Group #14564987 — subgroups

Subgroups — #14564987

Order 2432.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926416	C₂	1	3	yes	maximal
2	#11926311	C₂	1	3	yes	maximal
3	C₁₉×#543	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×C₂²⋊Q₈	—	2	3	no	—
6	C₁₉×C₂²⋊Q₈	—	2	3	no	—
7	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
8	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
9	C₂×Dic₁₉⋊C₄	—	2	3	no	—
10	C₁₉⋊#95	—	2	3	no	—
11	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×Q₈×C₁₉	—	2	1	no	—
13	C₂×Q₈×C₁₉	—	2	1	no	—
14	C₂²×C₄×C₁₉	D₄	1	3	yes	—
15	C₂²×C₄×C₁₉	D₄	1	3	yes	—
16	C₂²×Dic₁₉	—	2	3	no	—
17	C₂²×Dic₁₉	—	2	3	no	—
18	C₂²×Dic₁₉	—	4	2	no	—
19	C₄⋊C₄×C₁₉	—	2	3	no	—
20	C₄⋊C₄×C₁₉	—	2	3	no	—
21	C₂²⋊C₄×C₁₉	—	2	6	no	—
22	C₂²⋊Dic₁₉	—	2	3	no	—
23	C₂²⋊Dic₁₉	Q₈	1	6	yes	complemented
24	Dic₁₉⋊C₄	—	4	6	no	—
25	C₂³×C₁₉	—	4	1	no	—
26	C₂³×C₁₉	—	4	1	no	—
27	C₂³×C₁₉	C₂×D₄	1	3	yes	—
28	C₂³×C₁₉	C₂×Q₈	1	3	yes	—
29	C₂³×C₁₉	#41	1	1	yes	characteristic
30	Q₈×C₁₉	—	8	1	no	—
31	Q₈×C₁₉	—	8	1	no	—
32	C₂×C₄×C₁₉	—	2	3	no	—
33	C₂×C₄×C₁₉	—	2	3	no	—
34	C₂×C₄×C₁₉	—	4	3	no	—
35	C₂×C₄×C₁₉	—	4	3	no	—
36	C₂×Dic₁₉	—	2	6	no	—
37	C₂×Dic₁₉	—	2	6	no	—
38	C₂×Dic₁₉	—	4	3	no	—
39	C₂×Dic₁₉	—	4	3	no	—
40	C₂×Dic₁₉	—	4	3	no	—
41	C₂×Dic₁₉	—	4	1	no	—
42	#2062	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	2	3	no	—
44	C₂²×C₁₉	—	2	3	no	—
45	C₂²×C₁₉	—	4	3	no	—
46	C₂²×C₁₉	—	4	1	no	—
47	C₂²×C₁₉	#120	1	1	yes	characteristic
48	C₂²×C₁₉	C₂²⋊Q₈	1	3	yes	—
49	C₂²×C₁₉	C₄⋊Q₈	1	3	yes	—
50	C₄×C₁₉	—	4	3	no	—
51	C₄×C₁₉	—	4	3	no	—
52	Dic₁₉	—	4	6	no	—
53	Dic₁₉	—	4	2	no	—
54	#543	D₁₉	1	1	yes	characteristic
55	#385	—	19	3	no	—
56	#342	—	19	3	no	—
57	C₂×C₁₉	—	2	3	no	—
58	C₂×C₁₉	—	2	3	no	—
59	C₂×C₁₉	#395	1	1	yes	characteristic
60	C₂×C₁₉	B(4,𝔽₂)	1	1	yes	characteristic
61	C₂×C₁₉	#458	1	1	yes	characteristic
62	C₂³×C₄	—	19	1	no	—
63	C₂²⋊Q₈	—	2	3	no	—
64	C₂²⋊Q₈	—	2	3	no	—
65	C₂×C₄⋊C₄	—	38	3	no	—
66	C₂×C₂²⋊C₄	—	19	3	no	—
67	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
68	#95	—	38	3	no	—
69	C₁₉	#2062	1	1	yes	characteristic, complemented, Sylow
70	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
71	C₂×Q₈	—	2	1	no	—
72	C₂×Q₈	—	2	1	no	—
73	C₂²×C₄	—	38	3	no	—
74	C₂²×C₄	—	38	3	no	—
75	C₂²×C₄	—	76	2	no	—
76	C₂²×C₄	C₂²⋊D₁₉	1	3	yes	—
77	C₂²×C₄	C₂²⋊D₁₉	1	3	yes	—
78	C₄⋊C₄	—	2	3	no	—
79	C₄⋊C₄	—	2	3	no	—
80	C₄⋊C₄	—	76	6	no	—
81	C₂²⋊C₄	—	2	6	no	—
82	C₂²⋊C₄	—	19	6	no	—
83	C₂²⋊C₄	—	38	3	no	—
84	C₂³	—	4	1	no	—
85	C₂³	—	4	1	no	—
86	C₂³	Q₈×D₁₉	1	3	yes	—
87	C₂³	#64545	1	1	yes	characteristic
88	C₂³	C₂×C₂²⋊D₁₉	1	3	yes	—
89	Q₈	—	8	1	no	—
90	Q₈	—	8	1	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	4	3	no	—
94	C₂×C₄	—	4	3	no	—
95	C₂×C₄	—	38	6	no	—
96	C₂×C₄	—	38	6	no	—
97	C₂×C₄	—	76	3	no	—
98	C₂×C₄	—	76	3	no	—
99	C₂×C₄	—	76	3	no	—
100	C₂×C₄	—	76	1	no	—
101	C₂²	—	2	3	no	—
102	C₂²	—	2	3	no	—
103	C₂²	—	4	3	no	—
104	C₂²	—	4	1	no	—
105	C₂²	#10597390	1	3	yes	—
106	C₂²	#10597392	1	3	yes	—
107	C₂²	#10597399	1	1	yes	characteristic
108	C₄	—	4	3	no	—
109	C₄	—	4	3	no	—
110	C₄	—	76	6	no	—
111	C₄	—	76	2	no	—
112	C₂	—	2	3	no	—
113	C₂	—	2	3	no	—
114	C₂	#11926463	1	1	yes	characteristic
115	C₂	#11926731	1	1	yes	characteristic
116	C₂	#11926734	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926416

