Subgroups — #14561934

Order 2432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926595	C₂	1	3	yes	maximal
2	#11926266	C₂	1	3	yes	maximal, complemented
3	C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₁₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₉	C₂²	1	3	yes	—
6	(C₂×D₁₉)⋊C₈	C₄	1	6	yes	—
7	Dic₁₉⋊C₈	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	C₂²×D₁₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
16	C₂×Dic₁₉	C₄²	1	3	yes	—
17	C₄×D₁₉	—	2	6	no	—
18	C₈×C₁₉	—	2	6	no	—
19	C₁₉⋊C₈	—	2	6	no	—
20	#1454	—	19	1	no	maximal, Sylow
21	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₁₉	—	2	3	no	—
23	C₄×C₁₉	#131	1	6	yes	—
24	Dic₁₉	—	2	3	no	—
25	#431	—	19	3	no	—
26	#322	—	19	3	no	—
27	C₈²	D₁₉	1	1	yes	characteristic, complemented
28	C₂×C₁₉	#405	1	3	yes	—
29	D₁₉	—	4	1	no	—
30	C₂×C₄²	—	19	1	no	—
31	C₄⋊C₈	—	19	6	no	—
32	C₂²⋊C₈	—	19	6	no	—
33	C₄×C₈	—	19	3	no	—
34	C₄×C₈	C₂×D₁₉	1	3	yes	—
35	C₁₉	#1454	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	—	19	3	no	—
37	C₂×C₈	—	19	6	no	—
38	C₂×C₈	C₄×D₁₉	1	6	yes	—
39	C₄²	—	19	3	no	—
40	C₄²	C₂²×D₁₉	1	1	yes	characteristic
41	C₂³	—	19	1	no	—
42	C₂×C₄	—	19	3	no	—
43	C₂×C₄	—	38	6	no	—
44	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	38	6	no	—
47	C₂²	—	38	3	no	—
48	C₂²	C₄²×D₁₉	1	1	yes	characteristic
49	C₄	—	38	3	no	—
50	C₄	#10597347	1	6	yes	—
51	C₂	—	76	1	no	—
52	C₂	#11926498	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	#1454
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. #11926266	C₂	semidirect
3. C₈²×C₁₉	C₂	semidirect
27. C₈²	D₁₉	semidirect
35. C₁₉	#1454	semidirect

Maximal subgroups

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

subgroup	index
#11926595	2
#11926266	2
C₈²×C₁₉	2
#1454	19