Subgroups — #14561833

Order 2432.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926378	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉⋊C₃₂	—	2	2	no	—
7	C₂×C₈×C₁₉	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₁₉	C₈	1	1	yes	characteristic
10	C₁₆×C₁₉	—	2	1	no	—
11	C₁₆×C₁₉	D₄	1	1	yes	characteristic
12	C₁₆×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₉	—	2	1	no	—
14	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₉	C₁₆	1	2	yes	—
16	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₉	M₁₆	1	1	yes	characteristic
18	#1422	—	19	1	no	maximal, Sylow
19	C₂²×C₁₉	M₃₂	1	1	yes	characteristic
20	C₄×C₁₉	—	2	2	no	—
21	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
23	M₆₄	—	19	2	no	—
24	C₄×C₁₆	D₁₉	1	1	yes	characteristic
25	C₂×C₁₉	—	2	1	no	—
26	C₂×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
29	C₄×C₈	Dic₁₉	1	1	yes	characteristic
30	C₃₂	—	38	2	no	—
31	C₁₉	#1422	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	C₁₉⋊C₈	1	1	yes	characteristic
33	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
34	C₄²	C₁₉⋊C₈	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	Dic₃₈	1	1	yes	characteristic
37	C₁₆	D₇₆	1	1	yes	characteristic
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
40	C₈	C₁₉⋊C₁₆	1	2	yes	—
41	C₈	#64520	1	1	yes	characteristic
42	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
43	C₂²	#10597269	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
46	C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₇₆
commutator	C₄×C₁₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂×C₁₉	C₄⋊C₁₆
prime radical	C₂²×C₁₉	M₃₂
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#1422
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₁₉	#1422	semidirect

Maximal subgroups

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

subgroup	index
#11926378	2
C₄×C₁₆×C₁₉	2
#1422	19