Finite Group Databasebeta

← #14960215

Subgroups — #14960215

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#13076727C213yesmaximal, complemented
4#13076726C213yesmaximal, complemented
5#13076713C213yesmaximal, complemented
6#13076707C211yesmaximal, characteristic, complemented
7#13076703C211yesmaximal, characteristic, complemented
8#13076614C213yesmaximal, complemented
9#13071914C211yesmaximal, characteristic, complemented
10#13071897C211yesmaximal, characteristic, complemented
11#13071879C213yesmaximal, complemented
12#13071860C213yesmaximal, complemented
13#13071856C213yesmaximal, complemented
14C4×#66935C213yesmaximal, complemented
15C11×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C2×C4×C22⋊D11C2213yes—
18C2×#66935C2213yes—
19C2×C4×D44C2213yes—
20C2×C4×D44C2213yes—
21C2×C4×D44C2213yescomplemented
22C2×#66925C2213yescomplemented
23C11×#401C2211yescharacteristic, complemented
24C11×#400C2213yescomplemented
25C11×#397C2213yes—
26C11×#396C2211yescharacteristic
27C4×C11×C4⋊C4C2213yescomplemented
28C4×C11×C22⋊C4C2213yes—
29C11×#376C2211yescharacteristic, complemented
30#10622607C2213yes—
31#10622607C2213yescomplemented
32#10622606C2213yescomplemented
33#10622605C2213yes—
34#10622604C2213yes—
35#10622604C2213yes—
36#10622604C2213yescomplemented
37#10622597C2213yescomplemented
38#10622573C2213yes—
39#10622572C2213yes—
40#10622572C2213yes—
41#10622571C2213yes—
42#10622568C2213yes—
43#10622563C2213yes—
44#10622561C2213yes—
45C4×(C2×D11)⋊C4C2213yes—
46C4×(C2×D11)⋊C4C2213yes—
47C4×(C2×D11)⋊C4C2213yescomplemented
48C4×Dic11⋊C4C2213yescomplemented
49#10622290C2211yescharacteristic
50#10622290C2213yescomplemented
51#10622289C2211yescharacteristic
52#10622289C2213yescomplemented
53#10622288C2213yes—
54#10622288C2213yes—
55#10622288C2213yescomplemented
56#10622288C2213yescomplemented
57#10622287C2213yescomplemented
58#10622285C2213yes—
59#10622285C2213yes—
60#10622285C2213yescomplemented
61#10622284C2213yes—
62#10622284C2213yes—
63#10622284C2211yescharacteristic, complemented
64#10622281C2213yes—
65#10622281C2213yes—
66#10622278C2213yes—
67#10622278C2213yes—
68C11⋊#401C2211yescharacteristic, complemented
69#10622274C2213yescomplemented
70#10622273C2213yescomplemented
71#10622271C2213yescomplemented
72#10622270C2213yescomplemented
73C24×D11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11C2313yes—
76C23×Dic11C2311yescharacteristic
77C22×D44C2313yes—
78C22×D44C2313yes—
79C22×D44C2313yes—
80C22×C4×D11—46no—
81C22×C4×D11C2313yes—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C4⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C42×C11C2313yes—
91C2×C42×C11C2313yes—
92C2×C22⋊Dic11C2313yes—
93C4×C22⋊D11—46no—
94C2×(C2×D11)⋊C4C2313yes—
95C2×(C2×D11)⋊C4C2313yes—
96C2×(C2×D11)⋊C4C2313yes—
97C2×(C2×D11)⋊C4C2313yes—
98C2×(C2×D11)⋊C4C2313yes—
99C2×(C2×D11)⋊C4C2313yes—
100C2×(C2×D11)⋊C4C2313yes—
101C2×(C2×D11)⋊C4C2313yes—
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×(C2×D11)⋊C4C2313yes—
109C2×C4⋊Dic11C2313yes—
110C2×C4⋊Dic11C2313yes—
111C2×C4⋊Dic11C2313yes—
112C2×Dic11⋊C4C2313yes—
113C2×Dic11⋊C4C2313yes—
114C2×Dic11⋊C4C2313yes—
115C2×Dic11⋊C4C2313yes—
116C2×Dic11⋊C4C2313yes—
117C2×C4×Dic11C2313yes—
118#66935—212no—
119C4×D44—46no—
120C4×D44—46no—
121C4×D44—46no—
122#66925—46no—
123C11×#95C2313yes—
124C11×#95C2313yes—
125C11×#95C2313yes—
126C11×#95C2313yes—
127C11×#95C2311yescharacteristic
128C11×#95C2313yes—
129C11⋊#95C2313yes—
130C11⋊#95C2313yes—
131C11⋊#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137#36676—111nomaximal, Sylow
138C24×C11C2411yescharacteristic
139C23×D11—43no—
140C23×D11—43no—
141C23×D11#4114yes—
142C23×D11C2413yes—
143C23×D11C2411yescharacteristic
144C23×D11C2411yescharacteristic
145C22×C4×C11—26no—
146C22×C4×C11C2413yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2413yes—
