11C2214yes—
42C4⋊C4×Dic11C2212yes—
43#10622586C2212yes—
44#10622574C2214yes—
45#10622572C2214yes—
46#10622569C2214yes—
47#10622566C2214yes—
48#10622565C2214yes—
49#10622565C2214yes—
50#10622565C2214yes—
51#10622562C2214yes—
52#10622561C2214yes—
53#10622558C2214yes—
54#10622558C2214yes—
55#10622557C2214yes—
56C22⋊C4×Dic11C2214yes—
57C22⋊C4×Dic11C2214yes—
58#10622549C2211yescharacteristic
59#10622548C2211yescharacteristic
60#10622545C2211yescharacteristic
61C42×Dic11C2211yescharacteristic
62C42×Dic11C2211yescharacteristic
63#10622541C2212yes—
64#10622541C2212yes—
65#10622279C2212yes—
66#10622279C2212yes—
67#10622273C2214yes—
68#10622270C2214yes—
69#10622262C2212yes—
70#10622262C2212yes—
71C22×D4×C11C2312yes—
72C22×D4×C11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11C2314yes—
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C11×#127—24no—
79C11×#125—24no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95#66991—28no—
96D4×Dic11—28no—
97D4×Dic11—48no—
98C2×(C2×D11)⋊C4C2312yes—
99C2×(C2×D11)⋊C4C2312yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4C2312yes—
106C2×Dic11⋊C4C2312yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2311yescharacteristic
120(C22⋊D11)⋊C4—48no—
121#66930—48no—
122#66925—24no—
123#66925—24no—
124C42×D11—24no—
125C11×#95C2312yes—
126C11×#95C2312yes—
127C11⋊#95C2312yes—
128C11⋊#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#34621—111nomaximal, Sylow
137C24×C11C2414yes—
138C23×D11C2411yescharacteristic
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—28no—
142C2×D4×C11—24no—
143C2×D4×C11—44no—
144C2×D4×C11—44no—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2412yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—28no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—44no—
154C22×Dic11—28no—
155C22×Dic11—28no—
156C22×Dic11—28no—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2411yescharacteristic
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2411yescharacteristic
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—24no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—42no—
170C2×C4×D11#4114yes—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—24no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—44no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—44no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11#4114yes—
180C22⋊Dic11—28no—
181C22⋊Dic11—28no—
182C22⋊Dic11—44no—
183C22⋊Dic11—44no—
184C22⋊Dic11—44no—
185C22⋊Dic11—44no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—44no—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—44no—
192C4⋊Dic11—44no—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197Dic11⋊C4—44no—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—24no—
201C4×Dic11—28no—
202C4×Dic11—24no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11#4114yes—
208#2651—114no—
209#2648—114no—
210#2647—111no—
211#2644—112no—
212#2641D1111yescharacteristic, complemented
213#2629—111no—
214#2624—112no—
215#2619—111no—
216#2395—114no—
217#2392—114no—
218C4×#127—111no—
219C4×#125—111no—
220C4×#121—112no—
221#2293—112no—
222C4×#117—111no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11C2511yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11C2×#4112yes—
236D4×C11—416no—
237D4×C11—48no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11C2×#4114yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4112yes—
254C22⋊D11—416no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—416no—
271C2×Dic11C2×#4112yes—
272C2×Dic11C2×#4112yes—
273C2×Dic11C2×#4112yes—
274C2×Dic11H(5,𝔽2)14yes—
275C4×D11—28no—
276C4×D11—44no—
277C4×D11—44no—
278C2×#127C2×D1111yescharacteristic
279C2×#125C2×D1111yescharacteristic
280C2×#121—112no—
281C2×C4×D4—112no—
282C2×C4×D4—114no—
283C2×C4×D4—114no—
284C2×#117—114no—
285C2×#117—111no—
286C2×#117—111no—
287C22×C42—111no—
288#400—114no—
289#399—114no—
290#398—114no—
291#398—114no—
292#397—114no—
293#397—114no—
294#397—114no—
295#397—114no—
296#396—114no—
297#396—114no—
298#394—114no—
299#394—114no—
300#394—114no—
301#394C2×D1114yes—
302#394C2×D1114yes—
303#392—114no—
304#390—112no—
305#390—114no—
306#390—112no—
307#390C2×D1112yes—
308#390C2×D1112yes—
309#389—112no—
310#389—112no—
311#389—112no—
312#389—112no—
313#388—114no—
314#388—114no—
315#388—114no—
316#387—114no—
317#386—114no—
318#384—111no—
319#382—111no—
320#380—112no—
321C4×C4⋊C4—114no—
322C4×C4⋊C4—112no—
323C4×C4⋊C4—112no—
324C4×C4⋊C4—112no—
325C4×C22⋊C4—114no—
326C4×C22⋊C4—114no—
327C4×C22⋊C4—112no—
328C4×C22⋊C4—112no—
329#376—111no—
330#376C2×D1111yescharacteristic
331C43—111no—
