Group #14574138 — subgroups

Subgroups — C₂×#11926945 #14574138

Order 2432.

360 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10597336	C₂	1	2	yes	maximal
2	#11926945	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597265	C₂	1	2	yes	maximal
5	C₂×C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×Dic₁₉⋊C₄	—	2	2	no	—
12	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#10597336	—	2	4	no	—
15	#10597336	C₂²	1	8	yes	—
16	C₁₉×#107	C₂²	1	4	yes	—
17	#10597275	C₂²	1	4	yes	—
18	C₈×Dic₁₉	C₂²	1	4	yes	—
19	#10597265	C₂²	1	8	yes	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	2	no	—
23	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
24	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	Q₈	1	4	yes	—
26	C₂×C₈×C₁₉	C₂³	1	2	yes	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	8	no	—
31	C₄⋊Dic₁₉	C₂³	1	4	yes	—
32	Dic₁₉⋊C₄	—	2	8	no	—
33	C₄×Dic₁₉	D₄	1	2	yes	—
34	C₄×Dic₁₉	C₂³	1	2	yes	—
35	C₂×C₁₉⋊C₈	Q₈	1	4	yes	—
36	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	4	4	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂×Dic₁₉	—	2	2	no	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	4	4	no	—
48	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
49	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
50	C₈×C₁₉	C₂×Q₈	1	4	yes	—
51	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
52	C₂×#499	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
54	C₂²×C₁₉	#135	1	2	yes	—
55	C₂²×C₁₉	#135	1	2	yes	—
56	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
57	C₄×C₁₉	—	4	4	no	—
58	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
59	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
60	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
61	Dic₁₉	—	2	2	no	—
62	Dic₁₉	—	2	2	no	—
63	Dic₁₉	—	4	4	no	—
64	C₂×#125	—	19	2	no	—
65	#499	—	19	8	no	—
66	C₂×#107	—	19	1	no	—
67	C₂×#107	D₁₉	1	1	yes	characteristic
68	C₂×#106	—	19	2	no	—
69	C₂×C₄×C₈	—	19	1	no	—
70	C₂×C₁₉	#499	1	4	yes	complemented
71	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
73	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
74	C₂²×C₈	—	19	1	no	—
75	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
76	#125	—	19	8	no	—
77	#125	—	38	4	no	—
78	C₂×C₄⋊C₄	—	19	2	no	—
79	C₂×C₄⋊C₄	—	38	2	no	—
80	C₂×C₄⋊C₄	—	38	2	no	—
81	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
82	C₂×C₄²	—	19	1	no	—
83	#107	—	19	4	no	—
84	#107	C₂×D₁₉	1	4	yes	—
85	#106	—	19	8	no	—
86	C₄×C₈	—	19	4	no	—
87	C₁₉	C₂×#499	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	—	19	1	no	—
90	C₂²×C₄	—	19	1	no	—
91	C₂²×C₄	—	38	2	no	—
92	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
93	C₂×C₈	—	19	4	no	—
94	C₂×C₈	—	19	2	no	—
95	C₂×C₈	Dic₃₈	1	4	yes	—
96	C₂×C₈	C₂²×D₁₉	1	2	yes	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	19	4	no	—
99	C₄⋊C₄	—	38	8	no	—
100	C₄⋊C₄	—	38	8	no	—
101	C₄⋊C₄	—	38	2	no	—
102	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
103	C₄²	—	19	2	no	—
104	C₄²	—	19	2	no	—
105	C₂³	D₄×D₁₉	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	4	no	—
108	C₂×C₄	—	19	2	no	—
109	C₂×C₄	—	19	2	no	—
110	C₂×C₄	—	38	2	no	—
111	C₂×C₄	—	38	2	no	—
112	C₂×C₄	—	38	4	no	—
113	C₂×C₄	—	76	4	no	—
114	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
115	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
116	C₂×C₄	Q₈×D₁₉	1	2	yes	—
117	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
118	C₈	—	19	4	no	—
119	C₈	C₂×Dic₃₈	1	4	yes	—
120	C₂²	#10597334	1	2	yes	—
121	C₂²	#10597358	1	2	yes	—
122	C₂²	#10597365	1	2	yes	—
123	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
124	C₄	—	4	4	no	—
125	C₄	—	38	2	no	—
126	C₄	—	38	2	no	—
127	C₄	—	76	4	no	—
128	C₄	#10597334	1	2	yes	—
129	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
130	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
131	C₂	#11926945	1	4	yes	direct product factor
132	C₂	C₂×#10597334	1	1	yes	characteristic
133	C₂	C₂×#10597358	1	1	yes	characteristic
134	C₂	C₂×#10597365	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597336

C₂

yes

maximal

#11926945

C₂

yes

maximal, direct product factor

C₂×#10597275

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal

C₂×C₈×Dic₁₉

C₂

yes

maximal, characteristic

C₂×C₁₉×#107

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597336

—

#10597336

C₂²

yes

—

C₁₉×#107

C₂²

yes

—

#10597275

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

—

#10597265

C₂²

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

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×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₈×C₁₉

C₂×Q₈

yes

—

C₁₉⋊C₈

C₂×Q₈

yes

—

C₂×#499

—

maximal, Sylow

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

#135

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

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

C₂×#106

—

C₂×C₄×C₈

—

C₂×C₁₉

#499

yes

complemented

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

#107

—

#107

C₂×D₁₉

yes

—

#106

—

C₄×C₈

—

C₁₉

C₂×#499

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

C₂²×D₁₉

yes

—

103

C₄²

—

104

C₄²

—

105

C₂³

D₄×D₁₉

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂×Dic₃₈

yes

—

115

C₂×C₄

D₄×D₁₉

yes

characteristic

116

C₂×C₄

Q₈×D₁₉

yes

—

117

C₂×C₄

C₂³×D₁₉

yes

characteristic

118

C₈

—

119

C₈

C₂×Dic₃₈

yes

—

120

C₂²

#10597334

yes

—

121

C₂²

#10597358

yes

—

122

C₂²

#10597365

yes

—

123

C₂²

C₂×D₄×D₁₉

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

#10597334

yes

—

129

C₄

C₂²×Dic₃₈

yes

characteristic

130

C₄

C₂×Q₈×D₁₉

yes

characteristic

131

C₂

#11926945

yes

direct product factor

132

C₂

C₂×#10597334

yes

characteristic

133

C₂

C₂×#10597358

yes

characteristic

134

C₂

C₂×#10597365

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	C₂×#499
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#107

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
2. #11926945	C₂	direct (N × H)
70. C₂×C₁₉	#499	semidirect
87. C₁₉	C₂×#499	semidirect
131. C₂	#11926945	direct (N × H)

H ≅ G/N

type

2. #11926945

C₂

direct (N × H)

70. C₂×C₁₉

#499

semidirect

87. C₁₉

C₂×#499

semidirect

131. C₂

#11926945

direct (N × H)

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

subgroup	index
C₂×#10597336	2
#11926945	2
C₂×#10597275	2
C₂×#10597265	2
C₂×C₈×Dic₁₉	2
C₂×C₁₉×#107	2
C₂×#499	19

subgroup

index

C₂×C₈×Dic₁₉

C₂×C₁₉×#107

C₂×#499

Subgroups — C₂×#11926945 #14574138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926945 #14574138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926945 #14574138