Finite Group Databasebeta

← #29886455

Subgroups — #29886455

Order 15616.

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#21454082C211yesmaximal, characteristic, complemented
2#21454003C211yesmaximal, characteristic, complemented
3#21453930C213yesmaximal, complemented
4#21453929C213yesmaximal, complemented
5#21453916C213yesmaximal, complemented
6#21453910C211yesmaximal, characteristic, complemented
7#21453906C211yesmaximal, characteristic, complemented
8#21453817C213yesmaximal, complemented
9#21449117C211yesmaximal, characteristic, complemented
10#21449100C211yesmaximal, characteristic, complemented
11#21449082C213yesmaximal, complemented
12#21449063C213yesmaximal, complemented
13#21449059C213yesmaximal, complemented
14C4×#14519747C213yesmaximal, complemented
15C61×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C2×#14519747C2213yes—
18C2×C4×D244C2213yes—
19C2×C4×D244C2213yes—
20C2×C4×D244C2213yescomplemented
21C2×C4×C22⋊D61C2213yes—
22C2×#14519734C2213yescomplemented
23C61⋊#401C2211yescharacteristic, complemented
24#16839704C2213yescomplemented
25#16839703C2213yescomplemented
26#16839699C2211yescharacteristic
27#16839699C2213yescomplemented
28#16839697C2213yes—
29#16839696C2213yescomplemented
30#16839695C2213yescomplemented
31#16839694C2213yescomplemented
32#16839691C2213yes—
33#16839691C2213yes—
34#16839691C2213yescomplemented
35#16839691C2213yescomplemented
36#16839689C2213yescomplemented
37#16839688C2213yescomplemented
38#16839686C2211yescharacteristic
39#16839686C2213yescomplemented
40#16839685C2213yes—
41#16839684C2213yes—
42#16839684C2213yescomplemented
43#16839680C2213yes—
44#16839680C2213yes—
45#16839680C2213yescomplemented
46#16839679C2213yes—
47#16839679C2213yes—
48#16839679C2213yescomplemented
49#16839677C2213yes—
50#16839677C2213yes—
51#16839672C2213yes—
52#16839672C2213yes—
53#16839672C2211yescharacteristic, complemented
54#16839671C2213yes—
55#16839640C2213yes—
56#16839640C2213yes—
57#16839639C2213yes—
58#16839637C2213yes—
59#16839636C2213yes—
60#16839636C2213yes—
61#16839617C2213yes—
62C4×#11758196C2213yescomplemented
63C4×#11758198C2213yes—
64C4×#11758198C2213yes—
65C4×#11758198C2213yescomplemented
66C61×#401C2211yescharacteristic, complemented
67C61×#400C2213yescomplemented
68C61×#397C2213yes—
69C61×#396C2211yescharacteristic
70C4×C4⋊C4×C61C2213yescomplemented
71C4×C22⋊C4×C61C2213yes—
72C61×#376C2211yescharacteristic, complemented
73C24×D61C2311yescharacteristic
74C22×D244C2313yes—
75C22×D244C2313yes—
76C22×D244C2313yes—
77C22×C22⋊D61C2313yes—
78C23×Dic61C2311yescharacteristic
79C22×C4×D61—46no—
80C22×C4×D61C2313yes—
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85#14519747—212no—
86C4×D244—46no—
87C4×D244—46no—
88C4×D244—46no—
89C4×C22⋊D61—46no—
90#14519734—46no—
91C2×C4⋊Dic61C2313yes—
