Subgroups — #18069279

Order 4864.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561705	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₉	C₄	1	1	yes	characteristic
6	C₈²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₉	—	2	1	no	—
8	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₈	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	—	4	2	no	—
14	C₂×C₈×C₁₉	—	2	1	no	—
15	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
17	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
18	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
19	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
20	C₁₆×C₁₉	—	2	2	no	—
21	C₁₆×C₁₉	—	2	1	no	—
22	C₁₆×C₁₉	C₁₆	1	2	yes	complemented
23	C₁₉⋊C₁₆	—	8	2	no	—
24	#7100	—	19	1	no	maximal, Sylow
25	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
27	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
28	C₈×C₁₉	—	2	2	no	—
29	C₈×C₁₉	—	2	1	no	—
30	C₈×C₁₉	—	2	1	no	—
31	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₁₉	M₃₂	1	1	yes	characteristic
33	C₈×C₁₉	D₁₆	1	1	yes	characteristic
34	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
35	#1370	—	19	2	no	—
36	C₈×C₁₆	D₁₉	1	1	yes	characteristic
37	C₂²×C₁₉	#335	1	1	yes	characteristic
38	C₄×C₁₉	—	2	1	no	—
39	C₄×C₁₉	C₄⋊C₁₆	1	1	yes	characteristic
40	C₄×C₁₉	#364	1	1	yes	characteristic
41	C₄×C₁₉	#366	1	1	yes	characteristic
42	C₄×C₁₉	#368	1	1	yes	characteristic
43	C₄⋊C₁₆	—	38	2	no	—
44	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
45	C₄×C₁₆	Dic₁₉	1	1	yes	characteristic
46	C₈²	C₂×D₁₉	1	1	yes	characteristic
47	C₂×C₁₉	#1370	1	1	yes	characteristic
48	C₂×C₁₉	#1371	1	1	yes	characteristic
49	C₂×C₁₉	#1373	1	1	yes	characteristic
50	C₂×C₁₆	—	2	1	no	—
51	C₂×C₁₆	—	76	2	no	—
52	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
53	C₂×C₁₆	C₁₉⋊C₈	1	1	yes	characteristic
54	C₄×C₈	Dic₃₈	1	1	yes	characteristic
55	C₄×C₈	D₇₆	1	1	yes	characteristic
56	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
57	C₁₉	#7100	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	D₁₅₂	1	1	yes	characteristic
60	C₂×C₈	Dic₇₆	1	1	yes	characteristic
61	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
62	C₂×C₈	#64520	1	1	yes	characteristic
63	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
64	C₁₆	—	2	2	no	—
65	C₁₆	—	2	1	no	—
66	C₁₆	—	152	2	no	—
67	C₁₆	C₁₉⋊C₁₆	1	2	yes	complemented
68	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
69	C₂×C₄	#10597275	1	1	yes	characteristic
70	C₂×C₄	#10597276	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₈	—	2	1	no	—
73	C₈	—	2	1	no	—
74	C₈	D₃₀₄	1	1	yes	characteristic
75	C₈	Dic₁₅₂	1	1	yes	characteristic
76	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
77	C₈	#10597269	1	1	yes	characteristic
78	C₂²	#11926297	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	C₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
81	C₄	#11926365	1	1	yes	characteristic
82	C₄	#11926370	1	1	yes	characteristic
83	C₄	#11926374	1	1	yes	characteristic
84	C₂	#14561705	1	1	yes	characteristic
85	C₂	#14561707	1	1	yes	characteristic
86	C₂	#14561711	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₁₅₂
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₈²	C₂×D₁₉
Fitting	C₈×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	#335
cosocle	C₈²×C₁₉	C₂²
hypercenter	C₈×C₁₆	D₁₉
hypocenter	C₁₉	#7100
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₁₆×C₁₉	C₁₆	semidirect
57. C₁₉	#7100	semidirect
67. C₁₆	C₁₉⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
#14561705	2
C₈×C₁₆×C₁₉	2
#7100	19