Finite Group Databasebeta

← #29663064

Subgroups — #29663064

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456564C211yesmaximal, characteristic, complemented
2#21455891C211yesmaximal, characteristic
3#21455609C211yesmaximal, characteristic
4#21454837C211yesmaximal, characteristic
5#21445395C211yesmaximal, characteristic, complemented
6#21445367C211yesmaximal, characteristic, complemented
7#21445319C211yesmaximal, characteristic, complemented
8#21445309C211yesmaximal, characteristic, complemented
9#21445278C211yesmaximal, characteristic, complemented
10#21445250C211yesmaximal, characteristic, complemented
11#21445202C211yesmaximal, characteristic, complemented
12#21445190C211yesmaximal, characteristic, complemented
13#21444527C211yesmaximal, characteristic, complemented
14#21444517C211yesmaximal, characteristic, complemented
15C61×#1565C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840319C2211yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16840160C2211yescharacteristic
20#16840142C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840104—21no—
24#16840070—21no—
25#16840063—21no—
26#16840058C2211yescharacteristic
27#16840053C2211yescharacteristic
28#16840048C2211yescharacteristic
29#16840048C2211yescharacteristic
30#16840043C2211yescharacteristic
31#16840043C2211yescharacteristic
32#16840020—21no—
33#16840020—21no—
34#16839973C2211yescharacteristic
35#16839968C2211yescharacteristic
36#16839926—21no—
37C8×Dic122C2211yescharacteristic
38C8×Dic122C2211yescharacteristic
39#16839870—21no—
40#16839870—21no—
41C4×Dic244—21no—
42C4×#11758190—21no—
43#16839841C2211yescharacteristic
44#16839841C2211yescharacteristic
45#16839838—21no—
46#16839838—21no—
47#16839819C2211yescharacteristic
48#16839817—21no—
49#16839800—21no—
50#16839759—21no—
51#16839714—21no—
52#16839510C2211yescharacteristic
53#16839510C2211yescharacteristic
54#16839509C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839507C2211yescharacteristic
57#16839507C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×Dic244—21no—
69C2×Dic244—21no—
70C2×Dic244—21no—
71C2×#11758190—21no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519769—21no—
80#14519756—21no—
81#14519756—21no—
82#14519756—21no—
83#14519756—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122D411yescharacteristic
89C4×Dic122C2311yescharacteristic
90C4×D244D411yescharacteristic
91C4×D244C2311yescharacteristic
92C4×C22⋊D61—21no—
93C4×C22⋊D61—21no—
94#14519736—21no—
95#14519736—21no—
96#14519736D411yescharacteristic
97#14519734—21no—
98C42×D61—21no—
99#14519711—21no—
100#14519711—21no—
101#14519711—21no—
102#14519709—21no—
103#14519709—21no—
104#14519709—21no—
105#14519709—21no—
106#14519709—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109#14519706—21no—
110#14519706—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#14519688—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×M16×C61D411yescharacteristic
130C2×M16×C61D411yescharacteristic
131C22×C8×C61—21no—
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×C61D411yescharacteristic
140#97×C61D411yescharacteristic
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—41no—
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
159M16×C61—22no—
160M16×C61—41no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—42no—
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—
176C22⋊Dic61—41no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61C2×D411yescharacteristic
188C4⋊Dic61C2×D411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191#11758196—41no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C4×Dic61—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202Dic244—42no—
203Dic244—42no—
204Dic244—42no—
205#11758190—42no—
206#11758189—42no—
207#11758189—42no—
208C23×C61#12111yescharacteristic
209C22×D61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61#12111yescharacteristic
216C2×C4×C61#12111yescharacteristic
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C22×D411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C22⋊D61—42no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—41no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229D244—21no—
230D244—21no—
231C4×D61—42no—
232C4×D61—41no—
233C4×D61—41no—
234C4×D61—81no—
235Dic122—21no—
236Dic122—41no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—41no—
242Dic122—81no—
243Dic122#13712yes—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61#13512yes—
252#92418—41no—
253#92418—41no—
254#19185—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×#12111yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61C2×#13511yescharacteristic
267C4×C61C2×#13711yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57511yescharacteristic
270Dic61—22no—
271Dic61—41no—
272Dic61—41no—
273Dic61—81no—
274Dic61—81no—
275Dic61—81no—
276Dic61—81no—
277#3185—611no—
278#3107—611no—
279#3076—611no—
280#2971—611no—
281#1703—611no—
282#1699—611no—
283#1691—611no—
284#1689—611no—
285#1684—611no—
286#1680—611no—
287#1672—611no—
288#1670—611no—
289#1565D6111yescharacteristic, complemented
290#1554—611no—
291#1552—611no—
292C2×C61—41no—
293C2×C61#303511yescharacteristic
