Finite Group Databasebeta

← D61×#2483 #29848933

Subgroups — D61×#2483 #29848933

Order 15616.

4382 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D61C212yesmaximal
2#21450100C211yesmaximal, characteristic, complemented
3#21450099C214yesmaximal, complemented
4#21450098C214yesmaximal, complemented
5#21450097C212yesmaximal, complemented
6#21450096C214yesmaximal, complemented
7#397×D61C214yesmaximal, complemented
8#385×D61C214yesmaximal, complemented
9#381×D61C214yesmaximal, complemented
10#379×D61C211yesmaximal, characteristic
11C61×#2483C211yesmaximal, characteristic, complemented
12C25×D61C2211yescharacteristic
13C23×C4×D61C2212yes—
14C23×C4×D61C2212yes—
15C2×C4⋊C4×D61C2214yescomplemented
16C22×C22⋊Dic61C2212yes—
17C22×#11758198C2212yes—
18C22×#11758198C2212yes—
19C2×C22⋊C4×D61—216no—
20C2×C22⋊C4×D61C2214yes—
21C2×C22⋊C4×D61C2214yes—
22C2×C22⋊C4×D61C2214yes—
23C2×C22⋊C4×D61C2214yes—
24C2×C22⋊C4×D61C2214yes—
25C2×C22⋊C4×D61C2212yes—
26#16839691C2218yescomplemented
27#16839690C2218yescomplemented
28#16839689C2214yescomplemented
29#16839688C2214yescomplemented
30#16839687C2214yescomplemented
31#16839637C2214yescomplemented
32#16839636C2218yescomplemented
33#16839635C2214yescomplemented
34#16839634C2214yescomplemented
35#16839633C2218yescomplemented
36#16839625C2214yescomplemented
37#16839624C2218yescomplemented
38#16839624C2218yescomplemented
39#16839623C2214yescomplemented
40#16839623C2214yescomplemented
41#16839618C2211yescharacteristic
42#16839617C2212yes—
43#16839617C2214yes—
44#95×D61C2214yescomplemented
45#95×D61C2218yescomplemented
46C22×C22⋊C4×C61C2212yes—
47C61×#397C2214yescomplemented
48C61×#385C2214yescomplemented
49C61×#381C2214yescomplemented
50C61×#379C2211yescharacteristic
51C24×D61—216no—
52C24×D61—44no—
53C24×D61D418yes—
54C24×D61C2311yescharacteristic
55C24×D61C2311yescharacteristic
56C24×D61C2312yes—
57C24×D61C2312yes—
58C23×Dic61C2312yes—
59C23×Dic61C2312yes—
60C22×C4×D61—28no—
61C22×C4×D61—28no—
62C22×C4×D61—216no—
63C22×C4×D61—48no—
64C22×C4×D61C2314yes—
65C22×C4×D61C2314yes—
66C22×C4×D61C2314yes—
67C22×C4×D61C2314yes—
68C22×C4×D61C2314yes—
69C2×C4⋊Dic61C2314yescomplemented
70C2×#11758196C2318yescomplemented
71C4⋊C4×D61—48no—
72C2×C22⋊Dic61—28no—
73C2×C22⋊Dic61C2314yes—
74C2×C22⋊Dic61C2314yes—
75C2×C22⋊Dic61C2314yes—
76C2×C22⋊Dic61C2312yes—
77C2×#11758198—28no—
78C2×#11758198—28no—
79C2×#11758198C2314yes—
80C2×#11758198C2314yes—
81C2×#11758198C2314yes—
82C2×#11758198C2314yes—
83C2×#11758198C2318yes—
84C2×#11758198C2314yes—
85C22⋊C4×D61—216no—
86C22⋊C4×D61—216no—
87C22⋊C4×D61—216no—
88C22⋊C4×D61—216no—
89C22⋊C4×D61—216no—
