Subgroups — #11926941

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×#106	C₂	1	1	yes	maximal, characteristic
3	#10597274	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
5	#10597265	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	2	yes	—
17	Dic₃₈	—	4	4	no	—
18	C₈×C₁₉	Q₈	1	2	yes	complemented
19	C₁₉⋊C₈	Q₈	1	2	yes	complemented
20	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₁₉	—	4	2	no	—
22	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₁₉	—	4	2	no	—
25	Dic₁₉	SD₁₆	1	4	yes	—
26	#498	—	19	1	no	maximal, Sylow
27	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₁₉	C₂×SD₁₆	1	2	yes	—
29	C₄⋊Q₈	—	19	2	no	—
30	#106	—	19	1	no	—
31	#106	—	19	2	no	—
32	#106	D₁₉	1	1	yes	characteristic
33	C₄×C₈	—	19	1	no	—
34	C₁₉	#498	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	38	2	no	—
36	C₂×C₈	—	19	1	no	—
37	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
38	C₄⋊C₄	—	19	2	no	—
39	C₄⋊C₄	—	38	2	no	—
40	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
41	C₄²	—	19	1	no	—
42	Q₈	—	76	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	19	2	no	—
45	C₂×C₄	—	38	2	no	—
46	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
47	C₈	—	19	2	no	—
48	C₈	Dic₃₈	1	2	yes	complemented
49	C₂²	D₄×D₁₉	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	19	4	no	—
52	C₄	—	76	2	no	—
53	C₄	C₂×Dic₃₈	1	1	yes	characteristic
54	C₄	Q₈×D₁₉	1	1	yes	characteristic
55	C₂	#10597334	1	1	yes	characteristic
56	C₂	SD₁₆×D₁₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#106	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	#106	D₁₉
hypocenter	C₁₉	#498
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₁₉	Q₈	semidirect
19. C₁₉⋊C₈	Q₈	semidirect
34. C₁₉	#498	semidirect
48. 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×#106	2
#10597274	2
C₈×Dic₁₉	2
#10597265	2
#498	19