Finite Group Databasebeta

← #29837044

Subgroups — #29837044

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458188C211yesmaximal, characteristic, complemented
2#21448060C211yesmaximal, characteristic, complemented
3#21448007C211yesmaximal, characteristic, complemented
4#21447997C211yesmaximal, characteristic, complemented
5#21447976C211yesmaximal, characteristic, complemented
6#21447930C211yesmaximal, characteristic, complemented
7#21447913C211yesmaximal, characteristic, complemented
8#21447856C211yesmaximal, characteristic, complemented
9#21447748C211yesmaximal, characteristic, complemented
10#21447748C211yesmaximal, characteristic, complemented
11#21447683C211yesmaximal, characteristic, complemented
12#21447645C211yesmaximal, characteristic, complemented
13#21447535C211yesmaximal, characteristic, complemented
14C2×#16839563C211yesmaximal, characteristic, complemented
15D4×D8×C61C211yesmaximal, characteristic
16#16840452—21no—
17C2×#14519721C2211yescharacteristic
18C2×#14519721C2211yescharacteristic, complemented
19C2×#14519721C2211yescharacteristic, complemented
20C2×#14519717C2211yescharacteristic, complemented
21C22×#11758185C2211yescharacteristic, complemented
22#16840164C2211yescharacteristic, complemented
23#16840104—21no—
24#16840093—21no—
25#16840070—21no—
26#16840003C2211yescharacteristic, complemented
27#16840003C2211yescharacteristic, complemented
28C4×Dic244C2211yescharacteristic, complemented
29#16839800C2211yescharacteristic, complemented
30C2×#14519711C2211yescharacteristic, complemented
31#16839589C2211yescharacteristic, complemented
32#16839587C2211yescharacteristic, complemented
33#16839587C2211yescharacteristic, complemented
34C4⋊#11758185C2211yescharacteristic, complemented
35#16839565C2211yescharacteristic, complemented
36#16839563C2211yescharacteristic
37#16839563C2211yescharacteristic
38#16839563C2211yescharacteristic
39#16839563C2211yescharacteristic, complemented
40#16839563C2211yescharacteristic, complemented
41#16839563C2211yescharacteristic, complemented
42#16839563C2211yescharacteristic, complemented
43#16839563C2211yescharacteristic, complemented
44#16839563C2211yescharacteristic, complemented
45C22⋊#11758185C2211yescharacteristic, complemented
46C22⋊#11758185C2211yescharacteristic, complemented
47#16839538C2211yescharacteristic, complemented
48C22×D8×C61C2211yescharacteristic
49C22×D8×C61C2211yescharacteristic
50D42×C61—21no—
51C61×#493C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C61×#466C2211yescharacteristic
54C61×#459—21no—
55C61×#447—21no—
56C61×#447—21no—
57C4×D8×C61C2211yescharacteristic
58C8×D4×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60#14519770—41no—
61#14519769—21no—
62#14519767—41no—
63#14519758—41no—
64#14519756—21no—
65#14519756—21no—
66C4×Dic122—21no—
67#14519736—21no—
68#14519733—41no—
69C2×C4⋊Dic61—21no—
70#14519721—22no—
71#14519721—41no—
72#14519721—41no—
73#14519717—41no—
74C2×#11758185—41no—
75C2×#11758185C2311yescharacteristic
76C2×#11758185C2311yescharacteristic
77C2×#11758185C2311yescharacteristic
78C2×#11758185C2311yescharacteristic
79#14519711—21no—
80#14519711C2311yescharacteristic
81#14519711C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519709—21no—
84#14519709—21no—
85#14519702—21no—
