Finite Group Databasebeta

← D61×#1584 #29649529

Subgroups — D61×#1584 #29649529

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#446×D61C211yesmaximal, characteristic
2C8×Q8×D61C211yesmaximal, characteristic
3C4×Q16×D61C211yesmaximal, characteristic
4#21444672C211yesmaximal, characteristic, complemented
5#21444671C211yesmaximal, characteristic, complemented
6#21444670C211yesmaximal, characteristic, complemented
7#21444669C211yesmaximal, characteristic, complemented
8#21444668C211yesmaximal, characteristic, complemented
9#21444667C211yesmaximal, characteristic, complemented
10#21444666C211yesmaximal, characteristic, complemented
11#335×D61C211yesmaximal, characteristic
12Q8⋊C8×D61C211yesmaximal, characteristic
13Q8⋊C8×D61C211yesmaximal, characteristic
14#322×D61C211yesmaximal, characteristic
15C61×#1584C211yesmaximal, characteristic, complemented
16C2×Q16×D61C411yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16839893C2211yescharacteristic
20#16839892C2211yescharacteristic
21#16839891—21no—
22#16839890—21no—
23#16839889C2211yescharacteristic
24Q8×#92418C2211yescharacteristic
25C8×Dic122—21no—
26C8×Dic122C2211yescharacteristic
27#16839886—21no—
28#16839886C2211yescharacteristic
29C4×Dic244C2211yescharacteristic
30Q16×Dic61C411yescharacteristic
31#16839856C411yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758202C2211yescharacteristic
34#16839854C411yescharacteristic
35#16839854C411yescharacteristic
36#107×D61C411yescharacteristic
37C4⋊C8×D61—21no—
38C4⋊C8×D61—21no—
39C4⋊C8×D61C2211yescharacteristic
40C4⋊C8×D61C2211yescharacteristic
41#103×D61C411yescharacteristic
42#103×D61C411yescharacteristic
43#97×D61—21no—
44C4×C8×D61—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Q8×D61C2×C411yescharacteristic
69C2×Dic244C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71C2×#11758202C2×C411yescharacteristic
72Q16×D61—24no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76C2×C8×D61C2×C411yescharacteristic
77C2×C8×D61C2×C411yescharacteristic
78C2×C8×D61D411yescharacteristic
79C2×C8×D61D411yescharacteristic
80Q8×Dic61C2×C411yescharacteristic
81Q8×Dic61C2×C411yescharacteristic
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519742—21no—
88#14519742C2×C411yescharacteristic
89#14519742C2×C411yescharacteristic
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61C2×C411yescharacteristic
93C4⋊C4×D61C2×C411yescharacteristic
94C42×D61—21no—
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519711C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519710C2×C411yescharacteristic
100C4⋊#92418—21no—
101C4⋊#92418—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519701C2×C411yescharacteristic
113#14519701C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519700C2×C411yescharacteristic
116#14519688—21no—
117#14519687—21no—
118#14519687—21no—
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61C2×C411yescharacteristic
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×Q16×C61C2×C411yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#103×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147Q8×D61—22no—
148Q8×D61—22no—
149Q8×D61—22no—
150Q8×D61M1614yes—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61C22×C411yescharacteristic
156C2×C4×D61C2×D411yescharacteristic
157C2×C4×D61#4111yescharacteristic
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C22×C411yescharacteristic
161C2×Dic122C22×C411yescharacteristic
162Q16×C61—22no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C22×C411yescharacteristic
167C2×C8×C61C22×C411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22×C411yescharacteristic
173C4⋊C4×C61C22×C411yescharacteristic
174C42×C61—21no—
175C42×C61—21no—
176C42×C61C2411yescharacteristic
177#11758202—22no—
178#11758202—22no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61C22×C411yescharacteristic
182C4⋊Dic61C22×C411yescharacteristic
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205Dic244—22no—
206C8×D61—22no—
207C8×D61—22no—
208C8×D61—22no—
209C8×D61—42no—
210C8×D61—42no—
211C8×D61—42no—
212C8×D61Q1614yescomplemented
213C22×D61C4×D411yescharacteristic
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61C2×M1612yes—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C4×D411yescharacteristic
232C4×D61—24no—
233C4×D61—22no—
234C4×D61—42no—
235C4×D61—42no—
236C4×D61—42no—
237C4×D61C2×M1612yes—
238C4×D61#13112yes—
239C4×D61C2×Q1612yes—
240C4×D61#13512yes—
241Dic122—21no—
242Dic122—24no—
243Dic122—21no—
244Dic122—21no—
245Dic122—42no—
246Dic122C2×M1612yes—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61C2×Q1612yescomplemented
254#92418—21no—
255#92418—21no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418C2×Q1612yescomplemented
261C2×#1584—611nomaximal, Sylow
262C22×C61C2×C4×D411yescharacteristic
263C2×D61#43512yes—
264C2×D61C4×Q1612yes—
265C2×D61#44412yes—
266C4×C61—22no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61C22×M1611yescharacteristic
272C4×C61C2×#13111yescharacteristic
273C4×C61C22×Q1611yescharacteristic
274C4×C61C2×#13511yescharacteristic
275Dic61—22no—
276Dic61—21no—
277Dic61—41no—
278Dic61—41no—
279Dic61—41no—
280Dic61#43512yes—
281Dic61C4×Q1612yes—
282C2×#446—611no—