294C2×C61#305611yescharacteristic
295C2×C61#306911yescharacteristic
296D61—81no—
297#533—611no—
298#533—611no—
299C4×#41—611no—
300#498—611no—
301#494—611no—
302#487—611no—
303#487—611no—
304#485—1221no—
305#479—1221no—
306#478—1221no—
307#477—611no—
308#476—611no—
309#475—611no—
310#475—611no—
311#474—611no—
312#474—611no—
313#470—1221no—
314#470—1221no—
315#462—611no—
316#461—611no—
317#452—1221no—
318C8×Q8—611no—
319C8×Q8—611no—
320#441—1221no—
321#441—1221no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324#436—611no—
325#436—611no—
326#436—1221no—
327#436—1221no—
328#432—611no—
329#432—1221no—
330#431C2×D6111yescharacteristic
331#427—1221no—
332C2×C4⋊C8C2×D6111yescharacteristic
333#416—1221no—
334C4×M16—1221no—
335C4×M16C2×D6111yescharacteristic
336#335C2×D6111yescharacteristic
337#335C2×D6111yescharacteristic
338#334C2×D6111yescharacteristic
339#334C2×D6111yescharacteristic
340#333—611no—
341#333—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348C61#1918511yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—1221no—
351C2×Q16—1221no—
352C2×Q16—1221no—
353C2×SD16—1221no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16D24411yescharacteristic
357C2×M16D24411yescharacteristic
358C22×C8—21no—
359C4⋊Q8—611no—
360C4⋊Q8—611no—
361C4⋊Q8—611no—
362C4⋊Q8—611no—
363#125—1221no—
364#125—1221no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C22⋊Q8—1221no—
368C22⋊Q8—1221no—
369C4×Q8—611no—
370C4×Q8—611no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×D4—611no—
376C4×D4—611no—
377C4×D4—1221no—
378C4×D4—1221no—
379#117—611no—
380#117—1221no—
381#117—1221no—
382#117—1221no—
383C2×C42—1221no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#106—1221no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392#106—1221no—
393C4⋊C8—21no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401C4⋊C8C22×D6111yescharacteristic
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#103—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414C22⋊C8—21no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418#97—1221no—
419#97D24411yescharacteristic
420#97D24411yescharacteristic
421C4×C8—21no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—1222no—
427#41—2441no—
428C2×Q8—611no—
429C2×Q8—1221no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×D4—611no—
434C2×D4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4C2×D24411yescharacteristic
439C22×C4D4×D6111yescharacteristic
440C22×C4#1175822611yescharacteristic
441Q16—2442no—
442Q16—2442no—
443Q16—2442no—
444SD16—2442no—
445M16—22no—
446M16—41no—
447M16—2442no—
448M16—2442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8C2×D24411yescharacteristic
457C2×C8C2×D24411yescharacteristic
458C2×C8C2×D24411yescharacteristic
459C2×C8C2×D24411yescharacteristic
460C4⋊C4—611no—
461C4⋊C4—611no—
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—1221no—
471C4⋊C4—1221no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C4⋊C4—2441no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—2441no—
480C22⋊C4—2441no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—2441no—
485C42—2441no—
486C42C2×D24411yescharacteristic
487C42D4×D6111yescharacteristic
488C42#1175822611yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23#1451975211yescharacteristic
492Q8—612no—
493Q8—1221no—
494Q8—4881no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498Q8—2441no—
499Q8—2441no—
500Q8—2441no—
501D4—1221no—
502D4—1221no—
503D4—2442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4881no—
513C2×C4—2442no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4#1451975211yescharacteristic
521C2×C4#1451975211yescharacteristic
522C2×C4#1451975211yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4C22×D24411yescharacteristic
525C2×C4C2×#1175822611yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—2441no—
534C8—2441no—
535C8#1451979912yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C2×#1451975211yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—1222no—
548C4—4881no—
549C4—4881no—
550C4—4881no—
551C4—4881no—
552C4—2441no—
553C4—2441no—
554C4C2×#1451979911yescharacteristic
555C4#137×D6111yescharacteristic
556C4#1684055811yescharacteristic
557C4#1684056211yescharacteristic
558C2—41no—
559C2—4881no—
560C2#2145527611yescharacteristic
561C2#2145545011yescharacteristic
562C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1565C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#1565D61
hypocenterC61#19185
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
1. #21456564C2semidirect
5. #21445395C2semidirect
6. #21445367C2semidirect
7. #21445319C2semidirect
8. #21445309C2semidirect
9. #21445278C2semidirect
10. #21445250C2semidirect
11. #21445202C2semidirect
12. #21445190C2semidirect
13. #21444527C2semidirect
14. #21444517C2semidirect
15. C61×#1565C2semidirect
289. #1565D61semidirect
348. C61#19185semidirect

Maximal subgroups

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

subgroupindex
#214565642
#214558912
#214556092
#214548372
#214453952
#214453672
#214453192
#214453092
#214452782
#214452502
#214452022
#214451902
#214445272
#214445172
C61×#15652
#1918561