Finite Group Databasebeta

← #14960210

Subgroups — #14960210

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076879C211yesmaximal, characteristic, complemented
2#13076800C211yesmaximal, characteristic, complemented
3#13076721C213yesmaximal, complemented
4#13076720C213yesmaximal, complemented
5#13076712C213yesmaximal, complemented
6#13076705C211yesmaximal, characteristic, complemented
7#13076610C213yesmaximal, complemented
8#13071919C211yesmaximal, characteristic, complemented
9#13071918C211yesmaximal, characteristic, complemented
10#13071894C211yesmaximal, characteristic, complemented
11#13071874C213yesmaximal, complemented
12#13071859C213yesmaximal, complemented
13#13071851C213yesmaximal, complemented
14#13071121C213yesmaximal, complemented
15C11×#2825C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×#66990C2213yes—
18C2×D4×Dic11C2213yes—
19C2×D4×Dic11C2213yescomplemented
20C2×(C22⋊D11)⋊C4C2213yes—
21C2×(C22⋊D11)⋊C4C2213yes—
22C2×#66930C2213yescomplemented
23C11×#401C2211yescharacteristic, complemented
24C11×#397C2213yescomplemented
25C11×#396C2211yescharacteristic
26C11×#394C2213yescomplemented
27C11×#392C2213yes—
28C11×#392C2211yescharacteristic, complemented
29C11×#386C2213yes—
30#10622836C2213yes—
31#10622836C2213yes—
32#10622835C2213yes—
33#10622835C2213yes—
34#10622835C2213yescomplemented
35#10622823C2213yes—
36#10622607C2213yes—
37#10622605C2213yes—
38#10622599C2213yescomplemented
39C4⋊C4×Dic11C2213yescomplemented
40#10622574C2213yes—
41#10622574C2213yes—
42#10622572C2213yes—
43#10622572C2213yes—
44#10622569C2213yes—
45#10622569C2213yes—
46#10622568C2213yes—
47#10622566C2213yes—
48#10622566C2213yescomplemented
49#10622565C2213yescomplemented
50#10622565C2213yescomplemented
51#10622562C2213yescomplemented
52#10622561C2213yes—
53#10622561C2213yescomplemented
54#10622561C2213yescomplemented
55C22⋊C4×Dic11C2213yes—
56C22⋊C4×Dic11C2213yescomplemented
57#10622290C2211yescharacteristic
58#10622289C2211yescharacteristic
59#10622288C2213yes—
60#10622288C2213yes—
61#10622281C2213yes—
62#10622281C2213yes—
63#10622279C2213yes—
64#10622279C2213yes—
65C11⋊#401C2211yescharacteristic, complemented
66#10622274C2213yescomplemented
67#10622271C2213yescomplemented
68#10622271C2213yescomplemented
69#10622270C2213yescomplemented
70#10622270C2213yescomplemented
71#10622262C2213yescomplemented
72#10622261C2211yescharacteristic, complemented
73C24×D11C2311yescharacteristic
74C22×D4×C11C2313yes—
75C22×D4×C11C2313yes—
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11C2313yes—
78C22×C22⋊D11C2313yes—
79C23×Dic11C2313yes—
80C23×Dic11C2311yescharacteristic
81C22×C4×D11—46no—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C11×C22⋊C4C2313yes—
92C2×C22⋊Dic11C2313yes—
93C2×C22⋊Dic11C2313yes—
94C2×C22⋊Dic11C2313yes—
95C2×C22⋊Dic11C2313yes—
96C2×C22⋊Dic11C2313yes—
97C2×C22⋊Dic11C2313yes—
98C2×C22⋊Dic11C2313yes—
99#66990—212no—
100D4×Dic11—46no—
101D4×Dic11—46no—
102C2×(C2×D11)⋊C4C2313yes—
103C2×(C2×D11)⋊C4C2313yes—
104C2×(C2×D11)⋊C4C2313yes—
105C2×(C2×D11)⋊C4C2313yes—
106C2×(C2×D11)⋊C4C2313yes—
