Finite Group Databasebeta

← D61×#1885 #29681561

Subgroups — D61×#1885 #29681561

Order 15616.

1966 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D61C211yesmaximal, characteristic
2#518×D61C211yesmaximal, characteristic
3#419×D61C212yesmaximal, complemented
4C2×#100×D61C211yesmaximal, characteristic
5#21446208C211yesmaximal, characteristic, complemented
6#21446207C211yesmaximal, characteristic, complemented
7#21446206C212yesmaximal, complemented
8#21446205C211yesmaximal, characteristic, complemented
9#21446204C212yesmaximal, complemented
10#339×D61C212yesmaximal, complemented
11C61×#1885C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2211yescharacteristic
13C22×D4×D61C2211yescharacteristic
14C2×M16×D61C2212yes—
15C2×#14519766C2211yescharacteristic
16C2×#14519765C2211yescharacteristic
17C2×#14519764C2211yescharacteristic
18C2×#14519763—22no—
19#124×D61—24no—
20#124×D61C418yescomplemented
21#16840237C2211yescharacteristic
22#16840236C2212yes—
23#16840235—22no—
24#16840234—24no—
25C4×D4×D61—24no—
26#117×D61C2212yes—
27C2×C22⋊C4×D61—22no—
28C2×C22⋊C4×D61—22no—
29C2×C42×D61C2211yescharacteristic
30#16839772C2212yescomplemented
31#16839771C2212yescomplemented
32#16839770C2212yescomplemented
33#16839769—24no—
34#103×D61—24no—
35C2×#14519694C2211yescharacteristic
36C2×#14519693C2212yes—
37#100×D61—24no—
38#16839523C2212yescomplemented
39#16839522C2212yescomplemented
40#16839521C2212yescomplemented
41C2×#124×C61C2211yescharacteristic
42C61×#518C2211yescharacteristic
43C61×#419C2212yescomplemented
44C2×#100×C61C2211yescharacteristic
45C61×#339C2212yescomplemented
46C24×D61D412yes—
47C22×Dic122—21no—
48C22×Dic122C2311yescharacteristic
49C2×Q8×D61—22no—
50C2×Q8×D61—22no—
51C2×Q8×D61—22no—
52C2×Q8×D61—24no—
53C2×Q8×D61C2×C414yescomplemented
54C22×D244C2311yescharacteristic
55C22×C22⋊D61D412yes—
56C2×D4×D61—22no—
57C2×D4×D61—22no—
58C2×D4×D61—24no—
59C2×D4×D61C2×C414yes—
60C2×D4×D61D414yes—
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61—24no—
64C22×C4×D61C2311yescharacteristic
65C2×#11758194C2312yes—
66C2×#11758189—22no—
67M16×D61—24no—
68M16×D61—24no—
69C2×C8×D61—22no—
70#14519766—22no—
71#14519766C2×C414yescomplemented
72#14519765—22no—
73#14519765C2×C414yescomplemented
74#14519764—22no—
75#14519764C2×C414yescomplemented
76#14519763—216no—
77C4×D244—24no—
78D4×Dic61—24no—
79#14519739—24no—
80C4×C22⋊D61—28no—
81#14519737—28no—
82#14519736C2312yes—
83#14519735D414yes—
84#14519734—22no—
85#14519733—22no—
86C4⋊C4×D61D414yes—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×#11758198—24no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C22⋊C4×D61—24no—
93C22⋊C4×D61—24no—
94C22⋊C4×D61—216no—
95C22⋊C4×D61—22no—
96C22⋊C4×D61—24no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99C42×D61—22no—
100C42×D61—22no—
101C42×D61C2×C414yescomplemented
102#14519702—24no—
103#14519701—24no—
104#14519700—24no—
105#14519694—22no—
106#14519693—24no—
107C22×Q8×C61C2311yescharacteristic
108C22×D4×C61C2311yescharacteristic
109C2×M16×C61C2312yes—
110#124×C61—22no—
111#124×C61C2×C414yescomplemented
112C4×D4×C61—24no—
113#117×C61C2312yes—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C42×C61C2311yescharacteristic
117#103×C61—24no—
118#100×C61—22no—
119C24×C61C2×D412yes—
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—24no—
123C23×D61—48no—
124C23×D61C22⋊C418yes—
125C23×D61C2×D411yescharacteristic
126C23×D61C2×D412yes—
127C2×Q8×C61—21no—
128C2×Q8×C61—22no—
129C2×Q8×C61—22no—
130C2×Q8×C61C22×C412yescomplemented
131C2×D4×C61—22no—
132C2×D4×C61—22no—
133C2×D4×C61C22×C412yes—
134C2×D4×C61C2×D412yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—24no—
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—24no—
141C2×C22⋊D61C22⋊C418yes—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—24no—
145C22×Dic61C2×D411yescharacteristic
146Q8×D61—28no—
147Q8×D61—28no—
148Q8×D61—44no—
149Q8×D61—44no—
150D4×D61—28no—
151D4×D61—28no—
152D4×D61—28no—
153D4×D61—28no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244C22×C412yes—
157C2×D244C2×D412yes—
158C2×C4×D61—24no—
159C2×C4×D61—24no—
160C2×C4×D61—24no—
161C2×C4×D61—28no—
162C2×C4×D61—44no—
163C2×C4×D61—41no—
164C2×C4×D61—41no—
165C2×C4×D61—42no—
166C2×C4×D61—88no—
167C2×C4×D61C22×C412yes—
168C2×C4×D61C2×D412yes—
