Finite Group Databasebeta

← #29649804

Subgroups — #29649804

Order 15616.

648 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
1#21454782C211yesmaximal, characteristic
2#446×D61C211yesmaximal, characteristic, complemented
3C4×#14519806C211yesmaximal, characteristic
4#21444727C211yesmaximal, characteristic, complemented
5#21444725C211yesmaximal, characteristic, complemented
6#21444722C211yesmaximal, characteristic, complemented
7#21444718C211yesmaximal, characteristic, complemented
8#21444717C211yesmaximal, characteristic, complemented
9#21444714C211yesmaximal, characteristic, complemented
10#21444707C211yesmaximal, characteristic, complemented
11#21444568C211yesmaximal, characteristic, complemented
12#21444212C211yesmaximal, characteristic, complemented
13#21444203C211yesmaximal, characteristic
14C8×#11758189C211yesmaximal, characteristic, complemented
15C61×#1590C211yesmaximal, characteristic, complemented
16C2×#14519806C411yescharacteristic
17C4×#11758224C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16839893C2211yescharacteristic
20#16839892C2211yescharacteristic
21#16839892C2211yescharacteristic
22#16839891—21no—
23#16839890—21no—
24#16839889C2211yescharacteristic
25#16839889C2211yescharacteristic
26#16839868C411yescharacteristic
27#16839866C411yescharacteristic
28#16839863C411yescharacteristic
29#16839859C411yescharacteristic
30C4×Dic244C2211yescharacteristic
31C4×#11758202C2211yescharacteristic
32C4×#11758200C2211yescharacteristic
33#16839840C2211yescharacteristic
34#16839836—21no—
35#16839831—21no—
36#16839814C2211yescharacteristic
37#16839813C2211yescharacteristic
38#16839812—21no—
39#16839801C411yescharacteristic
40C4⋊C8×D61—21no—
41C4⋊C8×D61C2211yescharacteristic
42#16839769C411yescharacteristic
43#16839760C411yescharacteristic
44M16×Dic61—21no—
45C4×#11758189C2211yescharacteristic
46#97×D61—21no—
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×Q8×D61C2×C411yescharacteristic
69#14519806—24no—
70C2×Dic244C2×C411yescharacteristic
71C2×#11758202C2×C411yescharacteristic
72C2×#11758200C2×C411yescharacteristic
73C2×#11758194—21no—
74C2×#11758189C2×C411yescharacteristic
75C2×#11758189C2×C411yescharacteristic
76C2×C8×D61—21no—
77C2×C8×D61D411yescharacteristic
78C2×C8×D61D411yescharacteristic
79Q8×Dic61C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82C4×Dic122C2311yescharacteristic
83#14519742—21no—
84#14519742C2×C411yescharacteristic
85#14519742C2×C411yescharacteristic
86D4×Dic61C2×C411yescharacteristic
87C4×C22⋊D61—21no—
88#14519737—21no—
89#14519735C2×C411yescharacteristic
90#14519733—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61C2×C411yescharacteristic
93C2×C4×Dic61—21no—
94C42×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519701C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519700C2×C411yescharacteristic
113#14519698C2×C411yescharacteristic
114C22⋊#92418—21no—
115#14519689—21no—
116#14519689—21no—
117#14519688—21no—
118#14519687—21no—
119#14519687—21no—
120#14519687—21no—
121#14519687—21no—
122#14519687C2×C411yescharacteristic
123#14519687C2×C411yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C8×Dic61—21no—
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61C2×C411yescharacteristic
131C2×M16×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61C2311yescharacteristic
134#106×C61C2×C411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140C22⋊C8×C61—21no—
141#97×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C2×C22⋊D61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151Q8×D61—22no—
152Q8×D61—22no—
153#11758224—22no—
154#11758224—22no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61C22×C411yescharacteristic
158C2×C4×D61C2×D411yescharacteristic
159C2×C4×D61#4111yescharacteristic
160C2×Dic122—21no—
161C2×Dic122C22×C411yescharacteristic
162C2×Dic122C22×C411yescharacteristic
