Finite Group Databasebeta

← #29663928

Subgroups — #29663928

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#498×D61C211yesmaximal, characteristic, complemented
2#21455631C211yesmaximal, characteristic
3#21455301C211yesmaximal, characteristic
4C8×#11758224C211yesmaximal, characteristic
5#21445204C211yesmaximal, characteristic, complemented
6#21445202C211yesmaximal, characteristic, complemented
7#21445200C211yesmaximal, characteristic, complemented
8#21445198C211yesmaximal, characteristic, complemented
9#21445196C211yesmaximal, characteristic, complemented
10#21445194C211yesmaximal, characteristic, complemented
11#21445192C211yesmaximal, characteristic, complemented
12#21444573C211yesmaximal, characteristic, complemented
13#21444498C211yesmaximal, characteristic, complemented
14#21444489C211yesmaximal, characteristic, complemented
15C61×#1671C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17C4⋊Q8×D61C2211yescharacteristic
18C4⋊Q8×D61C2211yescharacteristic
19C4×#11758224C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840159—21no—
22#16840159—21no—
23#16840158C2211yescharacteristic
24#16840158C2211yescharacteristic
25#16840058C2211yescharacteristic
26#16840054C2211yescharacteristic
27#16840052C2211yescharacteristic
28#16840046—21no—
29#16840040—21no—
30#16839973C2211yescharacteristic
31#16839971—21no—
32#16839969C2211yescharacteristic
33#16839967C2211yescharacteristic
34#16839965—21no—
35C8×Dic122C2211yescharacteristic
36#16839886C2211yescharacteristic
37D4×#92418C2211yescharacteristic
38C8×C22⋊D61—21no—
39#16839825—21no—
40#16839814C2211yescharacteristic
41#16839812—21no—
42#16839801—21no—
43#106×D61—21no—
44#106×D61—21no—
45#16839784C2211yescharacteristic
46#16839784C2211yescharacteristic
47#16839769—21no—
48#16839760—21no—
49C2×C8×Dic61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#476C2211yescharacteristic
62C61×#461C2211yescharacteristic
63C8×D4×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758224D411yescharacteristic
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70#14519806—44no—
71C2×Dic244—21no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418—21no—
77C2×C8×D61D411yescharacteristic
78C2×C8×D61D411yescharacteristic
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519776—21no—
82#14519776—21no—
83#14519776—21no—
84#14519776—21no—
85#14519775—21no—
86#14519775—21no—
87C4×Dic122C2311yescharacteristic
88#14519742D411yescharacteristic
89D4×Dic61D411yescharacteristic
90C4×C22⋊D61—21no—
91#14519737—21no—
92#14519735D411yescharacteristic
93#14519733—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C2×C4×Dic61—21no—
99C42×D61C2311yescharacteristic
100#14519711—21no—
101#14519710—21no—
102#14519709—21no—
103#14519709—21no—
104#14519708—21no—
105#14519708—21no—
106#14519708—21no—
107#14519708—21no—
108#14519708—21no—
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111C4⋊#92418C2311yescharacteristic
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519702—21no—
117#14519702—21no—
118#14519701—21no—
119#14519700—21no—
120#14519700—21no—
121#14519698—21no—
122C22⋊#92418—21no—
123#14519689—21no—
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61D411yescharacteristic
129C8×Dic61D411yescharacteristic
130C2×SD16×C61—21no—
131C22×C8×C61—21no—
132C4⋊Q8×C61C2311yescharacteristic
133C4⋊Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141#103×C61—21no—
142#102×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×D4×C61C2×D411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152Q8×D61—42no—
153Q8×D61—42no—
154Q8×D61—82no—
155#11758224—22no—
156#11758224SD1614yes—
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×Dic122C2×D411yescharacteristic
167SD16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—42no—
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758202—42no—
183#11758200—42no—
184#11758198—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C2×D411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61C2×D411yescharacteristic
200C4×Dic61C2×D411yescharacteristic
201C4×Dic61#4111yescharacteristic
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206C2×#92418C2×D411yescharacteristic
207C2×#92418C2×D411yescharacteristic
208Dic244—42no—
209#11758189—42no—
210#11758189—42no—
211C8×D61—22no—
212C8×D61—22no—
213C23×C61—21no—
214C22×D61#12111yescharacteristic
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—81no—
218D4×C61—21no—
219D4×C61C2×SD1612yes—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C22⋊D61—24no—
229C2×Dic61—21no—
230C2×Dic61—24no—
231C2×Dic61—21no—
232C2×Dic61—42no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61#12111yescharacteristic
236C2×Dic61#12111yescharacteristic
237C2×Dic61#12111yescharacteristic
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—22no—
241C4×D61—82no—
242C4×D61—82no—
243C4×D61C2×SD1612yes—
244C4×D61#13512yes—
245Dic122—21no—
246Dic122—41no—
247Dic122—41no—
248Dic122—82no—
249Dic122—82no—
250Dic122—81no—
251Dic122C2×SD1612yes—
252C8×C61—21no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61#13712yescomplemented
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418#13712yescomplemented
262#19270—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×#12111yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61#46512yes—
270C4×C61—21no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61C22×SD1611yescharacteristic
275C4×C61C2×#13511yescharacteristic
276C4×C61C2×#13711yescharacteristic
277C4×C61C2×#13711yescharacteristic
278Dic61—21no—
279Dic61—22no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283Dic61#46512yes—
