Finite Group Databasebeta

← D61×#2401 #29846308

Subgroups — D61×#2401 #29846308

Order 15616.

2294 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449122C211yesmaximal, characteristic, complemented
2#21449121C211yesmaximal, characteristic, complemented
3#21449120C213yesmaximal, complemented
4#21449119C213yesmaximal, complemented
5#21449118C213yesmaximal, complemented
6#21449117C211yesmaximal, characteristic, complemented
7#21449116C213yesmaximal, complemented
8#401×D61C211yesmaximal, characteristic, complemented
9#400×D61C213yesmaximal, complemented
10#397×D61C213yesmaximal
11#396×D61C211yesmaximal, characteristic
12C4×C4⋊C4×D61C213yesmaximal, complemented
13C4×C22⋊C4×D61C213yesmaximal
14#376×D61C211yesmaximal, characteristic, complemented
15C61×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C2×C4⋊C4×D61C2213yes—
18C2×C4⋊C4×D61C2213yes—
19C2×C22⋊C4×D61C2213yes—
20C2×C22⋊C4×D61C2213yes—
21C2×C42×D61C2213yes—
22C2×C42×D61C2213yes—
23C61⋊#401C2213yescomplemented
24C61⋊#401C2211yescharacteristic, complemented
25C61⋊#401C2213yescomplemented
26#16839704C2213yescomplemented
27#16839704C2213yescomplemented
28#16839703C2213yescomplemented
29#16839703C2213yescomplemented
30#16839702C2213yescomplemented
31#16839701C2213yescomplemented
32#16839700C2213yescomplemented
33#16839691C2213yes—
34#16839691C2213yes—
35#16839690C2213yes—
36#16839690C2213yes—
37#16839689C2213yes—
38#16839688C2213yes—
39#16839687C2213yes—
40#16839686C2211yescharacteristic
41#16839685C2213yes—
42#16839684C2213yes—
43C4⋊C4×Dic61C2213yescomplemented
44C4⋊C4×Dic61C2213yescomplemented
45C4×#11758196C2213yescomplemented
46C4×#11758196C2213yescomplemented
47C4×C4⋊Dic61C2213yescomplemented
48#16839613C2213yescomplemented
49#16839613C2213yescomplemented
50C22⋊C4×Dic61C2213yes—
51C22⋊C4×Dic61C2213yes—
52C4×#11758198C2213yes—
53C4×#11758198C2213yes—
54C4×C22⋊Dic61C2213yes—
55#16839609C2213yes—
56#16839609C2213yes—
57#16839608C2213yescomplemented
58#16839607C2213yescomplemented
59#16839607C2211yescharacteristic, complemented
60#95×D61C2211yescharacteristic
61#95×D61C2213yes—
62#95×D61C2213yes—
63#95×D61C2213yes—
64#95×D61C2213yes—
65#95×D61C2213yes—
66C61×#401C2211yescharacteristic, complemented
67C61×#400C2213yescomplemented
68C61×#397C2213yes—
69C61×#396C2211yescharacteristic
70C4×C4⋊C4×C61C2213yescomplemented
71C4×C22⋊C4×C61C2213yes—
72C61×#376C2211yescharacteristic, complemented
73C24×D61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C22×C4×D61—212no—
76C22×C4×D61C2313yes—
77C22×C4×D61C2313yes—
78C22×C4×D61C2313yes—
79C22×C4×D61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C22×C4×D61C2311yescharacteristic
