Finite Group Databasebeta

← #14920929

Subgroups — #14920929

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#13074648C214yesmaximal, complemented
2#13074603C214yesmaximal, complemented
3#13074579C212yesmaximal, complemented
4#13074559C211yesmaximal, characteristic, complemented
5#13074449C211yesmaximal, characteristic, complemented
6#13074410C212yesmaximal, complemented
7#13074369C211yesmaximal, characteristic
8#13071882C214yesmaximal, complemented
9#13071857C214yesmaximal, complemented
10#13071178C211yesmaximal, characteristic, complemented
11#13071171C211yesmaximal, characteristic, complemented
12#13071124C212yesmaximal, complemented
13#13071074C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic, complemented
15C11×#2647C211yesmaximal, characteristic, complemented
16C2×#66948C2212yes—
17C2×#66946C2212yes—
18C2×#66946C2214yes—
19C2×#66946C2214yes—
20C2×#66945C2214yes—
21C2×#66927C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×#66923C2211yescharacteristic
26C11×#400C2214yes—
27C11×#398C2214yes—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#384C2211yescharacteristic
31C11×#382C2211yescharacteristic
32C11×#376C2211yescharacteristic
33#10622607C2214yes—
34#10622607C2214yes—
35#10622606C2214yes—
36#10622605C2214yes—
37#10622604C2214yes—
38#10622603C2214yes—
39#10622603C2214yes—
40#10622601C2212yes—
41#10622601C2214yes—
42#10622601C2212yes—
43#10622600C2212yes—
44#10622598C2212yes—
45#10622596C2214yes—
46C4⋊C4×Dic11C2212yes—
47#10622586C2212yes—
48#10622552C2212yes—
49#10622552C2212yes—
50#10622545C2211yescharacteristic
51C42×Dic11C2211yescharacteristic
52C42×Dic11C2211yescharacteristic
53#10622288C2214yes—
54#10622288C2214yes—
55#10622287C2214yes—
56#10622285C2214yes—
57#10622285C2214yes—
58#10622285C2214yes—
59#10622285C2214yes—
60#10622284C2214yes—
61#10622283C2214yes—
62#10622279C2214yes—
63#10622279C2214yes—
64#10622279C2212yes—
65#10622279C2212yes—
66#10622278C2214yes—
67#10622265C2214yes—
68#10622262C2212yes—
69#10622262C2214yes—
70#10622262C2212yes—
71C22×D44C2312yes—
72C22×D44C2314yes—
73C22×D44C2314yes—
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2314yes—
76C22×C4×D11C2311yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×(C2×D11)⋊C4C2312yes—
87C2×(C2×D11)⋊C4C2312yes—
88C2×(C2×D11)⋊C4C2314yes—
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—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2312yes—
103C2×Dic11⋊C4C2312yes—
104C2×Dic11⋊C4C2314yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2311yescharacteristic
115#66948—28no—
116#66946—28no—
117#66946—48no—
118#66946—48no—
119#66945—48no—
120#66927—24no—
121#66925—24no—
122#66925—24no—
123C42×D11—24no—
124#66923—24no—
125C11×#95C2314yes—
126C11×#95C2312yes—
127C11×#95C2312yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#34621—111nomaximal, Sylow
137C23×D11C2414yes—
138C23×D11C2411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2414yes—
141C22×C4×C11C2411yescharacteristic
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11C2412yes—
147C22×Dic11C2412yes—
148C22×Dic11C2414yes—
149C22×Dic11C2411yescharacteristic
150C22×Dic11C2411yescharacteristic
151C22×Dic11C2411yescharacteristic
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—44no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—28no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—42no—
170C2×C4×D11#4114yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C4⋊C4—44no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11#4114yes—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—44no—
184(C2×D11)⋊C4—44no—
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)⋊C4—44no—
191(C2×D11)⋊C4—44no—
192C4⋊Dic11—24no—
193C4⋊Dic11—44no—
194Dic11⋊C4—24no—
195Dic11⋊C4—28no—
196Dic11⋊C4—24no—
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#2647D1111yescharacteristic, complemented
211#2644—112no—
212#2641—111no—
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×C11C2511yescharacteristic
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11C2×#4112yes—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11C2×#4114yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4112yes—
254C2×C4×C11C2×#4112yes—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11C2×#4112yes—
268C2×Dic11C2×#4112yes—
269C2×Dic11C2×#4112yes—
270C2×Dic11H(5,𝔽2)14yes—
271D44—416no—
272D44—416no—
273D44—48no—
274C4×D11—28no—
275C4×D11—44no—
276C4×D11—44no—
277C4×D11—416no—
278C2×#127—111no—
279C2×#125—111no—
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#400C2×D1114yes—
289#399—114no—
290#398—114no—
291#398C2×D1114yes—
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#394—114no—
302#394—114no—
303#392—114no—
304#390—112no—
305#390—114no—
306#390—112no—
307#390—112no—
308#390—112no—
309#389—112no—
310#389—112no—
311#389C2×D1112yes—
312#389C2×D1112yes—
313#388—114no—
314#388—114no—
315#388—114no—
