Subgroups — #18070427

Order 4864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14565944	C₂	1	1	yes	maximal, characteristic
2	#14561837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926976	—	2	1	no	—
5	Dic₃₀₄	C₄	1	1	yes	characteristic, complemented
6	#11926383	—	2	1	no	—
7	D₆₀₈	C₄	1	1	yes	characteristic, complemented
8	#11926370	—	2	1	no	—
9	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×C₆₄	—	2	1	no	—
11	#10597350	—	4	1	no	—
12	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
13	#10597275	—	4	1	no	—
14	Dic₁₅₂	—	2	1	no	—
15	#10597257	—	4	1	no	—
16	D₃₀₄	—	2	1	no	—
17	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₉×C₃₂	D₄	1	1	yes	characteristic
19	#64541	—	8	1	no	—
20	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	8	1	no	—
22	Dic₇₆	—	4	1	no	—
23	D₁₅₂	—	4	1	no	—
24	#64516	—	8	1	no	—
25	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
27	#7540	—	19	1	no	maximal, Sylow
28	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
29	C₂²⋊D₁₉	—	16	1	no	—
30	C₂×Dic₁₉	—	16	1	no	—
31	D₇₆	—	8	1	no	—
32	C₄×D₁₉	—	16	1	no	—
33	Dic₃₈	—	8	1	no	—
34	C₈×C₁₉	#102	1	1	yes	characteristic
35	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
36	#2262	—	19	1	no	—
37	M₁₂₈	D₁₉	1	1	yes	characteristic, complemented
38	#1424	—	19	1	no	—
39	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
40	C₂×D₁₉	—	16	1	no	—
41	C₄×C₁₉	#357	1	1	yes	characteristic
42	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
43	Dic₁₉	—	16	1	no	—
44	Dic₁₉	—	32	1	no	—
45	#508	—	38	1	no	—
46	Q₆₄	—	19	1	no	—
47	SD₆₄	—	38	1	no	—
48	D₃₂	—	19	1	no	—
49	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
50	#366	—	38	1	no	—
51	C₆₄	—	2	1	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	#1415	1	1	yes	characteristic
54	D₁₉	—	32	1	no	—
55	#135	—	76	1	no	—
56	Q₃₂	—	38	1	no	—
57	SD₃₂	—	76	1	no	—
58	D₁₆	—	38	1	no	—
59	C₂×C₁₆	D₇₆	1	1	yes	characteristic
60	#107	—	76	1	no	—
61	C₃₂	C₄×D₁₉	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₁₉	#7540	1	1	yes	characteristic, complemented, Sylow
64	#41	—	152	1	no	—
65	Q₁₆	—	76	1	no	—
66	SD₁₆	—	152	1	no	—
67	D₈	—	76	1	no	—
68	C₂×C₈	D₁₅₂	1	1	yes	characteristic
69	C₄⋊C₄	—	152	1	no	—
70	C₁₆	#64516	1	1	yes	characteristic
71	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
72	Q₈	—	152	1	no	—
73	D₄	—	304	1	no	—
74	D₄	—	152	1	no	—
75	C₂×C₄	—	304	1	no	—
76	C₂×C₄	—	304	1	no	—
77	C₂×C₄	D₃₀₄	1	1	yes	characteristic
78	C₈	#10597257	1	1	yes	characteristic
79	C₈	#10597278	1	1	yes	characteristic
80	C₂²	—	304	1	no	—
81	C₂²	D₆₀₈	1	1	yes	characteristic
82	C₄	—	304	1	no	—
83	C₄	—	608	1	no	—
84	C₄	#11926346	1	1	yes	characteristic
85	C₄	#11926383	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	608	1	no	—
88	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	#14565944	C₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₉
hypocenter	C₁₉	#7540
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. #14561837	C₂	semidirect
3. C₁₉×M₁₂₈	C₂	semidirect
5. Dic₃₀₄	C₄	semidirect
7. D₆₀₈	C₄	semidirect
37. M₁₂₈	D₁₉	semidirect
63. C₁₉	#7540	semidirect

Maximal subgroups

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

subgroup	index
#14565944	2
#14561837	2
C₁₉×M₁₂₈	2
#7540	19