Subgroups — #14561832

Order 2432.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926378	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₉×C₃₂	—	2	1	no	—
8	C₁₉⋊C₃₂	—	2	1	no	—
9	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₁₉	C₈	1	1	yes	characteristic
11	C₂×C₁₉⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₁₆×C₁₉	Q₈	1	1	yes	characteristic
14	C₁₉⋊C₁₆	—	2	1	no	—
15	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₁₉	—	2	1	no	—
17	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₉	M₁₆	1	1	yes	characteristic
19	C₁₉⋊C₈	C₁₆	1	2	yes	—
20	#1422	—	19	1	no	maximal, Sylow
21	C₂²×C₁₉	M₃₂	1	1	yes	characteristic
22	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
24	Dic₁₉	—	2	2	no	—
25	M₆₄	—	19	1	no	—
26	M₆₄	D₁₉	1	1	yes	characteristic
27	C₄×C₁₆	—	19	1	no	—
28	C₂×C₁₉	—	2	1	no	—
29	C₂×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
30	C₂×C₁₆	—	19	1	no	—
31	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
32	C₄×C₈	—	19	1	no	—
33	C₃₂	—	2	1	no	—
34	C₃₂	—	38	1	no	—
35	C₁₉	#1422	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₈	—	19	1	no	—
37	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
38	C₄²	—	19	1	no	—
39	C₁₆	—	38	1	no	—
40	C₁₆	Dic₃₈	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
42	C₂×C₄	—	38	1	no	—
43	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
44	C₈	—	19	2	no	—
45	C₈	#64515	1	1	yes	characteristic
46	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
47	C₂²	#10597255	1	1	yes	characteristic
48	C₄	—	38	2	no	—
49	C₄	C₁₆×D₁₉	1	1	yes	characteristic
50	C₄	Dic₁₉⋊C₈	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	Dic₁₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₁₉×M₆₄	C₂
socle	C₂×C₁₉	C₄⋊C₁₆
prime radical	C₂²×C₁₉	M₃₂
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	M₆₄	D₁₉
hypocenter	C₁₉	#1422
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
35. 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
C₁₆×Dic₁₉	2
C₁₉×M₆₄	2
#1422	19