Finite Group Databasebeta

← D61×#1886 #29681573

Subgroups — D61×#1886 #29681573

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D61C211yesmaximal, characteristic
2#519×D61C211yesmaximal, characteristic
3#419×D61C212yesmaximal
4C2×#101×D61C211yesmaximal, characteristic
5#21446213C211yesmaximal, characteristic, complemented
6#21446212C211yesmaximal, characteristic, complemented
7#21446211C212yesmaximal, complemented
8#21446210C211yesmaximal, characteristic, complemented
9#21446209C212yesmaximal, complemented
10#339×D61C212yesmaximal
11C61×#1886C211yesmaximal, characteristic, complemented
12C22×Q8×D61C2211yescharacteristic
13C22×Q8×D61C2211yescharacteristic
14C2×M16×D61C2212yes—
15C2×#14519777C2211yescharacteristic
16C2×#14519776—22no—
17C2×#14519775C2211yescharacteristic
18C2×#14519775C2211yescharacteristic
19C4⋊Q8×D61—24no—
20C4⋊Q8×D61C418yescomplemented
21#16840240C2211yescharacteristic
22#16840239—22no—
23#16840239C2212yes—
24#16840238—24no—
25C4×Q8×D61—24no—
26#117×D61—22no—
27#117×D61C2212yes—
28C2×C4⋊C4×D61—22no—
29C2×C42×D61C2211yescharacteristic
30#16839772C2212yes—
31#16839771C2212yes—
32#16839770C2212yes—
33#16839769—24no—
34#103×D61—24no—
35C2×#14519696C2211yescharacteristic
36C2×#14519695C2212yes—
37#101×D61—24no—
38#16839523C2212yes—
39#16839522C2212yes—
40#16839521C2212yes—
41C2×C4⋊Q8×C61C2211yescharacteristic
42C61×#519C2211yescharacteristic
43C61×#419C2212yes—
44C2×#101×C61C2211yescharacteristic
45C61×#339C2212yes—
46C22×Dic122—21no—
47C22×Dic122D412yes—
48C22×Dic122C2311yescharacteristic
49C22×Dic122C2311yescharacteristic
50C2×Q8×D61—22no—
51C2×Q8×D61—22no—
52C2×Q8×D61—22no—
53C2×Q8×D61—24no—
54C2×Q8×D61—22no—
55C2×Q8×D61—22no—
56C2×Q8×D61—24no—
57C2×Q8×D61C2×C414yes—
58C2×Q8×D61C2×C414yes—
59C2×Q8×D61D414yes—
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61D412yes—
63C22×C4×D61C2311yescharacteristic
64C2×#11758194C2312yes—
65C2×#11758189—22no—
66M16×D61—24no—
67M16×D61—24no—
68C2×C8×D61—22no—
69#14519777—22no—
70#14519777C2×C414yescomplemented
71#14519776—216no—
72#14519775—22no—
73#14519775—22no—
74#14519775C2×C414yescomplemented
75#14519775C2×C414yescomplemented
76Q8×Dic61—24no—
77C4×Dic122—28no—
78C4×Dic122—24no—
79#14519742—28no—
80#14519742—24no—
81#14519736—22no—
82#14519736C2312yes—
83#14519735—24no—
84#14519735D414yes—
85#14519734—24no—
86#14519734—22no—
87#14519733—24no—
88#14519733—22no—
89C2×C4⋊Dic61—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C4⋊C4×D61—24no—
93C4⋊C4×D61—216no—
94C4⋊C4×D61D414yes—
95C22⋊C4×D61—22no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—24no—
99C42×D61—22no—
100C42×D61—22no—
101C42×D61C2×C414yes—
102#14519702—24no—
103#14519701—24no—
104#14519700—24no—
105#14519696—22no—
106#14519695—24no—
107C22×Q8×C61C2311yescharacteristic
108C22×Q8×C61C2311yescharacteristic
109C2×M16×C61C2312yes—
110C4⋊Q8×C61—22no—
111C4⋊Q8×C61C2×C414yescomplemented
112C4×Q8×C61—24no—
113#117×C61—22no—
114#117×C61C2312yes—
115C2×C4⋊C4×C61—22no—
116C2×C42×C61C2311yescharacteristic
117#103×C61—24no—
118#101×C61—22no—
119C23×D61C2×D411yescharacteristic
