Group #14575434 — subgroups

Subgroups — #14575434

Order 2432.

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

normal subgroups only

This group has 476 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	#11927345	C₂	1	4	yes	maximal, complemented
2	#11926811	C₂	1	4	yes	maximal, complemented
3	#11926711	C₂	1	4	yes	maximal, complemented
4	#11926662	C₂	1	2	yes	maximal, complemented
5	C₁₉×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597430	C₂²	1	4	yes	complemented
7	C₂×D₈×C₁₉	C₂²	1	4	yes	complemented
8	C₁₉×#127	C₂²	1	2	yes	complemented
9	#10597378	C₂²	1	8	yes	complemented
10	#10597358	—	2	4	no	—
11	#10597357	—	2	8	no	—
12	D₈×D₁₉	—	2	4	no	—
13	#10597350	C₂²	1	2	yes	—
14	#10597347	C₂²	1	4	yes	complemented
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	#10597290	C₂²	1	4	yes	complemented
17	#10597276	C₂²	1	2	yes	complemented
18	#10597262	C₂²	1	4	yes	complemented
19	C₂×D₄×C₁₉	—	4	2	no	—
20	C₂×D₄×C₁₉	C₂³	1	4	yes	—
21	C₂×C₂²⋊D₁₉	—	4	4	no	—
22	#64543	—	2	8	no	—
23	D₄×D₁₉	—	2	8	no	—
24	#64541	C₂³	1	4	yes	—
25	D₈×C₁₉	—	2	4	no	—
26	D₈×C₁₉	—	2	4	no	—
27	C₂×C₈×C₁₉	C₂³	1	2	yes	—
28	C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#64526	—	2	8	no	—
30	#64525	—	2	8	no	—
31	#64520	C₂³	1	4	yes	—
32	Dic₇₆	D₄	1	2	yes	complemented
33	D₁₅₂	D₄	1	2	yes	complemented
34	#64516	D₄	1	4	yes	complemented
35	#64515	—	2	4	no	—
36	C₈×D₁₉	—	2	4	no	—
37	C₂³×C₁₉	—	2	4	no	—
38	C₂²×D₁₉	—	4	4	no	—
39	D₄×C₁₉	—	2	8	no	—
40	D₄×C₁₉	—	8	4	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
43	C₂²⋊D₁₉	—	2	4	no	—
44	C₂²⋊D₁₉	—	4	8	no	—
45	C₂×Dic₁₉	—	4	4	no	—
46	D₇₆	C₂×D₄	1	4	yes	—
47	C₄×D₁₉	—	2	4	no	—
48	Dic₃₈	C₂×D₄	1	4	yes	—
49	C₈×C₁₉	C₂×D₄	1	2	yes	—
50	C₈×C₁₉	C₂×D₄	1	2	yes	—
51	C₁₉⋊C₈	—	2	4	no	—
52	#3292	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	4	4	no	—
54	C₂²×C₁₉	—	8	4	no	—
55	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
56	C₂×D₁₉	—	2	4	no	—
57	C₂×D₁₉	—	16	4	no	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	C₂²×D₄	1	2	yes	—
60	Dic₁₉	—	2	4	no	—
61	#576	—	19	4	no	—
62	#493	D₁₉	1	1	yes	characteristic, complemented
63	#472	—	19	4	no	—
64	#453	—	19	4	no	—
65	#443	—	19	2	no	—
66	C₂×C₁₉	—	2	1	no	—
67	C₂×C₁₉	—	8	4	no	—
68	C₂×C₁₉	D₄²	1	1	yes	characteristic
69	D₁₉	—	4	4	no	—
70	H(5,𝔽₂)	—	19	4	no	—
71	AGL(1,ℤ/8)	—	19	8	no	—
72	AGL(1,ℤ/8)	—	38	8	no	—
73	#135	—	19	2	no	—
74	#135	—	38	4	no	—
75	C₂×D₈	—	38	4	no	—
76	C₂×D₈	C₂×D₁₉	1	4	yes	complemented
77	#131	—	19	4	no	—
78	#127	C₂×D₁₉	1	2	yes	complemented
79	#108	—	19	2	no	—
80	#104	—	19	4	no	—
81	#100	—	19	4	no	—
82	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
83	C₁₉	#3292	1	1	yes	characteristic, complemented, Sylow
84	#41	—	19	4	no	—
85	#41	—	38	8	no	—
86	C₂×D₄	—	4	2	no	—
87	C₂×D₄	—	38	8	no	—
88	C₂×D₄	—	76	4	no	—
89	C₂×D₄	C₂²×D₁₉	1	4	yes	—
90	Q₁₆	—	19	2	no	—
91	SD₁₆	—	19	4	no	—
92	SD₁₆	—	38	8	no	—
93	D₈	—	2	4	no	—
94	D₈	—	2	4	no	—
95	D₈	—	19	2	no	—
96	D₈	—	38	8	no	—
97	M₁₆	—	19	4	no	—
98	M₁₆	—	38	4	no	—
99	C₂×C₈	—	38	4	no	—
100	C₂×C₈	C₂²×D₁₉	1	2	yes	—
101	C₄²	C₂²×D₁₉	1	1	yes	characteristic
102	C₂³	—	2	4	no	—
103	C₂³	—	76	4	no	—
104	Q₈	—	19	4	no	—
105	D₄	—	2	8	no	—
106	D₄	—	8	4	no	—
107	D₄	—	19	4	no	—
108	D₄	—	38	4	no	—
109	D₄	—	76	8	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	38	4	no	—
112	C₂×C₄	—	76	4	no	—
113	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
114	C₈	—	38	4	no	—
115	C₈	D₄×D₁₉	1	2	yes	—
116	C₈	D₄×D₁₉	1	2	yes	—
117	C₂²	—	4	4	no	—
118	C₂²	—	8	4	no	—
119	C₂²	—	38	4	no	—
120	C₂²	—	304	4	no	—
121	C₂²	#10597430	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	38	4	no	—
124	C₄	C₂×D₄×D₁₉	1	2	yes	—
125	C₂	—	2	1	no	—
126	C₂	—	8	4	no	—
127	C₂	—	76	4	no	—
128	C₂	#11927179	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927345

