Finite Group Databasebeta

← #29665527

Subgroups — #29665527

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456980C211yesmaximal, characteristic, complemented
2#21455982C211yesmaximal, characteristic
3#21455891C211yesmaximal, characteristic
4#21454927C211yesmaximal, characteristic
5#21445278C211yesmaximal, characteristic, complemented
6#21445271C211yesmaximal, characteristic, complemented
7#21445250C211yesmaximal, characteristic, complemented
8#21445243C211yesmaximal, characteristic, complemented
9#21445214C211yesmaximal, characteristic, complemented
10#21445209C211yesmaximal, characteristic, complemented
11#21445202C211yesmaximal, characteristic, complemented
12#21445195C211yesmaximal, characteristic, complemented
13#21444520C211yesmaximal, characteristic, complemented
14#21444474C211yesmaximal, characteristic, complemented
15C61×#1572C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840319C2211yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16840167C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840104—21no—
24#16840104—21no—
25#16840104—21no—
26#16840104—21no—
27#16840070—21no—
28#16840070—21no—
29#16840058C2211yescharacteristic
30#16840053C2211yescharacteristic
31#16840048C2211yescharacteristic
32#16840043C2211yescharacteristic
33#16839973C2211yescharacteristic
34#16839973C2211yescharacteristic
35#16839968C2211yescharacteristic
36#16839968C2211yescharacteristic
37#16839926—21no—
38#16839926—21no—
39C8×Dic122C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839870—21no—
42#16839864—21no—
43C4×Dic244—21no—
44C4×#11758190—21no—
45C8×D244C2211yescharacteristic
46C8×D244C2211yescharacteristic
47#16839825—21no—
48#16839825—21no—
49#16839814—21no—
50C2×C4⋊#92418C2211yescharacteristic
51C4⋊C8×D61—21no—
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×Dic244—21no—
69C2×Dic244—21no—
70C2×#11758190—21no—
71C2×#11758190—21no—
72C22×#92418—21no—
73C2×C8×D61—21no—
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519769—21no—
80#14519769—21no—
81#14519756—21no—
82#14519756—21no—
83#14519756—21no—
84#14519756—21no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122—21no—
89C4×Dic122D411yescharacteristic
90C4×Dic122C2311yescharacteristic
91C4×D244D411yescharacteristic
92C4×D244C2311yescharacteristic
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95#14519736—21no—
96#14519736—21no—
97#14519736D411yescharacteristic
98#14519734—21no—
99C42×D61—21no—
100#14519711—21no—
101#14519711—21no—
102#14519711—21no—
103#14519711—21no—
104#14519709—21no—
105#14519709—21no—
106#14519709—21no—
107#14519709—21no—
108C4⋊#92418—21no—
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519702—21no—
120#14519702—21no—
121#14519702—21no—
122#14519702—21no—
123#14519699—21no—
124#14519699—21no—
125#14519689—21no—
126#14519689—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148#11758222—22no—
149#11758222—22no—
150C2×D244C2×D411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C2×D411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172C22⋊Dic61—41no—
173C22⋊Dic61—41no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61C2×D411yescharacteristic
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×Dic61—41no—
196C4×Dic61—41no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200Dic244—42no—
201Dic244—42no—
202#11758190—42no—
203#11758190—42no—
204C8×D61—81no—
205C8×D61—81no—
206C23×C61#12111yescharacteristic
207C22×D61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—24no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227D244—21no—
228D244#13512yes—
229C4×D61—24no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—81no—
233Dic122—21no—
234Dic122—41no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—81no—
241Dic122#13512yes—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—41no—
251#92418—41no—
252#19418—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61C2×#12111yescharacteristic
257C2×D61—22no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61C2×#13511yescharacteristic
265C4×C61C2×#13511yescharacteristic
266C4×C61#57711yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—22no—
269Dic61—41no—
270Dic61—41no—
271Dic61—81no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275#3231—611no—
276#3116—611no—
277#3107—611no—
278#2988—611no—
279#1684—611no—
280#1683—611no—
281#1680—611no—
282#1679—611no—
283#1674—611no—
284#1673—611no—
285#1672—611no—
286#1671—611no—
287#1572D6111yescharacteristic, complemented
288#1552—611no—
289#1542—611no—
290C2×C61—41no—
291C2×C61#304611yescharacteristic
292C2×C61#305011yescharacteristic