92C2×C4⋊Dic61C2313yes—
93C2×C4⋊Dic61C2313yes—
94C2×#11758196C2313yes—
95C2×#11758196C2313yes—
96C2×#11758196C2313yes—
97C2×#11758196C2313yes—
98C2×#11758196C2313yes—
99C2×C22⋊Dic61C2313yes—
100C2×#11758198C2313yes—
101C2×#11758198C2313yes—
102C2×#11758198C2313yes—
103C2×#11758198C2313yes—
104C2×#11758198C2313yes—
105C2×#11758198C2313yes—
106C2×#11758198C2313yes—
107C2×#11758198C2313yes—
108C2×#11758198C2313yes—
109C2×#11758198C2313yes—
110C2×#11758198C2313yes—
111C2×#11758198C2313yes—
112C2×#11758198C2313yes—
113C2×#11758198C2313yes—
114C2×#11758198C2313yes—
115C2×C4×Dic61C2313yes—
116#14519684C2313yes—
117#14519684C2313yes—
118#14519684C2313yes—
119#14519684C2313yes—
120#14519684C2313yes—
121#14519684C2313yes—
122#14519684C2313yes—
123#14519684C2313yes—
124C23×C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2313yes—
126C2×C4⋊C4×C61C2313yes—
127C2×C22⋊C4×C61C2313yes—
128C2×C22⋊C4×C61C2313yes—
129C2×C42×C61C2313yes—
130C2×C42×C61C2313yes—
131#95×C61C2313yes—
132#95×C61C2313yes—
133#95×C61C2311yescharacteristic
134#95×C61C2313yes—
135#95×C61C2313yes—
136#95×C61C2313yes—
137C24×C61C2411yescharacteristic
138C23×D61—43no—
139C23×D61—43no—
140C23×D61#4114yes—
141C23×D61C2413yes—
142C23×D61C2411yescharacteristic
143C23×D61C2411yescharacteristic
144C22×C4×C61—26no—
145C22×C4×C61C2411yescharacteristic
146C22×C4×C61C2413yes—
147C22×C4×C61C2413yes—
148C22×C4×C61C2413yes—
149C22×C4×C61C2413yes—
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—26no—
152C2×C22⋊D61—43no—
153C2×C22⋊D61—43no—
154C22×Dic61—43no—
155C22×Dic61C2411yescharacteristic
156C22×Dic61C2411yescharacteristic
157C22×Dic61C2413yes—
158C22×Dic61C2413yes—
159C22×Dic61C2413yes—
160C2×D244—26no—
161C2×D244—26no—
162C2×D244—43no—
163C2×D244—43no—
164C2×D244—43no—
165C2×D244—43no—
166C2×D244—43no—
167C2×D244—43no—
168C2×D244—43no—
169C2×C4×D61—26no—
170C2×C4×D61—26no—
171C2×C4×D61—26no—
172C2×C4×D61—26no—
173C2×C4×D61—26no—
174C2×C4×D61—43no—
175C2×C4×D61—43no—
176C2×C4×D61—416no—
177C4⋊C4×C61—43no—
178C4⋊C4×C61—43no—
179C22⋊C4×C61—26no—
180C22⋊C4×C61—43no—
181C42×C61—26no—
182C42×C61—26no—
183C22⋊Dic61—43no—
184#11758198—26no—
185#11758198—26no—
186#11758198—43no—
187#11758198—43no—
188#11758198—43no—
189#11758198—43no—
190#11758198—43no—
191#11758198—43no—
192#11758198—43no—
193#11758198—43no—
194#11758198—43no—
195#11758198—43no—
196#11758198—43no—
197#11758198—43no—
198#11758198—43no—
199C4⋊Dic61—43no—
200C4⋊Dic61—43no—
201C4⋊Dic61—43no—
202#11758196—43no—
203#11758196—43no—
204#11758196—43no—
205#11758196—43no—
206#11758196—43no—
207C4×Dic61—26no—
208C23×C61—23no—
209C23×C61—23no—
210C23×C61C2×#4112yes—
211C23×C61C2511yescharacteristic
212C22×D61—23no—
213C22×D61—23no—
214C22×D61—23no—
215C22×D61—23no—
216C22×D61—23no—
217C22×D61—23no—
218C22×D61—23no—
219C22×D61—23no—