120C2×Q8×C61—22no—
121C2×Q8×C61—21no—
122C2×Q8×C61—22no—
123C2×Q8×C61—22no—
124C2×Q8×C61—22no—
125C2×Q8×C61C22×C412yes—
126C2×Q8×C61C22×C412yes—
127C2×Q8×C61C2×D412yes—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D412yes—
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61C2×D412yes—
135C22×Dic61C2×D411yescharacteristic
136Q8×D61—28no—
137Q8×D61—28no—
138Q8×D61—28no—
139Q8×D61—28no—
140Q8×D61—28no—
141Q8×D61—28no—
142Q8×D61—44no—
143Q8×D61—44no—
144C2×C4×D61—28no—
145C2×C4×D61—24no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—24no—
149C2×C4×D61—24no—
150C2×C4×D61—24no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—42no—
154C2×C4×D61C22⋊C418yes—
155C2×C4×D61C22×C412yes—
156C2×C4×D61C2×D412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×C4×D61#4114yes—
160C2×Dic122—22no—
161C2×Dic122—22no—
162C2×Dic122—24no—
163C2×Dic122—24no—
164C2×Dic122—22no—
165C2×Dic122—22no—
166C2×Dic122—21no—
167C2×Dic122—24no—
168C2×Dic122—42no—
169C2×Dic122—42no—
170C2×Dic122C22⋊C418yes—
171C2×Dic122C22×C412yes—
172C2×Dic122C22×C412yes—
173C2×Dic122C2×D412yes—
174M16×C61—22no—
175M16×C61—22no—
176C2×C8×C61—22no—
177C4⋊C4×C61—24no—
178C4⋊C4×C61—28no—
179C4⋊C4×C61C2×D414yes—
180C22⋊C4×C61—22no—
181C42×C61—24no—
182C42×C61—21no—
183C42×C61—22no—
184C42×C61C22×C412yes—
185C22⋊Dic61—22no—
186#11758198—24no—
187C4⋊Dic61—24no—
188C4⋊Dic61—28no—
189C4⋊Dic61C2×D414yes—
190#11758196—28no—
191#11758196—28no—
192#11758196—28no—
193#11758196—24no—
194C4×Dic61—28no—
195C4×Dic61—24no—
196C4×Dic61—21no—
197C4×Dic61—22no—
198C4×Dic61—24no—
199C4×Dic61—24no—
200C4×Dic61C22×C412yes—
201#11758194—22no—
202#11758194—22no—
203C2×#92418—22no—
204#11758189—44no—
205C8×D61—44no—
206C23×C61C22×D411yescharacteristic
207C22×D61—24no—
208C22×D61C2×C22⋊C412yes—
209C22×D61#12011yescharacteristic
210C22×D61#12011yescharacteristic
211C22×D61#12312yes—
212Q8×C61—24no—
213Q8×C61—24no—
214Q8×C61—24no—
215Q8×C61—42no—
216C2×C4×C61—24no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61C2×C22⋊C414yes—
225C2×C4×C61C23×C411yescharacteristic
226C2×C4×C61C22×D412yes—
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4112yes—
229C2×Dic61—24no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—24no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61C2×C22⋊C414yes—
238C2×Dic61C2×C22⋊C412yes—
239C2×Dic61#12012yes—
240C2×Dic61#12312yes—
241C4×D61—216no—
242C4×D61—28no—
243C4×D61—28no—
244C4×D61—44no—
245C4×D61—44no—
246C4×D61—48no—
247C4×D61C4×D414yes—
248C4×D61C4×D414yes—
249C4×D61#12114yes—
250C4×D61#12114yes—
251Dic122—24no—
252Dic122—24no—
253Dic122—216no—
254Dic122—24no—
255Dic122—42no—
256Dic122—48no—
257C8×C61—42no—
258#92418—42no—
259C2×#1886—611nomaximal, Sylow
260C22×C61—22no—
261C22×C61C22×C22⋊C411yescharacteristic
262C22×C61C2×#12011yescharacteristic
263C22×C61C2×#12311yescharacteristic
264C2×D61—22no—
265C2×D61—24no—
266C2×D61—24no—
267C2×D61#38612yes—
268C2×D61#38612yes—
269C2×D61#45614yes—
270C4×C61—24no—
271C4×C61—24no—
272C4×C61—44no—
273C4×C61—42no—
274C4×C61C2×C4×D412yes—
275C4×C61C2×#12112yes—