163SD16×C61—22no—
164M16×C61—42no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C22×C411yescharacteristic
169C2×C8×C61C22×C411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C4⋊C4×C61—21no—
173C4⋊C4×C61C22×C411yescharacteristic
174C4⋊C4×C61C22×C411yescharacteristic
175C22⋊C4×C61—21no—
176C42×C61—21no—
177C42×C61C2411yescharacteristic
178C22⋊Dic61—21no—
179#11758202—22no—
180#11758200—22no—
181#11758198—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61C22×C411yescharacteristic
184C4⋊Dic61C22×C411yescharacteristic
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61C22×C411yescharacteristic
197C4×Dic61C2×D411yescharacteristic
198C4×Dic61#4111yescharacteristic
199#11758194—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207Dic244—22no—
208#11758189—22no—
209#11758189M1614yescomplemented
210C8×D61—22no—
211C8×D61—41no—
212C8×D61—42no—
213C23×C61—21no—
214C22×D61C4×D411yescharacteristic
215Q8×C61—21no—
216Q8×C61—21no—
217D4×C61—21no—
218D4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61C23×C411yescharacteristic
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C22⋊D61—42no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C4×D411yescharacteristic
236C2×Dic61C4×D411yescharacteristic
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—41no—
240C4×D61—42no—
241C4×D61—42no—
242C4×D61C2×M1612yes—
243C4×D61#13112yes—
244Dic122—21no—
245Dic122—21no—
246Dic122—21no—
247Dic122—21no—
248Dic122—42no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61C2×M1612yes—
255C8×C61#13712yescomplemented
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418C2×M1612yes—
263#17892—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—21no—
269C2×D61—21no—
270C2×D61#43612yes—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61C22×M1611yescharacteristic
276C4×C61C2×#13111yescharacteristic
277C4×C61C2×#13711yescharacteristic
278C4×C61#57511yescharacteristic
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285Dic61#43612yes—
286#2965—611no—
287C2×#446—611no—
288C4×#137—611no—
289#1593—611no—
290#1593—611no—
291#1592—611no—
292#1592—611no—
293#1591—611no—
294#1591—611no—
295#1590—611no—
296#1590D6111yescharacteristic, complemented
297#1565—611no—
298#1479—611no—
299#1477—611no—
300C8×M16—611no—
301C2×C61—81no—
302C2×C61C2×#43611yescharacteristic
303C2×C61C4×#13711yescharacteristic
304C2×C61#295511yescharacteristic
305D61—22no—
306C2×#137—611no—
307C4×#41—611no—
308C2×C4×Q8—611no—
309#446—611no—
310#446—611no—
311#446—611no—
312#446—611no—
313#446—611no—
314#446—1221no—
315#446—1221no—
316#446C2×D6111yescharacteristic
317#441—611no—
318#441—611no—
319#440—611no—
320#440—611no—
321C4×Q16—611no—
322C4×Q16—611no—
323C4×SD16—611no—
324C4×SD16C2×D6111yescharacteristic
325#436—611no—
326#436C2×D6111yescharacteristic
327#435—1221no—
328#435—1221no—
329#431—611no—
330#431—611no—
331#431—1221no—
332#428—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—1221no—
335#419—611no—
336#417—611no—
337C4×M16—611no—
338C4×M16—1221no—
339C2×#97—1221no—
340C2×C4×C8—611no—
341#335—611no—
342#335—611no—
343#334—611no—
344#334C2×D6111yescharacteristic
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350Q8⋊C8C2×D6111yescharacteristic
351D4⋊C8—611no—
352D4⋊C8C2×D6111yescharacteristic
353#322—611no—
354#322—611no—
355C82—611no—
356C82C2×D6111yescharacteristic
357C61#1789211yescharacteristic, complemented, Sylow
358C2×#41—611no—
359C22×Q8—611no—
360#137—1224no—
361C2×Q16—611no—
362C2×Q16—611no—
363C2×SD16—611no—
364C2×SD16C4×D6111yescharacteristic
365C2×M16—21no—
366C2×M16—611no—
367C2×M16—611no—
368C2×M16—1221no—
369C22×C8—611no—
370C22×C8—611no—
371C22×C8—1221no—
372C4×Q8—611no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×Q8—1221no—
378C4×Q8—1221no—
379C4×Q8C22×D6111yescharacteristic
380C4×D4—611no—
381C4×D4—1221no—
