Group #14575439 — subgroups

Subgroups — #14575439

Order 2432.

444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927357	C₂	1	4	yes	maximal, complemented
2	#11926816	C₂	1	4	yes	maximal, complemented
3	#11926726	C₂	1	4	yes	maximal, complemented
4	#11926662	C₂	1	2	yes	maximal, complemented
5	C₁₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597433	C₂²	1	4	yes	—
7	C₂×Q₁₆×C₁₉	C₂²	1	4	yes	—
8	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
9	#10597388	C₂²	1	8	yes	—
10	#10597365	—	2	4	no	—
11	#10597364	—	2	8	no	—
12	Q₁₆×D₁₉	—	2	4	no	—
13	#10597350	C₂²	1	2	yes	—
14	#10597347	C₂²	1	4	yes	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#10597293	C₂²	1	4	yes	—
17	#10597276	C₂²	1	2	yes	—
18	#10597262	C₂²	1	4	yes	—
19	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
20	#64545	—	2	8	no	—
21	Q₈×D₁₉	—	2	8	no	—
22	#64541	—	4	4	no	—
23	#64541	C₂³	1	4	yes	—
24	Q₁₆×C₁₉	—	2	4	no	—
25	Q₁₆×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	C₂³	1	2	yes	—
27	C₄⋊C₄×C₁₉	—	4	2	no	—
28	C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#64528	—	2	8	no	—
30	#64527	—	2	8	no	—
31	#64520	C₂³	1	4	yes	—
32	Dic₇₆	D₄	1	2	yes	—
33	D₁₅₂	D₄	1	2	yes	—
34	#64516	D₄	1	4	yes	—
35	#64515	—	2	4	no	—
36	C₈×D₁₉	—	2	4	no	—
37	Q₈×C₁₉	—	2	8	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
41	C₂²⋊D₁₉	—	2	4	no	—
42	D₇₆	—	4	4	no	—
43	D₇₆	C₂×D₄	1	4	yes	—
44	C₄×D₁₉	—	2	4	no	—
45	C₄×D₁₉	—	4	8	no	—
46	Dic₃₈	—	4	4	no	—
47	Dic₃₈	C₂×D₄	1	4	yes	—
48	C₈×C₁₉	C₂×D₄	1	2	yes	—
49	C₈×C₁₉	C₂×D₄	1	2	yes	—
50	C₁₉⋊C₈	—	2	4	no	—
51	#3293	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
53	C₂×D₁₉	—	2	4	no	—
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	—	4	4	no	—
56	C₄×C₁₉	C₂²×D₄	1	2	yes	—
57	Dic₁₉	—	2	4	no	—
58	#578	—	19	4	no	—
59	#494	D₁₉	1	1	yes	characteristic, complemented
60	#473	—	19	4	no	—
61	#456	—	19	4	no	—
62	#443	—	19	2	no	—
63	C₂×C₁₉	—	2	1	no	—
64	C₂×C₁₉	D₄²	1	1	yes	characteristic
65	D₁₉	—	4	4	no	—
66	2₋¹⁺⁴	—	19	4	no	—
67	#137	—	19	8	no	—
68	#137	—	38	8	no	—
69	#135	—	19	2	no	—
70	#135	—	38	4	no	—
71	C₂×Q₁₆	—	38	4	no	—
72	C₂×Q₁₆	C₂×D₁₉	1	4	yes	—
73	#131	—	19	4	no	—
74	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
75	#108	—	19	2	no	—
76	#104	—	19	4	no	—
77	#101	—	19	4	no	—
78	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
79	C₁₉	#3293	1	1	yes	characteristic, complemented, Sylow
80	#41	—	19	4	no	—
81	#41	—	38	8	no	—
82	#41	—	76	4	no	—
83	C₂×Q₈	—	38	8	no	—
84	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
85	Q₁₆	—	2	4	no	—
86	Q₁₆	—	2	4	no	—
87	Q₁₆	—	19	2	no	—
88	Q₁₆	—	38	8	no	—
89	SD₁₆	—	19	4	no	—
90	SD₁₆	—	38	8	no	—
91	D₈	—	19	2	no	—
92	M₁₆	—	19	4	no	—
93	M₁₆	—	38	4	no	—
94	C₂×C₈	—	38	4	no	—
95	C₂×C₈	C₂²×D₁₉	1	2	yes	—
96	C₄⋊C₄	—	4	2	no	—
97	C₄²	C₂²×D₁₉	1	1	yes	characteristic
98	Q₈	—	2	8	no	—
99	Q₈	—	19	4	no	—
100	Q₈	—	76	4	no	—
101	D₄	—	19	4	no	—
102	D₄	—	38	4	no	—
103	D₄	—	76	4	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	38	4	no	—
107	C₂×C₄	—	76	8	no	—
108	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
109	C₈	—	38	4	no	—
110	C₈	D₄×D₁₉	1	2	yes	—
111	C₈	D₄×D₁₉	1	2	yes	—
112	C₂²	—	38	4	no	—
113	C₂²	#10597430	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	—	38	4	no	—
117	C₄	C₂×D₄×D₁₉	1	2	yes	—
118	C₂	—	2	1	no	—
119	C₂	—	76	4	no	—
120	C₂	#11927179	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927357