107C2×(C2×D11)⋊C4C2313yes—
108C2×C4⋊Dic11C2313yes—
109C2×C4⋊Dic11C2313yes—
110C2×C4⋊Dic11C2313yes—
111C2×Dic11⋊C4C2313yes—
112C2×Dic11⋊C4C2313yes—
113C2×Dic11⋊C4C2313yes—
114C2×Dic11⋊C4C2313yes—
115C2×Dic11⋊C4C2313yes—
116C2×Dic11⋊C4C2313yes—
117C2×C4×Dic11C2313yes—
118C2×C4×Dic11C2313yes—
119C2×C4×Dic11C2313yes—
120(C22⋊D11)⋊C4—46no—
121(C22⋊D11)⋊C4—46no—
122#66930—46no—
123C11×#95C2311yescharacteristic
124C11×#95C2313yes—
125C11×#95C2313yes—
126C11×#95C2313yes—
127C11⋊#95C2313yes—
128C11⋊#95C2313yes—
129C11⋊#95C2313yes—
130C11⋊#95C2313yes—
131C11⋊#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137#36676—111nomaximal, Sylow
138C24×C11C2413yes—
139C24×C11C2411yescharacteristic
140C23×D11—43no—
141C23×D11—43no—
142C23×D11#4114yes—
143C23×D11C2411yescharacteristic
144C23×D11C2411yescharacteristic
145C2×D4×C11—26no—
146C2×D4×C11—43no—
147C2×D4×C11—43no—
148C2×D4×C11—43no—
149C2×D4×C11—43no—
150C2×D4×C11—43no—
151C22×C4×C11—43no—
152C22×C4×C11C2413yes—
153C22×C4×C11C2411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2413yes—
156C22×C4×C11C2413yes—
157C2×C22⋊D11—26no—
158C2×C22⋊D11—26no—
159C2×C22⋊D11—43no—
160C2×C22⋊D11—43no—
161C2×C22⋊D11—43no—
162C2×C22⋊D11—43no—
163C22×Dic11—26no—
164C22×Dic11—26no—
165C22×Dic11—26no—
166C22×Dic11—26no—
167C22×Dic11C2413yes—
168C22×Dic11C2413yes—
169C22×Dic11C2411yescharacteristic
170C22×Dic11C2413yes—
171C22×Dic11C2413yes—
172C22×Dic11C2411yescharacteristic
173C2×C4×D11—26no—
174C2×C4×D11—26no—
175C2×C4×D11—43no—
176C2×C4×D11—43no—
177C2×C4×D11—416no—
178C11×C4⋊C4—43no—
179C11×C22⋊C4—43no—
180C11×C22⋊C4—43no—
181C11×C22⋊C4—43no—
182C11×C22⋊C4—43no—
183C11×C22⋊C4—43no—
184C22⋊Dic11—26no—
185C22⋊Dic11—43no—
186C22⋊Dic11—43no—
187C22⋊Dic11—43no—
188C22⋊Dic11—43no—
189C22⋊Dic11—43no—
190C22⋊Dic11—43no—
191(C2×D11)⋊C4—26no—
192(C2×D11)⋊C4—26no—
193(C2×D11)⋊C4—43no—
194(C2×D11)⋊C4—43no—
195(C2×D11)⋊C4—43no—
196(C2×D11)⋊C4—43no—
197C4⋊Dic11—43no—
198C4⋊Dic11—43no—
199C4⋊Dic11—43no—
200Dic11⋊C4—43no—
201Dic11⋊C4—43no—
202Dic11⋊C4—43no—
203Dic11⋊C4—43no—
204Dic11⋊C4—43no—
205Dic11⋊C4—43no—
206C4×Dic11—26no—
207C4×Dic11—26no—
208C4×Dic11—26no—
209#2842—111no—
210#2834—111no—
211#2827—113no—
212#2827—113no—
213#2826—113no—
214#2825—111no—
215#2825D1111yescharacteristic, complemented
216#2812—113no—
217#2401—111no—
218#2401—111no—
219#2397—111no—
220#2395—113no—
221#2392—113no—
222#2392—113no—
223C4×#120—113no—
224C23×C11—23no—
225C23×C11—23no—
226C23×C11—23no—
227C23×C11—23no—
228C23×C11—23no—
229C23×C11—23no—
230C23×C11—23no—
231C23×C11—23no—
232C23×C11—23no—
233C23×C11C2×#4112yes—
234C23×C11C2511yescharacteristic
235C22×D11—23no—
236C22×D11—23no—
237C22×D11—23no—
238C22×D11—23no—
239C22×D11—412no—
240C22×D11—44no—
241C22×D11—412no—
242C22×D11C2×#4112yes—
243C22×D11C2×#4112yes—
244D4×C11—412no—
245D4×C11—412no—
246C2×C4×C11—23no—
247C2×C4×C11—23no—
248C2×C4×C11—23no—
249C2×C4×C11—23no—
250C2×C4×C11—23no—
251C2×C4×C11—23no—
252C2×C4×C11—23no—
253C2×C4×C11—23no—
254C2×C4×C11—23no—
255C2×C4×C11—23no—
256C2×C4×C11—23no—
257C2×C4×C11—44no—
258C22⋊D11—412no—
259C22⋊D11—412no—
