Subgroups — #14565914

Order 2432.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926946	C₂	1	2	yes	maximal
2	#11926372	C₂	1	2	yes	maximal
3	#11926370	C₂	1	2	yes	maximal
4	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	#10597316	—	2	2	no	—
6	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597275	C₂²	1	4	yes	—
10	#10597274	—	2	2	no	—
11	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
13	C₄²×C₁₉	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₉	—	2	4	no	—
15	Dic₁₉⋊C₄	—	4	4	no	—
16	C₁₆×C₁₉	Q₈	1	2	yes	—
17	C₁₆×C₁₉	Q₈	1	2	yes	—
18	C₂×C₄×C₁₉	D₈	1	2	yes	—
19	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
20	C₂×Dic₁₉	—	4	4	no	—
21	C₈×C₁₉	Q₁₆	1	2	yes	—
22	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
23	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	#2253	—	19	1	no	maximal, Sylow
25	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
26	C₄×C₁₉	—	2	2	no	—
27	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
28	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
29	Dic₁₉	—	8	4	no	—
30	#499	—	19	2	no	—
31	#367	—	19	2	no	—
32	#366	—	19	2	no	—
33	C₄×C₁₆	D₁₉	1	1	yes	characteristic
34	C₂×C₁₉	#500	1	1	yes	characteristic
35	C₂×C₁₉	#508	1	2	yes	—
36	#125	—	38	2	no	—
37	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
38	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
39	#107	—	19	4	no	—
40	#106	—	38	2	no	—
41	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
42	C₁₉	#2253	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	D₇₆	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
45	C₄⋊C₄	—	38	4	no	—
46	C₄⋊C₄	—	76	4	no	—
47	C₄²	D₇₆	1	1	yes	characteristic
48	C₁₆	Dic₃₈	1	2	yes	—
49	C₁₆	Dic₃₈	1	2	yes	—
50	C₂×C₄	—	76	4	no	—
51	C₂×C₄	D₁₅₂	1	2	yes	—
52	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
53	C₈	Dic₇₆	1	2	yes	—
54	C₈	C₂×Dic₃₈	1	1	yes	characteristic
55	C₈	C₂×Dic₃₈	1	1	yes	characteristic
56	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	152	4	no	—
59	C₄	#10597315	1	1	yes	characteristic
60	C₄	C₂×Dic₇₆	1	1	yes	characteristic
61	C₂	#11926949	1	1	yes	characteristic
62	C₂	#11926976	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2253
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
42. C₁₉	#2253	semidirect

Maximal subgroups

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

subgroup	index
#11926946	2
#11926372	2
#11926370	2
C₄×C₁₆×C₁₉	2
#2253	19