Finite Group Databasebeta

← #29663991

Subgroups — #29663991

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#487×D61C211yesmaximal, characteristic, complemented
2#21455633C211yesmaximal, characteristic
3#21455629C211yesmaximal, characteristic
4C8×#11758226C211yesmaximal, characteristic
5#21445279C211yesmaximal, characteristic, complemented
6#21445277C211yesmaximal, characteristic, complemented
7#21445275C211yesmaximal, characteristic, complemented
8#21445273C211yesmaximal, characteristic, complemented
9#21445271C211yesmaximal, characteristic, complemented
10#21445269C211yesmaximal, characteristic, complemented
11#21445267C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic, complemented
13#21444502C211yesmaximal, characteristic, complemented
14#21444498C211yesmaximal, characteristic, complemented
15C61×#1684C211yesmaximal, characteristic, complemented
16C4⋊Q8×D61C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×#11758226C2211yescharacteristic
19#16840114C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840111—21no—
23#16840111—21no—
24#16840057C2211yescharacteristic
25#16840055—21no—
26#16840053C2211yescharacteristic
27#16840051—21no—
28#16840049C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840045—21no—
31#16840043C2211yescharacteristic
32#16840041—21no—
33#16840039C2211yescharacteristic
34Q8×#92418C2211yescharacteristic
35C8×D244—21no—
36C8×D244C2211yescharacteristic
37#16839827—21no—
38#16839827C2211yescharacteristic
39#16839814—21no—
40#16839814C2211yescharacteristic
41#16839803—21no—
42#16839801—21no—
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45#16839762—21no—
46#16839762—21no—
47#103×D61—21no—
48#103×D61—21no—
49C4×C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758226D411yescharacteristic
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C2×C8×D61D411yescharacteristic
75C2×C8×D61D411yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519776—21no—
79#14519776—21no—
80#14519776—21no—
81#14519776—21no—
82#14519775—21no—
83#14519775—21no—
84Q8×Dic61D411yescharacteristic
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87#14519739—21no—
88#14519739D411yescharacteristic
89#14519735—21no—
90#14519735D411yescharacteristic
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519711—21no—
98#14519710—21no—
99#14519710—21no—
100#14519709—21no—
101#14519708—21no—
102#14519708—21no—
103C4⋊#92418—21no—
104C4⋊#92418C2311yescharacteristic
105C4⋊#92418C2311yescharacteristic
106C4⋊#92418C2311yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519702—21no—
110#14519702—21no—
111#14519701—21no—
112#14519701—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519700—21no—
117#14519699—21no—
118#14519699—21no—
119#14519697—21no—
120#14519697—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124C4×#92418—21no—
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130C4⋊Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147#11758226—22no—
148#11758226Q1614yes—
149Q8×D61—42no—
150Q8×D61—42no—
151Q8×D61—82no—
152C2×D244—21no—
153C2×D244C2×D411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—41no—
165C2×Dic122—41no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179#11758198—21no—
180#11758198—21no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C2×D411yescharacteristic
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191#11758196—41no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202#11758189—42no—
203#11758189—42no—
204C8×D61—41no—
205C8×D61—41no—
206C8×D61—42no—
207C8×D61—42no—
208C22×D61—21no—
209C22×D61#12111yescharacteristic
210Q8×C61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—81no—
214Q8×C61C2×Q1612yes—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61#12111yescharacteristic
226C2×Dic61#12111yescharacteristic
227C2×Dic61#12111yescharacteristic
228D244—24no—
229D244—21no—
230D244C2×Q1612yes—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—24no—
234C4×D61—22no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—42no—
238C4×D61—82no—
239C4×D61—82no—
240C4×D61C2×Q1612yes—
241C4×D61#13512yes—
242Dic122—41no—
243Dic122—41no—
244Dic122—82no—
245Dic122—82no—
246Dic122—81no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#19277—611nomaximal, Sylow
258C22×C61C2×#12111yescharacteristic
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—22no—
262C2×D61—41no—
263C2×D61—41no—
264C2×D61#46712yes—
265C4×C61—22no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61C22×Q1611yescharacteristic
271C4×C61C2×#13511yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57511yescharacteristic
274Dic61—21no—
275Dic61—41no—
276Dic61—81no—
277Dic61—81no—
278Dic61#46712yes—
279Dic61#47112yes—
280C2×#487—611no—
281#3079—611no—
282#3079—611no—
283C8×#41—611no—
284#1684—611no—
285#1684—611no—
286#1684—611no—
287#1684D6111yescharacteristic, complemented
