Finite Group Databasebeta

← #29665132

Subgroups — #29665132

Order 15616.

572 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#21457193C211yesmaximal, characteristic
2#21457051C211yesmaximal, characteristic
3#21456200C211yesmaximal, characteristic, complemented
4#21454823C211yesmaximal, characteristic
5#21445402C211yesmaximal, characteristic, complemented
6#21445395C211yesmaximal, characteristic, complemented
7#21445374C211yesmaximal, characteristic, complemented
8#21445367C211yesmaximal, characteristic, complemented
9#21445278C211yesmaximal, characteristic, complemented
10#21445271C211yesmaximal, characteristic, complemented
11#21445250C211yesmaximal, characteristic, complemented
12#21445243C211yesmaximal, characteristic, complemented
13#21444530C211yesmaximal, characteristic, complemented
14#21444505C211yesmaximal, characteristic, complemented
15C61×#1569C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C2×#14519777C2211yescharacteristic
18#16840296C2211yescharacteristic
19#16840171—21no—
20#16840131—21no—
21#16840131—21no—
22#16840122—21no—
23#16840113C2211yescharacteristic
24#16840113C2211yescharacteristic
25#16840113C2211yescharacteristic
26#16840113C2211yescharacteristic
27#16840098—21no—
28#16840081—21no—
29#16840070—21no—
30#16840058C2211yescharacteristic
31#16840053C2211yescharacteristic
32#16840048C2211yescharacteristic
33#16840048C2211yescharacteristic
34#16840043C2211yescharacteristic
35#16840043C2211yescharacteristic
36#16840020—21no—
37#16840008—21no—
38#16839985—21no—
39#16839973C2211yescharacteristic
40#16839968C2211yescharacteristic
41#16839892C2211yescharacteristic
42C8×Dic122C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839838—21no—
45#16839831—21no—
46C8×D244C2211yescharacteristic
47#16839824—21no—
48#16839815C2211yescharacteristic
49#16839772—21no—
50#16839772—21no—
51#16839719—21no—
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839507C2211yescharacteristic
57#16839507C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C22×Dic122—21no—
68C2×Dic244—21no—
69C2×#11758190—21no—
70C2×#11758189—21no—
71C2×C8×D61—21no—
72#14519777—21no—
73#14519777—21no—
74#14519777—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519771—21no—
80#14519769—21no—
81#14519769D411yescharacteristic
82#14519765D411yescharacteristic
83#14519760—21no—
84#14519756—21no—
85#14519756—21no—
86#14519756D411yescharacteristic
87#14519751D411yescharacteristic
88C4×Dic122—21no—
89C4×Dic122—21no—
90C4×Dic122C2311yescharacteristic
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93#14519736—21no—
94#14519734—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97#14519711—21no—
98#14519711—21no—
99#14519711—21no—
100#14519709—21no—
101#14519709—21no—
102#14519709—21no—
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519702—21no—
108#14519702—21no—
109#14519702—21no—
110#14519702—21no—
111#14519702—21no—
112#14519702—21no—
113#14519702—21no—
114#14519702—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519702—21no—
120#14519699—21no—
121#14519699—21no—
122#14519699—21no—
123C22⋊#92418—21no—
124#14519689—21no—
125#14519689—21no—
126#14519687—21no—
127C4×#92418—21no—
128C8×Dic61—21no—
129C2×M16×C61—21no—
130C2×M16×C61D411yescharacteristic
131C2×M16×C61D411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139#97×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—41no—
149C2×D244C2×D411yescharacteristic
150C2×C4×D61—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—42no—
156C2×Dic122—42no—
157C2×Dic122—41no—
158C2×Dic122C2×D411yescharacteristic
159M16×C61—41no—
160M16×C61—41no—
161M16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61#4111yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175C22⋊Dic61—41no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—41no—
189C4⋊Dic61—41no—
190C4⋊Dic61C2×D411yescharacteristic
191C4⋊Dic61C2×D411yescharacteristic
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—41no—
197#11758196—41no—
198C4×Dic61—21no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202Dic244—81no—
203#11758190—81no—
204#11758189—42no—
205C8×D61—42no—
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—81no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—82no—
228D244—21no—
229D244—21no—
230C4×D61—41no—
231C4×D61—41no—
232Dic122—21no—
233Dic122—21no—
234Dic122—41no—
235Dic122—41no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—82no—
241Dic122—81no—
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#19381—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61C2×#12111yescharacteristic
257C2×D61—41no—
258C2×D61—41no—
259C2×D61—41no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61#57511yescharacteristic
265C4×C61#57511yescharacteristic
