Subgroups — C 2 3 × C 4 × #10596833 #34031059

maximal, direct product factor

C₂

yes

C₂³×C₄×Dic₇₃

C₂

yes

maximal, characteristic

C₄

yes

C₂²

yes

—

C₂×C₄×#10596833

C₂²

112

yes

C₂⁴×Dic₇₃

C₄

yes

C₂⁴×Dic₇₃

C₂²

yes

C₂²×C₄×Dic₇₃

C₄

yes

—

C₂²×C₄×Dic₇₃

C₂²

yes

—

C₂⁴×C₄×C₇₃

C₄

yes

C₂×C₄

224

yes

C₂³

yes

—

C₄×#10596833

C₂³

yes

C₂³×Dic₇₃

C₈

yes

C₂³×Dic₇₃

C₂×C₄

yes

—

C₂³×Dic₇₃

C₂×C₄

yes

—

C₂³×Dic₇₃

C₂×C₄

yes

—

C₂³×Dic₇₃

C₂³

yes

—

C₂×C₄×Dic₇₃

C₂×C₄

yes

—

C₂×C₄×Dic₇₃

C₂³

yes

—

C₂⁵×C₇₃

C₂×C₄

yes

C₂³×C₄×C₇₃

C₈

yes

C₂³×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄

224

yes

C₂⁴

yes

—

C₂²×Dic₇₃

C₄²

yes

—

C₂²×Dic₇₃

C₂×C₈

112

yes

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂²×C₄

yes

—

C₂²×Dic₇₃

C₂⁴

yes

—

C₄×Dic₇₃

C₂²×C₄

yes

—

C₄×Dic₇₃

C₂⁴

yes

—

C₂⁴×C₇₃

C₄²

yes

—

C₂⁴×C₇₃

C₂×C₈

yes

—

C₂⁴×C₇₃

C₂×C₈

yes

—

C₂⁴×C₇₃

C₂²×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₈

112

yes

C₂²×C₄×C₇₃

C₂²×C₄

yes

—

C₂³×C₇₃

C₄×C₈

yes

C₂³×C₇₃

C₂×C₄²

yes

—

C₂³×C₇₃

C₂²×C₈

yes

—

C₂³×C₇₃

C₂²×C₈

yes

—

C₂³×C₇₃

C₂³×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₈

112

yes

C₂×C₄×C₇₃

C₂³×C₄

yes

—

C₂×Dic₇₃

C₂×C₄²

yes

—

C₂×Dic₇₃

C₂²×C₈

112

yes

C₂×Dic₇₃

C₂³×C₄

yes

—

C₂×Dic₇₃

C₂³×C₄

yes

—

C₂×Dic₇₃

C₂³×C₄

yes

—

C₂×Dic₇₃

C₂⁵

yes

#10596833

C₂³×C₄

yes

C₂²×C₇₃

C₂×C₄×C₈

112

yes

C₂²×C₇₃

C₂²×C₄²

yes

—

C₂²×C₇₃

C₂³×C₈

yes

—

C₂²×C₇₃

C₂³×C₈

yes

—

C₂²×C₇₃

C₂⁴×C₄

yes

C₄×C₇₃

C₂³×C₈

yes

Dic₇₃

C₂²×C₄²

yes

—

Dic₇₃

C₂³×C₈

yes

Dic₇₃

C₂⁴×C₄

yes

—

C₂³×C₄×C₈

—

maximal, Sylow

C₂×C₇₃

C₂²×C₄×C₈

yes

C₂×C₇₃

C₂³×C₄²

yes

C₂×C₇₃

C₂⁴×C₈

yes

C₂×C₇₃

C₂⁴×C₈

yes

C₂⁴×C₈

—

C₂³×C₄²

—

C₂²×C₄×C₈

—

C₇₃

C₂³×C₄×C₈

yes

characteristic, complemented, Sylow

C₂⁴×C₄

—

C₂⁴×C₄

—

C₂⁴×C₄

#64408

yes

C₂³×C₈

—

C₂³×C₈

—

C₂²×C₄²

—

C₂²×C₄²

—

C₂×C₄×C₈

—

112

—

C₂⁵

C₂×#64408

yes

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

#10596833

yes

C₂³×C₄

C₂×#64408

yes

—

C₂²×C₈

—

224

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄×C₈

—

C₂⁴

C₄×#64408

yes

—

C₂⁴

yes

—

C₂⁴

#11924036

yes

—

C₂⁴

C₂²×#64408

yes

—

C₂²×C₄

—

112

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

112

yes

105

C₂²×C₄

C₂²×#64408

yes

—

106

C₂×C₈

—

224

—

107

C₂×C₈

—

108

C₄²

—

109

C₄²

—

110

C₂³

C₄×#10596833

yes

111

C₂³

C₂×C₄×#64408

yes

—

112

C₂³

yes

—

113

C₂³

C₂×#11924036

yes

—

114

C₂³

C₂³×#64408

yes

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

112

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

112

yes

122

C₂×C₄

C₂³×#64408

yes

—

123

C₈

—

124

C₂²

C₂×C₄×#10596833

112

yes

125

C₂²

