Finite Group Databasebeta

← #29663989

Subgroups — #29663989

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#21455631C211yesmaximal, characteristic
3#21455627C211yesmaximal, characteristic
4C8×#11758224C211yesmaximal, characteristic
5#21445280C211yesmaximal, characteristic, complemented
6#21445278C211yesmaximal, characteristic, complemented
7#21445276C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445272C211yesmaximal, characteristic, complemented
10#21445270C211yesmaximal, characteristic, complemented
11#21445268C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic, complemented
13#21444502C211yesmaximal, characteristic, complemented
14#21444498C211yesmaximal, characteristic, complemented
15C61×#1683C211yesmaximal, characteristic, complemented
16C4⋊Q8×D61C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×#11758224C2211yescharacteristic
19#16840114C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840111—21no—
23#16840111—21no—
24#16840058C2211yescharacteristic
25#16840056—21no—
26#16840054C2211yescharacteristic
27#16840052C2211yescharacteristic
28#16840050—21no—
29#16840048C2211yescharacteristic
30#16840046—21no—
31#16840044C2211yescharacteristic
32#16840042C2211yescharacteristic
33#16840040—21no—
34C8×Dic122C2211yescharacteristic
35#16839886C2211yescharacteristic
36D4×#92418C2211yescharacteristic
37C8×C22⋊D61—21no—
38#16839825—21no—
39#16839814C2211yescharacteristic
40#16839812—21no—
41#16839803—21no—
42#16839801—21no—
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45#16839760—21no—
46#16839760—21no—
47#103×D61—21no—
48#103×D61—21no—
49C2×C8×Dic61—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×#476C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758224D411yescharacteristic
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×#11758189—21no—
71C2×#11758189—21no—
72C22×#92418—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519776—21no—
80#14519776—21no—
81#14519775—21no—
82#14519775—21no—
83C4×Dic122C2311yescharacteristic
84#14519742D411yescharacteristic
85D4×Dic61D411yescharacteristic
86C4×C22⋊D61—21no—
87#14519737—21no—
88#14519735D411yescharacteristic
89#14519733—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C2×C4×Dic61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519710—21no—
98#14519710—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702—21no—
110#14519702—21no—
111#14519702—21no—
112#14519702—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519700—21no—
117#14519700—21no—
118#14519700—21no—
119#14519698—21no—
120#14519698—21no—
121C22⋊#92418—21no—
122#14519689—21no—
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C22×C8×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#107×C61—21no—
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×D4×C61C2×D411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151Q8×D61—42no—
152Q8×D61—42no—
153Q8×D61—82no—
154#11758224—22no—
155#11758224Q1614yes—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61#4111yescharacteristic
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—41no—
164C2×Dic122—41no—
165C2×Dic122C2×D411yescharacteristic
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—42no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—21no—
180#11758198—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61C2×D411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191#11758196—41no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—42no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204#11758189—42no—
205#11758189—42no—
206C8×D61—41no—
207C8×D61—41no—
208C23×C61—21no—
209C22×D61#12111yescharacteristic
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213D4×C61—21no—
214D4×C61C2×Q1612yes—
215C2×C4×C61—21no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C22⋊D61—24no—
224C2×Dic61—21no—
225C2×Dic61—24no—
226C2×Dic61—21no—
227C2×Dic61—42no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61#12111yescharacteristic
231C2×Dic61#12111yescharacteristic
232C2×Dic61#12111yescharacteristic
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—22no—
236C4×D61—82no—
237C4×D61—82no—
238C4×D61C2×Q1612yes—
239C4×D61#13512yes—
240Dic122—21no—
241Dic122—41no—
242Dic122—41no—
243Dic122—82no—
244Dic122—82no—
245Dic122—81no—
246Dic122C2×Q1612yes—