260C2×Dic11—23no—
261C2×Dic11—23no—
262C2×Dic11—23no—
263C2×Dic11—23no—
264C2×Dic11—23no—
265C2×Dic11—23no—
266C2×Dic11—23no—
267C2×Dic11—23no—
268C2×Dic11—23no—
269C2×Dic11—23no—
270C2×Dic11—23no—
271C2×Dic11—23no—
272C2×Dic11—23no—
273C2×Dic11—44no—
274C2×Dic11—412no—
275C2×Dic11H(5,𝔽2)16yes—
276C4×D11—44no—
277C4×D11—44no—
278C4×D11—44no—
279C4×D11—44no—
280C24×C4—111no—
281C2×#120—113no—
282C2×C4×D4—113no—
283C2×C4×D4—113no—
284C2×C4×D4—113no—
285C2×C4×D4—113no—
286C2×#117—113no—
287#401—111no—
288#401C2×D1111yescharacteristic, complemented
289#400—113no—
290#400—113no—
291#400—113no—
292#399—113no—
293#399—113no—
294#399—111no—
295#398—113no—
296#398—113no—
297#398—113no—
298#397—113no—
299#397—113no—
300#397—113no—
301#397—113no—
302#397—113no—
303#397—113no—
304#397C2×D1113yescomplemented
305#396—113no—
306#396—113no—
307#396—113no—
308#396—113no—
309#396—111no—
310#396C2×D1111yescharacteristic
311#394—113no—
312#394—113no—
313#394—113no—
314#394—113no—
315#394—113no—
316#394—113no—
317#394—113no—
318#394C2×D1113yescomplemented
319#392—113no—
320#392—113no—
321#392C2×D1113yes—
322#392C2×D1111yescharacteristic, complemented
323#386—113no—
324#386—113no—
325#386C2×D1113yes—
326#385—113no—
327#385—113no—
328#385—113no—
329#379—113no—
330C4×C4⋊C4—113no—
331C4×C4⋊C4—113no—
332C4×C22⋊C4—113no—
333C4×C22⋊C4—113no—
334C4×C22⋊C4—113no—
335C4×C22⋊C4—113no—
336#376—111no—
337C22×C11—26no—
338C22×C11—41no—
339C22×C11—43no—
340C22×C11—43no—
341C22×C11—43no—
342C22×C11—43no—
343C22×C11—43no—
344C22×C11—43no—
345C22×C11—43no—
346C22×C11—43no—
347C22×C11C22×#4111yescharacteristic
348C22×C11C2×H(5,𝔽2)13yes—
349C22×C11#58513yes—
350C2×D11—26no—
351C2×D11—26no—
352C2×D11—416no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—43no—
356C2×D11—43no—
357C4×C11—43no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—43no—
361C4×C11—43no—
362Dic11—43no—
363Dic11—43no—
364Dic11—41no—
365Dic11—43no—
366Dic11—43no—
367Dic11#56014yes—
368C25—111no—
369C22×D4—113no—
370C22×D4—113no—
371C22×D4C22×D1113yes—
372C22×D4C22×D1113yes—
373C23×C4—113no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—446no—
380C23×C4C22×D1111yescharacteristic
381#120—2212no—
382C4×D4—446no—
383C4×D4—446no—
384C4×D4—446no—
385C4×D4—446no—
386#117—446no—
387C2×C4⋊C4—113no—
388C2×C4⋊C4—113no—
389C2×C4⋊C4—113no—
390C2×C4⋊C4—113no—
391C2×C4⋊C4—113no—
392C2×C4⋊C4—113no—
393C2×C4⋊C4—113no—
394C2×C4⋊C4—113no—
395C2×C4⋊C4—113no—
396C2×C4⋊C4C22×D1113yes—
397C2×C22⋊C4—113no—
398C2×C22⋊C4—113no—
399C2×C22⋊C4—113no—
400C2×C22⋊C4—113no—
401C2×C22⋊C4—113no—
402C2×C22⋊C4—113no—
403C2×C22⋊C4—113no—
404C2×C22⋊C4—113no—
405C2×C22⋊C4—113no—
406C2×C22⋊C4—113no—
407C2×C22⋊C4—113no—
408C2×C22⋊C4—113no—
409C2×C22⋊C4—113no—
410C2×C22⋊C4C22×D1113yes—
411C2×C22⋊C4C22×D1113yes—
412C2×C22⋊C4C22×D1113yes—
413C2×C22⋊C4C22×D1113yes—
414C2×C22⋊C4C22×D1113yes—
415C2×C42—113no—
416C2×C42—113no—
417C2×C42—113no—
418#95—113no—
419#95—113no—
420#95—113no—
421#95—113no—
422#95—113no—
423#95—113no—
424#95—113no—
425#95—113no—
426#95—113no—
427#95—113no—
428#95C22×D1111yescharacteristic
