Subgroups — #18070205

Order 4864.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₉⋊C₃₂)	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉⋊C₃₂	—	2	2	no	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₈²×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₈	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₈	1	1	yes	characteristic
12	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₉⋊C₃₂	—	4	2	no	—
14	C₂×C₈×C₁₉	—	2	1	no	—
15	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
19	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
20	C₁₆×C₁₉	—	2	2	no	—
21	C₁₆×C₁₉	—	2	1	no	—
22	C₁₆×C₁₉	SD₁₆	1	2	yes	—
23	#7455	—	19	1	no	maximal, Sylow
24	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₄×C₁₉	M₃₂	1	1	yes	characteristic
27	C₈×C₁₉	—	2	2	no	—
28	C₈×C₁₉	—	2	1	no	—
29	C₈×C₁₉	—	2	1	no	—
30	C₈×C₁₉	C₃₂	1	2	yes	complemented
31	C₈×C₁₉	#106	1	1	yes	characteristic
32	C₈×C₁₉	#108	1	1	yes	characteristic
33	C₄⋊C₃₂	—	19	2	no	—
34	C₈×C₁₆	D₁₉	1	1	yes	characteristic
35	C₂²×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
36	C₄×C₁₉	—	2	1	no	—
37	C₄×C₁₉	#334	1	1	yes	characteristic
38	C₄×C₁₉	#364	1	1	yes	characteristic
39	C₄×C₁₉	C₂×C₃₂	1	1	yes	characteristic
40	C₄×C₁₉	M₆₄	1	1	yes	characteristic
41	C₂×C₃₂	—	38	2	no	—
42	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
43	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
44	C₈²	Dic₁₉	1	1	yes	characteristic
45	C₂×C₁₉	#1367	1	1	yes	characteristic
46	C₂×C₁₉	C₄⋊C₃₂	1	1	yes	characteristic
47	C₂×C₁₉	#1422	1	1	yes	characteristic
48	C₂×C₁₆	—	2	1	no	—
49	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
50	C₂×C₁₆	D₇₆	1	1	yes	characteristic
51	C₄×C₈	C₁₉⋊C₈	1	1	yes	characteristic
52	C₄×C₈	C₁₉⋊C₈	1	1	yes	characteristic
53	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
54	C₃₂	—	76	2	no	—
55	C₁₉	#7455	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
58	C₂×C₈	C₁₉⋊C₁₆	1	1	yes	characteristic
59	C₂×C₈	#64520	1	1	yes	characteristic
60	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
61	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	C₁₆	—	2	1	no	—
64	C₁₆	#64516	1	2	yes	—
65	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
66	C₂×C₄	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
67	C₂×C₄	#10597269	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₈	—	2	1	no	—
70	C₈	—	2	1	no	—
71	C₈	C₁₉⋊C₃₂	1	2	yes	complemented
72	C₈	#10597274	1	1	yes	characteristic
73	C₈	#10597276	1	1	yes	characteristic
74	C₂²	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#11926295	1	1	yes	characteristic
77	C₄	#11926365	1	1	yes	characteristic
78	C₄	C₂×C₁₉⋊C₃₂	1	1	yes	characteristic
79	C₄	#11926378	1	1	yes	characteristic
80	C₂	#14561699	1	1	yes	characteristic
81	C₂	C₄⋊(C₁₉⋊C₃₂)	1	1	yes	characteristic
82	C₂	#14561833	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	D₇₆
commutator	C₄×C₁₉	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₈×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₄⋊C₁₆
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	C₈×C₁₆	D₁₉
hypocenter	C₁₉	#7455
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
30. C₈×C₁₉	C₃₂	semidirect
55. C₁₉	#7455	semidirect
71. C₈	C₁₉⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₁₉⋊C₃₂)	2
C₈×C₁₆×C₁₉	2
#7455	19