Finite Group Databasebeta

← D61×#2608 #29851440

Subgroups — D61×#2608 #29851440

Order 15616.

2270 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451489C211yesmaximal, characteristic, complemented
2#21451488C214yesmaximal, complemented
3#21451487C214yesmaximal, complemented
4#21451486C212yesmaximal, complemented
5#21451485C214yesmaximal, complemented
6#396×D61C214yesmaximal
7#389×D61C214yesmaximal, complemented
8#387×D61C214yesmaximal, complemented
9#381×D61C211yesmaximal, characteristic
10C4×C22⋊C4×D61C212yesmaximal
11C61×#2608C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C2×C4⋊C4×D61C2214yes—
14C2×C4⋊C4×D61C2214yes—
15C2×C4⋊C4×D61C2214yes—
16C2×C22⋊C4×D61C2214yes—
17C2×C22⋊C4×D61C2212yes—
18C2×C42×D61C2212yes—
19C2×C42×D61C2212yes—
20#16839686C2214yes—
21#16839685C2214yes—
22#16839685C2214yes—
23#16839685C2214yes—
24#16839684C2214yes—
25#16839684C2214yes—
26#16839684C2214yes—
27#16839661C2214yescomplemented
28#16839660C2214yescomplemented
29#16839659C2214yescomplemented
30#16839659C2214yescomplemented
31#16839658C2214yescomplemented
32#16839657C2214yescomplemented
33#16839657C2214yescomplemented
34#16839649C2214yescomplemented
35#16839648C2214yescomplemented
36#16839647C2214yescomplemented
37#16839646C2214yescomplemented
38#16839645C2214yescomplemented
39#16839644C2214yescomplemented
40#16839643C2214yescomplemented
41#16839625C2211yescharacteristic
42#16839624C2214yes—
43#16839623C2212yes—
44C22⋊C4×Dic61C2214yes—
45C4×#11758198C2212yes—
46C4×#11758198C2212yes—
47C4×C22⋊Dic61C2212yes—
48#16839609C2214yes—
49#95×D61C2214yes—
50#95×D61C2214yes—
51#95×D61C2214yes—
52C61×#396C2214yes—
53C61×#389C2214yescomplemented
54C61×#387C2214yescomplemented
55C61×#381C2211yescharacteristic
56C4×C22⋊C4×C61C2212yes—
57C24×D61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C22×C4×D61—44no—
60C22×C4×D61Q818yes—
61C22×C4×D61C2314yes—
62C22×C4×D61C2314yes—
63C22×C4×D61C2312yes—
64C22×C4×D61C2314yes—
65C22×C4×D61C2312yes—
66C2×C4⋊Dic61C2314yes—
67C2×C4⋊Dic61C2314yes—
68C2×C4⋊Dic61C2314yes—
69C2×#11758196C2314yes—
70C2×#11758196C2314yes—
71C2×#11758196C2314yes—
72C2×#11758196C2314yes—
73C2×#11758196C2314yes—
74C2×#11758196C2314yes—
75C4⋊C4×D61—216no—
76C4⋊C4×D61—216no—
77C4⋊C4×D61—48no—
78C2×C22⋊Dic61C2314yes—
79C2×C22⋊Dic61C2312yes—
80C2×#11758198C2314yes—
81C2×#11758198C2314yes—
82C2×#11758198C2314yes—
83C22⋊C4×D61—216no—
84C22⋊C4×D61—44no—
85C2×C4×Dic61C2314yes—
86C2×C4×Dic61C2314yes—
87C2×C4×Dic61C2312yes—
88C2×C4×Dic61C2312yes—
89C42×D61—44no—
90C42×D61—44no—
91#14519684C2314yes—
92#14519684C2314yes—
93#14519684C2314yes—
94#14519684C2314yes—
95#14519684C2314yes—
96#14519684C2314yes—
97#14519684C2314yes—
98#14519684C2314yes—
99#14519684C2314yes—
100C23×C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2314yes—