149C22×C4×C11C2413yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—26no—
153C2×C22⋊D11—43no—
154C2×C22⋊D11—43no—
155C22×Dic11—43no—
156C22×Dic11C2413yes—
157C22×Dic11C2411yescharacteristic
158C22×Dic11C2411yescharacteristic
159C22×Dic11C2413yes—
160C22×Dic11C2413yes—
161C2×D44—26no—
162C2×D44—26no—
163C2×D44—43no—
164C2×D44—43no—
165C2×D44—43no—
166C2×D44—43no—
167C2×D44—43no—
168C2×D44—43no—
169C2×D44—43no—
170C2×C4×D11—26no—
171C2×C4×D11—26no—
172C2×C4×D11—26no—
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×C4⋊C4—43no—
180C11×C22⋊C4—26no—
181C11×C22⋊C4—43no—
182C42×C11—26no—
183C42×C11—26no—
184C22⋊Dic11—43no—
185(C2×D11)⋊C4—26no—
186(C2×D11)⋊C4—26no—
187(C2×D11)⋊C4—43no—
188(C2×D11)⋊C4—43no—
189(C2×D11)⋊C4—43no—
190(C2×D11)⋊C4—43no—
191(C2×D11)⋊C4—43no—
192(C2×D11)⋊C4—43no—
193(C2×D11)⋊C4—43no—
194(C2×D11)⋊C4—43no—
195(C2×D11)⋊C4—43no—
196(C2×D11)⋊C4—43no—
197(C2×D11)⋊C4—43no—
198(C2×D11)⋊C4—43no—
199(C2×D11)⋊C4—43no—
200C4⋊Dic11—43no—
201C4⋊Dic11—43no—
202C4⋊Dic11—43no—
203Dic11⋊C4—43no—
204Dic11⋊C4—43no—
205Dic11⋊C4—43no—
206Dic11⋊C4—43no—
207Dic11⋊C4—43no—
208C4×Dic11—26no—
209#2842—111no—
210#2834—111no—
211#2827—113no—
212#2827—113no—
213#2826—113no—
214#2825—111no—
215#2825—111no—
216#2812—113no—
217#2401—111no—
218#2401D1111yescharacteristic, complemented
219#2397—111no—
220#2395—113no—
221#2392—113no—
222#2392—113no—
223C4×#120—113no—
224C23×C11—23no—
225C23×C11—23no—
226C23×C11C2×#4112yes—
227C23×C11C2511yescharacteristic
228C22×D11—23no—
229C22×D11—23no—
230C22×D11—23no—
231C22×D11—23no—
232C22×D11—23no—
233C22×D11—23no—
234C22×D11—23no—
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—
244C2×C4×C11—23no—
245C2×C4×C11—23no—
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—
258C2×C4×C11H(5,𝔽2)16yes—
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—44no—
272D44—412no—
273D44—412no—
274D44—412no—
275C4×D11—44no—
276C4×D11—44no—
277C4×D11—412no—
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#400C2×D1113yescomplemented
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×D1113yes—
305#396—113no—
306#396—113no—
307#396—113no—
308#396—111no—
309#396—113no—
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#394—113no—
319#392—113no—
320#392—111no—
321#392—113no—
322#392—113no—
323#386—113no—
324#386—113no—
325#386—113no—
326#385—113no—
327#385—113no—
328#385—113no—
329#379—113no—
330C4×C4⋊C4—113no—
331C4×C4⋊C4C2×D1113yescomplemented
332C4×C22⋊C4—113no—
333C4×C22⋊C4—113no—
334C4×C22⋊C4—113no—
335C4×C22⋊C4C2×D1113yes—
336#376C2×D1111yescharacteristic, complemented
337C22×C11—26no—
338C22×C11—41no—
339C22×C11—43no—
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)13yes—
342C22×C11#58513yes—
343C2×D11—26no—
344C2×D11—26no—
345C2×D11—416no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—43no—
349C2×D11—43no—
350C2×D11—43no—
351C2×D11—43no—
352C2×D11—43no—
353C2×D11—43no—
354C2×D11—43no—
355C2×D11—43no—
356C2×D11—43no—
357C4×C11—43no—
358C4×C11—43no—
359C4×C11—41no—
360C4×C11—43no—
361C4×C11—43no—
362C4×C11#56014yes—
363Dic11—43no—
364Dic11—41no—
365Dic11—41no—
366Dic11—43no—
367Dic11—43no—
368C25—111no—
369C22×D4—113no—
370C22×D4—113no—
371C22×D4—113no—
372C22×D4—113no—
373C23×C4—111no—
374C23×C4—113no—
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⋊C4C22×D1113yes—
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⋊C4—113no—
411C2×C22⋊C4—113no—
412C2×C22⋊C4—113no—
413C2×C22⋊C4C22×D1113yes—
414C2×C22⋊C4C22×D1113yes—
415C2×C42—113no—
416C2×C42C22×D1113yes—
417C2×C42C22×D1113yes—
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#95C22×D1111yescharacteristic
427#95C22×D1113yes—
428#95C22×D1113yes—
429#95C22×D1113yes—
430#95C22×D1113yes—
431#95C22×D1113yes—
432C2×C11—42no—
433C2×C11#345913yes—
434C2×C11C2×#56011yescharacteristic
435C2×C11#352913yes—
436D11—42no—
