Subgroups — C₂⁴×C₁₉⋊C₈ #14578334

Order 2432.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₉⋊C₈	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂⁵×C₁₉	C₄	1	1	yes	characteristic
4	C₂³×C₄×C₁₉	C₄	1	15	yes	—
5	C₂³×C₄×C₁₉	C₂²	1	15	yes	—
6	C₂²×C₁₉⋊C₈	C₂²	1	140	yes	direct product factor
7	C₂⁴×C₁₉	C₈	1	16	yes	complemented
8	C₂⁴×C₁₉	C₂×C₄	1	15	yes	—
9	C₂²×C₄×C₁₉	C₂×C₄	1	105	yes	—
10	C₂²×C₄×C₁₉	C₂³	1	35	yes	—
11	C₂×C₁₉⋊C₈	C₂³	1	120	yes	direct product factor
12	C₂³×C₁₉	C₂×C₈	1	120	yes	complemented
13	C₂³×C₁₉	C₂²×C₄	1	35	yes	—
14	C₂×C₄×C₁₉	C₂²×C₄	1	105	yes	—
15	C₂×C₄×C₁₉	C₂⁴	1	15	yes	—
16	C₁₉⋊C₈	C₂⁴	1	16	yes	direct product factor
17	C₂⁴×C₈	—	19	1	no	maximal, Sylow
18	C₂²×C₁₉	C₂²×C₈	1	140	yes	complemented
19	C₂²×C₁₉	C₂³×C₄	1	15	yes	—
20	C₄×C₁₉	C₂³×C₄	1	15	yes	—
21	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
22	C₂⁴×C₄	D₁₉	1	1	yes	characteristic
23	C₂³×C₈	—	19	30	no	—
24	C₂×C₁₉	C₂³×C₈	1	30	yes	complemented
25	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
26	C₂⁵	Dic₁₉	1	1	yes	characteristic
27	C₂³×C₄	Dic₁₉	1	15	yes	—
28	C₂³×C₄	C₂×D₁₉	1	15	yes	—
29	C₂²×C₈	—	19	140	no	—
30	C₁₉	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂⁴	C₁₉⋊C₈	1	16	yes	direct product factor
32	C₂⁴	C₂×Dic₁₉	1	15	yes	—
33	C₂²×C₄	C₂×Dic₁₉	1	105	yes	—
34	C₂²×C₄	C₂²×D₁₉	1	35	yes	—
35	C₂×C₈	—	19	120	no	—
36	C₂³	C₂×C₁₉⋊C₈	1	120	yes	direct product factor
37	C₂³	C₂²×Dic₁₉	1	35	yes	—
38	C₂×C₄	C₂²×Dic₁₉	1	105	yes	—
39	C₂×C₄	C₂³×D₁₉	1	15	yes	—
40	C₈	—	19	16	no	—
41	C₂²	C₂²×C₁₉⋊C₈	1	140	yes	direct product factor
42	C₂²	C₂³×Dic₁₉	1	15	yes	—
43	C₄	C₂³×Dic₁₉	1	15	yes	—
44	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
45	C₂	C₂³×C₁₉⋊C₈	1	30	yes	direct product factor
46	C₂	C₂⁴×Dic₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	D₁₉
commutator, hypocenter	C₁₉	C₂⁴×C₈
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂⁴×C₄×C₁₉	C₂
socle, prime radical	C₂⁵×C₁₉	C₄
cosocle	C₄×C₁₉	C₂⁵
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₉⋊C₈	C₂	direct (N × H)
6. C₂²×C₁₉⋊C₈	C₂²	direct (N × H)
7. C₂⁴×C₁₉	C₈	semidirect
11. C₂×C₁₉⋊C₈	C₂³	direct (N × H)
12. C₂³×C₁₉	C₂×C₈	semidirect
16. C₁₉⋊C₈	C₂⁴	direct (N × H)
18. C₂²×C₁₉	C₂²×C₈	semidirect
24. C₂×C₁₉	C₂³×C₈	semidirect
30. C₁₉	C₂⁴×C₈	semidirect
31. C₂⁴	C₁₉⋊C₈	direct (N × H)
36. C₂³	C₂×C₁₉⋊C₈	direct (N × H)
41. C₂²	C₂²×C₁₉⋊C₈	direct (N × H)
45. C₂	C₂³×C₁₉⋊C₈	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×C₁₉⋊C₈	2
C₂⁴×C₄×C₁₉	2
C₂⁴×C₈	19

Subgroups — C24×C19⋊C8 #14578334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₁₉⋊C₈ #14578334