Finite Group Databasebeta

← #29671441

Subgroups — #29671441

Order 15616.

626 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#21458490C211yesmaximal, characteristic
2#21458457C211yesmaximal, characteristic, complemented
3#21457486C211yesmaximal, characteristic
4#21445421C211yesmaximal, characteristic, complemented
5#21445315C211yesmaximal, characteristic, complemented
6#21445291C211yesmaximal, characteristic, complemented
7#21445247C211yesmaximal, characteristic, complemented
8#21445237C211yesmaximal, characteristic, complemented
9#21445040C211yesmaximal, characteristic, complemented
10#21445018C211yesmaximal, characteristic
11#21444982C211yesmaximal, characteristic, complemented
12#21444915C211yesmaximal, characteristic, complemented
13#21444709C211yesmaximal, characteristic, complemented
14Q16×#92418C211yesmaximal, characteristic, complemented
15C61×#3387C211yesmaximal, characteristic, complemented
16C2×#14519809—21no—
17#16840434C2211yescharacteristic
18Q8×D244C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840112—21no—
21#16840112C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840110—21no—
24#16840110C2211yescharacteristic
25#16840110C2211yescharacteristic
26#16840049—21no—
27#16840049C2211yescharacteristic
28#16840047—21no—
29#16840047C2211yescharacteristic
30#16840009—21no—
31#16839972C2211yescharacteristic
32#16839964—21no—
33#16839964C2211yescharacteristic
34#16839962—21no—
35#16839962C2211yescharacteristic
36#16839962C2211yescharacteristic
37#16839927—21no—
38#16839902—21no—
39Q8×#92418C2211yescharacteristic
40Q8×#92418C2211yescharacteristic
41C4×#11758201—21no—
42C4×#11758201—21no—
43C4×#11758201C2211yescharacteristic
44#16839841C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#501—21no—
59C61×#498C2211yescharacteristic
60C61×#479—21no—
61C61×#477C2211yescharacteristic
62C61×#475—21no—
63C61×#475C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#441—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758226—21no—
68C2×Q8×D61—21no—
69#14519809—44no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758201—21no—
74C2×#11758201—21no—
75C2×#11758201—21no—
76C2×#11758201D411yescharacteristic
77C2×#11758189—21no—
78#14519777—21no—
79#14519777C2311yescharacteristic
80#14519774—21no—
81#14519774C2311yescharacteristic
82#14519757—21no—
83#14519757—41no—
84#14519752—21no—
85#14519752—41no—
86C4×D244—21no—
87C4×D244—21no—
88C4×D244C2311yescharacteristic
89#14519708—21no—
90#14519708—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—41no—
102#14519701D411yescharacteristic
103#14519700—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519697D411yescharacteristic
111#14519689—21no—
112C4×#92418—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×Q16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—41no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61—21no—
141#103×C61D411yescharacteristic
142#103×C61D411yescharacteristic
143#97×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—41no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151#11758226—42no—
152#11758226—81no—
153Q8×D61—42no—
154Q8×D61—81no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—41no—
159C2×D244—41no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×C4×D61—41no—
163C2×C4×D61—41no—
164C2×Dic122—21no—
165C2×Dic122—41no—
166Q16×C61SD1614yescomplemented
167C2×C8×C61—21no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
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×C61—41no—
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—41no—
189C42×C61—41no—
190C42×C61C2411yescharacteristic
191#11758202—42no—
192#11758201—41no—
193#11758201—42no—
194#11758201—42no—
195#11758201—42no—
196#11758198—21no—
197#11758198—41no—
198#11758198—41no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—41no—
202C4⋊Dic61C2×D411yescharacteristic
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758190—42no—
210#11758190—81no—
211#11758189—42no—
212C22×D61—21no—
213C22×D61—41no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—81no—
221Q8×C61—161no—
222Q8×C61C2×SD1612yes—
223Q8×C61C2×SD1612yes—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61H(5,𝔽2)11yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—41no—
237D244—21no—
238D244—21no—
239D244—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—82no—
244D244—81no—
245D244—161no—
246C4×D61—41no—
247C4×D61—41no—
248C4×D61—82no—
249C4×D61—82no—
250Dic122—41no—
251Dic122—41no—
252Dic122—82no—
253C8×C61—21no—
254C8×C61—41no—
255C8×C61C2×SD1612yes—
256#92418—21no—
257#92418—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#19896—611nomaximal, Sylow
263C22×C61D4211yescharacteristic
264C2×D61—41no—
265C2×D61—41no—
266C2×D61—41no—
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C4×C61—22no—
271C4×C61—22no—
272C4×C61—21no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61C22×SD1611yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57811yescharacteristic
283Dic61—41no—
284Dic61—81no—
285#3387D6111yescharacteristic, complemented
286#3362—611no—
287#3359—611no—
288#3278—611no—
289#1708—611no—
290#1691—611no—
291#1686—611no—
292#1680—611no—
293#1678—611no—
294#1645—611no—
295#1642—611no—
296#1637—611no—
297#1626—611no—
298#1590—611no—
299C8×Q16—611no—
