Finite Group Databasebeta

← D61⋊#1937 #30615965

Subgroups — D61⋊#1937 #30615965

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#424C211yesmaximal, characteristic, complemented
2C2×D61⋊#104C211yesmaximal, characteristic
3D61⋊#408C211yesmaximal, characteristic
4C22×C8×#6923C211yesmaximal, characteristic, complemented
5#21461913C214yesmaximal, complemented
6#21461912C214yesmaximal, complemented
7#21461511C211yesmaximal, characteristic, complemented
8#21461495C211yesmaximal, characteristic, complemented
9#416×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2211yescharacteristic
11C2×D61⋊M16C2211yescharacteristic
12C22×D61⋊C8C2211yescharacteristic
13C22×C4×#6923C2211yescharacteristic
14#16840769C2214yescomplemented
15#16840768—22no—
16D61⋊(C4⋊C8)—22no—
17C2×#14519842C2212yes—
18D61⋊#104—24no—
19C2×#14519841C2212yes—
20#16840737C2212yes—
21#16840736C2212yes—
22#16840735—22no—
23D61⋊(C22⋊C8)—22no—
24C2×C8×#6923—24no—
25C2×C8×#6923C2214yescomplemented
26#16840638C2214yescomplemented
27#16840632C2214yescomplemented
28C2×#41×D61C2211yescharacteristic
29C22×C8×D61C2211yescharacteristic
30#117×D61C2211yescharacteristic
31#16839759C411yescharacteristic, complemented
32#16839758C411yescharacteristic, complemented
33#16839757C2212yes—
34#16839756C411yescharacteristic, complemented
35#16839755C2212yes—
36#103×D61C412yescomplemented
37#102×D61C412yescomplemented
38C61×#416C411yescharacteristic, complemented
39C23×#6923—21no—
40C2×#11758213C2312yes—
41C2×#11758213C2312yes—
42D61⋊M16—22no—
43D61⋊M16—22no—
44D61⋊M16—22no—
45D61⋊M16—22no—
46C2×#11758217—21no—
47C2×#11758217—21no—
48C2×D61⋊C8—22no—
49C2×D61⋊C8—22no—
50C2×D61⋊C8—21no—
51C2×D61⋊C8—21no—
52C2×D61⋊C8D412yes—
53C2×D61⋊C8C2312yes—
54C22×#92420D412yes—
55C2×C4×#6923—21no—
56C2×C4×#6923—22no—
57C2×C4×#6923D414yes—
58C2×C4×#6923C2312yes—
59#14519844—24no—
60C4⋊#92420—24no—
61#14519842—24no—
62#14519841—24no—
63#14519834—24no—
64C22⋊#92420—24no—
65C8×#6923—28no—
66C2×#11758226C2311yescharacteristic
67C2×#11758222—21no—
68C2×#11758222C2×C411yescharacteristic
69C2×#11758224—21no—
70C2×#11758224C2311yescharacteristic
71#41×D61—22no—
72#41×D61—22no—
73#41×D61—22no—
74#41×D61—22no—
75C2×Q8×D61C2×C411yescharacteristic
76C2×D4×D61—21no—
77C2×D4×D61C2×C411yescharacteristic
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C22×#92418C2×C411yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61C2×C412yes—
84C2×C8×D61C2312yes—
85#14519736C2×C411yescharacteristic
86#14519735C2312yes—
87#14519734—21no—
88#14519733—21no—
89C4⋊C4×D61C2×C412yes—
90C22⋊C4×D61—21no—
91C42×D61—21no—
92#14519702C2×C412yescomplemented
93#14519701C2×C412yescomplemented
94#14519700C2×C412yescomplemented
95#14519699C2×C412yescomplemented
96#14519698C2×C412yescomplemented
97#14519697C2×C412yescomplemented
98C2×#41×C61C2×C411yescharacteristic
99C22×C8×C61C2×C411yescharacteristic
100#117×C61C2×C411yescharacteristic
101#103×C61C2×C412yescomplemented
102#102×C61C2×C412yescomplemented
103C23×D61—21no—
104C23×D61#4111yescharacteristic
105C22×#6923—28no—
106C22×#6923—24no—
107C22×#6923—22no—
108#41×C61—22no—
109#41×C61—22no—
110C2×Q8×C61C22×C411yescharacteristic
111C2×D4×C61—21no—
112C2×D4×C61C22×C411yescharacteristic
113C22×C4×C61—21no—