283C2×C8×Q8—611no—
284C2×C4×Q16—611no—
285#1584—611no—
286#1584—611no—
287#1584—611no—
288#1584—611no—
289#1584—611no—
290#1584—611no—
291#1584—611no—
292#1584D6111yescharacteristic, direct product factor
293C2×#335—611no—
294C2×Q8⋊C8—611no—
295C2×Q8⋊C8—611no—
296C2×#322—611no—
297C2×C61C2×#43511yescharacteristic
298C2×C61C2×C4×Q1611yescharacteristic
299C2×C61C2×#44411yescharacteristic
300D61#158414yesdirect product factor
301C22×Q16—611no—
302C2×C4×Q8—611no—
303C2×C4×Q8—611no—
304#446—611no—
305#446—611no—
306#446—611no—
307#446—1221no—
308#446—1221no—
309#446C2×D6111yescharacteristic
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8—1221no—
315C8×Q8C2×D6111yescharacteristic
316C4×Q16—611no—
317C4×Q16—611no—
318C4×Q16—611no—
319C4×Q16—611no—
320C4×Q16—611no—
321C4×Q16—611no—
322C4×Q16—611no—
323C4×Q16C2×D6111yescharacteristic
324C2×#107—611no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C4⋊C8—1221no—
328C2×C4⋊C8—1221no—
329C2×#103—611no—
330C2×#103—611no—
331C2×#97—1221no—
332C2×C4×C8—611no—
333C2×C4×C8—611no—
334C2×C4×C8—611no—
335C2×C4×C8—1221no—
336#335—611no—
337#335—611no—
338#335—611no—
339#335C2×D6111yescharacteristic
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8C2×D6111yescharacteristic
347Q8⋊C8C2×D6111yescharacteristic
348#322—611no—
349#322—611no—
350#322—611no—
351#322C2×D6111yescharacteristic
352C61C2×#158411yescharacteristic, complemented, Sylow
353C22×Q8—611no—
354C22×Q8—611no—
355C2×Q16—611no—
356C2×Q16—611no—
357C2×Q16—611no—
358C2×Q16—1224no—
359C2×Q16C4×D6111yescharacteristic
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8—1221no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×Q8—1221no—
376C4×Q8—1221no—
377C4×Q8C22×D6111yescharacteristic
378C4×Q8C22×D6111yescharacteristic
379C2×C4⋊C4—611no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C42—611no—
384C2×C42—1221no—
385C2×C42—1221no—
386#107—611no—
387#107—611no—
388#107—611no—
389#107C4×D6111yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404#103—611no—
405#103—611no—
406#103—611no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103C4×D6111yescharacteristic
411#103C4×D6111yescharacteristic
412#97—21no—
413#97—1221no—
414#97—1221no—
415#97—1221no—
416C4×C8—21no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429C4×C8C22×D6111yescharacteristic
430C4×C8C22×D6111yescharacteristic
431C2×Q8—614no—
432C2×Q8—611no—
433C2×Q8—611no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1222no—
437C2×Q8—1222no—
438C2×Q8—1222no—
439C2×Q8C2×C4×D6111yescharacteristic
440C2×Q8C2×C4×D6111yescharacteristic
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448Q16—22no—
449Q16—1222no—
450Q16—1222no—
451Q16—1222no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—611no—
456C2×C8—614no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—1222no—
461C2×C8—1222no—
462C2×C8—1222no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—2442no—
467C2×C8—2442no—
468C2×C8—2442no—
469C2×C8C2×C4×D6111yescharacteristic
470C2×C8C2×C4×D6111yescharacteristic
471C2×C8D4×D6111yescharacteristic
472C2×C8D4×D6111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—611no—
476C4⋊C4—611no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4C2×C4×D6111yescharacteristic
486C4⋊C4C2×C4×D6111yescharacteristic
487C42—21no—
488C42—21no—
489C42—611no—
490C42—611no—
491C42—611no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42C23×D6111yescharacteristic
499C23—611no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—612no—
504Q8—1224no—
505Q8—1221no—
506Q8—1221no—
507Q8—1221no—
508Q8—2442no—
509Q8M16×D6112yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—611no—
521C2×C4—1222no—
522C2×C4—1224no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4—2442no—
530C2×C4C22×C4×D6111yescharacteristic
531C2×C4C2×D4×D6111yescharacteristic
532C2×C4#41×D6111yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—612no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8Q16×D6112yescomplemented
547C22—612no—
548C22—612no—
549C22—612no—
550C22C4×D4×D6111yescharacteristic
551C4—21no—
552C4—22no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—612no—
557C4—612no—
558C4—1221no—
559C4—1222no—
560C4—2441no—
561C4—2441no—
562C4—2441no—
563C4C2×M16×D6111yescharacteristic
564C4#131×D6111yescharacteristic
565C4C2×Q16×D6111yescharacteristic
566C4#135×D6111yescharacteristic
567C2—614no—
568C2#435×D6111yescharacteristic
569C2C4×Q16×D6111yescharacteristic
570C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61C2×#1584
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #21444672C2semidirect
5. #21444671C2semidirect
6. #21444670C2semidirect
7. #21444669C2semidirect
8. #21444668C2semidirect
9. #21444667C2semidirect
10. #21444666C2semidirect
15. C61×#1584C2semidirect
212. C8×D61Q16semidirect
253. C8×C61C2×Q16semidirect
260. #92418C2×Q16semidirect
292. #1584D61direct (N × H)
300. D61#1584direct (N × H)
352. C61C2×#1584semidirect
546. C8Q16×D61semidirect

Maximal subgroups

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

subgroupindex
#446×D612
C8×Q8×D612
C4×Q16×D612
#214446722
#214446712
#214446702
#214446692
#214446682
#214446672
#214446662
#335×D612
Q8⋊C8×D612
#322×D612
C61×#15842
C2×#158461