Subgroups — #18070214

Order 4864.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561833	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926378	—	2	2	no	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₈²×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₉	—	2	1	no	—
12	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₁₉⋊C₃₂	—	4	2	no	—
14	C₂×C₈×C₁₉	—	2	2	no	—
15	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
18	C₁₆×C₁₉	—	2	1	no	—
19	C₁₆×C₁₉	—	2	1	no	—
20	C₁₆×C₁₉	C₁₆	1	2	yes	—
21	C₁₆×C₁₉	D₈	1	1	yes	characteristic
22	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
23	#7459	—	19	1	no	maximal, Sylow
24	C₂×C₄×C₁₉	—	2	1	no	—
25	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₉	—	2	4	no	—
27	C₈×C₁₉	#107	1	1	yes	characteristic
28	C₈×C₁₉	#108	1	1	yes	characteristic
29	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
30	C₈×C₁₉	M₃₂	1	1	yes	characteristic
31	#1422	—	19	2	no	—
32	C₈×C₁₆	D₁₉	1	1	yes	characteristic
33	C₂²×C₁₉	#364	1	1	yes	characteristic
34	C₄×C₁₉	—	2	2	no	—
35	C₄×C₁₉	#335	1	1	yes	characteristic
36	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
37	M₆₄	—	38	2	no	—
38	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
39	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
40	C₈²	Dic₁₉	1	1	yes	characteristic
41	C₂×C₁₉	—	2	1	no	—
42	C₂×C₁₉	#1370	1	1	yes	characteristic
43	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
44	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
45	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
46	C₂×C₁₆	D₇₆	1	1	yes	characteristic
47	C₄×C₈	—	2	1	no	—
48	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
49	C₃₂	—	76	2	no	—
50	C₁₉	#7459	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
53	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
54	C₄²	#64520	1	1	yes	characteristic
55	C₁₆	—	2	1	no	—
56	C₁₆	—	2	1	no	—
57	C₁₆	C₁₉⋊C₁₆	1	2	yes	—
58	C₁₆	D₁₅₂	1	1	yes	characteristic
59	C₁₆	Dic₇₆	1	1	yes	characteristic
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
64	C₈	#10597269	1	1	yes	characteristic
65	C₈	#10597275	1	1	yes	characteristic
66	C₈	#10597276	1	1	yes	characteristic
67	C₂²	#11926365	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#11926297	1	1	yes	characteristic
70	C₄	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14561705	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₁₅₂
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₈×C₁₆×C₁₉	C₂
socle	C₂×C₁₉	#1370
prime radical	C₂²×C₁₉	#364
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	C₈×C₁₆	D₁₉
hypocenter	C₁₉	#7459
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
50. C₁₉	#7459	semidirect

Maximal subgroups

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

subgroup	index
#14561833	2
C₈×C₁₆×C₁₉	2
#7459	19