Subgroups — #14565917

Order 2432.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926949	C₂	1	2	yes	maximal
2	#11926372	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	#10597315	—	2	2	no	—
5	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
6	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597275	—	2	2	no	—
8	#10597275	C₂²	1	4	yes	—
9	C₂×Dic₃₈	—	4	2	no	—
10	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
12	C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₄⋊Dic₁₉	—	2	4	no	—
14	C₄⋊Dic₁₉	—	4	2	no	—
15	C₁₆×C₁₉	Q₈	1	4	yes	complemented
16	C₂×C₄×C₁₉	D₈	1	2	yes	—
17	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
18	C₂×Dic₁₉	—	4	4	no	—
19	Dic₃₈	—	8	4	no	—
20	C₈×C₁₉	Q₁₆	1	2	yes	—
21	C₈×C₁₉	C₂×Q₈	1	2	yes	—
22	#2254	—	19	1	no	maximal, Sylow
23	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
24	C₄×C₁₉	SD₃₂	1	4	yes	—
25	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
26	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
27	Dic₁₉	—	8	4	no	—
28	#500	—	19	2	no	—
29	#367	—	19	4	no	—
30	C₄×C₁₆	D₁₉	1	1	yes	characteristic
31	C₂×C₁₉	#500	1	1	yes	characteristic
32	C₂×C₁₉	C₂×SD₃₂	1	2	yes	—
33	C₄⋊Q₈	—	38	2	no	—
34	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
35	#107	—	19	4	no	—
36	#107	—	38	2	no	—
37	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
38	C₁₉	#2254	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	76	2	no	—
40	C₂×C₈	D₇₆	1	1	yes	characteristic
41	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
42	C₄⋊C₄	—	38	4	no	—
43	C₄⋊C₄	—	76	2	no	—
44	C₄²	D₇₆	1	1	yes	characteristic
45	C₁₆	Dic₃₈	1	4	yes	complemented
46	Q₈	—	152	4	no	—
47	C₂×C₄	—	76	4	no	—
48	C₂×C₄	D₁₅₂	1	2	yes	—
49	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
50	C₈	Dic₇₆	1	2	yes	—
51	C₈	C₂×Dic₃₈	1	2	yes	—
52	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
53	C₄	—	152	4	no	—
54	C₄	#10597257	1	4	yes	—
55	C₄	#10597315	1	1	yes	characteristic
56	C₄	C₂×Dic₇₆	1	1	yes	characteristic
57	C₂	#11926949	1	1	yes	characteristic
58	C₂	C₂×#10597257	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2254
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₁₉	Q₈	semidirect
38. C₁₉	#2254	semidirect
45. C₁₆	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
#11926949	2
#11926372	2
C₄×C₁₆×C₁₉	2
#2254	19