Finite Group Databasebeta

← D61×#2646 #29846454

Subgroups — D61×#2646 #29846454

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451792C212yesmaximal, complemented
2#21451791C214yesmaximal, complemented
3#21451790C214yesmaximal, complemented
4#21451789C211yesmaximal, characteristic, complemented
5#21451788C214yesmaximal, complemented
6#400×D61C214yesmaximal, complemented
7#398×D61C214yesmaximal, complemented
8#385×D61C214yesmaximal
9#380×D61C212yesmaximal
10C2×#95×D61C211yesmaximal, characteristic
11C61×#2646C211yesmaximal, characteristic, complemented
12C23×C4×D61C2212yes—
13C23×C4×D61C2211yescharacteristic
14C2×C4⋊C4×D61C2214yes—
15C2×C4⋊C4×D61C2214yes—
16C2×C4⋊C4×D61C2212yes—
17C2×C4⋊C4×D61C2212yes—
18C2×C22⋊C4×D61C2214yes—
19#16839704C2214yescomplemented
20#16839704C2214yescomplemented
21#16839703C2214yescomplemented
22#16839703C2214yescomplemented
23#16839702C2214yescomplemented
24#16839701C2214yescomplemented
25#16839700C2214yescomplemented
26#16839696C2214yescomplemented
27#16839696C2214yescomplemented
28#16839695C2214yescomplemented
29#16839695C2214yescomplemented
30#16839694C2214yescomplemented
31#16839693C2214yescomplemented
32#16839692C2214yescomplemented
33#16839637C2214yes—
34#16839636C2214yes—
35#16839636C2214yes—
36#16839635C2214yes—
37#16839634C2214yes—
38#16839633C2214yes—
39#16839633C2214yes—
40#16839622C2212yes—
41#16839621C2214yes—
42#16839620C2214yes—
43#16839619C2212yes—
44#16839619C2212yes—
45C2×#14519684C2212yes—
46C2×#14519684C2211yescharacteristic
47#95×D61C2214yes—
48#95×D61C2214yes—
49#95×D61C2214yes—
50#95×D61C2214yes—
51#95×D61C2214yes—
52C61×#400C2214yescomplemented
53C61×#398C2214yescomplemented
54C61×#385C2214yes—
55C61×#380C2212yes—
56C2×#95×C61C2211yescharacteristic
57C24×D61C2311yescharacteristic
58C23×Dic61C2312yes—
59C23×Dic61C2311yescharacteristic
60C22×C4×D61—28no—
61C22×C4×D61—44no—
62C22×C4×D61—44no—
63C22×C4×D61—44no—
64C22×C4×D61Q818yes—
65C22×C4×D61C2314yes—
66C22×C4×D61C2314yes—
67C22×C4×D61C2314yes—
68C22×C4×D61C2312yes—
69C22×C4×D61C2314yes—
70C22×C4×D61C2312yes—
71C2×C4⋊Dic61C2314yes—
72C2×C4⋊Dic61C2312yes—
73C2×C4⋊Dic61C2314yes—
74C2×C4⋊Dic61C2312yes—
75C2×#11758196C2314yes—
76C2×#11758196C2314yes—
77C2×#11758196C2314yes—
78C2×#11758196C2314yes—
79C2×#11758196C2314yes—
80C2×#11758196C2314yes—
81C4⋊C4×D61—44no—
82C4⋊C4×D61—44no—
83C4⋊C4×D61—48no—
84C4⋊C4×D61—48no—
85C2×C22⋊Dic61C2314yes—
86C2×#11758198C2314yes—
87C2×#11758198C2314yes—
88C22⋊C4×D61—216no—
89#14519684C2314yes—
90#14519684C2314yes—
91#14519684C2314yes—
92#14519684C2314yes—
93#14519684C2314yes—
94#14519684C2314yes—
95#14519684C2314yes—
96#14519684C2314yes—
97#14519684C2314yes—
98#14519684C2314yes—
99#14519684C2314yes—
100#14519684C2314yes—
101C23×C4×C61C2312yes—
102C23×C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2314yes—
104C2×C4⋊C4×C61C2312yes—
105C2×C4⋊C4×C61C2314yes—
106C2×C4⋊C4×C61C2312yes—
107C2×C22⋊C4×C61C2314yes—
108#95×C61C2314yes—
109#95×C61C2314yes—
110#95×C61C2314yes—
111#95×C61C2314yes—
