Subgroups — #18070430

Order 4864.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₀₈	C₂	1	1	yes	maximal, characteristic
2	#14561839	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	—	2	1	no	—
5	D₆₀₈	—	2	1	no	—
6	D₆₀₈	C₄	1	2	yes	—
7	#11926374	—	2	1	no	—
8	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₉×C₆₄	—	2	1	no	—
10	C₂×D₁₅₂	—	4	1	no	—
11	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
12	#10597276	—	4	1	no	—
13	D₃₀₄	—	2	2	no	—
14	D₃₀₄	—	4	1	no	—
15	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₇₆	—	8	1	no	—
18	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
19	#64520	—	8	1	no	—
20	D₁₅₂	—	4	2	no	—
21	D₁₅₂	—	8	1	no	—
22	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	#7541	—	19	1	no	maximal, Sylow
25	C₂²×D₁₉	—	16	1	no	—
26	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
27	D₇₆	—	8	2	no	—
28	D₇₆	—	16	1	no	—
29	C₈×C₁₉	#102	1	1	yes	characteristic
30	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
31	C₁₉⋊C₈	—	16	1	no	—
32	C₂×D₃₂	—	19	1	no	—
33	M₁₂₈	D₁₉	1	1	yes	characteristic, complemented
34	#1425	—	19	1	no	—
35	C₂²×C₁₉	SD₆₄	1	1	yes	characteristic
36	C₂×D₁₉	—	16	2	no	—
37	C₂×D₁₉	—	32	2	no	—
38	C₄×C₁₉	#357	1	1	yes	characteristic
39	C₄×C₁₉	D₃₂	1	1	yes	characteristic
40	C₂×D₁₆	—	38	1	no	—
41	D₃₂	—	19	2	no	—
42	D₃₂	—	38	1	no	—
43	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
44	#368	—	38	1	no	—
45	C₆₄	—	2	1	no	—
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	#1415	1	1	yes	characteristic
48	D₁₉	—	32	2	no	—
49	C₂×D₈	—	76	1	no	—
50	D₁₆	—	38	2	no	—
51	D₁₆	—	76	1	no	—
52	C₂×C₁₆	D₇₆	1	1	yes	characteristic
53	#108	—	76	1	no	—
54	C₃₂	C₄×D₁₉	1	1	yes	characteristic
55	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
56	C₁₉	#7541	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	152	1	no	—
58	D₈	—	76	2	no	—
59	D₈	—	152	1	no	—
60	M₁₆	—	152	1	no	—
61	C₂×C₈	D₁₅₂	1	1	yes	characteristic
62	C₁₆	#64516	1	1	yes	characteristic
63	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
64	C₂³	—	304	1	no	—
65	D₄	—	304	1	no	—
66	D₄	—	152	2	no	—
67	C₂×C₄	D₃₀₄	1	1	yes	characteristic
68	C₈	—	304	1	no	—
69	C₈	#10597257	1	1	yes	characteristic
70	C₈	#10597278	1	1	yes	characteristic
71	C₂²	—	304	2	no	—
72	C₂²	—	608	2	no	—
73	C₂²	#11926383	1	1	yes	characteristic
74	C₄	#11926346	1	1	yes	characteristic
75	C₄	D₆₀₈	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	608	2	no	—
78	C₂	#14561814	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14561814
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×M₁₂₈	C₂
socle	C₂×C₁₉	#1415
prime radical	C₂×D₆₀₈	C₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₉
hypocenter	C₁₉	#7541
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #14561839	C₂	semidirect
3. C₁₉×M₁₂₈	C₂	semidirect
33. M₁₂₈	D₁₉	semidirect
56. C₁₉	#7541	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₆₀₈	2
#14561839	2
C₁₉×M₁₂₈	2
#7541	19