284Dic61#47112yes—
285C2×#498—611no—
286#3079—611no—
287#3039—611no—
288C8×#41—611no—
289#1672—611no—
290#1672—611no—
291#1672—611no—
292#1672—611no—
293#1671—611no—
294#1671—611no—
295#1671—611no—
296#1671D6111yescharacteristic, complemented
297#1566—611no—
298#1548—611no—
299#1546—611no—
300C2×C61—42no—
301C2×C61#303911yescharacteristic
302C2×C61C2×#46511yescharacteristic
303C2×C61C2×#47111yescharacteristic
304D61—22no—
305C2×#137—1221no—
306C2×C4⋊Q8—611no—
307C2×C4⋊Q8—611no—
308C4×#41—611no—
309#498—611no—
310#498—611no—
311#498—611no—
312#498—1221no—
313#498—1221no—
314#498C2×D6111yescharacteristic
315#477—611no—
316#477—611no—
317#476—611no—
318#476C2×D6111yescharacteristic
319#475—1221no—
320#474—1221no—
321#462—611no—
322#462—611no—
323#462—1221no—
324#461—611no—
325#461—1221no—
326#461C2×D6111yescharacteristic
327C8×Q8—611no—
328C8×Q8—611no—
329C8×D4—611no—
330C8×D4—1221no—
331C8×D4—1221no—
332C8×D4C2×D6111yescharacteristic
333#431—611no—
334#431—1221no—
335#428—1221no—
336C2×#106—1221no—
337C2×#106—1221no—
338#423—611no—
339#423—611no—
340#419—1221no—
341#417—1221no—
342C2×C4×C8—611no—
343C2×C4×C8—1221no—
344#334—611no—
345#334—611no—
346#334—611no—
347#334C2×D6111yescharacteristic
348#333—611no—
349#333—611no—
350#333—611no—
351#333C2×D6111yescharacteristic
352#332—611no—
353#332—611no—
354#332—611no—
355#332C2×D6111yescharacteristic
356C61#1927011yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C22×Q8—1221no—
359C22×Q8—1221no—
360#137—2444no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×SD16—21no—
364C2×SD16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C22×C8—21no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—1221no—
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377C4⋊Q8—1221no—
378C4⋊Q8—1221no—
379C4⋊Q8C22×D6111yescharacteristic
380C4⋊Q8C22×D6111yescharacteristic
381C4×Q8—611no—
382C4×Q8—611no—
383C4×D4—611no—
384C4×D4—1221no—
385C4×D4—1221no—
386C4×D4C22×D6111yescharacteristic
387#117—611no—
388#117—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C42—611no—
394C2×C42—1221no—
395#107—1221no—
396#107—1221no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—1221no—
401#106—1221no—
402#106—1221no—
403#106—1221no—
404#106—1221no—
405#106—1221no—
406#106—1221no—
407C4⋊C8—611no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—1221no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8C22×D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417#103—21no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#102—21no—
424#102—1221no—
425C22⋊C8—21no—
426C22⋊C8—1221no—
427C22⋊C8—1221no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8C22×D6111yescharacteristic
435#41—614no—
436#41—1222no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—4882no—
443C2×Q8—2441no—
444C2×Q8—2441no—
445C2×Q8—2442no—
446C2×Q8—2442no—
447C2×D4—1221no—
448C2×D4D4×D6111yescharacteristic
449C22×C4—21no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—2441no—
456C22×C4—2441no—
457Q16—2442no—
458Q16—2442no—
459SD16—42no—
460SD16—2442no—
461M16—2442no—
462M16—2442no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1222no—
470C2×C8—1222no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—2442no—
475C2×C8D4×D6111yescharacteristic
476C2×C8D4×D6111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—611no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4D4×D6111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42C23×D6111yescharacteristic
503C23—21no—
504C23—611no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508Q8—612no—
509Q8—1221no—
510Q8—4881no—
511Q8—4882no—
512Q8—4882no—
513Q8—2441no—
514Q8—2441no—
515D4—21no—
516D4—1224no—
517D4SD16×D6112yes—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—1222no—
529C2×C4—1224no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—4882no—
535C2×C4—4882no—
536C2×C4—2442no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4C2×D4×D6111yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4#41×D6111yescharacteristic
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—612no—
547C8—1221no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8#1451980612yescomplemented
552C22—22no—
553C22—41no—
554C22—41no—
555C22—612no—
556C22—1221no—
557C22—1221no—
558C22#121×D6111yescharacteristic
559C4—21no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—612no—
564C4—612no—
565C4—1222no—
566C4—1221no—
567C4—4881no—
568C4—4881no—
569C4—2441no—
570C4C2×SD16×D6111yescharacteristic
571C4#135×D6111yescharacteristic
572C4#137×D6111yescharacteristic
573C4C2×#1451980611yescharacteristic
574C2—42no—
575C2—1222no—
576C2#2145530111yescharacteristic
577C2#465×D6111yescharacteristic
578C2#471×D6111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1671C2
socleC22×C61C2×#121
prime radicalC2×#11758224D4
hypercenter#1671D61
hypocenterC61#19270
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #498×D61C2semidirect
5. #21445204C2semidirect
6. #21445202C2semidirect
7. #21445200C2semidirect
8. #21445198C2semidirect
9. #21445196C2semidirect
10. #21445194C2semidirect
11. #21445192C2semidirect
12. #21444573C2semidirect
13. #21444498C2semidirect
14. #21444489C2semidirect
15. C61×#1671C2semidirect
256. C8×C61#137semidirect
261. #92418#137semidirect
296. #1671D61semidirect
356. C61#19270semidirect
551. C8#14519806semidirect

Maximal subgroups

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

subgroupindex
#498×D612
#214556312
#214553012
C8×#117582242
#214452042
#214452022
#214452002
#214451982
#214451962
#214451942
#214451922
#214445732
#214444982
#214444892
C61×#16712
#1927061