114C22×C4×C61C22×C411yescharacteristic
115C2×C22⋊D61—21no—
116C2×C22⋊D61—21no—
117C2×C22⋊D61—21no—
118C22×Dic61—21no—
119C22×Dic61C2×D411yescharacteristic
120#11758226—21no—
121#11758226—21no—
122#11758226—21no—
123#11758226—21no—
124Q8×D61—22no—
125Q8×D61—22no—
126#11758224—21no—
127#11758224—21no—
128#11758224—21no—
129#11758224—21no—
130#11758224—42no—
131#11758224—42no—
132D4×D61—22no—
133D4×D61—22no—
134D4×D61—42no—
135D4×D61—42no—
136#11758222—22no—
137#11758222—22no—
138#11758222—42no—
139#11758222—42no—
140C2×D244—21no—
141C2×D244C22×C411yescharacteristic
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61C22×C411yescharacteristic
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×D411yescharacteristic
151C2×C4×D61#4112yes—
152C2×C4×D61#4112yes—
153C2×C4×D61#4112yes—
154C2×C4×D61#4111yescharacteristic
155C2×C4×D61C2411yescharacteristic
156C2×Dic122—21no—
157C2×Dic122C22×C411yescharacteristic
158#11758217—42no—
159#11758217—42no—
160C2×#92420—24no—
161C2×#92420—22no—
162C2×#92420—22no—
163C2×#92420C2×D414yes—
164C4×#6923—24no—
165C4×#6923—22no—
166C4×#6923C2×D414yes—
167#11758213—22no—
168#11758213—22no—
169#11758213—22no—
170#11758213—22no—
171D61⋊C8—24no—
172D61⋊C8—22no—
173D61⋊C8—22no—
174D61⋊C8—42no—
175D61⋊C8—42no—
176C2×C8×C61—22no—
177C2×C8×C61C22×C412yes—
178C4⋊C4×C61C22×C412yes—
179C22⋊C4×C61—21no—
180C42×C61—21no—
181C22⋊Dic61—21no—
182#11758198—22no—
183C4⋊Dic61C22×C412yes—
184#11758196—22no—
185C4×Dic61—21no—
186C4×Dic61—22no—
187C2×#92418—22no—
188C2×#92418C22×C412yes—
189C8×D61—24no—
190C8×D61—22no—
191C8×D61—22no—
192C23×C61—21no—
193C23×C61C4×D411yescharacteristic
194C22×D61—24no—
195C22×D61—21no—
196C22×D61—42no—
197C22×D61—44no—
198C22×D61C4×D411yescharacteristic
199C22×D61#12312yes—
200C22×D61#12612yes—
201C22×D61C2×#4111yescharacteristic
202C2×#6923—28no—
203C2×#6923—216no—
204C2×#6923—24no—
205Q8×C61—21no—
206Q8×C61—21no—
207D4×C61—21no—
208D4×C61—21no—
209D4×C61—42no—
210C2×C4×C61—22no—
211C2×C4×C61—21no—
212C2×C4×C61—42no—
213C2×C4×C61#11712yes—
214C2×C4×C61C4×D412yes—
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C22⋊D61—42no—
218C22⋊D61—41no—
219C22⋊D61—41no—
220C22⋊D61—42no—
221C2×Dic61—22no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61C4×D411yescharacteristic
226C2×Dic61#12112yes—
227C2×Dic61#12412yes—
228C2×Dic61C22×D411yescharacteristic
229D244—21no—
230D244—21no—
231D244—41no—
232D244—41no—
233C4×D61—42no—
234C4×D61—44no—
235C4×D61—42no—
236C4×D61—41no—
237C4×D61—41no—
238C4×D61#11712yes—
239C4×D61C4×D412yes—
240C4×D61#12112yes—
241C4×D61#12312yes—
242C4×D61#12412yes—
243C4×D61#12612yes—
244C4×D61C22×D411yescharacteristic
245C4×D61C2×#4111yescharacteristic
246C4×D61C2×#4111yescharacteristic
247C4×D61C2×#4111yescharacteristic
248Dic122—21no—
249Dic122—21no—
250Dic122—42no—
251#92420—24no—
252#92420—42no—
253#92420—42no—
254C8×C61—22no—
255#92418—22no—
256C2×#1937—611nomaximal, Sylow
257C22×C61—22no—
258C22×C61—42no—
259C22×C61—41no—
260C22×C61#38812yes—
261C22×C61C2×C4×D411yescharacteristic
262C2×D61—22no—
263C2×D61—24no—
264C2×D61—24no—
265C2×D61—42no—
266C2×D61—41no—
267C2×D61—84no—
268C2×D61#38812yes—
269C2×D61#44314yes—
270C2×D61C2×#12311yescharacteristic
