Finite Group Databasebeta

← #29677159

Subgroups — #29677159

Order 15616.

622 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#21458736C211yesmaximal, characteristic, complemented
2#21458397C211yesmaximal, characteristic
3#21457466C211yesmaximal, characteristic
4#21445435C211yesmaximal, characteristic, complemented
5#21445335C211yesmaximal, characteristic, complemented
6#21445330C211yesmaximal, characteristic, complemented
7#21445313C211yesmaximal, characteristic, complemented
8#21445305C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445066C211yesmaximal, characteristic, complemented
11#21445061C211yesmaximal, characteristic, complemented
12#21445052C211yesmaximal, characteristic
13#21444710C211yesmaximal, characteristic, complemented
14#21444709C211yesmaximal, characteristic, complemented
15C61×#3398C211yesmaximal, characteristic, complemented
16C2×#14519806—21no—
17Q8×D244C2211yescharacteristic
18#16840416C2211yescharacteristic
19#16840172—21no—
20#16840165C2211yescharacteristic
21#16840165C2211yescharacteristic
22#16840165C2211yescharacteristic
23#16840165C2211yescharacteristic
24#16840142C2211yescharacteristic
25#16840095—21no—
26#16840086—21no—
27#16840059—21no—
28#16840057—21no—
29#16840047C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840039C2211yescharacteristic
32#16840039C2211yescharacteristic
33#16840021—21no—
34#16840010—21no—
35#16839972C2211yescharacteristic
36#16839967C2211yescharacteristic
37#16839925—21no—
38#16839919—21no—
39#16839893C2211yescharacteristic
40#16839860—21no—
41C4×#11758201C2211yescharacteristic
42#16839841C2211yescharacteristic
43#16839840C2211yescharacteristic
44#16839805—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#556C2211yescharacteristic
58C61×#497—21no—
59C61×#494C2211yescharacteristic
60C61×#464—21no—
61C61×#462—21no—
62C61×#462C2211yescharacteristic
63C61×#461C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#441—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758224—21no—
68C2×Q8×D61—21no—
69#14519806—44no—
70C2×Dic244—21no—
71C2×Dic244—21no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758201D411yescharacteristic
75C2×#11758194—21no—
76C2×#11758189—21no—
77#14519777—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519761—41no—
81#14519757—21no—
82#14519757—21no—
83#14519757—41no—
84#14519751—21no—
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C2×C4⋊Dic61—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—41no—
95#14519710—41no—
96#14519708—21no—
97#14519708—21no—
98#14519708D411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519701—21no—
104#14519701—21no—
105#14519701D411yescharacteristic
106#14519700—21no—
107#14519700—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113#14519688—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×Q16×C61—21no—
117C2×Q16×C61—21no—
118C2×Q16×C61—21no—
119C2×SD16×C61—21no—
120C2×SD16×C61D411yescharacteristic
121C4⋊Q8×C61—21no—
122C4⋊Q8×C61C2311yescharacteristic
123C4⋊Q8×C61C2311yescharacteristic
124#126×C61—41no—
125#125×C61—21no—
126#125×C61—41no—
127#124×C61—21no—
128C22⋊Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×Q8×C61—21no—
132C4×Q8×C61C2311yescharacteristic
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136#106×C61D411yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143#97×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C2×C22⋊D61—41no—
152C22×Dic61—41no—
153Q8×D61—42no—
154Q8×D61—81no—
155#11758224—42no—
156#11758224—81no—
157C2×D244C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—41no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—41no—
163Q16×C61—42no—
164Q16×C61—81no—
165Q16×C61—81no—
166SD16×C61—22no—
167SD16×C61—81no—
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×C61—21no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C22⋊C4×C61—21no—
185C22⋊C4×C61—41no—
186C22⋊C4×C61—41no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—41no—
190C42×C61—41no—
191C42×C61C2411yescharacteristic
192#11758202—42no—
193#11758201—22no—
194#11758200—42no—
195#11758198—21no—
196#11758198—41no—
197#11758198—41no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—41no—
203C4⋊Dic61—41no—
204C4⋊Dic61C2×D411yescharacteristic
205#11758194—42no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212Dic244—42no—
213Dic244—81no—
214#11758189—42no—
215C23×C61—21no—
216C22×D61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—21no—
220Q8×C61—21no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—41no—
225D4×C61—21no—
226D4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C22⋊D61—82no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—82no—
244D244—21no—
245D244—21no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—82no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—82no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61AGL(1,ℤ/8)12yes—
257#92418—22no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418#13712yescomplemented
263#20311—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61D4211yescharacteristic
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C61C2×#13711yescharacteristic
281C4×C61#57611yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—41no—
284Dic61—81no—
285Dic61—81no—
286#3398D6111yescharacteristic, complemented
287#3386—611no—
288#3353—611no—
289#3276—611no—
290#1713—611no—
291#1694—611no—
