Subgroups — C₂×#11926377 #14565926

Order 2432.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926377	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₁₉	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₉⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₆×D₁₉	C₄	1	2	yes	—
9	C₁₆×D₁₉	C₂²	1	2	yes	—
10	C₁₉×C₃₂	C₂²	1	2	yes	complemented
11	C₁₉⋊C₃₂	C₂²	1	2	yes	complemented
12	C₂×C₄×D₁₉	C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₉⋊C₈	C₈	1	1	yes	characteristic
15	C₈×D₁₉	C₈	1	2	yes	—
16	C₈×D₁₉	C₂×C₄	1	2	yes	—
17	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
19	C₁₉⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂²×D₁₉	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₁₉	C₁₆	1	1	yes	characteristic
23	C₄×D₁₉	C₁₆	1	2	yes	—
24	C₄×D₁₉	C₂×C₈	1	2	yes	—
25	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
27	C₁₉⋊C₈	C₂×C₈	1	2	yes	—
28	C₂×M₆₄	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	C₂×C₁₆	1	1	yes	characteristic
30	C₂×D₁₉	—	2	2	no	—
31	C₂×D₁₉	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₉	C₂×C₁₆	1	2	yes	—
35	C₂²×C₁₆	—	19	1	no	—
36	M₆₄	—	19	4	no	—
37	C₂×C₃₂	—	19	1	no	—
38	C₂×C₃₂	D₁₉	1	1	yes	characteristic, complemented
39	C₂×C₁₉	M₆₄	1	2	yes	complemented
40	C₂×C₁₉	C₂²×C₁₆	1	1	yes	characteristic
41	D₁₉	—	2	2	no	—
42	C₂²×C₈	—	19	1	no	—
43	C₂×C₁₆	—	19	1	no	—
44	C₂×C₁₆	—	19	2	no	—
45	C₂×C₁₆	—	19	2	no	—
46	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
47	C₃₂	—	19	2	no	—
48	C₃₂	C₂×D₁₉	1	2	yes	complemented
49	C₁₉	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	19	1	no	—
51	C₂×C₈	—	19	1	no	—
52	C₂×C₈	—	19	2	no	—
53	C₂×C₈	—	19	2	no	—
54	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
55	C₁₆	—	19	2	no	—
56	C₁₆	C₄×D₁₉	1	1	yes	characteristic
57	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
58	C₂³	—	19	1	no	—
59	C₂×C₄	—	19	1	no	—
60	C₂×C₄	—	19	2	no	—
61	C₂×C₄	—	19	2	no	—
62	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
63	C₈	—	19	2	no	—
64	C₈	C₈×D₁₉	1	1	yes	characteristic
65	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
66	C₂²	—	19	2	no	—
67	C₂²	—	38	2	no	—
68	C₂²	C₁₆×D₁₉	1	1	yes	characteristic
69	C₄	—	19	2	no	—
70	C₄	C₁₆×D₁₉	1	1	yes	characteristic
71	C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
72	C₂	—	38	2	no	—
73	C₂	#11926377	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₁₉
commutator	C₂×C₁₉	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₂×C₁₉×C₃₂	C₂
socle	C₂²×C₁₉	C₂×C₁₆
prime radical	C₂²×D₁₉	C₁₆
cosocle	C₁₆×C₁₉	C₂³
hypercenter	C₂×C₃₂	D₁₉
hypocenter	C₁₉	C₂×M₆₄
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #11926377	C₂	direct (N × H)
3. C₂×C₁₉⋊C₃₂	C₂	semidirect
4. C₂×C₁₉×C₃₂	C₂	semidirect
10. C₁₉×C₃₂	C₂²	semidirect
11. C₁₉⋊C₃₂	C₂²	semidirect
38. C₂×C₃₂	D₁₉	semidirect
39. C₂×C₁₉	M₆₄	semidirect
48. C₃₂	C₂×D₁₉	semidirect
49. C₁₉	C₂×M₆₄	semidirect
73. C₂	#11926377	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₉	2
#11926377	2
C₂×C₁₉⋊C₃₂	2
C₂×C₁₉×C₃₂	2
C₂×M₆₄	19

Subgroups — C2×#11926377 #14565926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926377 #14565926