300C2×C61#327711yescharacteristic
301C2×C61D4×SD1611yescharacteristic
302C2×C61#329011yescharacteristic
303D61—81no—
304D61—161no—
305C2×#137—1221no—
306Q82C2×D6111yescharacteristic
307#557C2×D6111yescharacteristic
308#550—611no—
309D4×Q8—611no—
310#501—21no—
311#498C2×D6111yescharacteristic
312#492—611no—
313#487—611no—
314#487—611no—
315#487—1221no—
316#486—611no—
317#486—611no—
318#486—1221no—
319#479—21no—
320#477C2×D6111yescharacteristic
321#476—611no—
322#476—1221no—
323#475—21no—
324#475—611no—
325#475—1221no—
326#475C2×D6111yescharacteristic
327#468—1221no—
328#462—611no—
329#461—611no—
330#461—1221no—
331#460—611no—
332#460—611no—
333#460—1221no—
334#452—1221no—
335#448—1221no—
336#446C2×D6111yescharacteristic
337C8×Q8—611no—
338C8×Q8—611no—
339#441—21no—
340C4×Q16C2×D6111yescharacteristic
341C4×SD16—611no—
342C4×SD16—1221no—
343C4×SD16—1221no—
344#436—611no—
345#335—611no—
346#334—611no—
347#333—611no—
348#332—611no—
349#332—611no—
350#331—611no—
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354D4⋊C8—611no—
355C82—611no—
356C61#1989611yescharacteristic, complemented, Sylow
357C2×#41—1221no—
358C22×Q8—1221no—
359#137—2444no—
360C2×Q16—1221no—
361C2×Q16C22⋊D6111yescharacteristic
362C2×SD16—611no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×M16—1221no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—41no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377#127—611no—
378#127—1221no—
379#125—21no—
380#125—41no—
381C22⋊Q8—1221no—
382C22⋊Q8—2441no—
383#121—1221no—
384#121—2441no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C22×D6111yescharacteristic
390C4×Q8C22×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4—1221no—
395#107—21no—
396#107C22⋊D6111yescharacteristic
397#106—21no—
398#106—21no—
399#106—21no—
400#106—611no—
401#106—1221no—
402#106—1221no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410#103—21no—
411#103—21no—
412#103—611no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—2441no—
419#103C22⋊D6111yescharacteristic
420#103C22⋊D6111yescharacteristic
421#102—611no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—2441no—
428C22⋊C8—1221no—
429#97—21no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8C22×D6111yescharacteristic
435#41—4881no—
436#41—2442no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—1221no—
441C2×Q8—4881no—
442C2×Q8—2441no—
443C2×Q8—2442no—
444C2×Q8D4×D6111yescharacteristic
445C2×Q8C2×C22⋊D6111yescharacteristic
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—2441no—
452C2×D4—2441no—
453C22×C4—1221no—
454C22×C4—2441no—
455C22×C4—2441no—
456Q16—2442no—
457Q16#1175820114yescomplemented
458SD16—4881no—
459SD16—2441no—
460SD16—2442no—
461SD16—2442no—
462SD16—2442no—
463SD16—2442no—
464M16—2442no—
465C2×C8—21no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C4⋊C4—21no—
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—41no—
486C4⋊C4—611no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2441no—
490C4⋊C4D4×D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C4⋊C4C2×C22⋊D6111yescharacteristic
493C22⋊C4—1221no—
494C22⋊C4—2441no—
495C22⋊C4—2441no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—41no—
500C42—41no—
501C42C23×D6111yescharacteristic
502C23—1221no—
503C23—2441no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511Q8—161no—
512Q8—4882no—
513Q8—2441no—
514Q8—2441no—
515Q8C2×#1175820112yes—
516Q8C2×#1175820112yes—
517D4—1221no—
518D4—1221no—
519D4—9761no—
520D4—4881no—
521D4—4882no—
522D4—2441no—
523D4—2441no—
524D4—2441no—
525D4—2441no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—1221no—
535C2×C4—4882no—
536C2×C4—4882no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C22×C22⋊D6111yescharacteristic
542C2×C4#1451982211yescharacteristic
543C8—21no—
544C8—41no—
545C8—1221no—
546C8—1221no—
547C8—2441no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8C2×#1175820112yes—
552C22—4881no—
553C22—4881no—
554C22—4881no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22D4×C22⋊D6111yescharacteristic
559C4—22no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—4881no—
569C4—2441no—
570C4C22×#1175820111yescharacteristic
571C4#1684056111yescharacteristic
572C4#1684057011yescharacteristic
573C4#1684057811yescharacteristic
574C2—9761no—
575C2—4881no—
576C2#2145747011yescharacteristic
577C2D4×#1175820111yescharacteristic
578C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3387C2
socleC22×C61D42
prime radical#16840434C22
hypercenter#3387D61
hypocenterC61#19896
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3387

Complements

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

NH ≅ G/Ntype
2. #21458457C2semidirect
4. #21445421C2semidirect
5. #21445315C2semidirect
6. #21445291C2semidirect
7. #21445247C2semidirect
8. #21445237C2semidirect
9. #21445040C2semidirect
11. #21444982C2semidirect
12. #21444915C2semidirect
13. #21444709C2semidirect
14. Q16×#92418C2semidirect
15. C61×#3387C2semidirect
166. Q16×C61SD16semidirect
285. #3387D61semidirect
356. C61#19896semidirect
457. Q16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214584902
#214584572
#214574862
#214454212
#214453152
#214452912
#214452472
#214452372
#214450402
#214450182
#214449822
#214449152
#214447092
Q16×#924182
C61×#33872
#1989661