276Dic61—24no—
277Dic61—24no—
278Dic61—44no—
279Dic61—42no—
280Dic61#38614yes—
281C22×C4⋊Q8—611no—
282C2×#519—611no—
283C2×#419—612no—
284C22×#101—611no—
285#1886—612no—
286#1886—611no—
287#1886—612no—
288#1886—611no—
289#1886—611no—
290#1886D6111yescharacteristic, direct product factor
291C2×#339—612no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61C2×#38611yescharacteristic
295C2×C61C2×#45612yes—
296D61—22no—
297D61#188614yesdirect product factor
298C23×Q8—611no—
299C23×Q8—611no—
300C22×M16—612no—
301C2×C4⋊Q8—611no—
302C2×C4⋊Q8—611no—
303C2×C4⋊Q8—618no—
304C2×C4⋊Q8—611no—
305C2×C4⋊Q8—1222no—
306C2×C4⋊Q8—1224no—
307C2×C4⋊Q8C2×D6111yescharacteristic
308#519—611no—
309#519—612no—
310#519—1222no—
311#519—1224no—
312#519C2×D6111yescharacteristic
313C2×C4×Q8—1224no—
314C2×#117—612no—
315C2×#117—1222no—
316C22×C4⋊C4—1222no—
317C22×C42—611no—
318#419—612no—
319#419—612no—
320#419—612no—
321#419—1224no—
322#419C2×D6112yes—
323C2×#103—1224no—
324C2×#101—611no—
325C2×#101—612no—
326C2×#101—1224no—
327C2×#101C2×D6111yescharacteristic
328#339—612no—
329#339—612no—
330#339—612no—
331#339C2×D6112yes—
332C61C2×#188611yescharacteristic, complemented, Sylow
333C22×Q8—614no—
334C22×Q8—614no—
335C22×Q8—612no—
336C22×Q8—611no—
337C22×Q8—614no—
338C22×Q8—611no—
339C22×Q8—1221no—
340C22×Q8—1222no—
341C22×Q8—1222no—
342C22×Q8—1224no—
343C22×Q8—1222no—
344C22×Q8—1224no—
345C22×Q8—1222no—
346C22×Q8—1222no—
347C22×Q8C22×D6111yescharacteristic
348C22×Q8C22×D6111yescharacteristic
349C23×C4—611no—
350C23×C4—612no—
351C23×C4—1221no—
352C23×C4—1221no—
353C2×M16—612no—
354C2×M16—1222no—
355C2×M16—1224no—
356C2×M16—1224no—
357C2×M16C22×D6112yes—
358C22×C8—1222no—
359C4⋊Q8—22no—
360C4⋊Q8—614no—
361C4⋊Q8—614no—
362C4⋊Q8—614no—
363C4⋊Q8—1222no—
364C4⋊Q8—12216no—
365C4⋊Q8—1222no—
366C4⋊Q8—1222no—
367C4⋊Q8C4×D6114yescomplemented
368C4×Q8—24no—
369C4×Q8—1224no—
370C4×Q8—1228no—
371C4×Q8—1228no—
372C4×Q8—1224no—
373C4×Q8—1224no—
374#117—22no—
375#117—612no—
376#117—614no—
377#117—1222no—
378#117—1224no—
379#117—1222no—
380#117—1224no—
381#117—1224no—
382#117—1222no—
383#117C22×D6112yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—614no—
386C2×C4⋊C4—12216no—
387C2×C4⋊C4—1224no—
388C2×C4⋊C4—1222no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1222no—
391C2×C22⋊C4—1222no—
392C2×C42—611no—
393C2×C42—614no—
394C2×C42—1222no—
395C2×C42—1222no—
396C2×C42—1224no—
397C2×C42—1221no—
398C2×C42C22×D6111yescharacteristic
399#103—24no—
400#103—1224no—
401#103—1224no—
402#103—1224no—
403#101—22no—
404#101—1224no—
405#101—1222no—
406C24—611no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—612no—
413C2×Q8—612no—
414C2×Q8—618no—
415C2×Q8—612no—
416C2×Q8—1224no—
417C2×Q8—1224no—
418C2×Q8—1224no—
419C2×Q8—1228no—
420C2×Q8—1228no—
421C2×Q8—1228no—
422C2×Q8—1228no—
423C2×Q8—1228no—
424C2×Q8—1228no—
425C2×Q8—1222no—
426C2×Q8—1221no—
427C2×Q8—1222no—
428C2×Q8—1222no—
429C2×Q8—1222no—
430C2×Q8—2442no—
431C2×Q8—2442no—
432C2×Q8—2444no—
433C2×Q8—2444no—
434C2×Q8C2×C4×D6112yes—
435C2×Q8C2×C4×D6112yes—