82C22×C4×D61C2313yes—
83C22×C4×D61C2311yescharacteristic
84C2×C4⋊Dic61C2313yes—
85C2×C4⋊Dic61C2313yes—
86C2×#11758196C2313yes—
87C2×#11758196C2313yes—
88C2×#11758196C2313yes—
89C2×#11758196C2313yes—
90C4⋊C4×D61—212no—
91C4⋊C4×D61—212no—
92C2×C22⋊Dic61C2313yes—
93C2×C22⋊Dic61C2313yes—
94C2×#11758198C2313yes—
95C2×#11758198C2313yes—
96C2×#11758198C2313yes—
97C2×#11758198C2313yes—
98C22⋊C4×D61—212no—
99C22⋊C4×D61—212no—
100C2×C4×Dic61C2313yes—
101C2×C4×Dic61C2313yes—
102C2×C4×Dic61C2313yes—
103C2×C4×Dic61C2313yes—
104C2×C4×Dic61C2313yes—
105C2×C4×Dic61C2313yes—
106C42×D61—212no—
107C42×D61—212no—
108#14519684C2313yes—
109#14519684C2313yes—
110#14519684C2313yes—
111#14519684C2313yes—
112#14519684C2313yes—
113#14519684C2313yes—
114#14519684C2313yes—
115#14519684C2313yes—
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×C61C2311yescharacteristic
132#95×C61C2313yes—
133#95×C61C2313yes—
134#95×C61C2313yes—
135#95×C61C2313yes—
136#95×C61C2313yes—
137C24×C61C2411yescharacteristic
138C23×D61—26no—
139C23×D61—26no—
140C23×D61#4114yes—
141C23×D61C2411yescharacteristic
142C23×D61C2411yescharacteristic
143C22×C4×C61—26no—
144C22×C4×C61C2411yescharacteristic
145C22×C4×C61C2413yes—
146C22×C4×C61C2413yes—
147C22×C4×C61C2413yes—
148C22×C4×C61C2413yes—
149C22×C4×C61C2411yescharacteristic
150C22×Dic61—26no—
151C22×Dic61C2411yescharacteristic
152C22×Dic61C2413yes—
153C22×Dic61C2413yes—
154C22×Dic61C2413yes—
155C22×Dic61C2413yes—
156C22×Dic61C2411yescharacteristic
157C2×C4×D61—26no—
158C2×C4×D61—26no—
159C2×C4×D61—26no—
160C2×C4×D61—26no—
161C2×C4×D61—26no—
162C2×C4×D61—26no—
163C2×C4×D61—26no—
164C2×C4×D61—26no—
165C2×C4×D61—26no—
166C2×C4×D61—26no—
167C2×C4×D61—26no—
168C2×C4×D61—26no—
169C2×C4×D61—26no—
170C2×C4×D61—26no—
171C2×C4×D61—416no—
172C2×C4×D61#41112yes—
173C2×C4×D61#41112yes—
174C4⋊C4×C61—26no—
175C4⋊C4×C61—26no—
176C22⋊C4×C61—26no—
177C22⋊C4×C61—26no—
178C42×C61—26no—
179C42×C61—26no—
180C22⋊Dic61—26no—
181C22⋊Dic61—26no—
182#11758198—26no—
183#11758198—26no—
184#11758198—26no—
185#11758198—26no—
186C4⋊Dic61—26no—
187C4⋊Dic61—26no—
188#11758196—26no—
189#11758196—26no—
190#11758196—26no—
191#11758196—26no—
192C4×Dic61—26no—
193C4×Dic61—26no—
194C4×Dic61—26no—
195C4×Dic61—26no—
196C4×Dic61—26no—
197C4×Dic61—26no—
198C23×C61—23no—
199C23×C61—23no—
200C23×C61C2×#4112yes—
201C23×C61C2511yescharacteristic
202C22×D61—23no—
203C22×D61—23no—
204C22×D61—224no—
205C22×D61—44no—
206C22×D61—412no—
207C22×D61C2×#4112yes—
208C22×D61C2×#4116yes—
209C22×D61C2×#4112yes—
210C22×D61C2×#4116yes—
211C2×C4×C61—23no—
212C2×C4×C61—23no—
213C2×C4×C61—23no—
214C2×C4×C61—23no—
215C2×C4×C61—23no—
