Subgroups — #14561711

Order 2432.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926365	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	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	#10597269	—	2	2	no	—
7	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
9	C₄²×C₁₉	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₉	—	2	1	no	—
11	C₁₆×C₁₉	C₈	1	2	yes	—
12	C₁₉⋊C₁₆	—	4	2	no	—
13	C₂×C₄×C₁₉	—	2	1	no	—
14	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₉	M₁₆	1	1	yes	characteristic
17	C₈×C₁₉	D₈	1	1	yes	characteristic
18	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
19	#1373	—	19	1	no	maximal, Sylow
20	C₂²×C₁₉	#108	1	1	yes	characteristic
21	C₄×C₁₉	—	2	2	no	—
22	C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₉	#107	1	1	yes	characteristic
24	#364	—	19	2	no	—
25	C₄×C₁₆	D₁₉	1	1	yes	characteristic
26	C₂×C₁₉	—	2	1	no	—
27	C₂×C₁₉	#335	1	1	yes	characteristic
28	M₃₂	—	38	2	no	—
29	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
30	C₂×C₁₆	Dic₁₉	1	1	yes	characteristic
31	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
32	C₁₉	#1373	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	D₇₆	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
35	C₄²	Dic₃₈	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	76	2	no	—
38	C₁₆	C₁₉⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
41	C₈	D₁₅₂	1	1	yes	characteristic
42	C₈	Dic₇₆	1	1	yes	characteristic
43	C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
44	C₈	#64520	1	1	yes	characteristic
45	C₂²	#10597276	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
48	C₄	#10597275	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#11926297	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₅₂
commutator	C₈×C₁₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂×C₁₉	#335
prime radical	C₂²×C₁₉	#108
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#1373
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
32. C₁₉	#1373	semidirect

Maximal subgroups

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

subgroup	index
#11926365	2
C₄×C₁₆×C₁₉	2
#1373	19