Subgroups — #14565928

Order 2432.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926960	C₂	1	1	yes	maximal, characteristic
2	#11926378	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926377	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₉	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597347	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	#10597269	C₄	1	1	yes	characteristic
9	#10597255	C₄	1	2	yes	—
10	C₁₆×D₁₉	C₂²	1	2	yes	—
11	C₁₉×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₉×C₃₂	C₂²	1	1	yes	characteristic
13	C₁₉⋊C₃₂	C₂²	1	2	yes	—
14	#64541	C₈	1	1	yes	characteristic
15	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	#64520	C₈	1	1	yes	characteristic
17	#64515	C₈	1	2	yes	—
18	C₈×D₁₉	C₂×C₄	1	2	yes	—
19	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉⋊C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₁₉	C₁₆	1	2	yes	—
24	D₇₆	C₁₆	1	1	yes	characteristic
25	C₄×D₁₉	C₂×C₈	1	2	yes	—
26	Dic₃₈	C₁₆	1	1	yes	characteristic
27	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
28	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
29	C₁₉⋊C₈	C₂×C₈	1	2	yes	—
30	#2258	—	19	1	no	maximal, Sylow
31	C₂²×C₁₉	C₂×C₁₆	1	1	yes	characteristic
32	C₂×D₁₉	C₂×C₁₆	1	2	yes	—
33	C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
34	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
35	Dic₁₉	C₂×C₁₆	1	2	yes	—
36	#504	—	19	1	no	—
37	M₆₄	—	19	1	no	—
38	M₆₄	—	19	2	no	—
39	C₂×C₃₂	—	19	2	no	—
40	C₂×C₃₂	D₁₉	1	1	yes	characteristic, complemented
41	C₂×C₁₉	—	2	1	no	—
42	C₂×C₁₉	C₂²×C₁₆	1	1	yes	characteristic
43	D₁₉	—	2	2	no	—
44	#131	—	19	1	no	—
45	M₃₂	—	19	1	no	—
46	M₃₂	—	19	2	no	—
47	C₂×C₁₆	—	19	2	no	—
48	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
49	C₃₂	—	19	2	no	—
50	C₃₂	C₂×D₁₉	1	1	yes	characteristic
51	C₃₂	C₂×D₁₉	1	1	yes	characteristic
52	C₁₉	#2258	1	1	yes	characteristic, complemented, Sylow
53	#41	—	19	1	no	—
54	M₁₆	—	19	1	no	—
55	M₁₆	—	19	2	no	—
56	C₂×C₈	—	19	2	no	—
57	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
58	C₁₆	—	19	2	no	—
59	C₁₆	C₄×D₁₉	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
61	Q₈	—	19	1	no	—
62	D₄	—	19	2	no	—
63	D₄	—	19	1	no	—
64	C₂×C₄	—	19	2	no	—
65	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
66	C₈	—	19	2	no	—
67	C₈	C₈×D₁₉	1	1	yes	characteristic
68	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
69	C₂²	—	19	2	no	—
70	C₂²	C₁₆×D₁₉	1	1	yes	characteristic
71	C₄	—	19	2	no	—
72	C₄	C₁₆×D₁₉	1	1	yes	characteristic
73	C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	38	2	no	—
76	C₂	C₂×C₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₁₉
commutator, socle	C₂×C₁₉	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₂×C₁₉×C₃₂	C₂
prime radical	#64541	C₈
cosocle	C₁₆×C₁₉	C₂³
hypercenter	C₂×C₃₂	D₁₉
hypocenter	C₁₉	#2258
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #11926378	C₂	semidirect
3. #11926377	C₂	semidirect
4. C₃₂×D₁₉	C₂	semidirect
5. C₂×C₁₉×C₃₂	C₂	semidirect
40. C₂×C₃₂	D₁₉	semidirect
52. C₁₉	#2258	semidirect

Maximal subgroups

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

subgroup	index
#11926960	2
#11926378	2
#11926377	2
C₃₂×D₁₉	2
C₂×C₁₉×C₃₂	2
#2258	19