Subgroups — #14561737

Order 2432.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926582	C₂	1	2	yes	maximal
2	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
4	#10597372	—	2	2	no	—
5	C₁₉×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₁₉	C₄	1	2	yes	complemented
7	#10597275	—	2	2	no	—
8	#10597274	C₄	1	4	yes	complemented
9	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₉	D₄	1	2	yes	—
13	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₁₉	—	4	2	no	—
15	C₄⋊Dic₁₉	—	2	4	no	—
16	C₄×Dic₁₉	—	4	2	no	—
17	C₁₆×C₁₉	—	2	2	no	—
18	C₂³×C₁₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
22	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₁₉	—	4	4	no	—
24	C₈×C₁₉	C₄²	1	1	yes	characteristic
25	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
27	#1384	—	19	1	no	maximal, Sylow
28	C₂²×C₁₉	—	4	1	no	—
29	C₂²×C₁₉	#102	1	2	yes	—
30	C₂²×C₁₉	#107	1	1	yes	characteristic
31	C₄×C₁₉	#95	1	1	yes	characteristic
32	C₄×C₁₉	#103	1	2	yes	—
33	C₄×C₁₉	#106	1	1	yes	characteristic
34	Dic₁₉	—	8	4	no	—
35	C₂×M₃₂	D₁₉	1	1	yes	characteristic
36	#427	—	19	2	no	—
37	C₂×C₁₉	—	2	2	no	—
38	C₂×C₁₉	—	2	1	no	—
39	C₂×C₁₉	#340	1	1	yes	characteristic
40	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
41	#117	—	38	2	no	—
42	M₃₂	—	2	2	no	—
43	C₂×C₁₆	Dic₁₉	1	2	yes	complemented
44	#107	—	38	2	no	—
45	#106	—	19	4	no	—
46	C₁₉	#1384	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	D₇₆	1	1	yes	characteristic
48	C₂×C₈	Dic₃₈	1	1	yes	characteristic
49	C₂×C₈	C₄×D₁₉	1	2	yes	—
50	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
52	C₄⋊C₄	—	38	4	no	—
53	C₂²⋊C₄	—	76	2	no	—
54	C₄²	—	76	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₁₅₂	1	1	yes	characteristic
57	C₂×C₄	—	76	4	no	—
58	C₂×C₄	#64516	1	2	yes	—
59	C₂×C₄	Dic₇₆	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
61	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
62	C₈	C₄×Dic₁₉	1	1	yes	characteristic
63	C₈	Dic₁₉⋊C₄	1	2	yes	—
64	C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#10597275	1	1	yes	characteristic
67	C₂²	#10597278	1	2	yes	—
68	C₄	—	152	4	no	—
69	C₄	#10597273	1	2	yes	—
70	C₄	#10597274	1	1	yes	characteristic
71	C₄	C₁₉⋊#95	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#11926307	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597274
commutator	C₈×C₁₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	D₈
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#1384
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₆×C₁₉	C₄	semidirect
8. #10597274	C₄	semidirect
43. C₂×C₁₆	Dic₁₉	semidirect
46. C₁₉	#1384	semidirect

Maximal subgroups

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

subgroup	index
#11926582	2
C₂×C₁₉×M₃₂	2
#1384	19