Subgroups — #18071914

Order 4864.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597272	C₂	1	3	yes	maximal
2	C₂×#11926265	C₂	1	3	yes	maximal
3	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597272	C₄	1	12	yes	—
5	C₂×C₄×C₁₉⋊C₈	C₂²	1	3	yes	—
6	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
7	#11926265	C₄	1	12	yes	complemented
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₈²×C₁₉	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₉	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₂×C₄	1	6	yes	—
13	C₂²×C₁₉⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₉	C₂×C₄	1	6	yes	—
15	C₄×C₈×C₁₉	C₂×C₄	1	6	yes	—
16	#10597272	—	2	24	no	—
17	C₄×C₁₉⋊C₈	C₂×C₄	1	12	yes	—
18	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
19	C₂²×Dic₁₉	C₄²	1	4	yes	—
20	C₂×C₈×C₁₉	C₄²	1	12	yes	—
21	C₂×C₈×C₁₉	M₁₆	1	24	yes	—
22	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
23	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₁₉	—	2	12	no	—
25	C₂×C₁₉⋊C₈	—	2	12	no	—
26	C₂×C₁₉⋊C₈	C₄²	1	12	yes	—
27	#7846	—	19	1	no	maximal, Sylow
28	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×C₄²	1	3	yes	—
30	C₂×C₄×C₁₉	C₂×C₄²	1	3	yes	—
31	C₂×C₄×C₁₉	C₂×M₁₆	1	12	yes	—
32	C₂×Dic₁₉	—	2	12	no	—
33	C₈×C₁₉	#97	1	24	yes	complemented
34	C₁₉⋊C₈	—	2	12	no	—
35	C₄×#97	—	19	3	no	—
36	C₂×#322	—	19	3	no	—
37	C₂×C₈²	D₁₉	1	1	yes	characteristic
38	C₂²×C₁₉	C₄³	1	1	yes	characteristic
39	C₂²×C₁₉	C₄×M₁₆	1	6	yes	—
40	C₄×C₁₉	C₂×#97	1	6	yes	—
41	C₄×C₁₉	C₄×M₁₆	1	6	yes	—
42	Dic₁₉	—	4	4	no	—
43	C₂×#97	—	19	12	no	—
44	C₂×C₄×C₈	—	19	3	no	—
45	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
46	C₄³	—	19	1	no	—
47	#322	—	19	12	no	—
48	C₈²	Dic₁₉	1	4	yes	complemented
49	C₂×C₁₉	#1455	1	4	yes	—
50	C₂×C₁₉	C₄×#97	1	3	yes	—
51	C₂²×C₈	—	19	6	no	—
52	C₂²×C₈	C₄×D₁₉	1	6	yes	—
53	C₂×C₄²	—	19	6	no	—
54	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
55	#97	—	38	24	no	—
56	C₄×C₈	—	19	12	no	—
57	C₄×C₈	C₄×D₁₉	1	6	yes	—
58	C₄×C₈	C₂×Dic₁₉	1	6	yes	—
59	C₁₉	#7846	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₄	—	19	4	no	—
61	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
62	C₂×C₈	—	19	12	no	—
63	C₂×C₈	—	38	12	no	—
64	C₂×C₈	#64515	1	24	yes	—
65	C₂×C₈	C₄×Dic₁₉	1	12	yes	—
66	C₄²	—	38	12	no	—
67	C₄²	C₂×C₄×D₁₉	1	3	yes	—
68	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
69	C₂³	C₄²×D₁₉	1	1	yes	characteristic
70	C₂×C₄	—	38	12	no	—
71	C₂×C₄	C₄²×D₁₉	1	3	yes	—
72	C₂×C₄	C₂×#64515	1	12	yes	—
73	C₂×C₄	C₂×C₄×Dic₁₉	1	3	yes	—
74	C₈	—	38	12	no	—
75	C₈	#10597272	1	24	yes	complemented
76	C₂²	C₄²×Dic₁₉	1	1	yes	characteristic
77	C₂²	C₄×#64515	1	6	yes	—
78	C₄	—	76	4	no	—
79	C₄	C₂×#10597272	1	6	yes	—
80	C₄	C₄×#64515	1	6	yes	—
81	C₂	#14561937	1	4	yes	—
82	C₂	C₄×#10597272	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂²×C₁₉	C₄³
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#7846
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
7. #11926265	C₄	semidirect
9. C₈²×C₁₉	C₄	semidirect
33. C₈×C₁₉	#97	semidirect
48. C₈²	Dic₁₉	semidirect
59. C₁₉	#7846	semidirect
75. C₈	#10597272	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597272	2
C₂×#11926265	2
C₂×C₈²×C₁₉	2
#7846	19