Group #14574158 — subgroups

Subgroups — #14574158

Order 2432.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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	#11927097	C₂	1	2	yes	maximal
2	#11926952	C₂	1	4	yes	maximal, complemented
3	#11926951	C₂	1	4	yes	maximal, complemented
4	#11926582	C₂	1	1	yes	maximal, characteristic
5	#11926580	C₂	1	2	yes	maximal
6	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#427	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	2	yes	—
10	#10597372	C₂²	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#10597336	C₂²	1	4	yes	—
14	#10597334	C₂²	1	4	yes	—
15	#10597324	—	2	4	no	—
16	C₄×Dic₃₈	—	2	4	no	—
17	C₁₉×#107	C₂²	1	2	yes	—
18	C₁₉×#106	C₂²	1	2	yes	—
19	#10597275	C₂²	1	2	yes	—
20	#10597274	C₂²	1	2	yes	—
21	#10597272	C₂²	1	2	yes	—
22	#10597272	C₂²	1	2	yes	—
23	#10597265	C₂²	1	4	yes	—
24	#10597264	C₂²	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	D₄	1	2	yes	—
27	C₂×Dic₃₈	—	2	4	no	—
28	C₂×C₈×C₁₉	Q₈	1	4	yes	complemented
29	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
32	C₂²⋊C₄×C₁₉	—	2	2	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₂²⋊Dic₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	4	no	—
36	C₄⋊Dic₁₉	C₂³	1	4	yes	—
37	Dic₁₉⋊C₄	—	2	4	no	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	C₄×Dic₁₉	—	2	2	no	—
40	C₄×Dic₁₉	D₄	1	2	yes	—
41	C₄×Dic₁₉	C₂³	1	2	yes	—
42	C₂×C₁₉⋊C₈	Q₈	1	4	yes	complemented
43	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
44	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₁₉	—	2	4	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
53	Dic₃₈	—	4	8	no	—
54	C₈×C₁₉	C₂×Q₈	1	2	yes	—
55	C₈×C₁₉	C₂×Q₈	1	2	yes	—
56	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
57	#3162	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
60	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
61	C₄×C₁₉	—	4	4	no	—
62	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
63	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
64	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
65	Dic₁₉	—	2	4	no	—
66	Dic₁₉	—	4	4	no	—
67	#533	—	19	2	no	—
68	#501	—	19	4	no	—
69	#501	—	19	4	no	—
70	#427	—	19	1	no	—
71	#427	—	19	2	no	—
72	#427	D₁₉	1	1	yes	characteristic
73	C₂×#97	—	19	1	no	—
74	C₂×C₁₉	—	2	2	no	—
75	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
76	C₂×C₁₉	#575	1	2	yes	—
77	C₂²×C₈	—	19	1	no	—
78	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
79	C₄⋊Q₈	—	19	4	no	—
80	#125	—	19	4	no	—
81	C₂²⋊Q₈	—	38	4	no	—
82	C₄×Q₈	—	38	4	no	—
83	#117	—	19	2	no	—
84	#117	C₂×D₁₉	1	2	yes	—
85	C₂×C₄²	—	19	1	no	—
86	#107	—	19	2	no	—
87	#107	—	19	4	no	—
88	#107	C₂×D₁₉	1	2	yes	—
89	#106	—	19	2	no	—
90	#106	—	19	4	no	—
91	#106	C₂×D₁₉	1	2	yes	—
92	#97	—	19	2	no	—
93	#97	—	19	2	no	—
94	C₁₉	#3162	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	38	4	no	—
96	C₂²×C₄	—	19	2	no	—
97	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
98	C₂×C₈	—	19	4	no	—
99	C₂×C₈	—	19	2	no	—
100	C₂×C₈	Dic₃₈	1	4	yes	complemented
101	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
102	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
103	C₄⋊C₄	—	19	4	no	—
104	C₄⋊C₄	—	38	4	no	—
105	C₄⋊C₄	—	38	4	no	—
106	C₄⋊C₄	—	38	4	no	—
107	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₂²⋊C₄	—	38	2	no	—
110	C₄²	—	2	2	no	—
111	C₄²	—	19	2	no	—
112	C₄²	—	19	2	no	—
113	C₄²	—	38	2	no	—
114	C₂³	D₄×D₁₉	1	1	yes	characteristic
115	Q₈	—	76	8	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	19	4	no	—
118	C₂×C₄	—	38	4	no	—
119	C₂×C₄	—	76	2	no	—
120	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
121	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
122	C₂×C₄	Q₈×D₁₉	1	2	yes	—
123	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
124	C₈	—	19	4	no	—
125	C₈	C₂×Dic₃₈	1	2	yes	—
126	C₈	C₂×Dic₃₈	1	2	yes	—
127	C₂²	—	2	2	no	—
128	C₂²	#10597334	1	2	yes	—
129	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
130	C₄	—	4	4	no	—
131	C₄	—	38	4	no	—
132	C₄	—	76	4	no	—
133	C₄	#10597334	1	2	yes	—
134	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
135	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
136	C₂	—	2	2	no	—
137	C₂	C₂×#10597334	1	1	yes	characteristic
138	C₂	#11927341	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927097