220C22×D61—23no—
221C22×D61—23no—
222C22×D61—23no—
223C22×D61—412no—
224C22×D61—44no—
225C22×D61—412no—
226C22×D61C2×#4112yes—
227C22×D61C2×#4112yes—
228C2×C4×C61—23no—
229C2×C4×C61—23no—
230C2×C4×C61—23no—
231C2×C4×C61—23no—
232C2×C4×C61—23no—
233C2×C4×C61—23no—
234C2×C4×C61—23no—
235C2×C4×C61—23no—
236C2×C4×C61—23no—
237C2×C4×C61—23no—
238C2×C4×C61—23no—
239C2×C4×C61—23no—
240C2×C4×C61—23no—
241C2×C4×C61—44no—
242C2×C4×C61H(5,𝔽2)16yes—
243C22⋊D61—412no—
244C2×Dic61—23no—
245C2×Dic61—23no—
246C2×Dic61—23no—
247C2×Dic61—23no—
248C2×Dic61—23no—
249C2×Dic61—23no—
250C2×Dic61—23no—
251C2×Dic61—23no—
252C2×Dic61—23no—
253C2×Dic61—23no—
254C2×Dic61—23no—
255C2×Dic61—44no—
256D244—412no—
257D244—412no—
258D244—412no—
259C4×D61—44no—
260C4×D61—44no—
261C4×D61—412no—
262C4×D61—44no—
263C4×D61—44no—
264#36676—611nomaximal, Sylow
265C22×C61—26no—
266C22×C61—41no—
267C22×C61—43no—
268C22×C61C22×#4111yescharacteristic
269C22×C61C2×H(5,𝔽2)13yes—
270C22×C61#58513yes—
271C2×D61—26no—
272C2×D61—26no—
273C2×D61—416no—
274C2×D61—41no—
275C2×D61—41no—
276C2×D61—43no—
277C2×D61—43no—
278C2×D61—43no—
279C2×D61—43no—
280C2×D61—43no—
281C2×D61—43no—
282C2×D61—43no—
283C2×D61—43no—
284C2×D61—43no—
285C4×C61—43no—
286C4×C61—43no—
287C4×C61—41no—
288C4×C61—43no—
289C4×C61—43no—
290C4×C61#56014yes—
291Dic61—43no—
292Dic61—41no—
293Dic61—41no—
294Dic61—43no—
295Dic61—43no—
296#2842—611no—
297#2834—611no—
298#2827—613no—
299#2827—613no—
300#2826—613no—
301#2825—611no—
302#2825—611no—
303#2812—613no—
304#2401—611no—
305#2401D6111yescharacteristic, complemented
306#2397—611no—
307#2395—613no—
308#2392—613no—
309#2392—613no—
310C4×#120—613no—
311C2×C61—42no—
312C2×C61#345913yes—
313C2×C61C2×#56011yescharacteristic
314C2×C61#352913yes—
315D61—42no—
316D61—42no—
317D61—83no—
318C24×C4—611no—
319C2×#120—613no—
320C2×C4×D4—613no—
321C2×C4×D4—613no—
322C2×C4×D4—613no—
323C2×C4×D4—613no—
324C2×#117—613no—
325#401—611no—
326#401C2×D6111yescharacteristic, complemented
327#400—613no—
328#400—613no—
329#400C2×D6113yescomplemented
330#399—613no—
331#399—613no—
332#399—611no—
333#398—613no—
334#398—613no—
335#398—613no—
336#397—613no—
337#397—613no—
338#397—613no—
339#397—613no—
340#397—613no—
341#397—613no—
342#397C2×D6113yes—
343#396—613no—
344#396—613no—
345#396—613no—
346#396—611no—
347#396—613no—
348#396C2×D6111yescharacteristic
349#394—613no—
350#394—613no—
351#394—613no—
352#394—613no—
353#394—613no—
354#394—613no—
355#394—613no—
356#394—613no—
357#392—613no—
358#392—611no—
359#392—613no—
360#392—613no—
361#386—613no—
362#386—613no—
363#386—613no—
364#385—613no—
365#385—613no—
366#385—613no—
367#379—613no—
368C4×C4⋊C4—613no—
369C4×C4⋊C4C2×D6113yescomplemented
370C4×C22⋊C4—613no—
371C4×C22⋊C4—613no—
372C4×C22⋊C4—613no—
373C4×C22⋊C4C2×D6113yes—