382C4×D4—1221no—
383C4×D4C22×D6111yescharacteristic
384#117—611no—
385#117—1221no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1221no—
388C2×C42—611no—
389C2×C42—1221no—
390C2×C42—1221no—
391#107—611no—
392#107—611no—
393#106—611no—
394#106C4×D6111yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8C22×D6111yescharacteristic
406C4⋊C8C22×D6111yescharacteristic
407#103—611no—
408#103—611no—
409#103—611no—
410#103—611no—
411#103—611no—
412#103C4×D6111yescharacteristic
413#102—611no—
414#102C4×D6111yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418C22⋊C8—1221no—
419#97—21no—
420#97—611no—
421#97—611no—
422#97—1221no—
423#97—1221no—
424#97—1221no—
425#97—1221no—
426#97—1221no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8C22×D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—1222no—
437#41—1222no—
438C2×Q8—611no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1222no—
442C2×Q8—1222no—
443C2×Q8C2×C4×D6111yescharacteristic
444C2×D4—1221no—
445C2×D4C2×C4×D6111yescharacteristic
446C22×C4—21no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454Q16—1222no—
455Q16—1222no—
456SD16—22no—
457SD16—1222no—
458M16—42no—
459M16—614no—
460M16—1222no—
461M16—2442no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1222no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—2441no—
474C2×C8—2442no—
475C2×C8C2×C4×D6111yescharacteristic
476C2×C8C2×C4×D6111yescharacteristic
477C2×C8D4×D6111yescharacteristic
478C2×C8D4×D6111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—611no—
481C4⋊C4—611no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4C2×C4×D6111yescharacteristic
489C4⋊C4C2×C4×D6111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C42—21no—
494C42—611no—
495C42—611no—
496C42—611no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42C23×D6111yescharacteristic
504C23—21no—
505C23—611no—
506Q8—21no—
507Q8—21no—
508Q8—1221no—
509Q8—1221no—
510Q8—1221no—
511Q8—1221no—
512Q8—2442no—
513D4—21no—
514D4—21no—
515D4—2442no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—611no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—2441no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4C22×C4×D6111yescharacteristic
538C2×C4C2×D4×D6111yescharacteristic
539C2×C4#41×D6111yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—612no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8M16×D6112yes—
553C8#1451980612yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—612no—
558C22—1221no—
559C22—1221no—
560C22C4×D4×D6111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—612no—
566C4—1221no—
567C4—1221no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4—2441no—
572C4C2×M16×D6111yescharacteristic
573C4#131×D6111yescharacteristic
574C4C2×#1451980611yescharacteristic
575C4#1684055911yescharacteristic
576C2—81no—
577C2—1222no—
578C2#436×D6111yescharacteristic
579C2C4×#1451980611yescharacteristic
580C2#2145471711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1590C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C2×C4
cosocleC42×C61C24
hypercenter#1590D61
hypocenterC61#17892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #446×D61C2semidirect
4. #21444727C2semidirect
5. #21444725C2semidirect
6. #21444722C2semidirect
7. #21444718C2semidirect
8. #21444717C2semidirect
9. #21444714C2semidirect
10. #21444707C2semidirect
11. #21444568C2semidirect
12. #21444212C2semidirect
14. C8×#11758189C2semidirect
15. C61×#1590C2semidirect
209. #11758189M16semidirect
255. C8×C61#137semidirect
296. #1590D61semidirect
357. C61#17892semidirect
553. C8#14519806semidirect

Maximal subgroups

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

subgroupindex
#214547822
#446×D612
C4×#145198062
#214447272
#214447252
#214447222
#214447182
#214447172
#214447142
#214447072
#214445682
#214442122
#214442032
C8×#117581892
C61×#15902
#1789261