Subgroups — #18070420

Order 4864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#14561835	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	#11926370	—	2	1	no	—
5	C₁₉⋊C₆₄	—	2	1	no	—
6	C₂×C₁₉×Q₃₂	—	2	1	no	—
7	C₁₉×Q₆₄	—	2	1	no	—
8	C₁₉×Q₆₄	C₄	1	2	yes	complemented
9	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₉	—	4	1	no	—
11	C₁₉×Q₃₂	—	2	2	no	—
12	C₁₉×Q₃₂	—	4	1	no	—
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	#10597275	—	4	1	no	—
15	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	8	1	no	—
18	Q₁₆×C₁₉	—	4	2	no	—
19	Q₁₆×C₁₉	—	8	1	no	—
20	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
21	C₄⋊Dic₁₉	—	8	1	no	—
22	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	#7538	—	19	1	no	maximal, Sylow
25	Q₈×C₁₉	—	8	2	no	—
26	Q₈×C₁₉	—	16	1	no	—
27	C₂×C₄×C₁₉	—	16	1	no	—
28	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
29	C₂×Dic₁₉	—	16	1	no	—
30	C₈×C₁₉	#102	1	1	yes	characteristic
31	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
32	C₂×Q₆₄	D₁₉	1	1	yes	characteristic
33	C₂×C₆₄	—	19	1	no	—
34	#1423	—	19	1	no	—
35	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
36	C₄×C₁₉	—	16	2	no	—
37	C₄×C₁₉	#357	1	1	yes	characteristic
38	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
39	Dic₁₉	—	32	1	no	—
40	C₂×Q₃₂	—	2	1	no	—
41	Q₆₄	—	2	1	no	—
42	Q₆₄	Dic₁₉	1	2	yes	complemented
43	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
44	#366	—	38	1	no	—
45	C₆₄	—	38	1	no	—
46	C₂×C₁₉	#1415	1	1	yes	characteristic
47	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
48	C₂×C₁₉	Q₁₂₈	1	1	yes	characteristic
49	C₂×Q₁₆	—	4	1	no	—
50	Q₃₂	—	2	2	no	—
51	Q₃₂	—	4	1	no	—
52	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
53	#107	—	76	1	no	—
54	C₃₂	C₂×Dic₁₉	1	1	yes	characteristic
55	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
56	C₁₉	#7538	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	8	1	no	—
58	Q₁₆	—	4	2	no	—
59	Q₁₆	—	8	1	no	—
60	C₂×C₈	#64525	1	1	yes	characteristic
61	C₄⋊C₄	—	152	1	no	—
62	C₁₆	#64526	1	1	yes	characteristic
63	C₁₆	C₂²⋊Dic₁₉	1	1	yes	characteristic
64	Q₈	—	8	2	no	—
65	Q₈	—	16	1	no	—
66	C₂×C₄	—	16	1	no	—
67	C₂×C₄	—	304	1	no	—
68	C₂×C₄	#10597283	1	1	yes	characteristic
69	C₈	#10597284	1	1	yes	characteristic
70	C₈	#10597289	1	1	yes	characteristic
71	C₂²	#11926379	1	1	yes	characteristic
72	C₄	—	16	2	no	—
73	C₄	—	608	1	no	—
74	C₄	#11926345	1	1	yes	characteristic
75	C₄	#11926382	1	1	yes	characteristic
76	C₂	#14561813	1	1	yes	characteristic
77	C₂	#14561849	1	1	yes	characteristic
78	C₂	#14561852	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₂×C₁₉×Q₆₄	C₂
socle, prime radical	C₂²×C₁₉	D₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	C₂×Q₆₄	D₁₉
hypocenter	C₁₉	#7538
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
8. C₁₉×Q₆₄	C₄	semidirect
42. Q₆₄	Dic₁₉	semidirect
56. C₁₉	#7538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉⋊C₆₄	2
#14561835	2
C₂×C₁₉×Q₆₄	2
#7538	19