112C24×C61C2411yescharacteristic
113C23×D61—22no—
114C23×D61—24no—
115C23×D61—22no—
116C23×D61C2×Q814yes—
117C23×D61#4118yes—
118C23×D61C2411yescharacteristic
119C23×D61C2411yescharacteristic
120C22×C4×C61—24no—
121C22×C4×C61—42no—
122C22×C4×C61—42no—
123C22×C4×C61—42no—
124C22×C4×C61C2×Q814yes—
125C22×C4×C61C2414yes—
126C22×C4×C61C2414yes—
127C22×C4×C61C2414yes—
128C22×C4×C61C2412yes—
129C22×Dic61—24no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61—42no—
133C22×Dic61C2×Q814yes—
134C22×Dic61C2414yes—
135C22×Dic61C2414yes—
136C22×Dic61C2414yes—
137C22×Dic61C2412yes—
138C2×C4×D61—24no—
139C2×C4×D61—24no—
140C2×C4×D61—28no—
141C2×C4×D61—28no—
142C2×C4×D61—28no—
143C2×C4×D61—28no—
144C2×C4×D61—28no—
145C2×C4×D61—28no—
146C2×C4×D61—28no—
147C2×C4×D61—28no—
148C2×C4×D61—28no—
149C2×C4×D61—28no—
150C2×C4×D61—416no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—44no—
154C2×C4×D61—44no—
155C2×C4×D61—432no—
156C2×C4×D61C2×Q818yes—
157C2×C4×D61C2×Q818yes—
158C4⋊C4×C61—42no—
159C4⋊C4×C61—42no—
160C4⋊C4×C61—44no—
161C4⋊C4×C61—44no—
162C22⋊C4×C61—28no—
163C22⋊Dic61—28no—
164#11758198—28no—
165#11758198—28no—
166C4⋊Dic61—42no—
167C4⋊Dic61—44no—
168C4⋊Dic61—42no—
169C4⋊Dic61—44no—
170#11758196—44no—
171#11758196—44no—
172#11758196—44no—
173#11758196—44no—
174#11758196—44no—
175#11758196—44no—
176C23×C61—21no—
177C23×C61—22no—
178C23×C61—21no—
179C23×C61C22×Q812yes—
180C23×C61C2×#4114yes—
181C23×C61C2511yescharacteristic
182C22×D61—21no—
183C22×D61—22no—
184C22×D61—21no—
185C22×D61—216no—
186C22×D61—216no—
187C22×D61—28no—
188C22×D61—28no—
189C22×D61#125116yes—
190C22×D61C22×Q812yes—
191C22×D61C22×Q812yes—
192C22×D61C2×#4114yes—
193C22×D61C2×#4114yes—
194C22×D61H(5,𝔽2)12yes—
195C22×D61H(5,𝔽2)14yes—
196C22×D612−1+412yes—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—24no—
202C2×C4×C61—24no—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—44no—
209C2×C4×C61—48no—
210C2×C4×C61C22×Q814yes—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—24no—
215C2×Dic61—24no—
216C2×Dic61—24no—
217C2×Dic61—24no—
218C2×Dic61—24no—
219C2×Dic61—24no—
220C2×Dic61—24no—
221C2×Dic61—24no—
222C2×Dic61—44no—
223C2×Dic61—48no—
224C2×Dic61C22×Q814yes—
225C4×D61—216no—
226C4×D61—48no—
227C4×D61—416no—
228C4×D61—416no—
229C4×D61—416no—
230C4×D61—416no—
231C2×#2646—611nomaximal, Sylow
232C22×C61—24no—
233C22×C61—24no—
234C22×C61—22no—
235C22×C61—22no—
236C22×C61C2×#12514yes—
237C22×C61C23×Q811yescharacteristic
238C22×C61C22×#4112yes—
239C22×C61C2×H(5,𝔽2)11yescharacteristic
240C22×C61C2×H(5,𝔽2)12yes—
241C22×C61C2×2−1+411yescharacteristic
242C2×D61—24no—
243C2×D61—24no—
244C2×D61—22no—
245C2×D61—22no—
246C2×D61—232no—
247C2×D61C2×#12514yes—
248C2×D61C2×#12514yes—
249C2×D61#53818yes—
250C2×D61#53918yes—
251C2×D61#54314yes—
252C2×D61#54414yes—
253C4×C61—24no—
254C4×C61—44no—
255C4×C61—44no—
256C4×C61—44no—
257Dic61—24no—
258Dic61—44no—
259Dic61—44no—
260Dic61—44no—
261#2646—614no—
262#2646—614no—
263#2646—614no—
264#2646—612no—
265#2646—611no—