437D11—42no—
438D11—83no—
439C24—111no—
440C24—111no—
441C24—114no—
442C24—113no—
443C24—443no—
444C24—443no—
445C24C23×D1111yescharacteristic
446C2×D4—226no—
447C2×D4—226no—
448C2×D4—226no—
449C2×D4—443no—
450C2×D4—443no—
451C2×D4—443no—
452C2×D4—443no—
453C2×D4—443no—
454C2×D4—443no—
455C2×D4—443no—
456C2×D4—443no—
457C2×D4—443no—
458C22×C4—26no—
459C22×C4—113no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—113no—
463C22×C4—113no—
464C22×C4—226no—
465C22×C4—226no—
466C22×C4—226no—
467C22×C4—226no—
468C22×C4—226no—
469C22×C4—443no—
470C22×C4—443no—
471C22×C4—4416no—
472C22×C4—443no—
473C22×C4C23×D1113yes—
474C22×C4C23×D1113yes—
475C22×C4C23×D1113yes—
476C22×C4C23×D1113yes—
477C22×C4C23×D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479C4⋊C4—43no—
480C4⋊C4—43no—
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—26no—
490C22⋊C4—43no—
491C22⋊C4—226no—
492C22⋊C4—226no—
493C22⋊C4—443no—
494C22⋊C4—443no—
495C22⋊C4—443no—
496C22⋊C4—443no—
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—26no—
508C42—26no—
509C42—226no—
510C11#3667611yescharacteristic, complemented, Sylow
511C23—23no—
512C23—23no—
513C23—112no—
514C23—112no—
515C23—223no—
516C23—223no—
517C23—223no—
518C23—223no—
519C23—223no—
520C23—223no—
521C23—223no—
522C23—223no—
523C23—223no—
524C23—223no—
525C23—223no—
526C23—4412no—
527C23—444no—
528C23—4412no—
529C23#41×D1112yes—
530C23C24×D1111yescharacteristic
531D4—4412no—
532D4—4412no—
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—23no—
547C2×C4—23no—
548C2×C4—44no—
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—444no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—444no—
565C2×C4—4412no—
566C2×C4#6704216yes—
567C22—26no—
568C22—41no—
569C22—43no—
570C22—226no—
571C22—226no—
572C22—4416no—
573C22—441no—
574C22—441no—
575C22—443no—
576C22—443no—
577C22—443no—
578C22—443no—
579C22—443no—
580C22—443no—
581C22—443no—
582C22—443no—
583C22—443no—
584C22C2×#41×D1111yescharacteristic
585C22C2×#6704213yes—
586C22#1062345313yes—
587C4—41no—
588C4—43no—
589C4—43no—
590C4—43no—
591C4—43no—
592C4—441no—
593C4—441no—
594C4—443no—
595C4—443no—
596C4—443no—
597C4#1062324214yes—
598C2—42no—
599C2—442no—
600C2—442no—
601C2—883no—
602C2#1308202613yes—
603C2C2×#1062324211yescharacteristic
604C2#1308275513yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2401C2
hypercenter#2401D11
hypocenterC11#36676
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #13076879C2semidirect
2. #13076800C2semidirect
3. #13076727C2semidirect
4. #13076726C2semidirect
5. #13076713C2semidirect
6. #13076707C2semidirect
7. #13076703C2semidirect
8. #13076614C2semidirect
9. #13071914C2semidirect
10. #13071897C2semidirect
11. #13071879C2semidirect
12. #13071860C2semidirect
13. #13071856C2semidirect
14. C4×#66935C2semidirect
15. C11×#2401C2semidirect
21. C2×C4×D44C22semidirect
22. C2×#66925C22semidirect
23. C11×#401C22semidirect
24. C11×#400C22semidirect
27. C4×C11×C4⋊C4C22semidirect
29. C11×#376C22semidirect
31. #10622607C22semidirect
32. #10622606C22semidirect
36. #10622604C22semidirect
37. #10622597C22semidirect
47. C4×(C2×D11)⋊C4C22semidirect
48. C4×Dic11⋊C4C22semidirect
50. #10622290C22semidirect
52. #10622289C22semidirect
55. #10622288C22semidirect
56. #10622288C22semidirect
57. #10622287C22semidirect
60. #10622285C22semidirect
63. #10622284C22semidirect
68. C11⋊#401C22semidirect
69. #10622274C22semidirect
70. #10622273C22semidirect
71. #10622271C22semidirect
72. #10622270C22semidirect
218. #2401D11semidirect
288. #401C2×D11semidirect
291. #400C2×D11semidirect
331. C4×C4⋊C4C2×D11semidirect
336. #376C2×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
#130767272
#130767262
#130767132
#130767072
#130767032
#130766142
#130719142
#130718972
#130718792
#130718602
#130718562
C4×#669352
C11×#24012
#3667611