436C2×Q8D4×D6112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—611no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—614no—
445C22×C4—612no—
446C22×C4—618no—
447C22×C4—1224no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1224no—
451C22×C4—1228no—
452C22×C4—1224no—
453C22×C4—1224no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—2441no—
457C22×C4—2441no—
458C22×C4—2442no—
459C22×C4D4×D6112yes—
460C22×C4C23×D6111yescharacteristic
461M16—22no—
462M16—22no—
463M16—1222no—
464M16—1222no—
465M16—2444no—
466C2×C8—22no—
467C2×C8—1222no—
468C2×C8—2444no—
469C4⋊C4—24no—
470C4⋊C4—28no—
471C4⋊C4—614no—
472C4⋊C4—1224no—
473C4⋊C4—1228no—
474C4⋊C4—1228no—
475C4⋊C4—1228no—
476C4⋊C4—1224no—
477C4⋊C4—1228no—
478C4⋊C4D4×D6114yes—
479C22⋊C4—22no—
480C22⋊C4—1224no—
481C22⋊C4—1222no—
482C42—24no—
483C42—21no—
484C42—22no—
485C42—612no—
486C42—1224no—
487C42—1224no—
488C42—1224no—
489C42—1228no—
490C42—1221no—
491C42—1222no—
492C42C2×C4×D6112yes—
493C23—611no—
494C23—612no—
495C23—611no—
496C23—612no—
497C23—1224no—
498C23C2×D4×D6111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—24no—
502Q8—42no—
503Q8—12216no—
504Q8—1224no—
505Q8—1224no—
506Q8—1224no—
507Q8—2448no—
508Q8—2442no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—614no—
521C2×C4—614no—
522C2×C4—614no—
523C2×C4—614no—
524C2×C4—614no—
525C2×C4—1228no—
526C2×C4—1228no—
527C2×C4—12216no—
528C2×C4—1224no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1224no—
534C2×C4—2448no—
535C2×C4—2444no—
536C2×C4—2444no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C22⋊C4×D6114yes—
540C2×C4C22×C4×D6111yescharacteristic
541C2×C4C2×D4×D6112yes—
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4#41×D6112yes—
544C8—42no—
545C8—2442no—
546C22—22no—
547C22—612no—
548C22—614no—
549C22—612no—
550C22—1224no—
551C22—1224no—
552C22—1222no—
553C22C2×C22⋊C4×D6111yescharacteristic
554C22#120×D6111yescharacteristic
555C22#123×D6111yescharacteristic
556C4—24no—
557C4—24no—
558C4—42no—
559C4—44no—
560C4—614no—
561C4—1224no—
562C4—1224no—
563C4—2442no—
564C4—2444no—
565C4C4×D4×D6112yes—
566C4#121×D6112yes—
567C2—21no—
568C2—21no—
569C2—614no—
570C2—1222no—
571C2#386×D6111yescharacteristic
572C2#456×D6112yes—
subgroupG/H
centerC22#120×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1886C2
socleC22×C61C2×#120
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1886D61
hypocenterC61C2×#1886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1886

Complements

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

NH ≅ G/Ntype
5. #21446213C2semidirect
6. #21446212C2semidirect
7. #21446211C2semidirect
8. #21446210C2semidirect
9. #21446209C2semidirect
11. C61×#1886C2semidirect
20. C4⋊Q8×D61C4semidirect
70. #14519777C2×C4semidirect
74. #14519775C2×C4semidirect
75. #14519775C2×C4semidirect
111. C4⋊Q8×C61C2×C4semidirect
290. #1886D61direct (N × H)
297. D61#1886direct (N × H)
332. C61C2×#1886semidirect
367. C4⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D612
#519×D612
#419×D612
C2×#101×D612
#214462132
#214462122
#214462112
#214462102
#214462092
#339×D612
C61×#18862
C2×#188661