169C2×C4×D61C2×D412yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61#4114yes—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—21no—
175C2×Dic122—24no—
176C2×Dic122—42no—
177C2×Dic122—42no—
178C2×Dic122C22×C412yescomplemented
179M16×C61—22no—
180M16×C61—22no—
181C2×C8×C61—22no—
182C4⋊C4×C61C2×D414yes—
183C22⋊C4×C61—24no—
184C22⋊C4×C61—28no—
185C22⋊C4×C61—22no—
186C42×C61—21no—
187C42×C61—22no—
188C42×C61C22×C412yescomplemented
189C22⋊Dic61—24no—
190C22⋊Dic61—28no—
191C22⋊Dic61—22no—
192#11758198—28no—
193#11758198—28no—
194#11758198—28no—
195#11758198—24no—
196C4⋊Dic61C2×D414yes—
197#11758196—24no—
198C4×Dic61—21no—
199C4×Dic61—22no—
200C4×Dic61—24no—
201C4×Dic61—24no—
202C4×Dic61C22×C412yescomplemented
203#11758194—22no—
204#11758194—22no—
205C2×#92418—22no—
206#11758189—44no—
207C8×D61—44no—
208C23×C61—22no—
209C23×C61—22no—
210C23×C61—44no—
211C23×C61C2×C22⋊C414yes—
212C23×C61C22×D411yescharacteristic
213C22×D61—24no—
214C22×D61—22no—
215C22×D61—22no—
216C22×D61—28no—
217C22×D61—28no—
218C22×D61—416no—
219C22×D61—48no—
220C22×D61—44no—
221C22×D61—88no—
222C22×D61—84no—
223C22×D61C2×C22⋊C412yes—
224C22×D61C2×C22⋊C414yes—
225C22×D61#12011yescharacteristic
226C22×D61#12011yescharacteristic
227C22×D61#12312yes—
228Q8×C61—24no—
229Q8×C61—42no—
230D4×C61—24no—
231D4×C61—24no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—84no—
239C2×C4×C61C23×C411yescharacteristic
240C2×C4×C61C22×D412yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4112yes—
243C22⋊D61—216no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—24no—
247C2×Dic61—42no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—84no—
251C2×Dic61C2×C22⋊C412yes—
252C2×Dic61#12012yes—
253C2×Dic61#12312yes—
254D244—24no—
255D244—24no—
256C4×D61—48no—
257C4×D61—44no—
258C4×D61—44no—
259C4×D61—48no—
260C4×D61—88no—
261C4×D61C4×D414yes—
262C4×D61C4×D414yes—
263C4×D61#12114yes—
264C4×D61#12114yes—
265Dic122—24no—
266Dic122—42no—
267Dic122—48no—
268C8×C61—42no—
269#92418—42no—
270C2×#1885—611nomaximal, Sylow
271C22×C61—22no—
272C22×C61—24no—
273C22×C61—44no—
274C22×C61—44no—
275C22×C61—82no—
276C22×C61C22×C22⋊C411yescharacteristic
277C22×C61C2×#12011yescharacteristic
278C22×C61C2×#12311yescharacteristic
279C2×D61—22no—
280C2×D61—24no—
281C2×D61—24no—
282C2×D61—24no—
283C2×D61—44no—
284C2×D61—416no—
285C2×D61—44no—
286C2×D61—88no—
287C2×D61—82no—
288C2×D61#38612yes—
289C2×D61#38612yes—
290C2×D61#45514yes—
291C4×C61—42no—
292C4×C61—44no—
293C4×C61—42no—
294C4×C61C2×C4×D412yes—
295C4×C61C2×#12112yes—
296Dic61—42no—
297Dic61—44no—
298Dic61—42no—
299Dic61#38614yes—
300C22×#124—611no—
301C2×#518—611no—
302C2×#419—612no—
303C22×#100—611no—
304#1885—612no—
305#1885—611no—
306#1885—612no—
307#1885—611no—
308#1885—611no—
309#1885D6111yescharacteristic, direct product factor
310C2×#339—612no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—44no—
314C2×C61C2×#38611yescharacteristic
315C2×C61C2×#45512yes—
316D61—22no—
317D61—44no—
318D61#188514yesdirect product factor
319C23×Q8—611no—
320C23×D4—611no—
321C22×M16—612no—
322C2×#124—611no—
323C2×#124—611no—
324C2×#124—618no—
325C2×#124—611no—
326C2×#124—1222no—
327C2×#124—1224no—
328C2×#124C2×D6111yescharacteristic
329#518—611no—
330#518—612no—
331#518—1222no—
332#518—1224no—
333#518C2×D6111yescharacteristic
334C2×C4×D4—1224no—
335C2×#117—612no—
336C22×C22⋊C4—1222no—
337C22×C22⋊C4—1222no—
338C22×C42—611no—
339#419—612no—
340#419—612no—
341#419—612no—
342#419—1224no—
343#419C2×D6112yescomplemented
344C2×#103—1224no—
345C2×#100—611no—
346C2×#100—612no—
347C2×#100—1224no—
348C2×#100C2×D6111yescharacteristic
349#339—612no—
350#339—612no—
351#339—612no—
352#339C2×D6112yescomplemented
353C61C2×#188511yescharacteristic, complemented, Sylow
354C25—612no—
355C22×Q8—614no—
356C22×Q8—611no—
357C22×Q8—1221no—
358C22×Q8—1222no—
359C22×Q8—1224no—
360C22×Q8—1222no—
361C22×Q8—1222no—
362C22×Q8C22×D6111yescharacteristic
363C22×D4—612no—
364C22×D4—614no—
365C22×D4—614no—
366C22×D4—611no—
367C22×D4—1222no—
368C22×D4—1222no—
369C22×D4—1224no—
370C22×D4C22×D6111yescharacteristic
371C23×C4—611no—
372C23×C4—1224no—
373C23×C4—1221no—
374C23×C4—1221no—
375C2×M16—612no—
376C2×M16—1222no—
377C2×M16—1224no—
378C2×M16—1224no—
379C2×M16C22×D6112yes—
380C22×C8—1222no—
381#124—22no—