102C2×C4⋊C4×C61C2314yes—
103C2×C4⋊C4×C61C2314yes—
104C2×C22⋊C4×C61C2314yes—
105C2×C22⋊C4×C61C2312yes—
106C2×C42×C61C2312yes—
107C2×C42×C61C2312yes—
108#95×C61C2314yes—
109#95×C61C2314yes—
110#95×C61C2314yes—
111C24×C61C2411yescharacteristic
112C23×D61—28no—
113C23×D61—24no—
114C23×D61C2×Q814yes—
115C23×D61C2411yescharacteristic
116C23×D61C2411yescharacteristic
117C22×C4×C61—42no—
118C22×C4×C61C2×Q814yes—
119C22×C4×C61C2414yes—
120C22×C4×C61C2414yes—
121C22×C4×C61C2412yes—
122C22×C4×C61C2414yes—
123C22×Dic61—42no—
124C22×Dic61C2×Q814yes—
125C22×Dic61C2414yes—
126C22×Dic61C2414yes—
127C22×Dic61C2412yes—
128C22×Dic61C2414yes—
129C2×C4×D61—28no—
130C2×C4×D61—24no—
131C2×C4×D61—24no—
132C2×C4×D61—28no—
133C2×C4×D61—28no—
134C2×C4×D61—28no—
135C2×C4×D61—28no—
136C2×C4×D61—28no—
137C2×C4×D61—28no—
138C2×C4×D61—28no—
139C2×C4×D61—416no—
140C2×C4×D61—42no—
141C2×C4×D61—42no—
142C2×C4×D61C2×Q818yes—
143C2×C4×D61C2×Q818yes—
144C2×C4×D61#41116yes—
145C4⋊C4×C61—28no—
146C4⋊C4×C61—28no—
147C4⋊C4×C61—44no—
148C22⋊C4×C61—28no—
149C22⋊C4×C61—42no—
150C42×C61—42no—
151C42×C61—42no—
152C22⋊Dic61—28no—
153C22⋊Dic61—42no—
154#11758198—28no—
155#11758198—28no—
156#11758198—44no—
157C4⋊Dic61—28no—
158C4⋊Dic61—28no—
159C4⋊Dic61—44no—
160#11758196—28no—
161#11758196—28no—
162#11758196—28no—
163#11758196—28no—
164#11758196—44no—
165#11758196—44no—
166C4×Dic61—42no—
167C4×Dic61—44no—
168C4×Dic61—44no—
169C4×Dic61—42no—
170C23×C61—24no—
171C23×C61—22no—
172C23×C61C22×Q812yes—
173C23×C61C2511yescharacteristic
174C22×D61—24no—
175C22×D61—22no—
176C22×D61—216no—
177C22×D61—28no—
178C22×D61—416no—
179C22×D61C22×Q812yes—
180C22×D61C22×Q812yes—
181C22×D61C2×#4118yes—
182C22×D61H(5,𝔽2)14yes—
183C2×C4×C61—24no—
184C2×C4×C61—24no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—24no—
188C2×C4×C61—24no—
189C2×C4×C61—24no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—24no—
193C2×C4×C61—44no—
194C2×C4×C61C22×Q814yes—
195C2×C4×C61C2×#4118yes—
196C2×Dic61—24no—
197C2×Dic61—24no—
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—24no—
201C2×Dic61—24no—
202C2×Dic61—24no—
203C2×Dic61—24no—
204C2×Dic61—24no—
205C2×Dic61—24no—
206C2×Dic61—44no—
207C2×Dic61C22×Q814yes—
208C2×Dic61C2×#4118yes—
209C4×D61—216no—
210C4×D61—232no—
211C4×D61—48no—
212C4×D61—416no—
213C4×D61—416no—
214C2×#2608—611nomaximal, Sylow
215C22×C61—24no—
216C22×C61—22no—
217C22×C61—44no—
218C22×C61C23×Q811yescharacteristic
219C22×C61C22×#4114yes—
220C22×C61C2×H(5,𝔽2)12yes—
221C2×D61—24no—
222C2×D61—22no—
223C2×D61—44no—
224C2×D61—416no—
225C2×D61#53318yes—
226C2×D61#54314yes—
227C2×D61#553116yes—
228C4×C61—24no—
229C4×C61—28no—
230C4×C61—44no—
231C4×C61—44no—
232Dic61—24no—
233Dic61—28no—
234Dic61—44no—
235Dic61—44no—
236#2608—614no—
237#2608—614no—
238#2608—614no—
239#2608—611no—
