Subgroups — #14561510

Order 2432.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926568	C₂	1	2	yes	maximal
2	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₄	1	2	yes	—
4	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×#64520	—	2	2	no	—
6	C₁₉×C₄⋊C₈	—	2	2	no	—
7	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
8	C₄⋊(C₁₉⋊C₈)	C₄	1	4	yes	—
9	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₁₉	—	2	2	no	—
13	C₂×C₈×C₁₉	—	4	2	no	—
14	C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₄²×C₁₉	D₄	1	2	yes	—
16	#64520	—	4	2	no	—
17	#64520	—	4	2	no	—
18	C₂×C₁₉⋊C₈	—	2	4	no	—
19	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	—	4	1	no	—
23	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
29	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
30	C₈×C₁₉	—	4	2	no	—
31	C₁₉⋊C₈	—	4	4	no	—
32	#1292	—	19	1	no	maximal, Sylow
33	C₂²×C₁₉	—	2	1	no	—
34	C₂²×C₁₉	—	2	1	no	—
35	C₂²×C₁₉	#95	1	1	yes	characteristic
36	C₂²×C₁₉	#106	1	1	yes	characteristic
37	C₂²×C₁₉	#107	1	1	yes	characteristic
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	—	2	1	no	—
40	C₄×C₁₉	#100	1	1	yes	characteristic
41	C₄×C₁₉	#101	1	1	yes	characteristic
42	C₄×C₁₉	#102	1	2	yes	—
43	C₄×C₁₉	#103	1	2	yes	—
44	#423	—	19	2	no	—
45	C₂×C₄⋊C₈	D₁₉	1	1	yes	characteristic
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	2	1	no	—
48	C₂×C₁₉	#338	1	1	yes	characteristic
49	C₂×C₁₉	#340	1	1	yes	characteristic
50	C₂×C₁₉	#343	1	1	yes	characteristic
51	C₂×M₁₆	—	38	2	no	—
52	C₂²×C₈	Dic₁₉	1	2	yes	—
53	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
54	C₄⋊C₈	—	2	2	no	—
55	C₄⋊C₈	—	19	4	no	—
56	C₄⋊C₈	—	38	2	no	—
57	C₁₉	#1292	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
59	C₂²×C₄	D₇₆	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
61	M₁₆	—	76	2	no	—
62	M₁₆	—	76	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	38	4	no	—
66	C₄²	C₄×D₁₉	1	2	yes	—
67	C₄²	C₂²⋊D₁₉	1	2	yes	—
68	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#64516	1	2	yes	—
73	C₂×C₄	D₁₅₂	1	1	yes	characteristic
74	C₂×C₄	Dic₇₆	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
76	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
77	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	76	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#10597274	1	1	yes	characteristic
84	C₂²	#10597275	1	1	yes	characteristic
85	C₂²	C₁₉⋊#95	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#10597273	1	2	yes	—
89	C₄	#10597278	1	2	yes	—
90	C₄	#10597290	1	1	yes	characteristic
91	C₄	#10597293	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	C₁₉⋊#338	1	1	yes	characteristic
95	C₂	#11926307	1	1	yes	characteristic
96	C₂	#11926313	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₂×C₁₉×C₄⋊C₈	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#1292
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
57. C₁₉	#1292	semidirect

Maximal subgroups

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

subgroup	index
#11926568	2
C₂×C₁₉×C₄⋊C₈	2
#1292	19