Subgroups — C₂⁴×Dic₆₂ #16860506

Order 3968.

6264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₆₂	C₂	1	60	yes	maximal, direct product factor
2	C₂⁴×Dic₃₁	C₂	1	2	yes	maximal
3	C₂⁴×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×C₃₁	C₂²	1	1	yes	characteristic
5	C₂³×C₄×C₃₁	C₂²	1	30	yes	—
6	C₂³×Dic₃₁	C₂²	1	60	yes	—
7	C₂²×Dic₆₂	C₂²	1	560	yes	direct product factor
8	C₂⁴×C₃₁	Q₈	1	16	yes	complemented
9	C₂⁴×C₃₁	C₂³	1	15	yes	—
10	C₂²×C₄×C₃₁	C₂³	1	140	yes	—
11	C₂²×Dic₃₁	C₂³	1	280	yes	—
12	C₂×Dic₆₂	C₂³	1	960	yes	direct product factor
13	C₂³×C₃₁	C₂×Q₈	1	120	yes	complemented
14	C₂³×C₃₁	C₂⁴	1	35	yes	—
15	C₂×C₄×C₃₁	C₂⁴	1	120	yes	—
16	C₂×Dic₃₁	C₂⁴	1	240	yes	—
17	Dic₆₂	C₂⁴	1	256	yes	direct product factor
18	C₂⁴×Q₈	—	31	1	no	maximal, Sylow
19	C₂²×C₃₁	C₂²×Q₈	1	140	yes	complemented
20	C₂²×C₃₁	C₂⁵	1	15	yes	—
21	C₄×C₃₁	C₂⁵	1	16	yes	—
22	Dic₃₁	C₂⁵	1	32	yes	—
23	C₂³×Q₈	—	31	60	no	—
24	C₂⁴×C₄	—	31	2	no	—
25	C₂⁴×C₄	D₃₁	1	1	yes	characteristic
26	C₂×C₃₁	C₂³×Q₈	1	30	yes	complemented
27	C₂×C₃₁	C₂⁶	1	1	yes	characteristic
28	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
29	C₂²×Q₈	—	31	560	no	—
30	C₂³×C₄	—	31	60	no	—
31	C₂³×C₄	C₂×D₃₁	1	30	yes	—
32	C₃₁	C₂⁴×Q₈	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	Dic₆₂	1	16	yes	direct product factor
34	C₂⁴	C₂²×D₃₁	1	15	yes	—
35	C₂×Q₈	—	31	960	no	—
36	C₂²×C₄	—	31	280	no	—
37	C₂²×C₄	C₂²×D₃₁	1	140	yes	—
38	C₂³	C₂×Dic₆₂	1	120	yes	direct product factor
39	C₂³	C₂³×D₃₁	1	35	yes	—
40	Q₈	—	31	256	no	—
41	C₂×C₄	—	31	240	no	—
42	C₂×C₄	C₂³×D₃₁	1	120	yes	—
43	C₂²	C₂²×Dic₆₂	1	140	yes	direct product factor
44	C₂²	C₂⁴×D₃₁	1	15	yes	—
45	C₄	—	31	32	no	—
46	C₄	C₂⁴×D₃₁	1	16	yes	—
47	C₂	C₂³×Dic₆₂	1	30	yes	direct product factor
48	C₂	C₂⁵×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₃₁
commutator, cosocle	C₂×C₃₁	C₂⁶
Frattini	C₂	C₂⁵×D₃₁
Fitting	C₂⁴×C₄×C₃₁	C₂
socle, prime radical	C₂⁵×C₃₁	C₂²
hypercenter	C₂⁴×C₄	D₃₁
hypocenter	C₃₁	C₂⁴×Q₈
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×Dic₆₂	C₂	direct (N × H)
7. C₂²×Dic₆₂	C₂²	direct (N × H)
8. C₂⁴×C₃₁	Q₈	semidirect
12. C₂×Dic₆₂	C₂³	direct (N × H)
13. C₂³×C₃₁	C₂×Q₈	semidirect
17. Dic₆₂	C₂⁴	direct (N × H)
19. C₂²×C₃₁	C₂²×Q₈	semidirect
26. C₂×C₃₁	C₂³×Q₈	semidirect
32. C₃₁	C₂⁴×Q₈	semidirect
33. C₂⁴	Dic₆₂	direct (N × H)
38. C₂³	C₂×Dic₆₂	direct (N × H)
43. C₂²	C₂²×Dic₆₂	direct (N × H)
47. C₂	C₂³×Dic₆₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Dic₆₂	2
C₂⁴×Dic₃₁	2
C₂⁴×C₄×C₃₁	2
C₂⁴×Q₈	31

Subgroups — C24×Dic62 #16860506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×Dic₆₂ #16860506