293C2×C61#306911yescharacteristic
294D61—42no—
295#533—611no—
296#533—611no—
297C4×#41—611no—
298#500—611no—
299#498—611no—
300#487—611no—
301#487—611no—
302#485—1221no—
303#485—1221no—
304#485—1221no—
305#485—1221no—
306#479—1221no—
307#479—1221no—
308#477—611no—
309#476—611no—
310#475—611no—
311#474—611no—
312#462—611no—
313#462—611no—
314#461—611no—
315#461—611no—
316#452—1221no—
317#452—1221no—
318C8×Q8—611no—
319C8×Q8—611no—
320#441—1221no—
321#440—1221no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324C8×D4—611no—
325C8×D4—611no—
326C8×D4—1221no—
327C8×D4—1221no—
328#432C2×D6111yescharacteristic
329#431—1221no—
330#431C2×D6111yescharacteristic
331#431C2×D6111yescharacteristic
332C2×C4⋊C8—611no—
333C2×C4⋊C8—1221no—
334#335C2×D6111yescharacteristic
335#335C2×D6111yescharacteristic
336#334C2×D6111yescharacteristic
337#334C2×D6111yescharacteristic
338#333—611no—
339#333—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346C61#1941811yescharacteristic, complemented, Sylow
347C2×#41—611no—
348C2×Q16—1221no—
349C2×Q16—1221no—
350C2×SD16—1221no—
351C2×SD16—1221no—
352C22×C8—1221no—
353C22×C8—1221no—
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360#125—1221no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C22⋊Q8—1221no—
364C22⋊Q8—1221no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×D4—611no—
372C4×D4—611no—
373C4×D4—1221no—
374C4×D4—1221no—
375#117—611no—
376#117—1221no—
377#117—1221no—
378#117—1221no—
379C2×C42—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8D24411yescharacteristic
395C4⋊C8D24411yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8D24411yescharacteristic
417C22⋊C8D24411yescharacteristic
418#97—21no—
419C4×C8—21no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424#41—1222no—
425#41—1222no—
426C2×Q8—611no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×D4—611no—
432C2×D4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4C2×D24411yescharacteristic
437C22×C4D4×D6111yescharacteristic
438C22×C4#1175822611yescharacteristic
439Q16—2442no—
440Q16—2442no—
441SD16—2442no—
442SD16—2442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—4881no—
450C2×C8—4881no—
451C2×C8—4881no—
452C2×C8C2×D24411yescharacteristic
453C2×C8C2×D24411yescharacteristic
454C2×C8C2×D24411yescharacteristic
455C2×C8C2×D24411yescharacteristic
456C4⋊C4—611no—
457C4⋊C4—611no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—2441no—
476C22⋊C4—2441no—
477C42—1221no—
478C42—1221no—
479C42—1221no—
480C42—2441no—
481C42—2441no—
482C42C2×D24411yescharacteristic
483C42D4×D6111yescharacteristic
484C42#1175822611yescharacteristic
485C42C23×D6111yescharacteristic
486C23—1221no—
487C23#1451975211yescharacteristic
488Q8—612no—
489Q8—1221no—
490Q8—4881no—
491Q8—2441no—
492Q8—2441no—
493Q8—2441no—
494Q8—2441no—
495Q8—2441no—
496Q8—2441no—
497D4—612no—
498D4—1224no—
499D4—1221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—1224no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—4881no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451975211yescharacteristic
517C2×C4#1451975211yescharacteristic
518C2×C4#1451975211yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4C22×D24411yescharacteristic
521C2×C4C2×#1175822611yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—2441no—
531C8—2441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—1222no—
536C22—2441no—
537C22—2441no—
538C22C2×#1451975211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—1222no—
544C4—4881no—
545C4—4881no—
546C4—4881no—
547C4—4881no—
548C4—2441no—
549C4—2441no—
550C4#135×D6111yescharacteristic
551C4#135×D6111yescharacteristic
552C4#1684057411yescharacteristic
553C4#1684057911yescharacteristic
554C2—41no—
555C2—2442no—
556C2#2145537111yescharacteristic
557C2#2145540111yescharacteristic
558C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1572C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#1572D61
hypocenterC61#19418
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #21456980C2semidirect
5. #21445278C2semidirect
6. #21445271C2semidirect
7. #21445250C2semidirect
8. #21445243C2semidirect
9. #21445214C2semidirect
10. #21445209C2semidirect
11. #21445202C2semidirect
12. #21445195C2semidirect
13. #21444520C2semidirect
14. #21444474C2semidirect
15. C61×#1572C2semidirect
287. #1572D61semidirect
346. C61#19418semidirect

Maximal subgroups

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

subgroupindex
#214569802
#214559822
#214558912
#214549272
#214452782
#214452712
#214452502
#214452432
#214452142
#214452092
#214452022
#214451952
#214445202
#214444742
C61×#15722
#1941861