271C2×D61C2×#12611yescharacteristic
272#6923—28no—
273C4×C61—42no—
274C4×C61—41no—
275C4×C61#38812yes—
276C4×C61C2×#11711yescharacteristic
277C4×C61C2×C4×D411yescharacteristic
278Dic61—42no—
279Dic61—41no—
280Dic61#38812yes—
281Dic61C2×#12111yescharacteristic
282Dic61C2×#12411yescharacteristic
283C2×#424—611no—
284C22×#104—611no—
285C2×#416—611no—
286C2×#408—611no—
287C22×C4×C8—611no—
288#1937—614no—
289#1937—614no—
290C2×#341—611no—
291C2×#339—611no—
292C2×C61—22no—
293C2×C61—81no—
294C2×C61C2×#38811yescharacteristic
295C2×C61C2×#44312yes—
296D61—21no—
297D61—21no—
298D61—81no—
299D61#193714yescomplemented
300C22×#41—611no—
301C22×M16—611no—
302C22×M16—611no—
303C23×C8—611no—
304C23×C8—611no—
305C2×#117—611no—
306C22×C42—611no—
307#424—614no—
308#424—1222no—
309C2×C4⋊C8—1222no—
310C2×#104—612no—
311C2×#104—612no—
312C2×#104—1224no—
313#416—611no—
314#416—611no—
315#416—611no—
316#416—612no—
317#416—612no—
318#416#692311yescharacteristic, complemented
319C2×#103—612no—
320C2×#102—612no—
321#408—612no—
322#408—612no—
323#408—1222no—
324C2×C22⋊C8—1222no—
325C2×C4×C8—614no—
326C2×C4×C8—1224no—
327#341—614no—
328#339—614no—
329C61C2×#193711yescharacteristic, complemented, Sylow
330C2×#41—611no—
331C2×#41—611no—
332C2×#41—611no—
333C2×#41—1221no—
334C2×#41—1221no—
335C2×#41—1222no—
336C2×#41—1222no—
337C2×#41—1222no—
338C2×#41—1222no—
339C2×#41C2×#692311yescharacteristic
340C22×Q8—611no—
341C22×D4—611no—
342C22×D4—1221no—
343C23×C4—611no—
344C23×C4—1221no—
345C23×C4—1221no—
346C2×M16—612no—
347C2×M16—612no—
348C2×M16—1221no—
349C2×M16—1221no—
350C2×M16—1222no—
351C2×M16—1222no—
352C2×M16—1222no—
353C2×M16—1222no—
354C22×C8—612no—
355C22×C8—612no—
356C22×C8—612no—
357C22×C8—611no—
358C22×C8—612no—
359C22×C8—612no—
360C22×C8—1222no—
361C22×C8—1222no—
362C22×C8—1222no—
363C22×C8—1222no—
364C22×C8—1221no—
365C22×C8—1221no—
366C22×C8C2×#692311yescharacteristic
367#117—611no—
368#117—612no—
369#117—1221no—
370#117—1221no—
371#117C2×#692311yescharacteristic
372C2×C4⋊C4—612no—
373C2×C22⋊C4—1221no—
374C2×C42—614no—
375C2×C42—612no—
376C2×C42—1221no—
377C2×C42—1222no—
378C2×C42—1221no—
379C4⋊C8—1224no—
380C4⋊C8—1224no—
381#104—1224no—
382#104—1224no—
383#103—612no—
384#103—612no—
385#103—612no—
386#103C2×#692312yescomplemented
387#102—612no—
388#102—612no—
389#102—612no—
390#102C2×#692312yescomplemented
391C22⋊C8—1224no—
392C22⋊C8—1224no—
393C4×C8—1228no—
394C24—611no—
395C24—1221no—
396#41—22no—
397#41—22no—
398#41—1221no—
399#41—1221no—
400#41—1221no—
401#41—1221no—
402#41—1221no—
403#41—1221no—
404#41—1221no—
405#41—1221no—
406#41—1222no—
407#41—1222no—
408#41—2442no—
409#41—2442no—
410#41—2442no—
411#41—2442no—
412C2×Q8—611no—
413C2×Q8—1221no—
414C2×Q8—1222no—
415C2×Q8—1222no—
416C2×Q8C22×#692311yescharacteristic
417C2×D4—21no—
418C2×D4—611no—
419C2×D4—1221no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1221no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—2442no—
426C2×D4—2442no—
427C2×D4C22×#692311yescharacteristic
428C22×C4—21no—
429C22×C4—611no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1222no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1224no—
443C22×C4—1222no—
444C22×C4—1228no—
445C22×C4—1221no—
446C22×C4—2442no—
447C22×C4—2442no—