382#124—614no—
383#124—614no—
384#124—614no—
385#124—1222no—
386#124—12216no—
387#124—1222no—
388#124—1222no—
389#124C4×D6114yescomplemented
390C4×D4—24no—
391C4×D4—1224no—
392C4×D4—1228no—
393C4×D4—1224no—
394C4×D4—1228no—
395C4×D4—1224no—
396#117—612no—
397#117—614no—
398#117—1222no—
399#117—1222no—
400#117C22×D6112yes—
401C2×C4⋊C4—614no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—1222no—
405C2×C22⋊C4—1224no—
406C2×C22⋊C4—12216no—
407C2×C22⋊C4—1224no—
408C2×C22⋊C4—1224no—
409C2×C22⋊C4—1222no—
410C2×C22⋊C4—1222no—
411C2×C22⋊C4—1224no—
412C2×C22⋊C4—1222no—
413C2×C22⋊C4—1222no—
414C2×C42—611no—
415C2×C42—614no—
416C2×C42—1222no—
417C2×C42—1222no—
418C2×C42—1221no—
419C2×C42C22×D6111yescharacteristic
420#103—24no—
421#103—1224no—
422#103—1224no—
423#103—1224no—
424#100—22no—
425#100—1224no—
426#100—1222no—
427C24—611no—
428C24—612no—
429C24—618no—
430C24—1222no—
431C24—1224no—
432C24—1222no—
433C24—2448no—
434C24D4×D6112yes—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—612no—
439C2×Q8—1224no—
440C2×Q8—1228no—
441C2×Q8—1228no—
442C2×Q8—1221no—
443C2×Q8—1222no—
444C2×Q8—1222no—
445C2×Q8—2442no—
446C2×Q8—2442no—
447C2×Q8—2444no—
448C2×Q8—2444no—
449C2×Q8C2×C4×D6112yescomplemented
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—618no—
453C2×D4—612no—
454C2×D4—612no—
455C2×D4—1228no—
456C2×D4—1228no—
457C2×D4—1228no—
458C2×D4—1228no—
459C2×D4—1224no—
460C2×D4—1224no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4C2×C4×D6112yes—
464C2×D4D4×D6112yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—24no—
468C22×C4—611no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—612no—
472C22×C4—612no—
473C22×C4—614no—
474C22×C4—1228no—
475C22×C4—1224no—
476C22×C4—1224no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—4888no—
482C22×C4—2441no—
483C22×C4—2441no—
484C22×C4—2442no—
485C22×C4—2444no—
486C22×C4C23×D6111yescharacteristic
487M16—22no—
488M16—22no—
489M16—1222no—
490M16—1222no—
491M16—2444no—
492C2×C8—22no—
493C2×C8—1222no—
494C2×C8—2444no—
495C4⋊C4—614no—
496C4⋊C4—1224no—
497C4⋊C4D4×D6114yes—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—28no—
501C22⋊C4—1224no—
502C22⋊C4—1228no—
503C22⋊C4—1228no—
504C22⋊C4—1228no—
505C22⋊C4—1224no—
506C22⋊C4—1222no—
507C22⋊C4—1228no—
508C42—21no—
509C42—22no—
510C42—612no—
511C42—1224no—
512C42—1224no—
513C42—1221no—
514C42—1222no—
515C42C2×C4×D6112yescomplemented
516C23—22no—
517C23—22no—
518C23—44no—
519C23—611no—
520C23—612no—
521C23—611no—
522C23—612no—
523C23—614no—
524C23—1224no—
525C23—1228no—
526C23—1228no—
527C23—1222no—
528C23—1222no—
529C23—4884no—
530C23—4888no—
531C23—2444no—
532C23—2448no—
533C23—24416no—
534C23C22⋊C4×D6114yes—
535C23C2×D4×D6111yescharacteristic
536Q8—24no—
537Q8—42no—
538Q8—1224no—
539Q8—2448no—
540Q8—2442no—
541D4—24no—
542D4—24no—
543D4—12216no—
544D4—1224no—
545D4—1224no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—84no—
553C2×C4—612no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—614no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—614no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1224no—
563C2×C4—4888no—
564C2×C4—4884no—
565C2×C4—2448no—
566C2×C4—2444no—
567C2×C4—2444no—
568C2×C4—2448no—
569C2×C4—2442no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4C22×C4×D6111yescharacteristic
573C2×C4C2×D4×D6112yes—
574C2×C4C2×D4×D6111yescharacteristic
575C2×C4#41×D6112yes—
576C8—42no—
577C8—2442no—
578C22—22no—
579C22—24no—
580C22—44no—
581C22—44no—
582C22—82no—
583C22—612no—
584C22—614no—
585C22—612no—
586C22—1224no—
587C22—1224no—
588C22—1222no—
589C22—1224no—
590C22—4882no—
591C22—4888no—
592C22—2444no—
593C22—24416no—
594C22—2444no—
595C22C2×C22⋊C4×D6111yescharacteristic
596C22#120×D6111yescharacteristic
597C22#123×D6111yescharacteristic
598C4—42no—
599C4—42no—
600C4—44no—
601C4—614no—
602C4—2442no—
603C4—2442no—
604C4—2444no—
605C4C4×D4×D6112yes—
606C4#121×D6112yes—
607C2—21no—
608C2—21no—
609C2—44no—
610C2—614no—
611C2—1222no—
612C2—2444no—
613C2#386×D6111yescharacteristic
614C2#455×D6112yes—
subgroupG/H
centerC22#120×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1885C2
socleC22×C61C2×#120
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1885D61
hypocenterC61C2×#1885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1885