216C2×C4×C61—23no—
217C2×C4×C61—23no—
218C2×C4×C61—23no—
219C2×C4×C61—23no—
220C2×C4×C61—23no—
221C2×C4×C61—23no—
222C2×C4×C61—23no—
223C2×C4×C61—44no—
224C2×C4×C61C2×#4116yes—
225C2×C4×C61C2×#4116yes—
226C2×Dic61—23no—
227C2×Dic61—23no—
228C2×Dic61—23no—
229C2×Dic61—23no—
230C2×Dic61—23no—
231C2×Dic61—23no—
232C2×Dic61—23no—
233C2×Dic61—23no—
234C2×Dic61—23no—
235C2×Dic61—23no—
236C2×Dic61—23no—
237C2×Dic61—23no—
238C2×Dic61—44no—
239C2×Dic61C2×#4116yes—
240C2×Dic61C2×#4116yes—
241C4×D61—224no—
242C4×D61—44no—
243C4×D61—412no—
244C4×D61—412no—
245C4×D61—412no—
246C4×D61—44no—
247C4×D61—44no—
248C4×D61#126116yes—
249C2×#2401—611nomaximal, Sylow
250C22×C61—26no—
251C22×C61—41no—
252C22×C61—43no—
253C22×C61C22×#4113yes—
254C22×C61C22×#4111yescharacteristic
255C22×C61C22×#4113yes—
256C2×D61—26no—
257C2×D61—41no—
258C2×D61—43no—
259C2×D61—416no—
260C2×D61C2×#12614yes—
261C2×D61#529112yes—
262C2×D61#529112yes—
263C4×C61—26no—
264C4×C61—41no—
265C4×C61—43no—
266C4×C61—43no—
267C4×C61—43no—
268C4×C61C2×#12614yes—
269Dic61—26no—
270Dic61—41no—
271Dic61—43no—
272Dic61—43no—
273Dic61—43no—
274Dic61C2×#12614yes—
275#2401—611no—
276#2401—613no—
277#2401—613no—
278#2401—611no—
279#2401—613no—
280#2401—613no—
281#2401—611no—
282#2401D6111yescharacteristic, direct product factor
283C2×#401—611no—
284C2×#400—613no—
285C2×#397—613no—
286C2×#396—611no—
287C2×C4×C4⋊C4—613no—
288C2×C4×C22⋊C4—613no—
289C2×#376—611no—
290C2×C61—42no—
291C2×C61C22×#12611yescharacteristic
292C2×C61C2×#52913yes—
293C2×C61C2×#52913yes—
294D61—42no—
295D61#240118yesdirect product factor
296C24×C4—611no—
297C22×C4⋊C4—613no—
298C22×C4⋊C4—613no—
299C22×C22⋊C4—613no—
300C22×C22⋊C4—613no—
301C22×C42—613no—
302C22×C42—613no—
303#401—613no—
304#401—613no—
305#401—611no—
306#401C2×D6111yescharacteristic, complemented
307#400—613no—
308#400—613no—
309#400—613no—
310#400—613no—
311#400—613no—
312#400—613no—
313#400—613no—
314#400C2×D6113yescomplemented
315#397—613no—
316#397—613no—
317#397—613no—
318#397—613no—
319#397—613no—
320#397—613no—
321#397—613no—
322#397C2×D6113yes—
323#396—613no—
324#396—613no—
325#396—611no—
326#396C2×D6111yescharacteristic
327C4×C4⋊C4—613no—
328C4×C4⋊C4—613no—
329C4×C4⋊C4—613no—
330C4×C4⋊C4—613no—
331C4×C4⋊C4—613no—
332C4×C4⋊C4—613no—
333C4×C4⋊C4—613no—
334C4×C4⋊C4C2×D6113yescomplemented
335C4×C22⋊C4—613no—
336C4×C22⋊C4—613no—
337C4×C22⋊C4—613no—
338C4×C22⋊C4—613no—
339C4×C22⋊C4—613no—
340C4×C22⋊C4—613no—
341C4×C22⋊C4—613no—
342C4×C22⋊C4C2×D6113yes—
343#376—613no—
344#376—613no—
345#376—611no—
346#376C2×D6111yescharacteristic, complemented
347C2×#95—611no—
348C2×#95—613no—
349C2×#95—613no—
350C2×#95—613no—
