Subgroups — #14561586

Order 2432.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926326	C₂	1	2	yes	maximal
2	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₁₉	C₄	1	1	yes	characteristic
4	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×C₄⋊C₈	—	2	2	no	—
7	#10597269	—	2	2	no	—
8	C₂²×C₄×C₁₉	—	2	1	no	—
9	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	M₁₆×C₁₉	—	4	1	no	—
11	M₁₆×C₁₉	—	4	1	no	—
12	C₂×C₈×C₁₉	—	2	1	no	—
13	C₂×C₈×C₁₉	D₄	1	2	yes	—
14	C₄²×C₁₉	—	2	1	no	—
15	C₄²×C₁₉	C₈	1	1	yes	characteristic
16	C₄²×C₁₉	C₈	1	1	yes	characteristic
17	C₁₉⋊C₁₆	—	4	2	no	—
18	C₂³×C₁₉	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	—	4	2	no	—
24	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₉	—	2	2	no	—
27	C₈×C₁₉	—	4	1	no	—
28	#1327	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	—	2	1	no	—
30	C₂²×C₁₉	—	4	1	no	—
31	C₂²×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₁₉	—	2	2	no	—
33	C₄×C₁₉	—	2	1	no	—
34	C₄×C₁₉	—	4	1	no	—
35	C₄×C₁₉	#99	1	1	yes	characteristic
36	C₄×C₁₉	#101	1	1	yes	characteristic
37	#423	D₁₉	1	1	yes	characteristic
38	#349	—	19	2	no	—
39	C₂×C₁₉	—	2	1	no	—
40	C₂×C₁₉	—	4	1	no	—
41	C₂×C₁₉	#324	1	1	yes	characteristic
42	C₂×M₁₆	Dic₁₉	1	1	yes	characteristic
43	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
44	C₂×C₄²	Dic₁₉	1	1	yes	characteristic
45	M₃₂	—	38	2	no	—
46	C₄⋊C₈	—	2	2	no	—
47	C₁₉	#1327	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
54	C₄²	—	2	1	no	—
55	C₄²	C₁₉⋊C₈	1	1	yes	characteristic
56	C₄²	C₁₉⋊C₈	1	1	yes	characteristic
57	C₁₆	—	76	2	no	—
58	C₂³	#64520	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	4	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#10597291	1	1	yes	characteristic
75	C₄	#10597293	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#11926270	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597291
commutator	C₂×C₄×C₁₉	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₁₉
Fitting	C₁₉×#423	C₂
socle	C₂×C₁₉	#324
prime radical	C₂³×C₁₉	M₁₆
cosocle	C₂×M₁₆×C₁₉	C₂²
hypercenter	#423	D₁₉
hypocenter	C₁₉	#1327
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #423

Complements

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

N	H ≅ G/N	type
47. C₁₉	#1327	semidirect

Maximal subgroups

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

subgroup	index
#11926326	2
C₁₉×#423	2
#1327	19