C₂²×C₄×#64408

yes

—

126

C₂²

yes

—

127

C₂²

C₂²×#11924036

yes

—

128

C₂²

C₂⁴×#64408

yes

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

yes

133

C₂

yes

134

C₂

C₂³×C₄×#64408

yes

135

C₂

C₂⁴×#10596833

yes

136

C₂

C₂³×#11924036

yes

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	#64408
commutator, hypocenter	C₇₃	C₂³×C₄×C₈
Frattini	C₂²	C₂⁴×#64408
Fitting	C₂⁴×C₄×C₇₃	C₄
socle, prime radical	C₂⁵×C₇₃	C₂×C₄
cosocle	C₂×Dic₇₃	C₂⁵
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁴×C₄

subgroup

G/H

center, hypercenter

C₂⁴×C₄

#64408

commutator, hypocenter

C₇₃

C₂³×C₄×C₈

Frattini

C₂²

C₂⁴×#64408

Fitting

C₂⁴×C₄×C₇₃

C₄

socle, prime radical

C₂⁵×C₇₃

C₂×C₄

cosocle

C₂×Dic₇₃

C₂⁵

LCS

G ▷ C₇₃

UCS

C₁ ◁ C₂⁴×C₄

N	H ≅ G/N	type
2. C₂²×C₄×#10596833	C₂	direct (N × H)
4. C₂³×#10596833	C₄	direct (N × H)
6. C₂×C₄×#10596833	C₂²	direct (N × H)
12. C₂²×#10596833	C₂×C₄	direct (N × H)
14. C₄×#10596833	C₂³	direct (N × H)
15. C₂³×Dic₇₃	C₈	semidirect
23. C₂³×C₄×C₇₃	C₈	semidirect
25. C₂×#10596833	C₂²×C₄	direct (N × H)
28. C₂²×Dic₇₃	C₂×C₈	semidirect
39. C₂²×C₄×C₇₃	C₂×C₈	semidirect
41. C₂³×C₇₃	C₄×C₈	semidirect
46. C₂×C₄×C₇₃	C₂²×C₈	semidirect
49. C₂×Dic₇₃	C₂²×C₈	semidirect
54. #10596833	C₂³×C₄	direct (N × H)
55. C₂²×C₇₃	C₂×C₄×C₈	semidirect
60. C₄×C₇₃	C₂³×C₈	semidirect
62. Dic₇₃	C₂³×C₈	semidirect
65. C₂×C₇₃	C₂²×C₄×C₈	semidirect
72. C₇₃	C₂³×C₄×C₈	semidirect
87. C₂³×C₄	#10596833	direct (N × H)
104. C₂²×C₄	C₂×#10596833	direct (N × H)
110. C₂³	C₄×#10596833	direct (N × H)
121. C₂×C₄	C₂²×#10596833	direct (N × H)
124. C₂²	C₂×C₄×#10596833	direct (N × H)
132. C₄	C₂³×#10596833	direct (N × H)
133. C₂	C₂²×C₄×#10596833	direct (N × H)

H ≅ G/N

type

2. C₂²×C₄×#10596833

C₂

direct (N × H)

4. C₂³×#10596833

C₄

direct (N × H)

6. C₂×C₄×#10596833

C₂²

direct (N × H)

12. C₂²×#10596833

C₂×C₄

direct (N × H)

14. C₄×#10596833

C₂³

direct (N × H)

15. C₂³×Dic₇₃

C₈

semidirect

23. C₂³×C₄×C₇₃

C₈

semidirect

25. C₂×#10596833

C₂²×C₄

direct (N × H)

28. C₂²×Dic₇₃

C₂×C₈

semidirect

39. C₂²×C₄×C₇₃

C₂×C₈

semidirect

41. C₂³×C₇₃

C₄×C₈

semidirect

46. C₂×C₄×C₇₃

C₂²×C₈

semidirect

49. C₂×Dic₇₃

C₂²×C₈

semidirect

54. #10596833

C₂³×C₄

direct (N × H)

55. C₂²×C₇₃

C₂×C₄×C₈

semidirect

60. C₄×C₇₃

C₂³×C₈

semidirect

62. Dic₇₃

C₂³×C₈

semidirect

65. C₂×C₇₃

C₂²×C₄×C₈

semidirect

72. C₇₃

C₂³×C₄×C₈

semidirect

87. C₂³×C₄

#10596833

direct (N × H)

104. C₂²×C₄

direct (N × H)

110. C₂³

C₄×#10596833

direct (N × H)

121. C₂×C₄

direct (N × H)

124. C₂²

C₂×C₄×#10596833

direct (N × H)

132. C₄

direct (N × H)

133. C₂

direct (N × H)

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

subgroup	index
C₂⁴×#10596833	2
C₂²×C₄×#10596833	2
C₂³×C₄×Dic₇₃	2
C₂³×C₄×C₈	73

subgroup

index

C₂⁴×#10596833