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×C61—22no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×#12111yescharacteristic
262C2×D61—21no—
263C2×D61—21no—
264C2×D61#46712yes—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61C22×Q1611yescharacteristic
270C4×C61C2×#13511yescharacteristic
271C4×C61#57511yescharacteristic
272C4×C61#57511yescharacteristic
273Dic61—21no—
274Dic61—22no—
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#1684—611no—
288#1683—611no—
289#1683—611no—
290#1683—611no—
291#1683D6111yescharacteristic, complemented
292#1567—611no—
293#1549—611no—
294#1548—611no—
295C2×C61—42no—
296C2×C61#304011yescharacteristic
297C2×C61C2×#46711yescharacteristic
298C2×C61C2×#47111yescharacteristic
299D61—22no—
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—611no—
311#477—1221no—
312#476—611no—
313#476—1221no—
314#476C2×D6111yescharacteristic
315#475—611no—
316#475—611no—
317#475—1221no—
318#474—611no—
319#474—1221no—
320#474C2×D6111yescharacteristic
321C8×Q8—611no—
322C8×Q8—611no—
323C8×D4—611no—
324C8×D4—1221no—
325C8×D4—1221no—
326C8×D4C2×D6111yescharacteristic
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—21no—
358C22×C8—611no—
359C22×C8—611no—
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×Q8—611no—
373C4×D4—611no—
374C4×D4—1221no—
375C4×D4—1221no—
376C4×D4C22×D6111yescharacteristic
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—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
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—1221no—
406#103—1221no—
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—21no—
416#102—21no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—21no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—1221no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8C22×D6111yescharacteristic
429#41—614no—
430#41—1222no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—611no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—4882no—
437C2×Q8—2441no—
438C2×Q8—2441no—
439C2×Q8—2442no—
440C2×Q8—2442no—
441C2×D4—1221no—
442C2×D4D4×D6111yescharacteristic
443C22×C4—21no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
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—42no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—2441no—
463C2×C8—2441no—
464C2×C8—2442no—
465C2×C8D4×D6111yescharacteristic
466C2×C8D4×D6111yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—611no—
472C4⋊C4—1221no—
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—21no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—1221no—
490C42—1221no—
491C42—1221no—
492C42C23×D6111yescharacteristic
493C23—21no—
494C23—611no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—612no—
499Q8—1221no—
500Q8—4881no—
501Q8—4882no—
502Q8—4882no—
503Q8—2441no—
504Q8—2441no—
505D4—21no—
506D4—1224no—
507D4Q16×D6112yes—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—611no—
518C2×C4—1222no—
519C2×C4—1224no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—4882no—
525C2×C4—4882no—
526C2×C4—2442no—
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—22no—
543C22—41no—
544C22—41no—
545C22—612no—
546C22—1221no—
547C22—1221no—
548C22#121×D6111yescharacteristic
549C4—21no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—612no—
554C4—612no—
555C4—1222no—
556C4—1221no—
557C4—4881no—
558C4—4881no—
559C4—2441no—
560C4C2×Q16×D6111yescharacteristic
561C4#135×D6111yescharacteristic
562C4#1684055811yescharacteristic
563C4#1684055911yescharacteristic
564C2—42no—
565C2—1222no—
566C2#2145530811yescharacteristic
567C2#467×D6111yescharacteristic
568C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1683C2
socleC22×C61C2×#121
prime radicalC2×#11758224D4
hypercenter#1683D61
hypocenterC61#19277
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

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

NH ≅ G/Ntype
1. #487×D61C2semidirect
5. #21445280C2semidirect
6. #21445278C2semidirect
7. #21445276C2semidirect
8. #21445274C2semidirect
9. #21445272C2semidirect
10. #21445270C2semidirect
11. #21445268C2semidirect
12. #21444576C2semidirect
13. #21444502C2semidirect
14. #21444498C2semidirect
15. C61×#1683C2semidirect
291. #1683D61semidirect
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
#214556312
#214556272
C8×#117582242
#214452802
#214452782
#214452762
#214452742
#214452722
#214452702
#214452682
#214445762
#214445022
#214444982
C61×#16832
#1927761