Subgroups — #18070218

Order 4864.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561707	C₂	1	2	yes	maximal
2	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#11926297	—	2	2	no	—
4	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₃₂	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
9	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
10	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
11	C₁₉×C₃₂	—	2	1	no	—
12	C₁₉×C₃₂	C₈	1	2	yes	complemented
13	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
15	C₄²×C₁₉	D₈	1	1	yes	characteristic
16	C₂×C₁₉⋊C₈	—	8	2	no	—
17	C₁₆×C₁₉	—	2	1	no	—
18	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
20	#7461	—	19	1	no	maximal, Sylow
21	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
22	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
24	C₈×C₁₉	—	2	1	no	—
25	C₈×C₁₉	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₉	#108	1	1	yes	characteristic
27	C₁₉⋊C₈	—	16	2	no	—
28	C₄×C₃₂	D₁₉	1	1	yes	characteristic
29	#1371	—	19	2	no	—
30	C₂²×C₁₉	#366	1	1	yes	characteristic
31	C₄×C₁₉	—	2	1	no	—
32	C₄×C₁₉	#335	1	1	yes	characteristic
33	C₄×C₁₉	#368	1	1	yes	characteristic
34	C₄×C₁₉	SD₆₄	1	2	yes	—
35	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
36	C₂×C₃₂	Dic₁₉	1	1	yes	characteristic
37	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
38	#335	—	38	2	no	—
39	C₂×C₁₉	#1371	1	1	yes	characteristic
40	C₂×C₁₉	#1424	1	1	yes	characteristic
41	C₂×C₁₉	#1425	1	1	yes	characteristic
42	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
43	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
44	C₄⋊C₈	—	76	2	no	—
45	C₄×C₈	D₇₆	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	C₁₉⋊C₈	1	2	yes	complemented
48	C₁₉	#7461	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₈	—	152	2	no	—
50	C₂×C₈	Dic₇₆	1	1	yes	characteristic
51	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
52	C₄²	D₁₅₂	1	1	yes	characteristic
53	C₁₆	—	2	1	no	—
54	C₁₆	C₂×C₁₉⋊C₈	1	1	yes	characteristic
55	C₁₆	#64520	1	1	yes	characteristic
56	C₂×C₄	D₃₀₄	1	1	yes	characteristic
57	C₂×C₄	Dic₁₅₂	1	1	yes	characteristic
58	C₂×C₄	#10597275	1	1	yes	characteristic
59	C₈	—	2	1	no	—
60	C₈	—	304	2	no	—
61	C₈	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
62	C₈	#10597276	1	1	yes	characteristic
63	C₂²	#11926370	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	#11926297	1	1	yes	characteristic
66	C₄	#11926374	1	1	yes	characteristic
67	C₄	#11926383	1	2	yes	—
68	C₂	#14561707	1	1	yes	characteristic
69	C₂	#14561837	1	1	yes	characteristic
70	C₂	#14561839	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃₀₄
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₄×C₁₉×C₃₂	C₂
socle, prime radical	C₂²×C₁₉	#366
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	C₄×C₃₂	D₁₉
hypocenter	C₁₉	#7461
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
12. C₁₉×C₃₂	C₈	semidirect
47. C₃₂	C₁₉⋊C₈	semidirect
48. C₁₉	#7461	semidirect

Maximal subgroups

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

subgroup	index
#14561707	2
C₄×C₁₉×C₃₂	2
#7461	19