332C43—111no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11C22×#4111yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C2×H(5,𝔽2)12yes—
344C22×C11#58512yes—
345C2×D11—22no—
346C2×D11—24no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—42no—
350C4×C11—24no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—44no—
354C4×C11—42no—
355C4×C11#52914yes—
356Dic11—22no—
357Dic11—22no—
358Dic11—44no—
359Dic11—42no—
360Dic11—42no—
361Dic11—44no—
362Dic11#54014yes—
363C22×D4—114no—
364C22×D4C22×D1112yes—
365C22×D4C22×D1114yes—
366C23×C4—111no—
367C23×C4—114no—
368C23×C4—111no—
369C23×C4—111no—
370#127—24no—
371#125—24no—
372#121—228no—
373C4×D4—228no—
374C4×D4—448no—
375C4×D4—448no—
376#117—224no—
377#117—224no—
378#117—448no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4C22×D1112yes—
389C2×C4⋊C4C22×D1114yes—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4C22×D1114yes—
400C2×C22⋊C4C22×D1114yes—
401C2×C22⋊C4C22×D1114yes—
402C2×C22⋊C4C22×D1114yes—
403C2×C42—111no—
404C2×C42—112no—
405C2×C42—114no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—112no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—112no—
412C2×C42—112no—
413C2×C42—224no—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#95—112no—
418#95—112no—
419#95—114no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95—114no—
425#95—114no—
426#95C22×D1112yes—
427#95C22×D1112yes—
428C2×C11—84no—
429C2×C11C2×#52911yescharacteristic
430C2×C11C2×#54011yescharacteristic
431C2×C11#345511yescharacteristic
432C2×C11#346012yes—
433C2×C11#346012yes—
434D11—42no—
435C24—111no—
436C24C23×D1114yes—
437C2×D4—28no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—228no—
444C2×D4—444no—
445C2×D4—444no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—114no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—228no—
458C22×C4—228no—
459C22×C4—228no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—442no—
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1111yescharacteristic
467C22×C4C23×D1112yes—
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—28no—
470C4⋊C4—24no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—444no—
476C4⋊C4—444no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C22⋊C4—44no—
481C22⋊C4—44no—
482C22⋊C4—44no—
483C22⋊C4—44no—
484C22⋊C4—224no—
485C22⋊C4—228no—
486C22⋊C4—228no—
487C22⋊C4—224no—
488C22⋊C4—444no—
489C22⋊C4—444no—
490C22⋊C4—444no—
491C22⋊C4—444no—
492C22⋊C4—444no—
493C42—22no—
494C42—22no—
495C42—114no—
496C42—222no—
497C42—222no—
498C42—224no—
499C42—228no—
500C42—224no—
501C42—222no—
502C42—222no—
503C42—442no—
504C42—442no—
505C42#434114yes—
506C11#3462111yescharacteristic, complemented, Sylow
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—112no—
515C23—221no—
516C23—221no—
517C23—222no—
518C23—222no—
519C23C24×D1111yescharacteristic
520D4—416no—
521D4—48no—
522D4—4416no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—112no—
536C2×C4—114no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—444no—
556C2×C4—444no—
557C2×C4—4416no—
558C2×C4C2×#434114yes—
559C2×C4C2×#434112yes—
560C2×C4#41×D1112yes—
561C2×C4#41×D1112yes—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—222no—
570C22—224no—
571C22—441no—
572C22—441no—
573C22—442no—
574C22C22×#434111yescharacteristic
575C22C2×#41×D1111yescharacteristic
576C22C2×#41×D1111yescharacteristic
577C22D11×H(5,𝔽2)12yes—
578C22#1062345512yes—
579C4—24no—
580C4—41no—
581C4—41no—
582C4—44no—
583C4—42no—
584C4—114no—
585C4—222no—
586C4—222no—
587C4—444no—
588C4—442no—
589C4—444no—
590C4—442no—
591C4#1062321114yes—
592C2—84no—
593C2—442no—
594C2C2×#1062321111yescharacteristic
595C2D11×#54011yescharacteristic
596C2#1308200011yescharacteristic
597C2#1308202912yes—
598C2#1308203112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2641C2
prime radical#13074367C2
hypercenter#2641D11
hypocenterC11#34621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2641

Complements

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

NH ≅ G/Ntype
1. #13074646C2semidirect
2. #13074601C2semidirect
3. #13074591C2semidirect
4. #13074577C2semidirect
5. #13074447C2semidirect
6. #13074408C2semidirect
8. #13071872C2semidirect
9. #13071859C2semidirect
10. #127×Dic11C2semidirect
11. #125×Dic11C2semidirect
12. #13071132C2semidirect
13. #13071078C2semidirect
14. #13070955C2semidirect
15. C11×#2641C2semidirect
212. #2641D11semidirect
506. C11#34621semidirect

Maximal subgroups

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

subgroupindex
#130746462
#130746012
#130745912
#130745772
#130744472
#130744082
#130743672
#130718722
#130718592
#127×Dic112
#125×Dic112
#130711322
#130710782
#130709552
C11×#26412
#3462111