266#2646D6111yescharacteristic, direct product factor
267C2×#400—614no—
268C2×#398—614no—
269C2×#385—614no—
270C2×#380—612no—
271C22×#95—611no—
272C2×C61—24no—
273C2×C61C22×#12511yescharacteristic
274C2×C61C2×#53812yes—
275C2×C61C2×#53912yes—
276C2×C61C2×#54311yescharacteristic
277C2×C61C2×#54411yescharacteristic
278D61—24no—
279D61#264618yesdirect product factor
280C24×C4—611no—
281C24×C4—612no—
282C22×C4⋊C4—612no—
283C22×C4⋊C4—614no—
284C22×C4⋊C4—614no—
285C22×C4⋊C4—612no—
286C22×C22⋊C4—614no—
287#400—614no—
288#400—614no—
289#400—614no—
290#400—614no—
291#400—614no—
292#400—614no—
293#400—614no—
294#400C2×D6114yescomplemented
295#398—614no—
296#398—614no—
297#398—614no—
298#398—614no—
299#398—614no—
300#398—614no—
301#398—614no—
302#398C2×D6114yescomplemented
303#385—614no—
304#385—614no—
305#385—614no—
306#385—614no—
307#385—614no—
308#385—614no—
309#385—614no—
310#385C2×D6114yes—
311#380—612no—
312#380—612no—
313#380—612no—
314#380—614no—
315#380—614no—
316#380C2×D6112yes—
317C2×#95—612no—
318C2×#95—611no—
319C2×#95—614no—
320C2×#95—614no—
321C2×#95—614no—
322C2×#95—614no—
323C2×#95—614no—
324C2×#95C2×D6111yescharacteristic
325C61C2×#264611yescharacteristic, complemented, Sylow
326C25—611no—
327C23×C4—611no—
328C23×C4—612no—
329C23×C4—618no—
330C23×C4—612no—
331C23×C4—612no—
332C23×C4—614no—
333C23×C4—614no—
334C23×C4—614no—
335C23×C4—614no—
336C23×C4—1228no—
337C23×C4—2444no—
338C23×C4—2444no—
339C23×C4—2444no—
340C23×C4C22×D6112yes—
341C23×C4C22×D6111yescharacteristic
342C2×C4⋊C4—614no—
343C2×C4⋊C4—612no—
344C2×C4⋊C4—614no—
345C2×C4⋊C4—612no—
346C2×C4⋊C4—614no—
347C2×C4⋊C4—614no—
348C2×C4⋊C4—614no—
349C2×C4⋊C4—614no—
350C2×C4⋊C4—614no—
351C2×C4⋊C4—614no—
352C2×C4⋊C4—2444no—
353C2×C4⋊C4—2444no—
354C2×C4⋊C4—2448no—
355C2×C4⋊C4—2448no—
356C2×C4⋊C4C22×D6112yes—
357C2×C4⋊C4C22×D6112yes—
358C2×C4⋊C4C22×D6114yes—
359C2×C4⋊C4C22×D6114yes—
360C2×C22⋊C4—614no—
361C2×C22⋊C4—614no—
362C2×C22⋊C4—614no—
363C2×C22⋊C4—12216no—
364C2×C22⋊C4C22×D6114yes—
365#95—614no—
366#95—614no—
367#95—614no—
368#95—614no—
369#95—614no—
370#95—614no—
371#95—614no—
372#95—614no—
373#95—614no—
374#95—614no—
375#95—614no—
376#95—614no—
377#95C22×D6114yes—
378#95C22×D6114yes—
379#95C22×D6114yes—
380#95C22×D6114yes—
381C24—611no—
382C24—614no—
383C24—618no—
384C24—611no—
385C24—1224no—
386C24—1222no—
387C24—1222no—
388C24C23×D6111yescharacteristic
389C22×C4—24no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—612no—
394C22×C4—614no—
395C22×C4—618no—
396C22×C4—618no—
397C22×C4—614no—
398C22×C4—614no—
399C22×C4—614no—
400C22×C4—1224no—
401C22×C4—1224no—
402C22×C4—1228no—
403C22×C4—1228no—
404C22×C4—1228no—
405C22×C4—1228no—
406C22×C4—1228no—
407C22×C4—1228no—
408C22×C4—1228no—
409C22×C4—1228no—
410C22×C4—1228no—
411C22×C4—1228no—
412C22×C4—1224no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4—2444no—
416C22×C4—2444no—
417C22×C4—24416no—
418C22×C4—24432no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4Q8×D6114yes—
423C22×C4C23×D6114yes—
424C22×C4C23×D6114yes—