374#376C2×D6111yescharacteristic, complemented
375C61#3667611yescharacteristic, complemented, Sylow
376C25—611no—
377C22×D4—613no—
378C22×D4—613no—
379C22×D4—613no—
380C22×D4—613no—
381C23×C4—611no—
382C23×C4—613no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—611no—
387C23×C4—2446no—
388C23×C4C22×D6111yescharacteristic
389#120—12212no—
390C4×D4—2446no—
391C4×D4—2446no—
392C4×D4—2446no—
393C4×D4—2446no—
394#117—2446no—
395C2×C4⋊C4—613no—
396C2×C4⋊C4—613no—
397C2×C4⋊C4—613no—
398C2×C4⋊C4—613no—
399C2×C4⋊C4—613no—
400C2×C4⋊C4—613no—
401C2×C4⋊C4—613no—
402C2×C4⋊C4—613no—
403C2×C4⋊C4C22×D6113yes—
404C2×C4⋊C4C22×D6113yes—
405C2×C22⋊C4—613no—
406C2×C22⋊C4—613no—
407C2×C22⋊C4—613no—
408C2×C22⋊C4—613no—
409C2×C22⋊C4—613no—
410C2×C22⋊C4—613no—
411C2×C22⋊C4—613no—
412C2×C22⋊C4—613no—
413C2×C22⋊C4—613no—
414C2×C22⋊C4—613no—
415C2×C22⋊C4—613no—
416C2×C22⋊C4—613no—
417C2×C22⋊C4—613no—
418C2×C22⋊C4—613no—
419C2×C22⋊C4—613no—
420C2×C22⋊C4—613no—
421C2×C22⋊C4C22×D6113yes—
422C2×C22⋊C4C22×D6113yes—
423C2×C42—613no—
424C2×C42C22×D6113yes—
425C2×C42C22×D6113yes—
426#95—613no—
427#95—613no—
428#95—613no—
429#95—613no—
430#95—613no—
431#95—613no—
432#95—613no—
433#95—613no—
434#95C22×D6111yescharacteristic
435#95C22×D6113yes—
436#95C22×D6113yes—
437#95C22×D6113yes—
438#95C22×D6113yes—
439#95C22×D6113yes—
440C24—611no—
441C24—611no—
442C24—614no—
443C24—613no—
444C24—2443no—
445C24—2443no—
446C24C23×D6111yescharacteristic
447C2×D4—1226no—
448C2×D4—1226no—
449C2×D4—1226no—
450C2×D4—2443no—
451C2×D4—2443no—
452C2×D4—2443no—
453C2×D4—2443no—
454C2×D4—2443no—
455C2×D4—2443no—
456C2×D4—2443no—
457C2×D4—2443no—
458C2×D4—2443no—
459C22×C4—26no—
460C22×C4—613no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—613no—
464C22×C4—613no—
465C22×C4—1226no—
466C22×C4—1226no—
467C22×C4—1226no—
468C22×C4—1226no—
469C22×C4—1226no—
470C22×C4—2443no—
471C22×C4—2443no—
472C22×C4—24416no—
473C22×C4—2443no—
474C22×C4C23×D6113yes—
475C22×C4C23×D6113yes—
476C22×C4C23×D6113yes—
477C22×C4C23×D6113yes—
478C22×C4C23×D6111yescharacteristic
479C22×C4C23×D6111yescharacteristic
480C4⋊C4—43no—
481C4⋊C4—43no—
482C4⋊C4—2443no—
483C4⋊C4—2443no—
484C4⋊C4—2443no—
485C4⋊C4—2443no—
486C4⋊C4—2443no—
487C4⋊C4—2443no—
488C4⋊C4—2443no—
489C4⋊C4—2443no—
490C22⋊C4—26no—
491C22⋊C4—43no—
492C22⋊C4—1226no—
493C22⋊C4—1226no—
494C22⋊C4—2443no—
495C22⋊C4—2443no—
496C22⋊C4—2443no—
497C22⋊C4—2443no—
498C22⋊C4—2443no—
499C22⋊C4—2443no—
500C22⋊C4—2443no—
501C22⋊C4—2443no—
502C22⋊C4—2443no—
503C22⋊C4—2443no—
504C22⋊C4—2443no—
505C22⋊C4—2443no—
506C22⋊C4—2443no—
507C22⋊C4—2443no—
508C42—26no—
509C42—26no—
510C42—1226no—
511C23—23no—
512C23—23no—
513C23—612no—
514C23—612no—
515C23—1223no—
516C23—1223no—
517C23—1223no—
518C23—1223no—
519C23—1223no—
520C23—1223no—
521C23—1223no—
522C23—1223no—
523C23—1223no—
524C23—1223no—
