Subgroups — #14561697

Order 2432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926946	C₂	1	1	yes	maximal, characteristic
2	#11926365	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#364	C₂	1	1	yes	maximal, characteristic
4	#10597316	C₄	1	2	yes	—
5	C₁₉×M₃₂	—	2	1	no	—
6	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597275	—	2	1	no	—
8	#10597274	—	2	1	no	—
9	#10597269	—	2	1	no	—
10	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₄⋊Dic₁₉	—	2	2	no	—
14	Dic₁₉⋊C₄	—	4	2	no	—
15	C₁₆×C₁₉	—	4	1	no	—
16	C₁₉⋊C₁₆	—	4	1	no	—
17	C₂×C₄×C₁₉	—	2	1	no	—
18	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₁₉	—	4	2	no	—
20	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
22	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
23	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
24	#1366	—	19	1	no	maximal, Sylow
25	C₂²×C₁₉	#100	1	1	yes	characteristic
26	C₄×C₁₉	—	4	1	no	—
27	C₄×C₁₉	#103	1	1	yes	characteristic
28	C₄×C₁₉	#103	1	1	yes	characteristic
29	Dic₁₉	—	8	2	no	—
30	#499	—	19	1	no	—
31	#364	—	19	1	no	—
32	#364	D₁₉	1	1	yes	characteristic
33	C₂×C₁₉	—	2	1	no	—
34	C₂×C₁₉	#333	1	1	yes	characteristic
35	#125	—	19	2	no	—
36	M₃₂	—	2	1	no	—
37	M₃₂	—	38	1	no	—
38	#107	—	38	1	no	—
39	#106	—	38	1	no	—
40	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
41	C₁₉	#1366	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₈	D₇₆	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
44	C₄⋊C₄	—	38	2	no	—
45	C₄⋊C₄	—	76	2	no	—
46	C₄²	C₄×D₁₉	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	76	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	76	2	no	—
51	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
52	C₈	#64516	1	1	yes	characteristic
53	C₈	Dic₇₆	1	1	yes	characteristic
54	C₈	#64526	1	1	yes	characteristic
55	C₈	#64528	1	1	yes	characteristic
56	C₂²	#10597280	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	152	2	no	—
59	C₄	#10597267	1	1	yes	characteristic
60	C₄	#10597273	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#11926292	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926292
commutator	C₄²×C₁₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	#333
prime radical	C₂²×C₁₉	#100
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#364	D₁₉
hypocenter	C₁₉	#1366
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
41. C₁₉	#1366	semidirect

Maximal subgroups

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

subgroup	index
#11926946	2
#11926365	2
C₁₉×#364	2
#1366	19