Subgroups — #14561694

Order 2432.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926949	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#335	C₂	1	1	yes	maximal, characteristic
4	#10597315	—	2	1	no	—
5	C₁₉×C₄⋊C₈	—	2	1	no	—
6	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597275	—	2	1	no	—
8	#10597275	C₄	1	2	yes	—
9	C₂×C₁₉⋊C₁₆	—	2	1	no	—
10	C₂×Dic₃₈	—	4	1	no	—
11	C₂×C₈×C₁₉	—	4	1	no	—
12	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
14	C₄²×C₁₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₉	—	2	2	no	—
16	C₄⋊Dic₁₉	—	4	1	no	—
17	C₁₉⋊C₁₆	—	4	1	no	—
18	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₁₉	—	4	2	no	—
22	Dic₃₈	—	8	2	no	—
23	C₈×C₁₉	—	2	1	no	—
24	C₈×C₁₉	—	8	1	no	—
25	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
26	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
27	#1365	—	19	1	no	maximal, Sylow
28	C₂²×C₁₉	#102	1	1	yes	characteristic
29	C₄×C₁₉	—	2	1	no	—
30	C₄×C₁₉	#101	1	1	yes	characteristic
31	C₄×C₁₉	#103	1	1	yes	characteristic
32	C₄×C₁₉	SD₃₂	1	1	yes	characteristic
33	C₄×C₁₉	Q₃₂	1	1	yes	characteristic
34	Dic₁₉	—	8	2	no	—
35	#500	—	19	1	no	—
36	C₄⋊C₁₆	—	19	1	no	—
37	#335	D₁₉	1	1	yes	characteristic
38	C₂×C₁₉	#332	1	1	yes	characteristic
39	C₂×C₁₉	#358	1	1	yes	characteristic
40	C₂×C₁₉	#361	1	1	yes	characteristic
41	C₄⋊Q₈	—	38	1	no	—
42	C₂×C₁₆	—	38	1	no	—
43	#107	—	19	2	no	—
44	#107	—	38	1	no	—
45	C₄⋊C₈	—	2	1	no	—
46	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
47	C₁₉	#1365	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	76	1	no	—
49	C₂×C₈	—	4	1	no	—
50	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
51	C₂×C₈	D₇₆	1	1	yes	characteristic
52	C₄⋊C₄	—	38	2	no	—
53	C₄⋊C₄	—	76	1	no	—
54	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
55	C₁₆	—	76	1	no	—
56	Q₈	—	152	2	no	—
57	C₂×C₄	—	76	2	no	—
58	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
59	C₂×C₄	#64525	1	1	yes	characteristic
60	C₂×C₄	#64527	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	#64516	1	1	yes	characteristic
64	C₈	Dic₇₆	1	1	yes	characteristic
65	C₂²	#10597266	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	152	2	no	—
68	C₄	#10597273	1	1	yes	characteristic
69	C₄	#10597281	1	1	yes	characteristic
70	C₄	#10597284	1	1	yes	characteristic
71	C₄	#10597286	1	1	yes	characteristic
72	C₂	#11926291	1	1	yes	characteristic
73	C₂	#11926347	1	1	yes	characteristic
74	C₂	#11926356	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10597266
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#335	C₂
socle, prime radical	C₂²×C₁₉	#102
cosocle	C₄×C₈×C₁₉	C₂²
hypercenter	#335	D₁₉
hypocenter	C₁₉	#1365
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
47. C₁₉	#1365	semidirect

Maximal subgroups

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

subgroup	index
#11926949	2
C₄⋊(C₁₉⋊C₁₆)	2
C₁₉×#335	2
#1365	19