90C22⋊C4×D61—44no—
91#14519684C2314yescomplemented
92#14519684C2318yescomplemented
93#14519684C2318yescomplemented
94#14519684C2318yescomplemented
95#14519684C2318yescomplemented
96C25×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2312yes—
99C2×C4⋊C4×C61C2314yescomplemented
100C2×C22⋊C4×C61—28no—
101C2×C22⋊C4×C61C2314yes—
102C2×C22⋊C4×C61C2314yes—
103C2×C22⋊C4×C61C2314yes—
104C2×C22⋊C4×C61C2312yes—
105#95×C61C2314yescomplemented
106#95×C61C2318yescomplemented
107C24×C61—28no—
108C24×C61—42no—
109C24×C61C2×D414yes—
110C24×C61C2411yescharacteristic
111C24×C61C2412yes—
112C23×D61—28no—
113C23×D61—28no—
114C23×D61—28no—
115C23×D61—264no—
116C23×D61—28no—
117C23×D61—28no—
118C23×D61—28no—
119C23×D61—24no—
120C23×D61—416no—
121C23×D61—42no—
122C23×D61—44no—
123C23×D61—464no—
124C23×D61C2×D414yes—
125C23×D61C2×D414yes—
126C23×D61C2×D418yes—
127C23×D61C2×D418yes—
128C23×D61#41116yes—
129C23×D61C2411yescharacteristic
130C23×D61C2412yes—
131C23×D61C2411yescharacteristic
132C22×C4×C61—24no—
133C22×C4×C61—24no—
134C22×C4×C61—28no—
135C22×C4×C61—44no—
136C22×C4×C61C2414yes—
137C22×C4×C61C2414yes—
138C22×C4×C61C2414yes—
139C22×Dic61—24no—
140C22×Dic61—24no—
141C22×Dic61—28no—
142C22×Dic61—44no—
143C22×Dic61C2414yes—
144C22×Dic61C2414yes—
145C22×Dic61C2414yes—
146C2×C4×D61—28no—
147C2×C4×D61—28no—
148C2×C4×D61—28no—
149C2×C4×D61—28no—
150C2×C4×D61—216no—
151C2×C4×D61—216no—
152C2×C4×D61—216no—
153C2×C4×D61—216no—
154C2×C4×D61—28no—
155C2×C4×D61—48no—
156C2×C4×D61—432no—
157C2×C4×D61—432no—
158C4⋊C4×C61—44no—
159C22⋊C4×C61—28no—
160C22⋊C4×C61—28no—
161C22⋊C4×C61—28no—
162C22⋊C4×C61—42no—
163C22⋊Dic61—28no—
164C22⋊Dic61—28no—
165C22⋊Dic61—28no—
166C22⋊Dic61—42no—
167#11758198—28no—
168#11758198—28no—
169#11758198—28no—
170#11758198—28no—
171#11758198—216no—
172#11758198—44no—
173C4⋊Dic61—44no—
174#11758196—48no—
175C23×C61—24no—
176C23×C61—24no—
177C23×C61—216no—
178C23×C61—24no—
179C23×C61—22no—
180C23×C61—44no—
181C23×C61—416no—
182C23×C61C22×D412yes—
183C23×C61C22×D414yes—
184C23×C61C2×#4118yes—
185C23×C61C2511yescharacteristic
186C22×D61—24no—
187C22×D61—24no—
188C22×D61—216no—
189C22×D61—216no—
190C22×D61—264no—
191C22×D61—216no—
192C22×D61—24no—
193C22×D61—22no—
194C22×D61—216no—
195C22×D61—216no—
196C22×D61—216no—
197C22×D61—28no—
198C22×D61—44no—
199C22×D61—48no—
200C22×D61—416no—
201C22×D61—4128no—
202C22×D61—432no—
203C22×D61—416no—
204C22×D61#123132yes—
205C22×D61C22×D412yes—
206C22×D61C22×D414yes—
207C22×D61C22×D412yes—
208C22×D61C2×#4118yes—
209C22×D61C2×#4118yes—
210C22×D61H(5,𝔽2)14yes—
211C2×C4×C61—24no—
212C2×C4×C61—24no—