C₂

yes

maximal

#11926311

C₂

yes

maximal

C₁₉×#543

C₂

yes

maximal, characteristic

C₂³×Dic₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₁₉⋊#95

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

Q₈

yes

complemented

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2062

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#543

D₁₉

yes

characteristic

#385

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

C₁₉

#2062

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

Q₈×D₁₉

yes

—

C₂³

#64545

yes

characteristic

C₂³

C₂×C₂²⋊D₁₉

yes

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

#10597390

yes

—

106

C₂²

#10597392

yes

—

107

C₂²

#10597399

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₂

—

113

C₂

—

114

C₂

#11926463

yes

characteristic

115

C₂

#11926731

yes

characteristic

116

C₂

#11926734

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, prime radical, cosocle	C₂⁴×C₁₉	C₂³
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#543	C₂
socle	C₂²×C₁₉	#120
hypercenter	#543	D₁₉
hypocenter	C₁₉	#2062
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂²

#10597399

commutator, prime radical, cosocle

C₂⁴×C₁₉

C₂³

Frattini

C₂⁴

C₂²×D₁₉

Fitting

C₁₉×#543

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
23. C₂²⋊Dic₁₉	Q₈	semidirect
69. C₁₉	#2062	semidirect

H ≅ G/N

type

23. C₂²⋊Dic₁₉

Q₈

semidirect

69. C₁₉

#2062

semidirect

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

subgroup	index
#11926416	2
#11926311	2
C₁₉×#543	2
#2062	19

subgroup

index

#11926416

#11926311

C₁₉×#543

#2062

Subgroups — #14564987

Conjugacy classes of subgroups

Complements

Maximal subgroups