86#14519702—21no—
87#14519702—21no—
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—41no—
91C2×D8×C61—22no—
92C2×D8×C61—22no—
93C2×D8×C61—21no—
94C2×D8×C61—21no—
95C2×D8×C61—21no—
96C2×D8×C61—41no—
97C2×D8×C61—41no—
98C2×D8×C61C2311yescharacteristic
99C2×D8×C61C2311yescharacteristic
100C2×D8×C61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103#127×C61—21no—
104#121×C61—21no—
105#121×C61—21no—
106#121×C61—41no—
107#120×C61—41no—
108#120×C61—41no—
109C4×D4×C61—21no—
110C4×D4×C61D411yescharacteristic
111#107×C61C2311yescharacteristic
112C4⋊C8×C61D411yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115#102×C61—21no—
116C22⋊C8×C61D411yescharacteristic
117C22⋊C8×C61D411yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C24×C61—41no—
120C24×C61—41no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—42no—
125C2×D4×C61—42no—
126C2×D4×C61—41no—
127C2×D4×C61—41no—
128C2×D4×C61—41no—
129C2×D4×C61—41no—
130C2×D4×C61—41no—
131C2×D4×C61—41no—
132C2×D4×C61—81no—
133C2×D4×C61—81no—
134C2×D4×C61—84no—
135C2×D4×C61D811yescharacteristic
136C22×C4×C61—41no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×Dic61—41no—
140C2×Dic122—21no—
141D8×C61—21no—
142D8×C61—21no—
143D8×C61—21no—
144D8×C61—21no—
145D8×C61—21no—
146D8×C61—42no—
147D8×C61—42no—
148D8×C61—81no—
149D8×C61#4112yes—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61C2×D411yescharacteristic
155C2×C8×C61C2×D411yescharacteristic
156C2×C8×C61C2×D411yescharacteristic
157C2×C8×C61C2411yescharacteristic
158C4⋊C4×C61—21no—
159C4⋊C4×C61D811yescharacteristic
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊C4×C61—41no—
163C22⋊C4×C61D811yescharacteristic
164C22⋊C4×C61D811yescharacteristic
165C42×C61C2×D411yescharacteristic
166C22⋊Dic61—41no—
167C22⋊Dic61—41no—
168C22⋊Dic61—41no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—41no—
173#11758196—41no—
174#11758196—41no—
175#11758196—41no—
176#11758196—41no—
177#11758196—41no—
178C4×Dic61—41no—
179C4×Dic61—41no—
180Dic244—21no—
181Dic244—21no—
182#11758185—21no—
183#11758185—21no—
184#11758185—21no—
185#11758185—21no—
186C23×C61—41no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—82no—
190C23×C61—82no—
191C23×C61—82no—
192C23×C61—82no—
193C23×C61—161no—
194C23×C61—161no—
195C23×C61C2×D811yescharacteristic
196C23×C61C2×D811yescharacteristic
197D4×C61—22no—
198D4×C61—22no—
199D4×C61—41no—
200D4×C61—41no—
201D4×C61—41no—
202D4×C61—41no—
203D4×C61—41no—
204D4×C61—82no—
205D4×C61—82no—
206D4×C61—82no—
207D4×C61—82no—
208D4×C61—82no—
209D4×C61—161no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—82no—
216C2×C4×C61C2×D811yescharacteristic
217C2×C4×C61C2×D811yescharacteristic
218C2×C4×C61C2×D811yescharacteristic
219C2×C4×C61C2×D811yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—82no—
226Dic122—41no—
227Dic122—41no—
228C8×C61—21no—
229C8×C61—21no—
230C8×C61—21no—
231C8×C61C2×#4111yescharacteristic
232C8×C61H(5,𝔽2)11yescharacteristic
233#33877—611nomaximal, Sylow
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—42no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61—81no—
247C22×C61—81no—
248C22×C61—164no—
249C22×C61—164no—
250C22×C61#50912yes—
251C22×C61C22×D811yescharacteristic
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—81no—