Complements

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

NH ≅ G/Ntype
3. #419×D61C2semidirect
5. #21446208C2semidirect
6. #21446207C2semidirect
7. #21446206C2semidirect
8. #21446205C2semidirect
9. #21446204C2semidirect
10. #339×D61C2semidirect
11. C61×#1885C2semidirect
20. #124×D61C4semidirect
30. #16839772C22semidirect
31. #16839771C22semidirect
32. #16839770C22semidirect
38. #16839523C22semidirect
39. #16839522C22semidirect
40. #16839521C22semidirect
43. C61×#419C22semidirect
45. C61×#339C22semidirect
53. C2×Q8×D61C2×C4semidirect
71. #14519766C2×C4semidirect
73. #14519765C2×C4semidirect
75. #14519764C2×C4semidirect
101. C42×D61C2×C4semidirect
111. #124×C61C2×C4semidirect
130. C2×Q8×C61C22×C4semidirect
178. C2×Dic122C22×C4semidirect
188. C42×C61C22×C4semidirect
202. C4×Dic61C22×C4semidirect
309. #1885D61direct (N × H)
318. D61#1885direct (N × H)
343. #419C2×D61semidirect
352. #339C2×D61semidirect
353. C61C2×#1885semidirect
389. #124C4×D61semidirect
449. C2×Q8C2×C4×D61semidirect
515. C42C2×C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D612
#518×D612
#419×D612
C2×#100×D612
#214462082
#214462072
#214462062
#214462052
#214462042
#339×D612
C61×#18852
C2×#188561