Group #14565902 — subgroups

Subgroups — #14565902

Order 2432.

198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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×#10597285	C₂	1	2	yes	maximal, complemented
2	C₂×#10597283	C₂	1	2	yes	maximal, complemented
3	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×SD₁₆×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#124	—	2	1	no	—
10	C₂×D₁₅₂	—	2	1	no	—
11	C₂×D₁₅₂	C₂²	1	2	yes	—
12	#10597320	—	2	1	no	—
13	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#10597285	—	2	4	no	—
15	#10597283	—	2	4	no	—
16	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	—	2	1	no	—
18	C₂×D₄×C₁₉	—	2	1	no	—
19	C₂×D₇₆	—	2	2	no	—
20	C₂×D₇₆	—	4	2	no	—
21	Q₁₆×C₁₉	—	2	2	no	—
22	SD₁₆×C₁₉	—	4	2	no	—
23	D₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²⋊C₄×C₁₉	—	4	2	no	—
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	D₁₅₂	—	2	2	no	—
29	D₁₅₂	—	2	2	no	—
30	D₁₅₂	—	4	2	no	—
31	C₁₉⋊C₁₆	D₄	1	4	yes	complemented
32	C₂³×C₁₉	—	4	1	no	—
33	C₂²×D₁₉	—	4	2	no	—
34	Q₈×C₁₉	—	4	1	no	—
35	Q₈×C₁₉	—	4	1	no	—
36	D₄×C₁₉	—	4	1	no	—
37	D₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	D₈	1	2	yes	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	D₇₆	—	4	2	no	—
42	D₇₆	—	4	2	no	—
43	D₇₆	—	8	4	no	—
44	C₈×C₁₉	D₈	1	2	yes	—
45	C₈×C₁₉	C₂×D₄	1	2	yes	—
46	#2250	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	—	8	1	no	—
48	C₂²×C₁₉	—	8	2	no	—
49	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
50	C₂×D₁₉	—	8	2	no	—
51	C₂×D₁₉	—	8	4	no	—
52	C₄×C₁₉	—	2	2	no	—
53	C₄×C₁₉	—	8	1	no	—
54	C₄×C₁₉	#127	1	1	yes	characteristic
55	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
56	C₂×SD₃₂	—	19	2	no	—
57	C₂×D₁₆	—	19	2	no	—
58	#495	D₁₉	1	1	yes	characteristic, complemented
59	#493	—	19	1	no	—
60	#346	—	19	1	no	—
61	C₂×C₁₉	—	16	1	no	—
62	C₂×C₁₉	#493	1	1	yes	characteristic
63	C₂×C₁₉	#509	1	2	yes	—
64	D₁₉	—	16	2	no	—
65	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
66	C₂×SD₁₆	—	2	1	no	—
67	C₂×D₈	—	19	2	no	—
68	C₂×D₈	—	38	1	no	—
69	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
70	#127	—	38	1	no	—
71	#124	—	2	1	no	—
72	SD₃₂	—	38	4	no	—
73	D₁₆	—	38	4	no	—
74	C₂×C₁₆	—	19	2	no	—
75	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
76	C₁₉	#2250	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	2	1	no	—
78	C₂×D₄	—	2	1	no	—
79	C₂×D₄	—	38	2	no	—
80	C₂×D₄	—	76	2	no	—
81	Q₁₆	—	2	2	no	—
82	SD₁₆	—	4	2	no	—
83	D₈	—	2	2	no	—
84	D₈	—	38	2	no	—
85	D₈	—	38	2	no	—
86	D₈	—	76	2	no	—
87	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
88	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
89	C₂²⋊C₄	—	4	2	no	—
90	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₁₆	—	19	4	no	—
92	C₂³	—	4	1	no	—
93	C₂³	—	76	2	no	—
94	Q₈	—	4	1	no	—
95	Q₈	—	4	1	no	—
96	D₄	—	4	1	no	—
97	D₄	—	4	1	no	—
98	D₄	—	76	2	no	—
99	D₄	—	76	2	no	—
100	D₄	—	152	4	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	#64525	1	2	yes	—
103	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
104	C₈	#64525	1	2	yes	—
105	C₈	D₄×D₁₉	1	2	yes	—
106	C₂²	—	8	1	no	—
107	C₂²	—	8	2	no	—
108	C₂²	—	152	2	no	—
109	C₂²	—	152	4	no	—
110	C₂²	C₂×#64525	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	8	1	no	—
113	C₄	C₂×#64525	1	1	yes	characteristic
114	C₄	#10597386	1	1	yes	characteristic
115	C₂	—	16	1	no	—
116	C₂	—	304	2	no	—
117	C₂	#11926920	1	1	yes	characteristic
118	C₂	#11926979	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597285

C₂

yes

maximal, complemented

C₂×#10597283

C₂

yes

maximal, complemented

#11926921

C₂

yes

maximal, characteristic, complemented

#11926320

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

C₂×D₁₅₂

—

C₂×D₁₅₂

C₂²

yes

—

#10597320

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597285

—

#10597283

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

D₁₅₂

—

D₁₅₂

—

D₁₅₂

—

C₁₉⋊C₁₆

D₄

yes

complemented

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

D₈

yes

—

C₈×C₁₉

C₂×D₄

yes

—

#2250

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×SD₃₂

—

C₂×D₁₆

—

#495

D₁₉

yes

characteristic, complemented

#493

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

#509

yes

—

D₁₉

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#127

—

#124

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2250

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

D₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

100

D₄

—

152

—

101

C₂×C₄

—

102

C₂×C₄

#64525

yes

—

103

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

104

C₈

#64525

yes

—

105

C₈

D₄×D₁₉

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

152

—

109

C₂²

—

152

—

110

C₂²

C₂×#64525

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

C₂×#64525

yes

characteristic

114

C₄

#10597386

yes

characteristic

115

C₂

—

116

C₂

—

304

—

117

C₂

#11926920

yes

characteristic

118

C₂

#11926979

yes

—

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#495	C₂
socle	C₂²×C₁₉	C₂×D₈
hypercenter	#495	D₁₉
hypocenter	C₁₉	#2250
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#495

C₂

socle

C₂²×C₁₉

C₂×D₈

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#10597285	C₂	semidirect
2. C₂×#10597283	C₂	semidirect
3. #11926921	C₂	semidirect
4. #11926320	C₂	semidirect
5. C₁₉×#495	C₂	semidirect
31. C₁₉⋊C₁₆	D₄	semidirect
58. #495	D₁₉	semidirect
76. C₁₉	#2250	semidirect

H ≅ G/N

type

1. C₂×#10597285

C₂

semidirect

2. C₂×#10597283

C₂

semidirect

3. #11926921

C₂

semidirect

4. #11926320

C₂

semidirect

5. C₁₉×#495

C₂

semidirect

31. C₁₉⋊C₁₆

D₄

semidirect

58. #495

D₁₉

semidirect

76. C₁₉

#2250

semidirect

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

subgroup	index
C₂×#10597285	2
C₂×#10597283	2
#11926921	2
#11926320	2
C₁₉×#495	2
#2250	19

subgroup

index

C₁₉×#495

Subgroups — #14565902

Conjugacy classes of subgroups

Complements

Maximal subgroups