213C2×C4×C61—28no—
214C2×C4×C61—28no—
215C2×C4×C61—28no—
216C2×C4×C61—24no—
217C2×C4×C61—48no—
218C2×C4×C61—48no—
219C2×Dic61—24no—
220C2×Dic61—24no—
221C2×Dic61—28no—
222C2×Dic61—28no—
223C2×Dic61—24no—
224C2×Dic61—28no—
225C2×Dic61—48no—
226C2×Dic61—48no—
227C4×D61—416no—
228C4×D61—416no—
229C4×D61—416no—
230C4×D61—416no—
231C4×D61—416no—
232C2×#2483—611nomaximal, Sylow
233C22×C61—24no—
234C22×C61—24no—
235C22×C61—216no—
236C22×C61—24no—
237C22×C61—22no—
238C22×C61—416no—
239C22×C61—44no—
240C22×C61C2×#12318yes—
241C22×C61C23×D411yescharacteristic
242C22×C61C22×#4114yes—
243C22×C61C2×H(5,𝔽2)12yes—
244C2×D61—24no—
245C2×D61—24no—
246C2×D61—216no—
247C2×D61—264no—
248C2×D61—24no—
249C2×D61—22no—
250C2×D61—416no—
251C2×D61—432no—
252C2×D61—44no—
253C2×D61—416no—
254C2×D61C2×#12318yes—
255C2×D61C2×#12318yes—
256C2×D61#53414yes—
257C2×D61#551116yes—
258C4×C61—44no—
259C4×C61—44no—
260C4×C61—44no—
261Dic61—44no—
262Dic61—44no—
263Dic61—44no—
264C23×C22⋊C4—612no—
265#2483—614no—
266#2483—614no—
267#2483—614no—
268#2483—611no—
269#2483—612no—
270#2483D6111yescharacteristic, direct product factor
271C2×#397—614no—
272C2×#385—614no—
273C2×#381—614no—
274C2×#379—611no—
275C2×C61—28no—
276C2×C61—42no—
277C2×C61C22×#12312yes—
278C2×C61C2×#53411yescharacteristic
279C2×C61C2×#55114yes—
280D61—28no—
281D61—42no—
282D61#248318yesdirect product factor
283C26—611no—
284C24×C4—612no—
285C24×C4—612no—
286C22×C4⋊C4—614no—
287C22×C22⋊C4—612no—
288C22×C22⋊C4—612no—
289C22×C22⋊C4—612no—
290C22×C22⋊C4—614no—
291C22×C22⋊C4—614no—
292C22×C22⋊C4—614no—
293C22×C22⋊C4—614no—
294C22×C22⋊C4—614no—
295C22×C22⋊C4—612no—
296C22×C22⋊C4—12216no—
297C22×C22⋊C4C2×D6112yes—
298#397—614no—
299#397—614no—
300#397—618no—
301#397—614no—
302#397—618no—
303#397C2×D6114yescomplemented
304#385—614no—
305#385—618no—
306#385—614no—
307#385—614no—
308#385—618no—
309#385C2×D6114yescomplemented
310#381—614no—
311#381—614no—
312#381—614no—
313#381—618no—
314#381—618no—
315#381C2×D6114yescomplemented
316#379—611no—
317#379—614no—
318#379—612no—
319#379C2×D6111yescharacteristic
320C2×#95—614no—
321C2×#95—618no—
322C61C2×#248311yescharacteristic, complemented, Sylow
323C25—612no—
324C25—611no—
325C25—618no—
326C25—611no—
327C25—612no—
328C25—12216no—
329C25—2444no—
330C25C22×D6111yescharacteristic
331C23×C4—612no—
332C23×C4—612no—
333C23×C4—614no—
334C23×C4—614no—
335C23×C4—614no—
336C23×C4—614no—
337C23×C4—614no—
338C23×C4—1228no—
339C23×C4—1228no—
340C23×C4—12216no—
341C23×C4—2448no—
342C23×C4C22×D6112yes—
343C23×C4C22×D6112yes—
344C2×C4⋊C4—618no—
345C2×C4⋊C4—614no—
346C2×C4⋊C4—2448no—