351C2×#95—613no—
352C2×#95—613no—
353C61C2×#240111yescharacteristic, complemented, Sylow
354C25—611no—
355C23×C4—611no—
356C23×C4—613no—
357C23×C4—611no—
358C23×C4—613no—
359C23×C4—613no—
360C23×C4—613no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—12212no—
365C23×C4C22×D6111yescharacteristic
366C2×C4⋊C4—613no—
367C2×C4⋊C4—613no—
368C2×C4⋊C4—613no—
369C2×C4⋊C4—613no—
370C2×C4⋊C4—613no—
371C2×C4⋊C4—613no—
372C2×C4⋊C4—12212no—
373C2×C4⋊C4—12212no—
374C2×C4⋊C4C22×D6113yes—
375C2×C4⋊C4C22×D6113yes—
376C2×C22⋊C4—613no—
377C2×C22⋊C4—613no—
378C2×C22⋊C4—613no—
379C2×C22⋊C4—613no—
380C2×C22⋊C4—613no—
381C2×C22⋊C4—613no—
382C2×C22⋊C4—12212no—
383C2×C22⋊C4—12212no—
384C2×C22⋊C4C22×D6113yes—
385C2×C22⋊C4C22×D6113yes—
386C2×C42—613no—
387C2×C42—613no—
388C2×C42—613no—
389C2×C42—613no—
390C2×C42—613no—
391C2×C42—613no—
392C2×C42—12212no—
393C2×C42—12212no—
394C2×C42C22×D6113yes—
395C2×C42C22×D6113yes—
396#95—613no—
397#95—613no—
398#95—613no—
399#95—613no—
400#95—613no—
401#95—613no—
402#95—613no—
403#95—613no—
404#95—613no—
405#95—613no—
406#95—613no—
407#95—613no—
408#95—613no—
409#95—613no—
410#95—613no—
411#95—613no—
412#95C22×D6111yescharacteristic
413#95C22×D6113yes—
414#95C22×D6113yes—
415#95C22×D6113yes—
416#95C22×D6113yes—
417#95C22×D6113yes—
418C24—611no—
419C24—614no—
420C24—611no—
421C24—1226no—
422C24—1226no—
423C24C23×D6111yescharacteristic
424C22×C4—26no—
425C22×C4—611no—
426C22×C4—6112no—
427C22×C4—613no—
428C22×C4—6112no—
429C22×C4—611no—
430C22×C4—613no—
431C22×C4—613no—
432C22×C4—613no—
433C22×C4—1226no—
434C22×C4—1226no—
435C22×C4—1226no—
436C22×C4—1226no—
437C22×C4—1226no—
438C22×C4—1226no—
439C22×C4—1226no—
440C22×C4—1226no—
441C22×C4—1226no—
442C22×C4—1226no—
443C22×C4—1226no—
444C22×C4—1226no—
445C22×C4—1226no—
446C22×C4—1226no—
447C22×C4—1226no—
448C22×C4—24416no—
449C22×C4C23×D6111yescharacteristic
450C22×C4C23×D6113yes—
451C22×C4C23×D6113yes—
452C22×C4C23×D6113yes—
453C22×C4C23×D6113yes—
454C22×C4C23×D6111yescharacteristic
455C4⋊C4—26no—
456C4⋊C4—26no—
457C4⋊C4—1226no—
458C4⋊C4—1226no—
459C4⋊C4—1226no—
460C4⋊C4—1226no—
461C4⋊C4—1226no—
462C4⋊C4—1226no—
463C22⋊C4—26no—
464C22⋊C4—26no—
465C22⋊C4—1226no—
466C22⋊C4—1226no—
467C22⋊C4—1226no—
468C22⋊C4—1226no—
469C22⋊C4—1226no—
470C22⋊C4—1226no—
471C42—26no—
472C42—26no—
473C42—1226no—
474C42—1226no—
475C42—1226no—
476C42—1226no—
477C42—1226no—
478C42—1226no—
479C23—23no—
480C23—23no—
481C23—616no—
482C23—616no—
483C23—612no—
484C23—612no—
485C23—12224no—
486C23—1223no—
487C23—1223no—
488C23—2444no—
489C23—24412no—
490C23#41×D6112yes—
491C23C24×D6111yescharacteristic
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—44no—
