Group #14563790 — subgroups

Subgroups — #14563790

Order 2432.

280 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597274	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926413	C₂	1	2	yes	maximal
5	C₂×C₁₉×#106	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	C₂×Dic₁₉⋊C₄	—	2	4	no	—
10	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₉×#106	—	2	2	no	—
13	#10597274	—	2	2	no	—
14	C₈×Dic₁₉	C₄	1	4	yes	complemented
15	#10597265	—	2	4	no	—
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	—	2	2	no	—
19	C₂²×Dic₁₉	D₄	1	2	yes	—
20	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₈×C₁₉	Q₈	1	2	yes	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	Dic₁₉⋊C₄	—	4	8	no	—
28	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
29	C₄×Dic₁₉	Q₈	1	2	yes	—
30	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
31	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
32	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	—	4	4	no	—
36	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×Dic₁₉	—	4	2	no	—
43	C₂×Dic₁₉	—	4	4	no	—
44	C₂×Dic₁₉	C₄⋊C₄	1	4	yes	—
45	C₂×Dic₁₉	SD₁₆	1	8	yes	—
46	C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
47	C₁₉⋊C₈	C₄⋊C₄	1	4	yes	complemented
48	#1844	—	19	1	no	maximal, Sylow
49	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₁₉	#127	1	1	yes	characteristic
51	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₂²×C₁₉	C₂×SD₁₆	1	4	yes	—
53	C₄×C₁₉	—	8	2	no	—
54	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
57	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
58	Dic₁₉	—	8	2	no	—
59	Dic₁₉	#106	1	8	yes	complemented
60	C₂×#106	—	19	1	no	—
61	C₂×#106	—	19	2	no	—
62	C₂×#106	D₁₉	1	1	yes	characteristic
63	C₂×C₄×C₈	—	19	1	no	—
64	#384	—	19	2	no	—
65	C₂×C₁₉	#384	1	1	yes	characteristic
66	C₂×C₁₉	C₂×#106	1	2	yes	—
67	C₂×C₁₉	#492	1	2	yes	—
68	C₂×C₁₉	#498	1	2	yes	—
69	C₂²×C₈	—	19	1	no	—
70	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
71	C₂×C₄⋊C₄	—	19	2	no	—
72	C₂×C₄⋊C₄	—	38	4	no	—
73	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
74	C₂×C₄²	—	19	1	no	—
75	#106	—	2	2	no	—
76	#106	—	38	4	no	—
77	#106	—	38	2	no	—
78	C₄×C₈	—	19	4	no	—
79	C₁₉	#1844	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	—	2	2	no	—
81	C₂²×C₄	—	19	2	no	—
82	C₂²×C₄	—	38	2	no	—
83	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
84	C₂×C₈	—	19	2	no	—
85	C₂×C₈	—	19	2	no	—
86	C₂×C₈	—	19	2	no	—
87	C₂×C₈	Dic₃₈	1	2	yes	—
88	C₂×C₈	C₄×D₁₉	1	2	yes	—
89	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	38	2	no	—
93	C₄⋊C₄	—	38	2	no	—
94	C₄⋊C₄	—	76	8	no	—
95	C₄²	—	19	2	no	—
96	C₄²	—	19	2	no	—
97	C₂³	D₄×D₁₉	1	1	yes	characteristic
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	—	4	4	no	—
100	C₂×C₄	—	19	4	no	—
101	C₂×C₄	—	19	8	no	—
102	C₂×C₄	—	76	2	no	—
103	C₂×C₄	—	76	4	no	—
104	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
105	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
106	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
108	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
109	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
110	C₈	—	19	4	no	—
111	C₈	Dic₁₉⋊C₄	1	4	yes	complemented
112	C₂²	#10597334	1	1	yes	characteristic
113	C₂²	C₄⋊C₄×D₁₉	1	1	yes	characteristic
114	C₂²	SD₁₆×D₁₉	1	4	yes	—
115	C₂²	#10597386	1	1	yes	characteristic
116	C₄	—	8	2	no	—
117	C₄	—	19	8	no	—
118	C₄	—	152	2	no	—
119	C₄	#10597334	1	1	yes	characteristic
120	C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
121	C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
122	C₄	#10597390	1	1	yes	characteristic
123	C₂	#11926413	1	1	yes	characteristic
124	C₂	#106×D₁₉	1	2	yes	—
125	C₂	#11926915	1	2	yes	—
126	C₂	#11926941	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597274

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal

C₂×C₈×Dic₁₉

C₂

yes

maximal, characteristic

#11926413

C₂

yes

maximal

C₂×C₁₉×#106

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#106

—

#10597274

—

C₈×Dic₁₉

C₄

yes

complemented

#10597265

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

Q₈

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄⋊C₄

yes

—

C₂×Dic₁₉

SD₁₆

yes

—

C₈×C₁₉

C₄⋊C₄

yes

complemented

C₁₉⋊C₈

C₄⋊C₄

yes

complemented

#1844

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#127

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

yes

—

—

D₁₉

yes

characteristic

C₂×C₄×C₈

—

#384

—

C₂×C₁₉

#384

yes

characteristic

C₂×C₁₉

C₂×#106

yes

—

C₂×C₁₉

#492

yes

—

C₂×C₁₉

#498

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

#106

—

#106

—

#106

—

C₄×C₈

—

C₁₉

#1844

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

C₄×D₁₉

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

D₄×D₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×Dic₃₈

yes

characteristic

105

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

106

C₂×C₄

D₄×D₁₉

yes

characteristic

107

C₂×C₄

Q₈×D₁₉

yes

characteristic

108

C₂×C₄

Q₈×D₁₉

yes

characteristic

109

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

110

C₈

—

111

C₈

Dic₁₉⋊C₄

yes

complemented

112

C₂²

#10597334

yes

characteristic

113

C₂²

C₄⋊C₄×D₁₉

yes

characteristic

114

C₂²

SD₁₆×D₁₉

yes

—

115

C₂²

#10597386

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

152

—

119

C₄

#10597334

yes

characteristic

120

C₄

C₄⋊C₄×D₁₉

yes

characteristic

121

C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

122

C₄

#10597390

yes

characteristic

123

C₂

#11926413

yes

characteristic

124

C₂

#106×D₁₉

yes

—

125

C₂

#11926915

yes

—

126

C₂

#11926941

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#106	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#106	D₁₉
hypocenter	C₁₉	#1844
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#106

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
14. C₈×Dic₁₉	C₄	semidirect
46. C₈×C₁₉	C₄⋊C₄	semidirect
47. C₁₉⋊C₈	C₄⋊C₄	semidirect
59. Dic₁₉	#106	semidirect
79. C₁₉	#1844	semidirect
111. C₈	Dic₁₉⋊C₄	semidirect

H ≅ G/N

type

14. C₈×Dic₁₉

C₄

semidirect

46. C₈×C₁₉

C₄⋊C₄

semidirect

47. C₁₉⋊C₈

C₄⋊C₄

semidirect

59. Dic₁₉

#106

semidirect

79. C₁₉

#1844

semidirect

111. C₈

Dic₁₉⋊C₄

semidirect

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

subgroup	index
C₂×#10597274	2
C₂×#10597265	2
C₂×C₈×Dic₁₉	2
#11926413	2
C₂×C₁₉×#106	2
#1844	19

subgroup

index

C₂×C₈×Dic₁₉

C₂×C₁₉×#106

Subgroups — #14563790

Conjugacy classes of subgroups

Complements

Maximal subgroups