347C2×C4⋊C4C22×D6114yescomplemented
348C2×C22⋊C4—28no—
349C2×C22⋊C4—614no—
350C2×C22⋊C4—614no—
351C2×C22⋊C4—614no—
352C2×C22⋊C4—614no—
353C2×C22⋊C4—614no—
354C2×C22⋊C4—614no—
355C2×C22⋊C4—614no—
356C2×C22⋊C4—618no—
357C2×C22⋊C4—612no—
358C2×C22⋊C4—614no—
359C2×C22⋊C4—12216no—
360C2×C22⋊C4—12216no—
361C2×C22⋊C4—12216no—
362C2×C22⋊C4—12216no—
363C2×C22⋊C4—12216no—
364C2×C22⋊C4—1228no—
365C2×C22⋊C4—1228no—
366C2×C22⋊C4—1228no—
367C2×C22⋊C4—2444no—
368C2×C22⋊C4C22×D6114yes—
369C2×C22⋊C4C22×D6114yes—
370C2×C22⋊C4C22×D6114yes—
371C2×C22⋊C4C22×D6112yes—
372#95—614no—
373#95—618no—
374#95—618no—
375#95—618no—
376#95—618no—
377#95C22×D6114yescomplemented
378#95C22×D6118yescomplemented
379C24—28no—
380C24—42no—
381C24—611no—
382C24—618no—
383C24—6116no—
384C24—612no—
385C24—614no—
386C24—611no—
387C24—614no—
388C24—618no—
389C24—1228no—
390C24—1228no—
391C24—1224no—
392C24—1228no—
393C24—12264no—
394C24—1228no—
395C24—1228no—
396C24—1228no—
397C24—2444no—
398C24—2442no—
399C24—24416no—
400C24—24464no—
401C24D4×D6114yes—
402C24C23×D6111yescharacteristic
403C24C23×D6112yes—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—28no—
407C22×C4—44no—
408C22×C4—614no—
409C22×C4—614no—
410C22×C4—614no—
411C22×C4—1228no—
412C22×C4—1228no—
413C22×C4—1228no—
414C22×C4—1228no—
415C22×C4—12216no—
416C22×C4—1228no—
417C22×C4—12216no—
418C22×C4—12216no—
419C22×C4—12216no—
420C22×C4—1224no—
421C22×C4—1224no—
422C22×C4—1228no—
423C22×C4—2448no—
424C22×C4—24432no—
425C22×C4—24432no—
426C22×C4—2444no—
427C22×C4C23×D6114yes—
428C22×C4C23×D6114yes—
429C22×C4C23×D6114yes—
430C4⋊C4—44no—
431C4⋊C4—2448no—
432C4⋊C4—2444no—
433C22⋊C4—28no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—42no—
437C22⋊C4—1228no—
438C22⋊C4—1228no—
439C22⋊C4—1228no—
440C22⋊C4—1228no—
441C22⋊C4—12216no—
442C22⋊C4—1228no—
443C22⋊C4—1228no—
444C22⋊C4—1228no—
445C22⋊C4—2444no—
446C22⋊C4—2442no—
447C23—24no—
448C23—24no—
449C23—216no—
450C23—24no—
451C23—22no—
452C23—44no—
453C23—416no—
454C23—612no—
455C23—618no—
456C23—614no—
457C23—6132no—
458C23—614no—
459C23—618no—
460C23—612no—
461C23—12216no—
462C23—12216no—
463C23—12264no—
464C23—12216no—
465C23—12216no—
466C23—12216no—
467C23—1228no—
468C23—1224no—
469C23—1224no—
470C23—12216no—
471C23—1224no—
472C23—1222no—
473C23—2448no—
474C23—2444no—
475C23—24432no—
476C23—24416no—
477C23—244128no—
478C23—24416no—
479C23C2×D4×D6112yes—
480C23C2×D4×D6114yes—
481C23#41×D6118yes—
482C23C24×D6111yescharacteristic
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—28no—
486C2×C4—28no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—48no—
490C2×C4—48no—
