Group #14576746 — subgroups

Subgroups — C₂×Q₃₂×D₁₉ #14576746

Order 2432.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂×Q₁₆×D₁₉	C₂	1	2	yes	maximal
2	C₂×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597286	C₂	1	2	yes	maximal, complemented
4	Q₃₂×D₁₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈×D₁₉	—	2	2	no	—
8	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
9	C₂×#64528	—	2	2	no	—
10	Q₁₆×D₁₉	—	2	4	no	—
11	Q₁₆×D₁₉	C₂²	1	8	yes	—
12	C₂×Dic₇₆	C₂²	1	2	yes	—
13	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×Q₃₂	C₂²	1	4	yes	complemented
15	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	#10597286	C₂²	1	8	yes	complemented
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
18	Dic₁₅₂	C₂²	1	4	yes	complemented
19	C₁₆×D₁₉	C₂²	1	4	yes	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	Q₈×D₁₉	—	2	8	no	—
22	Q₈×D₁₉	—	4	4	no	—
23	C₂×C₄×D₁₉	—	4	2	no	—
24	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
25	C₂×Dic₃₈	—	2	2	no	—
26	C₂×Dic₃₈	—	4	2	no	—
27	Q₁₆×C₁₉	—	2	2	no	—
28	Q₁₆×C₁₉	C₂³	1	4	yes	—
29	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
30	#64528	—	2	8	no	—
31	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
32	Dic₇₆	—	2	2	no	—
33	Dic₇₆	C₂³	1	4	yes	—
34	C₈×D₁₉	D₄	1	2	yes	—
35	C₈×D₁₉	C₂³	1	2	yes	—
36	C₁₆×C₁₉	C₂³	1	2	yes	—
37	C₁₉⋊C₁₆	C₂³	1	2	yes	—
38	C₂²×D₁₉	D₈	1	1	yes	characteristic
39	Q₈×C₁₉	—	2	4	no	—
40	Q₈×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×Dic₁₉	—	4	2	no	—
44	C₂×Dic₁₉	D₈	1	1	yes	characteristic
45	C₄×D₁₉	—	4	8	no	—
46	C₄×D₁₉	D₈	1	2	yes	—
47	C₄×D₁₉	C₂×D₄	1	2	yes	—
48	Dic₃₈	—	2	4	no	—
49	Dic₃₈	—	4	2	no	—
50	Dic₃₈	—	4	8	no	—
51	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₈×C₁₉	C₂⁴	1	1	yes	characteristic
53	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
54	C₂²×Q₃₂	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
56	C₂×D₁₉	Q₃₂	1	4	yes	direct product factor
57	C₂×D₁₉	C₂×D₈	1	2	yes	—
58	C₄×C₁₉	—	4	4	no	—
59	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