448C22×C4C22×#692311yescharacteristic
449M16—1222no—
450M16—1222no—
451M16—1222no—
452M16—1222no—
453M16—2442no—
454M16—2442no—
455C2×C8—22no—
456C2×C8—614no—
457C2×C8—612no—
458C2×C8—1222no—
459C2×C8—1224no—
460C2×C8—1222no—
461C2×C8—1222no—
462C2×C8—1224no—
463C2×C8—1222no—
464C2×C8—1224no—
465C2×C8—1222no—
466C2×C8—1222no—
467C2×C8—1222no—
468C2×C8—2442no—
469C2×C8—2442no—
470C2×C8C22×#692312yes—
471C4⋊C4—612no—
472C4⋊C4—1222no—
473C4⋊C4C22×#692312yes—
474C22⋊C4—21no—
475C22⋊C4—1222no—
476C22⋊C4—1221no—
477C42—21no—
478C42—614no—
479C42—1222no—
480C42—1224no—
481C42—1222no—
482C42—1221no—
483C23—21no—
484C23—611no—
485C23—612no—
486C23—612no—
487C23—611no—
488C23—1224no—
489C23—1221no—
490C23—2442no—
491C23—2444no—
492C23D4×#692311yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—1221no—
496Q8—1221no—
497Q8—2442no—
498D4—21no—
499D4—21no—
500D4—42no—
501D4—1221no—
502D4—1221no—
503D4—2441no—
504D4—2441no—
505D4—2442no—
506D4—2441no—
507D4—2441no—
508D4—2442no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—612no—
513C2×C4—612no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1224no—
527C2×C4—12216no—
528C2×C4—1228no—
529C2×C4—1222no—
530C2×C4—1221no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2444no—
534C2×C4—2442no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2442no—
538C2×C4#1451985612yes—
539C2×C4D4×#692312yes—
540C2×C4D4×#692311yescharacteristic
541C2×C4C23×#692311yescharacteristic
542C8—22no—
543C8—1224no—
544C8—1222no—
545C8—2442no—
546C8—2442no—
547C22—22no—
548C22—41no—
549C22—42no—
550C22—612no—
551C22—614no—
552C22—611no—
553C22—611no—
554C22—1224no—
555C22—1224no—
556C22—1222no—
557C22—4884no—
558C22—2441no—
559C22—2442no—
560C22#1684071212yes—
561C22C2×D4×#692311yescharacteristic
562C4—41no—
563C4—42no—
564C4—611no—
565C4—611no—
566C4—612no—
567C4—1228no—
568C4—2441no—
569C4—2442no—
570C4#1684071212yes—
571C4C2×#1451985611yescharacteristic
572C4C2×D4×#692311yescharacteristic
573C2—22no—
574C2—81no—
575C2—614no—
576C2—1221no—
577C2—1221no—
578C2—4881no—
579C2C2×#1684071211yescharacteristic
580C2D61⋊#44312yes—
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#416C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#416#6923
hypocenterC61C2×#1937
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. D61⋊#424C2semidirect
4. C22×C8×#6923C2semidirect
5. #21461913C2semidirect
6. #21461912C2semidirect
7. #21461511C2semidirect
8. #21461495C2semidirect
14. #16840769C22semidirect
25. C2×C8×#6923C22semidirect
26. #16840638C22semidirect
27. #16840632C22semidirect
31. #16839759C4semidirect
32. #16839758C4semidirect
34. #16839756C4semidirect
36. #103×D61C4semidirect
37. #102×D61C4semidirect
38. C61×#416C4semidirect
92. #14519702C2×C4semidirect
93. #14519701C2×C4semidirect
94. #14519700C2×C4semidirect
95. #14519699C2×C4semidirect
96. #14519698C2×C4semidirect
97. #14519697C2×C4semidirect
101. #103×C61C2×C4semidirect
102. #102×C61C2×C4semidirect
299. D61#1937semidirect
318. #416#6923semidirect
329. C61C2×#1937semidirect
386. #103C2×#6923semidirect
390. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4242
C2×D61⋊#1042
D61⋊#4082
C22×C8×#69232
#214619132
#214619122
#214615112
#214614952
#416×D612
C2×#193761