491C2×C4—1224no—
492C2×C4—1224no—
493C2×C4—1228no—
494C2×C4—1228no—
495C2×C4—1224no—
496C2×C4—1228no—
497C2×C4—24416no—
498C2×C4—24416no—
499C2×C4—24416no—
500C2×C4—24416no—
501C2×C4—24416no—
502C2×C4—2448no—
503C2×C4—2448no—
504C22—24no—
505C22—216no—
506C22—24no—
507C22—24no—
508C22—22no—
509C22—416no—
510C22—44no—
511C22—618no—
512C22—6116no—
513C22—614no—
514C22—618no—
515C22—12264no—
516C22—1224no—
517C22—12216no—
518C22—1224no—
519C22—1224no—
520C22—1222no—
521C22—24432no—
522C22—24416no—
523C22—24416no—
524C22—2444no—
525C22#123×D6118yes—
526C22C22×D4×D6111yescharacteristic
527C22C2×#41×D6114yes—
528C22H(5,𝔽2)×D6112yes—
529C4—44no—
530C4—44no—
531C4—44no—
532C4—2444no—
533C4—2444no—
534C4—2444no—
535C2—28no—
536C2—42no—
537C2—618no—
538C2—1228no—
539C2—2442no—
540C2C2×#123×D6112yes—
541C2#534×D6111yescharacteristic
542C2#551×D6114yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2483C2
prime radicalC25×D61C22
hypercenter#2483D61
hypocenterC61C2×#2483
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2483

Complements

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

NH ≅ G/Ntype
2. #21450100C2semidirect
3. #21450099C2semidirect
4. #21450098C2semidirect
5. #21450097C2semidirect
6. #21450096C2semidirect
7. #397×D61C2semidirect
8. #385×D61C2semidirect
9. #381×D61C2semidirect
11. C61×#2483C2semidirect
15. C2×C4⋊C4×D61C22semidirect
26. #16839691C22semidirect
27. #16839690C22semidirect
28. #16839689C22semidirect
29. #16839688C22semidirect
30. #16839687C22semidirect
31. #16839637C22semidirect
32. #16839636C22semidirect
33. #16839635C22semidirect
34. #16839634C22semidirect
35. #16839633C22semidirect
36. #16839625C22semidirect
37. #16839624C22semidirect
38. #16839624C22semidirect
39. #16839623C22semidirect
40. #16839623C22semidirect
44. #95×D61C22semidirect
45. #95×D61C22semidirect
47. C61×#397C22semidirect
48. C61×#385C22semidirect
49. C61×#381C22semidirect
69. C2×C4⋊Dic61C23semidirect
70. C2×#11758196C23semidirect
91. #14519684C23semidirect
92. #14519684C23semidirect
93. #14519684C23semidirect
94. #14519684C23semidirect
95. #14519684C23semidirect
99. C2×C4⋊C4×C61C23semidirect
105. #95×C61C23semidirect
106. #95×C61C23semidirect
270. #2483D61direct (N × H)
282. D61#2483direct (N × H)
303. #397C2×D61semidirect
309. #385C2×D61semidirect
315. #381C2×D61semidirect
322. C61C2×#2483semidirect
347. C2×C4⋊C4C22×D61semidirect
377. #95C22×D61semidirect
378. #95C22×D61semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D612
#214501002
#214500992
#214500982
#214500972
#214500962
#397×D612
#385×D612
#381×D612
#379×D612
C61×#24832
C2×#248361