Subgroups — #14561937

Order 2432.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#64515	C₂	1	3	yes	maximal
2	#11926265	C₂	1	3	yes	maximal, complemented
3	C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#64515	C₄	1	6	yes	—
5	C₄²×D₁₉	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₁₉	C₂²	1	3	yes	—
7	#10597272	C₄	1	6	yes	—
8	C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
9	C₂×C₄×D₁₉	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₁₉	C₂×C₄	1	6	yes	—
11	C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₄×Dic₁₉	C₂×C₄	1	3	yes	—
13	C₂×C₁₉⋊C₈	C₂×C₄	1	6	yes	—
14	#64515	—	2	12	no	—
15	C₂²×D₁₉	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
17	C₂×Dic₁₉	C₄²	1	3	yes	—
18	C₄×D₁₉	—	2	6	no	—
19	C₈×C₁₉	M₁₆	1	12	yes	complemented
20	C₁₉⋊C₈	—	2	6	no	—
21	#1455	—	19	1	no	maximal, Sylow
22	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
23	C₂×D₁₉	—	2	3	no	—
24	C₄×C₁₉	C₂×M₁₆	1	6	yes	—
25	Dic₁₉	—	2	3	no	—
26	C₄×M₁₆	—	19	3	no	—
27	#322	—	19	3	no	—
28	C₈²	D₁₉	1	1	yes	characteristic, complemented
29	C₂×C₁₉	C₄×M₁₆	1	3	yes	—
30	D₁₉	—	4	1	no	—
31	C₂×M₁₆	—	19	6	no	—
32	C₂×C₄²	—	19	1	no	—
33	#97	—	19	6	no	—
34	C₄×C₈	—	19	3	no	—
35	C₄×C₈	C₂×D₁₉	1	3	yes	—
36	C₁₉	#1455	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	19	3	no	—
38	M₁₆	—	38	12	no	—
39	C₂×C₈	—	19	6	no	—
40	C₂×C₈	C₄×D₁₉	1	6	yes	—
41	C₄²	—	19	3	no	—
42	C₄²	C₂²×D₁₉	1	1	yes	characteristic
43	C₂³	—	19	1	no	—
44	C₂×C₄	—	19	3	no	—
45	C₂×C₄	—	38	6	no	—
46	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
47	C₈	—	38	6	no	—
48	C₈	#64515	1	12	yes	complemented
49	C₂²	—	38	3	no	—
50	C₂²	C₄²×D₁₉	1	1	yes	characteristic
51	C₄	—	38	3	no	—
52	C₄	C₂×#64515	1	6	yes	—
53	C₂	—	76	1	no	—
54	C₂	C₄×#64515	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂×C₄²
Fitting	C₈²×C₁₉	C₂
prime radical	C₂²×D₁₉	C₄²
cosocle	C₄²×C₁₉	C₂³
hypercenter	C₈²	D₁₉
hypocenter	C₁₉	#1455
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #11926265	C₂	semidirect
3. C₈²×C₁₉	C₂	semidirect
19. C₈×C₁₉	M₁₆	semidirect
28. C₈²	D₁₉	semidirect
36. C₁₉	#1455	semidirect
48. C₈	#64515	semidirect

Maximal subgroups

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

subgroup	index
C₄×#64515	2
#11926265	2
C₈²×C₁₉	2
#1455	19