316#387—114no—
317#386—114no—
318#384C2×D1111yescharacteristic
319#382C2×D1111yescharacteristic
320#380—112no—
321C4×C4⋊C4—112no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4—112no—
324C4×C4⋊C4—112no—
325C4×C22⋊C4—112no—
326C4×C22⋊C4—114no—
327C4×C22⋊C4—112no—
328C4×C22⋊C4—114no—
329#376—111no—
330#376C2×D1111yescharacteristic
331C43—111no—
332C43—111no—
333C22×C11C22×#4111yescharacteristic
334C22×C11C22×#4111yescharacteristic
335C22×C11C22×#4111yescharacteristic
336C22×C11C2×H(5,𝔽2)12yes—
337C22×C11#58512yes—
338C2×D11—22no—
339C2×D11—24no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—42no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C4×C11—24no—
351C4×C11—41no—
352C4×C11—44no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—44no—
356C4×C11#52914yes—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360Dic11—42no—
361Dic11—44no—
362Dic11#54014yes—
363C22×D4—112no—
364C22×D4—114no—
365C22×D4—114no—
366C23×C4—111no—
367C23×C4—114no—
368C23×C4—111no—
369C23×C4—111no—
370#127—224no—
371#125—224no—
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—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4C22×D1112yes—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C4⋊C4C22×D1114yes—
390C2×C22⋊C4—112no—
391C2×C22⋊C4—112no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4—114no—
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#95C22×D1112yes—
424#95C22×D1112yes—
425#95C22×D1114yes—
426#95C22×D1114yes—
427#95C22×D1114yes—
428C2×C11C2×#52911yescharacteristic
429C2×C11C2×#54011yescharacteristic
430C2×C11#345511yescharacteristic
431C2×C11#346012yes—
432C2×C11#346012yes—
433D11—42no—
434D11—84no—
435C24—111no—
436C24—114no—
437C2×D4—228no—
438C2×D4—228no—
439C2×D4—224no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—444no—
443C2×D4—444no—
444C2×D4—444no—
445C2×D4—444no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—114no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—228no—
456C22×C4—228no—
457C22×C4—224no—
458C22×C4—228no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—442no—
462C22×C4C23×D1111yescharacteristic
463C22×C4C23×D1114yes—
464C22×C4C23×D1111yescharacteristic
465C22×C4C23×D1114yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1112yes—
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—24no—
470C4⋊C4—24no—
471C4⋊C4—44no—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—228no—
477C4⋊C4—224no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C22⋊C4—228no—
481C22⋊C4—228no—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—444no—
487C22⋊C4—444no—
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#434314yes—
506C11#3462111yescharacteristic, complemented, Sylow
507C23—112no—
508C23—221no—
509C23—221no—
510C23—222no—
511C23—222no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—224no—
519C23C24×D1111yescharacteristic
520D4—4416no—
521D4—4416no—
522D4—448no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—112no—
539C2×C4—114no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—228no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—224no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—444no—
556C2×C4—4416no—
557C2×C4—444no—
558C2×C4C2×#434314yes—
559C2×C4C2×#434312yes—
560C2×C4#41×D1112yes—
561C2×C4#41×D1112yes—
562C22—222no—
563C22—224no—
564C22—441no—
565C22—441no—
566C22—442no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22—444no—
571C22—444no—
572C22—444no—
573C22—444no—
574C22C22×#434311yescharacteristic
575C22C2×#41×D1111yescharacteristic
576C22C2×#41×D1111yescharacteristic
577C22D11×H(5,𝔽2)12yes—
578C22#1062345712yes—
579C4—24no—
580C4—41no—
581C4—44no—
582C4—41no—
583C4—44no—
584C4—42no—
585C4—114no—
586C4—222no—
587C4—222no—
588C4—442no—
589C4—442no—
590C4—444no—
591C4#1062322214yes—
592C2—442no—
593C2—884no—
594C2C2×#1062322211yescharacteristic
595C2D11×#54011yescharacteristic
596C2#1308200711yescharacteristic
597C2#1308203612yes—
598C2#1308203912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2647C2
prime radical#13074369C2
hypercenter#2647D11
hypocenterC11#34621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2647

Complements

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

NH ≅ G/Ntype
1. #13074648C2semidirect
2. #13074603C2semidirect
3. #13074579C2semidirect
4. #13074559C2semidirect
5. #13074449C2semidirect
6. #13074410C2semidirect
8. #13071882C2semidirect
9. #13071857C2semidirect
10. #13071178C2semidirect
11. #13071171C2semidirect
12. #13071124C2semidirect
13. #13071074C2semidirect
14. #13070955C2semidirect
15. C11×#2647C2semidirect
210. #2647D11semidirect
506. C11#34621semidirect

Maximal subgroups

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

subgroupindex
#130746482
#130746032
#130745792
#130745592
#130744492
#130744102
#130743692
#130718822
#130718572
#130711782
#130711712
#130711242
#130710742
#130709552
C11×#26472
#3462111