288#1683—611no—
289#1683—611no—
290#1683—611no—
291#1683—611no—
292#1567—611no—
293#1549—611no—
294#1548—611no—
295C2×C61#304011yescharacteristic
296C2×C61C2×#46711yescharacteristic
297C2×C61C2×#47111yescharacteristic
298D61—22no—
299D61—42no—
300C2×C4⋊Q8—611no—
301C2×C4⋊Q8—611no—
302C4×#41—611no—
303#487—611no—
304#487—611no—
305#487—611no—
306#487—1221no—
307#487—1221no—
308#487C2×D6111yescharacteristic
309#477—611no—
310#477—1221no—
311#477C2×D6111yescharacteristic
312#476—611no—
313#476—611no—
314#476—1221no—
315#475—611no—
316#475—1221no—
317#475C2×D6111yescharacteristic
318#474—611no—
319#474—611no—
320#474—1221no—
321C8×Q8—611no—
322C8×Q8C2×D6111yescharacteristic
323C8×D4—611no—
324C8×D4—611no—
325C8×D4—1221no—
326C8×D4—1221no—
327#431—611no—
328#431—1221no—
329#428—1221no—
330#428—1221no—
331#423—611no—
332#423—611no—
333#417—1221no—
334#417—1221no—
335C2×#103—1221no—
336C2×#103—1221no—
337C2×C4×C8—611no—
338C2×C4×C8—1221no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335C2×D6111yescharacteristic
343#333—611no—
344#333—611no—
345#333—611no—
346#333C2×D6111yescharacteristic
347#332—611no—
348#332—611no—
349#332—611no—
350#332C2×D6111yescharacteristic
351C61#1927711yescharacteristic, complemented, Sylow
352C2×#41—611no—
353C22×Q8—1221no—
354C22×Q8—1221no—
355C2×M16—1221no—
356C2×M16—1221no—
357C22×C8—611no—
358C22×C8—611no—
359C22×C8—1221no—
360C22×C8—1221no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363C4⋊Q8—1221no—
364C4⋊Q8—1221no—
365C4⋊Q8—1221no—
366C4⋊Q8—1221no—
367C4⋊Q8—1221no—
368C4⋊Q8—1221no—
369C4⋊Q8C22×D6111yescharacteristic
370C4⋊Q8C22×D6111yescharacteristic
371C4×Q8—611no—
372C4×Q8C22×D6111yescharacteristic
373C4×D4—611no—
374C4×D4—611no—
375C4×D4—1221no—
376C4×D4—1221no—
377#117—611no—
378#117—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C42—611no—
384C2×C42—1221no—
385#107—21no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#106—21no—
390#106—1221no—
391#106—1221no—
392#106—1221no—
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C4×C8—21no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429#41—614no—
430#41—1222no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—4882no—
436C2×Q8—2441no—
437C2×Q8—2441no—
438C2×Q8—2442no—
439C2×Q8—2442no—
440C2×Q8D4×D6111yescharacteristic
441C2×D4—611no—
442C2×D4—1221no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—2441no—
450C22×C4—2441no—
451M16—2442no—
452M16—2442no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—2441no—
462C2×C8—2441no—
463C2×C8—2442no—
464C2×C8—2442no—
465C2×C8D4×D6111yescharacteristic
466C2×C8D4×D6111yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—611no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C4⋊C4D4×D6111yescharacteristic
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C42—21no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—1221no—
491C42—1221no—
492C42C23×D6111yescharacteristic
493C23—611no—
494C23—1221no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—4881no—
500Q8—4882no—
501Q8—4882no—
502Q8—2441no—
503Q8—2441no—
504Q8Q16×D6112yes—
505D4—612no—
506D4—1224no—
507D4—1221no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—611no—
517C2×C4—1222no—
518C2×C4—1224no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—4882no—
523C2×C4—4882no—
524C2×C4—2442no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4C2×D4×D6111yescharacteristic
530C2×C4C2×D4×D6111yescharacteristic
531C2×C4#41×D6111yescharacteristic
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C22—612no—
543C22—1221no—
544C22—1221no—
545C22—1222no—
546C22—2441no—
547C22—2441no—
548C22#121×D6111yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—612no—
555C4—612no—
556C4—1221no—
557C4—4881no—
558C4—4881no—
559C4—2441no—
560C4C2×Q16×D6111yescharacteristic
561C4#135×D6111yescharacteristic
562C4#1684055911yescharacteristic
563C4#1684056111yescharacteristic
564C2—1222no—
565C2—2442no—
566C2#2145531011yescharacteristic
567C2#467×D6111yescharacteristic
568C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1684C2
socleC22×C61C2×#121
prime radicalC2×#11758226D4
hypercenter#1684D61
hypocenterC61#19277
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
1. #487×D61C2semidirect
5. #21445279C2semidirect
6. #21445277C2semidirect
7. #21445275C2semidirect
8. #21445273C2semidirect
9. #21445271C2semidirect
10. #21445269C2semidirect
11. #21445267C2semidirect
12. #21444576C2semidirect
13. #21444502C2semidirect
14. #21444498C2semidirect
15. C61×#1684C2semidirect
287. #1684D61semidirect
351. C61#19277semidirect

Maximal subgroups

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

subgroupindex
#487×D612
#214556332
#214556292
C8×#117582262
#214452792
#214452772
#214452752
#214452732
#214452712
#214452692
#214452672
#214445762
#214445022
#214444982
C61×#16842
#1927761