60	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
61	Dic₁₉	—	4	4	no	—
62	Dic₁₉	C₂×D₈	1	2	yes	—
63	C₂²×Q₁₆	—	19	2	no	—
64	C₂×Q₃₂	—	19	2	no	—
65	C₂×Q₃₂	—	19	8	no	—
66	C₂×Q₃₂	—	19	1	no	—
67	C₂×Q₃₂	D₁₉	1	1	yes	characteristic, direct product factor
68	C₂²×C₁₆	—	19	1	no	—
69	C₂×C₁₉	C₂×Q₃₂	1	2	yes	complemented
70	C₂×C₁₉	C₂²×D₈	1	1	yes	characteristic
71	D₁₉	C₂×Q₃₂	1	4	yes	direct product factor
72	C₂²×Q₈	—	38	2	no	—
73	C₂×Q₁₆	—	19	8	no	—
74	C₂×Q₁₆	—	19	2	no	—
75	C₂×Q₁₆	—	38	4	no	—
76	C₂×Q₁₆	—	38	2	no	—
77	C₂×Q₁₆	C₂×D₁₉	1	2	yes	—
78	C₂²×C₈	—	19	1	no	—
79	Q₃₂	—	19	8	no	—
80	Q₃₂	—	19	4	no	—
81	Q₃₂	C₂×D₁₉	1	4	yes	direct product factor
82	C₂×C₁₆	—	19	1	no	—
83	C₂×C₁₆	—	19	4	no	—
84	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
85	C₁₉	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
86	C₂×Q₈	—	2	2	no	—
87	C₂×Q₈	—	38	8	no	—
88	C₂×Q₈	—	38	2	no	—
89	C₂×Q₈	—	76	2	no	—
90	C₂×Q₈	—	76	4	no	—
91	C₂²×C₄	—	19	1	no	—
92	C₂²×C₄	—	76	2	no	—
93	Q₁₆	—	2	2	no	—
94	Q₁₆	—	19	4	no	—
95	Q₁₆	—	38	8	no	—
96	Q₁₆	—	38	2	no	—
97	Q₁₆	C₂²×D₁₉	1	4	yes	—
98	C₂×C₈	—	19	1	no	—
99	C₂×C₈	—	19	2	no	—
100	C₂×C₈	—	19	2	no	—
101	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
102	C₁₆	—	19	2	no	—
103	C₁₆	C₂²×D₁₉	1	2	yes	—
104	C₂³	—	19	1	no	—
105	Q₈	—	2	4	no	—
106	Q₈	—	4	2	no	—
107	Q₈	—	38	4	no	—
108	Q₈	—	76	8	no	—
109	Q₈	—	76	2	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	—	19	1	no	—
112	C₂×C₄	—	19	2	no	—
113	C₂×C₄	—	19	2	no	—
114	C₂×C₄	—	76	8	no	—
115	C₂×C₄	—	76	2	no	—
116	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
117	C₈	—	19	2	no	—
118	C₈	D₄×D₁₉	1	1	yes	characteristic
119	C₈	C₂³×D₁₉	1	1	yes	characteristic
120	C₂²	—	19	2	no	—
121	C₂²	—	19	4	no	—
122	C₂²	D₈×D₁₉	1	1	yes	characteristic
123	C₄	—	4	4	no	—
124	C₄	—	19	2	no	—
125	C₄	—	76	4	no	—
126	C₄	D₈×D₁₉	1	1	yes	characteristic
127	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
128	C₂	—	19	4	no	—
129	C₂	Q₃₂×D₁₉	1	2	yes	direct product factor
130	C₂	C₂×D₈×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₁₉