240#2608—612no—
241#2608D6111yescharacteristic, direct product factor
242C2×#396—614no—
243C2×#389—614no—
244C2×#387—614no—
245C2×#381—611no—
246C2×C4×C22⋊C4—612no—
247C2×C61—42no—
248C2×C61C2×#53312yes—
249C2×C61C2×#54311yescharacteristic
250C2×C61C2×#55314yes—
251D61—42no—
252D61#260818yesdirect product factor
253C24×C4—611no—
254C22×C4⋊C4—614no—
255C22×C4⋊C4—614no—
256C22×C4⋊C4—614no—
257C22×C22⋊C4—614no—
258C22×C22⋊C4—612no—
259C22×C42—612no—
260C22×C42—612no—
261#396—614no—
262#396—614no—
263#396—614no—
264#396—614no—
265#396—614no—
266#396—614no—
267#396—614no—
268#396C2×D6114yes—
269#389—614no—
270#389—614no—
271#389—614no—
272#389—614no—
273#389—614no—
274#389—614no—
275#389—614no—
276#389C2×D6114yescomplemented
277#387—614no—
278#387—614no—
279#387—614no—
280#387—614no—
281#387—614no—
282#387—614no—
283#387—614no—
284#387C2×D6114yescomplemented
285#381—611no—
286#381—612no—
287#381—614no—
288#381C2×D6111yescharacteristic
289C4×C22⋊C4—612no—
290C4×C22⋊C4—614no—
291C4×C22⋊C4—612no—
292C4×C22⋊C4—612no—
293C4×C22⋊C4—614no—
294C4×C22⋊C4C2×D6112yes—
295C2×#95—614no—
296C2×#95—614no—
297C2×#95—614no—
298C61C2×#260811yescharacteristic, complemented, Sylow
299C25—611no—
300C23×C4—611no—
301C23×C4—614no—
302C23×C4—612no—
303C23×C4—618no—
304C23×C4—612no—
305C23×C4—614no—
306C23×C4—614no—
307C23×C4—2444no—
308C23×C4C22×D6111yescharacteristic
309C2×C4⋊C4—614no—
310C2×C4⋊C4—614no—
311C2×C4⋊C4—614no—
312C2×C4⋊C4—614no—
313C2×C4⋊C4—614no—
314C2×C4⋊C4—614no—
315C2×C4⋊C4—614no—
316C2×C4⋊C4—614no—
317C2×C4⋊C4—614no—
318C2×C4⋊C4—12216no—
319C2×C4⋊C4—12216no—
320C2×C4⋊C4—2448no—
321C2×C4⋊C4C22×D6114yes—
322C2×C4⋊C4C22×D6114yes—
323C2×C4⋊C4C22×D6114yes—
324C2×C22⋊C4—614no—
325C2×C22⋊C4—614no—
326C2×C22⋊C4—614no—
327C2×C22⋊C4—612no—
328C2×C22⋊C4—614no—
329C2×C22⋊C4—12216no—
330C2×C22⋊C4—2444no—
331C2×C22⋊C4C22×D6114yes—
332C2×C22⋊C4C22×D6112yes—
333C2×C42—614no—
334C2×C42—612no—
335C2×C42—614no—
336C2×C42—612no—
337C2×C42—2444no—
338C2×C42—2444no—
339C2×C42C22×D6112yes—
340C2×C42C22×D6112yes—
341#95—614no—
342#95—614no—
343#95—614no—
344#95—614no—
345#95—614no—
346#95—614no—
347#95—614no—
348#95—614no—
349#95—614no—
350#95C22×D6114yes—
351#95C22×D6114yes—
352#95C22×D6114yes—
353C24—611no—
354C24—614no—
355C24—611no—
356C24—1228no—
357C24—1224no—
358C24C23×D6111yescharacteristic
359C22×C4—42no—
360C22×C4—612no—
361C22×C4—614no—
362C22×C4—614no—
363C22×C4—618no—
364C22×C4—6116no—
365C22×C4—618no—
366C22×C4—614no—
367C22×C4—614no—
368C22×C4—1228no—
369C22×C4—1224no—
370C22×C4—1224no—
371C22×C4—1228no—
372C22×C4—1228no—
373C22×C4—1228no—
374C22×C4—1228no—
375C22×C4—1228no—
376C22×C4—1228no—
377C22×C4—1228no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—24416no—
381C22×C4—2442no—
382C22×C4Q8×D6114yes—
383C22×C4C23×D6114yes—
384C22×C4C23×D6114yes—