525C23—1223no—
526C23—24412no—
527C23—2444no—
528C23—24412no—
529C23#41×D6112yes—
530C23C24×D6111yescharacteristic
531D4—24412no—
532D4—24412no—
533D4—24412no—
534D4—24412no—
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—1223no—
550C2×C4—1223no—
551C2×C4—1223no—
552C2×C4—1223no—
553C2×C4—1223no—
554C2×C4—1223no—
555C2×C4—1223no—
556C2×C4—1223no—
557C2×C4—1223no—
558C2×C4—1223no—
559C2×C4—1223no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—2444no—
563C2×C4—24412no—
564C2×C4—2444no—
565C2×C4—2444no—
566C2×C4#1451982316yes—
567C22—26no—
568C22—41no—
569C22—43no—
570C22—1226no—
571C22—1226no—
572C22—24416no—
573C22—2443no—
574C22—2443no—
575C22—2443no—
576C22—2443no—
577C22—2443no—
578C22—2443no—
579C22—2443no—
580C22—2441no—
581C22—2441no—
582C22—2443no—
583C22—2443no—
584C22C2×#41×D6111yescharacteristic
585C22C2×#1451982313yes—
586C22#1684059813yes—
587C4—43no—
588C4—43no—
589C4—41no—
590C4—43no—
591C4—43no—
592C4—2443no—
593C4—2443no—
594C4—2441no—
595C4—2441no—
596C4—2443no—
597C4#1684050314yes—
598C2—42no—
599C2—4883no—
600C2—2442no—
601C2—2442no—
602C2#2145922913yes—
603C2C2×#1684050311yescharacteristic
604C2#2145995813yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC61×#2401C2
hypercenter#2401D61
hypocenterC61#36676
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #21454082C2semidirect
2. #21454003C2semidirect
3. #21453930C2semidirect
4. #21453929C2semidirect
5. #21453916C2semidirect
6. #21453910C2semidirect
7. #21453906C2semidirect
8. #21453817C2semidirect
9. #21449117C2semidirect
10. #21449100C2semidirect
11. #21449082C2semidirect
12. #21449063C2semidirect
13. #21449059C2semidirect
14. C4×#14519747C2semidirect
15. C61×#2401C2semidirect
20. C2×C4×D244C22semidirect
22. C2×#14519734C22semidirect
23. C61⋊#401C22semidirect
24. #16839704C22semidirect
25. #16839703C22semidirect
27. #16839699C22semidirect
29. #16839696C22semidirect
30. #16839695C22semidirect
31. #16839694C22semidirect
34. #16839691C22semidirect
35. #16839691C22semidirect
36. #16839689C22semidirect
37. #16839688C22semidirect
39. #16839686C22semidirect
42. #16839684C22semidirect
45. #16839680C22semidirect
48. #16839679C22semidirect
53. #16839672C22semidirect
62. C4×#11758196C22semidirect
65. C4×#11758198C22semidirect
66. C61×#401C22semidirect
67. C61×#400C22semidirect
70. C4×C4⋊C4×C61C22semidirect
72. C61×#376C22semidirect
305. #2401D61semidirect
326. #401C2×D61semidirect
329. #400C2×D61semidirect
369. C4×C4⋊C4C2×D61semidirect
374. #376C2×D61semidirect
375. C61#36676semidirect

Maximal subgroups

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

subgroupindex
#214540822
#214540032
#214539302
#214539292
#214539162
#214539102
#214539062
#214538172
#214491172
#214491002
#214490822
#214490632
#214490592
C4×#145197472
C61×#24012
#3667661