505C2×C4—616no—
506C2×C4—6116no—
507C2×C4—616no—
508C2×C4—12224no—
509C2×C4—1223no—
510C2×C4—1223no—
511C2×C4—1223no—
512C2×C4—1223no—
513C2×C4—1223no—
514C2×C4—1223no—
515C2×C4—1223no—
516C2×C4—1223no—
517C2×C4—1223no—
518C2×C4—1223no—
519C2×C4—1223no—
520C2×C4—1223no—
521C2×C4—2444no—
522C2×C4—24412no—
523C2×C4—24412no—
524C2×C4—24412no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2444no—
528C2×C4#41×D6116yes—
529C2×C4#41×D6116yes—
530C22—26no—
531C22—41no—
532C22—43no—
533C22—614no—
534C22—6112no—
535C22—6112no—
536C22—1226no—
537C22—24416no—
538C22—2441no—
539C22—2443no—
540C22C2×#41×D6113yes—
541C22C2×#41×D6111yescharacteristic
542C22C2×#41×D6113yes—
543C4—26no—
544C4—41no—
545C4—43no—
546C4—43no—
547C4—43no—
548C4—614no—
549C4—1226no—
550C4—2441no—
551C4—2443no—
552C4—2443no—
553C4—2443no—
554C4#126×D6114yes—
555C2—42no—
556C2—618no—
557C2—2442no—
558C2C2×#126×D6111yescharacteristic
559C2#529×D6113yes—
560C2#529×D6113yes—
subgroupG/H
centerC22×C4C23×D61
commutator, socle, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC61×#2401C2
prime radicalC24×D61C23
hypercenter#2401D61
hypocenterC61C2×#2401
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #21449122C2semidirect
2. #21449121C2semidirect
3. #21449120C2semidirect
4. #21449119C2semidirect
5. #21449118C2semidirect
6. #21449117C2semidirect
7. #21449116C2semidirect
8. #401×D61C2semidirect
9. #400×D61C2semidirect
12. C4×C4⋊C4×D61C2semidirect
14. #376×D61C2semidirect
15. C61×#2401C2semidirect
23. C61⋊#401C22semidirect
24. C61⋊#401C22semidirect
25. C61⋊#401C22semidirect
26. #16839704C22semidirect
27. #16839704C22semidirect
28. #16839703C22semidirect
29. #16839703C22semidirect
30. #16839702C22semidirect
31. #16839701C22semidirect
32. #16839700C22semidirect
43. C4⋊C4×Dic61C22semidirect
44. C4⋊C4×Dic61C22semidirect
45. C4×#11758196C22semidirect
46. C4×#11758196C22semidirect
47. C4×C4⋊Dic61C22semidirect
48. #16839613C22semidirect
49. #16839613C22semidirect
57. #16839608C22semidirect
58. #16839607C22semidirect
59. #16839607C22semidirect
66. C61×#401C22semidirect
67. C61×#400C22semidirect
70. C4×C4⋊C4×C61C22semidirect
72. C61×#376C22semidirect
282. #2401D61direct (N × H)
295. D61#2401direct (N × H)
306. #401C2×D61semidirect
314. #400C2×D61semidirect
334. C4×C4⋊C4C2×D61semidirect
346. #376C2×D61semidirect
353. C61C2×#2401semidirect

Maximal subgroups

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

subgroupindex
#214491222
#214491212
#214491202
#214491192
#214491182
#214491172
#214491162
#401×D612
#400×D612
#397×D612
#396×D612
C4×C4⋊C4×D612
C4×C22⋊C4×D612
#376×D612
C61×#24012
C2×#240161