385C22×C4C23×D6112yes—
386C22×C4C23×D6114yes—
387C4⋊C4—28no—
388C4⋊C4—28no—
389C4⋊C4—44no—
390C4⋊C4—1228no—
391C4⋊C4—1228no—
392C4⋊C4—1228no—
393C4⋊C4—1228no—
394C4⋊C4—1228no—
395C4⋊C4—1228no—
396C4⋊C4—2444no—
397C4⋊C4—2444no—
398C4⋊C4—2444no—
399C22⋊C4—28no—
400C22⋊C4—42no—
401C22⋊C4—1228no—
402C22⋊C4—1228no—
403C22⋊C4—1228no—
404C22⋊C4—2444no—
405C22⋊C4—2442no—
406C42—42no—
407C42—42no—
408C42—2444no—
409C42—2442no—
410C42—2442no—
411C42—2444no—
412C23—24no—
413C23—22no—
414C23—612no—
415C23—618no—
416C23—614no—
417C23—612no—
418C23—1228no—
419C23—12216no—
420C23—1224no—
421C23—1222no—
422C23—24416no—
423C23C2×Q8×D6112yes—
424C23C24×D6111yescharacteristic
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—614no—
437C2×C4—618no—
438C2×C4—12232no—
439C2×C4—12216no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1222no—
443C2×C4—1222no—
444C2×C4—1224no—
445C2×C4—1224no—
446C2×C4—1224no—
447C2×C4—1224no—
448C2×C4—1224no—
449C2×C4—1224no—
450C2×C4—2448no—
451C2×C4—24416no—
452C2×C4—24416no—
453C2×C4—2444no—
454C2×C4C2×Q8×D6114yes—
455C2×C4#41×D6118yes—
456C22—22no—
457C22—24no—
458C22—44no—
459C22—614no—
460C22—6116no—
461C22—618no—
462C22—1222no—
463C22—1224no—
464C22—24416no—
465C22—2444no—
466C22C22×Q8×D6111yescharacteristic
467C22C2×#41×D6114yes—
468C22H(5,𝔽2)×D6112yes—
469C4—24no—
470C4—28no—
471C4—44no—
472C4—44no—
473C4—1224no—
474C4—1228no—
475C4—2444no—
476C4—2444no—
477C2—42no—
478C2—618no—
479C2—2442no—
480C2#533×D6112yes—
481C2#543×D6111yescharacteristic
482C2#553×D6114yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2608C2
prime radicalC24×D61C23
hypercenter#2608D61
hypocenterC61C2×#2608
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2608

Complements

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

NH ≅ G/Ntype
1. #21451489C2semidirect
2. #21451488C2semidirect
3. #21451487C2semidirect
4. #21451486C2semidirect
5. #21451485C2semidirect
7. #389×D61C2semidirect
8. #387×D61C2semidirect
11. C61×#2608C2semidirect
27. #16839661C22semidirect
28. #16839660C22semidirect
29. #16839659C22semidirect
30. #16839659C22semidirect
31. #16839658C22semidirect
32. #16839657C22semidirect
33. #16839657C22semidirect
34. #16839649C22semidirect
35. #16839648C22semidirect
36. #16839647C22semidirect
37. #16839646C22semidirect
38. #16839645C22semidirect
39. #16839644C22semidirect
40. #16839643C22semidirect
53. C61×#389C22semidirect
54. C61×#387C22semidirect
241. #2608D61direct (N × H)
252. D61#2608direct (N × H)
276. #389C2×D61semidirect
284. #387C2×D61semidirect
298. C61C2×#2608semidirect

Maximal subgroups

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

subgroupindex
#214514892
#214514882
#214514872
#214514862
#214514852
#396×D612
#389×D612
#387×D612
#381×D612
C4×C22⋊C4×D612
C61×#26082
C2×#260861