292#1693—611no—
293#1690—611no—
294#1689—611no—
295#1650—611no—
296#1649—611no—
297#1648—611no—
298#1647—611no—
299#1590—611no—
300#1590—611no—
301C2×C61—81no—
302C2×C61#327411yescharacteristic
303C2×C61#327611yescharacteristic
304C2×C61#329311yescharacteristic
305D61—81no—
306C2×#137—1221no—
307#557C2×D6111yescharacteristic
308#556C2×D6111yescharacteristic
309D4×Q8—611no—
310#547—611no—
311#501—1221no—
312#500—611no—
313#500—611no—
314#500—611no—
315#500—611no—
316#497—21no—
317#494—611no—
318#494C2×D6111yescharacteristic
319#484—1221no—
320#482—1221no—
321#478—1221no—
322#477—1221no—
323#475—611no—
324#475—611no—
325#474—611no—
326#474—611no—
327#470—1221no—
328#468—1221no—
329#464—21no—
330#462—21no—
331#462—611no—
332#462C2×D6111yescharacteristic
333#461—611no—
334#461C2×D6111yescharacteristic
335#452—1221no—
336#451—1221no—
337#446—611no—
338#446C2×D6111yescharacteristic
339#441—21no—
340#440—1221no—
341C4×SD16—611no—
342C4×SD16C2×D6111yescharacteristic
343#436—611no—
344#436—611no—
345#428—1221no—
346#334—611no—
347#334—611no—
348#332—611no—
349#332—611no—
350#332—611no—
351#332—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356C82—611no—
357C61#2031111yescharacteristic, complemented, Sylow
358C2×#41—1221no—
359C22×Q8—1221no—
360#137—2444no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×Q16—1221no—
367C2×SD16—21no—
368C2×SD16—611no—
369C2×SD16—1221no—
370C2×SD16C22⋊D6111yescharacteristic
371C2×M16—1221no—
372C2×M16—1221no—
373C4⋊Q8—21no—
374C4⋊Q8—611no—
375C4⋊Q8—611no—
376C4⋊Q8—1221no—
377C4⋊Q8C22×D6111yescharacteristic
378C4⋊Q8C22×D6111yescharacteristic
379#126—41no—
380#125—21no—
381#125—41no—
382#124—21no—
383#123—2441no—
384C22⋊Q8—21no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—2441no—
388#121—1221no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C22×D6111yescharacteristic
393C4×Q8C22×D6111yescharacteristic
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4C22×D6111yescharacteristic
397#117—21no—
398C2×C4⋊C4—1221no—
399#107—1221no—
400#107—1221no—
401#107—1221no—
402#107—1221no—
403#107—1221no—
404#107—1221no—
405#107—2441no—
406#107—2441no—
407#106—611no—
408#106—1221no—
409#106—1221no—
410#106C22⋊D6111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417#103—21no—
418#103—21no—
419#103—611no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103C22⋊D6111yescharacteristic
425#102—611no—
426#102—1221no—
427#102—1221no—
428#102C22⋊D6111yescharacteristic
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—21no—
432#97—1221no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8C22×D6111yescharacteristic
436#41—4881no—
437#41—2442no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—4881no—
443C2×Q8—2441no—
444C2×Q8—2442no—
445C2×Q8D4×D6111yescharacteristic
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—611no—
448C2×D4—2441no—
449C2×D4C2×C22⋊D6111yescharacteristic
450C22×C4—21no—
451C22×C4—1221no—
452C22×C4—2441no—
453C22×C4—2441no—
454Q16—42no—
455Q16—81no—
456Q16—81no—
457Q16—4881no—
458Q16—2442no—
459Q16—2442no—
460SD16—22no—
461SD16—81no—
462SD16—1222no—
463SD16—2442no—
464M16—2442no—
465M16—2442no—
466C2×C8—21no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4D4×D6111yescharacteristic
493C4⋊C4C2×C22⋊D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—1221no—
499C22⋊C4—2441no—
500C22⋊C4—2441no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42—41no—
505C42C23×D6111yescharacteristic
506C23—21no—
507C23—1221no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—4882no—
517Q8—2441no—
518Q8—2441no—
519Q8—2441no—
520Q8—2441no—
521D4—21no—
522D4—21no—
523D4—1221no—
524D4—1221no—
525D4—4882no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—1221no—
536C2×C4—4882no—
537C2×C4—4882no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4C22×C22⋊D6111yescharacteristic
544C2×C4#1451982211yescharacteristic
545C8—21no—
546C8—41no—
547C8—612no—
548C8—1222no—
549C8—1221no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C8#1451980212yes—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—2441no—
558C22—2441no—
559C22—2441no—
560C22D4×C22⋊D6111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—4881no—
570C4—4881no—
571C4—2441no—
572C4C2×#1451980211yescharacteristic
573C4#137×D6111yescharacteristic
574C4#1684056511yescharacteristic
575C4#1684057811yescharacteristic
576C2—81no—
577C2—4881no—
578C2#2145743911yescharacteristic
579C2#2145745911yescharacteristic
580C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3398C2
socleC22×C61D42
prime radical#16840416C22
hypercenter#3398D61
hypocenterC61#20311
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3398

Complements

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

NH ≅ G/Ntype
1. #21458736C2semidirect
4. #21445435C2semidirect
5. #21445335C2semidirect
6. #21445330C2semidirect
7. #21445313C2semidirect
8. #21445305C2semidirect
9. #21445075C2semidirect
10. #21445066C2semidirect
11. #21445061C2semidirect
13. #21444710C2semidirect
14. #21444709C2semidirect
15. C61×#3398C2semidirect
262. #92418#137semidirect
286. #3398D61semidirect
357. C61#20311semidirect

Maximal subgroups

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

subgroupindex
#214587362
#214583972
#214574662
#214454352
#214453352
#214453302
#214453132
#214453052
#214450752
#214450662
#214450612
#214450522
#214447102
#214447092
C61×#33982
#2031161