C₂

yes

maximal

C₂×Dic₁₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#10597286

C₂

yes

maximal, complemented

Q₃₂×D₁₉

C₂

yes

maximal, direct product factor

C₂×C₁₆×D₁₉

C₂

yes

maximal, characteristic

C₂×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₂×#64528

—

Q₁₆×D₁₉

—

Q₁₆×D₁₉

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

C₂×C₈×D₁₉

C₂²

yes

characteristic

C₁₉×Q₃₂

C₂²

yes

complemented

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

#10597286

C₂²

yes

complemented

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

Dic₁₅₂

C₂²

yes

complemented

C₁₆×D₁₉

C₂²

yes

—

C₂×Q₈×C₁₉

—

Q₈×D₁₉

—

Q₈×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

#64528

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

C₂³

yes

—

C₈×D₁₉

D₄

yes

—

C₈×D₁₉

C₂³

yes

—

C₁₆×C₁₉

C₂³

yes

—

C₁₉⋊C₁₆

C₂³

yes

—

C₂²×D₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

D₈

yes

—

C₄×D₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂⁴

yes

characteristic

C₁₉⋊C₈

C₂×D₄

yes

—

C₂²×Q₃₂

—

maximal, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

Q₃₂

yes

direct product factor

C₂×D₁₉

C₂×D₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂²×D₄

yes

characteristic

Dic₁₉

—

Dic₁₉

C₂×D₈

yes

—

C₂²×Q₁₆

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×Q₃₂

D₁₉

yes

characteristic, direct product factor

C₂²×C₁₆

—

C₂×C₁₉

C₂×Q₃₂

yes

complemented

C₂×C₁₉

C₂²×D₈

yes

characteristic

D₁₉

C₂×Q₃₂

yes

direct product factor

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

C₂×D₁₉

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₁₉

C₂²×Q₃₂

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

C₂²×D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

C₂²×D₁₉

yes

characteristic

102

C₁₆

—

103

C₁₆

C₂²×D₁₉

yes

—

104

C₂³

—

105

Q₈

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

D₄×D₁₉

yes

characteristic

117

C₈

—

118

C₈

D₄×D₁₉

yes

characteristic

119

C₈

C₂³×D₁₉

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

D₈×D₁₉

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

D₈×D₁₉

yes

characteristic

127

C₄

C₂×D₄×D₁₉

yes

characteristic

128

C₂

—

129

C₂

Q₃₂×D₁₉

yes

direct product factor

130

C₂

C₂×D₈×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₈×C₁₉	C₂⁴
Frattini	C₈	C₂³×D₁₉
Fitting	C₂×C₁₉×Q₃₂	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂²×D₁₉	D₈
hypercenter	C₂×Q₃₂	D₁₉
hypocenter	C₁₉	C₂²×Q₃₂
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₈×C₁₉

C₂⁴

Frattini

C₈

C₂³×D₁₉

Fitting

C₂×C₁₉×Q₃₂

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂²×D₁₉

D₈

hypercenter

C₂×Q₃₂

D₁₉

hypocenter

C₁₉

C₂²×Q₃₂

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
2. C₂×Dic₁₅₂	C₂	semidirect
3. C₂×#10597286	C₂	semidirect
4. Q₃₂×D₁₉	C₂	direct (N × H)
6. C₂×C₁₉×Q₃₂	C₂	semidirect
14. C₁₉×Q₃₂	C₂²	semidirect
16. #10597286	C₂²	semidirect
18. Dic₁₅₂	C₂²	semidirect
56. C₂×D₁₉	Q₃₂	direct (N × H)
67. C₂×Q₃₂	D₁₉	direct (N × H)
69. C₂×C₁₉	C₂×Q₃₂	semidirect
71. D₁₉	C₂×Q₃₂	direct (N × H)
81. Q₃₂	C₂×D₁₉	direct (N × H)
85. C₁₉	C₂²×Q₃₂	semidirect
129. C₂	Q₃₂×D₁₉	direct (N × H)

H ≅ G/N

type

2. C₂×Dic₁₅₂

C₂

semidirect

3. C₂×#10597286

C₂

semidirect

4. Q₃₂×D₁₉

C₂

direct (N × H)

6. C₂×C₁₉×Q₃₂

C₂

semidirect

14. C₁₉×Q₃₂

C₂²

semidirect

16. #10597286

C₂²

semidirect

18. Dic₁₅₂

C₂²

semidirect

56. C₂×D₁₉

Q₃₂

direct (N × H)

67. C₂×Q₃₂

D₁₉

direct (N × H)

69. C₂×C₁₉

C₂×Q₃₂

semidirect

71. D₁₉

C₂×Q₃₂

direct (N × H)

81. Q₃₂

C₂×D₁₉

direct (N × H)

85. C₁₉

C₂²×Q₃₂

semidirect

129. C₂

Q₃₂×D₁₉

direct (N × H)

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

subgroup	index
C₂×Q₁₆×D₁₉	2
C₂×Dic₁₅₂	2
C₂×#10597286	2
Q₃₂×D₁₉	2
C₂×C₁₆×D₁₉	2
C₂×C₁₉×Q₃₂	2
C₂²×Q₃₂	19

subgroup

index

C₂×Q₁₆×D₁₉

C₂×Dic₁₅₂

C₂×#10597286

Q₃₂×D₁₉

C₂×C₁₆×D₁₉

C₂×C₁₉×Q₃₂

C₂²×Q₃₂

Subgroups — C₂×Q₃₂×D₁₉ #14576746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×Q32×D19 #14576746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₃₂×D₁₉ #14576746