Subgroups — #11926948

Order 1216.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597334	C₂	1	2	yes	maximal
2	C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	#10597275	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
5	#10597264	C₂	1	2	yes	maximal
6	C₂×Dic₃₈	—	2	2	no	—
7	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	Dic₁₉⋊C₄	—	2	2	no	—
11	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₉	—	2	2	no	—
14	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₉	—	2	2	no	—
16	C₂×Dic₁₉	D₄	1	1	yes	characteristic
17	C₂×Dic₁₉	D₄	1	1	yes	characteristic
18	Dic₃₈	—	4	4	no	—
19	C₈×C₁₉	Q₈	1	2	yes	complemented
20	C₁₉⋊C₈	Q₈	1	2	yes	complemented
21	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₉	—	4	2	no	—
23	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
25	Dic₁₉	—	4	2	no	—
26	Dic₁₉	D₈	1	2	yes	—
27	Dic₁₉	Q₁₆	1	2	yes	—
28	#500	—	19	1	no	maximal, Sylow
29	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
30	C₂×C₁₉	C₂×D₈	1	1	yes	characteristic
31	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
32	C₄⋊Q₈	—	19	2	no	—
33	#107	—	19	1	no	—
34	#107	—	19	2	no	—
35	#107	D₁₉	1	1	yes	characteristic
36	C₄×C₈	—	19	1	no	—
37	C₁₉	#500	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₈	—	38	2	no	—
39	C₂×C₈	—	19	1	no	—
40	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
41	C₄⋊C₄	—	19	2	no	—
42	C₄⋊C₄	—	38	2	no	—
43	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
44	C₄²	—	19	1	no	—
45	Q₈	—	76	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	19	1	no	—
48	C₂×C₄	—	19	1	no	—
49	C₂×C₄	—	38	2	no	—
50	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
51	C₈	—	19	2	no	—
52	C₈	Dic₃₈	1	2	yes	complemented
53	C₂²	D₄×D₁₉	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	19	2	no	—
56	C₄	—	19	2	no	—
57	C₄	—	76	2	no	—
58	C₄	C₂×Dic₃₈	1	1	yes	characteristic
59	C₄	Q₈×D₁₉	1	1	yes	characteristic
60	C₂	#10597334	1	1	yes	characteristic
61	C₂	D₈×D₁₉	1	1	yes	characteristic
62	C₂	Q₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#107	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	#107	D₁₉
hypocenter	C₁₉	#500
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₁₉	Q₈	semidirect
20. C₁₉⋊C₈	Q₈	semidirect
37. C₁₉	#500	semidirect
52. C₈	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
#10597334	2
C₁₉×#107	2
#10597275	2
C₈×Dic₁₉	2
#10597264	2
#500	19