C₂

yes

maximal, complemented

#11926816

C₂

yes

maximal, complemented

#11926726

C₂

yes

maximal, complemented

#11926662

C₂

yes

maximal, complemented

C₁₉×#494

C₂

yes

maximal, characteristic, complemented

#10597433

C₂²

yes

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

#10597388

C₂²

yes

—

#10597365

—

#10597364

—

Q₁₆×D₁₉

—

#10597350

C₂²

yes

—

#10597347

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597293

C₂²

yes

—

#10597276

C₂²

yes

—

#10597262

C₂²

yes

—

C₂×Q₈×C₁₉

C₂³

yes

—

#64545

—

Q₈×D₁₉

—

#64541

—

#64541

C₂³

yes

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

—

—

C₂³

yes

—

Dic₇₆

D₄

yes

—

D₁₅₂

D₄

yes

—

#64516

D₄

yes

—

#64515

—

C₈×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

D₇₆

C₂×D₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

#578

—

#494

D₁₉

yes

characteristic, complemented

#473

—

#456

—

#443

—

C₂×C₁₉

—

C₂×C₁₉

D₄²

yes

characteristic

D₁₉

—

2₋¹⁺⁴

—

—

—

—

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

—

#131

—

C₄⋊Q₈

C₂×D₁₉

yes

—

#108

—

#104

—

#101

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#3293

yes

characteristic, complemented, Sylow

#41

—

#41

—

#41

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₁₉

yes

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

101

D₄

—

102

D₄

—

103

D₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₂³×D₁₉

yes

characteristic

109

C₈

—

110

C₈

D₄×D₁₉

yes

—

111

C₈

D₄×D₁₉

yes

—

112

C₂²

—

113

C₂²

#10597430

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×D₄×D₁₉

yes

—

118

C₂

—

119

C₂

—

120

C₂

#11927179

yes

characteristic

	subgroup	G/H
center	C₂	#11927179
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#494	C₂
socle	C₂×C₁₉	D₄²
hypercenter	#494	D₁₉
hypocenter	C₁₉	#3293
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

subgroup

G/H

center

C₂

#11927179

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#494

C₂

socle

C₂×C₁₉

D₄²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #494

N	H ≅ G/N	type
1. #11927357	C₂	semidirect
2. #11926816	C₂	semidirect
3. #11926726	C₂	semidirect
4. #11926662	C₂	semidirect
5. C₁₉×#494	C₂	semidirect
59. #494	D₁₉	semidirect
79. C₁₉	#3293	semidirect

H ≅ G/N

type

1. #11927357

C₂

semidirect

2. #11926816

C₂

semidirect

3. #11926726

C₂

semidirect

4. #11926662

C₂

semidirect

5. C₁₉×#494

C₂

semidirect

59. #494

D₁₉

semidirect

79. C₁₉

#3293

semidirect

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

subgroup	index
#11927357	2
#11926816	2
#11926726	2
#11926662	2
C₁₉×#494	2
#3293	19

subgroup

index

C₁₉×#494

Subgroups — #14575439

Conjugacy classes of subgroups

Complements

Maximal subgroups