Subgroups — #11926950

Order 1216.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#10597316	C₂	1	1	yes	maximal, characteristic
3	#10597265	C₂	1	2	yes	maximal
4	#10597264	C₂	1	2	yes	maximal
5	#10597260	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₁₉	—	2	1	no	—
7	C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	Dic₁₉⋊C₄	—	2	1	no	—
13	Dic₁₉⋊C₄	—	2	1	no	—
14	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
15	Q₈×C₁₉	—	4	2	no	—
16	C₂×C₄×C₁₉	—	2	2	no	—
17	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₉	—	2	1	no	—
21	C₂×Dic₁₉	—	2	1	no	—
22	C₁₉⋊C₈	Q₈	1	4	yes	complemented
23	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₉	—	2	1	no	—
25	C₄×C₁₉	—	2	1	no	—
26	C₄×C₁₉	—	4	2	no	—
27	C₄×C₁₉	C₂×Q₈	1	2	yes	—
28	Dic₁₉	—	4	1	no	—
29	Dic₁₉	—	4	1	no	—
30	#501	—	19	1	no	maximal, Sylow
31	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
33	C₂×C₁₉	#137	1	1	yes	characteristic
34	C₄⋊Q₈	D₁₉	1	1	yes	characteristic
35	#125	—	19	1	no	—
36	#107	—	19	2	no	—
37	#106	—	19	2	no	—
38	#97	—	19	1	no	—
39	C₁₉	#501	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×C₈	—	19	2	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	19	1	no	—
44	C₄⋊C₄	—	19	1	no	—
45	C₄⋊C₄	—	38	1	no	—
46	C₄⋊C₄	—	38	1	no	—
47	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
48	C₄²	C₂×D₁₉	1	1	yes	characteristic
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	38	1	no	—
52	C₂×C₄	—	38	1	no	—
53	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
56	C₈	—	19	4	no	—
57	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	2	no	—
61	C₄	—	76	1	no	—
62	C₄	—	76	1	no	—
63	C₄	Q₈×D₁₉	1	2	yes	—
64	C₂	#10597378	1	1	yes	characteristic
65	C₂	#10597388	1	1	yes	characteristic
66	C₂	#10597390	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#501
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
22. C₁₉⋊C₈	Q₈	semidirect
39. C₁₉	#501	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₄⋊Q₈	2
#10597316	2
#10597265	2
#10597264	2
#10597260	2
#501	19