257C4×C61#54611yescharacteristic
258C4×C61#57711yescharacteristic
259Dic61—81no—
260Dic61—81no—
261Dic61—81no—
262Dic61—81no—
263#3336—611no—
264D4×D8D6111yescharacteristic
265#2244—611no—
266#2234—611no—
267#2232—611no—
268#2228—611no—
269#2220—611no—
270#2217—611no—
271#2207—611no—
272#2187—611no—
273#2187—611no—
274#2175—611no—
275#2168—611no—
276#2140—611no—
277C2×#357—611no—
278C2×C61—22no—
279C2×C61—41no—
280C2×C61—82no—
281C2×C61—161no—
282C2×C61—161no—
283C2×C61#329411yescharacteristic
284C2×C61C2×#50911yescharacteristic
285C2×C61#341611yescharacteristic
286C22×D8C2×D6111yescharacteristic
287C22×D8C2×D6111yescharacteristic
288#552—1221no—
289D42—21no—
290C2×SD32—611no—
291C2×SD32—611no—
292C2×SD32—611no—
293C2×M32—611no—
294C22×C16—611no—
295#499—611no—
296#493C2×D6111yescharacteristic
297#485—1221no—
298#483—1221no—
299#479—1221no—
300#467—611no—
301#467—611no—
302#466C2×D6111yescharacteristic
303#466C2×D6111yescharacteristic
304#459—21no—
305#447—21no—
306#447—21no—
307C4×Q16—611no—
308C4×D8C2×D6111yescharacteristic
309C8×D4C2×D6111yescharacteristic
310#427—611no—
311C2×#107—611no—
312#367—611no—
313#366—611no—
314#366—611no—
315C4⋊C16—611no—
316#358—611no—
317#357—611no—
318#357—611no—
319#357—611no—
320#357—611no—
321#357—611no—
322#357—611no—
323#357—611no—
324#357—611no—
325#357—611no—
326C22⋊C16—611no—
327C22⋊C16—611no—
328#346—611no—
329C61#3387711yescharacteristic, complemented, Sylow
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—41no—
333C2×Q16—611no—
334C2×D8—22no—
335C2×D8—22no—
336C2×D8—21no—
337C2×D8—21no—
338C2×D8—21no—
339C2×D8—41no—
340C2×D8—41no—
341C2×D8C22×D6111yescharacteristic
342C2×D8C22×D6111yescharacteristic
343C2×D8C22×D6111yescharacteristic
344C22×C8C22×D6111yescharacteristic
345C22×C8C22×D6111yescharacteristic
346#127—21no—
347#126—2441no—
348#125—1221no—
349#125—2441no—
350#123—2441no—
351C22⋊Q8—1221no—
352C22⋊Q8—1221no—
353#121—21no—
354#121—21no—
355#121—41no—
356#120—41no—
357#120—41no—
358C4×Q8—1221no—
359C4×D4—21no—
360C4×D4C22⋊D6111yescharacteristic
361#117—1221no—
362#117—2441no—
363C2×C4⋊C4—1221no—
364SD32—1222no—
365SD32—2441no—
366SD32—2441no—
367M32—2441no—
368C2×C16—611no—
369C2×C16—611no—
370C2×C16—611no—
371C2×C16—611no—
372C2×C16—2441no—
373#107—611no—
374#107—611no—
375#107—611no—
376#107—1221no—
377#107C22×D6111yescharacteristic
378#106—1221no—
379#106—1221no—
380C4⋊C8C22⋊D6111yescharacteristic
381#103—1221no—
382#103—1221no—
383#103—1221no—
384#102—21no—
385#102—21no—
386#102—21no—
387C22⋊C8C22⋊D6111yescharacteristic
388C22⋊C8C22⋊D6111yescharacteristic
389C4×C8C22×D6111yescharacteristic
390C24—41no—
391C24—41no—
392C2×Q8—1221no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—81no—
405C2×D4—81no—
406C2×D4—84no—
407C2×D4#1175819911yescharacteristic
408C22×C4—41no—
409C22×C4—2441no—
410C22×C4C2×C22⋊D6111yescharacteristic
411C22×C4C2×C22⋊D6111yescharacteristic
412Q16—1221no—
413Q16—1221no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—42no—
420D8—42no—
421D8—81no—
422D8#1175822412yes—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×C22⋊D6111yescharacteristic
428C2×C8C2×C22⋊D6111yescharacteristic
429C2×C8C2×C22⋊D6111yescharacteristic
430C2×C8C23×D6111yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—1221no—
