Group #14568877 — subgroups

Subgroups — #14568877

Order 2432.

380 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 165 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	#11926483	C₂	1	4	yes	maximal
2	#11926443	C₂	1	4	yes	maximal
3	#11926409	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₁₉	C₂	1	2	yes	maximal
5	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
13	C₁₉⋊#95	C₂²	1	4	yes	—
14	C₁₉⋊#95	C₂²	1	4	yes	—
15	C₁₉⋊#95	C₂²	1	8	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
19	C₂²×Dic₁₉	C₂³	1	4	yes	—
20	C₂²×Dic₁₉	C₂³	1	4	yes	—
21	C₄⋊C₄×C₁₉	—	2	8	no	—
22	C₄⋊C₄×C₁₉	—	4	2	no	—
23	C₄²×C₁₉	Q₈	1	4	yes	—
24	C₄⋊Dic₁₉	—	2	4	no	—
25	C₄⋊Dic₁₉	—	2	4	no	—
26	C₄⋊Dic₁₉	—	4	4	no	—
27	C₄×Dic₁₉	—	2	8	no	—
28	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	2	8	no	—
32	C₂×C₄×C₁₉	—	2	4	no	—
33	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₁₉	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₁₉	#41	1	4	yes	—
36	C₂×C₄×C₁₉	#41	1	4	yes	—
37	C₂×Dic₁₉	—	2	4	no	—
38	C₂×Dic₁₉	—	2	4	no	—
39	C₂×Dic₁₉	—	2	4	no	—
40	C₂×Dic₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	—	2	4	no	—
43	#2571	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
45	C₂²×C₁₉	C₂×#41	1	2	yes	—
46	C₂²×C₁₉	C₂×#41	1	2	yes	—
47	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
48	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
49	C₄×C₁₉	—	2	2	no	—
50	C₄×C₁₉	—	4	4	no	—
51	C₄×C₁₉	#125	1	8	yes	—
52	Dic₁₉	—	4	4	no	—
53	Dic₁₉	—	4	4	no	—
54	#400	—	19	4	no	—
55	#389	—	19	4	no	—
56	#384	D₁₉	1	1	yes	characteristic
57	#382	—	19	4	no	—
58	C₄×C₄⋊C₄	—	19	2	no	—
59	C₂×C₁₉	C₂×#125	1	2	yes	—
60	C₂×C₁₉	#544	1	1	yes	characteristic
61	C₂×C₁₉	#555	1	1	yes	characteristic
62	C₂×C₁₉	#556	1	2	yes	—
63	C₂×C₁₉	#559	1	1	yes	characteristic
64	C₂×C₄⋊C₄	—	19	2	no	—
65	C₂×C₄⋊C₄	—	19	2	no	—
66	C₂×C₄⋊C₄	—	19	4	no	—
67	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
68	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
69	C₂×C₄²	—	19	4	no	—
70	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
71	#95	—	19	4	no	—
72	#95	—	19	4	no	—
73	#95	—	19	8	no	—
74	C₁₉	#2571	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	19	4	no	—
76	C₂²×C₄	—	19	4	no	—
77	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
78	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
79	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
80	C₄⋊C₄	—	2	8	no	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄⋊C₄	—	38	4	no	—
83	C₄⋊C₄	—	38	4	no	—
84	C₄⋊C₄	—	76	4	no	—
85	C₄²	—	38	8	no	—
86	C₄²	Dic₃₈	1	4	yes	—
87	C₂³	C₂³×D₁₉	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	38	4	no	—
93	C₂×C₄	—	38	4	no	—
94	C₂×C₄	—	38	4	no	—
95	C₂×C₄	—	38	4	no	—
96	C₂×C₄	—	38	4	no	—
97	C₂×C₄	—	38	4	no	—
98	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
99	C₂×C₄	C₂×Dic₃₈	1	4	yes	—
100	C₂×C₄	#64543	1	4	yes	—
101	C₂×C₄	#64545	1	4	yes	—
102	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
103	C₂²	C₂×#64543	1	2	yes	—
104	C₂²	#10597430	1	1	yes	characteristic
105	C₂²	C₂×#64545	1	2	yes	—
106	C₂²	#10597433	1	1	yes	characteristic
107	C₄	—	2	2	no	—
108	C₄	—	4	4	no	—
109	C₄	—	76	4	no	—
110	C₄	—	76	4	no	—
111	C₄	#10597336	1	8	yes	—
112	C₂	C₂×#10597336	1	2	yes	—
113	C₂	#11927175	1	1	yes	characteristic
114	C₂	#11927260	1	1	yes	characteristic
115	C₂	#11927268	1	2	yes	—
116	C₂	#11927280	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926483

C₂

yes

maximal

#11926443

C₂

yes

maximal

#11926409

C₂

yes

maximal

C₄×C₄⋊Dic₁₉

C₂

yes

maximal

C₁₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2571

—

maximal, Sylow

C₂²×C₁₉

C₂²×Q₈

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#125

yes

—

Dic₁₉

—

Dic₁₉

—

#400

—

#389

—

#384

D₁₉

yes

characteristic

#382

—

C₄×C₄⋊C₄

—

C₂×C₁₉

C₂×#125

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#559

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2571

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₃₈

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₈

yes

—

C₂×C₄

C₂×Dic₃₈

yes

—

100

C₂×C₄

#64543

yes

—

101

C₂×C₄

#64545

yes

—

102

C₂²

C₂²×Dic₃₈

yes

characteristic

103

C₂²

C₂×#64543

yes

—

104

C₂²

#10597430

yes

characteristic

105

C₂²

C₂×#64545

yes

—

106

C₂²

#10597433

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

#10597336

yes

—

112

C₂

C₂×#10597336

yes

—

113

C₂

#11927175

yes

characteristic

114

C₂

#11927260

yes

characteristic

115

C₂

#11927268

yes

—

116

C₂

#11927280

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#384	C₂
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2571
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#384

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
74. C₁₉	#2571	semidirect

H ≅ G/N

type

74. C₁₉

#2571

semidirect

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

subgroup	index
#11926483	2
#11926443	2
#11926409	2
C₄×C₄⋊Dic₁₉	2
C₁₉×#384	2
#2571	19

subgroup

index

#11926483

#11926443

#11926409

C₄×C₄⋊Dic₁₉

C₁₉×#384

#2571

Subgroups — #14568877

Conjugacy classes of subgroups

Complements

Maximal subgroups