Subgroups — #18069270

Order 4864.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561705	C₂	1	2	yes	maximal, complemented
2	C₁₉×#1712	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₁₉×#493	—	2	2	no	—
5	C₁₉×#493	C₄	1	2	yes	—
6	C₈²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×D₈×C₁₉	—	4	2	no	—
8	C₂×D₈×C₁₉	—	4	2	no	—
9	C₂×D₈×C₁₉	—	4	2	no	—
10	C₁₉×#127	—	2	2	no	—
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	D₄	1	2	yes	—
13	C₂×C₁₉⋊C₁₆	—	4	2	no	—
14	C₂×D₄×C₁₉	—	4	2	no	—
15	C₂×D₄×C₁₉	—	4	4	no	—
16	D₈×C₁₉	—	8	4	no	—
17	D₈×C₁₉	—	8	4	no	—
18	D₈×C₁₉	—	8	2	no	—
19	D₈×C₁₉	—	8	2	no	—
20	C₂×C₈×C₁₉	—	2	1	no	—
21	C₂×C₈×C₁₉	D₈	1	2	yes	—
22	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
23	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₉⋊C₁₆	—	8	2	no	—
25	#7096	—	19	1	no	maximal, Sylow
26	C₂³×C₁₉	—	8	2	no	—
27	D₄×C₁₉	—	8	4	no	—
28	D₄×C₁₉	—	8	4	no	—
29	D₄×C₁₉	—	8	4	no	—
30	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
31	C₂×C₄×C₁₉	#102	1	2	yes	—
32	C₈×C₁₉	—	2	2	no	—
33	C₈×C₁₉	—	2	2	no	—
34	C₈×C₁₉	D₁₆	1	2	yes	—
35	C₈×C₁₉	SD₃₂	1	2	yes	—
36	#1712	D₁₉	1	1	yes	characteristic
37	#1370	—	19	2	no	—
38	C₂²×C₁₉	—	16	2	no	—
39	C₂²×C₁₉	—	16	4	no	—
40	C₂²×C₁₉	#331	1	1	yes	characteristic
41	C₄×C₁₉	—	2	1	no	—
42	C₄×C₁₉	#357	1	2	yes	—
43	C₄×C₁₉	#361	1	2	yes	—
44	#493	—	2	2	no	—
45	#493	Dic₁₉	1	2	yes	—
46	C₄⋊C₁₆	—	38	2	no	—
47	C₈²	C₂×D₁₉	1	1	yes	characteristic
48	C₂×C₁₉	—	32	2	no	—
49	C₂×C₁₉	#1357	1	1	yes	characteristic
50	C₂×C₁₉	#1361	1	2	yes	—
51	C₂×D₈	—	4	2	no	—
52	C₂×D₈	—	4	2	no	—
53	C₂×D₈	—	4	2	no	—
54	#127	—	2	2	no	—
55	C₂×C₁₆	—	76	2	no	—
56	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
57	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
58	C₁₉	#7096	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₄	—	4	4	no	—
60	C₂×D₄	—	4	2	no	—
61	D₈	—	8	4	no	—
62	D₈	—	8	4	no	—
63	D₈	—	8	2	no	—
64	D₈	—	8	2	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	#64525	1	2	yes	—
67	C₂×C₈	#64526	1	2	yes	—
68	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
69	C₁₆	—	152	2	no	—
70	C₂³	—	8	2	no	—
71	D₄	—	8	4	no	—
72	D₄	—	8	4	no	—
73	D₄	—	8	4	no	—
74	C₂×C₄	#10597289	1	2	yes	—
75	C₂×C₄	#10597290	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	2	2	no	—
78	C₈	#10597283	1	2	yes	—
79	C₈	#10597284	1	2	yes	—
80	C₂²	—	16	2	no	—
81	C₂²	—	16	4	no	—
82	C₂²	#11926288	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	#11926345	1	2	yes	—
85	C₄	#11926357	1	2	yes	—
86	C₂	—	32	2	no	—
87	C₂	#14561672	1	1	yes	characteristic
88	C₂	#14561681	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting, prime radical	C₁₉×#1712	C₂
socle	C₂²×C₁₉	#331
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1712	D₁₉
hypocenter	C₁₉	#7096
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

Complements

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

N	H ≅ G/N	type
1. #14561705	C₂	semidirect
58. C₁₉	#7096	semidirect

Maximal subgroups

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

subgroup	index
#14561705	2
C₁₉×#1712	2
#7096	19