429#95C22×D1113yes—
430#95C22×D1113yes—
431#95C22×D1113yes—
432C2×C11—42no—
433C2×C11—83no—
434C2×C11#345913yes—
435C2×C11C2×#56011yescharacteristic
436C2×C11#352913yes—
437D11—42no—
438D11—42no—
439C24—111no—
440C24—111no—
441C24—114no—
442C24—443no—
443C24—443no—
444C24C23×D1113yes—
445C24C23×D1111yescharacteristic
446C2×D4—26no—
447C2×D4—43no—
448C2×D4—43no—
449C2×D4—43no—
450C2×D4—43no—
451C2×D4—43no—
452C2×D4—226no—
453C2×D4—226no—
454C2×D4—443no—
455C2×D4—443no—
456C2×D4—443no—
457C2×D4—443no—
458C22×C4—43no—
459C22×C4—111no—
460C22×C4—113no—
461C22×C4—113no—
462C22×C4—111no—
463C22×C4—113no—
464C22×C4—113no—
465C22×C4—226no—
466C22×C4—226no—
467C22×C4—226no—
468C22×C4—226no—
469C22×C4—226no—
470C22×C4—226no—
471C22×C4—443no—
472C22×C4—443no—
473C22×C4—4416no—
474C22×C4C23×D1113yes—
475C22×C4C23×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477C22×C4C23×D1113yes—
478C22×C4C23×D1113yes—
479C4⋊C4—43no—
480C4⋊C4—443no—
481C4⋊C4—443no—
482C4⋊C4—443no—
483C4⋊C4—443no—
484C4⋊C4—443no—
485C4⋊C4—443no—
486C4⋊C4—443no—
487C4⋊C4—443no—
488C4⋊C4—443no—
489C22⋊C4—43no—
490C22⋊C4—43no—
491C22⋊C4—43no—
492C22⋊C4—43no—
493C22⋊C4—43no—
494C22⋊C4—226no—
495C22⋊C4—226no—
496C22⋊C4—226no—
497C22⋊C4—443no—
498C22⋊C4—443no—
499C22⋊C4—443no—
500C22⋊C4—443no—
501C22⋊C4—443no—
502C22⋊C4—443no—
503C22⋊C4—443no—
504C22⋊C4—443no—
505C22⋊C4—443no—
506C22⋊C4—443no—
507C42—226no—
508C42—226no—
509C42—226no—
510C11#3667611yescharacteristic, complemented, Sylow
511C23—23no—
512C23—23no—
513C23—23no—
514C23—23no—
515C23—23no—
516C23—23no—
517C23—23no—
518C23—23no—
519C23—23no—
520C23—112no—
521C23—112no—
522C23—223no—
523C23—223no—
524C23—223no—
525C23—223no—
526C23—4412no—
527C23—444no—
528C23—4412no—
529C23#41×D1112yes—
530C23C24×D1111yescharacteristic
531D4—412no—
532D4—412no—
533D4—4412no—
534D4—4412no—
535C2×C4—23no—
536C2×C4—23no—
537C2×C4—23no—
538C2×C4—23no—
539C2×C4—23no—
540C2×C4—23no—
541C2×C4—23no—
542C2×C4—23no—
543C2×C4—23no—
544C2×C4—23no—
545C2×C4—23no—
546C2×C4—44no—
547C2×C4—116no—
548C2×C4—223no—
549C2×C4—223no—
550C2×C4—223no—
551C2×C4—223no—
552C2×C4—223no—
553C2×C4—223no—
554C2×C4—223no—
555C2×C4—223no—
556C2×C4—223no—
557C2×C4—223no—
558C2×C4—223no—
559C2×C4—223no—
560C2×C4—223no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—444no—
565C2×C4—444no—
566C2×C4—4412no—
567C22—26no—
568C22—41no—
569C22—43no—
570C22—43no—
571C22—43no—
572C22—43no—
573C22—43no—
574C22—43no—
575C22—43no—
576C22—43no—
577C22—226no—
578C22—226no—
579C22—4416no—
580C22—441no—
581C22—441no—
582C22—443no—
583C22—443no—
584C22C2×#41×D1111yescharacteristic
585C22D11×H(5,𝔽2)13yes—
586C22#1062345513yes—
587C4—41no—
588C4—41no—
589C4—43no—
590C4—43no—
591C4—43no—
592C4—114no—
593C4—441no—
594C4—443no—
595C4—443no—
596C4—443no—
597C4—443no—
598C2—42no—
599C2—83no—
600C2—442no—
601C2—442no—
602C2#1308202713yes—
603C2D11×#56011yescharacteristic
604C2#1308275113yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2825C2
hypercenter#2825D11
hypocenterC11#36676
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2825