425C22×C4C23×D6114yes—
426C22×C4C23×D6112yes—
427C4⋊C4—42no—
428C4⋊C4—42no—
429C4⋊C4—44no—
430C4⋊C4—44no—
431C4⋊C4—2444no—
432C4⋊C4—2444no—
433C4⋊C4—2444no—
434C4⋊C4—2444no—
435C4⋊C4—2444no—
436C4⋊C4—2444no—
437C4⋊C4—2442no—
438C4⋊C4—2442no—
439C4⋊C4—2444no—
440C4⋊C4—2444no—
441C22⋊C4—28no—
442C22⋊C4—1228no—
443C22⋊C4—1228no—
444C22⋊C4—1228no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—612no—
449C23—614no—
450C23—614no—
451C23—612no—
452C23—612no—
453C23—6116no—
454C23—612no—
455C23—614no—
456C23—1228no—
457C23—12216no—
458C23—1228no—
459C23—12216no—
460C23—1222no—
461C23—1221no—
462C23—1221no—
463C23C2×Q8×D6112yes—
464C23#41×D6114yes—
465C23C24×D6111yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—614no—
480C2×C4—12216no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1224no—
484C2×C4—1224no—
485C2×C4—1224no—
486C2×C4—1224no—
487C2×C4—1224no—
488C2×C4—1224no—
489C2×C4—1224no—
490C2×C4—1224no—
491C2×C4—1224no—
492C2×C4—2448no—
493C2×C4—24416no—
494C2×C4—24416no—
495C2×C4—24416no—
496C2×C4—24416no—
497C2×C4—2444no—
498C2×C4—2448no—
499C2×C4C2×Q8×D6114yes—
500C22—22no—
501C22—22no—
502C22—24no—
503C22—24no—
504C22—614no—
505C22—614no—
506C22—614no—
507C22—618no—
508C22—618no—
509C22—614no—
510C22—12232no—
511C22—1222no—
512C22—1222no—
513C22—1224no—
514C22—1224no—
515C22#125×D6114yes—
516C22C22×Q8×D6111yescharacteristic
517C22C2×#41×D6112yes—
518C22H(5,𝔽2)×D6112yes—
519C22H(5,𝔽2)×D6111yescharacteristic
520C222−1+4×D6111yescharacteristic
521C4—24no—
522C4—44no—
523C4—44no—
524C4—44no—
525C4—1224no—
526C4—2444no—
527C4—2444no—
528C4—2444no—
529C2—24no—
530C2—618no—
531C2—1224no—
532C2C2×#125×D6111yescharacteristic
533C2#538×D6112yes—
534C2#539×D6112yes—
535C2#543×D6111yescharacteristic
536C2#544×D6111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2646C2
prime radicalC24×D61C23
hypercenter#2646D61
hypocenterC61C2×#2646
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2646

Complements

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

NH ≅ G/Ntype
1. #21451792C2semidirect
2. #21451791C2semidirect
3. #21451790C2semidirect
4. #21451789C2semidirect
5. #21451788C2semidirect
6. #400×D61C2semidirect
7. #398×D61C2semidirect
11. C61×#2646C2semidirect
19. #16839704C22semidirect
20. #16839704C22semidirect
21. #16839703C22semidirect
22. #16839703C22semidirect
23. #16839702C22semidirect
24. #16839701C22semidirect
25. #16839700C22semidirect
26. #16839696C22semidirect
27. #16839696C22semidirect
28. #16839695C22semidirect
29. #16839695C22semidirect
30. #16839694C22semidirect
31. #16839693C22semidirect
32. #16839692C22semidirect
52. C61×#400C22semidirect
53. C61×#398C22semidirect
266. #2646D61direct (N × H)
279. D61#2646direct (N × H)
294. #400C2×D61semidirect
302. #398C2×D61semidirect
325. C61C2×#2646semidirect

Maximal subgroups

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

subgroupindex
#214517922
#214517912
#214517902
#214517892
#214517882
#400×D612
#398×D612
#385×D612
#380×D612
C2×#95×D612
C61×#26462
C2×#264661