Subgroups — #18069874

Order 4864.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561771	C₂	1	1	yes	maximal, characteristic
2	#14561555	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1398	C₂	1	1	yes	maximal, characteristic
4	#11926378	C₄	1	2	yes	—
5	#11926320	C₄	1	1	yes	characteristic
6	#11926265	C₄	1	1	yes	characteristic
7	C₁₉×M₆₄	C₄	1	2	yes	—
8	C₁₉×#346	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	—	2	1	no	—
13	C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₁₉×C₃₂	C₈	1	4	yes	complemented
15	C₁₉⋊C₃₂	—	2	2	no	—
16	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
17	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
18	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
19	C₂×C₁₉⋊C₈	—	4	1	no	—
20	C₁₆×C₁₉	C₂×C₈	1	2	yes	—
21	C₁₆×C₁₉	M₁₆	1	2	yes	—
22	C₁₉⋊C₁₆	—	4	1	no	—
23	#7333	—	19	1	no	maximal, Sylow
24	C₂×C₄×C₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
26	C₈×C₁₉	—	2	1	no	—
27	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
28	C₈×C₁₉	#97	1	1	yes	characteristic
29	C₁₉⋊C₈	—	8	1	no	—
30	#1398	—	19	1	no	—
31	#1398	D₁₉	1	1	yes	characteristic
32	#1313	—	19	1	no	—
33	C₂²×C₁₉	#347	1	1	yes	characteristic
34	C₄×C₁₉	—	4	1	no	—
35	C₄×C₁₉	#322	1	1	yes	characteristic
36	C₄×C₁₉	#347	1	1	yes	characteristic
37	M₆₄	—	19	2	no	—
38	M₆₄	Dic₁₉	1	2	yes	—
39	#346	—	19	1	no	—
40	#346	C₂×D₁₉	1	1	yes	characteristic
41	#322	—	19	1	no	—
42	C₂×C₁₉	—	2	1	no	—
43	C₂×C₁₉	#1313	1	1	yes	characteristic
44	C₂×C₁₆	—	38	1	no	—
45	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
46	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
47	C₄×C₈	—	38	1	no	—
48	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
49	C₃₂	—	38	2	no	—
50	C₃₂	C₁₉⋊C₈	1	4	yes	complemented
51	C₁₉	#7333	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₈	—	76	1	no	—
53	C₂×C₈	#64515	1	1	yes	characteristic
54	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
55	C₄²	#64515	1	1	yes	characteristic
56	C₁₆	—	76	1	no	—
57	C₁₆	#64515	1	2	yes	—
58	C₁₆	C₂×C₁₉⋊C₈	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	#10597272	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	152	1	no	—
63	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
64	C₈	#10597272	1	1	yes	characteristic
65	C₂²	#11926321	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	#11926265	1	1	yes	characteristic
68	C₄	#11926321	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#14561555	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926265
commutator	C₈×C₁₉	C₄×C₈
Frattini	#346	C₂×D₁₉
Fitting	C₁₉×#1398	C₂
socle	C₂×C₁₉	#1313
prime radical	C₂²×C₁₉	#347
cosocle	C₁₉×#346	C₂²
hypercenter	#1398	D₁₉
hypocenter	C₁₉	#7333
LCS	G ▷ C₈×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ #346 ◁ #1398

Complements

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

N	H ≅ G/N	type
14. C₁₉×C₃₂	C₈	semidirect
50. C₃₂	C₁₉⋊C₈	semidirect
51. C₁₉	#7333	semidirect

Maximal subgroups

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

subgroup	index
#14561771	2
#14561555	2
C₁₉×#1398	2
#7333	19