Complements

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

NH ≅ G/Ntype
1. #13076879C2semidirect
2. #13076800C2semidirect
3. #13076721C2semidirect
4. #13076720C2semidirect
5. #13076712C2semidirect
6. #13076705C2semidirect
7. #13076610C2semidirect
8. #13071919C2semidirect
9. #13071918C2semidirect
10. #13071894C2semidirect
11. #13071874C2semidirect
12. #13071859C2semidirect
13. #13071851C2semidirect
14. #13071121C2semidirect
15. C11×#2825C2semidirect
19. C2×D4×Dic11C22semidirect
22. C2×#66930C22semidirect
23. C11×#401C22semidirect
24. C11×#397C22semidirect
26. C11×#394C22semidirect
28. C11×#392C22semidirect
34. #10622835C22semidirect
38. #10622599C22semidirect
39. C4⋊C4×Dic11C22semidirect
48. #10622566C22semidirect
49. #10622565C22semidirect
50. #10622565C22semidirect
51. #10622562C22semidirect
53. #10622561C22semidirect
54. #10622561C22semidirect
56. C22⋊C4×Dic11C22semidirect
65. C11⋊#401C22semidirect
66. #10622274C22semidirect
67. #10622271C22semidirect
68. #10622271C22semidirect
69. #10622270C22semidirect
70. #10622270C22semidirect
71. #10622262C22semidirect
72. #10622261C22semidirect
215. #2825D11semidirect
288. #401C2×D11semidirect
304. #397C2×D11semidirect
318. #394C2×D11semidirect
322. #392C2×D11semidirect
510. C11#36676semidirect

Maximal subgroups

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

subgroupindex
#130768792
#130768002
#130767212
#130767202
#130767122
#130767052
#130766102
#130719192
#130719182
#130718942
#130718742
#130718592
#130718512
#130711212
C11×#28252
#3667611