C₂

yes

maximal

#11926952

C₂

yes

maximal, complemented

#11926951

C₂

yes

maximal, complemented

#11926582

C₂

yes

maximal, characteristic

#11926580

C₂

yes

maximal

C₂×#10597272

C₂

yes

maximal, characteristic

C₁₉×#427

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

#10597372

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597336

C₂²

yes

—

#10597334

C₂²

yes

—

#10597324

—

C₄×Dic₃₈

—

C₁₉×#107

C₂²

yes

—

C₁₉×#106

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

#10597272

C₂²

yes

—

#10597272

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

D₄

yes

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

complemented

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

C₈×C₁₉

C₂×Q₈

yes

—

C₈×C₁₉

C₂×Q₈

yes

—

C₁₉⋊C₈

C₂×Q₈

yes

—

#3162

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂²×Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×#97

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#575

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

#117

C₂×D₁₉

yes

—

C₂×C₄²

—

#107

—

#107

—

#107

C₂×D₁₉

yes

—

#106

—

#106

—

#106

C₂×D₁₉

yes

—

#97

—

#97

—

C₁₉

#3162

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

Dic₃₈

yes

complemented

101

C₂×C₈

C₂²×D₁₉

yes

characteristic

102

C₂×C₈

C₂²×D₁₉

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

C₂²×D₁₉

yes

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₂³

D₄×D₁₉

yes

characteristic

115

Q₈

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂×Dic₃₈

yes

—

121

C₂×C₄

D₄×D₁₉

yes

characteristic

122

C₂×C₄

Q₈×D₁₉

yes

—

123

C₂×C₄

C₂³×D₁₉

yes

characteristic

124

C₈

—

125

C₈

C₂×Dic₃₈

yes

—

126

C₈

C₂×Dic₃₈

yes

—

127

C₂²

—

128

C₂²

#10597334

yes

—

129

C₂²

C₂×D₄×D₁₉

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

#10597334

yes

—

134

C₄

C₂²×Dic₃₈

yes

characteristic

135

C₄

C₂×Q₈×D₁₉

yes

characteristic

136

C₂

—

137

C₂

C₂×#10597334

yes

characteristic

138

C₂

#11927341

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#427	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#427	D₁₉
hypocenter	C₁₉	#3162
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#427

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
2. #11926952	C₂	semidirect
3. #11926951	C₂	semidirect
28. C₂×C₈×C₁₉	Q₈	semidirect
42. C₂×C₁₉⋊C₈	Q₈	semidirect
94. C₁₉	#3162	semidirect
100. C₂×C₈	Dic₃₈	semidirect

H ≅ G/N

type

2. #11926952

C₂

semidirect

3. #11926951

C₂

semidirect

28. C₂×C₈×C₁₉

Q₈

semidirect

42. C₂×C₁₉⋊C₈

Q₈

semidirect

94. C₁₉

#3162

semidirect

100. C₂×C₈

Dic₃₈

semidirect

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

subgroup	index
#11927097	2
#11926952	2
#11926951	2
#11926582	2
#11926580	2
C₂×#10597272	2
C₁₉×#427	2
#3162	19

subgroup

index

C₁₉×#427

Subgroups — #14574158

Conjugacy classes of subgroups

Complements

Maximal subgroups