Subgroups — #18070207

Order 4864.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561833	C₂	1	2	yes	maximal
2	C₁₉×#1311	C₂	1	1	yes	maximal, characteristic
3	#11926378	—	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	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₉	—	2	1	no	—
12	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₉⋊C₃₂	—	4	2	no	—
14	C₂×C₈×C₁₉	—	2	2	no	—
15	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
18	C₁₆×C₁₉	—	2	1	no	—
19	C₁₆×C₁₉	—	2	1	no	—
20	C₁₆×C₁₉	C₁₆	1	2	yes	—
21	C₁₆×C₁₉	SD₁₆	1	2	yes	—
22	#7456	—	19	1	no	maximal, Sylow
23	C₂×C₄×C₁₉	—	2	1	no	—
24	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₁₉	—	4	2	no	—
26	C₈×C₁₉	#106	1	1	yes	characteristic
27	C₈×C₁₉	#108	1	1	yes	characteristic
28	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₁₉	M₃₂	1	1	yes	characteristic
30	#1422	—	19	2	no	—
31	#1311	D₁₉	1	1	yes	characteristic
32	C₂²×C₁₉	#364	1	1	yes	characteristic
33	C₄×C₁₉	—	2	2	no	—
34	C₄×C₁₉	#334	1	1	yes	characteristic
35	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
36	M₆₄	—	38	2	no	—
37	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
38	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
39	C₈²	Dic₁₉	1	1	yes	characteristic
40	C₂×C₁₉	—	2	1	no	—
41	C₂×C₁₉	#1367	1	1	yes	characteristic
42	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
43	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
44	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
45	C₂×C₁₆	D₇₆	1	1	yes	characteristic
46	C₄×C₈	—	2	1	no	—
47	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
48	C₃₂	—	76	2	no	—
49	C₁₉	#7456	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₈	—	2	2	no	—
51	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
52	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
53	C₄²	#64520	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	—	2	1	no	—
56	C₁₆	C₁₉⋊C₁₆	1	2	yes	—
57	C₁₆	#64516	1	2	yes	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
60	C₈	—	4	2	no	—
61	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
62	C₈	#10597269	1	1	yes	characteristic
63	C₈	#10597274	1	1	yes	characteristic
64	C₈	#10597276	1	1	yes	characteristic
65	C₂²	#11926365	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	#11926295	1	1	yes	characteristic
68	C₄	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#14561699	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10597274
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1311	C₂
socle	C₂×C₁₉	#1367
prime radical	C₂²×C₁₉	#364
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1311	D₁₉
hypocenter	C₁₉	#7456
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1311

Complements

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

N	H ≅ G/N	type
49. C₁₉	#7456	semidirect

Maximal subgroups

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

subgroup	index
#14561833	2
C₁₉×#1311	2
#7456	19