266C4×C61#57711yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—41no—
269Dic61—41no—
270Dic61—41no—
271Dic61—81no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275#3252—611no—
276#3239—611no—
277#3139—611no—
278#2969—611no—
279#1704—611no—
280#1703—611no—
281#1700—611no—
282#1699—611no—
283#1684—611no—
284#1683—611no—
285#1680—611no—
286#1679—611no—
287#1569D6111yescharacteristic, complemented
288#1554—611no—
289#1549—611no—
290C2×C61—41no—
291C2×C61#304011yescharacteristic
292C2×C61#306311yescharacteristic
293C2×C61#306911yescharacteristic
294D61—81no—
295#533—611no—
296C2×C4⋊Q8—611no—
297#529—611no—
298#501—1221no—
299#491—1221no—
300#491—1221no—
301#489—1221no—
302#487—611no—
303#487—611no—
304#487—611no—
305#487—611no—
306#484—1221no—
307#481—1221no—
308#479—1221no—
309#477—611no—
310#476—611no—
311#475—611no—
312#475—611no—
313#474—611no—
314#474—611no—
315#470—1221no—
316#468—1221no—
317#464—1221no—
318#462—611no—
319#461—611no—
320#446—611no—
321C8×Q8—611no—
322#436—611no—
323#436—1221no—
324#435—1221no—
325C8×D4—611no—
326#433—1221no—
327#432C2×D6111yescharacteristic
328#431—611no—
329#423C2×D6111yescharacteristic
330#419—1221no—
331#419—1221no—
332#405—1221no—
333C4×M16C2×D6111yescharacteristic
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#1938111yescharacteristic, complemented, Sylow
347C22×Q8—1221no—
348C2×Q16—1221no—
349C2×SD16—1221no—
350C2×M16—21no—
351C2×M16—1221no—
352C2×M16D24411yescharacteristic
353C2×M16D24411yescharacteristic
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359C4⋊Q8—1221no—
360C4⋊Q8—1221no—
361C4⋊Q8—1221no—
362#126—1221no—
363#125—611no—
364#125—1221no—
365#124—611no—
366#123—1221no—
367C22⋊Q8—611no—
368C22⋊Q8—1221no—
369C22⋊Q8—1221no—
370#121—611no—
371C4×Q8—611no—
372C4×Q8—1221no—
373C4×Q8—1221no—
374C4×D4—611no—
375C4×D4—1221no—
376#117—1221no—
377#117—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C42C22×D6111yescharacteristic
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387C4⋊C8—21no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—1221no—
397#103—1221no—
398#103—1221no—
399#103—1221no—
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#102—1221no—
410#102—1221no—
411#102—1221no—
412C22⋊C8—21no—
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416#97—21no—
417#97—1221no—
418#97D24411yescharacteristic
419#97D24411yescharacteristic
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C2×Q8—611no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—2442no—
430C2×Q8—2442no—
431C2×Q8—2441no—
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—2441no—
436C22×C4C2×D24411yescharacteristic
437C22×C4D4×D6111yescharacteristic
438C22×C4#1175822611yescharacteristic
439Q16—4881no—
440SD16—4881no—
441M16—41no—
442M16—41no—
443M16—81no—
444M16—2442no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—2442no—
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—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—2441no—
480C42—1221no—
481C42—2441no—
482C42C2×D24411yescharacteristic
483C42D4×D6111yescharacteristic
484C42#1175822611yescharacteristic
485C42C23×D6111yescharacteristic
486C23—1221no—
487C23#1451975211yescharacteristic
488Q8—1221no—
489Q8—1221no—
490Q8—4881no—
491Q8—4882no—
492Q8—2441no—
493Q8—2441no—
494Q8—2441no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498D4—1221no—
499D4—1221no—
500D4—4881no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—4882no—
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—2441no—
536C22—2441no—
537C22—2441no—
538C22C2×#1451975211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—4881no—
544C4—4881no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4—2441no—
549C4—2441no—
550C4#1684056211yescharacteristic
551C4#1684056211yescharacteristic
552C4#1684057211yescharacteristic
553C4#1684057811yescharacteristic
554C2—41no—
555C2—4881no—
556C2#2145531411yescharacteristic
557C2#2145551111yescharacteristic
558C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1569C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1569D61
hypocenterC61#19381
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #21456200C2semidirect
5. #21445402C2semidirect
6. #21445395C2semidirect
7. #21445374C2semidirect
8. #21445367C2semidirect
9. #21445278C2semidirect
10. #21445271C2semidirect
11. #21445250C2semidirect
12. #21445243C2semidirect
13. #21444530C2semidirect
14. #21444505C2semidirect
15. C61×#1569C2semidirect
287. #1569D61semidirect
346. C61#19381semidirect

Maximal subgroups

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

subgroupindex
#214571932
#214570512
#214562002
#214548232
#214454022
#214453952
#214453742
#214453672
#214452782
#214452712
#214452502
#214452432
#214445302
#214445052
C61×#15692
#1938161