433C4⋊C4—1221no—
434C4⋊C4—1221no—
435C4⋊C4—2441no—
436C4⋊C4—2441no—
437C4⋊C4—2441no—
438C4⋊C4—2441no—
439C4⋊C4—2441no—
440C4⋊C4—2441no—
441C4⋊C4#1175819911yescharacteristic
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—2441no—
446C22⋊C4—2441no—
447C22⋊C4—2441no—
448C22⋊C4#1175819911yescharacteristic
449C22⋊C4#1175819911yescharacteristic
450C42—2441no—
451C42—2441no—
452C42C2×C22⋊D6111yescharacteristic
453C16—1221no—
454C16—1221no—
455C16—1221no—
456C16—1221no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—82no—
461C23—82no—
462C23—82no—
463C23—82no—
464C23—161no—
465C23—161no—
466C23C2×#1175819911yescharacteristic
467C23C2×#1175819911yescharacteristic
468Q8—2441no—
469Q8—2441no—
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—41no—
477D4—82no—
478D4—82no—
479D4—82no—
480D4—82no—
481D4—82no—
482D4—161no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—82no—
489C2×C4—4882no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4C2×#1175819911yescharacteristic
495C2×C4C2×#1175819911yescharacteristic
496C2×C4C2×#1175819911yescharacteristic
497C2×C4C2×#1175819911yescharacteristic
498C2×C4C22×C22⋊D6111yescharacteristic
499C8—21no—
500C8—21no—
501C8—21no—
502C8C2×#1175822411yescharacteristic
503C8#1451982211yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—164no—
519C22—164no—
520C22#1684019812yes—
521C22C22×#1175819911yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—81no—
527C4—4881no—
528C4—4881no—
529C4—4881no—
530C4—4881no—
531C4#1684040611yescharacteristic
532C4#1684057311yescharacteristic
533C2—22no—
534C2—41no—
535C2—82no—
536C2—161no—
537C2—161no—
538C2#2145763211yescharacteristic
539C2C2×#1684019811yescharacteristic
540C2#2145896611yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
Fitting, prime radicalD4×D8×C61C2
socleC22×C61C22×D8
hypercenterD4×D8D61
hypocenterC61#33877
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. #21458188C2semidirect
2. #21448060C2semidirect
3. #21448007C2semidirect
4. #21447997C2semidirect
5. #21447976C2semidirect
6. #21447930C2semidirect
7. #21447913C2semidirect
8. #21447856C2semidirect
9. #21447748C2semidirect
10. #21447748C2semidirect
11. #21447683C2semidirect
12. #21447645C2semidirect
13. #21447535C2semidirect
14. C2×#16839563C2semidirect
18. C2×#14519721C22semidirect
19. C2×#14519721C22semidirect
20. C2×#14519717C22semidirect
21. C22×#11758185C22semidirect
22. #16840164C22semidirect
26. #16840003C22semidirect
27. #16840003C22semidirect
28. C4×Dic244C22semidirect
29. #16839800C22semidirect
30. C2×#14519711C22semidirect
31. #16839589C22semidirect
32. #16839587C22semidirect
33. #16839587C22semidirect
34. C4⋊#11758185C22semidirect
35. #16839565C22semidirect
39. #16839563C22semidirect
40. #16839563C22semidirect
41. #16839563C22semidirect
42. #16839563C22semidirect
43. #16839563C22semidirect
44. #16839563C22semidirect
45. C22⋊#11758185C22semidirect
46. C22⋊#11758185C22semidirect
47. #16839538C22semidirect
329. C61#33877semidirect

Maximal subgroups

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

subgroupindex
#214581882
#214480602
#214480072
#214479972
#214479762
#214479302
#214479132
#214478562
#214477482
#214476832
#214476452
#214475352
C2×#168395632
D4×D8×C612
#3387761