C₂

yes

maximal, complemented

#11926811

C₂

yes

maximal, complemented

#11926711

C₂

yes

maximal, complemented

#11926662

C₂

yes

maximal, complemented

C₁₉×#493

C₂

yes

maximal, characteristic, complemented

#10597430

C₂²

yes

complemented

C₂×D₈×C₁₉

C₂²

yes

complemented

C₁₉×#127

C₂²

yes

complemented

#10597378

C₂²

yes

complemented

#10597358

—

#10597357

—

D₈×D₁₉

—

#10597350

C₂²

yes

—

#10597347

C₂²

yes

complemented

C₄×C₈×C₁₉

C₂²

yes

characteristic, complemented

#10597290

C₂²

yes

complemented

#10597276

C₂²

yes

complemented

#10597262

C₂²

yes

complemented

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

#64543

—

D₄×D₁₉

—

#64541

C₂³

yes

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

—

C₂³

yes

—

Dic₇₆

D₄

yes

complemented

D₁₅₂

D₄

yes

complemented

#64516

D₄

yes

complemented

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

C₂×D₄

yes

—

C₄×D₁₉

—

Dic₃₈

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

#3292

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

H(5,𝔽₂)

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²×D₄

yes

—

Dic₁₉

—

#576

—

#493

D₁₉

yes

characteristic, complemented

#472

—

#453

—

#443

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

D₄²

yes

characteristic

D₁₉

—

—

—

—

—

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

complemented

#131

—

#127

C₂×D₁₉

yes

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic, complemented

C₁₉

#3292

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²×D₁₉

yes

—

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

100

C₂×C₈

C₂²×D₁₉

yes

—

101

C₄²

C₂²×D₁₉

yes

characteristic

102

C₂³

—

103

C₂³

—

104

Q₈

—

105

D₄

—

106

D₄

—

107

D₄

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂³×D₁₉

yes

characteristic

114

C₈

—

115

C₈

D₄×D₁₉

yes

—

116

C₈

D₄×D₁₉

yes

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

304

—

121

C₂²

#10597430

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

C₂×D₄×D₁₉

yes

—

125

C₂

—

126

C₂

—

127

C₂

—

128

C₂

#11927179

yes

characteristic

	subgroup	G/H
center	C₂	#11927179
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#493	C₂
socle	C₂×C₁₉	D₄²
hypercenter	#493	D₁₉
hypocenter	C₁₉	#3292
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #493

subgroup

G/H

center

C₂

#11927179

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#493

C₂

socle

C₂×C₁₉

D₄²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #493

N	H ≅ G/N	type
1. #11927345	C₂	semidirect
2. #11926811	C₂	semidirect
3. #11926711	C₂	semidirect
4. #11926662	C₂	semidirect
5. C₁₉×#493	C₂	semidirect
6. #10597430	C₂²	semidirect
7. C₂×D₈×C₁₉	C₂²	semidirect
8. C₁₉×#127	C₂²	semidirect
9. #10597378	C₂²	semidirect
14. #10597347	C₂²	semidirect
15. C₄×C₈×C₁₉	C₂²	semidirect
16. #10597290	C₂²	semidirect
17. #10597276	C₂²	semidirect
18. #10597262	C₂²	semidirect
32. Dic₇₆	D₄	semidirect
33. D₁₅₂	D₄	semidirect
34. #64516	D₄	semidirect
62. #493	D₁₉	semidirect
76. C₂×D₈	C₂×D₁₉	semidirect
78. #127	C₂×D₁₉	semidirect
82. C₄×C₈	C₂×D₁₉	semidirect
83. C₁₉	#3292	semidirect

H ≅ G/N

type

1. #11927345

C₂

semidirect

2. #11926811

C₂

semidirect

3. #11926711

C₂

semidirect

4. #11926662

C₂

semidirect

5. C₁₉×#493

C₂

semidirect

6. #10597430

C₂²

semidirect

7. C₂×D₈×C₁₉

C₂²

semidirect

8. C₁₉×#127

C₂²

semidirect

9. #10597378

C₂²

semidirect

14. #10597347

C₂²

semidirect

15. C₄×C₈×C₁₉

C₂²

semidirect

16. #10597290

C₂²

semidirect

17. #10597276

C₂²

semidirect

18. #10597262

C₂²

semidirect

32. Dic₇₆

D₄

semidirect

33. D₁₅₂

D₄

semidirect

34. #64516

D₄

semidirect

62. #493

D₁₉

semidirect

76. C₂×D₈

C₂×D₁₉

semidirect

78. #127

C₂×D₁₉

semidirect

82. C₄×C₈

C₂×D₁₉

semidirect

83. C₁₉

#3292

semidirect

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

subgroup	index
#11927345	2
#11926811	2
#11926711	2
#11926662	2
C₁₉×#493	2
#3292	19

subgroup

index

C₁₉×#493

Subgroups — #14575434

Conjugacy classes of subgroups

Complements

Maximal subgroups