Subgroups — #11926952

Order 1216.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597336	C₂	1	1	yes	maximal, characteristic
2	#10597334	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#107	C₂	1	1	yes	maximal, characteristic
4	#10597274	C₂	1	1	yes	maximal, characteristic
5	#10597272	C₂	1	1	yes	maximal, characteristic
6	#10597265	C₂	1	1	yes	maximal, characteristic
7	#10597264	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₈	—	2	1	no	—
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₉	—	2	1	no	—
13	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	Dic₁₉⋊C₄	—	2	1	no	—
16	Dic₁₉⋊C₄	—	2	1	no	—
17	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₉	—	2	1	no	—
23	C₂×Dic₁₉	—	2	1	no	—
24	C₂×Dic₁₉	D₄	1	1	yes	characteristic
25	C₂×Dic₁₉	D₄	1	1	yes	characteristic
26	Dic₃₈	—	4	2	no	—
27	C₈×C₁₉	Q₈	1	2	yes	complemented
28	C₁₉⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₉	—	4	1	no	—
31	C₄×C₁₉	—	4	1	no	—
32	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₁₉	—	2	1	no	—
35	Dic₁₉	—	2	1	no	—
36	Dic₁₉	—	4	1	no	—
37	Dic₁₉	—	4	1	no	—
38	#501	—	19	1	no	maximal, Sylow
39	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×C₁₉	#137	1	1	yes	characteristic
42	C₄⋊Q₈	—	19	1	no	—
43	#125	—	19	1	no	—
44	#107	—	19	1	no	—
45	#107	D₁₉	1	1	yes	characteristic
46	#106	—	19	1	no	—
47	#106	—	19	1	no	—
48	#97	—	19	1	no	—
49	C₁₉	#501	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	38	1	no	—
51	C₂×C₈	—	19	1	no	—
52	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
53	C₄⋊C₄	—	19	1	no	—
54	C₄⋊C₄	—	19	1	no	—
55	C₄⋊C₄	—	38	1	no	—
56	C₄⋊C₄	—	38	1	no	—
57	C₄⋊C₄	—	38	1	no	—
58	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
60	C₄²	—	19	1	no	—
61	Q₈	—	76	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	19	1	no	—
65	C₂×C₄	—	19	1	no	—
66	C₂×C₄	—	38	1	no	—
67	C₂×C₄	—	38	1	no	—
68	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
69	C₈	—	19	2	no	—
70	C₈	Dic₃₈	1	2	yes	complemented
71	C₂²	D₄×D₁₉	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	38	1	no	—
75	C₄	—	38	1	no	—
76	C₄	—	76	1	no	—
77	C₄	—	76	1	no	—
78	C₄	C₂×Dic₃₈	1	1	yes	characteristic
79	C₄	Q₈×D₁₉	1	1	yes	characteristic
80	C₂	#10597334	1	1	yes	characteristic
81	C₂	#10597357	1	1	yes	characteristic
82	C₂	#10597364	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	#501
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
27. C₈×C₁₉	Q₈	semidirect
28. C₁₉⋊C₈	Q₈	semidirect
49. C₁₉	#501	semidirect
70. C₈	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
#10597336	2
#10597334	2
C₁₉×#107	2
#10597274	2
#10597272	2
#10597265	2
#10597264	2
#501	19